Last modified: 2020-08-04

#### Abstract

The computational inverse techniques can be used to convert the problem for internal characteristics, which are difficult to be determine, into external environmental parameters of complex structures. It provides an effective solution for many engineering problems. However, engineering problems are very complicated and the calculation scale is large, many inverse problems are ill-posed. The ill-conditioned system kernel matrix and the noise in the measurement response may severely affect the accuracy and stability of the inverse results. Since the artificial neural network does not rely on the selection of the initial value, it exhibits satisfactory ability of nonlinear mapping and global convergence. Based on the physical model and simulation model, Professor Liu Guirong proposed a two-way trumpet neural network direct weight inversion theory. The analytic solution of the inverse problem was derived by an explicit formula for the first time. Theoretically, inverse problem can be directly solved by the weights and biases of the forward problem neural network and the explicit formula without training the inverse problem neural network. It greatly improves the computational inverse method efficiency. However, this method has only been derived in theory. When generalized inverse processing is performed on the irreversible weight matrix of the forward problem neural network, regularization parameters should be introduced to improve its noise immunity and solution stability. The direct weight inverse method renders close-form solution to the inverse problem, which requires higher accuracy of the regularization parameters. If the regularization parameters are not selected properly, the solution of inverse problem will deviate from the real value.

To make amendment, this paper systematically explores the two-way neural network inverse method, and attempts to overcome the ill-conditioned of the inverse system and functions. Specifically, the research contents of this article are as follows.

(1) A two-way tube neural network inverse method is proposed. In this method, the number of neurons in each layer of the forward or inverse problem neural network is equal to the number of parameters to be obtained. This method takes advantage of reversibility of square matrices, effectively spares the introduction of regularization parameters, and overcomes the ill-condition of inverse systems and functions.

(2) A method of training an inverse problem neural network using a full trained forward problem neural network as a proxy model is proposed. The trained forward problem neural network is used as the forward problem solver to generate training data for the inverse problem neural network. More the samples required to the inverse problem neural network than the forward problem neural network is, the higher the computational efficiency of this method. This method improves the calculation efficiency while keeping up the completeness of forward problem output.

(3) Inverse calculation of composite material parameters is carried out based on the two-way tube neural network direct weight inverse method. This method is based on quasi-static numerical simulation experiments of composite laminates and structural response to perform inverse calculation of material parameters. Compared with other methods in (2), this method has higher accuracy and the solution efficiency increased by more than 40%.

(4) Methods that can improve the sensitivity of parameters are explored by adjusting the boundary conditions and loading strategy of the structure. Especially, the sensitivity of insensitive parameters is improved significantly.