A Probabilistic Approach to Multivariate Constrained Robust Design Simulation

Presented at the 2nd World AviationCongress and Exposition, Anaheim, CA, October 13-16, 1997.Several approaches to robust design have been proposed in the past. Only few acknowledged the paradigm shift from performance based design to design for cost. The incorporation of economics in the design process, however, makes a probabilistic approach to design necessary, due to the inherent ambiguity of assumptions and requirements as well as the operating environment of future aircraft. The approach previously proposed by the authors, linking Response Surface Methodology with Monte Carlo Simulations, has revealed itself to be cumbersome and at times impractical for multi-constraint, multi-objective problems. In addition, prediction accuracy problems were observed for certain scenarios that could not easily be resolved. Hence, this paper proposes an alternate approach to probabilistic design, which is based on a Fast Probability Integration technique. The paper critically reviews the combined Response Surface Equation/ Monte Carlo Simulation methodology and compares it against the Advanced Mean Value (AMV) method, one of several Fast Probability Integration techniques. Both methods are used to generate cumulative distribution functions, which are being compared in an example case study, employing a High Speed Civil Transport concept. Based on the outcome of this study, an assessment and comparison of the analysis effort and time necessary for both methods is performed. The Advanced Mean Value method shows significant time savings over the Response Surface Equation/Monte Carlo Simulation method, and generally yields more accurate CDF distributions. The paper also illustrates how by using the AMV method for distribution generation, robust design solutions to multivariate constrained problems may be obtained. These robust solutions are optimizing the objective function for a given level of risk the decision maker is willing to take

A Methodology for Fitting and Validating Metamodels in Simulation

This expository paper discusses the relationships among metamodels, simulation models, and problem entities. A metamodel or response surface is an approximation of the input/output function implied by the underlying simulation model. There are several types of metamodel: linear regression, splines, neural networks, etc. This paper distinguishes between fitting and validating a metamodel. Metamodels may have different goals: (i) understanding, (ii) prediction, (iii) optimization, and (iv) verification and validation. For this metamodeling, a process with thirteen steps is proposed. Classic design of experiments (DOE) is summarized, including standard measures of fit such as the R-square coefficient and cross-validation measures. This DOE is extended to sequential or stagewise DOE. Several validation criteria, measures, and estimators are discussed. Metamodels in general are covered, along with a procedure for developing linear regression (including polynomial) metamodels.

Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment

This paper presents a concise state-of-the-art review along with an exhaustive comparative investigation on surrogate models for critical comparative assessment of uncertainty in natural frequencies of composite plates on the basis of computational efficiency and accuracy. Both individual and combined variations of input parameters have been considered to account for the effect of low and high dimensional input parameter spaces in the surrogate based uncertainty quantification algorithms including the rate of convergence. Probabilistic characterization of the first three stochastic natural frequencies is carried out by using a finite element model that includes the effects of transverse shear deformation based on Mindlin’s theory in conjunction with a layer-wise random variable approach. The results obtained by different metamodels have been compared with the results of traditional Monte Carlo simulation (MCS) method for high fidelity uncertainty quantification. The crucial issue regarding influence of sampling techniques on the performance of metamodel based uncertainty quantification has been addressed as an integral part of this article

Contribuições ao estudo de grafos fuzzy : teoria e algoritmos

Orientadores: Akebo YamakamiTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoDoutorad