Document Type : Original Article

Authors

Department of Industrial Engineering, Robat Karim Branch, Islamic Azad University, Tehran, Iran.

Abstract

This paper presents an approach for the fault diagnosis in the state of fault in a machine by using a combination of the Dempster–Shafer (D-S) theory. At the first, feature extractions in each state have been combined based on evidential reasoning (ER) using kind of sensor information such as vibration, acoustic, pressure, and temperature, to detect and diagnose machine failure. Then, the main fusion will be obtained. In this process, the mass function assignment of any sensors to feature extraction, respectively, in every state of the machine is fused to indicate state quality. Within this framework, we propose a new way for main fusion to derive a consensus decision for fault diagnosis. In this paper, an approach developed to apply the evidential reasoning by defining adaptively weights into the improvement of the D–S evidence theory instead of the probability theory and the D–S evidence theory alone. Instead of using the evidential reasoning approach, this new approach applies entropy weighting in the D-S theory, in which all available data are used for making a decision. Entropy weighting can measure the uncertainty level of the fault decision and assist in obtaining a less uncertain fault decision. It is defined adaptively weights based on ambiguity measures associated with information obtained from each sensor. The ambiguity measure is defined by Shannon’s entropy. Many industries use old machines due to cost savings or lack of purchasing power. Maintenance policies in these factories are based on determining their fault experimentally and traditionally. Therefore, the main goal of this paper uses the improved evidence reasoning algorithm using a kind of sensor information to carry out fault diagnosis in these industrials. Then, a numerical example and a case study involving the ball mill machine in fault diagnosis are presented to show the rationality and efficiency of the proposed method.

Keywords

Basir, O., and Yuan, X., (2007). "Engine fault diagnosis based on multi-sensor information fusion using Dempster–Shafer evidence theory", Information Fusion, Vol. 8, No. 4, pp. 379–386. https://doi.org/10.1016/j.inffus.2005.07.003.
Behnamian, J., Rahami, Z., (2020). "Multi-objective scheduling and assembly line balancing with resource constraint and cost uncertainty: A “box” set robust optimization", Journal of Industrial Engineering and Management Studies, Vol. 7, No. 1, pp. 220-232. https://doi.org 10.22116/JIEMS.2020.110250.
Bessam, B., Menacer, A., Boumehraz, M., and Cherif, H., (2015). "Wavelet transform and neural network techniques for inter-turn short circuit diagnosis and location in induction motor", International Journal of System Assurance Engineering and Management, Vol. 8(S1), pp. 478–488. https://doi.org/10.1007/s13198-015-0400-4.
Bhalla, D., Bansal, R.K., and Gupta, H.O., (2013). "Integrating AI based DGA fault diagnosis using Dempster–Shafer Theory", International Journal of Electrical Power & Energy Systems, Vol. 48, pp. 31–38. https://doi.org/10.1016/j.ijepes.2012.11.018.
Cai, B., Liu, H., and Xie, M., (2016). "A real-time fault diagnosis methodology of complex systems using object-oriented Bayesian networks", Mechanical Systems and Signal Processing, Vol. 80, pp. 31–44. https://doi.org/10.1016/j.ymssp.2016.04.019.
Cheng, G., Chen, X., Li, H., Li, P., and Liu, H., (2016). "Study on planetary gear fault diagnosis based on entropy feature fusion of ensemble empirical mode decomposition", Measurement, Vol. 91, pp. 140–154. https://doi.org/10.1016/j.measurement.2016.05.059.
Dempster, A.P., (1968). "A Generalization of Bayesian Inference", Journal of the Royal Statistical Society: Series B (Methodological), Vol. 30, No. 2, pp. 205–232. https://doi.org/10.1111/j.2517-6161.1968.tb00722.x.
Deng, Y., (2016). "Deng entropy", Chaos, Solitons & Fractals, Vol. 91, pp. 549–553. https://doi.org/10.1016/j.chaos.2016.07.014.
Deng, X., Jiang, W., and Wang, Z., (2019). "Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution", Applied Mathematics and Computation, Vol. 340, pp. 101–112. https://doi.org/10.1016/j.amc.2018.08.032.
Deng, Y., Shi, W.K., Zhu, Z.F., and Liu, Q., (2004). "Combining belief functions based on distance of evidence", Decision Support Systems, Vol. 38, No. 3, pp. 489–493. https://doi.org/10.1016/j.dss.2004.04.015.
Fan, X., and Zuo, M.J., (2006). "Fault diagnosis of machines based on D–S evidence theory. Part 2: Application of the improved D–S evidence theory in gearbox fault diagnosis", Pattern Recognition Letters, Vol. 27, No. 5, pp. 377–385. https://doi.org/10.1016/j.patrec.2005.08.024.
