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A novel cause analysis approach of grey reasoning Petri net based on matrix operations

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Abstract

Cause analysis makes great contributions to identifying the priorities of the causes in fault diagnosis system. A fuzzy Petri net (FPN) is a preferable model for knowledge representation and reasoning and has become an effective fault diagnosis tool. However, the existing FPN has some limitations in cause analysis. It is criticized for the inability to fully consider incomplete and unknown knowledge in uncertain situations. In this paper, an enhanced grey reasoning Petri net (EGRPN) based on matrix operations is presented to address the limitations and improves the flexibility of the existing FPN. The proposed EGRPN model uses grey numbers to handle the greyness and inaccuracy of uncertain knowledge. Then, the EGRPN inference algorithm is executed based on the matrix operations, which can express the relevance of uncertain events in the form of grey numbers and improve the reliability of the knowledge reasoning process. Finally, industrial examples of cause diagnosis are used to illustrate the feasibility and reliability of the EGRPN model. The experimental results show that the new EGRPN model is promising for cause analysis.

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References

  1. Seixas F, Flavio L, Zadrozny B, Laks J (2014) A Bayesian network decision model for supporting the diagnosis of dementia, Alzheimers disease and mild cognitive impairment. Comput Biol Med 51:140–158

    Article  Google Scholar 

  2. Zhao Y, Xiao F, Wang S (2013) An intelligent chiller fault detection and diagnosis methodology using Bayesian belief network. Energy and Buildings 57:278–288

    Article  Google Scholar 

  3. Zhang Q (2015) Dynamic uncertain causality graph for knowledge representation and reasoning: continuous variable, uncertain evidence, and failure forecast. IEEE Transactions on Systems, Man, and Cybernetics 45:990–1003

    Article  Google Scholar 

  4. Zhang Q, Geng S (2015) Dynamic uncertain causality graph applied to dynamic fault diagnoses of large and complex systems. IEEE Trans Reliab 64:910–927

    Article  Google Scholar 

  5. Ben AJ, Fnaiech N, Saidi L (2015) Application of empirical mode decomposition and artificial neural network for automatic bearing fault diagnosis based on vibration signals. Appl Acoust 89:16–27

    Article  Google Scholar 

  6. Ahmed R, Sayed ME, Gadsden SA (2015) Automotive Internal-Combustion-Engine fault detection and classification using artificial neural network techniques. IEEE Trans Veh Technol 64:21–33

    Article  Google Scholar 

  7. Yang B, Li H (2018) A novel dynamic timed fuzzy Petri nets modeling method with applications to industrial processes. Expert Syst Appl 97:276–289

    Article  Google Scholar 

  8. Liu HC, You JX, You XY (2016) Linguistic reasoning petri nets for knowledge representation and reasoning. IEEE Transactions on Systems, Man, and Cybernetics:, Systems 46:499–511

    Article  Google Scholar 

  9. Liu HC, Lin QL, Mao LX (2013) Dynamic adaptive fuzzy petri nets for knowledge representation and reasoning. IEEE Transactions on Systems, Man, and Cybernetics: Systems 43(6):1399–1410

    Article  Google Scholar 

  10. Jia Q, Li SJ (2020) Process monitoring and fault diagnosis based on a regular vine and Bayesian network. Industrial & Engineering Chemistry Research 59(26):12144–12155

    Article  Google Scholar 

  11. Cai B, Liu Y, Xie M (2017) A dynamic-Bayesian-network-based fault diagnosis methodology considering transient and intermittent faults. IEEE Trans Autom Sci Eng 14(1):276–285

    Article  Google Scholar 

  12. Boutselis P, Mcnaught K (2019) Using Bayesian networks to forecast spares demand from equipment failures in changing service logistics context. International Journal of Production Economics 209:325–333

    Article  Google Scholar 

  13. Yu W, Zhao C (2019) Online fault diagnosis for industrial processes with Bayesian network-based probabilistic ensemble learning strategy. IEEE Transactions on Automation Science and Engineering 16(4):1922–1932

    Article  Google Scholar 

  14. Zhang Q, Dong C, Cui Y (2014) Dynamic uncertain causality graph for knowledge representation and probabilistic reasoning: statistics base, matrix, and application. IEEE Transactions on Neural Networks and Learning Systems 25(4):645–663

    Article  Google Scholar 

  15. Zhao Y, Dong CL, Zhang Q (2016) Fault diagnostics using DUCG in complex systems. Journal of Tsinghua University 56(05):530–537

    Google Scholar 

  16. Zou M, Wang HC (2018) An algorithm for solving minimal cut set of causality diagram by petri net model. Journal of Chongqing Normal University 35(03):130–136

    MATH  Google Scholar 

  17. Masud M, Eldin R (2020) Convolutional neural network-based models for diagnosis of breast cancer. Neural Comput & Applic. https://doi.org/10.1007/s00521-020-05394-5

