Abstract
Fault diagnosis (the process of finding out whether system or equipment is in fault and where the corresponding fault is by using various inspection and testing method) on the engine is a typical information fusion (the process of integrating multiple data sources to produce more consistent, accurate, and useful information than that provided by any individual data source) problem where the information can be obtained from engine vibration, temperature, pressure, etc. Due to the efficiency of data fusion, Dempster–Shafer evidence theory is widely used in fault diagnosis. One key step to using evidence theory is to obtain the so-called basic probability assignment (BPA), or belief function. In this article, a new mathematical framework is presented to determine weighted BPA (WBPA). This WBPA function is obtained by weighting the distance between sample data and empirical data. With the assumption that the empirical data are normally distributed, the weighting factor can be determined. Then, the WBPA can be combined with D–S evidence theory to determine the status of the engine. Finally, a case in fault diagnosis and comparison with Song and Jiang (Adv Mech Eng 8(10):1–16, 2016) method illustrate the efficiency of the proposed method.
Similar content being viewed by others
Data availability statement
The authors confirm that the data sources in this paper are public.
References
Arqub OA (2015) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl 28(7):1–20
Arqub OA, Al-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302
Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21:7191C7206
Arqub OA, Pinto C, Lpez RR, Ertrk VS (2018) Fuzzy calculus theory and its applications. Complexity 1–2(06):2018
Basir O, Yuan X (2007) Engine fault diagnosis based on multi-sensor information fusion using Dempster–Shafer evidence theory. Inf Fusion 8(4):379–386
Chatterjee K, Zavadskas EK, Tamosaitiene J, Adhikary K, Kar S (2017) A hybrid mcdm technique for risk management in construction projects. Symmetry 10(2):46
Chatterjee K, Pamucar D, Zavadskas EK (2018) Evaluating the performance of suppliers based on using the r’amatel-mairca method for green supply chain implementation in electronics industry. J Clean Prod 184:101–129
Chen L, Deng Y (2018a) A new failure mode and effects analysis model using Dempster–Shafer evidence theory and grey relational projection method. Eng Appl Artif Intell 76:13–20
Chen L, Deng X (2018b) A modified method for evaluating sustainable transport solutions based on ahp and Dempster–Shafer evidence theory. Appl Sci 8(4):Article ID 563
Cui H, Liu Q, Zhang J, Kang B (2019) An improved deng entropy and its application in pattern recognition. IEEE Access 7:18284–18292
Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38(2):325–339
Deng X, Deng Y (2019) D-AHP method with different credibility of information. Soft Comput 23(2):683–691
Deng X, Jiang W (2018a) An evidential axiomatic design approach for decision making using the evaluation of belief structure satisfaction to uncertain target values. Int J Intell Syst 33(1):15–32
Deng X, Jiang W (2018b) Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures. Ann Nucl Energy 117:183–193
Deng X, Jiang W (2019) D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment. Int J Approx Reason 106:194–213
Dutta P (2017) Modeling of variability and uncertainty in human health risk assessment. MethodsX 4:76–85
Dutta P (2018) An uncertainty measure and fusion rule for conflict evidences of big data via Dempster–Shafer theory. Int J Image Data Fusion 9(2):152–169
Fu C, Xu DL, Yang SL (2016) Distributed preference relations for multiple attribute decision analysis. J Oper Res Soc 67(3):457–473
Fu C, Xu DL, Xue M (2018) Determining attribute weights for multiple attribute decision analysis with discriminating power in belief distributions. Knowl Based Syst 143(1):127–141
Gao X, Deng Y (2019) The negation of basic probability assignment. IEEE Access. https://doi.org/10.1109/ACCESS.2019.2901932
