**8. Concluding remarks**

This chapter compiles and analyzes the main numerical approaches that have been proposed to predict and reproduce the fouling phenomenon that takes place inside the EGR system. Features of each option, its range of applicability, as well as their main strengths and weaknesses have been highlighted. The fouling prediction capabilities of each numerical approach have been analyzed in detail with the aim of reviewing the most relevant numerical approaches used in the study of the fouling process that occurs in the EGR system.

The stringent construction requirements of new EGR technologies and the development of new numerical techniques, and more particularly the use of computational fluid dynamics codes, have contributed to the creation of more sophisticated models that allow the simulation of the fouling phenomenon considering a large number of parameters and mechanisms. Nevertheless, the simulation of the deposit formation and evolution involves intricate matters, such as the particlefluid interaction, agglomerate formation, or the physicochemical reactions that take place inside the deposit, which make the fouling process a complex phenomenon that needs to be addressed coherently across all its parameters.

The information and knowledge about the numerical modeling of the fouling process in the EGR system collected in this study may help EGR designers and manufactures to improve and develop new vehicle emissions control techniques, which contribute to meet the Sustainable Development Goals.

#### **Acknowledgements**

The authors are grateful for the financial support from the Spanish Ministry of Economy, Industry, and Competitiveness through the ENE2017-87855-R project.

#### **Nomenclature**

models, and, although they provide detailed information about the fouling phe-

This chapter compiles and analyzes the main numerical approaches that have been proposed to predict and reproduce the fouling phenomenon that takes place inside the EGR system. Features of each option, its range of applicability, as well as their main strengths and weaknesses have been highlighted. The fouling prediction capabilities of each numerical approach have been analyzed in detail with the aim of reviewing the most relevant numerical approaches used in the study of the fouling

The stringent construction requirements of new EGR technologies and the development of new numerical techniques, and more particularly the use of computational fluid dynamics codes, have contributed to the creation of more sophisticated models that allow the simulation of the fouling phenomenon considering a large number of parameters and mechanisms. Nevertheless, the simulation of the deposit formation and evolution involves intricate matters, such as the particlefluid interaction, agglomerate formation, or the physicochemical reactions that take place inside the deposit, which make the fouling process a complex phenomenon

The information and knowledge about the numerical modeling of the fouling process in the EGR system collected in this study may help EGR designers and manufactures to improve and develop new vehicle emissions control techniques,

The authors are grateful for the financial support from the Spanish Ministry of Economy, Industry, and Competitiveness through the ENE2017-87855-R project.

that needs to be addressed coherently across all its parameters.

which contribute to meet the Sustainable Development Goals.

nomenon, they demand more computational resources.

*Environmental Issues and Sustainable Development*

**8. Concluding remarks**

**Acknowledgements**

**Nomenclature**

0-D zero-dimensional 1-D one-dimensional 2-D two-dimensional 3-D three-dimensional *A* surface area *AA* Antoine coefficient *BB* Antoine coefficient *CC* Antoine coefficient *C* soot concentration *c*05 constant coefficients

*CD* drag coefficient

**346**

CFD computational fluid dynamics

*Cm* thermophoretic constant *Cs* thermophoretic constant *Ct* thermophoretic constant *DB* molecular diffusivity

*Cc* Stokes-Cunningham slip correction factor

process that occurs in the EGR system.

**References**

[1] G. Assembly. Resolution adopted by

*DOI: http://dx.doi.org/10.5772/intechopen.93062*

*Numerical Modelling of Fouling Process in EGR System: A Review*

Performance and Emissions of a Heavy-Duty Diesel Engine. In: SAE 2003 World

Michigan, USA: SAE Technical Paper; 3- 6 March 2003. DOI: 10.4271/2003-01-

Schoenen M, Koetter M. Super ultra-low NOX emissions under extended RDE conditions - evaluation of light-off strategies of advanced diesel exhaust aftertreatment systems. In: SAE Technical Paper Series. 2019. DOI:

Congress & Exhibition. Detroit,

[9] Deppenkemper K, Lng ME,

[10] Wei H, Zhu T, Shu G, Tan L, Wang Y. Gasoline engine exhaust gas recirculation – A review. Applied Energy. 2012;**99**:534–544. DOI: 10.1016/

[11] Agarwal D, Singh SK, Agarwal AK. Effect of exhaust gas recirculation (EGR) on performance, emissions, deposits and durability of a constant speed compression ignition engine. Applied Energy. 2011;**88**(8):2900–2907. DOI: 10.1016/j.apenergy.2011.01.066

[12] Resitoglu IA. NOx pollutants from diesel vehicles and trends in the control technologies. In: Richard Viskup, editor.

Diesel and Gasoline Engines.

[13] Hoard J, Abarham M, Styles D, Giuliano JM, Sluder CS, Storey JME. Diesel EGR cooler fouling. SAE

[14] Ismail BI, Zhang R, Ewing D, Cotton JS, Chang J-S. The heat transfer

characteristics of exhaust gas

Proceedings of the ASME 2002 International Mechanical Engineering Congress and Exposition. Vol. 7.

International Journal of Engines. 2008; **1**(1):1234–1250. DOI: 10.4271/2008-01-

recirculation (EGR) cooling devices. In:

IntechOpen; 2018.

2475

10.4271/2019-01-0742

j.apenergy.2012.05.011

1068

September 2016. A/RES/71/1, 3 October 2016 (The New York Declaration); 2010

[2] Anenberg SC, Miller J, Minjares R, Du L, Henze DK, Lacey F, et al. Impacts and mitigation of excess diesel-related NOx emissions in 11 major vehicle markets. Nature. 2017;**545**(7655):467– 471. DOI: 10.1038/nature22086

[3] Joshi A. Review of vehicle engine efficiency and emissions. In: SAE Technical Paper Series. 2019. DOI:

[4] Vestreng V, Ntziachristos L, Semb A,

[5] Rissler J, Swietlicki E, Bengtsson A, Boman C, Pagels J, Sandström T, et al. Experimental determination of

deposition of diesel exhaust particles in the human respiratory tract. Journal of Aerosol Science. 2012;**48**:18–33. DOI: 10.1016/j.jaerosci.2012.01.005

[7] May J, Favre C, Bosteels D. Emissions

from Euro 3 to Euro 6 light-duty vehicles equipped with a range of emissions control technologies. In: Internal Combustion Engines: Performance, Fuel Economy and Emissions. London: Elsevier; 2013.

[8] Jacobs T, Assanis D, Filipi Z. The Impact of Exhaust Gas Recirculation on

pp. 55–65. DOI: 10.1533/<PHONE_NUMBER>849.2.55

**349**

[6] Brand C. Beyond 'Dieselgate': Implications of unaccounted and future air pollutant emissions and energy use for cars in the United Kingdom. Energy Policy. 2016;**97**:1–12. DOI: 10.1016/j.

enpol.2016.06.036

Reis S, Isaksen ISA, Tarrasón L. Evolution of NOx emissions in Europe with focus on road transport control measures. Atmospheric Chemistry and Physics. 2009;**9**(4):1503–1520. DOI:

10.5194/acp-9-1503-2009

10.4271/2019-01-0314

the General Assembly on 19


**5. Discussion**

The district had an average of two nurses manning each RHC. At any one time therefore one was likely to find just one trained nurse as a result of capacity building sessions and workshops being conducted from time to time on the various ministry programs, and at times the nurse aides were left on their own attending to patients. This was the case when the first cholera case presented to the health facility on the 3rd of May. Fortunately the nurse aide had attended to cholera patients during the 2008/2009 outbreak and quickly raised the alarm with

Chegutu cholera outbreak is one of the most recent cholera outbreaks the country faced. This outbreak had the potential to escalate into a massive outbreak because of the prevailing water and sanitation situation in the town, the easy link between the town and the capital, Harare City, which also had worse water and sanitation situation and being a link between the two major cities of the country, Harare and Bulawayo. However because of the built in resilience anchoring on health worker capacity, availability of extension workers, swiftness of response by RRTs and coordination of response through the Civil Protection Committee at district level and IACCH at national level, the outbreak was controlled in 20 days with 106 cases and 4 deaths reported. It should be noted that the four deaths were the alert which occurred before

On the 16th of January 2018, a report was made to the Chegutu District Medical Office of an increase in diarrhea cases at Chegutu Hospital in a male ward in which two cases had died. A follow up visit was made to the male ward and revealed that there were three male cases presenting with watery diarrhea and vomiting. Two deaths had occurred and a stool specimen had been collected from one of the deceased patients and sent to hospital laboratory for culture. The result was received on the 19th of January 2018 confirming *Vibrio cholerae*. The national office was immediately notified on the 19th of January 2018 who also notified WHO

Subsequent investigations revealed that all cases and deaths were associated with a funeral which had occurred in Pfupajena Township of Chegutu on the 8th of January 2018. A visit made to the given address revealed that the deceased (index case) had reported for treatment suffering from diarrhea and vomiting at a local private clinic before her death on the same day. The daughter to the index case also reported for treatment at Chegutu hospital on the 9th of January 2018 where she was admitted and discharged on the 11th. A stool specimen was

It was further established that there was a funeral which occurred on the 29th of December 2017 in the same neighborhood which was attended by two relatives from Zambia (Zambia was at the time experiencing a cholera outbreak). Among those who attended the funeral were members of a religious group who later visited the index case. It is highly possible that the source of infection could have been from those who came from Zambia who could have

On notification of the national office, the Minister of Health and Child Care immediately visited the area together with members of the National RRT to assess the situation and advise on

the district, resulting in the swift outbreak response that ensued.

