An arc reduction method to effectively handle highly non-linear reliability constraints in the first-order reliability method

1. Abstract Reliability Based Design Optimization (RBDO) aims to design systems that are both reliable and a good approximation of the optimal system. The conventional RBDO method involves the evaluation of reliability constraints by using the First-Order Reliability Method (FORM) to obtain a reliability index for each constraint. The Performance Measure Approach (PMA), especially the Advanced Mean Value (AMV) method and its variants, shows improved convergence for non-linear constraint functions. Unfortunately, all these methods are gradient based and if the gradient of the constraint function is noisy, they tend to diverge. Since noise is common in industrial applications, it forces the user to use response surfaces to smooth the noise present in the constraint. As the objective of RBDO is to compensate for outlying constraint values where uncertainty exists, smoothing has the negative effect of reducing the accuracy of the reliability estimate.