(2) Local Extremum of Correlation Coefficient Method

The local extremum of the correlation coefficient method was proposed to improve the variable selection strategy of correlation analysis to solve multicollinearity between the adjacent wavelength variables: the correlation coefficient of spectral reflectance and chlorophyll content were calculated, and the correlation coefficient curve was drawn. Thereafter, the local extreme points of the correlation curve (the zero-crossing positions of the correlation first-derivative curve) were calculated as the chlorophyll characteristic wavelengths [46]. The maximum correlation wavelengths were also selected on the basis of the maximum correlation coefficient method for comparative analysis.

#### 2.5.2. Continuous Wavelet Analysis

From the perspective of signal processing, wavelet analysis can be used to perform data analysis in the frequency and time domains and extract available information from the signal [47]. The reflection spectrum analysis is highly similar to electronic signal analysis. Accordingly, CWT can be used to decompose the reflection spectrum curve at different frequency scales to generate a series of wavelet energy coefficients. The CWT process is shown in Equation (8).

$$\mathcal{W}\_f(a,b) = \frac{1}{\sqrt{a}} f(\lambda) \psi(\frac{\lambda - b}{a}) d\lambda,\tag{8}$$

where *a* is the frequency scale factor which is set to 2*n* (*n* = 1, 2, ... , 10) gradients, and translation factor *b* is the center wavelength of the mother wavelet function. The mother wavelet function ψ(λ) uses the second-order Gaussian function. *f*(*x*) is a 1D reflection spectrum, and the wavelet coefficient *Wf*(*a*,*b*) (denoted as *WFa,b*) is 2D data, including frequency scale (1, 2, ... , 10) and wavelength (325–1075 nm).

Correlation analysis of the wavelet energy coefficient and chlorophyll content was performed. The local extreme value of the correlation was calculated as the sensitive wavelet feature. The wavelet coefficient with the highest correlation was selected for comparative analysis.

The extreme point was calculated using the peak function in MATLAB software. The parameters of the peaks' function were set as follows: the correlation extreme value peak distance of the spectral reflectance was set to 10, and the minimum peak value was set to 0.1; the correlation extreme value peak distance of the wavelet coefficient was set to 50, and the minimum peak value was set to 0.3.


*3.2.7. Wear/friction*

obtained depending on the several test parameters. Details of the test method can be reached

Corrosion is known to be influenced by a variety of factors. It is not possible to separate corrosion from many of the other property issues related to coatings. For the proper selection of a coating, it is necessary to take its position, with respect to its substrate in the galvanic series for the intended application, into consideration [27]. Decorative nickel-chromium coatings developed for automotive industry applications are a suitable example of the application of

There are several examples of electro codepositited composite coatings for corrosion protection [28-30]. According to these results, it is supported that corrosion resistance of composite coatings increase significantly with respect to the pure metallic or alloy coatings [15, 21]. This phenomenon is suggested to be the effect of the inert properties of the reinforcements.

For the Ni-Co alloy matrix SiC reinforced composite coatings, Bahkit & Akbari [21] expressed the corrosion behaviour of these coatings through potentiodynamic polarization curves (Figure 7). Calculated corrosion current densities and measured corrosion potentials are

materials science and electrochemistry for the corrosion protection of materials.

**Figure 7.** The potentiodynamic polarization curves of alloy coating and composite coatings

**βa (mV/dec)**

**Table 1.** Calculated and measured corrosion data for alloy and composite coatings

**βc (mV/dec)**

Ni-Co -346 177.26 120.9 -354 6.570 4.75 Microcomposite -277 71.94 162.1 -257 0.137 158.48 Nanocomposite -201 71.18 176.5 -199 0.050 439.46

**Ecorr (mV)**

**icorr (μA.cm−2)**

**Rp (kΩ.cm2)**

from ASTM-C1624 standard [26].

70 Electrodeposition of Composite Materials

*3.2.6. Corrosion*

summerized in Table 1.

**Coating Eocp**

**(mV)**

To give some examples for the practical wear applications of coatings, one can count chromi‐ um, electroless nickel, precious metals, anodized aluminium and so on [31]. But for engineering applications pure metallic coatings, or the conventional coatings mentioned are not enough to satisfy. Based on this idea, researchers have been focussed on recent advancements include codeposition of dispersed particles with metals. There are two alternatives to improve the wear resistance of a composite coating. The first method is to use hard particles in the metal matrix so as to increase the strenght of the surface against to the other frictive part. The second way includes creating the composite structure by using self lubricant reinforcements such as graphite, MoS2, h-BN and WS2 [16, 32-34].

