**Figure 13.** Instantaneous power spectrum under no-load conditions of the motor (a) healthy motor and (b) defected

faults in rotor, stator and eccentricity.

106 Fault Diagnosis and Detection

bearing with 2 mm outer race defect.

## **7. Impact of environmental noise on decision making of existence of fault signatures**

Incipient defects are defined as slowly developing defects or small unpredictable variations in the system. They are characterized by small amplitude compared to the useful signal. Considering the definition of incipient defects, as a slowly developing defect, it is important to address the issue of detecting these defects at the earliest possible stage meaning smallest amplitude (smallest severity). It has been observed that the low energy harmonics are produced due to incipient bearing localized faults and stator current analysis technique proves to be less efficient to detect low energy fault signatures especially under noisy environment. The IPA method has the ability to detect low energy fault signatures but in an online testing system it is difficult to discriminate the amplitude changes due to environment noise and due to existence of the fault. Therefore, it is unlikely to make decisions without considering the noise variations. As related to this, in an online fault diagnosis system the environmental noise modelling has been a practical issue and many studies have been performed to deal with it.

The averaging of multiple spectrums of stator current was used to eliminate the noise disturbances [124]. Recently, in Ref. [125], Wiener filter is used to eliminate all signatures that are irrelevant to the motor fault signatures. To achieve the high performance of the condition monitoring system, a statistical process control (SPC) is used [63]. Golafshan et al. [126, 127] presented the Singular Value Decomposition (SVD) and Hankel matrix-based de-noising process for the elimination of the background noise and the improvement in the reliability of the fault detection process. However, the proposed method is proven to be computationally intensive. A classical multiple signal classification method has been proposed by Kia et al. [128] to suppress the noise during the fault diagnosis of the motor. However, the proposed method takes long computation time to find fault signatures and is affected by the low signal-to-noise ratio. To solve this problem, an algorithm that is based on zooming in a specific frequency range of the FFT spectrum was proposed in [129]. Kim et al. [130] proposed the idea for separating rotor faults and load oscillations to reduce the false alarm rates in an online fault diagnosis system. It was reported in Ref. [131] that Wigner–Ville spectrum analysis based on cyclic spectral density (CSWVS) was able to separate the bearing fault patterns from random noise in the vibration signal. As compared with the envelope analysis for rolling element bearing diagnosis, the strongest element of CSWVS may be its diagnostic ability for bearing with distributed faults. In the experimental study, the results of envelope analysis, no matter what filtering techniques are used, fail to extract bearing fault features and might be misinterpreted as a gear fault. However, CSWVS utilizes the second order cyclo-stationary property of the vibration signals produced by bearing distributed fault, and clearly extracts its fault features reducing the masking effect of additive stationary noise. Wang et al. [132] addressed challenging issues on de-noising and identification of the incipient fault deterioration grade from the noisy vibration signal for aircraft engine rotor prognostics. The enhanced robust methods include an adaptive wavelet de-noising technique for weak signature enhancement and correlation dimension for performance degradation assessment. The experimental results verified that the weak vibration signal features of rotor are successfully revealed and enhanced using adaptive wavelet de-noising method, and correlation well identify the rotor rub-impact fault deterioration grade.

Eccentricity faults in induction motor were analysed by Refs. [133, 134] using a cross-correlation method. The pre-determined threshold levels that have been used are as follows: amplitude less than –60 dB healthy motor, amplitude –60 dB to –40 dB tolerable defects and amplitude higher than –40 dB severe defects. A statistically derived adaptive threshold definition was proposed by Toliyat et al. [135]. The experimental results confirm the validity of the proposed approach to diagnose eccentricity and rotor fault at 70% loading condition of the motor. Although, the proposed approach considers the noise variations in real time applications; however, the performance of the proposed approach was not tested under variable operating points of the motor. In a similar work, Rajagopalan et al. [136] use an adaptive threshold scheme based on percentage of the fundamental current signal. The advanced signal processing algorithms are used to diagnose fault signatures [137]. In this study, the threshold is pre-determined based on prior tests before the diagnostic procedure starts. Although, the statistical performances of the instantaneous noise and bias with respect to motor operating points are not provided in that study but the suggested solutions present an intuitive way to design a performance oriented adaptive threshold scheme for an online fault diagnosis system. An analytical model to detect the incipient faults in the plant process in presence of an arbitrary noise was recently presented in Refs. [138–141]. Their modelled threshold scheme that is based on the probability distribution function has shown higher efficiency for incipient fault detection in noisy environment.

Notably, the pre-determined threshold schemes for reliable diagnosis of electrical faults in induction motor faults using MCSA presented in Refs. [133–137] could be used to estimate the fault severity, but these threshold schemes tend to detect sufficiently strong fault signatures to avoid noise interference. Thus the scheme could not be used to diagnose small fault signatures associated to motor mechanical faults under no-load conditions.

Fournier et al. [142] defined the threshold references in healthy condition of the motor based on the statistical spectral kurtosis measurements. The threshold scheme produces efficient results at specific speed and load levels of the motor. However, this threshold scheme does not consider instantaneous noise variations with respect to motor operating point (load, speed), so errors in the detection occur when operating point of the motor changes. Picot et al. [143] proposed a threshold scheme for the detection of small fault signatures related to bearing cage defects in permanent magnet synchronous motor (PMSM). The noise variance of the measured motor current spectrum was minimized by integration process and threshold was designed by calculating mean and standard deviation of the frequency bins. Although, the proposed method was shown to produce good performance at various speeds (variable supply frequency) of the PMSM, however, it has some limitations. Firstly, the performance of their designed threshold was not measured at various load conditions. Secondly, the designed threshold scheme is dependent on the sampling size and window size. The large window size may attenuate the amplitude of bearing fault signatures. The impact of noise variations with respect to load variations on the reliable decision making of the existence of small fault signatures needs to be investigated. Notably, this work provides intuitive way towards the design of performance-based decision making system independent of environment impacts and motor operating points.

distributed faults. In the experimental study, the results of envelope analysis, no matter what filtering techniques are used, fail to extract bearing fault features and might be misinterpreted as a gear fault. However, CSWVS utilizes the second order cyclo-stationary property of the vibration signals produced by bearing distributed fault, and clearly extracts its fault features reducing the masking effect of additive stationary noise. Wang et al. [132] addressed challenging issues on de-noising and identification of the incipient fault deterioration grade from the noisy vibration signal for aircraft engine rotor prognostics. The enhanced robust methods include an adaptive wavelet de-noising technique for weak signature enhancement and correlation dimension for performance degradation assessment. The experimental results verified that the weak vibration signal features of rotor are successfully revealed and enhanced using adaptive wavelet de-noising method, and correlation well identify the rotor rub-impact fault

Eccentricity faults in induction motor were analysed by Refs. [133, 134] using a cross-correlation method. The pre-determined threshold levels that have been used are as follows: amplitude less than –60 dB healthy motor, amplitude –60 dB to –40 dB tolerable defects and amplitude higher than –40 dB severe defects. A statistically derived adaptive threshold definition was proposed by Toliyat et al. [135]. The experimental results confirm the validity of the proposed approach to diagnose eccentricity and rotor fault at 70% loading condition of the motor. Although, the proposed approach considers the noise variations in real time applications; however, the performance of the proposed approach was not tested under variable operating points of the motor. In a similar work, Rajagopalan et al. [136] use an adaptive threshold scheme based on percentage of the fundamental current signal. The advanced signal processing algorithms are used to diagnose fault signatures [137]. In this study, the threshold is pre-determined based on prior tests before the diagnostic procedure starts. Although, the statistical performances of the instantaneous noise and bias with respect to motor operating points are not provided in that study but the suggested solutions present an intuitive way to design a performance oriented adaptive threshold scheme for an online fault diagnosis system. An analytical model to detect the incipient faults in the plant process in presence of an arbitrary noise was recently presented in Refs. [138–141]. Their modelled threshold scheme that is based on the probability distribution function has shown higher efficiency for incipient

Notably, the pre-determined threshold schemes for reliable diagnosis of electrical faults in induction motor faults using MCSA presented in Refs. [133–137] could be used to estimate the fault severity, but these threshold schemes tend to detect sufficiently strong fault signatures to avoid noise interference. Thus the scheme could not be used to diagnose small fault signa-

Fournier et al. [142] defined the threshold references in healthy condition of the motor based on the statistical spectral kurtosis measurements. The threshold scheme produces efficient results at specific speed and load levels of the motor. However, this threshold scheme does not consider instantaneous noise variations with respect to motor operating point (load, speed), so errors in the detection occur when operating point of the motor changes. Picot et al. [143] proposed a threshold scheme for the detection of small fault signatures related to bearing cage defects in permanent magnet synchronous motor (PMSM). The noise variance of

tures associated to motor mechanical faults under no-load conditions.

deterioration grade.

108 Fault Diagnosis and Detection

fault detection in noisy environment.

Limitations of the existing non-invasive fault diagnosis techniques considering environment impacts are described in **Table 1**.

**Table 1.** Limitations of previously used MCSA-based fault diagnosis techniques considering environment impacts.

## **8. Park vector analysis for bearing localized defects**

Park vector analysis (PVA) of motor current which is mainly used for field oriented control of induction motor has received a growing attention in the recent years in condition monitoring applications. Few researchers have used PVA with emphasis on the bearing localized faults, rotor faults, eccentricity faults and stator faults [144–147]. In Park's transformation process, the three balanced AC quantities (*I a* , *Ib* , *Ic* ) are reduced to two DC quantities (*Id* , *Iq* ). In analysis of three-phase synchronous machines, Park's transformation transfers three-phase stator and rotor quantities into a single rotating reference frame to eliminate the effect of time varying inductances [144, 145].

The Park vectors under ideal conditions of the motor represent a circular pattern centred at the origin. However, the shape of the circle changes in presence of the faults inside the motor and the various types of faults generate various types of shapes. Thus by detection of various patterns, one can analyse the type of fault inside the motor. The Park's transform is a graphical method to analyse the status of motor and does not require analytical expressions to calculate any specific defect frequency.

Zarie et al. [144] performed experiments on induction motor to diagnose bearing localized and extended defects (multiple holes in inner or outer race). Classification of the various faults was achieved through utilization of neural networks. It was concluded in their study that the proposed method provides a powerful and general approach to incipient fault detection. Spyropoulos et al. [145], Laughman et al. [146] and Parra et al. [148] reported that impact of the motor stator related faults could be examined through the Park vector transformation approach. It was claimed that by using this approach, effects of stator faults can be differentiated from time-varying loads. Salem et al. [147] measure the thickness of Park vector curve using curve splitting factor. The experimental results on bearing outer race defect indicate that thickness of the Park vector curve increases due to fault. Rezig et al. [149] and Salem et al. [150, 151] conducted experimental study to diagnose the bearing localized defects and eccentricity faults through Park vector transform of motor stator current. Experimental results indicate that Park vector transform method can detect the occurrence of faults but unable to identify the fault locations. In a recent study, Kuruppu et al. 152] demonstrated that Park vector analysis method has capability to diagnose stator inter-turn faults in inverter-fed field-oriented control motors. Proof of accurate fault detection capability for a wide speed range is presented through simulation and experimental results.

