Importance measure analysis with epistemic uncertainty and its moving least squares solution

For the structural systems with both epistemic and aleatory uncertainties, in order to analyze the effect of the epistemic uncertainty on the safety of the systems, a variance based importance measure of failure probability is constructed. Due to the large computational cost of the proposed measure, a novel moving least squares (MLS) based method is employed. By fitting the relationship of parameters and failure probability with moving least squares strategy, the conditional failure probability can be obtained conveniently, then the corresponding importance measure can be calculated. Compared with Sobol's method for the variance based importance measure, the proposed method is more efficient with sufficient accuracy. The Ishigami function is used to test the efficiency of the proposed method. Then the proposed importance measure is used in two engineering applications, including a roof truss and a riveting process.

[1]  M. Langseth,et al.  The effect of the riveting process and aging on the mechanical behaviour of an aluminium self-piercing riveted connection , 2011 .

[2]  Jon C. Helton,et al.  Alternative representations of epistemic uncertainty , 2004, Reliab. Eng. Syst. Saf..

[3]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[4]  Eduard Hofer,et al.  An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties , 2002, Reliab. Eng. Syst. Saf..

[5]  S. Hora,et al.  A Robust Measure of Uncertainty Importance for Use in Fault Tree System Analysis , 1990 .

[6]  Nilay Shah,et al.  The identification of model effective dimensions using global sensitivity analysis , 2011, Reliab. Eng. Syst. Saf..

[7]  P. Verheijen,et al.  Local and Global Sensitivity Analysis for a Reactor Design with Parameter Uncertainty , 2004 .

[8]  Zhenzhou Lu,et al.  Global Sensitivity Analysis Using Moving Least Squares for Models with Correlated Parameters , 2011 .

[9]  E. Borgonovo.  Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

[10]  Paul-Henry Cournède,et al.  An efficient computational method for global sensitivity analysis and its application to tree growth modelling , 2012, Reliab. Eng. Syst. Saf..

[11]  P. Villon,et al.  Moving least squares response surface approximation: Formulation and metal forming applications , 2005 .

[12]  T. Ishigami,et al.  An importance quantification technique in uncertainty analysis for computer models , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[13]  I. Sobol.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[14]  S. Khu,et al.  Separating aleatory and epistemic uncertainties: Probabilistic sewer flooding evaluation using probability box , 2012 .

[15]  Wei Wang,et al.  Application of low-discrepancy sampling method in structural reliability analysis , 2009 .

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

[17]  G. Klir,et al.  Uncertainty-based information: Elements of generalized information theory (studies in fuzziness and soft computing). , 1998 .

[18]  Jing Cheng,et al.  The complex variable interpolating moving least-squares method , 2012, Appl. Math. Comput..

[19]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[20]  Wei Yu,et al.  Parameter uncertainty effects on variance-based sensitivity analysis , 2009, Reliab. Eng. Syst. Saf..

[21]  Jon C. Helton,et al.  Survey of sampling-based methods for uncertainty and sensitivity analysis , 2006, Reliab. Eng. Syst. Saf..

[22]  Zhenzhou Lu,et al.  Moving least squares based sensitivity analysis for models with dependent variables , 2013 .

[23]  P. Lancaster,et al.  Surfaces generated by moving least squares methods , 1981 .

[24]  A. Kiureghian,et al.  Aleatory or epistemic? Does it matter? , 2009 .

[25]  Moon-Hyun Chun,et al.  An uncertainty importance measure using a distance metric for the change in a cumulative distribution function , 2000, Reliab. Eng. Syst. Saf..

[26]  Nilay Shah,et al.  Metamodelling with independent and dependent inputs , 2013, Comput. Phys. Commun..

[27]  A. Saltelli,et al.  Importance measures in global sensitivity analysis of nonlinear models , 1996 .

[28]  Bernard Krzykacz-Hausmann.  An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties , 2006, Reliab. Eng. Syst. Saf..

[29]  Xiaoping Du,et al.  Sensitivity Analysis with Mixture of Epistemic and Aleatory Uncertainties , 2007 .

[30]  Andrea Saltelli,et al.  Sensitivity Analysis for Importance Assessment , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[31]  Enrico Zio,et al.  Neural network approach to sensitivity and uncertainty analysis , 1999 .

[32]  A. Saltelli,et al.  Making best use of model evaluations to compute sensitivity indices , 2002 .

[33]  Stefano Tarantola,et al.  Estimating the approximation error when fixing unessential factors in global sensitivity analysis , 2007, Reliab. Eng. Syst. Saf..