Due to their specific study [9], as a function of graphite particle content in the electrolyte, reduction in the hardness is appeared but decrease in the wear loss (Figure 8a). It can be expressed by the self lubricant property of graphite. Furthermore, the phenomenon of composite friction/wear for Ni-Al2O3/graphite composite structure are described in Figure 8b as shown.

**Figure 8.** Wear loss versus graphite content in the electrolyte (a) and the schematic illustration of composite friction/ wear phenomenon [9]

Friction coefficient and wear loss of composites initially decrease and then increase slowly back with the graphite particle concentration in the electrolyte. The results show an optimum graphite concentration in the electrolyte as 1.5g/L. Under this condition, the lowest friction coefficient, relatively high microhardness, and less wear loss was obtained.

### *3.2.8. Residual stress*

Stress in coatings also adversely affects properties. Nowadays, a variety of options are available for stress reduction of coatings. These include: choice of substrate plating solution, use of additives, and higher plating temperatures. A number of theories have been assumed regarding the origins of stress, however, none of them covers every single situation. Several methods for stress measurement vary from the simple rigid strip technique to complicated methods. Both phase transformations in the composite and additional post-treatment of the coatings can decrease residual stress value in a composite coating [12].


Despite all those discoveries, there are still many obstacles that hinder the application of mode controlling in practical industrial applications. For example, the most favored condition in practical applications is that the discharge mode needs to switch to SP1 mode right after asymmetric discharges occur, which was not achieved in previous studies. In addition, the existing method needs to compute the initial moment of the flat-top stage, which is inconvenient for practical devices. Note that the frequency of the applied voltage can also influence the distribution of seed electrons as the amplitude of the voltage does, and changing the frequency of the power supply is much easier to implement for practical power supply devices. Therefore, in this paper, we try to use a more practical method to switch AP1 discharge into SP1 discharge by changing the driving frequency. More specifically, we first adjust the original driving frequency *f* d to a different controlling frequency *f* c for a certain period of time, right after the establishment of AP1 discharge. Once the discharge stabilizes under *f* c, the driving frequency will be changed back to the initial value (i.e., *f* d). The rest of this paper is organized as follows: Section 2 briefly introduces the one-dimensional fluid model and its qualitative validation; the numerical regulating example and its underneath mechanism are shown in Section 3; the key conclusions are drawn in Section 4; Appendix A presents the chemical scheme used in our simulation.

#### **2. Model Description**

As shown in Figure 1, the atmospheric DBD considered in the simulation is generated in a gap filled with pure helium between two parallel-plate electrodes, both covered by a thin dielectric layer with a relative permittivity of 7.5, corresponding to the value of mica glass. The upper electrode is connected to a sinusoidal voltage with an amplitude *V*am of 2 kV, whereas the lower one is grounded. The width of the gas gap *d*g is fixed to 4.4 mm and the dielectric layer thickness *d*b is 1 mm. Note that the gap width is not very large (<5 mm) and much shorter compared with the radius of electrodes (≈56.4 mm) [20]; in this case, the radially homogeneous assumption should be reasonable and accepted. On this basis, a one-dimensional fluid model is appropriate to simulate the discharge process, which has also been successfully applied to investigate the nonlinear phenomena in [6,21,22].

In the 1-D fluid model, electron properties, including the electron density and energy density, are governed by the Boltzmann equation under drift-diffusion approximation [23–25], as given by Equations (1)–(4); Equations (5) and (6) are multi-component transport equations [26,27] determining the flux of heavy species. Besides, in order to determine the electric field distribution, Poisson's equation is firmly coupled.

$$
\frac{
\partial \mathbf{u\_e}
}{
\partial t
} + \nabla \cdot \Gamma\_\mathbf{e} = \mathbf{S\_e} \tag{1}
$$

$$
\frac{
\partial n\_{\varepsilon}
}{
\partial t
} + \nabla \cdot \Gamma\_{\varepsilon} + E\Gamma\_{\varepsilon} = \mathcal{S}\_{\text{en}} \tag{2}
$$

$$
\Gamma\_{\rm e} = -\mu\_{\rm e} n\_{\rm e} \mathbf{E} - D\_{\rm e} \nabla \cdot n\_{\rm e} \tag{3}
$$

$$
\Gamma\_{\varepsilon} = -\frac{5}{3} \mu\_{\text{e}} n\_{\varepsilon} E - \frac{5}{3} D\_{\text{e}} \nabla \cdot n\_{\varepsilon} \tag{4}
$$

$$
\rho \frac{\partial \omega\_k}{\partial t} = \nabla \cdot \mathbf{J}\_k + \mathbf{S}\_k \tag{5}
$$

$$J\_k = \rho \omega\_k (D\_k \frac{\nabla \omega\_k}{\omega\_k} + D\_k \frac{\nabla M\_\text{H}}{M\_n} - z\_k \mu\_k \mathbf{E}) \tag{6}$$

