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Study on the construction and application of discrete space fault tree modified by fuzzy structured element

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Abstract

Some fault data in an actual system operation has the strong discretization and big data characteristics. Meanwhile, the external factors affect the system reliability, and the change of factors may lead to the change of system reliability. At present, the methods in safety system engineering lack the ability to process the multi-factor influence and fault big data simultaneously. But these are the general problems that the actual system reliability analysis must face to be resolved. In order to solve the problems, on the basis of Discrete Space Fault Tree (DSFT), the Fuzzy Structured Element method is introduced to construct the Fuzzy Structured Element Discrete Space Fault Tree (EDSFT). The method can analyze the multi-factor influence on system reliability with DSFT, and use Fuzzy Structured Element (E) to denote the discrete characteristics of fault big data. The results of EDSFT with E can preserve the characteristics of the original fault data distribution and lay the foundation for the analysis of fault big data. The research is particularly suitable for the analysis of system reliability under the fault big data and multi-factor influence.

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Abbreviations

\(P_{i}^{{d_{k} }} (x_{k} )\) :

Characteristic function of component fault probability

i :

ith component

d k :

kth factor name

x k :

Value of factor dk, k = 1–n

n :

Number of influencing factors

\(P_{i} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Component fault probability distribution

\(P_{T} (x_{1} ,x_{2} , \ldots x_{n} )\) :

System fault probability distribution

\(P_{i}^{{d_{k} }}\) :

Component fault probability distribution trend

\(P_{T}^{{d_{k} }}\) :

System fault probability distribution trend

\(I_{g} (i)\) :

Probability importance distribution

\(I_{g}^{c} (i)\) :

Criticality importance distribution

\(FI_{i} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Component factor (joint) importance distribution

\(FI_{T} (x_{1} ,x_{2} , \ldots x_{n} )\) :

System factor (joint) importance distribution

\(ZI_{g} (i)\) :

Component domain probability importance

\(ZI_{g}^{c} (i)\) :

Component domain criticality importance

\(P_{1}^{t} (t)\;{\text{and}}\;P_{1}^{c} (c)\) :

Characteristic function of X1 for t and c respectively

\(P_{i}^{t} (t)\;{\text{and}}\;P_{i}^{c} (c)\) :

Characteristic function of Xi for t and c respectively

C :

Sinusoid cycle

c 0 :

Horizontal offset of sine curve

A :

Vertical offset of sine curve

λ :

Fault rate

\(P_{1 - 5}\) :

Abbreviation for \(P_{1 - 5} (t,c)\), respectively, the fault probability of component \(X_{1 - 5}\)

\(\prod\) :

‘and’ relationship among the components

\(\coprod\) :

‘or’ relationship among the components

\(\tilde{f}\) :

Fuzzy valued function on X

E(x):

Membership function

\(\tilde{f}(x) = g(x,E)\) :

Fuzzy valued function generated by Fuzzy Structured Element E

\(\bar{x}\;{\text{and}}\;\bar{y}\) :

Average value of observation data

\(\hat{\sigma }^{2}\) :

Average dispersion of variable y

N :

Number of data

\(\hat{a}_{k} \sim \hat{a}_{0} \;{\text{and}}\;\hat{b}_{p} \sim \hat{b}_{0}\) :

Coefficients determined by fitting

α and β :

Maximum fitting times

E :

Fuzzy Structured Element

\(\hat{f}(x)\) :

Kernel function of fuzzy valued function

\(\hat{\omega }(x)\) :

Fluctuation of data, \(\hat{\omega }_{i}^{t} (t)\) and \(\hat{\omega }_{i}^{c} (c)\) are the fluctuation of data for t and c respectively

\(\hat{f}_{i}^{t} (t)\;{\text{and}}\;\hat{f}_{i}^{c} (c)\) :

Kernel function of Xi for t and c respectively

\(\mathop {\hat{f}_{i}^{t} }\limits_{\text{U}} (t),\;\mathop {\hat{f}_{i}^{t} }\limits_{\text{D}} (t)\;{\text{and}}\;\mathop {\hat{f}_{i}^{c} }\limits_{\text{U}} (c),\;\mathop {\hat{f}_{i}^{c} }\limits_{\text{D}} (c)\) :