*4.3.2. Chegutu cholera outbreak 2018*

56 Current Issues in Global Health

the outbreak was detected.

on the 22nd of January.

been healthy carriers.

collected and the results were negative.

Among the major issues we single out as having been strengthened over the years are the political commitment, multisectoral engagement, capacity to harness resources and coordinate actors, surveillance and RRT and, the health system capacity.

Political commitment is evidenced by the personal involvement of the Minister and other senior MOHCC staff, provincial and district health leadership. The role of political commitment in implementation of health programs is emphasized in literature and indeed effective institutionalization of cholera control measures has been reported in Mexico following the recognition of cholera as a national security problem [27]. The central role of high level political commitment in instituting rapid response measures and mobilization of resources is underscored [27]. Leadership at high level is a necessity for the response if properly managed, but in situations where it is not properly managed [28] it may lead to conflicts among workers in the field thereby delaying the implementation of activities and allowing the prolonged progression of the outbreak. Liberia offers a good example of proper coordination of response with high political leadership during the Ebola outbreak [29]. In the Zimbabwe cholera outbreak of 2008–2009, the failure by the political leadership to accept that a cholera outbreak was brewing led to delays in the response allowing uncontrolled continued infection and the resultant mortality. In years after 2008/2009 outbreak, political leadership has been prominent in all the outbreaks and their control within reasonable time can be explained.

We also note the importance of multisectoral engagement in emergency response and in particular, these reported recent cholera outbreaks. Multisectoral engagement is observed in the name of the cluster system during the cholera outbreak of 2008/2009, the civil protection committees at various levels led by the ministry of local government and the IACCH, all for the purposes of streamlining and coordinating the response. The success of controlling the cholera outbreaks is built upon functional multisectoral engagement. The Global Task Force on Cholera Control's Ending Cholera—A Global roadmap to 2030, recognizes multisectoral engagement as one of the three key axis for cholera control [30]. The key cholera drivers are largely known and most of them are outside the health sector. The tools for prevention and control of cholera outbreaks are also known to work and anchor on improving access to clean water and improving sanitation, improving community awareness and hygiene practices including the hand washing [10–13]. The health sector is mainly responsible for responding to outbreaks in terms of case management and surveillance. The requirement of multisectoral engagement becomes more important realizing the limitations of the health sector in cholera prevention efforts.

country faced [3]. Furthermore, surveillance is a key requirement for epidemic detection and control. Zimbabwe has registered improvement in this area and has built capacity for real time reporting. This has enabled fast detection and response to outbreaks. Capacitation of health workers in IDSR has improved their interpretation and use of data at local level.

Responding to Cholera Outbreaks in Zimbabwe: Building Resilience over Time

http://dx.doi.org/10.5772/intechopen.79794

59

Emergencies and in particular outbreaks of infectious hazards remain a global concern. The IHR (2005) together with other guiding documents on specific themes on emergency preparedness and response remain available to guide countries in building capacities for emergency preparedness and response. The capacity of countries to mount adequate response to control emergencies depend on the resilience of their health systems build upon organizational, community and individual resilience and to a large extent dependent health systems

Zimbabwe having gone through a period of economic difficulties, faced one of its worst ever cholera outbreaks, which resulted in high rates of infection and deaths. This being said the country managed to use this event as a stepping stone which has resulted in the country building resilience to mount adequate response to outbreaks in the recent years. Understandably, resilience is not an all or none event but a process with levels of attributes, and Zimbabwe continues to work towards achieving all resilience attributes. Other countries can learn from

The authors would like to appreciate all who made this work possible, which include but not limited to the Ministry of Health and Child Care, WHO Country office staff, UNICEF, and

This work was conceived by Dr. Juliet Nabyonga-Orem when she was Officer in Charge of WHO Country Office in Zimbabwe having observed with appreciation the country's response

to the cholera outbreak which occurred in Chegutu district starting in January 2018.

institutional capacities as defined by the WHO health systems building blocks.

**6. Conclusion**

Zimbabwe's experience to build resilience.

**Notes/Thanks/Other declarations**

**Acknowledgements**

MSF offices in Zimbabwe.

**Conflict of interest**

None declared.

Over the years Zimbabwe has witnessed rapid response to, and reducing case fatality rates from, cholera. The investments made over the years to strengthen the health system partly explain this phenomenon given the fact that the cholera case fatality rate reflects the access to basic health care [31]. Availability of HRH, strengthened surveillance and improved availability of basic commodities have been realized over the years. The per capita expenditure on health increased from \$9 in 2009 to \$24 in 2015. Regarding retention of health workers, average in-post rate stands at 81% [32]. Indeed the Ebola viral diseases outbreak in West Africa brought to the fore the central role of strengthened health systems in responding to diseases outbreaks [3, 4, 33].

The presence of skilled rapid response teams, especially following the scale up of training following the 2008/2009 cholera outbreaks, as well as the recent training sessions in response to the typhoid outbreaks in Harare, has improved the capacity of health workers to manage epidemics. Health worker capacity for rapid detection and swift control of outbreaks is essential in emergency preparedness and response [34]. RRTs which are multidisciplinary teams ensure this takes place and where they are functional this has led to reduced mortality and shortened period for control [35]. The timing of activation of RRTs is also important for good outcome for delayed activation may also lead to increased mortality.

Correct information is necessary for the communities to take appropriate action to prevent infection or to get immediate assistance when they get infected [36, 37]. The sustained information dissemination through the district structures made the people**'s** perception of risk remain high and to quickly adopt responsible behaviors as advised. Majority of the population anywhere in Zimbabwe still remember and reminisce the events of 2008/2009 which left them devastated and hence are very responsive to behavior change communication messages. Lessons from the field show us that when inadequate information is given it may lead to information gaps allowing unorthodox sources to lead with misinformation resulting in panic or inappropriate actions [3]. On the other hand clear information dissemination on a regular basis from trusted sources has led to communities taking part in the response measures leading to rapid containment of epidemics as reported in Uganda during an EVD outbreak the country faced [3]. Furthermore, surveillance is a key requirement for epidemic detection and control. Zimbabwe has registered improvement in this area and has built capacity for real time reporting. This has enabled fast detection and response to outbreaks. Capacitation of health workers in IDSR has improved their interpretation and use of data at local level.


**Elemental Mercury Exposure and Sleep Disorder**

Alfred Bogomir Kobal1 and Darja Kobal Grum2 *1Department of Occupational Medicine, Idrija Mercury Mine, Idrija, 2Department of Psychology, Faculty of Arts, University of Ljubljana, Ljubljana, Slovenia*


*4.2. Gaze Estimation Algorithm*

In this paper, different solutions are proposed to estimate gaze directions: Template matching-based classifiers, LBP, and the CNN. Although the former alternative yielded a very satisfactory performance (i.e., average accuracy of 95%) for all indoors lighting condition, it failed to preserve this accuracy when images were collected outdoors because of the simplicity of the underlying algorithm. To clarify, this depreciation in performance is not because of the change of illumination, however, it is because of the physical difference of the shape of the eye between indoors and outdoors conditions. Two major changes occur when the user is exposed to direct sunlight: the iris shrinks when exposed to high intensity light and the eyelids tend to close.

One way to tackle this issue is to take distinct templates for the various lighting conditions that can be discerned by a light sensor, and then match the input with the template of the corresponding lighting condition. Conversely, the CNN is inherently complex enough to be able to generalize to all lighting conditions without the need of any additional hardware. Template matching technique was used as an aiding tool to the CNN to achieve better performance.

#### 4.2.1. Collecting Training Dataset for the CNN—Calibration Phase

To make use of the accurate and fast CNNs, a training dataset should be available to train the model. The performance of the CNN is dependent on the selection of the training dataset; if the training dataset is not properly selected, the accuracy of the gaze estimation system dramatically decreases. Thus, a calibration phase is required for any new user of the wheelchair. The output of this calibration phase is the trained CNN model that can be used later for gaze estimation. To prepare a nice training dataset, a template matching technique was used. Template matching does not require any prior knowledge of the dataset. Note that the calibration phase faces two problems: the first problem arises from the fact that the user blinks during the collection of the training data. This leads to a flawed model prediction. The second issue is that the user may not respond immediately to the given instructions, i.e., the user may be asked to gaze right for couple of seconds, but he or she responds one or two seconds later.

Fortunately, template matching, if smartly used, can overcome these two problems, and can be used to make sure that the training dataset is 100% correctly labeled. Moreover, the training dataset should be diverse enough to account for different lighting conditions, and different placement of glasses. The cameras could zoom the user's eyes, thus if the user slightly changes the position of glasses, noticeable differences occur between the images.

Figure 13 shows a flowchart of the calibration phase. For simplicity, illustration is discussed on only one eye; however, the same applies for the second eye. First, to have a wide-ranging dataset, the calibration stage was repeated for different conditions, each condition is named as a Scenario.

For each lighting condition, the user was asked to change the position of glasses (slightly slide the glasses either down or up). Thus, four different scenarios were needed. However, that is not enough to ensure a diverse dataset. Therefore, for each scenario, images were acquired for the four classes in three nonconsecutive attempts to capture all the possible patterns of the user's gaze in a particular direction. Every time, the user, indeed, gazed in a different manner. Thus, the importance of collecting images three times can be seen. Each time, 200 frames were collected (a net of 600 frames per class). These frames (that are contaminated with blinks) constitute a temporary training dataset. As previously mentioned, template matching was used to remove these blinks; a random frame was selected from each class to be used as a template.