Here, *n*e, *n*ε, Γe, and Γε respectively denote the electron number density, electron energy, total electron flux, and electron energy flux; *Jk* is the flux vector for heavy species *k*, and its mass fraction and charge number are ω*k* and *zk*, respectively; *S*e, *S*en, and *Sk* respectively represent the source terms describing the net changing rate of electron density, electron energy loss/gain, and the source term for heavy species *k*; the electron mobility μe is solved by Bolsig+ with the cross-section data from IST-Lisbon Database [28–30], then the electron diffusion coefficient *D*e can be obtained through Einstein's relation [29]; the mobility and diffusion coefficient for heavy species *k*, i.e., μ*k* and *Dk*, are referenced from [25]; *E* is the electric field intensity; the mixture properties ρ and *M*n stand for the density of mixture and its mean molar mass.

**Figure 1.** Schematic of the model geometry. ε denotes the relative permittivity of the dielectric layer; *d*b and *d*g represent the widths of the dielectric layer and gas gap, respectively.

The "wall" boundary applied at the surfaces sandwiched between plasma and dielectrics provides two sets of equations, describing the particle flux (Equations (7)–(9)) and the charge accumulation (Equations (10) and (11)), respectively.

$$\mathbf{n} \cdot \Gamma\_{\mathbf{e}} = \frac{1}{2} \upsilon\_{\mathbf{e}, \mathbf{th}} \boldsymbol{\mu}\_{\mathbf{e}} - \alpha\_{\mathbf{s}} \boldsymbol{\mu}\_{\mathbf{e}} \boldsymbol{\mu}\_{\mathbf{e}} \boldsymbol{E} \cdot \mathbf{n} - \sum\_{i} \boldsymbol{\gamma}\_{i} (\Gamma\_{i} \cdot \mathbf{n}) \tag{7}$$

$$\mathbf{n} \cdot \Gamma\_{\varepsilon} = \frac{5}{6} \upsilon\_{\text{e,th}} \mu\_{\varepsilon} - \alpha\_{\text{s}} \mu\_{\varepsilon} \mu\_{\varepsilon} E \cdot \mathbf{n} - \sum\_{i} \nu\_{i} \overline{\varepsilon\_{i}} (\Gamma\_{i} \cdot \mathbf{n}) \tag{8}$$

$$\mathbf{n} \cdot \mathbf{r}\_k = M\_k \mathbf{R}\_{\text{surf},k} + \alpha\_5 M\_k \mathbf{c}\_k \mu\_{k,m} \mathbf{z}\_k \mathbf{E} \cdot \mathbf{n} \tag{9}$$

$$\frac{\mathbf{d}\sigma\_{\mathbf{s}}}{\mathbf{d}t} = f\_{\mathbf{e}} \cdot \mathbf{n} + f\_{\mathbf{i}} \cdot \mathbf{n} \tag{10}$$

$$
\sigma\_{\\$} = (\mathbf{D}\_2 - \mathbf{D}\_1) \cdot \mathbf{n} \tag{11}
$$

Here, **n** is the unit normal vector towards the surface; both Γ*k* and Γ*i* stand for the boundary flux of heavy species but the latter only denotes the term for ions; *v*e,th is the thermal velocity; *Mk* represents the molar weight; *R*surf,*k* is the surface reaction rate; γ*i* is the emission coefficient of the secondary electron cited from [25] and ε*i* is its mean energy; σs represents the surface charge density on the wall, and *J*e and *J*i respectively denote the electron density and the ion density there; *D*1 and *D*2 are the electric displacement vectors on both sides of the interface; αs is a switching function as given below.

$$\alpha\_{\mathbf{s}} = \begin{cases} 1, \text{sgn}(q)E \cdot \mathbf{n} > 0 \\ 0, \text{sgn}(q)E \cdot \mathbf{n} \le 0 \end{cases} \tag{12}$$

Here, *q* represents the signed charge.

For chemical kinetics, we reused ones from our previous work [19]. To be specific, the model sustains itself under the pressure of 760 Torr and temperature of 300 K, and it considers six particles (i.e., e (electron), He, He\*, He2\*, He+ and He2 +) and 27 reactions which are listed in Table A1 in the Appendix A. The initial densities of e, He+, and He2 + were set to 1 × 1013 m−3, 5 × 1012 m−3, and 5 × 1012 m−3, respectively, to ensure the initial neutral condition. The whole calculating domains were discretized through finite element method (log formulation, linear shape function), and a direct solver PARDISO of COMSOL software was employed to solve the above equations. Besides, we have taken a numerical test in terms of the initial densities and concluded that such values did not significantly influence the results in the steady state but affected the calculation time. Based on the above, a qualitative validation compared with the experimental results presented by Mangolini et al. [28] is further given, as shown in Figure 2.