Up and down envelope function of Xi for t and c respectively

\(f(E) \to E(x)\) :

\(f(E)\) After Fuzzy Structured Element, the domain where the variable falls in \(E(x)\), \(- 1 \le x < 0\), x = 0, \(0 < x \le 1\)

\(\tilde{F}_{i}^{t} (t)\;{\text{and}}\;\tilde{F}_{i}^{c} (c)\) :

Fuzzy Structured Element Characteristic Function of Xi for t and c respectively

\(\tilde{F}_{i} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Fuzzy Structured Element Component Fault Probability Distribution of Xi, such as \(\tilde{F}_{i} (t,c)\)

\(\tilde{F}_{T} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Fuzzy Structured Element System Fault Probability Distribution, such as \(\tilde{F}_{T} (t,c)\)

\(\tilde{I}_{g} (i)\) :

Fuzzy Structured Element Probability Importance Distribution

\(\tilde{I}_{g}^{c} (i)\) :

Fuzzy Structured Element Criticality Importance Distribution

\(\tilde{F}_{T}^{{d_{k} }}\) :

Fuzzy Structured Element System Fault Probability Distribution Trend

\(Z\tilde{I}_{g} (i)\) :

Fuzzy Structured Element Component Domain Probability Importance

\(Z\tilde{I}_{g}^{c} (i)\) :

Fuzzy Structured Element Component Domain Criticality Importance

\(F\tilde{I}_{i} (x_{k} )\) :

Fuzzy Structured Element Component Factor Importance Distribution

\(F\tilde{I}_{T} (x_{k} )\) :

Fuzzy Structured Element System Factor Importance Distribution

\(F\tilde{I}_{i} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Fuzzy Structured Element Component Factor Joint Importance Distribution

\(F\tilde{I}_{T} (x_{1} ,x_{2} , \ldots x_{n} )\) :

Fuzzy Structured Element System Factor Joint Importance Distribution

\(\tilde{F}_{1 - 5}\) :

Abbreviation for \(\tilde{F}_{1\sim 5} (t,c)\), respectively, \(P_{1\sim 5} (t,c)\) modified by Fuzzy Structured Element

\(\mu = 1 - n\) :

Number of factors in Factor Joint Importance Distribution

K j(j = 1,2,…,r):

The jth set in r minimal cut set of fault tree

E i/E ii :

ith/iith basic event in Kj, basic event is equivalent to component

subscript k :

Corresponding parameters of the kth factors

c :

Using temperature

t :

Using time

T :

Instance system

X 1–5 :

5 components in the instance system

References

  1. Cui, T.-J.: The Construction of Space Fault Tree Theory and Research. Liaoning Technical University, Fuxin (2015)

    Google Scholar 

  2. Saradarzade, M., Sanaye-Pasand, M.: An accurate fuzzy logic-based fault classification algorithm using voltage and current phase sequence components. Int. Trans. Electr. Energy Syst. 25(10), 2275–2288 (2015)

    Google Scholar 

  3. Mansour, M.M., Wahab, M.A.A., Soliman, W.M.: Fault diagnosis system for large power generation station and its transmission lines based on fuzzy relations. Int. Trans. Electr. Energy Syst. 25(5), 753–769 (2015)

    Google Scholar 

  4. Cui, Y., Shi, J., Wang, Z.: Analog circuits fault diagnosis using multi-valued Fisher’s fuzzy decision tree (MFFDT). Int. J. Circuit Theory Appl. 44(1), 240–260 (2015)

    Google Scholar 

  5. Ebrahimian, H., Gollou, A.R., Bayramzadeh, F., Rahimi, A.: Multimachine power system stabilizer based on optimal multistage fuzzy PID attendant honey bee mating optimization. Complexity 21(6), 234–245 (2016)

    MathSciNet  Google Scholar 

  6. Akbarimajd, A., Yousefi, N.: A novel of fuzzy PSS based on new objective function in multimachine power system. Complexity 21(6), 288–298 (2016)