**Figure 13.** Flowchart for the calibration phase.

There are numerous scenarios that may happen: the first and most probable scenario is that the user has followed the instructions and the template selection was successful, that is, the template image is not a blinking frame. In such a case, and from the testing on the benchmark dataset, the accuracy of template matching was higher than 80%. This accuracy had been set as the threshold; if this accuracy was attained, this means that the image acquisition was successful. The second possibility was that while running the template-matching algorithm, a low accuracy was returned. The cause of this low accuracy can be wrong acquisition or wrong template selection. Thus, it was better to test first for a wrong template selection; thus, a different template was randomly selected, and the template matching was carried out again. If the accuracy increases to reach the threshold, the issue was with the template; i.e., it might have been an irrelevant blinking image. However, if the low accuracy persists, there is a high probability that the user has gazed in a wrong direction during the image acquisition phase, and therefore the image acquisition was repeated.

With the threshold accuracy obtained, it was certainly known that the template image is correctly selected. The next stage was to clean the 600 images of each class from those blinking frames and to keep 500 useful images for each class. Then, 400 images were randomly selected for training while 100 images tested the trained model. After finishing all the four scenarios, the final training dataset was fed to the CNN to get the trained CNN model. It was worth mentioning that even if this calibration requires few minutes to accomplish, it is required to execute once only.

By having the trained CNN, the system was ready for real-time gaze estimation to steer the wheelchair. Between the real-time gaze estimation and moving the wheelchair, there are two points that should be taken into consideration. The first is the safety of the user; whether there is an obstacle in his/her way. The second point is that the real-time estimation for the right eye may give a different classification from the left eye (because of a wrong classification or because of different gazing at the instance the images are collected).

Figure 14 shows a flowchart for the real-time classification, where these two points are tackled. As discussed earlier, proximity sensors were used to scan the region in the wheelchair way. In the decision-making part, the minicomputer first measured the distance for the closest obstacle. If there was no close obstacle, then the wheelchair moved in the predicted direction. Nevertheless, if there was an object in the danger area (threshold), the wheelchair stopped immediately.

**Figure 14.** Flowchart for real-time classification and controlling the movement of the wheelchair.

If there was no close obstacle, when the real-time classification runs, two classification results are returned, one for each eye. In fact, it is very important to make use of this redundancy of results; otherwise, there is no need of having two cameras. If the two eyes returned the same class, and considering the high classification performance of the CNN, this predicted class was used to move the wheelchair in the determined direction. However, if the two eyes gave different classifications, no action will be taken, as the safety of the user had the priority.


**Multi-Sensor Feature Extraction and Data Fusion Using ANFIS and 2D Wavelet Transform in Structural Health Monitoring**

Ponciano Jorge Escamilla-Ambrosio, Xuefeng Liu, Juan Manuel Ramírez-Cortés, Abraham Rodríguez-Mota and María del Pilar Gómez-Gil

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68147

#### Abstract

**References**

Kingdom. Parts 1 to 11, 2013

pp.6177-6184

1998;**50**:(11): 1-14

2009, pp. 2–4.

[1] EU Commission Database on Number of FPS Drilling in European Waters. October 2010

[3] Lloyds Rules and Regulations for the Classification of a Floating Offshore Installation at a Fixed Location. Published by Lloyd's Register Group Limited, London, United

[4] Floating production system. JIP FPS mooring integrity. Prepared by Noble Denton Europe Limited for the Health and Safety Executive, Norwich, United Kingdom, 2006 [5] International Energy Outlook 2016. Chapter 1. World energy demand and economic outlook. U.S. Energy Information Administration's, DOE/EIA-0484, May 11, 2016

[6] Richard Youngs. Energy Security, Europe's New Foreign Policy Challenge. Taylor &

[7] Farleyefndt M. Guidelines on the overall NDT quality system in Europe. In 17th World

[8] Raj B. Non-Destructive Testing and Evaluation: Overview, Encyclopaedia of Materials: Science and Technology. India: Indira Gandhi Centre for Atomic Research; 2011.

[10] Sanderson, R. M., & Smith, S. D.. The application of finite element modelling to guided wave testing systems. In D. O. Thompson, D. E. Chimenti, C. Nessa, S. Kallsen, & L.

Poore, AIP Conference Proceedings (Vol. 657, No. 1, pp. 256–263). March 2003

[11] Huang, M, et al. Using acoustic emission in fatigue and fracture materials research. JOM.

[12] Catton. Long range ultrasonic guided waves for the quantitative inspection of pipelines. Eng.D. thesis, School of Engineering and Design, Brunel University, London, England,

[9] Larsen and Fylling, SeaTek Corp, Potts, Texas United States. 1982, 1981, 1993.

[2] Applicable to the DnV Standard, International NDT (EN473 or ISO 9712)

108 Structural Health Monitoring - Measurement Methods and Practical Applications

Francis, Abingdon, United Kindom, January 2009 Jan 28, 2009

Conference on Non-destructive Testing, Shanghai, China; 2008

In this chapter, a novel feature extraction and data fusion approach for structural damage detection and localisation is presented. This approach combines adaptive network-based fuzzy inference systems (ANFIS) and two-dimensional wavelet transform (2D-WT) technologies. Simultaneous multi-sensor feature extraction and data fusion based on 2D-WT is carried out by forming a 2D multivariate signal, which is used to analyse the structure vibration response by measuring all sensors jointly. Energy values obtained from two-level db3 wavelet decomposition are arranged in a so-called energy percentage matrix (EPM), which is taken as an input for the ANFIS. The system is further trained by defining its output as the structural condition represented by a condition index. A set of output index patterns are defined depending on the level of damage assessment performed. The proposed method was tested through experiments using a cantilever beam structure. The testing results showed that the method is successful in detecting and localising damage by vibration analysis in structural health monitoring.

Keywords: sensor fusion, structural health monitoring, structural damage, ANFIS, 2D wavelet transform

#### 1. Introduction

Structural health monitoring (SHM) refers to the process of damage detection, localization, quantification, or prediction, in infrastructure associated to fields such as aerospace, civil, or

© 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.

mechanical engineering. In engineering structures, damage is regarded as changes to physical and/or geometric properties of these systems which adversely affect their current or future performance [1, 2]. The interest in the ability to detect and locate structural damage at the earliest possible stage relies on safety issues with a consequence in economic benefits. Damage identification methods can be classified into four levels of damage assessment: level 1 (detection): determination that damage is present in the structure; level 2 (localisation): level 1 plus determination of the geometric location of the damage; level 3 (quantification): level 2 plus quantification of the severity of the damage; and level 4 (prediction): level 3 plus prediction of the remaining service life of the structure [3–5]. A variety of signal processing techniques have been attempted with good results in the field of SHM, such as statistical time series models, Fourier analysis, Wigner-Ville transform, Cohen class, Hilbert-Huang transform and different variations of wavelet analysis [6]. Data interpretation includes approaches such as neural networks, support vector machine, fuzzy and neurofuzzy schemes, Bayesian classifiers, or hybrid classifiers [7–11]. Among these, wavelet techniques (WT) have been proven to be an effective approach for damage detection, based on their characteristics to analyse non-stationary signals in both time and frequency domains. This analytical tool has gained preference in the research community to explore its applicability to perform structural damage assessment. Therefore, a variety of wavelet-based methods for damage detection have been proposed [12–14]. These methods can be broadly classified into three categories [15]: (1) variation of wavelet coefficients, (2) local perturbation of wavelet coefficients in a space domain and (3) reflected wave caused by local damage. The first category is generally used to find the existence and severity of damage. The second category is used to localise the damage in structures. The third category is used to measure the severity as well as the location of damage.

Under the premise that damage (e.g., cracks) in a structure will cause structural response perturbations at damage sites, a number of wavelet-based variants have been reported in the last decade in the field of SHM. In Ref. [16], an algorithm based on the wavelet packet transform and the Karhunen-Loéve transform is used to decompose the signals coming from an accelerometer on a vibrating composite beam. Wavelet packet transform was used as a feature extraction tool in SHM with good results. Integration of the discrete wavelet transform, an autoregressive model, damage-sensitive features, and support vector machine are proposed in Ref. [17] as a novel and efficient framework for damage detection of smart structures. Winkelman et al. [18] reported a novel signal-processing technique based on wavelet thresholding/denoising and Gabor wavelet transform. A damage identification method using unsupervised blind source separation with a wavelet-based pre-processing is presented in Ref. [19]. The authors report that independent component analysis biases to extract sparse components from the observed mixture signals, revealing damage instant and location.

In this chapter, an approach to structural damage detection and localisation (i.e. level 1 and level 2 damage assessments) based on the combination of two-dimensional WT (2D-WT) and adaptive network-based fuzzy inference system (ANFIS) techniques is described. The main novelty of the proposed approach resides in using 2D-WT to simultaneously perform multisensor data fusion and feature extraction for structural damage detection and localisation purposes. In addition, the use of an ANFIS system provides a fuzzy index damage representation for simultaneous identification and location of the damage.

