Analysis of complex system reliability with correlated random vectors |
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| Affiliation: | 1. Key Laboratory of New Technique for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China;2. School of Civil Engineering, Chongqing University, Chongqing 400045, China;3. Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697, USA;1. NatHaz Modeling Laboratory, Department of Civil and Environmental Engineering and Earth Sciences, University of Notre Dame, Notre Dame, IN 46556, USA;2. Department of Civil, Structural and Environmental Engineering, University at Buffalo, State University of New York, Buffalo, NY 14260, USA;1. Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, CA, USA;2. Electrical Engineering Department, California State University, Long Beach, CA, USA;3. Department of Electrical & Computer Engineering, Democritus University of Thrace, Greece;1. School of Civil Engineering, Chongqing University, Chongqing, 400044, China;2. College of Engineering and Technology, Southwest University, Chongqing, 400715, China |
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| Abstract: | The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately.The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability. |
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| Keywords: | System reliability Correlated random vectors Transformation Taylor series expansion Complete system failure process Fourth-moment method |
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