Farugh, H., Mostafayi, S., Afrasiabi, A., (2019). "Bi-objective robust optimization model for configuring cellular manufacturing system with variable machine reliability and parts demand: A real case study", Journal of Industrial Engineering and Management Studies, Vol. 6, No. 2, pp. 120-146. https://doi.org/120-146. 10.22116/ JIEMS.2019.93028.
Guedidi, S., Zouzou, S. E., Laala, W., Yahia, K., and Sahraoui, M., (2013). "Induction motors broken rotor bars detection using MCSA and neural network: Experimental research", International Journal of System Assurance Engineering and Management, Vol. 4, No. 2, pp. 173–181. https://doi.org/10.1007/s13198-013-0149-6.
Guo, M., Yang, J.B., Chin, K.S., and Wang, H., (2008). The evidential reasoning approach for multi-attribute decision analysis under both fuzzy and interval uncertainty, Interval/probabilistic uncertainty and non-classical logics, part of the advances in soft computing book series (AINSC) 46:129-140.
Han, Y., and Deng, Y., (2018). "An evidential fractal analytic hierarchy process target recognition method, Defence Science Journal, Vol. 68, No. 4, p. 367. https://doi.org/10.14429/dsj.68.11737.
Han, Y., and Deng, Y., (2018b). "A novel matrix game with payoffs of Maxitive Belief Structure", International Journal of Intelligent Systems, Vol. 34, No. 4, pp. 690–706. https://doi.org/10.1002/int.22072.
Hang, J., Zhang, J., and Cheng, M., (2016). "Application of multi-class fuzzy support vector machine classifier for fault diagnosis of wind turbine", Fuzzy Sets and Systems, Vol. 297, pp. 128–140. https://doi.org/10.1016/j.fss.2015.07.005.
Huang, Y., McMurran, R., Dhadyalla, G., and Peter Jones, R., (2008). "Probability based vehicle fault diagnosis: Bayesian network method", Journal of Intelligent Manufacturing, Vol. 19, No. 3, pp. 301–311. https://doi.org/10.1007/s10845-008-0083-7.
Hui, K. H., Lim, M. H., Leong, M. S., and Al-Obaidi, S.M., (2017). "Dempster-Shafer evidence theory for multi-bearing faults diagnosis", Engineering Applications of Artificial Intelligence, Vol. 57, pp. 160–170. https://doi.org/10.1016/j.engappai.2016.10.017.
Huynh, V.-N., Nguyen, T.T., and Le, C.A., (2010). "Adaptively entropy-based weighting classifiers in combination using Dempster–Shafer theory for word sense disambiguation", Computer Speech & Language, Vol. 24, No. 3, pp. 461–473. https://doi.org/10.1016/j.csl.2009.06.003.
Jian-Bo Yang, and Dong-Ling Xu., (2002). "Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty", IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, Vol. 32, No. 3, pp. 376–393. https://doi.org/10.1109/tsmca.2002.802809.
Jian-Bo Yang, and Singh, M. G., (1994). "An evidential reasoning approach for multiple-attribute decision making with uncertainty", IEEE Transactions on Systems, Man, and Cybernetics, Vol. 24, No. 1, pp. 1–18. https://doi.org/10.1109/21.259681.
Jiang, W., Wei, B., Xie, C., and Zhou, D., (2016). "An evidential sensor fusion method in fault diagnosis", Advances in Mechanical Engineering, Vol. 8, No. 3, 168781401664182. https://doi.org/10.1177/1687814016641820.
Jousselme, A.-L., Grenier, D., and Bossé, É., (2001). "A new distance between two bodies of evidence", Information Fusion, Vol. 2, No. 2, pp. 91–101. https://doi.org/10.1016/s1566-2535(01)00026-4.
Kaftandjian, V., Dupuis, O., Babot, D., and Min Zhu, Y., (2003). "Uncertainty modelling using Dempster–Shafer theory for improving detection of weld defects", Pattern Recognition Letters, Vol. 24(1–3), pp. 547–564. https://doi.org/10.1016/s0167-8655(02)00276-3.
Kang, B., Deng, Y., Hewage, K., and Sadiq, R. (2019). "A Method of Measuring Uncertainty for Z-Number", IEEE Transactions on Fuzzy Systems, Vol. 27, No. 4, pp. 731–738. https://doi.org/10.1109/tfuzz.2018.2868496.
Khalaj, F.,  Khalaj, M., (2020). "Developed cosine similarity measure on belief function theory: An application in medical diagnosis", Communications in Statistics - Theory and Methods, pp. 1-12. https://doi.org/10.1080/03610926.2020.1782935.
Khalaj, M., Tavakkoli-Moghaddam, R., Khalaj, F.,  Siadat, A., (2020). "New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process",
Communications in Statistics - Theory and Methods, Vol. 49, No. 4, pp. 909-923. https://doi.org/10.1080/03610926.2018.1554123.
