Recovery of parameters of a homogeneous elastic layer using neural networks

Abstract

The problem of recovery of parameters of an elastic uniform layer is considered. The solution method of this problem is proposed by means of neural networks. For the input network parameters, amplitudes of transmitted or reflected waves are chosen. We consider the output parameter of network density and longitudinal speed of the environment filling a layer. Three types of neurons activation function are chosen: piecewise-linear, sigmoid and radial function (Gauss's function). The following algorithms of perseptron training are considered: the backpropagation algorithm and the genetic algorithm. In the genetic algorithm, the crossover method, in which the next gene is selected equiprobable and incidental from genes of the ancestors located in the same position is chosen. Then genes of a new chromosome with small probability are exposed to mutations at a small value. Training of neural network takes place according to the calculated data of the direct problem solved multiply times with various elastic parameters varying in the defined intervals. Dependences graphs of an error of parameter recovery on such parameters of neural network as selection dimension and neurons’ number are provided. Deterioration in accuracy of recovery of required data, when training network, is shown. Results of comparison of neural networks with various activation functions are described. For density and speed of a layer recovery at the same time, the method of calculation of unknown elastic parameters using the neural network trained for recovery of acoustic rigidity and wave number is proposed. The conclusion is drawn that radial function of neurons activation yields steadier results.

Keywords: parameter recovery, uniform elastic layer, neural network