### 2. Background on 2D-WT and ANFIS

#### 2.1. Wavelet transform (WT)

mechanical engineering. In engineering structures, damage is regarded as changes to physical and/or geometric properties of these systems which adversely affect their current or future performance [1, 2]. The interest in the ability to detect and locate structural damage at the earliest possible stage relies on safety issues with a consequence in economic benefits. Damage identification methods can be classified into four levels of damage assessment: level 1 (detection): determination that damage is present in the structure; level 2 (localisation): level 1 plus determination of the geometric location of the damage; level 3 (quantification): level 2 plus quantification of the severity of the damage; and level 4 (prediction): level 3 plus prediction of the remaining service life of the structure [3–5]. A variety of signal processing techniques have been attempted with good results in the field of SHM, such as statistical time series models, Fourier analysis, Wigner-Ville transform, Cohen class, Hilbert-Huang transform and different variations of wavelet analysis [6]. Data interpretation includes approaches such as neural networks, support vector machine, fuzzy and neurofuzzy schemes, Bayesian classifiers, or hybrid classifiers [7–11]. Among these, wavelet techniques (WT) have been proven to be an effective approach for damage detection, based on their characteristics to analyse non-stationary signals in both time and frequency domains. This analytical tool has gained preference in the research community to explore its applicability to perform structural damage assessment. Therefore, a variety of wavelet-based methods for damage detection have been proposed [12–14]. These methods can be broadly classified into three categories [15]: (1) variation of wavelet coefficients, (2) local perturbation of wavelet coefficients in a space domain and (3) reflected wave caused by local damage. The first category is generally used to find the existence and severity of damage. The second category is used to localise the damage in structures. The third category is used to

Under the premise that damage (e.g., cracks) in a structure will cause structural response perturbations at damage sites, a number of wavelet-based variants have been reported in the last decade in the field of SHM. In Ref. [16], an algorithm based on the wavelet packet transform and the Karhunen-Loéve transform is used to decompose the signals coming from an accelerometer on a vibrating composite beam. Wavelet packet transform was used as a feature extraction tool in SHM with good results. Integration of the discrete wavelet transform, an autoregressive model, damage-sensitive features, and support vector machine are proposed in Ref. [17] as a novel and efficient framework for damage detection of smart structures. Winkelman et al. [18] reported a novel signal-processing technique based on wavelet thresholding/denoising and Gabor wavelet transform. A damage identification method using unsupervised blind source separation with a wavelet-based pre-processing is presented in Ref. [19]. The authors report that independent component analysis biases to extract sparse compo-

In this chapter, an approach to structural damage detection and localisation (i.e. level 1 and level 2 damage assessments) based on the combination of two-dimensional WT (2D-WT) and adaptive network-based fuzzy inference system (ANFIS) techniques is described. The main novelty of the proposed approach resides in using 2D-WT to simultaneously perform multisensor data fusion and feature extraction for structural damage detection and localisation purposes. In addition, the use of an ANFIS system provides a fuzzy index damage representa-

nents from the observed mixture signals, revealing damage instant and location.

tion for simultaneous identification and location of the damage.

measure the severity as well as the location of damage.

110 Structural Health Monitoring - Measurement Methods and Practical Applications

In the WT, a signal f(t) is written as a series expansion in terms of wavelet families [20]:

$$\begin{aligned} f(t) &= \sum\_{k=-\varkappa}^{+\varkappa} < f(t), \varphi(t-k) > \varphi(t-k) + \\ &\sum\_{j=-\varkappa}^{-1} \sum\_{k=-\varkappa}^{+\varkappa} < f(t), \psi\_{j,k}(t) > \psi\_{j,k}(t) \end{aligned} \tag{1}$$

where the father wavelet family {ϕðt � kÞ, k ∈Z} is used to describe the smooth part of f(t) and the mother wavelet family {ψj, kðtÞ, j ≥ 0} is used to describe the details of f(t) at different levels. This expansion can expose the information originally hidden in f(t).

An efficient way to implement the WT, and its inverse (IWT), is to use filter banks and downsampling/upsampling techniques. Moreover, the connection of WT with filter banks is a tool to understand the frequency allocation property of WT. Figure 1 shows a two-level discrete wavelet decomposition and reconstruction, which demonstrates the idea of using filter banks to calculate WT and IWT.

The original signal f(t) is broken down into three sub-signals: A2, D1, and D2. From f(t) to A2, D2, and D1, the whole process could be seen as passing f(t) through three filters (see Figure 1b). Each filter has different frequency characteristics and thus a frequency allocation is achieved through wavelet analysis. For example, the spectrum of the three filters associated with a two-level Haar wavelet analysis is shown in Figure 2. Note that the spectrum is plotted over the range [0, 0.5], where 0.5 corresponds to the Nyquist frequency (half of the sampling frequency).

The figure shows that the filter 1 acts as a low pass filter, the filter 2 serves as a band-pass filter and the filter 3 can be taken as a high-pass filter. Hence, by passing through these three filters, the original signal is split into three sub-signals and each sub-signal holds a different frequency content of the original signal f(t): A2 conserves most low-frequency content of f(t), that is why it is called 'approximation'; D1 contains the high-frequency content of f(t), that is why it is called 'detail'; D2 is another detail signal including the information of f(t) which is not contained in A2 and D1. In this case, D2 covers most of the middle-frequency content. These details and approximations at various levels may reveal valuable information of the signal characteristics that may not be clearly seen in the original signal f(t).

#### 2.2. Two-dimensional wavelet transform (2D-WT)

The two-dimensional (2D) wavelet representation is a straightforward generalisation of the onedimensional (1D) wavelet representation. As in 1D, a 2D signal f(x, y) can also be represented in terms of wavelet families. One difference between the 2D-WT in comparison with the 1D version is that all the signals in these wavelet families are 2D signals. In 1D wavelets, the mother wavelet family is generated by a basis wavelet function, i.e. a mother wavelet ψ(t), and the father wavelet

Figure 1. Filtering process of DWT and IDWT. (a) Two-level DWT decomposition and IDWT reconstruction using filter banks and (b) the three filters in (a).

Figure 2. Frequency spectrum of the three filters associated with a two-level Haar wavelet analysis.

family is generated by another basis wavelet function, i.e. a father wavelet ϕ(t). Similarly, in 2D-WT, wavelet families can also be generated from basis 2D wavelet functions [21, 22]. These basis 2D wavelet functions can be constructed by taking the tensor product (denoted as '⊗' in the following equations) of a horizontal basis 1D wavelet function and a vertical basis 1D wavelet function. This leads to four different types of 2D basis wavelet functions:

$$\Phi(\mathbf{x}, y) = \varphi\_{\hbar}(\mathbf{x}) \otimes \varphi\_{v}(y) \quad \text{horizontal father } \otimes \text{ vertical father} \tag{2a}$$

$$\Psi^v(\mathbf{x}, \mathbf{y}) \;= \; \psi\_h(\mathbf{x}) \otimes \varphi\_v(\mathbf{y}) \;= \; \text{horizontal mother} \; \otimes \text{ vertical father} \tag{2b}$$

$$\Psi^\hbar(\mathbf{x}, \mathbf{y}) \, = \, \!\!\! \phi\_\hbar(\mathbf{x}) \otimes \!\!\psi\_v(\mathbf{y}) \, = \text{ horizontal father } \!\!\! \otimes \text{ vertical mother} \, \!\!\/ \text \, \tag{2c}$$

$$\Psi^{\mathfrak{g}}(\mathbf{x},\mathbf{y}) = \psi\_{\mathfrak{h}}(\mathbf{x}) \otimes \psi\_{\mathfrak{v}}(\mathbf{y}) \quad \text{[horizontal mother } \otimes \text{ vertical mother} \text{ }\tag{2d}$$

From Eq. (2a) to (2d), the basis 2D wavelet functions include one father wavelet and three mother wavelets. The corresponding four 2D wavelet families {Φm,nðx, yÞ}, {Ψv j,m,nðx, yÞ, j ≥ 0}, {Ψh j,m,nðx, yÞ, j ≥ 0} and {Ψd j,m,nðx, yÞ, j ≥ 0} are generated by scaling and translating these fourbasis 2D wavelet functions as follows:

$$\Phi\_{m,n}(\mathbf{x}, \mathbf{y}) = \Phi(\mathbf{x} - m, \ y - n) \tag{3a}$$

$$
\Psi\_{j,m,n}^{v}(\mathbf{x},y) = 2^{-j}\Psi^{v}(2^{-j}\mathbf{x} - m, \ 2^{-j}y - n) \tag{3b}
$$

$$\Psi\_{j,m,n}^{\hbar}(\mathbf{x},y) = 2^{-j}\Psi^{\hbar}(2^{-j}\mathbf{x} - m, \ 2^{-j}y - n) \tag{3c}$$

$$\Psi\_{j,m,n}^{d}(\mathbf{x},\mathbf{y}) = 2^{-j}\Psi^{d}(2^{-j}\mathbf{x} - m, \ 2^{-j}\mathbf{y} - n) \tag{3d}$$

As with 1D wavelets, the father wavelet family is good at representing the smooth part and the mother wavelets are good at representing the details of a 2D signal. Hence, in 2D wavelets, the father wavelet family {Φm,nðx, yÞ} is used to describe the smooth part of fðx, yÞ, and three mother wavelet families, {Ψv j,m,nðx, yÞ, j ≥ 0}, {Ψh j,m,nðx, yÞ, j ≥ 0}, and {Ψd j,m,nðx, yÞ, j ≥ 0}, are used to capture the vertical detail, the horizontal detail, and the diagonal detail of f(x, y), respectively.

