Fitting method of concrete damage Poisson’s ratio model based on Kolmogorov-Arnold network

Abstract

The prediction model for the Poisson’s ratio of concrete damage is of significant importance in the field of Structural Health Monitoring (SHM). Seeking a concrete damage Poisson’s ratio prediction model that comprehensively reflects the characteristics of concrete while also being simple and accurate is a challenging task. This study proposes a combination of the Kolmogorov-Arnold Network (KAN), which can fit complex nonlinear relationships with high precision, and the Finite Element Method (FEM) to address this challenge. The research first summarizes the influencing factors of the concrete damage Poisson’s ratio model from classical theories, then uses data obtained from measurements and finite element analysis to train the KAN to develop the concrete damage Poisson’s ratio prediction model. Finally, the accuracy of the model is validated on a test set, and its performance is compared with that of Multi-Layer Perceptron (MLP) networks and classical models. The validation results indicate that the formula model trained by KAN achieves a Root Mean Square Error (RMSE) of 0.055 when predicting the damage Poisson’s ratio of actual test specimens, outperforming four classical models (RMSE ≥ 0.176). The novelty of this study lies in the innovative application of KAN in the concrete damage Poisson’s ratio prediction model, as well as the approach of combining a small amount of measured data with FEM to enhance the efficiency of generating training and testing data. This research not only validates the interpretability and accuracy of KAN but also demonstrates the practicality and effectiveness of the KAN and FEM combination method in the application of predicting the concrete damage Poisson’s ratio, making a significant contribution to the field.