  18. Liu R, Yang B, Enrico Z (2018) Artificial intelligence for fault diagnosis of rotating machinery: a review. Mechanical Systems and Signal Processing 108:33–47

    Article  Google Scholar 

  19. Chen G, Liu M, Chen J (2020) Frequency-temporal-logic-based bearing fault diagnosis and fault interpretation using Bayesian optimization with Bayesian neural networks. Mechanical Systems and Signal Processing. https://doi.org/10.1016/j.ymssp.2020.106951

  20. Yuan CL, Liao YY, Kong LS (2020) Fault diagnosis method of distribution network based on time sequence hierarchical fuzzy petri nets. Electric Power Systems Research https://doi.org/10.1016/J.EPSR.2020.106870

  21. Wang Y, Qiu D (2016) A method of synthetical fault diagnosis for power system based on fuzzy hierarchical Petri net. 2016 IEEE international conference on mechatronics and automation, 254–258

  22. Teh CY, Kerk YW, Tay KM (2018) On modeling of data-driven monotone zero-order TSK fuzzy inference systems using a system identification framework. IEEE Transactions on Fuzzy Systems 26(6):3860–3874

    Google Scholar 

  23. Liu HC, Liu L, Lin QL (2013) Knowledge acquisition and representation using fuzzy evidential reasoning and dynamic adaptive fuzzy Petri nets. IEEE Transactions on Systems, Man, and Cybernetics-Part B:Cybernetics 43:1059–1072

    Google Scholar 

  24. Gao MM, Zhou MC, Huang XG (2003) Fuzzy reasoning Petri nets. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 33:314–324

    Article  Google Scholar 

  25. Sun J, Qin SY, Song YH (2004) Fault diagnosis of electric power systems based on fuzzy Petri nets. IEEE Transactions on Power Systems 19:2053–2059

    Article  Google Scholar 

  26. Luo X, Kezunovic M (2008) Implementing fuzzy reasoning Petri-nets for fault section estimation. IEEE Transactions on Power Delivery 23:676–685

    Article  Google Scholar 

  27. Chen WL, Kan CD, Lin CH (2014) A rule-based decision-making diagnosis system to evaluate arteriovenous shunt stenosis for hemodialysis treatment of patients using fuzzy petri nets. IEEE Journal of Biomedical and Health Informatics 18(2):703–713

    Article  Google Scholar 

  28. Liu HC, Liu L, Lin QL (2013) Knowledge acquisition and representation using fuzzy evidential reasoning and dynamic adaptive fuzzy Petri nets. IEEE Transactions on Systems, Man, and Cybernetics -Part B: Cybernetics 43:1059–1072

    Google Scholar 

  29. Liu HC, Luan X, Li ZW (2017) Linguistic Petri nets based on cloud model theory for knowledge representation and reasoning. IEEE Trans Knowl Data Eng 30(4):717–728

    Article  Google Scholar 

  30. Liu HC, Lin QL, Ren ML (2013) Fault diagnosis and cause analysis using fuzzy evidential reasoning approach and dynamic adaptive fuzzy Petri nets. Comput Ind Eng 66(4):899–908

    Article  Google Scholar 

  31. Hu HS, Li ZW, Al-Ahmari A (2011) Reversed fuzzy Petri nets and their application for fault diagnosis. Comput Ind Eng 60:505–510

    Article  Google Scholar 

  32. Zhou J (2020) A fuzzy Petri-net approach for fault analysis considering factor influences. IEEE Access 8:72229–722238

    Article  Google Scholar 

  33. Roy SK, Midya S (2019) Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment. Appl Intell 49:3524–3538

    Article  Google Scholar 

  34. Song Y, Wang X, Zhu J (2018) Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets. Appl Intell 48(11):3950–3962

    Article  Google Scholar 

  35. Cuong BC, Kreinovich V (2014) Picture fuzzy sets. J Comput Sci Cybern 30:409–420

    Google Scholar 

  36. Son LH, Van VP, Van HP (2017) Picture inference system: a new fuzzy inference system on picture fuzzy set. Appl Intell 46:652–669

  37. Wang L, Zhang H, Wang J (2018) Picture fuzzy multicriteria group decision making method to hotel building energy efficiency retrofit project selection. RAIRO-Oper Res. https://doi.org/10.1051/ro/2019004

  38. Ye J, Dang Y, Ding S (2019) A novel energy consumption forecasting model combining an optimized DGM (1,1) model with interval grey numbers. Journal of Cleaner Production 229(20): 256–267

    Article  Google Scholar 

  39. Li Q, Zhao N (2015) Stochastic interval grey number VIKOR method based on prospect theory. Grey Systems 5(1):105–116

    Article  Google Scholar 

  40. Liu HC, Luan X, Lin W (2019) Grey reasoning Petri nets for large group knowledge representation and reasoning. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2019.2949770

  41. Deng JL (1982) Control problems of grey systems. Systems and Control Letters 1(5):288–294

    Article  MathSciNet  MATH  Google Scholar 

  42. Liu S, Fang Z, Yang Y (2012) General grey numbers and their operations. Grey Systems: Theory and Application 2(3):341–349

    Article  Google Scholar 

  43. Amirian H, Sahraeian R (2017) Solving a grey project selection scheduling using a simulated shuffled frog leaping algorithm. Comput Ind Eng 107:141–149

    Article  Google Scholar 

  44. Mishra S, Datta S, Mahapatra SS (2013) Grey-based and fuzzy TOPSIS decision-making approach for agility evaluation of mass customization systems. Benchmarking: An International Journal 20(4):440–462

    Article  Google Scholar 

  45. Lin YH, Lee PC, Ting HI (2008) Dynamic multi-attribute decision making model with grey number evaluations. Expert Systems with Applications 35(4):1638–1644

    Article  Google Scholar 

  46. Stanujkic D, Magdalinovic N, Jovanovic R (2012) An objective multi-criteria approach to optimization using MOORA method and interval grey numbers. Technological and Economic Development of Economy 18 (2):331–363

    Article  Google Scholar 

  47. Salmeron JL, Papageorgiou EI (2014) Fuzzy grey cognitive maps and nonlinear Hebbian learning in process control. Appl Intell 41:223–234

    Article  Google Scholar 

  48. Yue WC, Gui WH, Xie YF (2020) Experiential knowledge representation and reasoning based on linguistic Petri nets with application to aluminum electrolysis cell condition identification. Information Sciences 529:141–165

    Article  MathSciNet  Google Scholar 

  49. Yue WC, Gui WH, Chen XF (2019) Knowledge representation and reasoning using self-learning interval type-2 fuzzy Petri nets and extended TOPSIS. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-019-00940-7

  50. Liu HC, Lin QL, Ren ML (2013) Fault diagnosis and cause analysis using fuzzy evidential reasoning approach and dynamic adaptive fuzzy Petri nets. Comput Ind Eng 66(4):899–908

    Article  Google Scholar 

  51. Zhou J, Reniers G (2017) Analysis of emergency response actions for preventing fire-induced domino effects based on an approach of reversed fuzzy Petri-net. J Loss Prevention Process Ind 47:169–173

    Article  Google Scholar 

  52. Dong C, Zhang Q (2020) The cubic dynamic uncertain causality graph: a methodology for temporal process modeling and diagnostic logic inference. IEEE Transactions on Neural Networks and Learning Systems 31:4239–4253

    Article  MathSciNet  Google Scholar 

  53. Ning DP, Zhang Z, Qiu K (2020) Efficacy of intelligent diagnosis with a dynamic uncertain causality graph model for rare disorders of sex development. Frontiers of Medicine 14(4):498–505

    Article  Google Scholar 

  54. Li L, Yue WC (2020) Dynamic uncertain causality graph based on Intuitionistic fuzzy sets and its application to root cause analysis. Applied Intelligence 50(1):241–255

    Article  Google Scholar 

  55. Li L, Xie YF, Chen XF (2020) Dynamic uncertain causality graph based on cloud model theory for knowledge representation and reasoning. Int J Mach Learn Cybern 11(8):1781–1799

    Article  Google Scholar 

  56. Beloslav R, Krassimir T (2010) Operation division by n over intuitionistic fuzzy sets. Notes on Instuitionistic Fuzzy Sets 16:1–4

    MATH  Google Scholar 

  57. Chen T (2007) Remarks on the subtraction and division operations over intuitionistic fuzzy sets and interval-valued fuzzy sets. International Journal of Fuzzy Systems 9:169–172

    MathSciNet  Google Scholar 

Download references

Acknowledgements

This project is partly supported by the National Natural Science Foundation of China (Grant Nos. 61725306, 61751312, 61773405 and 61533020), the Fundamental Research Funds for the Central Universities of Central South University (2019zzts063), and the Engineering Research Center for Metallurgical Automation and Measurement Technology of Ministry of Education, Wuhan University of Science and Technology, Wuhan, China under the Grant No. MADT0F2019B01.

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Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, China

    Li Li, Yongfang Xie, Lihui Cen & Zhaohui Zeng

  2. Peng Cheng Laboratory, Shenzhen, 518000, China

    Li Li

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  1. Li Li
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Correspondence to Lihui Cen.

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Li, L., Xie, Y., Cen, L. et al. A novel cause analysis approach of grey reasoning Petri net based on matrix operations. Appl Intell 52, 1–18 (2022). https://doi.org/10.1007/s10489-021-02377-4

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