Inverse of initial stress in carbon fiber reinforced polymer laminates using lamb waves and deep neural network.

• Legendre Orthogonal Polynomial Expansion (LOPE) method mapping the relationship between the wave velocity and initial stresses was developed to generate the input characteristics of linear and non-linear variation for deep neural network. • A Deep Neural Network (DNN) was combined with LOPE for the inverse of initial stress based on Lamb wave dispersion date rather than objective function obtained from wave equations. • The performances of ReLU activation function and Sigmoid activation function were illustrated in detail for current inverse work. The prediction of the initial stress in composites is essential for the non-destructive testing (NDT) and structural health monitoring (SHM) of carbon fibre reinforced polymer (CFRP). This paper examines the potential of Lamb waves in the inverse of initial stress by calculating the influence of initial stress on the dispersion characteristics of Lamb waves propagating in multilayered CFRP laminates. By introducing the mechanics of incremental deformation into the linear three-dimensional elasticity theory, the Legendre orthogonal polynomial expansion (LOPE) method is used to mathematically model the Lamb wave propagating in multilayered CFRP laminates subjected to horizontal and vertical homogeneous initial stresses. Then, a three-hidden-layers Feed Forward Deep Neural Network (DNN) with Back Propagation (BP) algorithm is constructed to invert the magnitude and direction of the initial stresses. The input features are the phase velocities of fundamental Lamb wave A 0 mode at five different frequencies. Both training and testing samples are obtained by LOPE forward calculation. An ablation experiment is presented to compare the two different activation functions. Finally, the accuracy of the inverse is verified by comparing with the available outcomes of LOPE forward calculation. [ABSTRACT FROM AUTHOR]