A Simple Explicit Meta-Model for Probabilistic Design of Dynamic Systems with Multiple Mixed Inputs

Abstract

Most systems have multiple inputs that comprise of a mixture of excitations and component parameters. Excitations are different from component parameters in that they are always functions of time. In mechanical systems, these include applied forces, applied displacements, system settings, systems configurations and operating conditions. It would be convenient to include multiple excitations and multiple component parameters in a meta-model to take advantage of the inherent computation speed needed for timely probability-based design optimization. In the development of the meta-model in this paper, we treat the component parameters in the same manner as the excitations and thus, in both cases, form time-sampled vectors. A design-of-experiments training regime creates a single input matrix, and using the mechanistic model, a single output matrix. Finally, a simple, explicit, meta-model is developed that turns an arbitrary vector of contiguous multiple excitations and multiple component parameters into the corresponding output vector (herein, the response). The approach provides an appealing and efficient solution to the multiple, mixed input problem, and in addition, requires only off-the-shelf computer software. The efficacy of the meta-model is shown through probability-based design optimization (PBDO) of a tire-wheel assembly, modelled as a mass-spring-damper system with nonlinear hysteresis, under a combination of practical inputs.