Approximate probabilistic optimization using exact-capacity-approximate-response-distribution (ECARD)

Abstract

Probabilistic structural design deals with uncertainties in response (e.g. stresses) and capacity (e.g. failure stresses). The calculation of the structural response is typically expensive (e.g., finite element simulations), while the capacity is usually available from tests. Furthermore, the random variables that influence response and capacity are often disjoint. In previous work we have shown that this disjoint property can be used to reduce the cost of obtaining the probability of failure via Monte Carlo simulations. In this paper we propose to use this property for an approximate probabilistic optimization based on exact capacity and approximate response distributions (ECARD). In Approximate Probabilistic Optimization Using ECARD, the change in response distribution is approximated as the structure is re-designed while the capacity distribution is kept exact, thus significantly reducing the number of expensive response simulations. ECARD may be viewed as an extension of SORA (Sequential Optimization and Reliability Assessment), which proceeds with deterministic optimization iterations. In contrast, ECARD has probabilistic optimization iterations, but in each iteration, the response distribution is approximated so as not to require additional response calculations. The use of inexpensive probabilistic optimization allows easy incorporation of system reliability constraints and optimal allocation of risk between failure modes. The method is demonstrated using a beam problem and a ten-bar truss problem. The former allocates risk between two different failure modes, while the latter allocates risk between members. It is shown that ECARD provides most of the improvement from risk re-allocation that can be obtained from full probabilistic optimization.