**Figure 2.** Comparison between (**a**) and (**c**) previous experimental waveforms and (**b**) and (**d**) their corresponding simulation results obtained from our model under mostly the same conditions. *J*, *V*a, and *V*g respectively denote the total discharge current density, applied voltage, and gap voltage. The experiment was assumed to have 100 ppm nitrogen impurities, whereas our simulation considers the pure helium. The main external parameters in (**a**) and (**b**) are: *V*am = 1776 V, *f* = 10 kHz, *d*g = 5 mm, *d*b = 1 mm; in (**c**) and (**d**) are: *V*am = 1813 V, *f* = 10 kHz, *d*g = 5 mm, *d*b = 1.5 mm.

Obviously, although the discharge current phase in the experiment was slightly ahead of that in our model, and the current pulse magnitude shows a difference between the experiment and simulation, the sketches of the total discharge current density (*J*) and gap voltage (*V*g) waveforms predicted by our model principally match well with those observed in the experiment. Note that such a discrepancy in the current waveform might be contributed to the Penning ionization induced by the nitrogen impurities; that is, the extra Penning ionization causes a higher seed electron level which boosts the breakdown though this causes extinguishment more quickly. Therefore, our model is qualified to study the discharge characteristics in the homogeneous He DBD under atmospheric pressure.

#### **3. Examples and Mechanisms of the Discharge Mode Control**

#### *3.1. SP1, AP1P, and AP1N*

Before discussing the specific examples of manipulating the discharge symmetry, it is necessary to first clarify the three period-one discharge modes, i.e., SP1 discharge, asymmetric period-one discharge with a higher positive current pulse (denoted as AP1P hereinafter), and asymmetric period-one discharge with a higher negative current pulse (denoted as AP1N hereinafter), as shown in Figure 3, where the waveforms of total discharge current density under different driving frequencies are given, as well as the corresponding spatiotemporal distributions of electron density.

**Figure 3.** Waveforms of the total discharge current density (**a**–**c**) and the corresponding spatiotemporal distributions of electron density (**d**–**f**) under different driving frequencies. The voltage amplitude *V*am, gap width *d*g, and dielectric thickness *d*b are fixed at 2 kV, 4.4 mm, and 1 mm, respectively.

Figure 3a shows a typical SP1 discharge where the cycles of the discharge current and the applied voltage are equal, and the shape of the discharge current in positive and negative half-cycles are also identical. Figure 3b presents an AP1P discharge whose current cycle is the same as that of the applied voltage, but the peak value of the positive current pulse is 15 times as large as that of the negative one. Contrary to AP1P, the peak value of the negative current pulse exceeds the positive current amplitude in AP1N mode, as shown in Figure 3c. Moreover, Figure 3d–f illustrate the corresponding spatiotemporal distributions of electron density in SP1, AP1P, and AP1N mode, respectively, in order to explain the reasons for the formation of three discharge modes. From Figure 3d, one can see that, before the initiation of each discharge, the residual electrons generated by the last discharge have decayed to a relatively low level. Therefore, the subsequent discharge can develop to a strong one, whose intensity is the same as that of the last discharge. Under this circumstance, the SP1 discharge mode is maintained. Figure 3e illustrates the influence of the massive residual electrons on the discharge performance in AP1P mode. With a strong positive current pulse, a large number of electrons are generated within the discharge phase. Thus, there are still a lot of electrons left in the gas gap prior to the negative discharge, which serves as the seed electrons of the subsequent negative discharge. Since a high seed electron density leads to a relatively low breakdown voltage [29], the subsequent negative discharge will start earlier, and a weak multi-pulse feature will be observed. As a result,

AP1P discharge ensues. The generation process of AP1N discharge is similar to AP1P, and the only difference lies in the polarity of the strong current pulse, as shown in Figure 3f.

