Stochastic subset optimization incorporating moving least squares response surface methodologies for stochastic sampling

The design of engineering systems under probabilistic model uncertainty using stochastic simulation techniques is discussed in this paper. A recently developed algorithm, called Stochastic Subset Optimization (SSO), is adopted for solution of the associated optimization problem. SSO is based on formulation of an augmented stochastic design problem and relies on simulation of samples from an auxiliary probability density function to establish a sensitivity analysis for the design variables. This stochastic sampling requires repeated evaluation of system model response and corresponds to the computationally most intensive part of the algorithm. A Moving Least Squares (MLS) response surface approximation is introduced here for reduction of this computational burden. The paper focuses on the efficient integration of the MLS approximation within SSO. Specifically, adaptive selection of the MLS weights is proposed exploiting information directly available from SSO to quantify the importance of the uncertain model parameters and the design variables in affecting the system response. A measure based on relative information entropy concepts is introduced for this purpose and its efficient evaluation is examined in detail. The selection of support points for generating the response surface is also addressed, and a novel measure is finally introduced for evaluating the efficiency of the response surface approximation in terms of the stochastic sampling accuracy.