An Enhanced Quadratic WPI Approximation with Applications to Nonlinear System Reliability Assessment

In Chap. 9 , the accuracy degree of the Wiener path integral technique is enhanced by employing a quadratic approximation in the Wiener path integral functional series expansion. It is shown that compared to the standard most probable path Wiener path integral approximation, the quadratic approximation yields enhanced accuracy in evaluating the system response joint probability density function. This is primarily due to the fact that fluctuations around the most probable path are also accounted for by introducing a localized state-dependent factor in the approximate evaluation of the Wiener path integral. Further, a significant advantage of the enhancement relates to structural reliability assessment and to the fact that the required in the most probable path approach probability density function normalization step is circumvented. Thus, low-probability events, e.g., failure probabilities, can be determined in a direct manner without the need for obtaining the complete response joint probability density function first.