The example of Park vector analysis of stator current for bearing localized defects is shown in **Figure 14**. It can be observed from Figure 14 that bearing localized defects cause an increase in thickness of the *Id* , *Iq* curves. The increase in curve thickness is due to the harmonics induced by the localized defects inside the bearing of the motor. Therefore the analysis of the *Id* , *Iq* curves can be a useful means for the fault diagnosis of induction motors.

An Assessment on the Non-Invasive Methods for Condition Monitoring of Induction Motors http://dx.doi.org/10.5772/67917 111

**8. Park vector analysis for bearing localized defects**

*a* , *Ib* , *Ic*

the three balanced AC quantities (*I*

culate any specific defect frequency.

cause an increase in thickness of the *Id*

, *Iq*

the analysis of the *Id*

inductances [144, 145].

110 Fault Diagnosis and Detection

results.

motors.

Park vector analysis (PVA) of motor current which is mainly used for field oriented control of induction motor has received a growing attention in the recent years in condition monitoring applications. Few researchers have used PVA with emphasis on the bearing localized faults, rotor faults, eccentricity faults and stator faults [144–147]. In Park's transformation process,

of three-phase synchronous machines, Park's transformation transfers three-phase stator and rotor quantities into a single rotating reference frame to eliminate the effect of time varying

The Park vectors under ideal conditions of the motor represent a circular pattern centred at the origin. However, the shape of the circle changes in presence of the faults inside the motor and the various types of faults generate various types of shapes. Thus by detection of various patterns, one can analyse the type of fault inside the motor. The Park's transform is a graphical method to analyse the status of motor and does not require analytical expressions to cal-

Zarie et al. [144] performed experiments on induction motor to diagnose bearing localized and extended defects (multiple holes in inner or outer race). Classification of the various faults was achieved through utilization of neural networks. It was concluded in their study that the proposed method provides a powerful and general approach to incipient fault detection. Spyropoulos et al. [145], Laughman et al. [146] and Parra et al. [148] reported that impact of the motor stator related faults could be examined through the Park vector transformation approach. It was claimed that by using this approach, effects of stator faults can be differentiated from time-varying loads. Salem et al. [147] measure the thickness of Park vector curve using curve splitting factor. The experimental results on bearing outer race defect indicate that thickness of the Park vector curve increases due to fault. Rezig et al. [149] and Salem et al. [150, 151] conducted experimental study to diagnose the bearing localized defects and eccentricity faults through Park vector transform of motor stator current. Experimental results indicate that Park vector transform method can detect the occurrence of faults but unable to identify the fault locations. In a recent study, Kuruppu et al. 152] demonstrated that Park vector analysis method has capability to diagnose stator inter-turn faults in inverter-fed field-oriented control motors. Proof of accurate fault detection capability for a wide speed range is presented through simulation and experimental

The example of Park vector analysis of stator current for bearing localized defects is shown in **Figure 14**. It can be observed from Figure 14 that bearing localized defects

the harmonics induced by the localized defects inside the bearing of the motor. Therefore

curves. The increase in curve thickness is due to

curves can be a useful means for the fault diagnosis of induction

, *Iq*

) are reduced to two DC quantities (*Id*

, *Iq*

). In analysis

**Figure 14.** Example of Park vector analysis of stator current for (a) healthy bearing, (b) outer race localized defect and (c) inner race localized defect.

## **9. Non-invasive method for diagnosis of bearing distributed defects**

Most of the published work on the bearing condition monitoring via non-invasive techniques as discussed in focused on diagnosis of bearing localized defects. It is based on some characteristic fault frequencies that appear in spectrum of the stator current or instantaneous power. However, the absence of clear characteristic fault frequencies should not be interpreted as a completely healthy condition of the bearing. On the other hand, the bearing distributed faults produce unpredictable broadband effects which are not necessarily related with specific fault frequencies. These faults are common in industry, while they are often neglected in the research literature.

Time-domain analysis is a useful feature extraction tool for condition monitoring and fault diagnosis of electrical motors. Time domain averaging (TDA) is a traditional and typical method to detect fault signals in electrical motors. It extracts a periodic component of interest from a noisy compound signal. Data-clustering techniques are used to extract an average pattern that serves as the mechanical imbalance indicator. Zhang et al. [153] proposed the idea of creating artificial distributed defects in bearings of induction motor via externally applied shaft current. This idea was important as the defects would be sorted according to the kind of signatures generated by defects instead of where the defects were located physically. Most of the condition monitoring approaches concerning fault detection found in the literature have been mainly focused on identifying single-point defects. Indeed this class of defects is quite important, however, an approach that is comprehensive and robust must have the capability of detecting not only single-point defect but also distributed defects in the bearing. The data obtained from 10 bearings failed by their proposed method, was analysed in time domain. It was shown that drastic variations in machine vibration and stator current occur in case of defected bearings. A method to segregate the bearing localized and distributed defects based on the time domain analysis of vibration, stator current and acoustic emission signals was presented by Navarro et al. [154]. The RMS values of the multi-sensory signal for healthy bearing, bearing localized and distributed defects were collected and faults were classified based on fuzzy inference analysis. In Refs. [155, 156], it was reported that generalized roughness in bearings of the motor produces a frequency spreading of the characteristic fault frequencies, thus making it difficult to detect with MCSA method. In the papers, it was proposed to use a statistical analysis of typical bearing faults in order to identify the spreading bandwidth related to bearing surface roughness faults, relying on current and vibration measurements only. A diagnostic index based on computation of energy in the previously defined bandwidth was used to diagnose bearing surface roughness faults. The proposed method was validated experimentally with vibration and current signals, with robust and reliable results. However, implementation of their proposed method needs computational efforts and implementation of this method for inner and outer race surface roughness was not given. In a recent study, Dalvand et al. [157] analyse bearing distributed defects in inner and outer race of bearing simultaneously. They use statistical analysis of the instantaneous frequency of motor voltage space vector (MVSV) and vibration signal. The statistical indices like mean value (M), RMS value, standard deviation (SD), global kurtosis (GK), skew factor (SF) and crest factor (CF) were utilized to analyse the measured signal. It was shown that mean value and RMS are not proper indices to analyse the distributed defects in bearings because the values of these indices for healthy and defected bearings are not significantly different. However, the GK, SF and CF are proper indices to diagnose bearing distributed faults. Experimental results indicate that although the statistical time domain analysis of MVSV and vibration signals have capability to diagnose the bearing distributed defects; however the reliability of MVSV is better than vibration monitoring. The analysis of individual defect in bearing elements was not presented in their study.

## **10. Condition monitoring issues**

**9. Non-invasive method for diagnosis of bearing distributed defects**

neglected in the research literature.

112 Fault Diagnosis and Detection

Most of the published work on the bearing condition monitoring via non-invasive techniques as discussed in focused on diagnosis of bearing localized defects. It is based on some characteristic fault frequencies that appear in spectrum of the stator current or instantaneous power. However, the absence of clear characteristic fault frequencies should not be interpreted as a completely healthy condition of the bearing. On the other hand, the bearing distributed faults produce unpredictable broadband effects which are not necessarily related with specific fault frequencies. These faults are common in industry, while they are often

Time-domain analysis is a useful feature extraction tool for condition monitoring and fault diagnosis of electrical motors. Time domain averaging (TDA) is a traditional and typical method to detect fault signals in electrical motors. It extracts a periodic component of interest from a noisy compound signal. Data-clustering techniques are used to extract an average pattern that serves as the mechanical imbalance indicator. Zhang et al. [153] proposed the idea of creating artificial distributed defects in bearings of induction motor via externally applied shaft current. This idea was important as the defects would be sorted according to the kind of signatures generated by defects instead of where the defects were located physically. Most of the condition monitoring approaches concerning fault detection found in the literature have been mainly focused on identifying single-point defects. Indeed this class of defects is quite important, however, an approach that is comprehensive and robust must have the capability of detecting not only single-point defect but also distributed defects in the bearing. The data obtained from 10 bearings failed by their proposed method, was analysed in time domain. It was shown that drastic variations in machine vibration and stator current occur in case of defected bearings. A method to segregate the bearing localized and distributed defects based on the time domain analysis of vibration, stator current and acoustic emission signals was presented by Navarro et al. [154]. The RMS values of the multi-sensory signal for healthy bearing, bearing localized and distributed defects were collected and faults were classified based on fuzzy inference analysis. In Refs. [155, 156], it was reported that generalized roughness in bearings of the motor produces a frequency spreading of the characteristic fault frequencies, thus making it difficult to detect with MCSA method. In the papers, it was proposed to use a statistical analysis of typical bearing faults in order to identify the spreading bandwidth related to bearing surface roughness faults, relying on current and vibration measurements only. A diagnostic index based on computation of energy in the previously defined bandwidth was used to diagnose bearing surface roughness faults. The proposed method was validated experimentally with vibration and current signals, with robust and reliable results. However, implementation of their proposed method needs computational efforts and implementation of this method for inner and outer race surface roughness was not given. In a recent study, Dalvand et al. [157] analyse bearing distributed defects in inner and outer race of bearing simultaneously. They use statistical analysis of the instantaneous frequency of motor voltage space vector (MVSV) and vibration signal. The statistical indices like mean value (M), RMS value, standard deviation (SD), global kurtosis (GK), skew factor (SF) and crest factor (CF) were utilized to analyse the measured signal. It was shown that mean value and RMS are not proper indices to analyse the distributed The literature review has shown that the invasive methods like vibration analysis, acoustic emission, noise analysis, chemical analysis and temperature measurements were applied to protect motors from various faults. However, sensors used in these methods are very expensive. Another disadvantage of these methods is that they require access to machine for sensor installation which is not possible in every application. Also it requires special expertise for the proper installation of sensors on the machine for accurate results. Therefore sensor-based condition monitoring methods are not reliable.

Review papers presented in Refs. [158–163] on the condition monitoring techniques for the induction motors demonstrate that extensive research has been carried out in the last decade on the development of a non-invasive condition monitoring system for diagnosis of gear defects and bearing localized faults. It has been found that the mechanical vibration produce characteristic frequencies in stator current spectrum. The magnitude of the specific characteristic frequencies increases with the increase of vibration. Every type of the motor defect has its own unique characteristic defect frequencies. The MCSA has been extensively used to find out these frequency modulations.

