Title: Prediction of the dynamic contact resistance of circuit breaker based on the kernel partial least squares
Abstract: IET Generation, Transmission & DistributionVolume 12, Issue 8 p. 1815-1821 Research ArticleFree Access Prediction of the dynamic contact resistance of circuit breaker based on the kernel partial least squares Yakui Liu, Yakui Liu State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorGuogang Zhang, Corresponding Author Guogang Zhang [email protected] State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorHao Qin, Hao Qin State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorYingsan Geng, Yingsan Geng State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorJianhua Wang, Jianhua Wang State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorJinggang Yang, Jinggang Yang State Grid Jiangsu Electric Power Company Research Institute, Nanjing, 211103 People's Republic of ChinaSearch for more papers by this authorKe Zhao, Ke Zhao State Grid Jiangsu Electric Power Company Research Institute, Nanjing, 211103 People's Republic of ChinaSearch for more papers by this author Yakui Liu, Yakui Liu State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorGuogang Zhang, Corresponding Author Guogang Zhang [email protected] State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorHao Qin, Hao Qin State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorYingsan Geng, Yingsan Geng State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorJianhua Wang, Jianhua Wang State Key Lab of Electrical Insulation and Power Equipment, Xi'an Jiaotong University, Xi'an, 710049 People's Republic of ChinaSearch for more papers by this authorJinggang Yang, Jinggang Yang State Grid Jiangsu Electric Power Company Research Institute, Nanjing, 211103 People's Republic of ChinaSearch for more papers by this authorKe Zhao, Ke Zhao State Grid Jiangsu Electric Power Company Research Institute, Nanjing, 211103 People's Republic of ChinaSearch for more papers by this author First published: 01 March 2018 https://doi.org/10.1049/iet-gtd.2017.1235Citations: 3AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In order to diagnose the ablation characteristics of circuit breakers, the dynamic contact resistance measurement (DRM) has been proposed for almost 20 years. The dynamic resistance curves are easily influenced by two factors: injected current and opening velocity. The two factors are greatly affected the curves and may led a wrong diagnosis in DRM tests. Through analysis of the influence factors, an experimental model is used to simulate the opening process of the breaker in this study. The effective contact area of contact finger which is used in the experimental model under different velocities and current are measured by using the laser scanning microscope. The measurement proves that the changing of effective contact area plays determinative roles in the influencing of injected current and opening velocity. Then, the kernel partial least squares regression method is used to establish the model formula between influencing parameters and the dynamic contact resistance to realise the prediction of the dynamic contact resistance curves. Furthermore, the prediction model also can be used in other current carrying dry sliding friction conditions. 1 Introduction High-voltage circuit breaker is the most important protective device in power system, and its security and stability largely affect the safety of the whole system. The effects of switching operation and its influence on the observed phenomenon of circuit breaker have been discussed [1–3]. Some researchers are focusing on experimental investigation on ablation properties of the arc extinguish chamber in recent years, and dynamic contact resistance measurement (DRM) is one of the most effective methods [4]. The method has been widely used for many years because it does not need to dismantle the arc extinguish chamber [5–8]. Five essential diagnostic parameters were extracted from the contact resistance curves as a function of contact travel to build an effective condition assessment method for contact sets [9]. In practical application process, if injected current and opening velocity cannot keep stable, the dynamic contact resistance curves are often hard to replicate from the same circuit breaker. Besides, the uncertainty of the procedure during measurement should also be noticed [10, 11]. Injected current and opening velocity will influence the condition of the contact area in the arc extinguish chamber. For the purpose of testing accuracy and efficiency, DRM is suggested to be used in high injected current and low opening velocity [7]. The DRM test can be considered as a problem of the dry sliding friction with current. There are a lot of researches on the calculation methods of contact resistance for general materials, such as a general form of contact resistance mathematical model for the relationship between contact area and pressure, the calculation methods of contact conductance, contact pressure and contact area are also given [12]. In addition, the contact resistance calculation model can also be established by using the multiple