Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Application of dynamic evidential networks in reliability analysis of complex systems with epistemic uncertainty and multiple life distributions

  • S.I.: Reliability Modeling with Applications Based on Big Data
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

With the modernization and intelligent of industrial equipment and systems, the challenges of dynamic characteristics, failure dependency and uncertainties have aroused by the increasing of system complexity. Besides, various types of components may follow different life distributions which bring the multiple life distributions problem in systems. In order to model the impact of time dependency and epistemic uncertainty on the failure behavior of system, this paper combines the flexible dynamic modeling with the uncertainty expression. Its advantages are intuitively graphical representation and reasoning that brought by evidential network (EN). After that, the discrete time dynamic evidential network (DT-DEN) is introduced to analyze the reliability of complex systems, and the network inference mechanism is clearly defined. The evidence theory and original definition and inference mechanism of conventional EN is firstly recommended, and the DT-DEN is further presented. Furthermore, the multiple life distributions are synthesized into the DT-DEN to tackle the epistemic uncertainty and mixed life distribution challenges. Specifically, the dynamic logic gates are converted into equivalent DENs with distinguished conditional mass tables, and then the belief interval of system reliability can be calculated by network forward reasoning. Finally, the availability and efficiency of the proposed method is verified by some numerical examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Abbreviations

\( \varOmega \) :

Frame of discernment

\( {2^{\varOmega}} \) :

Power set

\( m\left( \cdot \right) \) :

Mass function

\( Bel\left( \cdot \right) \) :

Belief function

\( Pl\left( \cdot \right) \) :

Plausibility function

\( \zeta \) :

An evidential network (EN)

N :

Node set of EN

E :

Edge set of EN

M :

Belief mass set of EN

\( \zeta_{ \to } \) :

A dynamic evidential network (DEN)

\( N_{ \to } \) :

Node set of DEN

\( E_{ \to } \) :

Edge set of DEN

\( M_{ \to } \) :

Belief mass set of DEN

\( M(X) \) :

Belief mass assignment of variable X

\( \pi \left( \cdot \right) \) :

Set of parent nodes

\( \Delta \) :

Length of each time slice

\( {\mathbf{M}}\left( \cdot \right) \) :

State transition matrix

BN:

Bayesian network

CN:

Credal network

EN:

Evidential network

DT-DEN:

Discrete time dynamic evidential network

BDD:

Binary decision diagram

DFT:

Dynamic fault tree

P-box:

Probability box

BPA:

Basic probability assignment

CMT:

Conditional mass table

CBMT:

Conditional belief mass table

DAG:

Directed acyclic graph

CSP:

Cold spare gate

HSP:

Hot spare gate

FDEP:

Functional dependent gate

References

  • Bryant, R. E. (2018). Binary decision diagrams. Handbook of model checking (pp. 191–217). Cham: Springer.

    Book  Google Scholar 

  • Deng, X., & Jiang, W. (2018). Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures. Annals of Nuclear Energy, 117, 183–193.

    Article  Google Scholar 

  • Duan, R., Hu, L., & Lin, Y. (2017). Fault diagnosis for complex systems based on dynamic evidential network and multi-attribute decision making with interval numbers. Eksploatacja I Niezawodnosc, 19(4), 580.

    Article  Google Scholar 

  • Kabir, S. (2017). An overview of fault tree analysis and its application in model based dependability analysis. Expert Systems with Application, 77, 114–135.

    Article  Google Scholar 

  • Khadiev, K., & Khadieva, A. (2017). Reordering method and hierarchies for quantum and classical ordered binary decision diagrams. In International computer science symposium in Russia (pp. 162–175). Cham: Springer.

  • Khakzad, N., Landucci, G., & Reniers, G. (2017). Application of dynamic Bayesian network to performance assessment of fire protection systems during domino effects. Reliability Engineering & System Safety, 167, 232–247.

    Article  Google Scholar 

  • Li, X. Y., Huang, H. Z., & Li, Y. F. (2018a). Reliability analysis of phased mission system with non-exponential and partially repairable components. Reliability Engineering & System Safety, 175, 119–127.

    Article  Google Scholar 

  • Li, H., Huang, H. Z., Li, Y. F., et al. (2018b). Physics of failure-based reliability prediction of turbine blades using multi-source information fusion. Applied Soft Computing, 72, 624–635.

    Article  Google Scholar 

  • Li, C., & Mahadevan, S. (2016). Relative contributions of aleatory and epistemic uncertainty sources in time series prediction. International Journal of Fatigue, 82, 474–486.

    Article  Google Scholar 

  • Li, Y. F., Mi, J., Liu, Y., et al. (2015). Dynamic fault tree analysis based on continuous-time Bayesian networks under fuzzy numbers. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 229(6), 530–541.