The implementation of MCSA for motor condition monitoring is not so complex. However, low amplitude fault signatures are induced due to incipient faults under no-load condition and thus could not be reliably diagnosed through MCSA. Recent developments in non-invasive condition monitoring scheme demonstrate that PVA of motor stator current has the capability to diagnose the motor faults at incipient stages. It was shown that the proposed method would give good analysis of machine faults even if accurate fault frequency information is unavailable. In recent years, IPA method to diagnose rotor, stator and eccentricity faults at incipient stages conditions was proposed by few researchers. However, applicability of the IPA for mechanical fault diagnosis in induction motor has not been reported in literature [164–170].

The incipient defect diagnosis in the machinery with unknown distribution of measured signals and unknown changed parameters is an important issue. However, most of the fault diagnosis techniques need a priori knowledge on the signal distribution, changed parameters and the changed amplitude. Fault detection plays a key role in enhancing today's technological system's high demands for performance, productivity and security. The sensitivity of the condition monitoring and fault diagnosis methods depends on the application of main goals. When productivity is the main goal then the sensitivity requirement of condition monitoring and fault diagnosis system is weak and only large defects should be detected. However, when security is the main goal, undetected defects even with very small severity assessment may result in catastrophic growing failures. For online fault diagnosis, when safety is the main priority, it is crucial to be able to diagnose incipient faults in presence of environment noise. Although IPA has some implementation advantages over MCSA for incipient fault detection but the signatures of IPA are affected by industrial noise perturbations. There is much scope for research to improve the capabilities of IPA in reliable online fault diagnosis in an arbitrary environment noise.

Notably, the substantial number of research studies has been found focusing into detection of bearing localized faults via non-invasive condition monitoring methods. Nonetheless, bearing distributed defects does not produce localized defect frequencies and thus could not be analysed via these methods. Recently, few studies have been found focusing on time domain analysis of stator current signal and extracting the features like RMS and kurtosis values. However, complexity involved in time domain analysis of stator current signal is the major drawback. As PVA performs the graphical analysis of stator current and does not require frequency information for fault detection thus its capability to diagnose bearing distributed defects should be further researched.

The advantages and drawbacks of the existing non-invasive condition monitoring methods are presented in **Table 2**.

**Table 2.** Advantages and drawbacks of non-invasive condition monitoring methods.

## **11. Future directions**

Based on the findings, there are further problems to be considered both in the development of the technique and in the experimental design. These include

• Development of non-invasive condition monitoring scheme to diagnose faults in an arbitrary environment noise conditions

The non-invasive IPA has shown some implementation advantages over MCSA to reliably diagnose mechanical faults. However, small fault signatures under low load conditions are buried in noise and it is difficult to discriminate amplitude changes due to fault and due to noise. Thus, there is a need to develop a robust non-invasive condition monitoring scheme to make reliable decisions on the existence of fault signatures.

• Development of non-invasive condition monitoring scheme to diagnose bearing distributed faults

Most of the published work on the bearing condition monitoring via non-invasive techniques is focused on diagnosis of bearing localized defects. It is based on the some characteristic fault frequencies that appear in spectrum of the stator current or instantaneous power. Nonetheless, bearing distributed defects does not produce characteristic defect frequencies and thus could not been analysed via MCSA or IPA. These faults are common in industry, while they are often neglected in the research literature. As PVA performs the graphical analysis of stator current and does not require characteristic defect frequencies information for fault detection thus its capability to diagnose bearing distributed defects should be further researched.

• Development of hand-held instrument for on-site machine condition monitoring

The IPA and PVA algorithms could be embedded to develop a hand-held instrument for on-site condition monitoring of induction motors. This will help to reduce the installation cost of the data acquisition system especially for small and medium scale industrial use.

• Reliability tests for mainstream industries

The developed IPA and PVA algorithms should be expanded and utilized to analyse faults in turbines and generators. For consideration to be acceptable by the main stream industries, a reliability test of the developed algorithms should be conducted on large size motors (more than 40 HP).

• Multiple bearing faults analysis

Even though the two techniques as proposed i.e. the instantaneous power analysis and Park vector analysis can monitor the conditions of induction motors from various scenarios, however these are not sufficient for most applications because outcomes of the analysis are based on the assumptions that each fault occurs independently. The extension of the approach as proposed in this work, to understand how each approach reacts to a combination of several faults (e.g. stator, rotor, eccentricity, bearings, etc.), would be useful.

## **12. Conclusion**

security is the main goal, undetected defects even with very small severity assessment may result in catastrophic growing failures. For online fault diagnosis, when safety is the main priority, it is crucial to be able to diagnose incipient faults in presence of environment noise. Although IPA has some implementation advantages over MCSA for incipient fault detection but the signatures of IPA are affected by industrial noise perturbations. There is much scope for research to improve the capabilities of IPA in reliable online fault diagnosis in an arbitrary

Notably, the substantial number of research studies has been found focusing into detection of bearing localized faults via non-invasive condition monitoring methods. Nonetheless, bearing distributed defects does not produce localized defect frequencies and thus could not be analysed via these methods. Recently, few studies have been found focusing on time domain analysis of stator current signal and extracting the features like RMS and kurtosis values. However, complexity involved in time domain analysis of stator current signal is the major drawback. As PVA performs the graphical analysis of stator current and does not require frequency information for fault detection thus its capability to diagnose bearing distributed

The advantages and drawbacks of the existing non-invasive condition monitoring methods

stages

noise

noise

needs to be tested

• Unable to detect defects at incipient

• Fault detection affected by environment

• Further investigation required to test its capability for bearing distributed defects

• Fault detection affected by environment

• Capability to diagnose mechanical faults

[25, 38, 52–73]

[144–152, 171]

[119–123]

**No CM technique Advantages Drawbacks Reference**

Based on the findings, there are further problems to be considered both in the development of

• Development of non-invasive condition monitoring scheme to diagnose faults in an arbi-

the technique and in the experimental design. These include

**Table 2.** Advantages and drawbacks of non-invasive condition monitoring methods.

• Non-invasive

• Non-invasive

• Non-invasive • Can detect rotor and eccentricity defects at incipient stages

environment noise.

114 Fault Diagnosis and Detection

defects should be further researched.

1. MCSA • Inexpensive

2. PVA • Inexpensive

3. IPA • Inexpensive

are presented in **Table 2**.

**11. Future directions**

trary environment noise conditions

The ability to forecast motor faults at incipient stages is vital to reducing maintenance costs, operation down-time and safety hazards. This paper synthesized the progress in the research and development in condition monitoring and fault diagnosis of induction motors. The review presented in this paper has contributed to an improved understanding of the development of practical non-invasive condition monitoring and diagnostic tool for induction motors. The non-invasive methods, namely MCSA, PVA and IPA overcome the disadvantages associated to invasive methods. The MCSA, PVA and IPA can successfully diagnose the gear and bearing localized defects. However, further research is required to analyse bearing distributed faults via non-invasive condition monitoring methods. It has been observed that IPA has some implementation advantages over MCSA for incipient fault detection but IPA can be affected by environment noise perturbations. There is much scope for research to improve the capabilities of IPA in reliable online fault diagnosis system operating in an arbitrary environment noise. Furthermore, to realize the greatest economic and implementation benefits of IPA and PVA, it is important to design a hand-held condition monitoring system based on IPA and PVA techniques by considering the asset management perspective.

## **Acknowledgements**

The authors acknowledge the support from Universiti Teknologi PETRONAS for providing Universiti Research Innovation Fund (URIF) and the Ministry of Higher Education (MOHE) Malaysia for the award of the Prototype Research Grant Scheme (PRGS).

## **Author details**

Muhammad Irfan1 \*, Nordin Saad2 , Rosdiazli Ibrahim2 , Vijanth S. Asirvadam2 , Abdullah S. Alwadie1 and Muhammad Aman Sheikh2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Faculty of Engineering, Electrical Engineering Department, Najran University, Kingdom of Saudi Arabia

2 Electrical and Electronics Engineering Department, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, Tronoh, Perak, Malaysia

## **References**

[3] Irfan M, Saad, Ibrahim R, Asirvadam VS, Magzoub M. An intelligent fault diagnosis of induction motors in an arbitrary noisy environment. Journal of Nondestructive Evaluation. March 2016;**35**(12)

and development in condition monitoring and fault diagnosis of induction motors. The review presented in this paper has contributed to an improved understanding of the development of practical non-invasive condition monitoring and diagnostic tool for induction motors. The non-invasive methods, namely MCSA, PVA and IPA overcome the disadvantages associated to invasive methods. The MCSA, PVA and IPA can successfully diagnose the gear and bearing localized defects. However, further research is required to analyse bearing distributed faults via non-invasive condition monitoring methods. It has been observed that IPA has some implementation advantages over MCSA for incipient fault detection but IPA can be affected by environment noise perturbations. There is much scope for research to improve the capabilities of IPA in reliable online fault diagnosis system operating in an arbitrary environment noise. Furthermore, to realize the greatest economic and implementation benefits of IPA and PVA, it is important to design a hand-held condition monitoring system based on IPA

The authors acknowledge the support from Universiti Teknologi PETRONAS for providing Universiti Research Innovation Fund (URIF) and the Ministry of Higher Education (MOHE)

, Rosdiazli Ibrahim2

1 Faculty of Engineering, Electrical Engineering Department, Najran University, Kingdom of

2 Electrical and Electronics Engineering Department, Universiti Teknologi PETRONAS,

[1] Irfan M, Saad N, Ibrahim R, Asirvadam VS, Magzoub M. An online fault diagnosis system for induction motors via instantaneous power analysis. Tribology Transactions. 2016. [2] Irfan M, Saad N, Ibrahim R, Asirvadam VS, Hung NT, Magzoub MA. Analysis of bearing surface roughness defects in induction motors. Journal of Failure Analysis and

, Vijanth S. Asirvadam2

, Abdullah S.

and PVA techniques by considering the asset management perspective.

Malaysia for the award of the Prototype Research Grant Scheme (PRGS).

