A novel reliability evaluation method for large engineering systems

Abstract A novel reliability evaluation method for large nonlinear engineering systems excited by dynamic loading applied in time domain is presented. For this class of problems, the performance functions are expected to be function of time and implicit in nature. Available first- or second-order reliability method (FORM/SORM) will be challenging to estimate reliability of such systems. Because of its inefficiency, the classical Monte Carlo simulation (MCS) method also cannot be used for large nonlinear dynamic systems. In the proposed approach, only tens instead of hundreds or thousands of deterministic evaluations at intelligently selected points are used to extract the reliability information. A hybrid approach, consisting of the stochastic finite element method (SFEM) developed by the author and his research team using FORM, response surface method (RSM), an interpolation scheme, and advanced factorial schemes, is proposed. The method is clarified with the help of several numerical examples.

[1]  Achintya Haldar,et al.  A novel reliability evaluation method for large dynamic engineering systems , 2010, 2010 2nd International Conference on Reliability, Safety and Hazard - Risk-Based Technologies and Physics-of-Failure Methods (ICRESH).

[2]  M. Deaton,et al.  Response Surfaces: Designs and Analyses , 1989 .

[3]  Herschel Rabitz,et al.  Efficient Implementation of High Dimensional Model Representations , 2001 .

[4]  A. Meher Prasad,et al.  High dimensional model representation for piece‐wise continuous function approximation , 2007 .

[5]  Rajib Chowdhury,et al.  Enhanced high‐dimensional model representation for reliability analysis , 2009 .

[6]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[7]  A. Basudhar,et al.  Adaptive explicit decision functions for probabilistic design and optimization using support vector machines , 2008 .

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

[9]  F. S. Wong,et al.  Slope Reliability and Response Surface Method , 1985 .

[10]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[11]  Bruce R. Ellingwood,et al.  A new look at the response surface approach for reliability analysis , 1993 .

[12]  J. Beck,et al.  A new adaptive importance sampling scheme for reliability calculations , 1999 .

[13]  Zhenzhou Lu,et al.  A new high-order response surface method for structural reliability analysis , 2010 .

[14]  Achintya Haldar,et al.  Reliability of Frame and Shear Wall Structural Systems. I: Static Loading , 2003 .

[15]  Dong Wei,et al.  A univariate decomposition method for higher- order reliability analysis and design optimization , 2006 .

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

[17]  Henri P. Gavin,et al.  High-order limit state functions in the response surface method for structural reliability analysis , 2008 .

[18]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[19]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[20]  Y. K. Wen,et al.  Response Surface Method for Time-Variant Reliability Analysis , 1996 .

[21]  J. S. Hunter,et al.  Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. , 1979 .

[22]  Achintya Haldar,et al.  Seismic reliability of non-linear frames with PR connections using systematic RSM , 2002 .

[23]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[24]  Samy Missoum,et al.  Failure Prediction and Robust Design of Grafts for Aortic Aneurysms , 2007 .

[25]  Michael D. Kotsovos,et al.  Behavior of Reinforced Concrete Structural Walls: Strength, Deformation Characteristics, and Failure Mechanism , 1990 .

[26]  Achintya Haldar,et al.  Reliability Assessment Using Stochastic Finite Element Analysis , 2000 .

[27]  Sharif Rahman,et al.  Structural reliability analysis by univariate decomposition and numerical integration , 2007 .

[28]  S. Rahman,et al.  Decomposition methods for structural reliability analysis , 2005 .

[29]  Robert E. Melchers,et al.  Structural system reliability assessment using directional simulation , 1994 .

[30]  Antonio Harrison Sánchez,et al.  Limit state function identification using Support Vector Machines for discontinuous responses and disjoint failure domains , 2008 .

[31]  P. E. James T. P. Yao,et al.  Probability, Reliability and Statistical Methods in Engineering Design , 2001 .

[32]  H. Rabitz,et al.  High Dimensional Model Representations , 2001 .

[33]  Raphael T. Haftka,et al.  A convex hull approach for the reliability-based design optimization of nonlinear transient dynamic problems , 2007 .

[34]  R. Rackwitz,et al.  Non-Normal Dependent Vectors in Structural Safety , 1981 .

[35]  R. Rackwitz,et al.  Quadratic Limit States in Structural Reliability , 1979 .

[36]  Ilya M. Sobol,et al.  Theorems and examples on high dimensional model representation , 2003, Reliab. Eng. Syst. Saf..