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.

1.
Allik, H., Dees, R., Moore, S., and Pan, D., 1992, SARA-2D User’s Manual, Version 92-5, BBN Systems and Technologies.
2.
Bernhard
R. J.
, “
A Finite Element Method for Synthesis of Acoustical Shapes
,”
Journal of Sound and Vibration
, Vol.
98
, No.
1
, pp.
55
65
.
3.
Broydon
C. G.
,
1970
, “
The Convergence of a Class of Double Rank Minimization Algorithms
,” Parts I and II,
Journal of Mathematics Applications
, Vol.
6
, pp.
76
90
.
4.
Corana, A., Marchesi, M., Martini, C., and Ridella, S., 1987, “Minimizing Multi-Modal Functions of Continuous Variables with the Simulated Annealing Algorithm,” ACM Transactions on Mathematical Software 13, pp. 262–280.
5.
Cunefare
K. A.
, and
Koopmann
G. H.
,
1992
, “
Acoustic Design Sensitivity for Structural Radiators
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, pp.
178
186
, Apr.
6.
Fletcher
R.
,
1970
, “
A New Approach to Variable Metric Algorithms
,”
Computer Journal
, Vol.
13
, pp.
317
322
.
7.
Goffe, W. L., Ferrier, G. D., and Rogers, J., 1993, “Global Optimization of Statistical Functions with Simulated Annealing,” Journal of Econometrics, Fall, in press.
8.
Goldfarb
D.
, “
A Family of Variable Metric Methods Derived by Variational Means
,”
Math Computing
, Vol.
24
, pp.
23
36
.
9.
Grandhi, 1992, “Structural Optimization with Frequency Constraints—A Review,” AIAA Paper 92-4813, September.
10.
Hambric, S. A., 1992, “Structural—Acoustic Optimization of a Point-Excited, Submerged Cylindrical Shell,” Proceedings of the 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, Cleveland, OH, pp. 1096–1103, September 21–23.
11.
Kane
J. H.
,
Mao
S.
, and
Everstine
G. C.
,
1991
, “
A Boundary Element Formulation for Acoustic Shape Sensitivity Analysis
,”
Journal of the Acoustical Society of America
, Vol.
90
, No.
1
, pp.
561
573
, July.
12.
Miura
H.
, and
Schmit
L. A.
,
1978
, “
Second Order Approximation of Natural Frequency Constraints in Structural Synthesis
,”
International Journal for Numerical Methods in Engineering
, Vol.
13
, pp.
337
351
.
13.
Mlejnek
H. P.
,
Jehle
U.
, and
Schirrmacher
R.
,
1992
, “
Second Order Approximations in Structural Genesis and Shape Finding
,”
International Journal for Numerical Methods in Engineering
, Vol.
34
, No.
3
, pp.
853
872
.
14.
Sepulveda, A. E., and Jin, I. M., 1992, “Design of Structure/Control Systems with Transient Response Constraints Exhibiting Relative Minima,” Proceedings of the 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization. Cleveland OH, pp. 371–378, September 21–23.
15.
Shanno
D. F.
,
1970
, “
Conditioning of Quasi-Newton Methods for Function Minimization
,”
Math Computing
, Vol.
24
, pp.
647
656
.
16.
Vanderplaats
G. N.
,
1984
, “
An Efficient Feasible Directions Algorithm for Design Synthesis
,”
AIAA Journal
, Vol.
22
, No.
11
, pp.
1633
1640
.
17.
Vanderplaats, G. N., 1985, ADS-A FORTRAN Program for Automated Design Synthesis, Version 1.10, Engineering Design Optimizations, Inc.
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