\*, Nordin Saad2

\*Address all correspondence to<EMAIL_ADDRESS>
and Muhammad Aman Sheikh2

Bandar Seri Iskandar, Tronoh, Perak, Malaysia

Prevention. October 2015;**15**(5):730–736

**Acknowledgements**

116 Fault Diagnosis and Detection

**Author details**

Muhammad Irfan1

Alwadie1

Saudi Arabia

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## **Evaluation of Novelty Detection Methods for Condition Monitoring applied to an Electromechanical System**

Miguel Delgado Prieto, Jesús A. Cariño Corrales, Daniel Zurita Millán, Marta Millán Gonzalvez, Juan A. Ortega Redondo and René de J. Romero Troncoso

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/67531

#### Abstract

Dealing with industrial applications, the implementation of condition monitoring schemes must overcome a critical limitation, that is, the lack of a priori information about fault patterns of the system under analysis. Indeed, classical diagnosis schemes, in general, outdo the membership probability of a measure in regard to predefined operating scenarios. However, dealing with noncharacterized systems, the knowledge about faulty operating scenarios is limited and, consequently, the diagnosis performance is insufficient. In this context, the novelty detection framework plays an essential role for monitoring systems in which the information about different operating scenarios is initially unavailable or restricted. The novelty detection approach begins with the assumption that only data corresponding to the healthy operation of the system under analysis is available. Thus, the challenge is to detect and learn additional scenarios during the operation of the system in order to complement the information obtained by the diagnosis scheme. This work has two main objectives: first, the presentation of novelty detection as the current trend toward the new paradigm of industrial condition monitoring and, second, the introduction to its applicability by means of analyses of different novelty detection strategies over a real industrial system based on rotatory machinery.

Keywords: condition monitoring, electromechanical systems, failure diagnosis, feature reduction, industrial monitoring applications, novelty detection, open set recognition

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1. Introduction

Currently, condition monitoring plays a key role in the reliability and safety strategies of most of the industrial applications [1]. Classical industrial condition monitoring methodologies imply the estimation of numerical features and their posterior processing in order to characterize the available physical magnitudes acquired during the operation of the system under analysis. Such numerical feature vectors are, then, presented to a classification algorithm in order to obtain a diagnosis outcome [2]. In this procedure, the algorithm of classification is previously trained with available data representative of different system conditions. Thus, during the regular operation of the condition monitoring scheme, each measurement acquired from the system will be transformed to a vector of numerical features, and its similarities with previous patterns will be evaluated in order to obtain the related probability. During the last decades, a great deal of studies has been done around different aspects of the electromechanical condition monitoring, that is, the potentiality of different physical magnitudes for fault detection, the analysis of time, frequency and time-frequency domains for numerical features' estimation, the effect of feature reduction techniques for patterns' characterization and dealing with data-based approaches and multiple classification strategies for diagnosis improvement [3, 4]. All of these works are, with no doubt, a major step forward to the study, research and development of enhanced condition monitoring schemes to be applied to electromechanical systems. However, currently, the scientific and industrial communities are working together toward more demanding industrial challenges in the frameworks of Industry 4.0 [5] and Zero-defect manufacturing [6]. Indeed, further capabilities are expected from the condition monitoring developments in order to face questions about their practical implementations, questions such as: How must condition monitoring be managed in front of new operating scenarios not previously considered?, How to detect new operating scenarios?, Which numerical features should be used for unknown patterns' detection?, How to preserve the diagnosis reliability in the presence of new patterns?, Is it possible to automate these considerations or is the aid of an expert required? In order to find answers to such questions, specific research is being gathered around the so-called novelty detection topic, which can be defined as the task of recognizing that the data under analysis differ, in some respect, from the initial available data.

Indeed, a priori characteristic fault patterns of specific rotatory machinery are not usually available and highly difficult to estimate through theoretical approaches. Thus, condition monitoring strategies capable of detecting novel operating conditions, alongside the classification of known conditions, represent the most convenient solutions [7]. This approach is known as the open set recognition problem, where only a reduced set of known operating scenarios are included in the initial dataset and used during the training stage, and, then, novel (unknown) scenarios may appear during the online diagnosis stage. In general terms, in order to deploy a novel detection strategy, a model must be trained with all the available data describing the initial-known scenarios of the machinery under monitoring. Thus, the model generates a threshold system that allows to discriminate between known scenarios and measurements corresponding to new cases, novelties. Different approaches differ in the way that the threshold system is generated [8].

In this chapter, first, a more comprehensive description of the novelty detection topic, including different approaches and their dependencies, is introduced. Later, the practical application of novelty detection applied over an industrial electromechanical system is described. The performances obtained with different novelty detection strategies, including the effect of feature reduction, are discussed finally.

## 2. Novelty detection

1. Introduction

132 Fault Diagnosis and Detection

the initial available data.

the threshold system is generated [8].

Currently, condition monitoring plays a key role in the reliability and safety strategies of most of the industrial applications [1]. Classical industrial condition monitoring methodologies imply the estimation of numerical features and their posterior processing in order to characterize the available physical magnitudes acquired during the operation of the system under analysis. Such numerical feature vectors are, then, presented to a classification algorithm in order to obtain a diagnosis outcome [2]. In this procedure, the algorithm of classification is previously trained with available data representative of different system conditions. Thus, during the regular operation of the condition monitoring scheme, each measurement acquired from the system will be transformed to a vector of numerical features, and its similarities with previous patterns will be evaluated in order to obtain the related probability. During the last decades, a great deal of studies has been done around different aspects of the electromechanical condition monitoring, that is, the potentiality of different physical magnitudes for fault detection, the analysis of time, frequency and time-frequency domains for numerical features' estimation, the effect of feature reduction techniques for patterns' characterization and dealing with data-based approaches and multiple classification strategies for diagnosis improvement [3, 4]. All of these works are, with no doubt, a major step forward to the study, research and development of enhanced condition monitoring schemes to be applied to electromechanical systems. However, currently, the scientific and industrial communities are working together toward more demanding industrial challenges in the frameworks of Industry 4.0 [5] and Zero-defect manufacturing [6]. Indeed, further capabilities are expected from the condition monitoring developments in order to face questions about their practical implementations, questions such as: How must condition monitoring be managed in front of new operating scenarios not previously considered?, How to detect new operating scenarios?, Which numerical features should be used for unknown patterns' detection?, How to preserve the diagnosis reliability in the presence of new patterns?, Is it possible to automate these considerations or is the aid of an expert required? In order to find answers to such questions, specific research is being gathered around the so-called novelty detection topic, which can be defined as the task of recognizing that the data under analysis differ, in some respect, from

Indeed, a priori characteristic fault patterns of specific rotatory machinery are not usually available and highly difficult to estimate through theoretical approaches. Thus, condition monitoring strategies capable of detecting novel operating conditions, alongside the classification of known conditions, represent the most convenient solutions [7]. This approach is known as the open set recognition problem, where only a reduced set of known operating scenarios are included in the initial dataset and used during the training stage, and, then, novel (unknown) scenarios may appear during the online diagnosis stage. In general terms, in order to deploy a novel detection strategy, a model must be trained with all the available data describing the initial-known scenarios of the machinery under monitoring. Thus, the model generates a threshold system that allows to discriminate between known scenarios and measurements corresponding to new cases, novelties. Different approaches differ in the way that The introduction of novelty detection into the classical monitoring chain represents a previous condition to the diagnosis assessment. The classical step flow to implement novelty detection is shown in Figure 1. The procedure begins with the off-line processing of the available information (generally, the healthy behavior of the electromechanical chain). Such processing, in regard to the raw data acquired (stator currents, temperatures, etc.), consists of the definition of the same blocks as in classical diagnosis procedures, that is, feature estimation (calculation of a set of numerical features) and feature reduction (feature vector transformation for improved characterization). Once the available data is characterized by vectors of D features, the configuration of the novelty detection model follows. This part depends entirely on the nature of the novelty model (different approaches can be applied); however, the objective is the

Figure 1. Implementation scheme of novelty detection, including the offline initialization for knowledge delimitation and the online monitoring for novelty evaluation.

delimitation of the available knowledge defining a set of mathematical descriptions in the D-dimensional feature space in which the available database is projected [9].

Thus, during the online monitoring, the novelty detection model will analyze the new acquisitions and will determine if the new data correspond to known operating scenarios previously learned or present different characteristics and can be considered novel representations. In case of known operating scenarios, the diagnosis follows. It must be noted that the diagnosis procedure could include different feature estimation and feature reduction stages because its objective is completely different. In this sense, the novelty detection does not require different labels since all data belongs to the class knowledge or normal. The diagnosis, however, requires to maintain different labels in order to allow the identification of the different operating scenarios. In case of unknown operating scenarios, the diagnosis cannot be carried out since the diagnosis reliability would be affected. In this case, the presence of novel data is reported and, after the supervision of an expert, the measurements are stored in order to upgrade the known operating scenarios, which will imply the retraining of the novelty model [10].

In order to illustrate the novelty detection operation, an example is shown in Figure 2. A D = 2-dimensional feature space is considered, in which a set of measurements representing the available data has led to the definition of the boundaries corresponding to the known conditions. When new measurements are acquired, the novelty model analyzes them and determines, in this example by means of their position in the 2-dimensional feature space, if they represent novelty or if the behavior is still considered known. If a significant amount of novel acquisitions with the same characteristics are detected, then, a novel operation mode is detected and, if validated, the data will be included as known behaviors.

Indeed, the detection of novel events is an important ability of any condition monitoring scheme. Considering the fact that it cannot be trained within a machine learning system with all possible systems' variability, it becomes important to include the differentiation capability between known and unknown object information during the system's monitoring. However, it has been considered in practice by several studies that the novelty detection is an extremely

Figure 2. Example of a novelty detection basic operation, including available data, Δ, mathematical description of the available data, --, novel behaviors detected as outliers, □ and novel behaviors detected as the novel operating scenario, Ο.

challenging task. It is for this reason that there exist different approaches of novelty detection that have been demonstrated to perform well under different applications [11, 12]. Unfortunately, it is clearly evident that there is no single best model for novelty detection, and the success depends not only on the type of the method used but also on the statistical properties of the available data. Next, the three basic novelty detection approaches are described, including probabilistic, domain-based and distance-based methods.

### 2.1. Probabilistic methods

delimitation of the available knowledge defining a set of mathematical descriptions in the

Thus, during the online monitoring, the novelty detection model will analyze the new acquisitions and will determine if the new data correspond to known operating scenarios previously learned or present different characteristics and can be considered novel representations. In case of known operating scenarios, the diagnosis follows. It must be noted that the diagnosis procedure could include different feature estimation and feature reduction stages because its objective is completely different. In this sense, the novelty detection does not require different labels since all data belongs to the class knowledge or normal. The diagnosis, however, requires to maintain different labels in order to allow the identification of the different operating scenarios. In case of unknown operating scenarios, the diagnosis cannot be carried out since the diagnosis reliability would be affected. In this case, the presence of novel data is reported and, after the supervision of an expert, the measurements are stored in order to upgrade the

known operating scenarios, which will imply the retraining of the novelty model [10].

detected and, if validated, the data will be included as known behaviors.