    MathSciNet  Google Scholar 

  7. Xu, J., Meng, Z., Xu, L.: Integrated system health management-based fuzzy on-board condition prediction for manned spacecraft avionics. Qual. Reliab. Eng. Int. 32(1), 153–165 (2016)

    Google Scholar 

  8. Yao, L., Lei, C.: Fault Diagnosis and sliding mode fault tolerant control for non-gaussian stochastic distribution control systems using T-s fuzzy model. Asian J. Control 19(2), 636–646 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Huai-Ning, Wu: H∞ fuzzy control design of discrete-time nonlinear active fault-tolerant control systems. Int. J. Robust Nonlinear Control 19(10), 1129–1149 (2009)

    MathSciNet  MATH  Google Scholar 

  10. Kaewpraek, N., Assawinchaichote, W.: H∞ fuzzy state-feedback control plus state-derivative-feedback control synthesis for photovoltaic systems. Asian J. Control 18(4), 1441–1452 (2016)

    MathSciNet  MATH  Google Scholar 

  11. Wang, W., Wang, D., Peng, Z., Wang, H.: Cooperative adaptive fuzzy output feedback control for synchronization of nonlinear multi-agent systems in the presence of input saturation. Asian J. Control 18(2), 619–630 (2016)

    MathSciNet  MATH  Google Scholar 

  12. Dridger, A., Caylak, I., Mahnken, R.: A linear elastic fuzzy finite element method with two fuzzy input parameters. PAMM 16(1), 667–668 (2016)

    Google Scholar 

  13. Shahnazi, R., Zhao, Q.: Adaptive fuzzy descriptor sliding mode observer-based sensor fault estimation for uncertain nonlinear systems. Asian J. Control 18(4), 1478–1488 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Kar, I.: An indirect adaptive fuzzy control scheme for a class of nonlinear systems. Asian J. Control 18(3), 1153–1158 (2016)

    MathSciNet  MATH  Google Scholar 

  15. Zhong, Z., Shao, Z., Chen, T.: Decentralized piecewise fuzzy. ℋ∞ output feedback control for large-scale nonlinear systems with time-varying delay. Complexity 21(S2), 268–288 (2016)

    MathSciNet  Google Scholar 

  16. Li, P.F., Ning, Y.W., Jing, J.F.: Research on the detection of fabric color difference based on T-S fuzzy neural network. Color Res. Appl. (2017). https://doi.org/10.1002/col.22113

    Article  Google Scholar 

  17. Wei, Y., Watada, J., Pedrycz, W.: Design of a qualitative classification model through fuzzy support vector machine with type-2 fuzzy expected regression classifier preset. IEEJ Trans. Electr. Electron Eng. 11(3), 348–356 (2016)

    Google Scholar 

  18. Wang, L., Wang, W.: H∞ fault detection for two-dimensional T-S fuzzy systems in FM second model. Asian J. Control 17(2), 554–568 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Zio, E., Baraldi, P., Popescu, I.C.: A fuzzy decision tree for fault classification. Risk Anal. 28(1), 49–67 (2015)

    Google Scholar 

  20. Anzilli, L., Facchinetti, G.: A fuzzy quantity mean-variance view and its application to a client financial risk tolerance model. Int. J. Intell. Syst. 31(10), 963–988 (2016)

    Google Scholar 

  21. Selim, H., Yunusoglu, M.G., Yılmaz Balaman, Ş.: A dynamic maintenance planning framework based on fuzzy TOPSIS and FMEA: application in an international food company. Qual. Reliab. Eng. Int. 32(3), 795–804 (2016)

    Google Scholar 

  22. Feng, X., Huo, S., Zhang, J., Shen, H.: Fuzzy predictive temperature control for a class of metallurgy lime kiln models. Complexity 21(S2), 249–258 (2016)

    Google Scholar 

  23. dos Santos Guimarães, R., Strafacci, V., Tasinaffo, P.M.: Implementing fuzzy logic to simulate a process of inference on sensory stimuli of deaf people in an e-learning environment. Comput. Appl. Eng. Educ. 24(2), 320–330 (2016)

