Safety analysis for the posfust reliability model under possibilistic input and fuzzy state

Abstract The structural input can be simply classified as probabilistic one and possibilistic one, and the structural state can be divided into binary state and fuzzy state. Combining different kinds of structural input and state, the reliability analysis model can be sorted into four types, i.e., the one based on probabilistic input and binary state (probist), the one based on probabilistic input and fuzzy state (profust), the one based on possibilistic input and binary state (posbist) and the one based on possibilistic input and fuzzy state (posfust). Various researches about the former three reliability models have been developed, whereas the study on the posfust reliability model is rare. Due to this fact, the fuzzy failure credibility is established to measure the safety degree of the posfust model, and it is a fuzzy safety index defined by the definite integral of the failure membership function. Then, to estimate the defined fuzzy failure credibility efficiently, two adaptive Kriging based methods are proposed. The first one is based on the definition of the fuzzy failure credibility, in which the lower and upper bounds of performance function are mainly concerned by the strategy of constructing the Kriging model. The second one combines the adaptive Kriging and fuzzy simulation algorithm, and it is based on the relationship between the defined fuzzy failure credibility and the failure credibility in the posbist reliability model. Several examples are provided to verify the rationality of the established fuzzy failure credibility, and the efficiency and accuracy of the proposed methods.

[1]  Xiaoping Du,et al.  One-class support vector machines with a bias constraint and its application in system reliability prediction , 2019, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[2]  Hakjin Lee,et al.  Development of an optimized trend kriging model using regression analysis and selection process for optimal subset of basis functions , 2018, Aerospace Science and Technology.

[3]  Zhenzhou Lu,et al.  Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability , 2019, Reliab. Eng. Syst. Saf..

[4]  Xiaoping Du,et al.  Integration of Statistics- and Physics-Based Methods – A Feasibility Study on Accurate System Reliability Prediction , 2018 .

[5]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[6]  Pingfeng Wang,et al.  A double-loop adaptive sampling approach for sensitivity-free dynamic reliability analysis , 2015, Reliab. Eng. Syst. Saf..

[7]  Wei Wang,et al.  Reliability analysis using radial basis function networks and support vector machines , 2011 .

[8]  Zhenzhou Lu,et al.  Safety life analysis under required failure credibility constraint for unsteady thermal structure with fuzzy input parameters , 2019 .

[9]  Yan Shi,et al.  Aircraft icing safety analysis method in presence of fuzzy inputs and fuzzy state , 2018 .

[10]  W. Graf,et al.  Fuzzy structural analysis using α-level optimization , 2000 .

[11]  Hong-shuang Li,et al.  A sampling-based method for high-dimensional time-variant reliability analysis , 2019, Mechanical Systems and Signal Processing.

[12]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[13]  Cai Kaiyuan,et al.  Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context , 1991 .

[14]  Cai Kaiyuan,et al.  Fuzzy reliability modeling of gracefully degradable computing systems , 1991 .

[15]  Jérôme Morio,et al.  A survey of rare event simulation methods for static input-output models , 2014, Simul. Model. Pract. Theory.

[16]  Kai-Yuan Cai,et al.  Fuzzy states as a basis for a theory of fuzzy reliability , 1993 .

[17]  Yan Shi,et al.  Time-dependent failure possibility analysis under consideration of fuzzy uncertainty , 2019, Fuzzy Sets Syst..

[18]  Zhenzhou Lu,et al.  An efficient method combining active learning Kriging and Monte Carlo simulation for profust failure probability , 2020, Fuzzy Sets Syst..

[19]  Zhenzhou Lu,et al.  Efficient numerical algorithm of profust reliability analysis: An application to wing box structure , 2018, Aerospace Science and Technology.

[20]  Kai-Yuan Cai,et al.  System failure engineering and fuzzy methodology An introductory overview , 1996, Fuzzy Sets Syst..

[21]  Zhenzhou Lu,et al.  Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis , 2020 .

[22]  João Cardoso,et al.  Review and application of Artificial Neural Networks models in reliability analysis of steel structures , 2015 .

[23]  Jérôme Morio,et al.  Estimation of a launch vehicle stage fallout zone with parametric and non-parametric importance sampling algorithms in presence of uncertain input distributions , 2016 .

[24]  Zhenzhou Lu,et al.  Efficient numerical simulation methods for estimating fuzzy failure probability based importance measure indices , 2019 .

[25]  Zhenzhou Lu,et al.  Root finding method of failure credibility for fuzzy safety analysis , 2018 .

[26]  Jørgen Juncher Jensen,et al.  Efficient estimation of extreme non-linear roll motions using the first-order reliability method (FORM) , 2007 .

[27]  Zhenzhou Lu,et al.  A novel step-wise AK-MCS method for efficient estimation of fuzzy failure probability under probability inputs and fuzzy state assumption , 2019, Engineering Structures.

[28]  Chong Wang,et al.  Hybrid reliability analysis and optimization for spacecraft structural system with random and fuzzy parameters , 2018 .

[29]  Fu Chen,et al.  Kriging surrogate model applied in the mechanism study of tip leakage flow control in turbine cascade by multiple DBD plasma actuators , 2019, Aerospace Science and Technology.

[30]  Xiuli Shen,et al.  Surrogate-based optimization with improved support vector regression for non-circular vent hole on aero-engine turbine disk , 2020 .

[31]  Xiaojun Wang,et al.  Sequential multidisciplinary design optimization and reliability analysis under interval uncertainty , 2018, Aerospace Science and Technology.

[32]  Zhenzhou Lu,et al.  Aircraft Icing Severity Analysis Considering Three Uncertainty Types , 2019, AIAA Journal.

[33]  Zhenzhou Lu,et al.  An efficient method combining adaptive Kriging and fuzzy simulation for estimating failure credibility , 2019, Aerospace Science and Technology.

[34]  Zhenzhou Lu,et al.  Time-dependent failure credibility analysis and its optimization based computational methods , 2019 .

[35]  S. Chakraborty,et al.  Reliability analysis of structures by iterative improved response surface method , 2016 .

[36]  Feng Zhang,et al.  Icing severity forecast algorithm under both subjective and objective parameters uncertainties , 2016 .

[37]  H. U. Köylüoglu,et al.  New Approximations for SORM Integrals , 1994 .

[38]  Cai Kaiyuan,et al.  Posbist reliability behavior of fault-tolerant systems , 1995 .

[39]  Vincenzo Cutello,et al.  Structure functions with fuzzy states , 1996, Fuzzy Sets Syst..

[40]  A. Neely,et al.  Efficient uncertainty quantification for a hypersonic trailing-edge flap, using gradient-enhanced kriging , 2018, Aerospace Science and Technology.

[41]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[42]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[43]  Jérôme Morio,et al.  Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems , 2015 .