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A Probabilistic Approach to Multivariate Constrained Robust Design Simulation

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Probabilistic and Robust Engineering Design Product Development and Customization Advanced Multi-Objective Optimization Algorithms

Abstract

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.

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References

1989Design and Analysis of Computer Experiments 1979Statistics for Experimenters 1988Empirical Model Building and Response Surfaces 1990A Primer on the Taguchi Method 1989Designs for Computer Experiments 1992Screening, Predicting, and Computer Experiments 1990Statistical tools for simulation practitioners 1991Life-cycle cost and economic analysis

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2000A probabilistic multi-criteria decision making technique for conceptual and preliminary aerospace systems design 2005Robust design optimization of structures under uncertainties 1998A Stochastic Design Approach for Aircraft Affordability 1998Probabilistic assessment of handling qualities characteristics in preliminary aircraft design

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