    Google Scholar 

  24. Banakar, A., Zareiforoush, H., Baigvand, M., Montazeri, M., Khodaei, J., Behroozi-Khazaei, N.: Combined application of decision tree and fuzzy logic techniques for intelligent grading of dried figs. J. Food Process Eng. (2016). https://doi.org/10.1111/jfpe.12456

    Article  Google Scholar 

  25. Lu, S.-L., Tsai, C.-F.: Petroleum demand forecasting for Taiwan using modified fuzzy-grey algorithms. Expert Syst. 33(1), 60–69 (2016)

    Google Scholar 

  26. Soto, C., Robles‐Baldenegro, M.E., López, V., Camalich, J.A..: MQDM: an iterative fuzzy method for group decision making in structured social networks. Int. J. Intell. Syst. 32(1), 17–30 (2017)

    Google Scholar 

  27. Cui, T.-J., Wang, P.-Z., Li, S.-S.: The function structure analysis theory based on the factor space and space fault tree. Clust. Comput. 20(2), 1387–1398 (2017)

    Google Scholar 

  28. Cui, T.-J., Li, S.-S.: Study on the relationship between system reliability and influencing factors under big data and multi-factors. Comput, Clust (2017). https://doi.org/10.1007/s10586-017-1278-5

    Book  Google Scholar 

  29. Li, S.-S., Cui, T.-J., Liu, J.: Study on the construction and application of cloudization space fault tree. Clust. Comput. (2017). https://doi.org/10.1007/s10586-017-1398-y

    Article  Google Scholar 

  30. Cui, T.-J., Li, S.-S.: Deep learning of system reliability under multi-factor influence based on space fault tree. Neural Comput. Appl. (2018). https://doi.org/10.1007/s00521-018-3416-2

    Article  Google Scholar 

  31. Cui, T.-J., Ma, Y.-D.: Definition and understand on size set domain and cut set domain based on multi-dimensional space fault tree. China Saf. Sci. J. 24(4), 27–32 (2014)

    Google Scholar 

  32. Cui, T.-J., Ma, Y.-D.: The definition and cognition of the factor importance distribution in Continuous Space Fault Tree. China Saf. Sc. J. 25(3), 24–28 (2015)

    Google Scholar 

  33. Cui, T.-J., Ma, Y.-D.: Research on the maintenance method of system reliability based on multi-dimensional space fault tree. J. Syst. Sci. Math. Sci. 34(6), 682–692 (2014)

    MATH  Google Scholar 

  34. Cui, T.-J., Ma, Y.-D.: The method research on decision criterion discovery of system reliability. Syst. Eng.-Theory Pract. 35(12), 3210–3216 (2015)

    Google Scholar 

  35. Li, S.-S, Cui, T.-J., Ma, Y.-D.: System reliability assessment method based on space fault tree. J. Saf. Sci. Technol. 11(6), 86–92 (2015)

    Google Scholar 

  36. Cui, T.-J., Ma, Y.-D.: Reliability assessment method based on space fault tree. Fuzzy Syst. Math. 29(5), 173–182 (2015)

    MATH  Google Scholar 

  37. Cui, T.-J., Ma, Y.-D.: Discrete Space Fault Tree Construction and Application Research. J. Syst. Sci. Math. Sci. 36(10), 1753–1761 (2016)

    MATH  Google Scholar 

  38. Cui, T.-J., Ma, Y.-D.: Discrete space fault tree construction and failure probability space distribution determine. Syst. Eng.-Theory Pract. 36(4), 1081–1088 (2016)

    Google Scholar 

  39. Cui, T.-J., Li, S.-S., Ma, Y.-D.: Research on trend of failure probability in DSFT based on ANN derivation. Appl. Res. Comput. http://www.cnki.net/kcms/detail/51.1196.TP.20160509.1433.138.html (2017)

  40. Cui, T.-J., Wang, P.-Z., Ma, Y.-D.: Inward analysis of system factor structure in 01 space fault tree. Syst. Eng.-Theory Pract. 36(8), 2152–2160 (2016)

