Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.

[1]  Scott Ferson,et al.  Varying correlation coefficients can underestimate uncertainty in probabilistic models , 2006, Reliab. Eng. Syst. Saf..

[2]  T. Bedford,et al.  Vines: A new graphical model for dependent random variables , 2002 .

[3]  Fan Wang,et al.  System reliability under prescribed marginals and correlations: Are we correct about the effect of correlations? , 2017, Reliab. Eng. Syst. Saf..

[4]  M. Rosenblatt Remarks on a Multivariate Transformation , 1952 .

[5]  Wei Wang,et al.  Non-linear partial least squares response surface method for structural reliability analysis , 2017, Reliab. Eng. Syst. Saf..

[6]  A Dutfoy,et al.  Practical approach to dependence modelling using copulas , 2009 .

[7]  K. Phoon,et al.  Copula-based approaches for evaluating slope reliability under incomplete probability information , 2015 .

[8]  G. Schuëller,et al.  Chair of Engineering Mechanics Ifm-publication 2-374 a Critical Appraisal of Reliability Estimation Procedures for High Dimensions , 2022 .

[9]  Zequn Wang,et al.  Time-variant reliability assessment through equivalent stochastic process transformation , 2016, Reliab. Eng. Syst. Saf..

[10]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[11]  Anne Dutfoy,et al.  Do Rosenblatt and Nataf isoprobabilistic transformations really differ , 2009 .

[12]  Hao Zhang,et al.  A Multiwavelet Neural Network‐Based Response Surface Method for Structural Reliability Analysis , 2015, Comput. Aided Civ. Infrastructure Eng..

[13]  H. Joe Families of $m$-variate distributions with given margins and $m(m-1)/2$ bivariate dependence parameters , 1996 .

[14]  R. Suresh,et al.  Experimental characterisation of random field models for CFRP composite panels , 2015 .

[15]  Yi Zhang,et al.  Long-term performance assessment and design of offshore structures , 2015 .

[16]  Wei Chen,et al.  Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation , 2017 .

[17]  G. Schuëller,et al.  Uncertain linear structural systems in dynamics: Efficient stochastic reliability assessment , 2010 .

[18]  Quanwang Li,et al.  Reliability assessment of aging structures subjected to gradual and shock deteriorations , 2017, Reliab. Eng. Syst. Saf..

[19]  B. Biller,et al.  Copula-based multivariate input modeling , 2012 .

[20]  Aristidis K. Nikoloulopoulos,et al.  Tail dependence functions and vine copulas , 2010, J. Multivar. Anal..

[21]  Gang Zhou,et al.  Experimental analysis of the pore structure and fractal characteristics of different metamorphic coal based on mercury intrusion‑nitrogen adsorption porosimetry , 2020 .

[22]  Guan Rong,et al.  Impact of copula selection on geotechnical reliability under incomplete probability information , 2013 .

[23]  Monica Menendez,et al.  Extending Morris method for qualitative global sensitivity analysis of models with dependent inputs , 2017, Reliab. Eng. Syst. Saf..

[24]  Gang Zhou,et al.  Experimental investigation on physicochemical characteristics of coal treated with synthetic sodium salicylate–imidazole ionic liquids , 2020 .

[25]  Lambros S. Katafygiotis,et al.  Bayesian post-processor and other enhancements of Subset Simulation for estimating failure probabilities in high dimensions , 2011 .

[26]  Árpád Rózsás,et al.  The effect of copulas on time-variant reliability involving time-continuous stochastic processes , 2017 .

[27]  A. Sellier,et al.  Adaptive response surface method based on a double weighted regression technique , 2009 .

[28]  G. I. Schuëller,et al.  Benchmark Study on Reliability Estimation in Higher Dimensions of Structural Systems – An Overview , 2007 .

[29]  Heng Li,et al.  Towards reliability evaluation involving correlated multivariates under incomplete probability information: A reconstructed joint probability distribution for isoprobabilistic transformation , 2017 .

[30]  Heng Li,et al.  The role of copulas in random fields: Characterization and application , 2018, Structural Safety.

[31]  Jorge E. Hurtado,et al.  Tighter bounds on the probability of failure than those provided by random set theory , 2017 .

[32]  Kong Fah Tee,et al.  Application of subset simulation in reliability estimation of underground pipelines , 2014, Reliab. Eng. Syst. Saf..

[33]  Hyun-Moo Koh,et al.  System reliability analysis using dominant failure modes identified by selective searching technique , 2013, Reliab. Eng. Syst. Saf..

[34]  C. Bucher,et al.  A fast and efficient response surface approach for structural reliability problems , 1990 .

[35]  Jerzy Bauer,et al.  Reliability with respect to settlement limit-states of shallow foundations on linearly-deformable subsoil , 2000 .

[36]  Hongzhe Dai,et al.  An Adaptive Wavelet Frame Neural Network Method for Efficient Reliability Analysis , 2014, Comput. Aided Civ. Infrastructure Eng..