Database Adaptive Fuzzy Membership Function Generation for Possibility-Based Aircraft Design Optimization

Abstract

Aircraft conceptual design traditionally uses simplified analysis and optimization methods to generate the basic configuration of the aircraft. Analysis methods cannot fully represent the real physical phenomena, and hence the optimum solution may fail to satisfy the constraints when more sophisticated analysis is applied. This research proposes the use of a database to estimate the prediction errors associated with a particular analysis method. Newly proposed adaptive piecewise-linear fuzzy membership functions accurately represent the intervals of prediction errors to compensate for the discrepancies caused by analysis. A possibility-based design optimization framework is developed to solve nonprobabilistic design problems with uncertainties represented by the adaptive piecewise-linear fuzzy membership intervals. A two-seater light aircraft design problem has been solved to demonstrate the proposed method. The adaptive piecewise-linear fuzzy membership fu\nctions for six major analysis modules of in-house software were constructed using information about 15 aircraft stored in the database. Estimated errors of the analysis stay within 10% range. The adaptive piecewise-linear fuzzy membership function for selected parameters stores 39% more samples on average than the triangular functions that are traditionally used for possibility-based design optimization. The results of the design problem show that the objective function is improved by 3.4% with uncertain intervals covering 100% of database samples and by 46.1% with 12.3% database coverage.

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