In order to illustrate the novelty detection operation, an example is shown in Figure 2. A D = 2-dimensional feature space is considered, in which a set of measurements representing the available data has led to the definition of the boundaries corresponding to the known conditions. When new measurements are acquired, the novelty model analyzes them and determines, in this example by means of their position in the 2-dimensional feature space, if they represent novelty or if the behavior is still considered known. If a significant amount of novel acquisitions with the same characteristics are detected, then, a novel operation mode is

Indeed, the detection of novel events is an important ability of any condition monitoring scheme. Considering the fact that it cannot be trained within a machine learning system with all possible systems' variability, it becomes important to include the differentiation capability between known and unknown object information during the system's monitoring. However, it has been considered in practice by several studies that the novelty detection is an extremely

Figure 2. Example of a novelty detection basic operation, including available data, Δ, mathematical description of the available data, --, novel behaviors detected as outliers, □ and novel behaviors detected as the novel operating scenario, Ο.

D-dimensional feature space in which the available database is projected [9].

134 Fault Diagnosis and Detection

Probabilistic approaches to novelty detection are based on estimating the probability density function (PDF) of the available data. The resulting distribution may then be thresholded to define the boundaries of normality in the feature space and assess whether a new measurement belongs to the same distribution or not. The training data is assumed to be generated from some underlying probability distribution. This estimation usually represents the novelty model, and a novelty threshold can be set over such estimation. The estimation of the underlying data density from a multivariate training dataset is a well-established topic [10].

Probabilistic methods are divided in parametric and nonparametric approaches. Parametric approaches impose a restrictive model on the data, which results in a large bias when the model does not fit the data. Nonparametric approaches set up a very flexible model by making fewer assumptions over the data: The model grows in size to accommodate the complexity of the data, but it requires a large sample size for a reliable fit out of all the free parameters. The opinion in the scientific literature is divided as to whether various techniques should be classified as parametric or nonparametric. For the purposes of providing probabilistic estimators, Gaussian Mixture Model (GMM) and Kernel Density Estimator (KDE) have proven popular. The GMM is typically classified as a parametric technique [11] because of the assumption that the data is generated from a weighted mixture of Gaussian distributions. The KDE is typically classified as a nonparametric technique [13] as it is closely related to histogram methods, one of the earliest forms of nonparametric density estimation approaches.

#### 2.1.1. Gaussian-mixture model

The GMM is a parametric probability density function represented as a weighted sum of Gaussian component densities. The GMM parameters are estimated from the available training data using, for example, the iterative expectation-maximization algorithm or the maximum a posteriori estimation. Thus, a GMM is a weighted sum of M component Gaussian densities, mathematically described as,

$$p(\mathbf{x}|\boldsymbol{\lambda}) = \sum\_{i=1}^{M} w\_i g\left(\mathbf{x}|\boldsymbol{\mu}\_i, \sum \mathbf{i}\right) \tag{1}$$

where x is a D-dimensional vector, wi, i=1,..M are the mixture weights and gðxjui, <sup>X</sup> <sup>i</sup>Þ, i=1,..,<sup>M</sup> are the component Gaussian densities. Each component density is a D-variate Gaussian function of the form,

$$g(\mathbf{x}|\mu\_i, \sum i) = \frac{1}{(2\pi)^{D/2} |\sum i|^{1/2}} \exp\left\{-\frac{1}{2} (\mathbf{x} - \mu\_i)' \sum\_{i}^{-1} (\mathbf{x} - \mu\_i)\right\} \tag{2}$$

with mean vector µi and covariance matrix Σi. The mixture weights satisfy the constraint that XM <sup>i</sup>¼<sup>1</sup>wi <sup>¼</sup> 1. The complete Gaussian mixture model is parameterized by the mean vectors, covariance matrices and mixture weights from all component densities. These parameters are collectively represented by the notation λ ¼ fwi, μ<sup>i</sup> , Σig, i ¼ 1, ::, M. There are several variants on the GMM. The covariance matrices, Σi, can be in full rank or constrained to be diagonal. Additionally, parameters can be shared, or tied, among the Gaussian components, such as having a common covariance matrix for all components. The choice of model configuration is often determined by the amount of data available for estimating the GMM parameters and how the GMM is used in a particular application [14]. In fact, GMM can suffer from the requirement of large numbers of training examples to estimate model parameters. A further limitation of parametric techniques is that the chosen functional form for the data distribution may not be a good model of the distribution that generates the data.

One of the major issues in novelty detection is the selection of a suitable novelty threshold. Within a probabilistic approach, novelty scores can be defined using the unconditional probability distribution zðxÞ ¼ pðxÞ and a typical approach to setting a novelty threshold k is to threshold this value, that is, pðxÞ ¼ k. However, because pðxÞ is a probability density function, a threshold on pðxÞ has no direct probabilistic interpretation. Some studies have interpreted the model output pðxÞ probabilistically, by considering the cumulative probability P associated with pðxÞ, that is, determining the probability mass obtained by numerically estimating the integral of pðxÞ over a region R for which the value of pðxÞ is above the novelty threshold k [15]. For unimodal distributions, one can integrate from the mode of the probability density function to the probability contour defined by the novelty threshold pðxÞ ¼ k, which can be achieved in a closed form for most regular distributions.

#### 2.1.2. Kernel density estimator

Nonparametric approaches do not assume that the structure of a model is fixed, that is, the model grows in size necessary to fit the data and accommodates the complexity of the data. The simplest nonparametric statistical technique is the use of histograms. The algorithm typically defines a distance measure between a new test data point and the histogram-based model of normality to determine if it is an outlier or not [10]. For multivariate data, attributewise histograms are constructed and an overall novelty score for a test data point is obtained by aggregating the novelty scores from each attribute. However, when a histogram is defined, it is necessary to consider the width of the bins (equal subintervals in which the whole data interval is divided) and the end points of the bins (where each of the bins starts). In consequence, the histograms present a nonsmooth behavior. In order to alleviate this deficiency, the kernel estimators were proposed.

It must be considered that observations are being drawn from some unknown probability density function pðxÞ in a Euclidian D-dimensional feature space. Thus, considering a region R containing the D-dimensional measurement x, the probability mass associated with this region is given by P ¼ ð R pðxÞdx. Taking into account a dataset comprising N observations drawn from pðxÞ, each data point has a probability P of falling within R, and the total number K of points that lie inside R will be distributed according to the binomial distribution BinðKjN, <sup>P</sup>Þ ¼ <sup>N</sup>! <sup>K</sup>!ðN�KÞ! PKð<sup>1</sup> � <sup>P</sup><sup>Þ</sup> 1�k . The mean fraction of points falling inside the region is E½KjN� ¼ P, and the variance around this mean is var½KjN� ¼ Pð1 � PÞ=N. For large N, this distribution will sharply peak around the mean and so K ffi NP. If, however, it is assumed that the region R is sufficiently small that the probability density pðxÞ is roughly constant over the region, then P ffi pðxÞV, where V is the volume of R. Thus, density estimate is obtained in the form,

gðxjμ<sup>i</sup> ,

collectively represented by the notation λ ¼ fwi, μ<sup>i</sup>

XM

136 Fault Diagnosis and Detection

<sup>X</sup>iÞ ¼ <sup>1</sup> ð2πÞ D=2 j <sup>X</sup>i<sup>j</sup> 1=2

may not be a good model of the distribution that generates the data.

achieved in a closed form for most regular distributions.

2.1.2. Kernel density estimator

kernel estimators were proposed.

exp � <sup>1</sup> 2 ðx � μ<sup>i</sup> Þ 0 X�1 i

with mean vector µi and covariance matrix Σi. The mixture weights satisfy the constraint that

on the GMM. The covariance matrices, Σi, can be in full rank or constrained to be diagonal. Additionally, parameters can be shared, or tied, among the Gaussian components, such as having a common covariance matrix for all components. The choice of model configuration is often determined by the amount of data available for estimating the GMM parameters and how the GMM is used in a particular application [14]. In fact, GMM can suffer from the requirement of large numbers of training examples to estimate model parameters. A further limitation of parametric techniques is that the chosen functional form for the data distribution

One of the major issues in novelty detection is the selection of a suitable novelty threshold. Within a probabilistic approach, novelty scores can be defined using the unconditional probability distribution zðxÞ ¼ pðxÞ and a typical approach to setting a novelty threshold k is to threshold this value, that is, pðxÞ ¼ k. However, because pðxÞ is a probability density function, a threshold on pðxÞ has no direct probabilistic interpretation. Some studies have interpreted the model output pðxÞ probabilistically, by considering the cumulative probability P associated with pðxÞ, that is, determining the probability mass obtained by numerically estimating the integral of pðxÞ over a region R for which the value of pðxÞ is above the novelty threshold k [15]. For unimodal distributions, one can integrate from the mode of the probability density function to the probability contour defined by the novelty threshold pðxÞ ¼ k, which can be

Nonparametric approaches do not assume that the structure of a model is fixed, that is, the model grows in size necessary to fit the data and accommodates the complexity of the data. The simplest nonparametric statistical technique is the use of histograms. The algorithm typically defines a distance measure between a new test data point and the histogram-based model of normality to determine if it is an outlier or not [10]. For multivariate data, attributewise histograms are constructed and an overall novelty score for a test data point is obtained by aggregating the novelty scores from each attribute. However, when a histogram is defined, it is necessary to consider the width of the bins (equal subintervals in which the whole data interval is divided) and the end points of the bins (where each of the bins starts). In consequence, the histograms present a nonsmooth behavior. In order to alleviate this deficiency, the

It must be considered that observations are being drawn from some unknown probability density function pðxÞ in a Euclidian D-dimensional feature space. Thus, considering a region R containing the D-dimensional measurement x, the probability mass associated with this

<sup>i</sup>¼<sup>1</sup>wi <sup>¼</sup> 1. The complete Gaussian mixture model is parameterized by the mean vectors, covariance matrices and mixture weights from all component densities. These parameters are

ðx � μ<sup>i</sup> Þ

, Σig, i ¼ 1, ::, M. There are several variants

(2)

( )

$$P(\mathbf{x}) = \frac{K}{NV} \tag{3}$$

Note that the validity of Eq. (3) depends on two contradictory assumptions, namely that the region R is sufficiently small that the density is approximately constant over the region and yet sufficiently large (in relation to the value of that density) that the number K of points falling inside the region is sufficient for the binomial distribution to sharply peak. The resultant Eq. (3) can be exploited in two different ways. Either it can be fixed K and the value of V can be determined from the data, which gives rise to the K-nearest-neighbor technique that will be presented later, or it can be fixed V and K can be determined from the data, giving rise to the kernel approach. It can be shown that both the K-nearest-neighbor density estimator and the kernel density estimator converge to the true probability density in the limit N ! ∞, provided V shrinks suitably with N, and K grows with N [13]. Thus, considering the region R as a small hypercube centered on the point x at which is desired to determine the probability density, the number K of points falling within region is defined as follows,

$$K(u) = \begin{cases} 1, \ |u\_i| \le \frac{1}{2}, \ i = 1, \ldots, D \\ 0, \ \text{otherwise} \end{cases} \tag{4}$$

which represents a unit cube centered on the origin. The function KðuÞ is an example of a kernel function and in this context is also called a Parzen window. From Eq. (4), the quantity K <sup>x</sup>�xi h � � will be one if the data point xi lies inside a cube of side h centered on x and zero otherwise. The total number of data points lying inside this cube will therefore be <sup>K</sup> <sup>¼</sup> <sup>X</sup><sup>N</sup> i¼1 k <sup>x</sup>�xi h � �. Substituting this expression in Eq. (3) gives the following result for the estimated density at x,

$$p(\mathbf{x}) = \frac{1}{N} \sum\_{i=1}^{N} \frac{1}{h^D} k\left(\frac{\mathbf{x} - \mathbf{x}\_i}{h}\right) \tag{5}$$

where <sup>V</sup> <sup>¼</sup> hD for the volume of a hypercube of side <sup>h</sup> in <sup>D</sup> dimensions. Eq. (5) represents the kernel density estimator [16]. Even though Gaussian kernels are the most often used, there are various choices among kernels that can be found in the literature [17].