contraction theory [13–15]. However, it is very difficult to describe the mathematical model between the two parameters (injected current and opening velocity) and the dynamic contact resistance curve. Therefore, this paper presents a theory of partial least squares (PLS), which can be used to find a suitable mathematical model to describe a relationship between the variables. The traditional PLS method and its improved algorithm can establish the prediction model by extracting useful information and eliminating the redundant information from a large amount data. However, PLS is a linear regression problem, and the modelling accuracy is not enough when dealing with the non-linear system. In nature, except near the steady working condition, most of the industrial processes are non-linear. In order to solve this problem, the PLS method is extended to the non-linear field, and a series of non-linear PLS methods have been developed. The NLPLS algorithm is proposed to describe the relationship between each pair of features by using local linear smoothing approaches [16]. Smoothing spline function is used to express the non-linear relationship between each pair of feature vectors by Word [17], the method assumes that the relationship between input and output vectors can be described as a special polynomial. Qin and McAvoy propose a neural network partial least square by combining the neural network with the PLS method [18]. The problems related to input variables can be solved by the external PLS model and the non-linear system can be described by the internal neural network in this method. The non-linear PLS method can also be combined with the genetic algorithm [19]. Besides, kernel methods have been used to combine with PLS method and become one of the simple and elegant approaches. kernel partial least squares (KPLS) method can model non-linear data effectively with well prediction performance in terms of non-linear latent variables (LVs) [20–23]. In the research of sliding friction, a heuristic wear model for the contact wire which accounts for these contributions to wear was built by using the PLS method [24]. The prediction model of the dynamic contact resistance has not been established in DRM tests and even in dry sliding friction with current. In this paper, the DRM experiments are carried out under different conditions from the high-voltage SF6 circuit breaker. The influence mechanism of injected current and opening velocity is analysed, and the effective contact area of contact finger from the experimental model is measured. Based on the above analysis, KPLS is selected to describe the prediction model of the dynamic contact resistance. 2 Equipment and parameters of the DRM 2.1 Equipment Before the DRM tests, it is essential to prepare some kind of important equipment, there are: (1) Circuit breaker : The SF6 circuit breaker with a spring operating mechanism is used in DRM tests, the rated voltage is 252 kV, and the rated current is 3150 A. The opening velocity can be changed by adjusting the freedom of the operating spring. (2) Battery : The rated voltage is 15 V of the battery, at this time the injected current is 3000 A in the DRM tests. The voltage can also be changed to provide different values of injected current. (3) Acceleration sensor : The sensor can be used to measure the travel of the circuit breaker. (4) Analytic instrument : The DRM curves can be obtained at the analytic instrument, including travel, contact resistance and time. Four-wire testing is the most accurate method when measuring circuit <10 Ω, as shown in Fig. 1. Fig. 1Open in figure viewerPowerPoint Equipment of DRM tests 2.2 Parameters DRM curves during closing operation are not generally useful, it is because that the curves will be seriously disturbed by the vibration of the breakers in this time. The high-voltage SF6 circuit breakers have two parallel contact sets. The main contacts are low-resistance contacts, which are silver plated, whereas arcing contacts are of tungsten-copper which helps in initiating arc quenching and current interruption. In SF6 and air-blast breakers, the arcing contact is burned off and becomes shorter for each live operation of the circuit breaker. Based on mechanical structure of the circuit breaker, the curve should be divided into two parts: main contact touching part and arcing contact touching part. In main contact touching part, both the main contact and the arc contact make touch, so the resistance curve is influenced by the contact resistance of the main contact and the arc contact, and they are considered to be parallel. When the process enters the arc contact touching part, it is considered that the arc contact resistance alone is affecting the resistance curve, as a result that the main contact has been separated. The structure of the arc extinguishing chamber can be seen in Fig. 2, the DRM curves during opening operation can be seen in Fig. 3. The parameters of main contact part are not discussed in this paper, since the parameters cannot give information about the arcing contact condition and the parameters can be easily extracted from the static contact resistance measurement. Fig. 