## 4 Analyses of the Applications of Digital Twin Models
### Digital Twin in Other Domains
By collecting, processing, and integrating data from sensors into artificial intelligence algorithms, Digital Twins can provide accurate information about the state of bridges, helping to detect problems early, optimizing not only costs and durability but also facilitating rapid interventions. In the same field, [PERSON] et al. [107] conducted a study to highlight the importance of detecting deteriorations in structural elements, focusing particularly on rubber bearings, essential for the proper functioning of bridges. The authors proposed an innovative method for identifying bearing deterioration, considering the limitations faced by traditional methods in this regard. The proposed method is divided into two stages, the first involving the introduction of a deterioration localization indicator, called the Mean Squared Error (MSE), which helps determine the precise location of deteriorations. The second stage contributes to estimating the deteriorations by combining knowledge of deterioration optimization with Saifish Optimization (SFO). The method's validation was performed through experimental tests, demonstrating its effectiveness for both simple and complex structures. Integrating this method of bearing deterioration identification into the Digital Twin concept can significantly contribute to the safety and durability of bridge infrastructure. Thus, with real-time sensor-acquired data and the use of the MSE indicator, the condition of the bearings can be monitored. Using simulation and prediction methods for bearing deterioration, employing SFO, the location and severity of deteriorations can be rapidly identified, facilitating immediate interventions and reducing operational risks and maintenance costs. In the field of Structural Health Monitoring (SHM), [PERSON] et al. [108] highlighted the significant impact of missing sensor measurement signals on the accuracy of deterioration identification and the assessment process of structural health. They conducted a study to examine the current advantages and limitations of methods for recovering missing data in SHM, emphasizing that machine learning algorithms provide increased precision and computational efficiency. Additionally, [PERSON] et al., underscored the need for in-depth research in this direction, focusing on abnormal sensor measurement signal treatment, complete response recovery, and few-shot learning approaches. They also proposed establishing standardized criteria for evaluating data recovery accuracy, considering not only computational efficiency but also model complexity. Thus, to ensure algorithm applicability, expansion to complex and varied structures such as dams and tunnels is necessary. In this context, utilizing Digital Twin involves integrating mathematical models and artificial intelligence algorithms to detect and fill in missing sensor signals. Consequently, continuous and precise system state evaluation is facilitated through machine learning algorithms and statistical inference techniques. All of these contribute to the development of robust monitoring systems for critical infrastructure. In ref. [109], [PERSON] et al., proposed an innovative method for nonlinear spatio-temporal modeling of temperature and Temperature-Induced Bearing Displacement (TIBD) in rigid frame bridges with a single large-span pier to reduce structural deformations and instability. This method, based on the DCNN-LSTM (Deep Convolutional Neural Network-Long-Short-Term Memory) network with elastic module fusion, utilizes monitoring data from the second bridge over the Yangtze River in Wuhan and addresses three major issues: insufficient selection of characteristic temperature values, inadequate research on the correlation between structural temperature and TIBD for bridges, and low accuracy of temperature-TIBD regression models. The authors identified positive linear correlations between temperature sensor data placed inside the box girder and measurements from the same box.