Frequency Domain Optimization of Homogeneous Anechoic Multi-Layers ‎Using ‎Genetic Programming‎

Sound-absorbing coatings are of great importance in noise control, thus to make them technically and economically effective, their design optimization is a necessity. Multi-layered homogeneous linings, intended to provide a certain level of absorption, have recently been of much interest among the anechoic coatings. In the present work, first, a mathematical model, called Transfer Matrix Method (TMM) is introduced and validated to properly predict the acoustic response of cavity-less multi-layers. Next, a two-loop optimization technique aimed at maximizing the mean value of echo reduction and minimizing the layers’ total thickness is developed. The outer loop (GP) focuses on the number and order of the layers, while the inner (ICA) is dedicated to the thickness modification of each layer. Finally, results are demonstrated for some specific cases, where promising solutions are found for different constraints and conditions. As an example, comparing a homogeneous coating invented by the GP-ICA (#Generation ۵۰ of Section ۵.۳) with a typical cavity-included coating used for sound absorption shows that the thickness of this new coating is reduced by nearly two-thirds (from ۵۰ mm to ۱۸ mm), while the first hit of the ۲۰ dB band of Echo Reduction (ER) has reduced by ۶۵ % (from ۲۰ kHz to ۷ kHz), and almost did not fall from this level until the end of the frequency domain of interest (۴۰ kHz). That’s while the conventional coating frequency response dropped soon after hitting the ۲۰ dB threshold.

Keywords:

Sound Absorption ‎ , Imperialistic Competitive Algorithm (ICA) , Genetic Programming (GP) , Transfer Matrix Method (TMM) , Frequency Domain , Anechoic , Multi-Layer