2Open in figure viewerPowerPoint Arc extinguishing chamber Fig. 3Open in figure viewerPowerPoint Dynamic contact resistance curve and travel curve versus time during opening operation When plotting contact resistance as a function of the contact travel and the time, the following vital diagnostic parameters can be extracted in Table 1 : Ra : average arcing contact resistance Dp : main contact wipe Da : arcing contact wipe Pa : position of the breaker contacts at the arcing contact part Va : average contact velocity during arcing contact part Table 1. Parameters of the dynamic resistance curve Feature Unit Value Ra μΩ 199.32 Dp mm 13.30 Da mm 8.20 Pa mm 21.50 Va m/s 2.28 3 Injected current and opening velocity There are three major factors may affect the contact resistance in current carrying friction theory, stress acting on the contact area, current and velocity. For the circuit breaker, it is thought that the stress acting on the contact area stayed pretty constant in DRM tests. Therefore, only the injected current and opening velocity will be discussed in this chapter. 3.1 Classic theory of contact resistance in circuit breaker In sliding contact theory, there are only a small number of points or surface touching on contact area, which resulting in the contraction of current line near the touching surface. It means that the effective conductive area is reduced, and the contraction of the current is named as contraction resistance. Sometimes the contact surface may be covered by some bad conductivity materials, such as dust, oxide film etc. while there is another additional resistance, known as membrane resistance [4]. For SF6 circuit breaker, the contact force of circuit breaker will wear off the oxide film and it will not regenerate in SF6 gas. Metallic fluorides will be melt in high injected current, which are usually present in the form of a non-conductive dust powder (CuF2, AlF3, WF6 etc.) that is deposited on the breaker contacts. Therefore, only the contraction resistance is considered in DRM tests. The contraction resistance Rf has been described as follows: (1) where ρ is specific resistivity, F is contact force, H is contact hardness. It can be seen from (1): specific resistivity, contact force and contact hardness can affect the contraction resistance. Besides, the contraction resistance can be described as (2) where n is the number of contact region, a is average radius of each contact region. It can be seen that the contact area can also affect the contact resistance because the positive correlation between the contact area and contact region. 3.2 Injected current The value of injected current should meet the need of the validity of experiments and the safety of the breaker for assuring that the DRM tests can be carried successfully. As the voltage of test equipment is given, the maximum current is limited by the total loop resistance of the test cables. Accordingly, the value of DC injected current should be between the minimum effective current and the rated current of the breaker. Based on the above considerations, the range of the injected current varies from 787 to 3000 A. The curve of average arcing contact resistance versus injected current can be seen in Fig. 4. This curve only works if the opening velocity does not change. Fig. 4Open in figure viewerPowerPoint Dynamic arcing contact resistance versus injected current The figure shows that Ra decreasing with the increasing of the injected current, the resistance may be affected by the injected current in two ways. 3.2.1 Joule heat The current flow through the contact area will generated a large number of Joule heat, and the heat will change the hardness of the contact area, as shown in (3) where A is assumed hardness when the absolute temperature is 0, B is softening coefficient, T is absolute temperature. From the formula (3), it can be easily find that the hardness is negatively associated with Joule heat. Then the relationship can be taken into formula (1), with the increasing of the injected current, the contact resistance decrease. It is because that the changing of hardness will change the effective contact area. Besides, the specific resistivity will also change with the changing of the temperature. 3.2.2 Electromagnetic force The contact force F has been described as (4) where FS is the applied spring force, FA is the Lorentz force applied to the contact from the overall structure, and FB is the Lorentz repulsion force due to constriction inside the contact. The injected current will change the contact force F by changing the FA and FB. Electromagnetic force has been proved that it has little effect on contact force [25], and the force will not influence the contact resistance in DRM. Therefore, the changing of effective area by Joule heat is critical to the contact resistance, and the mathematical model between the injected current and contact resistance is non-linearity. 