Approximation Techniques for Broad-Band Acoustic Radiated Noise Design Optimization Problems

Abstract

This study investigates the applicability of various approximation methods to broadband radiated noise design optimization problems. Low-order series approximations of dynamic response may be used to replace full numerical system solutions to effect significant computer cost savings during design iterations. Also, the ease of evaluating the approximate functions may be further exploited by using global optimization search methods, such as simulated annealing, at individual design iterations. The combination of approximating radiated noise spectra and evaluating the approximate spectra for all possible design alternatives greatly increases the possibility of finding a truly optimal design. The effectiveness of the approximations is measured by considering optimization accuracy, evaluated by the algorithm’s ability to find a global or near-global minimum independent of the initial design; computational efficiency, based on the number of numerical design analyses required for convergence; and generality, where the method should be relatively independent of the problem type. Finite element models of three test cases with varying performance goals and design parameters were used to evaluate the optimization methods. Shell thicknesses, shell loss factors, and rib stiffener locations were varied to minimize structural weight and manufacturing costs while lowering broad-band radiated noise levels below a specified goal. First-order Taylor and half-quadratic series approximation optimization approaches were compared to traditional local minimization methods (Modified Method of Feasible Directions and Broydon-Fletcher-Goldfarb-Shanno). For all test cases, the approximation approaches found the global optimum design more frequently than the local minimization methods. Also, the half-quadratic method converged using fewer design evaluations than the first-order Taylor method for most test cases.