Facilitating Probabilistic Multidisciplinary Optimization Using Kriging Approximation Models

Abstract

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions-including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties-is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation-input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

Multi-objective optimal approach for injection molding based on surrogate model and particle swarm optimization algorithm

“…1. As a new kind of surrogate model technique, Kriging model has been widely used in recent years for surrogate modeling of computationally expensive deterministic simulations [7] . This model was applied in geology firstly.…”

Decoupled approach to multidisciplinary design optimization under uncertainty

“…The MDO solution methods proposed by Koch et al (2002), Mahadevan and Gantt (2000), and Oakley et al (1998) are based on the traditional techniques from RBDO that have been developed for structural design since the 1970's. These traditional RBDO techniques estimate the system reliability (via reliability index) within the optimization algorithm and are often referred to as nested-loop (or double-loop) methods.…”

“…In particular, we use in the proposed procedure an integrated approach known as the single-loop method developed by Chen et al (1997) and Liang et al (2004) and a sequential approach known as the sequential optimization and reliability analysis (SORA) method developed by in the context of singledisciplinary RBDO. In (Koch et al 2002) and (Oakley et al 1998), response surfaces are utilized (within the nested-loop methods) in order to improve computational efficiency in solving probabilistic MDO problems.…”

A Combined Cooperative Braking Model with a Predictive Control Strategy in an Electric Vehicle

“…The predictive model is also called the Kriging approximation model. It is a type of the interpolation technique, of which the basic theory was presented in reference [26]. The predictive model can be built through MATLAB.…”