Methodologies for Complex Reliability Analysis, 18-9240Printer Friendly Version
Inclusive Dates: 01/08/01 - 06/20/01
Background - Numerical simulation is now routinely used to predict the behavior and response of complex systems as a means of reducing testing. Because structural performance is directly affected by uncertainties associated with models, physical parameters, and loadings, the development and application of probabilistic analysis methods suitable for use with complex numerical models are needed. The cornerstone of efficient probabilistic analysis methods is locating the most probable point (MPP) with minimal function evaluations. Many optimization algorithms are available for locating the MPP including some developed specifically for probabilistic analysis such as the Rackwitz-Feissler (RF) algorithm. However, locating the MPP may be difficult or impossible in certain situations, and no optimization algorithm is guaranteed to converge due to such factors as highly nonlinear or discontinuous response functions or multiple MPPs. The difficulty in assuring a correct solution is a recurring discussion in the probabilistic mechanics community and is viewed as requiring experts in the field to perform the analysis. Therefore, improved MPP search algorithms and error detection techniques are required for this technology to be accepted in the engineering community.
Approach - The approach for this effort was to determine the root cause of failure for traditional probabilistic analysis methods when solving a suite of benchmark test problems proposed by the Society of Automotive Engineers (SAE) G-11 Probabilistic Methods Committee and identify algorithms and analysis procedures that can correctly solve these problems.
Accomplishments - A tool was developed to visualize the limit state in the transformed space to reveal the nonlinearity and possible existence of multiple MPPs. The visualization tool identified the cause of failure for the SAE test cases and led to the implementation of several improved MPP convergence checks to indicate nonconvergence. Several robust optimization algorithms were implemented to locate the MPP if and when the RF method failed. These methods were able to solve all the SAE test cases except for those containing multiple MPPs. A sampling-based procedure was developed to approximate the MPPs when all other optimization approaches failed. The proposed sampling approach avoids many of the problems encountered by optimization methods, is able to identify multiple MPPs, and is very fast since the sampling operates on an approximate analytical function. Finally, a system reliability approach was applied to compute the probability of failure for cases with multiple MPPs.