Accurate response surface approximations for weight equations based on structural optimization.

摘要

Accurate weight prediction methods are vitally important for aircraft design optimization. Therefore, designers seek weight prediction techniques with low computational cost and high accuracy, and usually require a compromise between the two. The compromise can be achieved by combining stress analysis and response surface (RS) methodology. While stress analysis provides accurate weight information, RS techniques help to transmit effectively this information to the optimization procedure.; The focus of this dissertation is structural weight equations in the form of RS approximations and their accuracy when fitted to results of structural optimizations that are based on finite element analyses. Use of RS methodology filters out the numerical noise in structural optimization results and provides a smooth weight function that can easily be used in gradient-based configuration optimization. In engineering applications RS approximations of low order polynomials are widely used, but the weight may not be modeled well by low-order polynomials, leading to bias errors. In addition, some structural optimization results may have high-amplitude errors (outliers) that may severely affect the accuracy of the weight equation.; Statistical techniques associated with RS methodology are sought in order to deal with these two difficulties: (1) high-amplitude numerical noise (outliers) and (2) approximation model inadequacy.; The investigation starts with reducing approximation error by identifying and repairing outliers. A potential reason for outliers in optimization results is premature convergence, and outliers of such nature may be corrected by employing different convergence settings. It is demonstrated that outlier repair can lead to accuracy improvements over the more standard approach of removing outliers. The adequacy of approximation is then studied by a modified lack-of-fit approach, and RS errors due to the approximation model are reduced by using higher order polynomials. In addition, remaining error in the RS weight equation is characterized, and two error measures are introduced. One of the measures is qualitative, and it is used to identify regions of design space where RS accuracy may be poor. The second measure is quantitative, but conservative. Its use is demonstrated for incorporating the uncertainty due to RS weight equation with parameter uncertainty in order to compare competing designs for robustness.