#### *3.2. Numerical Regulating Example and the Underlying Mechanism*

Under the source parameters and initial values described in Section 2, the discharge under *f* d of 14 kHz will finally stabilize in the AP1P mode after about 10 applied voltage cycles, as shown in Figure 4a. Starting from the 15th cycle, we change *f* d to a different frequency for 20 cycles, and then adjust the frequency back to 14 kHz at the 35th cycle. The results indicate that the final stabilized discharge mode depends on *f* c to some extent. Figure 4b shows that when *f* c is set to 8 kHz, the discharge mode at the frequency-altered stage is SP1. However, after this stage, the discharge mode evolves back to AP1P; when *f* c is set to 20 kHz, the discharge mode of the control section and the section after the 35th cycles are both AP1N, as shown in Figure 4c; when *f* c increases to 30 kHz, an AP1P discharge is observed at the frequency-altered stage, but the discharge mode after the 35th cycle evolves into SP1, as shown in Figure 4d. Note that, when *f* c rises beyond 30 kHz (the largest *f* c considered in our simulation is 100 kHz), the initial AP1P discharge under 14 kHz can always be adjusted to SP1.

**Figure 4.** Temporal profiles of current density when the controlling frequency *f* c is set to be (**a**) 14 kHz, (**b**) 8 kHz, (**c**) 20 kHz and (**d**) 30 kHz respectively.

At first sight, the discharge mode of the controlling section, as illustrated in Figure 4, is not directly relevant to that of the after-controlling section. To gain a deeper insight into how the frequency impacts the discharge mode, the evolution of the seed electron level has been extracted as a function of the breakdown number, as further given in Figure 5. Combined with two such figures, one can observe that, before the first breakdown of the controlling section, although the seed electron maintains at the same level (the first red circle in Figure 5), the discharge intensity and residual electron density of the subsequent breakdown show an obvious difference. This phenomenon may be qualitatively related to the equivalent gap resistance. Since the lower driving frequency causes lower angular frequency but higher equivalent gap resistance, the discharge intensity of the first breakdown in the controlling section is relatively weak when *f* c is lower than *f* d (14 kHz). On this basis, when *f* c is set to a lower value like 8 kHz, the discharge in the controlling section develops from a relatively lower seed electron density and provides sufficient dissipative time for the residual electrons before the next breakdown, leading to an SP1 mode. The opposite leading to AP1 mode can be inferred by analogy.

**Figure 5.** Evolution of the seed electron level as a function of the breakdown number, i.e., the average electron density right at the beginning moment of each breakdown. The *f* c in (**a**–**c**) are 8 kHz, 20 kHz, 30 kHz, respectively. The red circles indicate the transition points of the driving frequency.

Through 20 controlling cycles, the driving frequency is adjusted back to 14 kHz. Theoretically speaking, the period of controlling section is not fixed, and the criteria considered here is to choose one relatively long period of time that ensures the discharge in the controlling section to achieve the steady state. As can be observed in Figure 5a,b, both low and high seed electron levels (the second red circle) will trigger the AP1 mode in the after-controlling section. In this case, one can understand that, in order to generate an SP1 discharge, the seed electron must retain a moderate level. Figure 6 presents the space–average seed electron relationship and the peak current density under the driving frequency of 14 kHz. In particular, the seed electron density in Figure 6a indicates the value before the breakdown, whereas the one in Figure 6b represents the residual value after the breakdown and dissipative stage. Obviously, if the seed electron density maintains at a low level at the beginning of a discharge (<2 × 1013 m−3), then the discharge intensity of the subsequent discharge will be strong (>1.23 mA/cm2). Correspondingly, the residual electron density after the breakdown, as further depicted in Figure 7a, can not be dissipated completely and exceeds 1 × 1017 m−3 (Figure 6b). Such a high initial value of electron density can only ignite an unmatured discharge, forming an AP1 mode. Analogously, if the seed electron density reaches a high level at the beginning of discharge (>8 × 1015 m−3), then the subsequent discharge cannot develop to a mature one and will form several weak current pulses with the maximum density being less than 0.2 mA/cm2, as shown in Figures 6a and 7b.

**Figure 6.** The relationship between the average electron density and discharge current density. (**a**) average electron density at the starting moment of the discharge vs. current density at the instant of current peak, (**b**) current density at the instant of current peak vs. maximum average electron density.

**Figure 7.** Spatiotemporal distribution of log10 (*n*e) during the 33, 34, 35, 36 and 37 applied voltage cycle when *f* c is set to be (**a**) 8 kHz, (**b**) 20 kHz, (**c**)30 kHz. The black dashed lines divide off different applied voltage cycles.

