# Global Mechanical Response Sensing of Corrugated Compensators Based on Digital Twins
## 4 Conclusions  
The corrugated compensators are important components in the piping system, absorbing mechanical deformation flexibly. It is important to study the effective strategy of global mechanical response sensing of corrugated compensators and to accurately obtain complete state information of the equipment with limited sensing devices to reduce the risk of the piping system with corrugated compensators and improve the safety and stability of industrial equipment. However, the stress monitoring method of corrugated compensators with limited localized sensors lack real-time and full-domain sensing. Given this, this paper proposes a construction method of the DT for global mechanical response sensing of corrugated compensators, which combines Gaussian process regression (GPR) in machine learning and finite element analysis (FEA). The training samples and test samples are sampled by the Latin hypercube sampling (LHS) method, the GPR is performed by MATLAB, and the FEA is carried out by the commercial software ABAQUS and Python secondary development scripts. 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.  
Figure 6: Dynamic monitoring data and FEA loading curves.  
Figure 7: Comparison of Mises stress values of DT and FEA outputs at observation points A, B, C and D.  
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 DT satisfy the recommended threshold, which indicates that the DT has excellent predictive performance. The single prediction time of DT is 0.76% of the time spent on FEA, and the prediction result shows a satisfactory consistency with the true response under dynamic change of the load, indicating that DT 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. The study of global mechanical response sensing based on digital twins provides a new approach for intelligent sensing and feedback of corrugated compensators in the piping system.  
Conceptualization, R.Z.; Methodology, J.J.; Software, J.Q.; Investigation, N.D.; Writing--original draft, H.S.; Writing--review & editing, Y.W. All authors have read and agreed to the published version of the manuscript.  
The works described in this paper are substantially supported by a grant from the Key Technologies Research and Development Program (Grant No. 2021 YFF0602005), the National Natural Science Foundation of China (No. 51678135), and the Fundamental Research Funds for the Central Universities (No. 2242022k30031, 2242022k30033), which are gratefully acknowledged.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the privacy implications of the study.  
The authors declare that there is no conflict of interest regarding the publication of this paper.