#### 2.2. Domain-based method

Domain-based method requires a boundary to be created based on the structure of the training dataset. These methods are typically insensitive to the specific sampling and the density of the target class because they describe the target class boundary, or the domain, and not the class density. Class membership of unknown data is then determined by their location with respect to the boundary. Domain-based novelty detection is approached with the two-class problem in terms of Support Vector Machine (SVM), where the location of the novelty boundary is determined using only those data that lie closest to it (in a kernel-based transformed space), by means of the support vectors. All other data from the training set (those that are not support vectors) are not considered when setting the novelty boundary. Hence, the distribution of data in the training set is not considered, which is seen as an easy novelty detection approach [7]. The original SVM is a network that is ideally suited for binary pattern classification of data that are linearly separable. Indeed, the SVM defines a hyperplane that maximizes the separating margin between two classes. Since the introduction of the original idea, several modifications and improvements have been made.

#### 2.2.1. Support vector data description

A data domain description method, inspired by the support vector machine approach, called the Support Vector Data Description (SVDD), is used for novelty or outlier detection. The objective is the definition of a spherically shaped decision boundary around a set of measurements by a set of support vectors describing the hypersphere boundary. The method allows the possibility of transforming the data to new feature spaces, where the SVDD can obtain more flexible and more accurate data descriptions. The minimizing problem to delimitate the radius of the hypersphere is expressed as the Lagrangian, <sup>L</sup> <sup>¼</sup> <sup>X</sup> i <sup>α</sup>iðxi�xiÞ �<sup>X</sup> i, j αiαjðxi�xjÞ, under the constraints of 0 <sup>≤</sup> <sup>α</sup><sup>i</sup> <sup>≤</sup> <sup>C</sup> and <sup>X</sup> i α<sup>i</sup> ¼ 1, where αi,<sup>j</sup> are the Lagrange multipliers, xi,<sup>j</sup> are the data training points, the variable C gives the trade-off between simplicity (or volume of the sphere) and the number of errors (number of target objects rejected). For those objects the coefficients αi,<sup>j</sup> will be nonzero and are called the support objects. In order to determine whether a new measurement is within the hypersphere, the distance to the center of the sphere has to be calculated. A new measurement z is considered known when this distance is smaller than the radius,

$$(z \cdot z) - 2\sum\_{i} a\_i (z \cdot x\_i) + \sum\_{i,j} a\_i a\_j (\mathbf{x}\_i \cdot \mathbf{x}\_j) \le r^2 \tag{6}$$

where a is the center of the sphere and r is the radius [18]. Kernels could be applied to soften the margins of the sphere, being applied over the measures and data descriptors.

#### 2.2.2. One-class support vector machine

The One-Class SVM, OC-SVM, is based on the definition of the novelty boundary in the feature space corresponding to a kernel, by separating the transformed training data from the origin in the feature space, with the maximum margin. This approach requires fixing a priori the percentage of positive data allowed to fall outside the description of the normal class. This makes the OC-SVM more tolerant to outliers in the normal training data. However, setting this parameter strongly influences the performance of this approach. The shape of the domain delimiting the boundaries depends on the kernel selected. Thus, the development of the algorithm is the classic SVM approach. The difference with the other domain-based method approach is that OC-SVM does not consider a specific structure (e.g., a hypersphere) to delimit the domain and therefore does not automatically optimize the model parameters by using artificially generated unlabeled data which are uniformly distributed. The detection of novelty is therefore delimited by,

$$f(\mathbf{x}) = \sum\_{i=1}^{N} \alpha\_i K(\mathbf{x}\_i, \mathbf{x}) - p \tag{7}$$

where p is an offset. The famous kernel trick is the procedure of using a kernel function in input space, Kðxi, xÞ, to replace the inner product of two vectors into a huge, or even infinite, dimensional feature space. Some drawbacks of these methods are found in literature reviews [7], and it turns out to be surprisingly sensitive to specific choices of representations and kernels in ways which are not very transparent. In addition, the proper choice of a kernel is dependent on the number of features in the binary vector. Since the difference in performance is very dramatic based on these choices, this means that the method is not robust without a deeper understanding of these representation issues.

#### 2.3. Distance-based method

2.2. Domain-based method

138 Fault Diagnosis and Detection

and improvements have been made.

2.2.1. Support vector data description

the constraints of 0 <sup>≤</sup> <sup>α</sup><sup>i</sup> <sup>≤</sup> <sup>C</sup> and <sup>X</sup>

2.2.2. One-class support vector machine

than the radius,

of the hypersphere is expressed as the Lagrangian, <sup>L</sup> <sup>¼</sup> <sup>X</sup>

ðz�zÞ � 2

X i

the margins of the sphere, being applied over the measures and data descriptors.

i

Domain-based method requires a boundary to be created based on the structure of the training dataset. These methods are typically insensitive to the specific sampling and the density of the target class because they describe the target class boundary, or the domain, and not the class density. Class membership of unknown data is then determined by their location with respect to the boundary. Domain-based novelty detection is approached with the two-class problem in terms of Support Vector Machine (SVM), where the location of the novelty boundary is determined using only those data that lie closest to it (in a kernel-based transformed space), by means of the support vectors. All other data from the training set (those that are not support vectors) are not considered when setting the novelty boundary. Hence, the distribution of data in the training set is not considered, which is seen as an easy novelty detection approach [7]. The original SVM is a network that is ideally suited for binary pattern classification of data that are linearly separable. Indeed, the SVM defines a hyperplane that maximizes the separating margin between two classes. Since the introduction of the original idea, several modifications

A data domain description method, inspired by the support vector machine approach, called the Support Vector Data Description (SVDD), is used for novelty or outlier detection. The objective is the definition of a spherically shaped decision boundary around a set of measurements by a set of support vectors describing the hypersphere boundary. The method allows the possibility of transforming the data to new feature spaces, where the SVDD can obtain more flexible and more accurate data descriptions. The minimizing problem to delimitate the radius

data training points, the variable C gives the trade-off between simplicity (or volume of the sphere) and the number of errors (number of target objects rejected). For those objects the coefficients αi,<sup>j</sup> will be nonzero and are called the support objects. In order to determine whether a new measurement is within the hypersphere, the distance to the center of the sphere has to be calculated. A new measurement z is considered known when this distance is smaller

<sup>α</sup>iðz�xiÞ þ<sup>X</sup>

where a is the center of the sphere and r is the radius [18]. Kernels could be applied to soften

The One-Class SVM, OC-SVM, is based on the definition of the novelty boundary in the feature space corresponding to a kernel, by separating the transformed training data from the origin in the feature space, with the maximum margin. This approach requires fixing a priori

i, j

i

αiαjðxi�xjÞ ≤ r

<sup>α</sup>iðxi�xiÞ �<sup>X</sup>

α<sup>i</sup> ¼ 1, where αi,<sup>j</sup> are the Lagrange multipliers, xi,<sup>j</sup> are the

i, j

<sup>2</sup> (6)

αiαjðxi�xjÞ, under

Distance-based methods represent a novelty detection approach similar to that of estimating the PDF of data. Distance-based methods such as nearest neighbors or clustering are based on well-defined distance metrics to compute distance, as the similarity criterion, among data points.

#### 2.3.1. Nearest neighbor

The main idea that rears this technique is that the normal data is projected near their neighborhoods, while novelties will be projected far from their neighbors. That is, considering an unknown data point x, this point is accepted as normal if the distance to its nearest neighbor y, in the training set, is less than or equal to the distance from y to the nearest neighbor of y in the training set. Otherwise, x is considered as novelty. Euclidian distance is the most popular choice for univariate and multivariate continuous attributes,

$$\|\mathbf{x} - \mathbf{y}\| = \sqrt{\sum\_{i=1}^{D} (\mathbf{x}\_i - \mathbf{y}\_i)^2} \tag{8}$$

Several well-defined distance metrics to compute the distance (or the similarity measure) between two data points can be used, which can broadly be divided into distance-based methods, such as the distance to the kth nearest neighbor and local density-based methods in which the distance to the average of the k's nearest neighbors is considered [11].

In conclusion, novelty detection approaches differ on the assumptions made about the nature of the available data. Each approach exhibits its own advantages and disadvantages and faces different challenges for complex datasets. Table 1 collects the main characteristics of the considered methods. Thus, probabilistic methods make use of the distribution of the training data to determine the location of the novelty boundary. Domain-based methods determine the location of the novelty boundary using only those data that lie closest to it and do not make any assumptions about the data distribution. Distance-based methods require the definition of an appropriate distance measure for the given data.

Table 1. Summary of the main characteristics of the novelty detection approaches.