Based on the above analyses, the seed electron density for pursuing SP1 mode should be approximately limited in the range from 2 × 1013 to 8 × 1015 m−3 under our simulation conditions. Ignited by an appropriate seed electron level, the intensity of the subsequent discharge should be moderate so that the residual electrons can be dissipated completely, as shown in Figure 7c, leading to the SP1 mode. It should be pointed out that, being a control method of seed electron density, the higher driving frequency is able to limit the dissipative process of discharge. Therefore, the cooperation between seed electron level and dissipative time will lead to a less intense AP1 mode when *f* c is beyond 30 kHz, as can be seen from the current waveform and seed electron evolution illustrated by Figures 4 and 5. We have carried out a parameterized sweep in terms of *f* c from 30 to 100 kHz, and the results show that, within this range of frequency, such a less intense AP1 discharge can impose a restriction on the drastic variation of the seed electron density and finally, the initial density of electrons before the breakdown varies within the abovementioned range (from 2 × 1013 to 8 × 1015 m−3). That is to say,

increasing the driving frequency would be a practical strategy to manipulate the discharge symmetry and some more in-depth investigations would be carried out in our future study.

#### **4. Conclusions**

In this paper, we put forward a practical method for controlling the discharge symmetry of atmospheric homogeneous dielectric barrier discharges by adjusting the driving frequency. Through a qualitatively validated 1D fluid model, the discharge evolution, manipulating process, and underlying mechanism are presented. Some important conclusions are drawn as follows:

**Author Contributions:** Conceptualization, L.L. (Ling Luo); Funding acquisition, D.D.; Methodology, Q.W. and Y.Z.; Project administration, D.D.; Supervision, L.L. (Licheng Li); Writing—original draft, L.L. (Ling Luo); Writing—review & editing, Q.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the National Natural Science Foundation of China (Grant No. 51877086).

**Conflicts of Interest:** The authors declared no conflict of interest.

#### **Appendix A**

**Table A1.** Chemical reactions considered in the model.

**Table A1.** *Cont*.

Note: *T*e denotes the electron temperature in eV. He∗ represents He(23 S) and He(21 S). He∗ 2 represents He2(a3Σ+ u ). *n*e is the electron density in m-3. The unit of reaction rate coefficient for two body reactions and three body reactions are m3/s and m6/s, respectively. *f*(*T*e) indicates the rate coefficient as function of the electron mean temperature calculated by Bolsig+ [30], and the cross-section data from IST-Lisbon database [36] was used as the input parameter of the calculation.

#### **References**

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**6.5 Example of robot route optimization under limitations on risk of "failure" in conditions of uncertainties**

Applicability of the proposed probabilistic methods and models is demonstrated to improve some of the existing capabilities of rescue robot for route optimization. This subsection contains an explanation on how problem 2 may be cognitively solved. Similar problems of specific robot route optimization from point A (Start) to point F (Finish) can arise on water, under water (**Figure 15**), in burning wood (**Figure 16**), in the conditions of a city or in mountains (**Figure 17**), and in other situations in conditions of uncertainties. Specific cases of uncertainties can be connected additionally with complex conditions of environment and necessity of robotics orientation, localization, and mapping that influences on input for the proposed probabilistic models.

Here, we demonstrate the proposed approach by a simplified example of moving a special rescue robot from point A to the final point F of the route (from where the SOS signals from tourists are following). It is required to optimize the route of the robot in space under uncertainty of weather, complex snow conditions in mountains to achieve the goal in 2 h with an acceptable risk of failure less than 0.1 (i.e., a probability of success should be more than 0.9). Interaction with the drone-

*A system view on situation for robot route from point A (Start) to point F (Finish) in mountains.*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems*

The applications to cognitive solving the problem of robot route optimization

**Step 1**. The complete set of route variants to achieve the goal within about 2 h: first route is ABCF, second route AGKF, third route if AHLDEF, and fourth variant is a combination of routes 1–3. Points A, B, C, G, K, H, L, D, E, F mean that they may change the route (including return to the previous point). Respectively, it may be a refinement of the further route at these points. Robot speed allows to overcome

For each variant, a set of system compared by modeling is defined: there are ABCF, AGKF, AHLDEF, and possible combinations. Inputs characterizing every part of route for each of the variants are formed by K-base and gathered data from

• Frequencies of the occurrences of potential threats are for route ABCF σ = 1 time at 10 h, AGKF σ = 1.5 times at 10 h, AHLDEF σ = 2 times at 10 h (since

• Time between the end of diagnostics and the beginning of the next diagnostics

• Recovery time of robot availability = 10 min (for modified model [42–44])

informant is supposed, see **Figure 17**.

*DOI: http://dx.doi.org/10.5772/intechopen.89168*

are demonstrated by the next steps.

8.00 a.m. to 8.00 p.m.)

• Mean activation time of threats Tactiv = 30 min

• Diagnostics time of robot availability Tdiag = 30 s

of robot availability Tbetw. = 2 min

• Given prognostic period Tgiven =2h

any route in time.

