Ruichen Jin

Comparative studies of metamodeling techniques under multiple modeling criteria

Despite the advances in computer capacity, the enormous computational cost of complex engineering simulations makes it impractical to rely exclusively on simulation for the purpose of design optimization. To cut down the cost, surrogate models, also known as metamodels, are constructed from and then used in lieu of the actual simulation models. In the paper, we systematically compare four popular metamodeling techniques —Polynomial Regression, Multivariate Adaptive Regression Splines, Radial Basis Functions, and Kriging —based on multiple performance criteria using fourteen test problems representing different classes of problems. Our objective in th is study is to investigate the advantages and disadvantages these four metamodeling techniques using multiple modeling criteria and multiple test problems rather than a single measure of merit and a single test problem.

ON SEQUENTIAL SAMPLING FOR GLOBAL METAMODELING IN ENGINEERING DESIGN

Approximation models (also known as metamodels) have been widely used in engineering design to facilitate analysis and optimization of complex systems that involve computationally expensive simulation programs. The accuracy of metamodels is directly related to the sampling strategies used. Our goal in this paper is to investigate the general applicability of sequential sampling for creating global metamodels. Various sequential sampling approaches are reviewed and new approaches are proposed. The performances of these approaches are investigated against that of the one-stage approach using a set of test problems with a variety of features. The potential usages of sequential sampling strategies are also discussed.Copyright

Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. in this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels. The approach is especially applicable to simulation-based design because metamodels are often created to replace expensive simulation programs, and therefore readily available to designers. In this work, we identify the needs of GSA in design under uncertainty, and then develop generalized analytical formulations that can provide GSA for a variety of metamodels commonly used in engineering applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results of univariate integrals can be constructed to calculate the multivariate integrals in GSA. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.

Analytical Metamodel-Based Global Sensitivity Analysis and Uncertainty Propagation for Robust Design

Metamodeling approach has been widely used due to the high computational cost of using high-fidelity simulations in engineering design. Interpretation of metamodels for the purpose of design, especially design under uncertainty, becomes important. The computational expenses associated with metamodels and the random errors introduced by sample-based methods require the development of analytical methods, such as those for global sensitivity analysis and uncertainty propagation to facilitate a robust design process. In this work, we develop generalized analytical formulations that can provide efficient as well as accurate global sensitivity analysis and uncertainty propagation for a variety of metamodels. The benefits of our proposed techniques are demonstrated through vehicle related robust design applications.

Analytical global sensitivity analysis and uncertainty propagation for robust design

Simulation-based robust design is playing an increasingly important role in industrial practice where design analyses involve extensive computer simulations. In simulation-based robust design, metamodels, also called response surface models, are often created to replace computationally expensive, high-fidelity, and black-box type of simulation programs. Interpretation of metamodels for the purpose of robust design becomes important. The computational expenses associated with certain types of metamodels and the random errors introduced by the data-sampling approach require the development of analytical methods, such as those for global sensitivity analysis (GSA) and uncertainty propagation (UP) to facilitate a robust-design process. In this work, generalized analytical formulations are developed for GSA and UP in robust design via the use of a variety of metamodels commonly used in engineering design applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results can be derived based on decomposed univariate integrals. The benefits of our proposed techniques are demonstrated using the robust engine piston design as an example. Even though our discussion is oriented toward simulation-based robust design, the same approach can be applied to quality engineering applications where metamodels are constructed based on physical experiments.

An efficient algorithm for constructing optimal design of computer experiments

Metamodeling approach has been widely used due to the high computational cost of using high-fidelity simulations in engineering design. The accuracy of metamodels is directly related to the experimental designs used. Optimal experimental designs have been shown to have good “space filling” and projective properties. However, the high cost in constructing them limits their use. In this paper, a new algorithm for constructing optimal experimental designs is developed. There are two major developments involved in this work. One is on developing an efficient global optimal search algorithm, named as enhanced stochastic evolutionary (ESE) algorithm. The other is on developing efficient algorithms for evaluating optimality criteria. The proposed algorithm is compared to two existing algorithms and is found to be much more efficient in terms of the computation time, the number of exchanges needed for generating new designs, and the achieved optimality criteria. The algorithm is also very flexible to construct various classes of optimal designs to retain certain structural properties.Copyright

Analytical Uncertainty Propagation via Metamodels in Simulation-Based Design under Uncertainty

In spite of the benefits, one of the most challenging issues for implementing optimization under uncertainty, such as the use of robust design approach, is associated with the intensive computational demand of uncertainty propagation, especially when the simulation programs are computationally expensive. In this paper, an efficient approach to uncertainty propagation via the use of metamodels is presented. Metamodels, created through computer simulations to replace expensive simulation programs, are widely used in simulation-based design. Different from existing techniques that apply sample-based methods to metamodels for uncertainty propagation, our method utilizes analytical derivations to eliminate the random errors as well as to reduce the computational expenses of sampling. In this paper, we provide analytical formulations for mean and variance evaluations via a variety of metamodels commonly used in engineering design applications. The benefits of our proposed techniques are demonstrated through the robust design for improving vehicle handling. In addition to the improved accuracy and efficiency, our proposed analytical approach can greatly improve the convergence behavior of optimization under uncertainty.

Analytical variance-based global sensitivity analysis in simluation-based design under uncertainty

The importance of sensitivity analysis in engineering design cannot be over-emphasized. In design under uncertainty, sensitivity analysis is performed with respect to the probabilistic characteristics. Global sensitivity analysis (GSA), in particular, is used to study the impact of variations in input variables on the variation of a model output. One of the most challenging issues for GSA is the intensive computational demand for assessing the impact of probabilistic variations. Existing variance-based GSA methods are developed for general functional relationships but require a large number of samples. In this work, we develop an efficient and accurate approach to GSA that employs analytic formulations derived from metamodels of engineering simulation models. We examine the types of GSA needed for design under uncertainty and derive generalized analytical formulations of GSA based on a variety of metamodels commonly used in engineering applications. The benefits of our proposed techniques are demonstrated and verified through both illustrative mathematical examples and the robust design for improving vehicle handling performance.Copyright

Occupant Restraint System Design Under Uncertainty Using Analytical Uncertainty Propagation Via Metamodels

The effectiveness of using Computer Aided Engineering (CAE) tools to support design decisions is often hindered by the enormous computational demand of complex analysis models, especially when uncertainty is considered. Approximations of analysis models, also known as “metamodels”, are widely used to replace analysis models for optimization under uncertainty. However, due to the inherent nonlinearity in occupant responses during a crash event and relatively large numbers of uncertain variables and responses, naive application of metamodeling techniques can yield misleading results with little or no warning from the algorithms which generate the metamodels. Furthermore, in order to improve the quality of metamodels, a relatively large number of design of experiments (DOE) and comparatively expensive metamodeling techniques, such as Kriging or radial basis function (RBF), are necessary. Thus, sampling-based methods, e.g. Monte Carlo simulations, for obtaining the statistical quantities of system responses during the optimization loop may still be inefficient even for these metamodels. In recent years, analytical uncertainty propagation via metamodels is proposed by Chen et al. 2004, which provides analytical formulation of mean and variance evaluations via a variety of metamodeling techniques to reduce the computational time and improve the convergence behavior of optimization under uncertainty. An occupant restraint system design problem is used as an example to test the applicability of this method.Copyright