#### 2.3. Adaptive network-based fuzzy inference system (ANFIS)

The combination of artificial neural networks (ANN) and fuzzy inference systems (FIS) has attracted the interest of researchers in various scientific and engineering areas due to the growing need of adaptive intelligent systems to solve real-world problems. ANNs learn by adjusting the interconnections between layers. FIS is a popular computing framework based on the concept of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. There are several approaches that integrate ANN and FIS, and ANFIS is one of them. ANFIS can be treated as a FIS with a network-like structure or as an ANN containing fuzzy rules. Due to that, by adopting ANFIS in the form of an ANN clearly reveals its training ability, this form of treating ANFIS is explained as follows. For the explanation of ANFIS as a FIS, the interested reader is referred to Ref. [23]. For simplicity, it is assumed that a zero-order Sugeno fuzzy model has been adopted in the ANFIS structure. Hence, the ANFIS under consideration has two inputs x and y and one output z. Each input is assumed to have two fuzzy sets defined as their possible values, from the FIS point of view. Therefore, the ANFIS structure in this case can be seen as the five-layer ANN shown in Figure 3. The output of the i th node in layer j is denoted as Oj i .

The function of each layer is as follows:

family is generated by another basis wavelet function, i.e. a father wavelet ϕ(t). Similarly, in 2D-WT, wavelet families can also be generated from basis 2D wavelet functions [21, 22]. These basis 2D wavelet functions can be constructed by taking the tensor product (denoted as '⊗' in the following equations) of a horizontal basis 1D wavelet function and a vertical basis 1D wavelet

Figure 1. Filtering process of DWT and IDWT.  This leads to four different types of 2D basis wavelet functions:

Figure 2. Frequency spectrum of the three filters associated with a two-level Haar wavelet analysis.

Ψv

banks and (b) the three filters in (a).

112 Structural Health Monitoring - Measurement Methods and Practical Applications

Ψh

Ψd

Layer 1: The function of nodes in the first layer is equivalent to the 'fuzzification' process in a fuzzy system.

$$\mathbf{O}\_i^1 = \mu\_{A\_i}(\mathbf{x}), \text{ for } i = 1, 2 \tag{4a}$$

$$O\_i^1 = \mu\_{\mathbb{B}\_{i-2}}(y), \text{for } i = \mathbf{3}, \mathbf{4} \tag{4b}$$

Figure 3. ANFIS architecture for a two-input Sugeno fuzzy model with four rules (from ANN point of view).

where μAi and μBi�2 are the activation functions or membership functions (MF) defining the fuzzy sets for the inputs x and y, respectively.

Layer 2: Every node in this layer generates an output which is the product of all the incoming signals to that node. This process is equivalent to applying an 'AND' operator in the counterpart fuzzy system.

$$\mathbf{O}\_i^2 = \mathbf{O}\_1^1 \mathbf{O}\_{i+2}^1 \text{ for } i = 1, 2 \tag{5a}$$

$$\mathbf{O}\_i^2 = \mathbf{O}\_2^1 \mathbf{O}\_{i'}^1 \text{ for } i = \mathbf{3, 4} \tag{5b}$$

The output of this layer O2 i is the wi, i th firing strength, in the fuzzy system.

Layer 3: The i th node in this layer calculates the ratio between the output of the i th node in the previous layer and the sum of the outputs of all nodes in that layer:

$$O\_i^3 = \frac{O\_i^2}{\sum\_{j=1}^4 O\_i^2} \tag{6}$$

The step in the counterpart fuzzy system is the normalisation of firing strengths.

Layer 4: Every node in this layer has a function of O4 i ¼ diO3 i , which applies the normalised firing strength (O3 i ) to the corresponding consequent parameter (di). The function of this layer corresponds to applying the implication method from a FIS point of view.

Layer 5: For the current ANFIS, there is only one node in this output layer. The node computes the overall ANFIS output through the summation of all incoming signals:

Multi-Sensor Feature Extraction and Data Fusion Using ANFIS and 2D Wavelet Transform in Structural Health… http://dx.doi.org/10.5772/intechopen.68147 115

$$O^5 = \sum\_{i=1}^4 O\_i^4 \tag{7}$$

The function of this node combines the steps of aggregation and defuzzification from the FIS point of view. Therefore, given a training set (input and output data pairs), ANFIS adjusts its parameters using well-developed learning algorithms. The parameters to be estimated in ANFIS are the premise parameters which define the membership functions in Layer 1, and the consequent parameters in Layer 4. ANFIS uses a hybrid-learning algorithm to estimate these parameters: a back-propagation learning algorithm is used to determine the premise parameters and least mean square estimation is adopted to determine the consequent parameters [23].

#### 3. Multi-sensor data fusion and feature extraction using 2D-WT

where μAi and μBi�2 are the activation functions or membership functions (MF) defining the

Figure 3. ANFIS architecture for a two-input Sugeno fuzzy model with four rules (from ANN point of view).

Layer 2: Every node in this layer generates an output which is the product of all the incoming signals to that node. This process is equivalent to applying an 'AND' operator in the counter-

th node in this layer calculates the ratio between the output of the i

j¼1 O2 i

Layer 5: For the current ANFIS, there is only one node in this output layer. The node computes

O3 i ¼ O2 i X 4

The step in the counterpart fuzzy system is the normalisation of firing strengths.

corresponds to applying the implication method from a FIS point of view.

the overall ANFIS output through the summation of all incoming signals:

th firing strength, in the fuzzy system.

i ¼ diO3

i ) to the corresponding consequent parameter (di). The function of this layer

iþ2, for i ¼ 1, 2 ð5aÞ

i , for i ¼ 3, 4 ð5bÞ

th node in the

i , which applies the normalised

ð6Þ

O2 i ¼ O1 1O1

O2 i ¼ O1 2O1

i is the wi, i

Layer 4: Every node in this layer has a function of O4

previous layer and the sum of the outputs of all nodes in that layer:

fuzzy sets for the inputs x and y, respectively.

114 Structural Health Monitoring - Measurement Methods and Practical Applications

part fuzzy system.

Layer 3: The i

firing strength (O3

The output of this layer O2

The most common, as well as the most successful, application of 2D-WT is image compression. For instance, 2D-WT-based compression algorithms for transmitting and storing digitised fingerprints have been widely studied and used in the last decade [24, 25]. However, not much literature can be found of using the 2D-WT in structural health monitoring. In most applications, a set of many sensors are placed along different sections of a structure to measure its vibration response, accordingly the information from all the sensors needs to be integrated in some meaningful way. In this section, a novel method of using 2D-WT to carry out damage detection and localisation tasks is introduced. The 2D-WT provides an efficient and natural way to simultaneously extract features and integrate the information of many sensors, which makes the structural damage identification reliable and efficient.

The main idea of using the 2D-WT as a feature extraction and sensor data fusion mechanism is as follows: the structural response measured by one sensor i is a vector denoted as:

$$f\_i(t) = \begin{bmatrix} f\_i(t\_1) & f\_i(t\_2) & \dots & f\_i(t\_n) \end{bmatrix}^T \tag{8}$$

where n denotes the sampling number. Without losing any generality, it is assumed that l sensors (from sensor 1 to sensor l) are used to measure the vibration response of the structure under consideration. Thus, there are l measurement response vectors {f 1ðtÞ, f 2ðtÞ … f l ðtÞ}. If these vectors are concatenated along rows and the result denoted as F, it gives:

$$F = \begin{bmatrix} f\_1(t) & f\_2(t) & \dots & f\_l(t) \end{bmatrix} \tag{9}$$

with F being an n-by-l matrix, which can be seen as an image, a 2D signal. A certain column of this image represents n vibration response samples measured by a sensor at some particular point of the structure, and a certain row of this image represents the vibration response samples measured by each sensor at l different location points of the structure at a particular sample time. The image F includes the information provided by all of the sensors throughout the measurement experiment duration and therefore gives a whole picture describing the dynamic behaviour of the structure under study. Therefore, if 2D-WT is applied to image F, then its important features are revealed. A feature vector can be formulated in the following way: at the L-level 2D-WT, the original 2D signal (image) F is decomposed into 1 + 3L sub-2D signals (images): i.e. A1, Dv 1, Dh 1, Dd 1, for a level 1 2D-WT decomposition.

The ratio of energy content of the 1 + 3L sub-signals in F is then defined as:

$$V = \begin{bmatrix} \frac{\varepsilon\_1}{\varepsilon\_f}, \frac{\varepsilon\_2}{\varepsilon\_f}, \dots, \frac{\varepsilon\_{1+3L}}{\varepsilon\_f} \end{bmatrix} \tag{10}$$

By arranging the 2D signal as a 1D signal, the terms ε1,ε2, …ε1+3L in Eq. (10) are calculated using:

$$\varepsilon\_{\pi} \stackrel{def}{=} \sum\_{n=1}^{N} |\mathfrak{x}\_{n}|^{2} \tag{11}$$

which determines the energy of a discrete signal x ¼ ½x1, x2,…,xN� T. The ε1,ε2, …,ε1+3L terms represent the energy content in the sub-signals obtained from the 2D-WT. The term εf is the energy content in the original signal F. Each one of the components of V represents the energy percentage content of each of the 1 + 3L sub-signals in F. Therefore, a feature vector can be formed selecting some p components of V, which in turns would mean choosing some of the sub-2D signals as significant sub-signals contributing large energy percentages in F. The selection can be based on the following two criteria:

Although the two criteria above can be used, in this study, for convenience, we only choose the significant sub-signals, the ones with higher energy percentage content values, to form the feature vector.

Having chosen the energy percentage vector as the feature, the procedures for damage identification depend on the availability of the a-priori data. In an 'unsupervised learning mode', where data are only available from the undamaged structure, damage identification methods are based on feature comparison: two features, one extracted from the system in undamaged condition and the other from the current system, are compared in some way to obtain the damage indicator. The damage indicator is then compared to some threshold value and the conclusion about if the structure has deviated from the reference condition is obtained. On the other hand, in a 'supervised learning mode', where data from a system in different structural conditions (including the undamaged and some damaged conditions) are known in advance, the damage identification techniques are based on pattern classification: a database including models of the structure in different conditions is established using feature vectors for the apriori data sets. Given a new data set which is to be classified as one of the conditions of the system, the task is to search through the database for the model which gives the best fit to the data. The corresponding condition of this database model is then applied to the data.

