Multi-layer additive tensor decomposition of infrared video for titanium alloy tensile testing

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Infrared video (in mathematics terms, tensor) has been widely used in the tensile testing of metallic materials, such as titanium alloy and steel. The infrared video of the tensile testing process can effectively and efficiently determine the properties of metallic materials, e.g., Young’s modulus, Poisson’s ratio, yield strength, etc. The infrared video with structural properties, such as smoothness and sparsity, can be used to characterize the tensile testing process. To extract the features in the infrared video with structural properties, we propose a multi-layer additive tensor decomposition (MLATD) method based on regularization tensor regression for tensile testing. It decomposes a tensor into three classes of components: the multi-smooth layers (including background and foreground), the sparse layers (including between-tensor and in-tensor), and the noise layer. The scree plot is proposed to determine the number of multi-smooth layers, which is a downward curve of the difference between the smooth layers and the sparse layer. The alternating direction method of multipliers (ADMM) algorithm is proposed to solve the proposed method. The decomposition results of the simulation data and real-world case study revealed that the proposed method outperforms the existing state-of-the-art methods.