A numerical optimization approach is presented to optimize passive broadband detection performance of hull arrays through the adjustment of array shading weights. The approach is developed for general hull arrays in low signal-to-noise ratio scenarios, and is shown to converge rapidly to optimal solutions that maximize the array’s deflection coefficient. The beamformer is not redesigned in this approach; only the shading weights of the conventional beamformer are adjusted. This approach allows array designers to use the array to minimize the impact of known sources of noise on detection at the beamformer output while maintaining acoustic array gain against an unknown source. The technique is illustrated through numerical examples using hull-borne structural noise as the noise source; however, the design concept can be applied to other design parameters of the array such as element position, material selection, etc.

1.
C. L.
Dolph
, “
A current distribution for broadside arrays which optimizes the relationship between beam width and sidelobe level
,”
Proc. IRE
34
,
335
348
(
1946
).
2.
T. T.
Taylor
, “
Design of line-source antennas for narrow beamwidth and low side lobes
,”
IRE Trans. Antennas Propag.
AP-1
,
17
20
(
1955
).
3.
B. D.
Van Veen
and
K. M.
Buckley
, “
Beamforming: A versatile approach to spatial filtering
,”
IEEE ASSP Mag.
5
,
4
24
(
1988
).
4.
J. P. Casey, and D. Wu, “Numerical acoustic hull array optimization,” NUWC-NPT Technical Report 11239, Naval Undersea Warfare Center Division, Newport, RI (2000).
5.
H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Part I, Chap. 2.
6.
P. T.
Boggs
and
J. W.
Tolle
, “
Sequential quadratic programming
,”
Acta Numerica
4
,
1
51
(
1996
).
7.
J. Nocedal and S. J. Wright, Numerical Optimization (Springer, New York, 1999), Chap. 18.
8.
P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright, “User’s guide for NPSOL 5.0: A FORTRAN package for nonlinear programming,” Report SOL 86-1, Dept. of Operations Research, Stanford University (1998), available online at 〈http://www.stanford.edu/group/SOL〉.
9.
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration (Academic, New York, 1975), Sec. 2.3.
10.
M. C. Junger and D. Feit, Sound, Structures, and Their Interaction (MIT Press, Cambridge, MA, 1986), Secs. 7.17–7.19.
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