### 3. Case study

In order to illustrate the practical implementation of novelty detection in an industrial application, an interesting case study is proposed next. Indeed, as it has been mentioned, currently, due to the worldwide market situation, the industrial sector is being subjected to a high degree of competitiveness. Critical sectors as the automotive industry are investing in higher levels of quality and safety assessment procedures in order to reduce costs without compromising the attributes of their mechanical manufactured assets. In regard to the automotive rotatory mechanical components, such as the electrical-assisted power steering columns (EPS), end-ofline tests (EOLs) are carried out to analyze their performances. The EPS column is rotated by a test machine in order to quantify the required torque to perform a complete revolution of the EPS column without the influence of any external load. Thus, if the recorded torque is compared with a reference pattern for decision support purposes, then, the EOL test is complete. However, the condition monitoring of the EOL machines, as the represented in Figure 3, has

Evaluation of Novelty Detection Methods for Condition Monitoring applied to an Electromechanical System http://dx.doi.org/10.5772/67531 141

In conclusion, novelty detection approaches differ on the assumptions made about the nature of the available data. Each approach exhibits its own advantages and disadvantages and faces different challenges for complex datasets. Table 1 collects the main characteristics of the considered methods. Thus, probabilistic methods make use of the distribution of the training data to determine the location of the novelty boundary. Domain-based methods determine the location of the novelty boundary using only those data that lie closest to it and do not make any assumptions about the data distribution. Distance-based methods require the definition of

> Several configuration parameters. Sensitive to the scaling of the feature values. Requires a minimum number of training.

of the covariance matrix.

evaluation of test objects.

presented in training. Sensitive to noise.

Requires a large number of training samples to overcome the curse of dimensionality. The distribution of the data is assumed. Unlabeled outliers in training affect the estimation

Requires a large number of training samples to overcome the curse of dimensionality. Expensive computational cost for testing. Limited applicability of the method when there is a large dataset in high-dimensional feature spaces.

Scale sensitive due to the use of distances in the

Performance affected when unlabeled outliers are

In order to illustrate the practical implementation of novelty detection in an industrial application, an interesting case study is proposed next. Indeed, as it has been mentioned, currently, due to the worldwide market situation, the industrial sector is being subjected to a high degree of competitiveness. Critical sectors as the automotive industry are investing in higher levels of quality and safety assessment procedures in order to reduce costs without compromising the attributes of their mechanical manufactured assets. In regard to the automotive rotatory mechanical components, such as the electrical-assisted power steering columns (EPS), end-ofline tests (EOLs) are carried out to analyze their performances. The EPS column is rotated by a test machine in order to quantify the required torque to perform a complete revolution of the EPS column without the influence of any external load. Thus, if the recorded torque is compared with a reference pattern for decision support purposes, then, the EOL test is complete. However, the condition monitoring of the EOL machines, as the represented in Figure 3, has

an appropriate distance measure for the given data.

them to lie outside the description. Robust to unlabeled outliers in training.

distribution is assumed.

Flexible density model.

each feature direction.

the target distribution.

samples.

Method Advantages Disadvantages

Robust to labeled outliers in training by forcing

Great advantage when a good probability

Provides a more flexible density method.

Low computational cost for training.

Possible configuration of the kernel width h on

The density estimation is only influenced locally.

Rejects parts of the feature space which are within

Table 1. Summary of the main characteristics of the novelty detection approaches.

Lack of configuration parameters, besides k; therefore, it relies completely on the training

3. Case study

Domainbased i.e. One-class SVM

140 Fault Diagnosis and Detection

Probabilistic parametric i.e. Gaussian mixture models

Probabilistic nonparametric i.e. Kernel density estimator

Distancebased i.e. k-NN

Figure 3. End-of-test machine, composed by a servomotor, a gearbox, an encoder, a torque transducer and a pneumatic clamp to hold the intermediate shaft of the EPS column.

not being attended classically. The maintenance program is limited to a preventive approach, leading to torque response deviations due to EOL machine degradation that are not detected by the machine operator until an evident malfunction. In this regard, the detection and identification of EOL malfunctions during its operation becomes an impactful contribution to the sector and is considered a challenging condition-based monitoring scenario.

In this work, a specific end-of-line test machinery is analyzed. The system under monitoring is based on an electrical drive, where a 1.48 kW at 3000 rpm servomotor connected to a 60:1 reduction gearbox emulates the input torque of the steering wheel to perform a 180 turn in order to evaluate the mechanical performances of power-assisted steering systems. The measurement equipment is focused on the acquisition of the torque signal and the rotatory shaft position from the encoder. Data acquisition is done at 1 kHz of sampling frequency by means of a NI cDAQ-9188, composed by the modules NI-9411 and NI 9215.

The torque induced by the drive is expected to follow a specific predefined set point pattern. However, these test systems present two main limitations: first, if the test machine does not generate the input of the torque set point correctly, an inaccurate result is obtained during the assessment of the power-assisted steering system, leading to the nonvalidation of the components under test and second, the lack of malfunctions' characterization over the testing machine, since the faults' variability and appearance in the torque generation test are unpredictable. Thus, this work presents an electromechanical system novelty detection approach, based on the temporal torque signal characterization by statistical time features and the evaluation of different novelty detection algorithms (probabilistic, domain-based and distance-based), for novelty assessment.

In order to analyze the performance of the proposed methodology, some faulty conditions have been induced in the machine to provoke different severity degrees of a common fault scenario. Three operating scenarios are considered, that is, healthy, H, a coupling low wear, CLW, and a coupling high wear, CHW. The coupling wear fault is emulated by employing two different intermediate elastomers in the torque limiter coupling, each one with different dynamic torsional stiffness (DTS). The values of the DTS of the pieces under test are all lower than the standard used in the machine in order to emulate classical wear, thus, 2580 Nm/rad corresponds to CLW and 2540 Nm/rad to CHW.

#### 3.1. Method

During the test, the assisting motor of the EPS is not powered. The test starts smoothly in a clockwise direction for the first 45 until a speed set point is reached. The acceleration time depends on the drive capability. During the next 360, the speed is fixed at the set point, in this case 15 rpm. The last additional 45 is for a mild brake of the EPS column under test. Then, the same procedure is employed to return to the original start point in the opposite direction. The drive is applied to the steering shaft of the EPS. Then, the torque signal analysis is carried out during the stationary speed set point corresponding to a 360 turn of the EPS column. It is expected that malfunctions and anomalies could appear during segments of the revolution of the EPS column; therefore, the segmentation represents a viable strategy to gain resolution during the characterization. That is, the 4-second torque signal (time taken to perform the 360 turn) is segmented in four parts of 1 second. A set of five statistical time-domain features is calculated from each segment of the torque signal. The proposed features are listed in Table 2. These features have been successfully employed in different studies for electromechanical systems' fault detection [19]. Therefore, a total of 20 features are calculated from each torque signal measurement.

High-dimensional datasets complicate the learning task of novelty detection as well as multiclass classification methods, because of the possible presence of nonsignificant and redundant information in the data, compromising the proper convergence of the algorithms. Indeed, the empty space phenomenon states that to cover the whole space, it needs a number of samples that grows

Table 2. Statistical time-domain features used for torque signal characterization.

measurement equipment is focused on the acquisition of the torque signal and the rotatory shaft position from the encoder. Data acquisition is done at 1 kHz of sampling frequency by

The torque induced by the drive is expected to follow a specific predefined set point pattern. However, these test systems present two main limitations: first, if the test machine does not generate the input of the torque set point correctly, an inaccurate result is obtained during the assessment of the power-assisted steering system, leading to the nonvalidation of the components under test and second, the lack of malfunctions' characterization over the testing machine, since the faults' variability and appearance in the torque generation test are unpredictable. Thus, this work presents an electromechanical system novelty detection approach, based on the temporal torque signal characterization by statistical time features and the evaluation of different novelty detection algorithms (probabilistic, domain-based and distance-based), for novelty

In order to analyze the performance of the proposed methodology, some faulty conditions have been induced in the machine to provoke different severity degrees of a common fault scenario. Three operating scenarios are considered, that is, healthy, H, a coupling low wear, CLW, and a coupling high wear, CHW. The coupling wear fault is emulated by employing two different intermediate elastomers in the torque limiter coupling, each one with different dynamic torsional stiffness (DTS). The values of the DTS of the pieces under test are all lower than the standard used in the machine in order to emulate classical wear, thus, 2580 Nm/rad

During the test, the assisting motor of the EPS is not powered. The test starts smoothly in a clockwise direction for the first 45 until a speed set point is reached. The acceleration time depends on the drive capability. During the next 360, the speed is fixed at the set point, in this case 15 rpm. The last additional 45 is for a mild brake of the EPS column under test. Then, the same procedure is employed to return to the original start point in the opposite direction. The drive is applied to the steering shaft of the EPS. Then, the torque signal analysis is carried out during the stationary speed set point corresponding to a 360 turn of the EPS column. It is expected that malfunctions and anomalies could appear during segments of the revolution of the EPS column; therefore, the segmentation represents a viable strategy to gain resolution during the characterization. That is, the 4-second torque signal (time taken to perform the 360 turn) is segmented in four parts of 1 second. A set of five statistical time-domain features is calculated from each segment of the torque signal. The proposed features are listed in Table 2. These features have been successfully employed in different studies for electromechanical systems' fault detection [19]. Therefore, a total of 20 features are calculated from each torque

High-dimensional datasets complicate the learning task of novelty detection as well as multiclass classification methods, because of the possible presence of nonsignificant and redundant information in the data, compromising the proper convergence of the algorithms. Indeed, the empty space phenomenon states that to cover the whole space, it needs a number of samples that grows

means of a NI cDAQ-9188, composed by the modules NI-9411 and NI 9215.

assessment.

142 Fault Diagnosis and Detection

3.1. Method

signal measurement.

corresponds to CLW and 2540 Nm/rad to CHW.

exponentially with dimensionality. Thus, the curse of dimensionality implies that in order to learn successfully, it needs a number of training examples that also grows exponentially with the dimensionality. The "concentration of measure" phenomenon seems to render distance measures not relevant to whatever concept is to be learned as the dimension of the data increased. For these reasons, there is a necessity to apply dimensionality reduction techniques in condition monitoring applications. Thus, in order to analyze the performance of different novelty detection approaches, two main dimensionality reduction approaches are applied over the 20-dimensional vectors, that is, Principal Component Analysis, PCA, and Laplacian Score, LS.

Indeed, the dimensionality reduction strategies differ in the criteria applied over the data in order to reach a reduced feature space. PCA is one of the most commonly used techniques for unsupervised dimensionality reduction. It aims to find the linear projections that best capture the variability of the data [13]. Another well-known technique is the LS, where the merit of each feature is measured according to its locality preservation power. A nearest neighborbased graph is constructed from the training set and analyzed to rank each feature individually according to a weighting approach selected for the graph's edges. To rank each feature, its LS is computed, which is a measure of the extent to which the analyzed feature preserves the structure present in the graph divided by the variance of the feature. For a feature to be selected, it must have a low LS, which implies high variance and locality [20].

Finally, the necessity of evaluating the novelty detection performance is critical. The use of a particular score depends on multiple interests, and then, the analysis of complementary scores represents the most interesting solution. Next, the most useful and common scores in a discrete scenario are described in order to be used later during the analysis of the experimental results.

