A probability-box-based method for propagation of multiple types of epistemic uncertainties and its application on composite structural-acoustic system

Abstract The response analysis of the composite structural-acoustic systems with multiple types of epistemic uncertainties is investigated in this paper. Based on the available information for the uncertain parameters, the multiple types of epistemic uncertainties refer to probability-box (p-box) variables, evidence variables and interval variables. The proposed development focused on an efficient computation of the output bounds of the cumulative distribution function of the sound pressure response when dealing with the combination of p-box variables, evidence variables and interval variables. To reduce the involved computational cost but ensuring the accuracy, all evidence variables and interval variables are transformed into p-box-form variables. Then, a modified interval Monte Carlo method (MIMCM) is developed to estimate the bounds of the cumulative distribution function of the system response. In MIMCM, a sparse Gegenbauer polynomial surrogate model is established with focus on the efficiency and accuracy and then applied for the interval analysis in each iteration. A numerical example and two engineering examples with respect to multiple types of epistemic uncertainties are carried out to illustrate the accuracy and efficiency of the MIMCM by conducting comparisons with traditional algorithms. The ability of the proposed method for risk and conservative reliability analysis is also investigated.

[1]  F. O. Hoffman,et al.  Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[2]  Jian Liu,et al.  Uncertainty propagation analysis using sparse grid technique and saddlepoint approximation based on parameterized p-box representation , 2018, Structural and Multidisciplinary Optimization.

[3]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[4]  S. Mcwilliam.  Anti-optimisation of uncertain structures using interval analysis , 2001 .

[5]  Zhiping Qiu,et al.  Improved numerical prediction and reliability-based optimization of transient heat conduction problem with interval parameters , 2015 .

[6]  Wen-Bin Shangguan,et al.  A unified method and its application to brake instability analysis involving different types of epistemic uncertainties , 2018 .

[7]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[8]  V. Kreinovich,et al.  Imprecise probabilities in engineering analyses , 2013 .

[9]  Luis G. Crespo,et al.  Reliability analysis of polynomial systems subject to p-box uncertainties , 2013 .

[10]  Alex H. Barbat,et al.  Monte Carlo techniques in computational stochastic mechanics , 1998 .

[11]  Michael Beer,et al.  Non-intrusive stochastic analysis with parameterized imprecise probability models: II. Reliability and rare events analysis , 2019, Mechanical Systems and Signal Processing.

[12]  Michael Beer,et al.  Non-intrusive stochastic analysis with parameterized imprecise probability models: I. Performance estimation , 2019, Mechanical Systems and Signal Processing.

[13]  Hui Yin,et al.  Interval and random analysis for structure–acoustic systems with large uncertain-but-bounded parameters , 2016 .

[14]  Qibai Huang,et al.  A new hybrid uncertain analysis method for structural-acoustic systems with random and interval parameters , 2016 .

[15]  Scott Ferson,et al.  Arithmetic with uncertain numbers: rigorous and (often) best possible answers , 2004, Reliab. Eng. Syst. Saf..

[16]  Scott Ferson,et al.  Dependence in Dempster-Shafer theory and probability bounds analysis* , 2004 .

[17]  Fulvio Tonon.  Using random set theory to propagate epistemic uncertainty through a mechanical system , 2004, Reliab. Eng. Syst. Saf..

[18]  Mattias Schevenels,et al.  Topology optimization with geometric uncertainties by perturbation techniques , 2012 .

[19]  Wei Gao,et al.  Uncertain static plane stress analysis with interval fields , 2017 .

[20]  Jian Liu,et al.  A sparse polynomial surrogate model for phononic crystals with uncertain parameters , 2018, Computer Methods in Applied Mechanics and Engineering.

[21]  Xiaojun Wang,et al.  Uncertainty propagation in SEA for structural–acoustic coupled systems with non-deterministic parameters , 2014 .

[22]  Jon C. Helton,et al.  Challenge Problems : Uncertainty in System Response Given Uncertain Parameters ( DRAFT : November 29 , 2001 ) , 2001 .

[23]  Donald J. Nefske,et al.  Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice , 1982 .

[24]  Hui Yin,et al.  A new evidence-theory-based method for response analysis of acoustic system with epistemic uncertainty by using Jacobi expansion , 2017 .

[25]  Sheng Zhang,et al.  Sparse regression Chebyshev polynomial interval method for nonlinear dynamic systems under uncertainty , 2017 .

[26]  Michael Beer,et al.  Uncertainty analysis of a structural–acoustic problem using imprecise probabilities based on p-box representations , 2016 .

[27]  M. Beer,et al.  Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method , 2013 .

[28]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[29]  A. Nouy.  Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations , 2009 .

[30]  Baizhan Xia,et al.  Interval analysis of acoustic field with uncertain-but-bounded parameters , 2012 .

[31]  Zhan Kang,et al.  Perturbation-based stochastic FE analysis and robust design of inelastic deformation processes , 2006 .

[32]  M. Kaminski.  A generalized stochastic perturbation technique for plasticity problems , 2010 .

[33]  Di Wu,et al.  Hybrid uncertain static analysis with random and interval fields , 2017 .

[34]  C. Jiang,et al.  A decoupling approach for evidence-theory-based reliability design optimization , 2017 .

[35]  Baizhan Xia,et al.  A unified model approach for probability response analysis of structure-acoustic system with random and epistemic uncertainties , 2018, Mechanical Systems and Signal Processing.

[36]  Michael Beer,et al.  A polynomial expansion approach for response analysis of periodical composite structural–acoustic problems with multi-scale mixed aleatory and epistemic uncertainties , 2018, Computer Methods in Applied Mechanics and Engineering.

[37]  R. Mullen,et al.  Interval Monte Carlo methods for structural reliability , 2010 .

[38]  Pol D. Spanos,et al.  A multiscale Monte Carlo finite element method for determining mechanical properties of polymer nanocomposites , 2008 .