#### 4. Structural damage detection combining 2D-WT and ANFIS

F, then its important features are revealed. A feature vector can be formulated in the following way: at the L-level 2D-WT, the original 2D signal (image) F is decomposed into 1 + 3L sub-2D

1, for a level 1 2D-WT decomposition.

:::: ε1þ3L εf

ð10Þ

2 ð11Þ

T. The ε1,ε2, …,ε1+3L terms

� �

By arranging the 2D signal as a 1D signal, the terms ε1,ε2, …ε1+3L in Eq. (10) are calculated

n¼1 jxnj

represent the energy content in the sub-signals obtained from the 2D-WT. The term εf is the energy content in the original signal F. Each one of the components of V represents the energy percentage content of each of the 1 + 3L sub-signals in F. Therefore, a feature vector can be formed selecting some p components of V, which in turns would mean choosing some of the sub-2D signals as significant sub-signals contributing large energy percentages in F. The

1. The sub-signals selected should be significant sub-signals contributing large energy percentages in F. The reason for this criterion lies in the fact that the insignificant sub-signals generated by WT are normally contributing to noise and should be removed. Empirically, it is assumed that a sub-signal is significant if its ratio of energy contribution to the

2. The sub-signals selected should be sensitive to the damage. Damage usually has different effects on different frequency bands. For example, the effect of a crack on a beam is only noticeable within a high frequency band. Hence different sub-signals have different sensitivities to damage. By selecting the sub-signals sensitive to the damage, it is guaranteed that the damage could be effectively captured. The sensitivity analysis can be derived either by finite element modal analysis of the structure (analytical method) or by prior

Although the two criteria above can be used, in this study, for convenience, we only choose the significant sub-signals, the ones with higher energy percentage content values, to form the

Having chosen the energy percentage vector as the feature, the procedures for damage identification depend on the availability of the a-priori data. In an 'unsupervised learning mode', where data are only available from the undamaged structure, damage identification methods are based on feature comparison: two features, one extracted from the system in undamaged condition and the other from the current system, are compared in some way to obtain the

εx¼ defX N

signals (images): i.e. A1, Dv

using:

1, Dh 1, Dd

116 Structural Health Monitoring - Measurement Methods and Practical Applications

The ratio of energy content of the 1 + 3L sub-signals in F is then defined as:

which determines the energy of a discrete signal x ¼ ½x1, x2,…,xN�

selection can be based on the following two criteria:

original signal is no less than 3%.

experiments (experimental method).

feature vector.

V ¼ ε1 εf , ε2 εf

> In this section, a detailed description on how to use the proposed ANFIS-2D-WT feature extraction method in structural damage identification is presented. As described before, the measurements of all the sensors are processed at the same time. Firstly, the measurements from all the l sensors in each test are arranged as a matrix and seen as a 2D signal (image), as it was explained in Section 3. Therefore, let us assume that the number of all possible conditions for the system is r + 1 (one healthy condition denoted as D0 and r damaged conditions D1 : Dr). It is assumed also, that for each condition, and considering all the sensors, a total of N images, or 2D data measurements are available. This results altogether in ðr þ 1Þ · N image data sets that can be arranged as a data matrix:

$$\text{Data Matrix } 2D = \begin{bmatrix} \langle a^{D\_0 - 1} \rangle\_\prime & \langle a^{D\_0 - 2} \rangle\_\prime & \dots & \langle a^{D\_0 - N} \rangle\_\prime \\ \langle a^{D\_1 - 1} \rangle\_\prime & \langle a^{D\_1 - 2} \rangle\_\prime & \dots & \langle a^{D\_1 - N} \rangle\_\prime \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \langle a^{D\_r - 1} \rangle\_\prime & \langle a^{D\_r - 2} \rangle\_\prime & \dots & \langle a^{D\_r - N} \rangle\_\prime \end{bmatrix} \tag{12}$$

where the 2D signals {αDj\_i }(i ¼ 1…N, j ¼ 0…r) correspond to output measurement data images from the i th test at condition Dj (2D signals, considered as images) from all the sensors. Each row of the matrix contains all the available image data sets for a certain condition.

Then, select a typical measurement 2D signal (or image) {α} in the data matrix and perform 2D-WT analysis on it. The original 2D signal {α} is decomposed into a number of sub-2D signals and the energy percentage contribution of each sub-2D signal into the original 2D signal is calculated. Based on the calculated energy percentages, p sub-signals are selected and the corresponding energy percentage feature vector is formulated. The energy percentages of the selected sub-signals are the inputs to the ANFIS model. Therefore, the number of input variables to the ANFIS is p. Three linguistic values characterised using linguistic terms as 'small', 'medium' and 'large' are defined for each of the p input variables. The type of these MFs for these linguistic values is 'bell-shape' and is defined by:

$$\mu\_s(\mathbf{x}) = \frac{1}{1 + |\frac{\mathbf{x} - \mathbf{c}\_i}{a\_i}|^{2b\_i}} \tag{13}$$

Note that the linguistic values such as 'small', 'medium' or 'large' have different meanings for different input variables. There is only one output variable defined in the ANFIS: the structural health condition. For convenience, it is normally represented by a condition index. A zeroorder Sugeno fuzzy model has been adopted in the ANFIS structure, which means that singleton values are defined for the output variable and the type of the corresponding MF is a distinct constant. So far, only the architecture of the ANFIS model has been determined: it contains p inputs (corresponding to p energy percentages) and one output (condition index). Each input variable has 'small', 'medium' and 'large' linguistic values characterized by three bell-shape MFs. The number of ANFIS rules is determined by the combination of linguistic values for the input variables. For p input variables, each with three linguistic values, the number of resultant combinations is 3p . Correspondingly, the number of rules is 3p . For example, assume that only two sub-signals are selected (p = 2). The two input variables and one output variable are denoted respectively as x1, x2 and z. For each input variable, three linguistic values denoted as {Mx1 1 , Mx1 2 , Mx1 3 } (for x1) and {Mx2 1 , Mx2 2 , Mx2 3 } (for x2) are defined. Therefore, a total of nine rules are contained in the ANFIS model:

Rule 1: If x1 is Mx1 1 and x2 is Mx2 1 , then z is d1

Rule 2: If x1 is Mx1 1 and x2 is Mx2 2 , then z is d2

Rule 3: If x1 is Mx1 1 and x2 is Mx2 3 , then z is d3

Rule 4: If x1 is Mx1 2 and x2 is Mx2 1 , then z is d4

…….

Rule 9: If x1 is Mx1 3 and x2 is Mx2 3 , then z is d9

Once the ANFIS architecture and rules are determined, it is necessary to prepare data sets for training use. For each available output data {yDj\_i } (i ¼ 1…N, j ¼ 0…r) in the data matrix, perform the same 2D-WT analysis and the same p sub-signals are selected to form the feature vector. Their energy percentages are arranged as a vector denoted as PerDj\_i. This procedure is applied to all the data set in Eq. (12), and a matrix referred to as energy percentage matrix (EPM) is obtained:

$$EPM(WPT) = \begin{bmatrix} \{Per^{D\_{0}}1\} & \{Per^{D\_{0}}2\} & \dots & \{Per^{D\_{0}}N\} \\ \{Per^{D\_{1}}\} & \{Per^{D\_{1}}2\} & \dots & \{Per^{D\_{1}}N\} \\ \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot \\ \{Per^{D\_{r}}\} \\_ & \{Per^{D\_{r}}2\} & \dots & \{Per^{D\_{r}}N\} \end{bmatrix} \tag{14}$$

The vector {PerDj\_i }, containing p elements, is taken as an input vector for the ANFIS. EPM Matrix contains a total of ðr þ 1Þ · N such input vectors for ANFIS. They are used as training data for ANFIS. The current ANFIS use a supervised learning algorithm, which means that the target output for each input vector is needed. It has been mentioned earlier that the ANFIS output is the structural condition represented by a condition index. Depending on the level of damage assessment conducted, different output index patterns are adopted. If the ANFIS is used only to identify damage occurrence (level 1 damage assessment), the output indices are Boolean values (0 for healthy condition D0, 1 to r for damaged cases D1eDr). In this situation, the EPM data matrix can be appended to contain a total of ðr þ 1Þ · N input and desired output data pairs:

Multi-Sensor Feature Extraction and Data Fusion Using ANFIS and 2D Wavelet Transform in Structural Health… http://dx.doi.org/10.5772/intechopen.68147 119

$$\text{Data Matrix}(\text{Level }1) = \begin{bmatrix} \langle \text{Per}^{D\_{0},1}, 0 \rangle, & \langle \text{Per}^{D\_{0},2}, 0 \rangle, & \dots & \langle \text{Per}^{D\_{0},N}, 0 \rangle\\ \langle \text{Per}^{D\_{1},1}, 1 \rangle, & \langle \text{Per}^{D\_{1},2}, 1 \rangle, & \dots & \langle \text{Per}^{D\_{1},N}, 1 \rangle\\ \cdot & \cdot & \cdot & \cdot\\ \cdot & \cdot & \cdot & \cdot\\ \langle \text{Per}^{D\_{r},1}, 1 \rangle, & \langle \text{Per}^{D\_{r},2}, 1 \rangle, & \dots & \langle \text{Per}^{D\_{r},N}, 1 \rangle \end{bmatrix} \tag{15}$$

