Here we propose a detailed protocol to enable an accelerated inverse design of acoustic coatings for underwater sound attenuation application by coupling Machine Learning and an optimization algorithm with Finite Element Models (FEM). The FEMs were developed to obtain the realistic performance of the polyurethane (PU) acoustic coatings with embedded cylindrical voids. The frequency dependent viscoelasticity of PU matrix is considered in FEM models to substantiate the impact on absorption peak associated with the embedded cylinders at low frequencies. This has been often ignored in previous studies of underwater acoustic coatings, where usually a constant frequency-independent complex modulus was used for the polymer matrix. The key highlight of the proposed optimization framework for the inverse design lies in its potential to tackle the computational hurdles of the FEM when calculating the true objective function. This is done by replacing the FEM with an efficiently computable surrogate model developed through a Deep Neural Network. This enhances the speed of predicting the absorption coefficient by a factor of $$4.5 \times 10^3$$ 4.5 × 10 3 compared to FEM model and is capable of rapidly providing a well-performing, sub-optimal solution in an efficient way. A significant, broadband, low-frequency attenuation is achieved by optimally configuring the layers of cylindrical voids. This is accomplished by accommodating attenuation mechanisms, including Fabry–P$$\acute{e}$$ e ´ rot resonance and Bragg scattering of the layers of voids. Furthermore, the proposed protocol enables the inverse and targeted design of underwater acoustic coatings through accelerating the exploration of the vast design space compared to time-consuming and resource-intensive conventional trial-and-error forward approaches.
Here, we report the development of a detailed "Materials Informatics" framework for the design of acoustic coatings for underwater sound attenuation through integrating Machine Learning (ML) and statistical optimization algorithms with a Finite Element Model (FEM). The finite element models were developed to simulate the realistic performance of the acoustic coatings based on polyurethane (PU) elastomers with embedded cylindrical voids. The FEM results revealed that the frequency-dependent viscoelastic behavior of the polyurethane matrix has a significant impact on the magnitude and frequency of the absorption peak associated with the cylinders at low frequencies, which has been commonly ignored in previous studies on similar systems. The data generated from the FEM was used to train a Deep Neural Network (DNN) to accelerate the design process, and subsequently, was integrated with a Genetic Algorithm (GA) to determine the optimal geometric parameters of the cylinders to achieve maximized, broadband, low-frequency waterborne sound attenuation. A significant, broadband, low-frequency attenuation is achieved by optimally configuring the layers of cylindrical voids and using attenuation mechanisms, including Fabry-Pérot resonance and Bragg scattering of the layers of voids. Integration of the machine learning technique into the optimization algorithm further accelerated the exploration of the high dimensional design space for the targeted performance. The developed DNN exhibited significantly increased speed (by a factor of 4.5 × 10 3 ) in predicting the absorption coefficient compared to the conventional FEM(s). Therefore, the acceleration brought by the materials informatics framework brings a paradigm shift to the design and development of acoustic coatings compared to the conventional trial-and-error practices.
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