A procedure for generating a customized weight function for wing bending material weight of the High Speed Civil Transport (HSCT) is described. The weight function is based on the shape parameters. A response surface methodology is used to t a quadratic polynomial to data gathered from a large number of structural optimizations. The results of the structural optimization are noisy. Noise reduction in the structural optimization results is discussed. Several techniques are used to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to nd regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT, while the response surfaces themselves are created employing detailed analysis methods. Intervening variables and analysis of variance are used to reduce the number of polynomial terms in the response surface model functions. Minimum variance and minimum bias procedures for creation of response surfaces are compared. Con guration optimization of the HSCT employing customized weight functions with di erent response surfaces are compared.

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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.

This paper describes the flexible implementation of approximation concepts in an MDO framework offered by the commercial-off-theshelf software package iSIGHT. Three different types of approximation models-Response Surface Modeling, Taylor Series Approximations, and Variable Complexity Modeling-are implemented in such a way that they may be used interchangeably in any combination to approximate any segment of an MDO analysis problem, as well as the complete system analysis sequence as a whole. The novelty of the implementation is in the fact that all approximation models are implemented as "smart" objects. Each of the objects possesses certain characteristics defined by the "tuning parameters" specific to each approximation type, and a suite of methods (actions) which operate on the data of each model. The concept of Response Surface Modeling is taken to the extreme of simplicity and efficiency by using a minimum number of design analyses for model construction and then gradually improving the quality of the model following the path of the optimizer The category of Taylor Series Approximations actually spans a whole suite of approximation techniques that are based on using the first derivatives of the response function. Applications demonstrate the utility and flexibility of the approach.