3.3 Opening velocity Opening velocity is defined in various ways. In order to give an accurate description of the motion characteristics of the arcing contact, the average velocity during arcing contact part (Va) will be used to represent the opening velocity in this paper. The range of opening velocity is from 1.38–2.59 m/s, the changing of contact resistance can be seen in Fig. 5, and the value of inject current is 3000 A at this time. Fig. 5Open in figure viewerPowerPoint Dynamic arcing contact resistance versus opening velocity The figure shows a positive correlation between contact resistance and opening velocity. The resistance may also be affected by the opening velocity in two ways. 3.3.1 Frictional heat Two metal surfaces rubbing together cause friction and heat. Friction heat formed in the roughness surface influences surface morphology, as the same of Joule heat. The relationship between frictional heat and velocity can be described as [26] (5) where ζ is empirical coefficient which is related with material of the contact, µ is friction coefficient, v is opening velocity, and λ is thermal conductivity. The formula intuitively reveals that the positive correlation between opening velocity and frictional heat. According to formula (3), the increasing of frictional heat also decreases the contact resistance, so the increasing of opening velocity could have a negative impact on contact resistance. However, the conclusion presents a striking contrast to the experimental results. 3.3.2 Effective contact area The velocity will change the effective contact area, the conclusion will be proved by the using of a measuring instrument for surface profile in this paper. Increasing of the velocity will lead to the decreasing of the effective area, and then make the increase in contact area, which is in good agreement with the experimental results. But up to now, whether a linear or non-linear mathematical model between the opening velocity and the contact resistance has not been established. 3.4 Micro measurement of effective contact area On the basis of the analysis above, these results led us to conclude that the changing of the effective contact area play determinative roles in the influencing of injected current and opening velocity. However, the contact finger which is surrounded by SF6 gas in breaker is hard to measure the contact area. In order to verify the correctness and reliability of the conclusions, the experimental model is used to simulate the opening process of the breaker, and current and velocity can be easily changed. There is only one contact finger carry the injected current in the experiment model, which is different with the actual breaker. The purpose is to reduce the values of current, which will be beneficial for the convenience and safety of the experiment. The experimental model can be seen in Fig. 6. The contact finger will be replaced after every experiment, and the purpose is to save the condition of the contact area. Fig. 6Open in figure viewerPowerPoint Experimental model of DRM The surface of the finger is silver-plated, and the coatings will disappear when the finger and copper disk are rubbed together. According to this, the contact area can be easily distinguished. The surface is rough and contains many peaks and valleys, and, only a part of the peaks touching on micro level, it is called effective contact area. The contact area and effective contact area of the contact finger can be measured by the laser scanning microscope, as shown in Fig. 7. Fig. 7Open in figure viewerPowerPoint Contact area and effective contact area of the contact finger (a) Contact area, (b) Effective contact area It can be seen that the contact resistance varies inversely with the contact region in formula (2), therefore, the contact resistance is direct proportion to the inverse of effective contact area. However, there is no standard to definite whether the peaks can be regarded as effective contact area or not, so three different perpendicular distances above the base of the geometric figure are picked in this paper. The three standards picked in this paper are 8.5, 6.37 and 4.25 μm, accounting for 80, 60 and 40% for the total distance, respectively. Contact resistance and inverse of effective contact area under different conditions can be seen in Figs. 8 and 9. Fig. 8Open in figure viewerPowerPoint Contact resistance and inverse of effective contact area under different velocities Fig. 9Open in figure viewerPowerPoint Contact resistance and inverse of effective contact area under different current The figure shows that the general trend of the contact resistance curve is consistent with the inverse of effective contact area. The trend of the curves can be used to prove that injected current and velocity affect the contact resistance by changing the contact area. 4 Predictions of DRM 4.1 Basic theory of PLS and KPLS PLS constructs linear multivariable regression model by extracted LVs from the original input/output data space. Thus, PLS has been used widely in collinear data modelling. The objective of PLS method is to search for weight vectors w and c in terms of maximisation covariance between latent scores t and u. PLS decomposes input data X and output data Y into the form as follows: (6) where T and U are matrices of the extracted h score vectors, P and Q indicate loading matrices, and E and F present residual matrices. Then, PLS regression model can