# Global Mechanical Response Sensing of Corrugated Compensators Based on Digital Twins
###### Abstract  
The corrugated compensators are important components in the piping system, absorbing mechanical deformation flexibly. To reduce the risk of the piping system with corrugated compensators and improve the safety and stability of industrial equipment, condition monitoring and fault diagnosis of bellows is necessary. However, the stress monitoring method of corrugated compensators with limited localized sensors lack real-time and full-domain sensing. Therefore, this paper proposes a digital twin construction method for global mechanical response sensing of corrugated compensators, combining Gaussian process regression in machine learning and finite element analysis. The sensing data of three types of displacements are used as the associated information of a finite element model with 19,800 elements and its digital twin. The results show that the values of performance metrics correlation of determination \(R^{2}\) and standardized average leave-one-out cross-validation \(CV_{\text{avg}}\) of the digital twin satisfy the recommended threshold, which indicates that the digital twin has excellent predictive performance. The single prediction time of the digital twin is 0.76% of the time spent on finite element analysis, and the prediction result has good consistency with the true response under dynamic input, indicating that the digital twin can achieve fast and accurate stress field prediction. The important state information hidden in the multi-source data obtained by limited sensors is effectively mined to achieve the real-time prediction of the stress field. This paper provides a new approach for intelligent sensing and feedback of corrugated compensators in the piping system. corrugated compensators; digital twin; Gaussian process regression; finite element analysis 202313408 13390/  
For the industrial equipment system, the local accidental failure of mechatronic production equipment can cause the whole production system to be difficult to control, and can also easily cause a series of chain reactions, endangering the reliability of industrial equipment operation [4]. Condition monitoring and fault diagnosis of corrugated compensators are required to reduce the production risk of modern piping systems with corrugated compensators and improve the safety and stability of industrial equipment operation. The global service state information of corrugated compensators such as deformation, pressure, and temperature are easy to obtain based on the corresponding sensors [5]. However, for the acquisition of the stress field, we can only obtain local stress data through finite strain gauges. [PERSON] et al. [6,7] investigated the effect of angular rotational misalignment in pipe structure on the deflection-based convolution stresses by mounting the strain gauges at the prescribed locations of U-shape bellows specimens. Failures of the corrugated compensators are very unpredictable during the functioning [8], hence in-depth stress monitoring and analysis of the corrugated portion are required. Therefore, to achieve the effect of advanced prediction and timely maintenance, it is of great significance to study the effective strategy of mechanical response sensing of the corrugated compensators and to accurately obtain complete information representing the time domain and space domain of the equipment by limited sensing devices, to ensure the safe and stable operation of the equipment [9]. With the current rapid development and improvement of sensing technology, numerical simulation methods, and Artificial Intelligence (AI) algorithms, it is possible to apply the actual monitoring data in the digital model to make full-domain and real-time performance predictions of the equipment according to different load conditions. In this background, digital twin (DT) is gradually applied to the structural analysis of complex mechanical equipment to realize the interaction between the real world and the virtual world [9].