Reliability Based Optimization Method

Performance Measure Approach (PMA) and Reliability Index Approach (RIA) methods

One of the most challenging issues of implementing the probabilistic design is associated with intense computational demand of uncertainty analysis. To capture the probabilistic characteristic of a system performance from a design perspective, we need to perform a number of deterministic analyses around the nominal point. One of the existing reliability based optimization methods is the decoupled method, where in, there are two loops, namely the (i) optimization synthesis or the outer loop that optimizes the original objective function based on the fact that the reliability constraints are formulated as deterministic constraints that approximate MPP and (ii) reliability assessment or the inner loop (there are two approaches used for solving this inner loop which are (i) Performance Measure Approach (PMA) method (Figure 12.7) and (ii) Reliability Index Approach (RIA) method (Figure 12.8) about we will discuss briefly), that finds the equivalent deterministic version of each probabilistic constraint by formulating and solving an optimization problem. It must be remember that these two loops, which are decoupled from one another, are applied one after another in a sequence. Since this decoupled loop method does not conduct the expensive MPP search at each step, its time efficiency is very high, but as it performs an approximation at each step, hence this may not guarantee that the results would always be optimal. But this decoupled method does generates a solution, even if sub-optimal, for maximum of the complex optimization problem formulations.