be expressed as: (7) However, the application of PLS is limited by its linear assumption. Non-linear PLS approaches are developed to solve the non-linear problem of the input data. By extended non-linear item to input matrix, KPLS constructs non-linear model using LVs in the non-linear kernel feature space. Assume the input data X are non-linear transformed into the high dimension features space, i.e. mapping given by Φ: x l → Φ(x l). Then, linear PLS is performed in this high dimension feature space. Effectively, it means that non-linear model of the original input data is obtained. By using the kernel functions, i.e. K = Φ(x l)T Φ(x m), l, m = 1, 2, … k, high dimensional, even infinite-dimensional feature space is obtained. After extracting the desired kernel LVs, the corresponding prediction outputs on training samples can be represented ass (8) 4.2 Comparison between PLS and KPLS Through the foregoing analysis, the relationship between injected current and contact resistance can be identified as non-linear, but the relationship between opening velocity and contact resistance cannot be confirmed, so both PLS and KPLS are adopted in this paper to make a comparison. Fifty average contact resistance values are used as training samples to build the prediction model, as shown in Fig. 10. Fig. 10Open in figure viewerPowerPoint Contact resistance as a function of contact force and electrical current The curves of fitted values versus actual values, that is an ellipse determined by the injected current and the opening velocity by using PLS, is given out clearly in this paper, as shown in Fig. 11a. With the Gaussian function as the kernel, the curves of KPLS method can be seen in Fig. 11b. Black line means fitted values and black symbol means actual values. The fitting coefficient of both methods can be seen in Table 2. Fig. 11Open in figure viewerPowerPoint Fitted values versus actual values by using PLS and KPLS (a) PLS method, (b) KPLS method Table 2. Fitting coefficients of PLS and KPLS PLS KPLS fitting coefficient 0.7653 0.8909 From the table, the fitting coefficient of KPLS is larger than PLS. Due to the fitting coefficient is the key parameter to determine the validity of the fitting, KPLS is considered more valid. The other parameters of KPLS can be seen in Table 3. Table 3. Parameters of KPLS Injected current Opening velocity variable importance 1.39 0.27 coefficient −0.87 0.17 The contribution of the parameters to the curve is determined by the variable importance, and coefficient means the relationship between curves and parameters. So, it can be seen that the contact resistance is greatly affected by the injected current in this test. The relationship between injected current and contact resistance is negative correlation, while the relationship between opening velocity and contact resistance is positive correlation. 5 Discussions There are many kinds of equipment using in DRM tests, and injected current varies greatly from 200 A (TM1800, Megger) to 3000 A. Based on the preceding theory, the accuracy of the tests is not satisfying due to the lack of uniform standards, and the confusion may lead to a wrong judgment of the ablation condition. Besides, the breaker itself cannot hold a constant velocity in practical operation, particularly in the condition of fatigue of operating mechanism and any other mechanical failure of the mechanism. In summary, in most cases, the dynamic contact resistance curves during arcing part may give different conclusions. Therefore, the prediction of the contact resistance becomes particularly important. Another ten sets of dynamic contact resistance curves are used to compare with the prediction values which verify the confidence of model and computation. The comparison between actual values and prediction values can be seen in Fig. 12. Black line means predicted values and square means actual values. The errors can be seen in Table 4. Fig. 12Open in figure viewerPowerPoint Predicted values versus actual values by using KPLS Table 4. Errors between actual values and prediction values Predicted values Actual values Error, % 210.31 219.91 4.37 211.69 225.16 5.98 216.90 226.35 4.17 222.82 232.63 4.22 241.30 242.20 0.37 243.62 245.20 0.64 249.99 246.46 1.43 251.75 264.61 4.86 251.82 278.75 9.66 291.77 296.74 1.68 From the table, the errors all below 10%, and most of them below 5%. The results of prediction demonstrate the effectiveness and advantage of this approach. 6 Conclusions KPLS is used in this paper to predict the contact resistance during arcing part in DRM tests, the following conclusions can be drawn from the results: (1) The increasing of the injected current will decrease the contact resistance. (2) The increasing of opening velocity will have the opposite effect on contact resistance. (3) The trend of the inverse of effective contact area curves can be used to prove that injected current and velocity affect the contact resistance by changing the contact area. (4) Compared with opening velocity, the contact resistance is more affected by injected current. (5) According to the changing of injected current and opening velocity, the prediction model can be used to predict the contact resistance, and avoid the wrong judgment. (6) What is more, the prediction model can also be used in other current carrying dry sliding friction conditions. 