Gong Y, Su X, Qian H, Yang N (2018) Research on fault diagnosis methods for the reactor coolant system of nuclear power plant based on D–S evidence theory. Ann Nucl Energy 112:395–399
Han Y, Deng Y (2018a) A hybrid intelligent model for assessment of critical success factors in high risk emergency system. J Ambient Intell Humaniz Comput 9(6):1933–1953
Han Y, Deng Y (2018b) An enhanced fuzzy evidential DEMATEL method with its application to identify critical success factors. Soft Comput 22(15):5073–5090
Han Y, Deng Y (2019) A novel matrix game with payoffs of maxitive belief structure. Int J Intell Syst 34(4):690–706
Hou D, He H, Huang P, Zhang G, Loaiciga H (2013) Detection of water-quality contamination events based on multi-sensor fusion using an extented Dempster–Shafer method. Meas Sci Technol 24(5):055801
Janghorbani A, Moradi MH (2017) Fuzzy evidential network and its application as medical prognosis and diagnosis models. J Biomed Inform 72:96–107
Jiang W (2018) A correlation coefficient for belief functions. Int J Approx Reason 103:94–106
Jiang W, Wei B, Xie C, Zhou D (2016) An evidential sensor fusion method in fault diagnosis. Adv Mech Eng 8(3):1–7
Kahraman C, Onar SC, Oztaysi B (2015) Fuzzy multicriteria decision-making: a literature review. Int J Comput Intell Syst 8(4):637–666
Kang B, Deng Y, Hewage K, Sadiq R (2018) A method of measuring uncertainty for Z-number. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2018.2868496
Kang B, Zhang P, Gao Z, Chhipi-Shrestha G, Hewage K, Sadiq R (2019) Environmental assessment under uncertainty using Dempster–Shafer theory and z-numbers. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-019-01228-y
Khazaee M, Ahmadi H, Omid M, Moosavian A, Khazaee M (2014) Classifier fusion of vibration and acoustic signals for fault diagnosis and classification of planetary gears based on Dempster–Shafer evidence theory. ARCHIVE Proc Inst Mech Eng Part E J Process Mech Eng 1989–1996 228(1):21–32
Lee JM, Kim SJ, Hwang Y, Song CS (2004) Diagnosis of mechanical fault signals using continuous hidden Markov model. J Sound Vib 276(3C5):1065–1080
Li Y, Deng Y (2018) Generalized ordered propositions fusion based on belief entropy. Int J Comput Commun Control 13(5):792–807
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
Liu YT, Pal NR, Marathe AR, Lin CT (2018) Weighted fuzzy Dempster–Shafer framework for multimodal information integration. IEEE Trans Fuzzy Syst 26(1):338–352
Mcclean S, Scotney B, Shapcott M (2001) Aggregation of imprecise and uncertain information in databases. IEEE Trans Knowl Data Eng 13(6):902–912
Mo H, Deng Y (2018) A new MADA methodology based on D numbers. Int J Fuzzy Syst 20(8):2458–2469
Mo H, Deng Y (2019) An evaluation for sustainable mobility extended by D numbers. Technol Econ Dev Econ (accepted)
Momani S, Arqub OA, Al-Mezel S, Kutbi M (2015) Existence and uniqueness of fuzzy solution for the nonlinear second-order fuzzy Volterra integrodifferential equations. J Comput Anal Appl 21:08
Nakamori S, Caballero-Aguila R, Hermoso-Carazo A, Linares-Perez J (2003) Linear recursive discrete-time estimators using covariance information under uncertain observations. Signal Process 83(7):1553–1559
Offer GJ, Yufit V, Howey DA, Wu B, Brandon NP (2012) Module design and fault diagnosis in electric vehicle batteries. J Power Sources 206(206):383–392
Omerdic E, Roberts G (2004) Thruster fault diagnosis and accommodation for open-frame underwater vehicles. Control Eng Pract 12(12):1575–1598
Palash D, Hazarika GC (2017) Construction of families of probability boxes and corresponding membership functions at different fractiles. Expert Syst 34(3):e1220
Porebski S, Straszecka E (2018) Extracting easily interpreted diagnostic rules. Inf Sci 426:19–37
Purushotham V, Narayanan S, Prasad SAN (2005) Multi-fault diagnosis of rolling bearing elements using wavelet analysis and hidden Markov model based fault recognition. NDT E Int 38(8):654–664
