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The locally resonant sonic material (LRSM) is an artificial metamaterial that can block underwater sound. The low-frequency insulation performance of LRSM can be enhanced by coupling local resonance and Bragg scattering effects. However, such method is hard to be experimentally proven as the best optimizing method. Hence, this paper proposes a statistical optimization method, which first finds a group of optimal solutions of an object function by utilizing genetic algorithm multiple times, and then analyzes the distribution of the fitness and the Euclidean distance of the obtained solutions, in order to verify whether the result is the global optimum. By using this method, we obtain the global optimal solution of the low-frequency insulation of LRSM. By varying parameters of the optimum, it can be found that the optimized insulation performance of the LRSM is contributed by the coupling of local resonance with Bragg scattering effect, as well as a distinct impedance mismatch between the matrix of LRSM and the surrounding water. This indicates coupling different effects with impedance mismatches is the best method to enhance the low-frequency insulation performance of LRSM.
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