Impedance calculations for elements of sonar arrays by neural-network-based integration

In this paper, a technique of neural network based integration is proposed to calculate the self- and mutual-impedances within arrays of sonar transducers. The ulti-dimensional integrals appearing in self- and mutual-impedance formulations are transformed into neural-network-based integration and the final results can be found from look-up tables in mathematical handbooks. Initially, the integrand is modeled by a trained neural network. Integration on the integrand then becomes integration on the linear combination of weights and basis functions within the neural network. The results will become the linear combination of error functions which can be looked up in mathematical handbooks. Numerical simulation shows that the results calculated by the proposed method are consistent with those given in other existing studies. The proposed technique requires neither numerical nor artificial integration procedure. Due to the inherent learning and predicting property of neural network, only a small number of sampling points for the integrand are required in the proposed integration technique.