**Figure 17.**

drone-informant:

**27**

#### **Figure 15.**

*A system view on situation for robot route from point A (Start) to point F (Finish) on water and under water.*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems DOI: http://dx.doi.org/10.5772/intechopen.89168*

#### **Figure 17.**

4.Analyzed project of AISs operation effectiveness (that transform all system components to the level which is proper to medium-level workers of floating

**6.5 Example of robot route optimization under limitations on risk of "failure"**

Applicability of the proposed probabilistic methods and models is demonstrated to improve some of the existing capabilities of rescue robot for route optimization. This subsection contains an explanation on how problem 2 may be cognitively solved. Similar problems of specific robot route optimization from point A (Start) to point F (Finish) can arise on water, under water (**Figure 15**), in burning wood (**Figure 16**), in the conditions of a city or in mountains (**Figure 17**), and in other situations in conditions of uncertainties. Specific cases of uncertainties can be connected additionally with complex conditions of environment and necessity of robotics orientation, localization, and mapping that influences on input for the

*A system view on situation for robot route from point A (Start) to point F (Finish) on water and under water.*

*A system view on situation for robot route from point A (Start) to point F (Finish) in burning wood.*

oil and gas platform) can be added to K-base history as precedent.

**in conditions of uncertainties**

*Probability, Combinatorics and Control*

proposed probabilistic models.

**Figure 15.**

**Figure 16.**

**26**

*A system view on situation for robot route from point A (Start) to point F (Finish) in mountains.*

Here, we demonstrate the proposed approach by a simplified example of moving a special rescue robot from point A to the final point F of the route (from where the SOS signals from tourists are following). It is required to optimize the route of the robot in space under uncertainty of weather, complex snow conditions in mountains to achieve the goal in 2 h with an acceptable risk of failure less than 0.1 (i.e., a probability of success should be more than 0.9). Interaction with the droneinformant is supposed, see **Figure 17**.

The applications to cognitive solving the problem of robot route optimization are demonstrated by the next steps.

**Step 1**. The complete set of route variants to achieve the goal within about 2 h: first route is ABCF, second route AGKF, third route if AHLDEF, and fourth variant is a combination of routes 1–3. Points A, B, C, G, K, H, L, D, E, F mean that they may change the route (including return to the previous point). Respectively, it may be a refinement of the further route at these points. Robot speed allows to overcome any route in time.

For each variant, a set of system compared by modeling is defined: there are ABCF, AGKF, AHLDEF, and possible combinations. Inputs characterizing every part of route for each of the variants are formed by K-base and gathered data from drone-informant:

i = 1.

**Step 2** (i = 1). Using probabilistic model, a calculation of the probability of failure is carried out for each variant. From the set of variants ABCF, AGKF, and AHLDEF, the shorter variant ABCF for which risk is equal to 0.034 is chosen (for the route AGKF risk = 0.051, for route AHLDEF risk = 0.067), see **Figure 18**. The relevant data from the drone about the forecasted conditions and the weather on the part CF to 8.30 a.m. are taken into account.

**Step 4**. After overcoming the part GHLDEF, the robot arrived at the intended

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems*

Thus, the way ABCBGHLDEF is the result of optimization. The robot purpose was achieved owing to preventive measures which were defined by using risk

1.The input (used for modeling) characterizes possible complex conditions for rescue robot route optimization under limitations on risk of "failure" in conditions of uncertainties. In particular, the information updates every 2 min for robot route optimization under limitations on risk of "failure" less than 0.1

2.The acceptable risk 0.1 is justified; the predicted risks for all variants of the

The proposed approach to build and implement the probabilistic methods and

• The problem of planning the possibilities of functions performance on the base

• The problem of robot route optimization under limitations on risk of "failure"

There is proposed to carry out probabilistic prediction of critical processes in time so that not only to act according to the prediction, but also to compare pre-

The described analytical solutions are demonstrated by practical examples

Forming input for probabilistic modeling from monitored data

A cognitive solving of the chosen problems consists in improvements,

System planning the possibilities of functions performance in space by using robot-manipulators, by AIS for a coal company and for a floating oil and gas

Robot route optimization under limitations on risk of "failure" in conditions of

According to the proof of formula (1): because between diagnostics system is not protected from threats an influence (a loss of integrity) will take place only after danger occurrence and activation during given time before the next diagnostic (**Figure 6**). A risk to lose integrity (i.e., probability of "failure") is equal to

3.Analyzed project can be added to K-base history as precedent.

models is demonstrated by application to cognitive solving:

of monitored information about events and conditions

dictions against their coincidence to the subsequent realities.

accumulation, analysis, and use of appearing knowledge.