    Google Scholar 

  • Lü, H., Shangguan, W. B., & Yu, D. (2018). A unified method and its application to brake instability analysis involving different types of epistemic uncertainties. Applied Mathematical Modelling, 56, 158–171.

    Article  Google Scholar 

  • Mi, J., Li, Y. F., Peng, W., et al. (2018). Reliability analysis of complex multi-state system with common cause failure based on evidential networks. Reliability Engineering & System Safety, 2018(174), 71–81.

    Article  Google Scholar 

  • Mi, J., Li, Y. F., Yang, Y. J., et al. (2016). Reliability assessment of complex electromechanical systems under epistemic uncertainty. Reliability Engineering & System Safety, 152, 1–15.

    Article  Google Scholar 

  • Misuri, A., Khakzad, N., Reniers, G., et al. (2018). Tackling uncertainty in security assessment of critical infrastructures: Dempster-Shafer Theory vs. Credal Sets Theory. Safety Science, 107, 62–76.

    Article  Google Scholar 

  • Peng, W., Balakrishnan, N., & Huang, H. Z. (2018). Reliability modelling and assessment of a heterogeneously repaired system with partially relevant recurrence data. Applied Mathematical Modelling, 59, 696–712.

    Article  Google Scholar 

  • Pliego Marugán, A., García Márquez, F. P., & Lev, B. (2017). Optimal decision-making via binary decision diagrams for investments under a risky environment. International Journal of Production Research, 55(18), 5271–5286.

    Article  Google Scholar 

  • Rahman, S., Karanki, D. R., Epiney, A., et al. (2018). Deterministic sampling for propagating epistemic and aleatory uncertainty in dynamic event tree analysis. Reliability Engineering & System Safety, 175, 62–78.

    Article  Google Scholar 

  • Simon, C., & Bicking, F. (2017). Hybrid computation of uncertainty in reliability analysis with p-box and evidential networks. Reliability Engineering & System Safety, 167, 629–638.

    Article  Google Scholar 

  • Simon, C., Weber, P., & Sallak, M. (2018). Data uncertainty and important measures. Berlin: Wiley.

    Book  Google Scholar 

  • Sun, M. X., Li, Y. F., & Zio, E. (2017). On the optimal redundancy allocation for multi-state series–parallel systems under epistemic uncertainty. Reliability Engineering & System Safety, online.

  • Volk, M., Junges, S., & Katoen, J. P. (2018). Fast dynamic fault tree analysis by model checking techniques. IEEE Transactions on Industrial Informatics, 14(1), 370–379.

    Article  Google Scholar 

  • Weber, P., & Simon, C. (2008). Dynamic evidential networks in system reliability analysis: A Dempster Shafer approach. In Mediterranean conference on control and automation (pp. 603–608).

  • Wei, P. F., Lu, Z. Z., & Song, J. W. (2015). Variable importance analysis: A comprehensive review. Reliability Engineering and System Safety, 142, 399–432.

    Article  Google Scholar 

  • Xiahou, T., Liu, Y., & Jiang, T. (2018). Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment. Mechanical Systems and Signal Processing, 109, 305–329.

    Article  Google Scholar 

  • Zarei, E., Azadeh, A., Khakzad, N., et al. (2017). Dynamic safety assessment of natural gas stations using Bayesian network. Journal of Hazardous Materials, 321, 830–840.

    Article  Google Scholar 

  • Zhang, X., Gao, H., Huang, H. Z., et al. (2018a). Dynamic reliability modeling for system analysis under complex load. Reliability Engineering & System Safety, 180, 345–351.

    Article  Google Scholar 

  • Zhang, Z., Ruan, X. X., Duan, M. F., et al. (2018b). An efficient epistemic uncertainty analysis method using evidence theory. Computer Methods in Applied Mechanics and Engineering, 339, 443–466.

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under contact Nos. 51805073 and 51607024, the Chinese Universities Scientific Fund under contact No. ZYGX2018J061, and the National Key Research and Development Program of China under contact No. 2017YFC1501005.

Author information

Authors and Affiliations

  1. School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Jinhua Mi, Yuhua Cheng, Yufei Song, Libing Bai & Kai Chen

  2. Center for System Reliability and Safety, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Jinhua Mi

  3. Institute for Risk and Reliability, Leibniz University Hannover, Hannover, 30167, Germany

    Jinhua Mi

Authors
  1. Jinhua Mi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuhua Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yufei Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Libing Bai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kai Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuhua Cheng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mi, J., Cheng, Y., Song, Y. et al. Application of dynamic evidential networks in reliability analysis of complex systems with epistemic uncertainty and multiple life distributions. Ann Oper Res 311, 311–333 (2022). https://doi.org/10.1007/s10479-019-03211-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03211-4

Keywords

Search

Navigation