Laala, W., Zouzou, S.-E., and Guedidi, S., (2013). "Induction motor broken rotor bars detection using fuzzy logic: experimental research", International Journal of System Assurance Engineering and Management, Vol. 5, No. 3, pp. 329–336. https://doi.org/10.1007/s13198-013-0171-8.
Mabrouk, A. E., Zouzou, S. E., Khelif, S., and Ghoggal, A., (2015). "On-line fault diagnostics in operating three-phase induction motors by the active and reactive currents", International Journal of System Assurance Engineering and Management, Vol. 8(S1), pp. 160–168. https://doi.org/10.1007/s13198-015-0364-4.
Meng, D., Liu, M., Yang, S., Zhang, H., and Ding, R. (2018). A fluid–structure analysis approach and its application in the uncertainty-based multidisciplinary design and optimization for blades. Advances in Mechanical Engineering, 10(6), 168781401878341. https://doi.org/10.1177/1687814018783410.
Meng, D., Li, Y., Zhu, S.-P., Lv, G., Correia, J., and de Jesus, A., (2019). "An enhanced reliability index method and its application in reliability-based collaborative design and optimization", Mathematical Problems in Engineering, pp. 1–10. https://doi.org/10.1155/2019/4536906.
Moosavian, A., Khazaee, M., Najafi, G., Kettner, M., and Mamat, R., (2015). "Spark plug fault recognition based on sensor fusion and classifier combination using Dempster–Shafer evidence theory", Applied Acoustics, Vol. 93, pp. 120–129. https://doi.org/10.1016/j.apacoust.2015.01.008.
Murphy, C. K., (2000). "Combining belief functions when evidence conflicts", Decision Support Systems, Vol. 29, No. 1, pp. 1–9. https://doi.org/10.1016/s0167-9236(99)00084-6.
Oukhellou, L., Debiolles, A., Denœux, T., and Aknin, P. (2010). "Fault diagnosis in railway track circuits using Dempster–Shafer classifier fusion", Engineering Applications of Artificial Intelligence, Vol.  23, No. 1, pp. 117–128. https://doi.org/10.1016/j.engappai.2009.06.005.
Parikh, C. R., Pont, M. J., and Barrie Jones, N., (2001). "Application of Dempster–Shafer theory in condition monitoring applications: a case study", Pattern Recognition Letters, Vol. 22(6–7), pp. 777–785. https://doi.org/10.1016/s0167-8655(01)00014-9.
Petersen, D. R., Link, R. E., Wang, H. F., and Wang, J. P., (2000). "Fault Diagnosis Theory: Method and Application Based on Multisensor Data Fusion", Journal of Testing and Evaluation, Vol. 28, No. 6, pp. 513-518. https://doi.org/10.1520/jte12143j.
Rodríguez Ramos, A., Llanes-Santiago, O., Bernal de Lázaro, J. M., Cruz Corona, C., Silva Neto, A. J., and Verdegay Galdeano, J. L., (2017). "A novel fault diagnosis scheme applying fuzzy clustering algorithms", Applied Soft Computing, Vol. 58, pp. 605–619. https://doi.org/10.1016/j.asoc.2017.04.071.
Rong, H., Ge, M., Zhang, G., and Zhu, M. (2018). "An Approach for Detecting Fault Lines in a Small Current Grounding System using Fuzzy Reasoning Spiking Neural P Systems", International Journal of Computers Communications & Control, Vol. 13, No. 4, pp. 521–536. https://doi.org/10.15837/ijccc.2018.4.3220.
Sakhara, S., Saad, S., and Nacib, L., (2016). "Diagnosis and detection of short circuit in asynchronous motor using three-phase model", International Journal of System Assurance Engineering and Management, Vol. 8, No. 2, pp. 308–317. https://doi.org/10.1007/s13198-016-0435-1.
Seiti, H., and Hafezalkotob, A., (2019). "Developing the R-TOPSIS methodology for risk-based preventive maintenance planning: A case study in rolling mill company", Computers & Industrial Engineering, Vol. 128, pp. 622–636. https://doi.org/10.1016/j.cie.2019.01.012.
Shafer, G., (1976). A mathematical theory of evidence, Princeton University Press, New Jersey.
Smets, P., and Kennes, R., (1994). "The transferable belief model", Artificial Intelligence, Vol. 66, No. 2, pp. 191–234. https://doi.org/10.1016/0004-3702(94)90026-4.
Smith, A. F. M., and Shafer, G., (1976). "A Mathematical theory of evidence", Biometrics, Vol. 32, No. 3, p. 703. https://doi.org/10.2307/2529769.
Singh, B., Grover, S., and Singh, V., (2016). "Evaluation of benchmarking attribute for service quality using multi attitude decision making approach", International Journal of System Assurance Engineering and Management, Vol. 8(S2), pp. 617–630. https://doi.org/10.1007/s13198-016-0485-4.
