A noise abatement method using an eigen function in conjunction with an optimizer (Genetic Algorithm) under a space-constrain situation is proposed in this study concerning a high order wave propagation effect. An eigen function is used to describe an acoustical field and shorten the acoustical model in a four-pole transfer matrix form. The system’s four-pole matrix estimates the Transmission Loss (TL) for the silencers by multiplying individual four-pole matrices.

Additionally, a case study of an air compressor’s broadband noise elimination is introduced. Three types of circular reverse silencers (silencers A-C) internally hybridized with multiple straight chambers are adopted to efficiently suppress the noise wave. Considering broadband characteristics and space-constrained situations, an average-deviation-integrating form used as an objective function is presented and linked to an optimizer-GA (Genetic Algorithm). Acoustical models for silencers A to C are checked before the numerical optimization is performed. A pure tone optimization is executed to assure the consistency of the GA scheme. The result shows that the overall noise drop is enhanced and the number of straight expansion chambers installed at the inlet/outlet of the circular reverse silencer increases. Consequently, concerning a space-constrained situation in the real world and the characteristics of the broadband noise spectrum, an efficient method is proposed in this paper for designing an optimally shaped hybrid muffler using the objective function in conjunction with an optimization scheme.