TY - JOUR

T1 - Analysis for Mutual Impedance of Pistons by Neural Network and Its Extension of Derivative

AU - Lee, Kun Chou

N1 - Funding Information:
The authors would like to thank the financial support from the Ministry of Science and Technology, Taiwan, under Grant MOST 108-2221-E-006-091 and the National Center for High Performance Computing, Taiwan, for computer time and facilities
Publisher Copyright:
© 2020 Kun-Chou Lee.

PY - 2020

Y1 - 2020

N2 - This study is basically a mathematical problem in sonar engineering. The sonar plays a very important role in underwater communication, detection, and remote sensing. Pistons are key sensors in a sonar system. The mutual coupling is a challenging problem in designing a sonar array. The mutual impedance of pistons is required in analyzing the mutual coupling of a sonar array. In this paper, a mathematical model consisting of a neural network and its extension of derivative is given and then utilized to analyze the mutual impedance of pistons. Initially, the mutual impedance of pistons is modelled and predicted by a neural network. By suitably extending the neural network, the derivative, i.e., slope information, for the neural-network output is obtained easily. Therefore, the mutual impedance and its slope information are obtained simultaneously almost in real time as the neural network is well trained in advance. Numerical examples show that the neural network can accurately predict the mutual impedance and its extension of derivative gives the slope information of mutual impedance simultaneously. It should be emphasized that the training work of a neural network is performed only once, i.e., only the training work in mapping the mutual impedance is required. No additional training work is required in obtaining the slope information.

AB - This study is basically a mathematical problem in sonar engineering. The sonar plays a very important role in underwater communication, detection, and remote sensing. Pistons are key sensors in a sonar system. The mutual coupling is a challenging problem in designing a sonar array. The mutual impedance of pistons is required in analyzing the mutual coupling of a sonar array. In this paper, a mathematical model consisting of a neural network and its extension of derivative is given and then utilized to analyze the mutual impedance of pistons. Initially, the mutual impedance of pistons is modelled and predicted by a neural network. By suitably extending the neural network, the derivative, i.e., slope information, for the neural-network output is obtained easily. Therefore, the mutual impedance and its slope information are obtained simultaneously almost in real time as the neural network is well trained in advance. Numerical examples show that the neural network can accurately predict the mutual impedance and its extension of derivative gives the slope information of mutual impedance simultaneously. It should be emphasized that the training work of a neural network is performed only once, i.e., only the training work in mapping the mutual impedance is required. No additional training work is required in obtaining the slope information.

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U2 - 10.1155/2020/3635785

DO - 10.1155/2020/3635785

M3 - Article

AN - SCOPUS:85082679478

SN - 1024-123X

VL - 2020

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

M1 - 3635785

ER -