Metamodel-Based Probabilistic Design Optimization of Static Systems With an Extension to Dynamic Systems

Abstract

In design, much research deals with cases where design variables are deterministic thus ignoring possible uncertainties present in manufacturing or environmental conditions. When uncertainty is considered, the design variables follow a particular distribution whose parameters are defined. Probabilistic design aims to reduce the probability of failure of a system by moving the distribution parameters of the design variables. The most popular method to estimate the probability of failure is a Monte Carlo Simulation where, using the distribution parameters, many runs are generated and the number of times the system does not meet specifications is counted. This method, however, can become time-consuming as the mechanistic model developed to model a physical system becomes increasingly complex. From structural reliability theory, the First Order Reliability Method (FORM) is an efficient method to estimate probability and efficiently moves the parameters to reduce failure probability. However, if the mechanistic model is too complex FORM becomes difficult to use. This paper presents a methodology to use approximating functions, called 'metamodels', with FORM to search for a design that minimizes the probability of failure. The method will be applied to three examples and the accuracy and speed of this metamodel-based probabilistic design method will be discussed. The speed and accuracy of three popular metamodels, the response surface model, the Radial Basis Function and the Kriging model are compared. Later, some theory will be presented on how the method can be applied to systems with a dynamic performance measure where the response lifetime is required to computer another performance measure.

Reliability based optimization of fiber reinforced elastomeric bearings

“…Metamodels or surrogate models have been used extensively [9][10][11] to approximate nonlinear models. Using metamodels for optimization problems of time demanding applications increases the efficiency of the optimization, [12][13][14]. Reliability based optimization allow to search for the optimal design point while considering uncertainty in the input factors.…”

Performance-Based Optimal Design of a Dynamic System for a Guided Projectile

“…Response characteristics of a dynamic system vary according to initial conditions and variation in either component due to the manufacturing processes or operating conditions, as well as input uncertainty. For design of dynamic systems with uncertainties in the components, there have been three different approaches: a) mechanistic model-based approach [1], b) eigenvalue-based approach [2], and c) metamodel-based approach using a series of responses over time [3].…”