journal article·2025-04-07Open access

Importance Measure for Fuzzy Structural Systems from the Probabilistic Perspective and Its Solving Algorithms

Guijie Li, Miaomiao Zhu, Sanyuan Li

Applied Sciences· Volume 15· Issue 7

Abstract

To effectively determine the influences of fuzzy uncertainties on structural systems in engineering, according to the fuzzy failure probability (FFP) model, which is based on the probabilistic perspective, the importance measure (IM) technique is extended to fuzzy uncertain structural systems. A novel IM framework, i.e., the fuzzy-failure-probability-based IM (FFP-IM), is established. By transforming the fuzzy failure probability into the expected value of the function for the failure domain, the proposed FFP-IM index can be represented as the variance-based IM of that index function. Then, an efficient solution algorithm for the proposed FFP-IM index is established based on the state-dependent parameter method. Ultimately, the Ishigami function, alongside three practical engineering examples, validates the proposed FFP-IM’s rationality and applicability. Furthermore, these examples illustrate the solution algorithm’s superior computational efficiency and accuracy.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Remote Sensing and Land Use · Structural Engineering and Vibration Analysis · Simulation and Modeling Applications

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

School of Mechanics and Aerospace Engineering, Dalian University of Technology, Dalian 116024, China

Key Laboratory of Advanced Technology for Aerospace Vehicles of Liaoning Province, Dalian University of Technology, Dalian 116024, China

Aircraft Strength Research Institute, Xi’an 710065, China

National Key Laboratory of Strength and Structural Integrity, Xi’an 710065, China

Funding

National Key Laboratory of Strength and Structural Integrity Opening Fund · National Natural Science Foundation of China

References (35)

Show source-provided references
1. A General Procedure for First/Second-Order Reliability method (FORM/SORM)10.1016/S0167-4730(99)00008-9 ↗
2. Hamiltonian Monte Carlo Methods for Subset Simulation in Reliability Analysis10.1016/j.strusafe.2018.05.005 ↗
3. Representation of Analysis Results Involving Aleatory and Epistemic Uncertainty10.1080/03081079.2010.486664 ↗
4. Fuzzy Reliability Analysis of Nanocomposite ZnO Beams Using Hybrid Analytical-Intelligent Method10.1007/s00366-020-00965-5 ↗
5. System Reliability Analysis for Mixed Uncertain Variables10.1016/j.strusafe.2009.02.001 ↗
6. Epistemic Uncertainty-Based Reliability Analysis for Engineering System with Hybrid Evidence and Fuzzy Variables10.1016/j.cma.2019.06.036 ↗
7. Fuzzy Sets as a Basis for a Theory of Possibility10.1016/S0165-0114(99)80004-9 ↗
9. A Fuzzy Safety Measure10.1061/JMCEA3.0002528 ↗
10. Fuzzy Variables as a Basis for a Theory of Fuzzy Reliability in the Possibility Context10.1016/0165-0114(91)90143-E ↗
11. A General Formal Approach for Fuzzy Reliability Analysis in the Possibility Context10.1016/0165-0114(95)00391-6 ↗
12. Fuzzy System Reliability Analysis by Interval of Confidence10.1016/0165-0114(93)90182-H ↗
13. Fuzzy System Reliability Analysis for Components with Different Membership Functions10.1016/0165-0114(94)90330-1 ↗
14. The Possibilistic Reliability Theory: Theoretical Aspects and Applications10.1016/S0167-4730(97)00093-3 ↗
15. A Fuzzy Reliability Approach for Structures in the Possibility Context
16. A Fuzzy Reliability Approach for Structures Based on the Probability Perspective10.1016/j.strusafe.2014.09.008 ↗
17. A New Reliability Approach for the Fuzzy and Random Structure Based on the Uniformly Distributed Membership Level10.1007/s40815-022-01281-4 ↗
18. Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches10.1111/j.1539-6924.2006.00806.x ↗
19. A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis10.1111/j.1539-6924.1990.tb00523.x ↗
20. Sensitivity Estimates for Nonlinear Mathematical Models
21. A New Uncertainty Importance Measure10.1016/j.ress.2006.04.015 ↗
22. An Uncertainty Importance Measure Using a Distance Metric for the Change in a Cumulative Distribution Function10.1016/S0951-8320(00)00068-5 ↗
23. A New Computational Method of a Moment-Independent Uncertainty Importance Measure10.1016/j.ress.2008.10.005 ↗
24. Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems10.1016/S0951-8320(03)00058-9 ↗
25. Moment-Independent Importance Measure of Correlated Input Variable and Its State Dependent Parameter Solution10.1016/j.ast.2015.11.019 ↗
26. Moment-Independent Importance Measure of Basic Random Variable and Its Probability Density Evolution Solution10.1007/s11431-009-0386-8 ↗
27. A Generalized Borgonovo’s Importance Measure for Fuzzy Input Uncertainty10.1016/j.fss.2011.06.002 ↗
28. An Entropy-Based Global Sensitivity Analysis for the Structures with Both Fuzzy Variables and Random Variables10.1177/0954406212448575 ↗
29. The Importance Measure of Fuzzy Input on Failure Credibility under the Fuzzy Uncertainty10.1016/j.ast.2020.106320 ↗
30. Young, P.M. (1993). Time Variable and State Dependent Modelling of Nonstationary and Nonlinear Time Series. Developments in Time Series Analysis, Chapman Hall.10.1007/978-1-4899-4515-0_26 ↗
31. Time Variable and State Dependent Parameter Estimation10.1016/S1474-6670(17)39760-4 ↗
32. Ratto, M., Tarantola, S., Saltelli, A., and Young, P. (2004, January 8–11). Accelerated Estimation of Sensitivity Indices Using State Dependent Parameter Models, Sensitivity Analysis of Model Output. Proceedings of the 4th International Conference on Sensitivity Analysis of Model Output, Santa Fe, NM, USA.
33. State Dependent Parameter Metamodelling and Sensitivity Analysis10.1016/j.cpc.2007.07.011 ↗
34. Efficient Input—Output Model Representations10.1016/S0010-4655(98)00152-0 ↗
35. An Efficient Method by Nesting Adaptive Kriging into Importance Sampling for Failure-Probability-Based Global Sensitivity Analysis10.1007/s00366-021-01402-x ↗