New knowledge for accumulating and improving K-base is as follows:

control on the way (with probability of "success" more than 0.9).

is admissible for considered situation.

routes did not exceed 0.1.

in conditions of uncertainties

**7. Conclusion**

such as:

platform

**Appendix**

**29**

uncertainties

Proofs for formulas (1)–(3)

point F of route in time.

*DOI: http://dx.doi.org/10.5772/intechopen.89168*

**Step 3** (i = 1). The robot overcomes the part AB of route. For the new initial point B, the input for modeling every part of possible route is updated in real time for routes BCF, BGKF, and BGHLDEF.

**Step 4** (i = 1). The robot has not yet arrived at the intended point F (i.e., the last part of the route is not overcome).

i = i + 1 = 2.

**Step 2** (i = 2 for variants BCF, BGKF, and BGHLDEF). Input for modeling is not changed. Risks are the same. From the route variants BCF, BGKF, and BGHLDEF, the shorter one BCF (with minimal risk) is chosen.

**Step 3** (i = 2 for variant BCDEF). The robot overcomes the part BC. For the new initial point C, the input for modeling every part of possible route is updated in real time: bad weather on the CF part does not allow further movement. And weather improvements in the next 2 h are not expected. Part CF is impassable. The comeback to the initial point B of the part is being.

**Step 2** (i = 2 for two remaining variants). From variants BGKF and BGHLDEF, the shorter one BGKF (with minimal risk 0.051) is chosen.

**Step 3** (i = 2 for variant BGKF). The robot overcomes the part BG. For the new initial point G, the input for modeling every part of possible route is updated in real time: according drone from 9.00 a.m. on parts GK and KF the imminent avalanche are detected. The accumulated knowledge is used to clarify the input for modeling, namely: the frequency threats in the part GKF increases from 1.5 to 2.5 times at 10 h. Using a probabilistic model for each variant, a recalculation of the risk of failure is carried out. Of the variants GKF and GHLDEF, the variant GHLDEF is chosen (risk is equal to 0.067, for the route GKF risk equals 0.083).

#### **Figure 18.**

*The risk of "failure" in dependence on prognostic period during the robot route from point A (Start) to point F (Finish).*

*Probabilistic Methods for Cognitive Solving of Some Problems in Artificial Intelligence Systems DOI: http://dx.doi.org/10.5772/intechopen.89168*

**Step 4**. After overcoming the part GHLDEF, the robot arrived at the intended point F of route in time.

Thus, the way ABCBGHLDEF is the result of optimization. The robot purpose was achieved owing to preventive measures which were defined by using risk control on the way (with probability of "success" more than 0.9).

New knowledge for accumulating and improving K-base is as follows:


Rehabilitation Systems

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**73**

**Chapter 5**

Project

**Abstract**

**1. Introduction**

focused on the user.

Technical Contributions to the

Platforms: Case Study—ePHoRt

*Patricia Acosta-Vargas, Janio Jadán-Guerrero, Cesar Guevara,*

This chapter proposes three main technical contributions for the development of a telerehabilitation platform, named ePHoRT, for patients recovering from hip surgery. The first contribution is the application of a diffuse 3D model for the detection of rehabilitation exercises after hip surgery. The model applies fuzzy logic, which allows identifying in real time if a patient is performing a right or wrong movement, assisted by an avatar in 3D. The avatar copies the movements of the patient through a Kinect camera. The second contribution involves the proposal of an iterative method to improve the usability of telerehabilitation platforms along the development life cycle. The proposed method involves the use of an inspection method and includes protocols and instruments. This method has been validated in the ePHoRT project. Finally, the chapter describes accessibility guidelines for educational resources. It proposes accessibility standards for the content of educational resources in video and PDF formats in the telerehabilitation platform according to

Quality of Telerehabilitation

*Sandra Sanchez-Gordon and Tania Calle-Jimenez*

the Web Content Accessibility Guidelines (WCAG).

**Keywords:** eHealth, telemedicine, telerehabilitation, hip surgery patients,

The ePHoRT platform allows hip replacement patients to perform part of the rehabilitation treatment at home and communicate the evolution of the recovery process to the physiotherapist. The ePHoRT platform has a "practice module" organized into three stages that are meaningful for the patient's recovery process. These stages are characterized by a growing level in the intensity of the exercises. Stage 1 is carried out during the week following the surgery and consists mainly of exercises performed lying down. Foot rehabilitation movements begin in stage 2 (the second week after surgery). Finally, stage 3 is characterized by functional exercises, which consist of preparing the patient to recover a regular walk. The ePHoRT platform is in the design stage and follows a process of agile and collaborative development

fuzzy logic, usability, accessibility, educational resources, WCAG