Statistical correlation neural network for small sample data and its engineering application: Predicting maximum mises stress on ultrasonic-assisted grinding surfaces

We propose a statistical correlation neural network applied to small sample data, which intuitively characterizes the statistical correlation between input and output variables, improves the generalization ability of the BP neural network, and reduces data dependency. As an engineering example, we apply the new model to construct a correlation model between rough surface characterization parameters and maximum mises stress in ultrasonic-assisted grinding. In particular, the correlation between the set of crucial characterization parameters in the virtual samples was characterized using the Johnson transformation method mathematical model, and the mises stress calculation was built using the ellipsoidal asperity fitting method. Then, ultrasonic-assisted grinding experiments were carried out to verify the validity of the new model. The comparison between the BP neural network and the statistical correlation neural network shows a reduction in the mean absolute percentage error of maximum Mises stress from 6.36 % to 2.97 %, and the mean absolute error of Kendall’s tau correlation coefficient was reduced from 0.25 to 0.11. The results show that the statistical correlation neural network constructs a more effective agent model based on the small sample data by characterizing the statistical correlation between the input and the output variables. It reduces the manufacturing cost and provides a theoretical basis for subsequent machining parameter optimization.