A verified training support vector machine in bearing fault diagnosis

Abstract

Abstract The combination of support vector machine (SVM) and deep learning is widely used in bearing fault diagnosis. The SVM-based bearing fault diagnosis method usually uses features extracted from bearing vibration signals as input. However, environmental noise in industrial applications can affect the feature representation, potentially leading to failures in SVM-based fault diagnosis methods. Adversarial robustness verification methods can evaluate the robustness of models to small perturbations in feature representations. Certified defense methods achieve robustness enhancement by embedding adversarial robustness verification into the learning process of the model. Thus, we propose a certified defense method named verified training SVM (VT-SVM) based on Lagrange duality. The proposed method incorporates adversarial robustness verification into the SVM learning framework, thereby enhancing the robustness of SVM in noisy environments. First, the certified defense optimization problem of SVM is constructed by combining the original optimization problem of SVM with the adversarial robustness verification problem. Then, the certified defense optimization problem is converted into an equivalent convex quadratic programming problem by introducing slack variables. Next, the Lagrange duality is used to transform the convex quadratic programming problem into a dual problem. Finally, the solution to the original optimization problem can be obtained by solving the dual problem. We validate the effectiveness of VT-SVM on the artificial dataset, the rolling bearing dataset from Case Western Reserve University, and the VBL-VA001 dataset from Sepuluh Nopember Institute of Technology. Experimental results demonstrate that our method both ensures high predictive performance and improves the resistance of the model to small noise.