• Accuracy and classification error (1-accuracy): One of the most frequent scores used to evaluate discrete classification in electromechanical diagnosis is accuracy. This score is indicative of the classification error committed while evaluating, in our case, two classes,

$$Accuracy = \frac{FP + FN}{N} \tag{9}$$

where FP is the number of false positives, FN is the number of false negatives and N, the total number of analyzed measures. Two novelty detection approaches could exhibit the same accuracy but provide a different novelty ratio for each class (normal data and novelty data).

• True positive rate (recall or sensitivity): This measure provides a proportion of one kind of sample that was correctly assessed. But it only evaluates the positive cases,

$$\text{Recall} = \frac{TP}{TP + FN} \tag{10}$$

where TP is the number of true positives.

• Precision: This performance metric evaluates the correct classification of the positive class,

$$Precision = \frac{TP}{TP + FP} \tag{11}$$

• F-measure: This score can help to solve any contradiction that may appear between precision and recall scores. F-measure leaves out the TN performance. Several versions exist. The most common expression is,

$$F\_1 = \frac{2[Precision\*Recall]}{[2\*Precision + Recall]} \tag{12}$$

#### 3.2. Experimental results

In order to expose the novelty detection performances, the outline of the experimental results is presented as follows: The initial database is characterized by the proposed set of features, then both feature reduction approaches are applied and, finally, over each reduced set of features, the three novelty detection approaches are applied. The application of the novelty detection is done sequentially, that is, first, the data corresponding to the healthy, H, operating scenario is characterized by the novelty model. Second, the first fault operating scenario, CLW, is presented as well as additional measures of the H operating scenarios. At this point, the performance of the novelty detection model is analyzed. Third, the novel data identified is included in the upgraded version of the novelty model by retraining, and over this updated novelty model, the second fault operating scenario, CHW, is presented as well as the additional measures of the CLW and H operating scenarios. At this point, the performance of the novelty detection models is analyzed again. Finally, the novel data identified is included in an upgraded version of the novelty model by a new retraining.

Three novelty detection methods have been implemented, that is, the mixture of Gaussians as the probabilistic approach, one-class support vector machines as the domain-based novelty detection approach and, finally, k-nearest neighbors as the distance-based novelty detection approach. Next, the PCA variant of the novelty detection methodology is shown in Figure 4.

The proposed scores during the assessment of the novelty detection models in front of a new set of measurements are shown next. Thus, in Table 3, the scores in regard to the PCA feature reduction and the novelty detection models 'performance, dealing with the projection of new measurements corresponding to H and CLW operating scenarios over the novelty models trained with the H operating scenario, can be seen. It should be noted that, in regard to all the scores shown in the next tables, a 10-fold cross validation strategy has been considered, in which the mean and the dispersion ratio of the obtained scores is shown.

• True positive rate (recall or sensitivity): This measure provides a proportion of one kind of

Recall <sup>¼</sup> TP

• Precision: This performance metric evaluates the correct classification of the positive class,

• F-measure: This score can help to solve any contradiction that may appear between precision and recall scores. F-measure leaves out the TN performance. Several versions

<sup>F</sup><sup>1</sup> <sup>¼</sup> <sup>2</sup>½Precision � Recall�

In order to expose the novelty detection performances, the outline of the experimental results is presented as follows: The initial database is characterized by the proposed set of features, then both feature reduction approaches are applied and, finally, over each reduced set of features, the three novelty detection approaches are applied. The application of the novelty detection is done sequentially, that is, first, the data corresponding to the healthy, H, operating scenario is characterized by the novelty model. Second, the first fault operating scenario, CLW, is presented as well as additional measures of the H operating scenarios. At this point, the performance of the novelty detection model is analyzed. Third, the novel data identified is included in the upgraded version of the novelty model by retraining, and over this updated novelty model, the second fault operating scenario, CHW, is presented as well as the additional measures of the CLW and H operating scenarios. At this point, the performance of the novelty detection models is analyzed again. Finally, the novel data identified is included in an

Three novelty detection methods have been implemented, that is, the mixture of Gaussians as the probabilistic approach, one-class support vector machines as the domain-based novelty detection approach and, finally, k-nearest neighbors as the distance-based novelty detection approach. Next, the PCA variant of the novelty detection methodology is shown in Figure 4. The proposed scores during the assessment of the novelty detection models in front of a new set of measurements are shown next. Thus, in Table 3, the scores in regard to the PCA feature reduction and the novelty detection models 'performance, dealing with the projection of new measurements corresponding to H and CLW operating scenarios over the novelty models

Precision <sup>¼</sup> TP

TP <sup>þ</sup> FN (10)

TP <sup>þ</sup> FP (11)

<sup>½</sup><sup>2</sup> � Precision <sup>þ</sup> Recall� (12)

sample that was correctly assessed. But it only evaluates the positive cases,

where TP is the number of true positives.

exist. The most common expression is,

upgraded version of the novelty model by a new retraining.

3.2. Experimental results

144 Fault Diagnosis and Detection

Figure 4. Performance of the three novelty detection models in a PCA-based 2-dimensional feature space. MG mixture of Gaussian, OC-SVM, one-class support vector machine and k-NN, k-nearest neighbor. (a) Novelty models' boundaries during the characterization of the H operating scenario. (b) Projection of new measurements corresponding to H and CLW operating scenarios over the novelty models trained with the H operating scenario. (c) Novelty model boundaries' update by the incorporation of the H and CLW operating scenarios' measures detected as novelties and the projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models. (d) Novelty model boundaries' update by the incorporation of the H, CLW and CHW operating scenarios' measures detected as novelties.

Table 3. Associated scores to the PCA and novelty detection performance dealing with the class H as normal and CLW as novelty.

Also, in Table 4, the scores in regard to the PCA feature reduction and the novelty detection models' performance, dealing with the projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models trained with the H and CLW operating scenarios, can be seen.

Table 4. Associated scores to the PCA and novelty detection performance dealing with the H and CLW as known operating scenarios and CHW as novelty.

Similarly, next, the LS variant of the novelty detection methodology is shown in Figure 5.

The proposed scores during the assessment of this variant of novelty detection models in front of a new set of measurements are also shown next. Thus, in Table 5, the scores in regard to the LS feature reduction and novelty detection models' performance, dealing with the projection of new measurements corresponding to H and CLW operating scenarios over the novelty models trained with the H operating scenario can be seen.

Table 5. Associated scores to the LS and novelty detection performance dealing with the class H as normal and CLW as novelty.

Also, in Table 6, the scores in regard to the LS feature reduction and novelty detection models' performance, dealing with the projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models trained with the H and CLW operating scenarios can be seen.

Table 6. Associated scores to the LS and novelty detection performance dealing with the H and CLW as known operating scenarios and CHW as novelty.

Evaluation of Novelty Detection Methods for Condition Monitoring applied to an Electromechanical System http://dx.doi.org/10.5772/67531 147

Also, in Table 4, the scores in regard to the PCA feature reduction and the novelty detection models' performance, dealing with the projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models trained with the H and CLW operat-

Accuracy 0.930 (0.025) 0.863 (0.014) 0.966 (0.014) Recall 0.997 (0.005) 0.995 (0.006) 0.985 (0.005) Precision 0.902 (0.033) 0.822 (0.013) 0.962 (0.022) F1 score 0.947 (0.018) 0.901 (0.01) 0.973 (0.010)

MG OC-SVM k-NN

MG OC-SVM k-NN

MG OC-SVM k-NN

Similarly, next, the LS variant of the novelty detection methodology is shown in Figure 5.

Table 4. Associated scores to the PCA and novelty detection performance dealing with the H and CLW as known

models trained with the H operating scenario can be seen.

The proposed scores during the assessment of this variant of novelty detection models in front of a new set of measurements are also shown next. Thus, in Table 5, the scores in regard to the LS feature reduction and novelty detection models' performance, dealing with the projection of new measurements corresponding to H and CLW operating scenarios over the novelty

Accuracy 0.956 (0.021) 0.971 (0.026) 0.967 (0.028) Recall 1.000 (0.000) 1.000 (0.000) 1.000 (0.000) Precision 0.940 (0.023) 0.965 (0.031) 0.960 (0.033) F1 score 0.969 (0.012) 0.982 (0.016) 0.980 (0.017)

Also, in Table 6, the scores in regard to the LS feature reduction and novelty detection models' performance, dealing with the projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models trained with the H and CLW operating

Accuracy 0.910 (0.016) 0.841 (0.032) 0.890 (0.014) Recall 0.955 (0.017) 0.925 (0.021) 0.865 (0.044) Precision 0.922 (0.027) 0.840 (0.044) 0.940 (0.030) F1 score 0.938 (0.012) 0.879 (0.021) 0.899 (0.014)

Table 6. Associated scores to the LS and novelty detection performance dealing with the H and CLW as known operating

Table 5. Associated scores to the LS and novelty detection performance dealing with the class H as normal and CLW as

ing scenarios, can be seen.

146 Fault Diagnosis and Detection

operating scenarios and CHW as novelty.

scenarios can be seen.

scenarios and CHW as novelty.

novelty.

Figure 5. Performance of the three novelty detection models in a LS based 2-dimensional feature space. MG mixture of Gaussian, OC-SVM, one class support vector machine, and k-NN, k-nearest neighbor. (a) Novelty models boundaries during the characterization of the H operating scenario. (b) Projection of new measurements corresponding to H and CLW operating scenarios over the novelty model trained with the H operating scenario. (c) Novelty model boundaries update by the incorporation of the H and CLW operating scenarios measures detected as novelties, and projection of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models. (d) Novelty model boundaries update by the incorporation of the H, CLW and CHW operating scenarios measures detected as novelties.

In regard to the feature reduction effect over the novelty detection performance, it has been taken into account that both methods, PCA and LS, represent linear approaches to the reduction of the initial 20-dimensional feature set. This premise is not a limitation to the analysis of the novelty detection models considered; however, the feature space could be further improved in order to maximize the obtained results for the specific application.

Independently of the novelty detection model, the first test stage, that is, the assessment of new measurements corresponding to H and CLW operating scenarios over the novelty models trained with the H operating scenario, shows a clear superiority of the LS approach. The accuracy obtained with the LS approach reaches till 97% and is, in all cases, better than using PCA that reaches a maximum of 92%. However, the second test stage, that is, the assessment of new measurements corresponding to H, CLW and CHW operating scenarios over the novelty models trained with the H and CLW operating scenarios, shows a clear superiority of the PCA approach. The accuracy obtained with the PCA approach reaches till 96% and is, in most of the cases, better than using LS that reaches a maximum of 91%.