A new cumulated temporal causal-effects based model for predicting the aging deformation of metal structural parts

The aging deformation of metal structural parts has emerged as a key factor affecting the dimensional accuracy, and the prediction ability of aging deformation is fundamental for its control. Causal deep learning methods have prominent advantages by introducing inductive biases for making the prediction using other observable variables than residual stress. However, the natural aging process of metal parts involves creep and stress relaxation, where the aging deformation is resulted by the cumulated temporal effects of time-varying residual stress from previous time stages. Existing causal deep learning methods are carried out only based on instant causal-effects of cause variables at a certain time stage, which ignores the cumulation of temporal causal-effects and restricts the prediction accuracy. To this end, this paper proposes a new cumulated temporal causal-effects based model. The cumulated causal-effects are defined as the convolution of time-varying causal variables and their mechanisms, and a modified dynamic convolutional neural network is applied in the model to learn the cumulated temporal causal-effects of residual stress and make aging deformation prediction. The machining of die forged structural parts is taken as a case study, and a Digital Image Correlation system is employed for aging deformation measurement. Experimental results show that the proposed model could beat all comparison models and predict aging deformation accurately and stably.