A Sequential Algorithm for Possibility-Based Design Optimization

Deterministic optimal designs that are obtained without taking into account uncertainty/variation are usually unreliable. Although reliability-based design optimization accounts for variation, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. After the fundamentals of possibility theory and fuzzy measures are described, a double-loop, possibility-based design optimization algorithm is presented where all design constraints are expressed possibilistically. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. In order to reduce the high computational cost, a sequential algorithm for possibility-based design optimization is presented. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. Two examples demonstrate the accuracy and efficiency of the proposed sequential algorithm.