If the ANFIS is used for the damage localisation (level 2 damage assessment), a total of r + 1 condition indices each corresponding to a structural condition need to be defined. Defining j as the index for condition Dj , the data matrix containing the input and desired output data pairs is:

Note that the linguistic values such as 'small', 'medium' or 'large' have different meanings for different input variables. There is only one output variable defined in the ANFIS: the structural health condition. For convenience, it is normally represented by a condition index. A zeroorder Sugeno fuzzy model has been adopted in the ANFIS structure, which means that singleton values are defined for the output variable and the type of the corresponding MF is a distinct constant. So far, only the architecture of the ANFIS model has been determined: it contains p inputs (corresponding to p energy percentages) and one output (condition index). Each input variable has 'small', 'medium' and 'large' linguistic values characterized by three bell-shape MFs. The number of ANFIS rules is determined by the combination of linguistic values for the input variables. For p input variables, each with three linguistic values, the

example, assume that only two sub-signals are selected (p = 2). The two input variables and one output variable are denoted respectively as x1, x2 and z. For each input variable, three

Once the ANFIS architecture and rules are determined, it is necessary to prepare data sets for

the same 2D-WT analysis and the same p sub-signals are selected to form the feature vector. Their energy percentages are arranged as a vector denoted as PerDj\_i. This procedure is applied to all the data set in Eq. (12), and a matrix referred to as energy percentage matrix (EPM) is obtained:

contains a total of ðr þ 1Þ · N such input vectors for ANFIS. They are used as training data for ANFIS. The current ANFIS use a supervised learning algorithm, which means that the target output for each input vector is needed. It has been mentioned earlier that the ANFIS output is the structural condition represented by a condition index. Depending on the level of damage assessment conducted, different output index patterns are adopted. If the ANFIS is used only to identify damage occurrence (level 1 damage assessment), the output indices are Boolean values (0 for healthy condition D0, 1 to r for damaged cases D1eDr). In this situation, the EPM data matrix can be appended to contain a total of ðr þ 1Þ · N input and desired output data pairs:

{PerD0\_1}, {PerD0\_2}, … {PerD0\_N} {PerD1\_1}, {PerD1\_2}, … {PerD1\_N}

{PerDr\_1}, {PerDr\_2}, … {PerDr\_N}

}, containing p elements, is taken as an input vector for the ANFIS. EPM Matrix

: : : :

: :

3 } (for x1) and {Mx2

1 , Mx1

1 , then z is d1

2 , then z is d2

3 , then z is d3

1 , then z is d4

3 , then z is d9

: :

Therefore, a total of nine rules are contained in the ANFIS model:

118 Structural Health Monitoring - Measurement Methods and Practical Applications

2 , Mx1

. Correspondingly, the number of rules is 3p

1 , Mx2

2 , Mx2

} (i ¼ 1…N, j ¼ 0…r) in the data matrix, perform

. For

ð14Þ

3 } (for x2) are defined.

number of resultant combinations is 3p

1 and x2 is Mx2

1 and x2 is Mx2

1 and x2 is Mx2

2 and x2 is Mx2

3 and x2 is Mx2

training use. For each available output data {yDj\_i

EPMðWPTÞ ¼

linguistic values denoted as {Mx1

Rule 1: If x1 is Mx1

Rule 2: If x1 is Mx1

Rule 3: If x1 is Mx1

Rule 4: If x1 is Mx1

Rule 9: If x1 is Mx1

The vector {PerDj\_i

…….

$$\text{Data Matrix}(\text{Level } 2) = \begin{bmatrix} \langle \text{Per}^{D\_0 - 1}, \, 0 \rangle, & \langle \text{Per}^{D\_0 - 2}, \, 0 \rangle, & \dots & \langle \text{Per}^{D\_0 - N}, \, 0 \rangle \\\langle \text{Per}^{D\_1 - 1}, \, 1 \rangle, & \langle \text{Per}^{D\_1 - 2}, \, 1 \rangle, & \dots & \langle \text{Per}^{D\_1 - N}, \, 1 \rangle \\\ . & . & . & . & . \\\ . & . & . & . & . \\\ \langle \text{Per}^{D\_r - 1}, \, r \rangle, & \langle \text{Per}^{D\_r - 2}, \, r \rangle, & \dots & \langle \text{Per}^{D\_r - N}, \, r \rangle \end{bmatrix} \tag{16}$$

Data matrices Level 1 and Level 2 (Eqs. (15) and (16)) are used, respectively, for training ANFIS with two different levels of damage assessment.

The next step is ANFIS training. The number of the premise parameters to be determined is 3 · 3 · p. This comes from the fact that for each of the p input variables, three MFs, each defined by three premise parameters, were established. The number of the consequent parameters to be determined is 3p . The ANFIS architecture uses a hybrid learning algorithm [23] to estimate these 9p þ 3p premise parameters all together with the consequent parameters.

Usually, in the implementation of a structural health monitoring system, a large number of sensors on the structure under analysis are strategically placed to provide an early indication of damage. The problem then is the processing of the signals collected from all the sensors. This problem is approached in this work by using the 2D-WT to process all the information provided by the sensors at once. This is possible by integrating all the signals into a matrix that can be considered as a 2D image. In this way the information provided by each sensor individually is taken into account, preserved and fused with the information from the other sensors.

ANFIS is used for the purpose of structural damage identification. However, there are various levels of damage assessments. Two ANFIS models, ANFIS1 and ANFIS2 are established accordingly. ANFIS1 is used to identify damage occurrence (level 1 damage assessment) while ANFIS2 is used for damage localisation (level 2 damage assessment). The architecture of these two ANFIS models is the same, but they produce different output values. ANFIS1 is only used to distinguish healthy and damaged conditions; therefore the output is a Boolean value (0 for healthy, 1 for damaged). The output of ANFIS2 is designed to differentiate all the possible conditions, which is performed by defining a numerical value j (j = 0 to 5), where j corresponds to damage condition Dj.

#### 5. Experimental setup with a cantilever beam

For the sake of repeatability and insight, cantilevered beam experiment settings have been used by several researchers to demonstrate the feasibility of their proposed approaches to damage detection and localisation using a plethora of techniques, examples include Refs. [26–28]. Furthermore, several aerospace and civil structures such as rotor blades and bridges could be modelled as cantilever beams. Therefore, in this section the results of an experimental study involving shaker-excited vibration tests of an aluminium cantilever beam carried out in the laboratory are presented. The beam is 90 cm length and crosssection 2.545 · 0.647 cm. Zero-mean band-limited (0–500 Hz) Gaussian white noise was used as the input signal to the amplifier. The amplifier gain was controlled manually and the shaker provided an approximately 10 N peak, via a random force input to the beam. A force gauge screwed on the bottom surface of the beam was used to directly measure the input. The shaker was attached with this force transducer through a stinger. Figure 4 shows the experimental setup.

Six accelerometers (7 g each) were screwed to the top surface along the centreline at selected positions (15, 30, 45, 60, 75, and 90 cm from the left fixed point, respectively). The data from each test came from these six accelerometers and one force transducer. The data were collected at a sampling rate of 10 kHz for a duration of 4 seconds. Five damage scenarios (D1 to D5) were simulated by adding a lumped mass (22 g) at 30, 45, 60, 75, and 90 cm, respectively (see Figure 4). A summary of the experimental damage conditions is provided in Table 1.

Figure 4. Cantilever beam experiment; setup schematic representation.

Table 1. Summary of damage case D1–D5: adding a lumped mass at different locations.

#### 6. Results

damage detection and localisation using a plethora of techniques, examples include Refs. [26–28]. Furthermore, several aerospace and civil structures such as rotor blades and bridges could be modelled as cantilever beams. Therefore, in this section the results of an experimental study involving shaker-excited vibration tests of an aluminium cantilever beam carried out in the laboratory are presented. The beam is 90 cm length and crosssection 2.545 · 0.647 cm. Zero-mean band-limited (0–500 Hz) Gaussian white noise was used as the input signal to the amplifier. The amplifier gain was controlled manually and the shaker provided an approximately 10 N peak, via a random force input to the beam. A force gauge screwed on the bottom surface of the beam was used to directly measure the input. The shaker was attached with this force transducer through a stinger. Figure 4

120 Structural Health Monitoring - Measurement Methods and Practical Applications

Six accelerometers (7 g each) were screwed to the top surface along the centreline at selected positions (15, 30, 45, 60, 75, and 90 cm from the left fixed point, respectively). The data from each test came from these six accelerometers and one force transducer. The data were collected at a sampling rate of 10 kHz for a duration of 4 seconds. Five damage scenarios (D1 to D5) were simulated by adding a lumped mass (22 g) at 30, 45, 60, 75, and 90 cm, respectively (see Figure 4). A summary of the experimental damage conditions is provided

shows the experimental setup.

Figure 4. Cantilever beam experiment; setup schematic representation.

Damage case Location of damage Damage description

Table 1. Summary of damage case D1–D5: adding a lumped mass at different locations.

D1 0.30 m Adding a lumped mass of 0.022 kg D2 0.45 m Adding a lumped mass of 0.022 kg D3 0.60 m Adding a lumped mass of 0.022 kg D4 0.75 m Adding a lumped mass of 0.022 kg D5 0.90 m Adding a lumped mass of 0.022 kg

in Table 1.