7 Acknowledgment The work was supported by the State Grid Corporation of China. 8 References 1Mostić, D., Osmokrović, P., Stanković, K. et al.: 'Dielectric characteristics of vacuum circuit breakers with CUCR and CUBI contacts before and after short-circuit breaking operations', Vacuum, 2011, 86, (2), pp. 156– 164 2Todorović, R., Škatarić, D., Bajramović, Z. et al.: 'Correlation and regression between the breakdown voltage and pre-breakdown parameters of vacuum switching elements', Vacuum, 2016, 123, pp. 111– 120 3Xin, W., Zhang, G., Wang, J. et al.: 'Simulation of very fast transient overvoltage caused by disconnector switch operation in SF6 Gas insulated switchgear using multi-restrike arcing model'. 2013 2nd Int. Conf. Electric Power Equipment – Switching Technology (ICEPE-ST), Matsue, Japan, October, 2013 4Stanisic, Z., Neimanis, R.: 'A new ultra light weight method for static and dynamic resistance measurements'. Conf. Record of the 2010 IEEE Int. Symp. Electrical Insulation, 2010 5Obarcanin, K., Secic, A., Hadzimejlic, N.: 'Design and development of the software solution for analysis and acquisition of the high voltage circuit breakers dynamic resistance measurement results'. Int. Convention on Information and Communication Technology, Electronics and Microelectronics, 2015 6Cheng, T., Zhu, W., Jin, G. et al.: 'Influence of the injected current on dynamic contact resistance measurements of HV circuit breakers'. China Int. Conf. Electricity Distribution, 2014 7Stanisic, Z.: 'Method for static and dynamic resistance measurements of Hv circuit breaker'. IEEE PES Int. Conf. Exhibition on Innovative Smart Grid Technologies, 2012 8Ding, C., He, J., Yuan, X. et al.: 'A comparison of contact erosion for two types arcing contact of Sf6 circuit breakers in making process'. Electrical Contacts, 2015 9Chen, G., Lan, L., Pan, Z. et al.: 'Electrical erosion test and condition assessment of Sf6 Cb contact sets', IET Gener. Transm. Distrib., 2017, 11, (8), pp. 1901– 1909 10Kovacevic, A., Despotovic, D., Rajovic, Z. et al.: 'Uncertainty evaluation of the conducted emission measurements', Nucl. Technol. Radiat. Prot., 2013, 28, (2), pp. 182– 190 11Kovacevic, A.M., Kovacevic, A.V., Stankovic, K.D. et al.: 'The combined method for uncertainty evaluation in electromagnetic radiation measurement', Nucl. Technol. Radiat. Prot., 2014, 29, (4), pp. 279– 284 12Boyer, L.: 'Contact resistance calculations: generalizations of greenwood's formula including interface films', IEEE Trans. Compon. Packag. Technol., 2001, 24, (1), pp. 50– 58 13Caven, R.W., Jalali, J.: 'Predicting the contact resistance distribution of electrical contacts by modeling the contact interface'. Proc. Thirty-Seventh IEEE Holm Conf. Electrical Contacts, 1991, 1991 14Malucci, R.D.: 'Multispot model of contacts based on surface features'. Electrical Contacts, 1990., Proc. Thirty-Sixth IEEE Holm Conf. Fifteenth Int. Conf. Electrical Contacts, 1990 15Russakoff, R., Snowball, R.F.: 'Measurement of contact resistance', Rev. Sci. Instrum., 1967, 38, (3), pp. 395– 397 16Frank, I.E.: 'A nonlinear PLS model', Chemometr. Intell. Lab. Syst., 1990, 8, (2), pp. 109– 119 17Wold, S.: 'Nonlinear partial least squares modelling: 2. Spline inner relation', Chemometr. Intell. Lab. Syst., 1992, 14, (1), pp. 71– 84 18Qin, S.J., Mcavoy, T.J.: 'Nonlinear PLS modeling using neural networks', Comput. Chem. Eng., 1992, 16, (4), pp. 379– 391 19Li, T., Mei, H., Cong, P.: 'Combining nonlinear PLS with the numeric genetic algorithm for QSAR', Chemometr. Intell. Lab. Syst., 1999, 45, (1–2), pp. 177– 184 20Wang, G., Jiao, J.: 'A kernel least squares based approach for nonlinear quality-related fault detection', IEEE Trans. Ind. Electron., 2017, 64, (4), pp. 3195– 3204 21Zhang, Y., Sun, R., Fan, Y.: 'Fault diagnosis of nonlinear process based on KCPLS reconstruction', Chemometr. Intell. Lab. Syst., 2015, 140, pp. 49– 60 22Jia, Q., Zhang, Y.: 'Quality-related fault detection approach based on dynamic kernel partial least squares', Chem. Eng. Res. Des., 2016, 106, pp. 242– 252 23Rosipal, R., Trejo, L.J.: 'Kernel partial least squares regression in reproducing kernel Hilbert space', J. Mach. Learn. Res., 2002, 2, (2), pp. 97– 123 24Bucca, G., Collina, A.: 'Electromechanical interaction between carbon-based pantograph strip and copper contact wire: a Heuristic wear model', Tribol. Int., 2015, 92, pp. 47– 56 25Ferree, J., Petrovic, L., Anheuser, M.: 'Contact blow-apart forces: experience in molded case circuit breaker contact systems'. ICEC 2014; Proc. Int. Conf. Electrical Contacts, 2014 26Bouchoucha, A., Chekroud, S., Paulmier, D.: 'Influence of the electrical sliding speed on friction and wear processes in an electrical contact copper–stainless steel', Appl. Surf. Sci., 2004, 223, (4), pp. 330– 342 Citing Literature Volume12, Issue8April 2018Pages 1815-1821 FiguresReferencesRelatedInformation
Publication Year: 2018
Publication Date: 2018-03-01
Language: en
Type: article
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