# Global Mechanical Response Sensing of Corrugated Compensators Based on Digital Twins
###### Abstract
As an important way to realize the real-time connection and dynamic interaction between the physical entity and the virtual twin, the digital twin can map the working state and mechanical properties of the physical entity to the virtual space [10]. In the last decade, NASA and the U.S. Air Force have continued the exploration of grounded applications of the digital twin in the aerospace field [11]. [PERSON] et al. [12], based on the concept of the digital twin, envisaged the construction of a high-fidelity DT model of the vehicle to improve the life prediction and management capabilities of the vehicle and discussed the difficulties and potentially feasible technical solutions. [PERSON] et al. [13] established and applied a digital twin for aircraft tires to improve the prediction accuracy of tire landing wear, and constructed a nonlinear landing wear response model based on high-fidelity test data. In terms of digital twin applications that integrate real-time numerical computation and performance prediction, [PERSON] et al. [14] demonstrated how the digital twin can be applied to a real cantilever beam model, which was based on a simulation model and sensor data to calculate the displacement field of the cantilever beam in real-time. Although the structural form of this case is simple, it demonstrates the application effect of structural digital twin vividly. [PERSON] et al. [15] proposed a digital twin solution for condition monitoring of a small-scale knuckle boom crane and developed an inverse method based on strain gauges to calculate force vector weights, which can calculate the real-time stress, strain, and load at specific locations of the crane, thus enabling real-time  
Figure 1: Movement capabilities of bellows. condition monitoring of the crane. [PERSON] et al. [16; 17] developed a digital twin technology framework for shape-performance integration with multi-model fusion and introduced the DT model construction method for structural analysis of mechanical equipment using a boom crane and a 2D truss as examples. The prediction of mechanical response fields of cranes and trusses is achieved by using multi-source dynamic sensing data as model inputs and by real-time computation of analytical, numerical, and AI models. [PERSON] et al. [18; 19] constructed a digital twin of the human lumbar spine based on this framework and realized real-time monitoring of the mechanical properties of the human lumbar spine by combining data-filling technology and inverse kinematics technology. With multi-source sensing data as model input, the prediction of mechanical response can be achieved by the real-time calculation of the analytic model, numerical model, and AI model. However, the digital twin model for equipment of piping systems such as corrugated compensators, which are under multiple loads, is rarely involved. 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 ensure the safe and stable operation of the equipment. 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 (2020) 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. 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.