Dynamically Constrained Digital Twin-Based Mechanical Diagnosis Framework Under Undetermined States Without Fault Data

Intelligent applications of artificial intelligence techniques have become widely used in industrial maintenance. However, obtaining and labeling fault data is costly, particularly when machines operate under time-varying conditions and harsh environments, leading to challenges in intelligent diagnosis when mechanical states are undetermined and fault data is missing. Inspired by the digital twin concept and the Runge-Kutta method for dynamic solutions, this paper proposes a dynamic-constrained digital twin (DC-DT) framework for mechanical system modeling under undetermined mechanical states and fault diagnosis when the fault data is missing. In this paper, a dynamic-constrained Runge-Kutta Network is introduced for key parameter estimation using only healthy vibration signals. A parametric fault impact embedding method is proposed to predict fault signals under dynamic constraints, enabling systematic integration of fault mechanisms into the digital twin model. To ensure high-quality digital twinned fault samples, measurement noise is modulated and added. Experimental investigation illustrates the effectiveness of the proposed framework. The results of undetermined state estimation show that the dynamic constrained digital twin framework is capable of accurate digital twin modeling for mechanical system. The diagnostic results demonstrate the proposed framework enables effective fault diagnosis without fault samples and outperforms other unsupervised diagnostic methods with acceptable accuracy.