    Google Scholar 

  41. Cui, T.-J., Ma, Y.-D.: Definition of the attribute circle in factors space and its application in object classification. Comput. Eng. Sci. 37(11), 2170–2174 (2015)

    Google Scholar 

  42. Cui, T.-J., Ma, Y.-D.: System security classification decision rules considering the Scope attribute. J. Saf. Sci. Technol. 10(11), 6–9 (2014)

    Google Scholar 

  43. Cui, T.-J., Ma, Y.-D.: Research on the classification method about coal mine safety situation based on the factor space. Syst. Eng.-Theory Pract. 35(11), 2891–2897 (2015)

    Google Scholar 

  44. Cui, T.-J., Ma, Y.-D.: Research on the number of failures of repairable systems based on imperfect repair model. Syst. Eng.-Theory Pract. 36(1), 184–188 (2016)

    Google Scholar 

  45. Guo, S.: Principle of Fuzzy Mathematical Analysis Based on Structural Element Theory. Northeastern University Press, Shenyang (2004)

    Google Scholar 

  46. Wu, C., Xue, X.: Advances in the analysis of fuzzy valued functions. Fuzzy Syst. Math. 16, 1–6 (2002)

    Google Scholar 

  47. Luo, C.: Introduction to Fuzzy Sets. Beijing Normal University Press, Beijing (1994)

    Google Scholar 

  48. Chang, S.L., Zadeh, L.A.: On fuzzy maping and control. IEEE Trans. SMC 2, 30–40 (1972)

    Google Scholar 

  49. Dubois, D., Prade, H.: Systems of linear fuzzy constraints. Fuzzy Sets Syst. 17(3), 37–48 (1980)

    MathSciNet  MATH  Google Scholar 

  50. Dubois, D., Prade, H.: Fuzzy differential calculus. Int. J. FSS 8(1), 1–7 (1982)

    MATH  Google Scholar 

  51. Mizumoto, M., Tanaka, K.: Algebraic Properties of Fuzzy Numbers. International Conference on Cybernetics and Society, Washington, DC (1976)

    MATH  Google Scholar 

  52. Dubois, D., Prade, H.: Operations on fuzzy numbers. Int. J. Syst. Sci. 9(6), 613–626 (1978)

    MathSciNet  MATH  Google Scholar 

  53. Nahmisa, S.: Fuzzy variables. Int. J. Fuzzy Sets Syst. 1(2), 97–111 (1978)

    MathSciNet  Google Scholar 

  54. Wang, J.: Reliability Analysis and Application of Coal Face Production System Based on Structural Element Method, p. 12. Liaoning Technical University, Fuxin (2010)

    Google Scholar 

  55. Guo, S.: Structural element method in fuzzy analysis (I), (II). J. Liaon. Tech. Univ. 21(5), 670–677 (2002)

    Google Scholar 

  56. Yue, L.: Development and Application of Fuzzy Structural Element Theory. Liaoning Technical University, Fuxin (2011)

    Google Scholar 

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Acknowledgements

The author wishes to thank all his friends for their valuable critics, comments and assistances on this paper. This study was partially supported by the grants (Grant Nos. 51704141, 51474121, 51674127) from the Natural Science Foundation of China.

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Authors and Affiliations

  1. College of Safety Science and Engineering, Liaoning Technical University, Fuxin, 123000, China

    Tie-Jun Cui & Sha-Sha Li

  2. Key Laboratory of Mine Thermodynamic Disasters and Control of Ministry of Education, Fuxin, 123000, China

    Tie-Jun Cui & Sha-Sha Li

  3. Tunnel & Underground Structure Engineering Center of Liaoning, Liaoning Dalian Jiaotong University, Dalian, 116028, China

    Tie-Jun Cui

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Cui, TJ., Li, SS. Study on the construction and application of discrete space fault tree modified by fuzzy structured element. Cluster Comput 22 (Suppl 3), 6563–6577 (2019). https://doi.org/10.1007/s10586-018-2342-5

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