Seiti H, Hafezalkotob A (2018) Developing pessimistic-optimistic risk-based methods for multi-sensor fusion: an interval-valued evidence theory approach. Appl Soft Comput 72:609–623
Seiti H, Hafezalkotob A, Najafi SE, Khalaj M (2018) A risk-based fuzzy evidential framework for FMEA analysis under uncertainty: an interval-valued DS approach. J Intell Fuzzy Syst 35:1–12
Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton
Song M, Jiang W (2016) Engine fault diagnosis based on sensor data fusion using evidence theory. Adv Mech Eng 8(10):1–16
Su X, Li L, Shi F, Qian H (2018) Research on the fusion of dependent evidence based on mutual information. IEEE Access 6:71839–71845
Su X, Li L, Qian H, Sankaran M, Deng Y (2019) A new rule to combine dependent bodies of evidence. Soft Comput. https://doi.org/10.1007/s00500-019-03804-y
Sun R, Deng Y (2019) A new method to identify incomplete frame of discernment in evidence theory. IEEE Access 7(1):15547–15555
Tabassian M, Ghaderi R, Ebrahimpour R (2012) Combining complementary information sources in the Dempster–Shafer framework for solving classification problems with imperfect labels. Knowl Based Syst 27(3):92–102
Wang Y, Deng Y (2018) Base belief function: an efficient method of conflict management. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-018-1099-2
Wang J, Qiao K, Zhang Z (2019) An improvement for combination rule in evidence theory. Future Gener Comput Syst 91:1–9
Xiao F (2017a) An improved method for combining conflicting evidences based on the similarity measure and belief function entropy. Int J Fuzzy Syst 1:1–11
Xiao F (2017b) A novel evidence theory and fuzzy preference approach-based multi-sensor data fusion technique for fault diagnosis. Sensors 17(11):1–20
Xiao F (2018a) A hybrid fuzzy soft sets decision making method in medical diagnosis. IEEE Access 6:25300–25312. https://doi.org/10.1109/ACCESS.2018.2820099
Xiao F (2018b) A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers. Eng Appl Artif Intell 71(2018):216–225
Xiao F (2018c) Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy. Inf Fusion. https://doi.org/10.1016/j.inffus.2018.04.003
Xiao F (2019) A multiple criteria decision-making method based on D numbers and belief entropy. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-019-00620-2
Xu C, Zhang H, Peng D, Yu Y, Xu C, Zhang H (2012) Study of fault diagnosis of integrate of D–S evidence theory based on neural network for turbine. Energy Procedia 16:2027–2032
Yao X-H, Fu J-Z, Chen Z-C (2009) Intelligent fault diagnosis using rough set method and evidence theory for nc machine tools. Int J Comput Integr Manuf 22(5):472–482
Yin L, Deng X, Deng Y (2019) The negation of a basic probability assignment. IEEE Trans Fuzzy Syst 27(1):135–143
Zhang H, Deng Y (2018a) Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory. Adv Mech Eng. https://doi.org/10.1177/1687814018809184
Zhang W, Deng Y (2018b) Combining conflicting evidence using the DEMATEL method. Soft Comput. https://doi.org/10.1007/s00500-018-3455-8
Zhang X, Mahadevan S (2017) Aircraft re-routing optimization and performance assessment under uncertainty. Decis Support Syst 96:67–82
Zhang X, Mahadevan S, Deng X (2017) Reliability analysis with linguistic data: an evidential network approach. Reliab Eng Syst Saf 162:111–121
Zhou D, Qian P, Chhipishrestha G, Li X, Zhang K, Hewage K, Sadiq R (2017) A new weighting factor in combining belief function. PloS ONE 12(5):e0177695
Acknowledgements
The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61573290, 61503237), and China Scholarship Council.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
Hepeng Zhang declares that he has no conflict of interest. Yong Deng declares that he has no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, H., Deng, Y. Weighted belief function of sensor data fusion in engine fault diagnosis. Soft Comput 24, 2329–2339 (2020). https://doi.org/10.1007/s00500-019-04063-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04063-7