The experiment was repeatedly carried out under each of the six possible conditions of the system. The system response data and the corresponding condition were recorded during the test. From each condition, 20 test data are used, within which the first 10 are for the training use and the remaining 10 are for the testing use. Therefore, altogether there are 60 training data sets and 60 test data sets available. Thus, ANFIS is used for the purpose of structural damage identification. However, there are various levels of damage assessments. Two ANFIS models, ANFIS1 and ANFIS2 are established accordingly. ANFIS1 is used to identify damage occurrence (level 1 damage assessment) while ANFIS2 is used for damage localisation (level 2 damage assessment). The architecture of these two ANFIS models is the same, but they produce different output values. ANFIS1 is only used to distinguish healthy and damaged conditions; therefore the output is a Boolean value (0 for healthy, 1 for damaged). The output of ANFIS2 is designed to differentiate all the possible conditions, which is performed by defining a numerical value j (j = 0–5), where j corresponds to damage condition Dj .

As previously described, in the proposed ANFIS-2D-WT method the measurements from all six sensors in each test are arranged as a matrix. The two-level db3 2D-WT is performed on this matrix. From the obtained seven sub-signals, three are selected and their energy percentages are taken as inputs for ANFIS. Note that only one ANFIS1 model is needed for level 1 damage assessment and one ANFIS2 model is required for level 2 damage assessment. Each of these two ANFIS models includes the information of all six sensors. The mapping between the three inputs and one output of the trained ANFIS1 using ANFIS-2DWT method is shown in Figure 5. While Figure 6 shows the results when applying the trained ANFIS1 to the testing data. In this figure, Exp means expected values, and Act means actual values. The testing error of ANFIS1 is 2.7567e-5. For the level 2 damage assessment, ANFIS-2D-WT also performs well. Figure 7 shows the mapping relationship of the ANFIS2 model. The testing result of the trained ANFIS2 model is shown in Figure 8. We can see that the testing error of the ANFIS2 model is 0.0021.

The effect of noise is an influencing factor always present in the vibration response signals of structures. Therefore, to study the effect of noise on the proposed ANFIS-2D-WT method, random Gaussian white noise is added to the response of these 120 test cases. The noise intensity is defined by the signal-to-noise ratio (SNR):

$$SNR(dB) = 20 \log\_{10} \frac{A\_{\text{signal}}}{A\_{\text{noise}}} \tag{17}$$

where Asignaland Anoise refer to the root mean square (rms) amplitude of signal and noise, respectively. Figures 9–11 show the testing results of ANFIS1 (level 1 damage assessment) with SNR = 20, 10, 5, respectively. The ratios of the RMS values between the noise and the signal for these three cases are 10, 31.6 and 56.2%, respectively. As can be seen in the figures, by using the ANFIS-2D-WT method, the damage can be correctly detected when SNR is no smaller than 10 dB.

Figures 12–14 show the testing results of ANFIS2 (level 2 damage assessment) at these noise levels. It can be seen that ANFIS2 can locate damage even when SNR = 10 dB. These

Figure 5. Output surface between ANFIS output and inputs: (a) input 3 is fixed to be 50.387 and (b) input 1 is fixed to be 20.5281 (ANFIS1, ANFIS-2D-WT method, using ALL six sensors).

Figure 6. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, using all six sensors).

Multi-Sensor Feature Extraction and Data Fusion Using ANFIS and 2D Wavelet Transform in Structural Health… http://dx.doi.org/10.5772/intechopen.68147 123

Figure 7. Output surface between ANFIS output and inputs: (a) input 3 is fixed to be 50.387 and (b) input 1 is fixed to be 20.5281 (ANFIS2, ANFIS-2D-WT method, using all six sensors).

Figure 5. Output surface between ANFIS output and inputs: (a) input 3 is fixed to be 50.387 and (b) input 1 is fixed to be

Figure 6. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, using all six sensors).

20.5281 (ANFIS1, ANFIS-2D-WT method, using ALL six sensors).

122 Structural Health Monitoring - Measurement Methods and Practical Applications

Figure 8. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, using all six sensors).

Figure 9. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, SNR = 20).

Figure 10. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, SNR = 10).

Multi-Sensor Feature Extraction and Data Fusion Using ANFIS and 2D Wavelet Transform in Structural Health… http://dx.doi.org/10.5772/intechopen.68147 125

Figure 11. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, SNR = 5).

Figure 9. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, SNR = 20).

124 Structural Health Monitoring - Measurement Methods and Practical Applications

Figure 10. Testing results and the corresponding error curves (ANFIS1, ANFIS-2D-WT method, SNR = 10).

Figure 12. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, SNR = 20).

Figure 13. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, SNR = 10).

Figure 14. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, SNR = 5).

results suggest that measurement of noise does not seem to affect much of the proposed method for these two levels of damage assessment. This property can be attributed to the wavelet transform: the effect of noise can be alleviated by choosing sub-signals less affected by noise.

### 7. Conclusions

In this chapter, the ANFIS and 2D-WT technologies were combined to perform structural damage identification. The structure vibration response is decomposed by 2D-WT into a number of sub-signals, from which some are selected based on their energy percentages. The energy percentages of the selected signals are taken as inputs to the ANFIS model. The output of the ANFIS is a condition index, which can be a Boolean value (0 or 1) for level 1 damage assessment use, or a number of values for level 2 damage assessment use. Provided an ANFIS model is welltrained by the available data, it can be used for health monitoring and damage localisation. The proposed feature extraction method was applied to the data from a cantilever beam for damage detection and localisation. The testing results showed that the proposed method is successful in performing the two described levels of damage assessment. In addition, the ANFIS-2D-WT can process efficiently information from many sensors at the same time, performing simultaneously multi-sensor feature extraction and data fusion. The proposed damage assessment methodology of combining ANFIS with wavelet transform has great potential to implement systems which are able to interrogate sensor measurements autonomously for indications of structural damage.

#### Author details

results suggest that measurement of noise does not seem to affect much of the proposed method for these two levels of damage assessment. This property can be attributed to the

Figure 14. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, SNR = 5).

Figure 13. Testing results and the corresponding error curves (ANFIS2, ANFIS-2D-WT method, SNR = 10).

126 Structural Health Monitoring - Measurement Methods and Practical Applications

Ponciano Jorge Escamilla-Ambrosio1 \*, Xuefeng Liu2 , Juan Manuel Ramírez-Cortés3 , Abraham Rodríguez-Mota4 and María del Pilar Gómez-Gil5

\*Address all correspondence to<EMAIL_ADDRESS>
1 Instituto Politécnico Nacional, Centro de Investigación en Computación, México, Ciudad de México, Mexico

2 Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

3 Department of Electronics, National Institute for Astrophysics Optics and Electronics, Tonantzintla, Puebla, Mexico

4 Instituto Politécnico Nacional, Escuela Superior de Ingeniería Mecánica y Eléctrica Unidad Zacatenco, Ciudad de México, Mexico

5 Department of Computer Science, National Institute for Astrophysics Optics and Electronics, Tonantzintla, Puebla, Mexico

#### References

[15] Kim H, Melhem H. Damage detection of structures by wavelet analysis. Engineering Structures. 2004;26:347-362

References

2006.

[1] Farrar CR, Worden K. Structural Health Monitoring: A Machine Learning Perspective,

[2] Balageas D, Fritzen CP, Güemes A. Structural Health Monitoring. London: ISTE Ltd;

[3] Srinivasan G, Massimo R, Sathyanaraya H. Computational Techniques for Structural

[4] Sohn H, Farrar CR, Hemez FM, Shunk DD, Stinemates DW, Nadler BR. A review of structural health monitoring literature: 1996–2001, Los Alamos National Laboratory,

[5] Santos JP, Cremona C, Orcesi AD, Silveira P. Multivariate statistical analysis for early

[6] Goyal D, Pabla BS. The vibration monitoring methods and signal processing techniques for structural health monitoring: A review. Archives of Computational Methods in Engi-

[7] Amezquita-Sanchez JP, Adeli H. Signal processing techniques for vibration-based health monitoring of smart structures. Archives of Computational Methods in Engineering.

[8] Aminpour H, Foad N, Baghalian S. Applying artificial neural network and wavelet analysis for multiple cracks identification in beams. International Journal of Vehicle Noise

[9] Wei F, Qiao P. Vibration-based damage identification methods: A review and compara-

[10] Ganguli R. Fuzzy cognitive maps for structural damage detection. Fuzzy Cognitive Maps for Applied Sciences and Engineering, Berlin, Heidelberg: Springer; 2014. pp. 267-290 [11] Arangio S, Bontempi F. Structural health monitoring of a cable-stayed bridge with Bayesian neural networks. Structure and Infrastructure Engineering, 2015;11(4):575-587 [12] Katunin A. Modal-based non-destructive damage assessment in composite structures using wavelet analysis: A review. International Journal of Composite Materials. 2013;3

[13] He WY, Songye Z. Progressive damage detection based on multi-scale wavelet finite element model: Numerical study. Computers & Structures. 2013;125:177-186

[14] Vafaei M, Alih SC, Baharuddin A, Rahman A, Adnan AB. A wavelet-based technique for damage quantification via mode shape decomposition. Structure and Infrastructure Engi-

West Sussex, UK: John Wiley and Sons; 2013.

128 Structural Health Monitoring - Measurement Methods and Practical Applications

Health Monitoring. London: Springer-Verlag; 2011.

damage detection. Engineering Structures. 2013;56:273–285

tive study. Structural Health Monitoring. 2011;10(1):83-111

Report LA-13976-MS, 2003.

neering. 2016;23(4):585–594.

and Vibration. 2012;8(1):51-59

neering. 2014;11(7):869-883

2016;23(1):1–15.

(6):1-9