Sun, R., and Deng, Y., (2019). "A new method to identify incomplete frame of discernment in evidence theory", IEEE Access, Vol. 7, pp. 15547–15555. https://doi.org/10.1109/access.2019.2893884.
Tang, W.H., Wu, Q.H., (2011). Dealing with uncertainty for dissolved gas analysis, condition monitoring and assessment of power transformers using computational intelligence, Part of the power systems book series (POWSYS), pp. 125-162.
Torabi Jahromi, A., Er, M.J., Li, X., and Lim, B.S., (2016). "Sequential fuzzy clustering based dynamic fuzzy neural network for fault diagnosis and prognosis", Neurocomputing, Vol. 196, pp. 31–41. https://doi.org/10.1016/j.neucom.2016.02.036.
Verbert, K., Babuška, R., and De Schutter, B., (2017). "Bayesian and Dempster–Shafer reasoning for knowledge-based fault diagnosis–A comparative study", Engineering Applications of Artificial Intelligence, Vol. 60, pp. 136–150. https://doi.org/10.1016/j.engappai.2017.01.011.
Wang, D., Tsui, KL., Zhou, Q., (2016). "Novel Gauss–Hermite integration based Bayesian inference on optimal wavelet parameters for bearing fault diagnosis", Mech. Syst. Signal. Process, Vol 72–73, pp.80-91.
Wang, Y., Zhang, K., and Deng, Y., (2018). "Base belief function: an efficient method of conflict management", Journal of Ambient Intelligence and Humanized Computing, Vol. 10, No. 9, pp. 3427–3437. https://doi.org/10.1007/s12652-018-1099-2.
Yang, J.B., (2001). "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties", European Journal of Operational Research, Vol. 131, No. 1, pp. 31–61. https://doi.org/10.1016/s0377-2217(99)00441-5.
Xiao, F., (2019). "A multiple-criteria decision-making method based on D numbers and belief entropy", International Journal of Fuzzy Systems, Vol. 21, No. 4, pp. 1144–1153. https://doi.org/10.1007/s40815-019-00620-2.
Xiao, F., (2018). "A novel multi-criteria decision-making method for assessing health-care waste treatment technologies based on D numbers", Engineering Applications of Artificial Intelligence, Vol. 71, pp. 216–225. https://doi.org/10.1016/j.engappai.2018.03.002.
Yager, R.R., (1987). "On the Dempster-Shafer framework and new combination rules", Information Sciences, Vol. 41, No. 2, pp. 93–137. https://doi.org/10.1016/0020-0255(87)90007-7.
Yaghoubi, A., Amiri, M., (2015). "Designing a new multi-objective fuzzy stochastic DEA model in a dynamic ‎environment to estimate efficiency of decision-making units (Case Study: An Iranian petroleum company), Journal of Industrial Engineering and Management Studies, Vol. 2, No. 2, pp. 26-42.
Yang, H.C., Deng, Y., Jones, J., (2018). "Network division method based on cellular growth and physarum-inspired network adaptation", International Journal of Unconventional Computing, Vol. 13, No. 6, pp. 477–491.
Yang, J.B., Xu, D.L., (2002). "Nonlinear information aggregation via evidential reasoning in multi attribute decision analysis under uncertainty", IEEE Trans. Syst., Man, Cybern Part A: Systems and Humans, Vol. 32, No. 3, pp.1–18.
Yu, J., (2013). "A new fault diagnosis method of multimode processes using Bayesian inference based Gaussian mixture contribution decomposition", Engineering Applications of Artificial Intelligence, Vol. 26, No. 1, pp. 456–466. https://doi.org/10.1016/j.engappai.2012.09.003.
Yu, Y., Li, W., Sheng, D., and Chen, J., (2015). "A novel sensor fault diagnosis method based on modified ensemble empirical mode decomposition and probabilistic", Neural Network. Measurement, Vol. 68, pp. 328–336. https://doi.org/10.1016/j.measurement.2015.03.003.
Zhang, C., Li, D., Mu, Y., and Song, D., (2017). "An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis", Applied Mathematical Modelling, Vol. 42, pp. 693–704. https://doi.org/10.1016/j.apm.2016.10.048.
Zhang, H., and Deng, Y., (2018). "Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory", Advances in Mechanical Engineering, Vol. 10, No. 11, 168781401880918. https://doi.org/10.1177/1687814018809184.
Zhang, L., Wu, X., Zhu, H., and Abou Rizk, S.M., (2017). "Perceiving safety risk of buildings adjacent to tunneling excavation: An information fusion approach", Automation in Construction, Vol. 73, pp. 88–101. https://doi.org/10.1016/j.autcon.2016.09.003.