An enhanced unified uncertainty analysis approach based on first order reliability method with single-level optimization

Abstract In engineering, there exist both aleatory uncertainties due to the inherent variation of the physical system and its operational environment, and epistemic uncertainties due to lack of knowledge and which can be reduced with the collection of more data. To analyze the uncertain distribution of the system performance under both aleatory and epistemic uncertainties, combined probability and evidence theory can be employed to quantify the compound effects of the mixed uncertainties. The existing First Order Reliability Method (FORM) based Unified Uncertainty Analysis (UUA) approach nests the optimization based interval analysis in the improved Hasofer–Lind–Rackwitz–Fiessler (iHLRF) algorithm based Most Probable Point (MPP) searching procedure, which is computationally inhibitive for complex systems and may encounter convergence problem as well. Therefore, in this paper it is proposed to use general optimization solvers to search MPP in the outer loop and then reformulate the double-loop optimization problem into an equivalent single-level optimization (SLO) problem, so as to simplify the uncertainty analysis process, improve the robustness of the algorithm, and alleviate the computational complexity. The effectiveness and efficiency of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.

[1]  Z. Mourelatos,et al.  A Design Optimization Method Using Evidence Theory , 2006, DAC 2005.

[2]  Michel van Tooren,et al.  Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles , 2011 .

[3]  Xiaoping Du.  Unified Uncertainty Analysis by the First Order Reliability Method , 2008 .

[4]  Sankaran Mahadevan,et al.  Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty , 2011, Reliab. Eng. Syst. Saf..

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

[6]  Ramana V. Grandhi,et al.  Comparison of evidence theory and Bayesian theory for uncertainty modeling , 2004, Reliab. Eng. Syst. Saf..

[7]  Ramana V. Grandhi,et al.  An approximation approach for uncertainty quantification using evidence theory , 2004, Reliab. Eng. Syst. Saf..

[8]  Jon C. Helton,et al.  Quantification of Margins and Uncertainties , 2011, Reliab. Eng. Syst. Saf..

[9]  Sharon L. Padula,et al.  Aerospace applications of optimization under uncertainty , 2006 .

[10]  Jon C. Helton,et al.  Investigation of Evidence Theory for Engineering Applications , 2002 .

[11]  Jon C. Helton,et al.  Quantification of margins and uncertainties: Alternative representations of epistemic uncertainty , 2011, Reliab. Eng. Syst. Saf..

[12]  Dan M. Frangopol,et al.  Life-cycle reliability-based optimization of civil and aerospace structures , 2003 .

[13]  R. Rackwitz,et al.  New light on first- and second-order reliability methods , 1987 .

[14]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[15]  C. Jiang,et al.  Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique , 2011 .

[16]  Sankaran Mahadevan,et al.  A probabilistic approach for representation of interval uncertainty , 2011, Reliab. Eng. Syst. Saf..

[17]  Jay D. Johnson,et al.  A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory , 2007 .

[18]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[19]  James R. Wertz,et al.  Space Mission Analysis and Design , 1992 .

[20]  Ramana V. Grandhi,et al.  Epistemic uncertainty quantification techniques including evidence theory for large-scale structures , 2004 .

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

[22]  Xiaoping Du,et al.  Uncertainty Analysis With Probability and Evidence Theories , 2006, DAC 2006.

[23]  Robert E. Melchers,et al.  Structural Reliability: Analysis and Prediction , 1987 .

[24]  Yan-Gang Zhao,et al.  A general procedure for first/second-order reliabilitymethod (FORM/SORM) , 1999 .

[25]  Stephen Kemble,et al.  Preliminary space mission design under uncertainty , 2010 .

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

[27]  John E. Renaud,et al.  Uncertainty quantification using evidence theory in multidisciplinary design optimization , 2004, Reliab. Eng. Syst. Saf..

[28]  Xiaoqian Chen,et al.  Utilizing Uncertainty Multidisciplinary Design Optimization for Conceptual Design of Space Systems , 2010 .

[29]  Byeng D. Youn,et al.  Bayesian Reliability Based Design Optimization under Both Aleatory and Epistemic Uncertainties , 2006 .

[30]  Kyung K. Choi,et al.  Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty , 2007 .

[31]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .