A parallel gradient method for the determination of the design point in probabilistic analysis

Abstract

In the probabilistic analysis of engineering systems, the design point denotes a particular set of input parameters where the system response is most likely to take a given design value. It provides important information on the system behaviour and its sensitivity to input parameters. The design point is determined from the joint probability distribution function (pdf) of input parameters. Mathematically, the problem is equivalent to an isoperimetric problem: find a stationary point of the joint pdf subject to the given value of the system response. The proposed method depends on the response and the joint pdf being parallel at the stationary point. This requires the projection of the pdf gradient to be zero on the hyperplane orthogonal to the response