17. Efficient Use of Meta-Models for Reliability-Based Design Optimization of Systems Under Stochastic Excitations and Stochastic Deterioration

The main difficulty in the application of reliability-based design optimization (RBDO) to time-dependent systems is the continual interplay between calculating time-variant reliability (to ensure reliability policies are met) and moving the design point to minimize some objective function, such as cost, weight or size. In many cases, the reliability can be obtained readily using, for example, first-order reliability methods (FORM). However, this option is not available when certain stochastic processes are invoked to model, for example, gradual damage or deterioration. In this case, inefficient Monte Carlo simulation (MCS) must be used. The work herein provides a novel way to obviate this inefficiency. First, a meta-model is built to relate the system cumulative distribution function of time to failure (cdf) to the design space. A design of experiments paradigm helps determine a few training sets and then the mechanistic model and the uncertain characteristics of the variables, with MCS, help produce the corresponding cdf curves. The meta-model (using matrix methods) directly links an arbitrary sample from the design space to its cdf. The optimization process accesses the meta-model to quickly evaluate both objectives and failure constraints. A case study uses a electromechanical servo system. The meta-model approach is compared to the traditional MCS approach and found to be simple, accurate and very fast, suggesting an attractive means for RBDO of time-dependent systems under stochastic excitations and stochastic deterioration.