###### Abstract
They show the effectiveness of compression by evaluating the model over a laboratory beam bridge and recorded data of a bridge in Guangdong, China, with 100% damage identification. Even though the works mentioned above can reach perfect accuracy, training, and inferring are excellences on unconstrained remote devices after data transmission and collection. [PERSON] et al. [16] introduced History PCA, a streaming algorithm to train the PCA without storing data, which was later deployed on edge/nodes by [17]. Compared to other streaming approaches, HPCA exploits the history of the data and new samples to update the partial covariance matrix, allowing faster convergence and better accuracy [16; 17]. Subsequently, [PERSON] et al. [18] deployed the HPCA algorithm on the sensor nodes, moving both training and detection from the gateway to the leaf nodes of the SHM sensor network. In comparison to [17], ref. [18] not only applied PCA for data compression but also employed it for anomaly detection in Italian bridge data at the edge of the sensor network, achieving effectiveness in reducing network traffic and energy consumption. However, it should be noted that the sensitivity of the detector was lower. [PERSON] et al. [19] applied Kernel PCA and greedy KPCA to anomaly detection on a bridge, addressing the issue of PCA's inability to filter nonlinear effects present in observations caused by structural freezing. On the other hand, [PERSON] et al. [20] employed PCA on sensor data to determine whether the wind turbine blades were damaged, and experimental results confirmed the method's effectiveness. However, it should be noted that the complexity of the damage types was relatively low as they simulated damage by adding mass at different positions on the structure. [PERSON] et al. [17] used a reconstruction error measured by the PCA method to identify anomalies for structural damage detection on an oil platform. They concluded that PCA can be an affordable approach to eliminate the influence of varying wave conditions and provides a technique on damage indices to improve the accuracy of detection [21]. [PERSON] et al. used fiber optic sensors to record longitudinal displacements over a bridge in Mexico. It exploits PCA to find Q-statistics of collected data to detect damaged features of the bridge, and the authors concluded the work by constructing a threshold value for anomaly detection. [PERSON] et al. (2020) combined PCA with system identification using the Auto-Regressive Moving-Average (ARMAX) model to extract data features. They then utilized a machine learning classification algorithm within a fault classification module to carry out the fault detection of wind turbine blades. However, PCA is sensitive to the presence of outliers in the data, and large scattered points can significantly impact the quality of the low-rank approximation. To address this, [PERSON] et al. proposed a novel Robust PCA framework [PERSON] et al. (2020). The framework is well-suited for detecting anomalies in the given data. Subsequently, [PERSON] et al. conducted a comparative analysis of various robust principal component analysis algorithms [PERSON] et al. (2020). Experimental data showed that three algorithms, namely low-rank matrix fitting, the Inexact Augmented Lagrangian Method (IALM), and Robust Principal Component Analysis-Go Decomposition (RPCA-GD), outperformed other RPCA algorithms in terms of time efficiency. For the low-rank component, scholars usually use the kernel norm as a convex approximation to the matrix rank function. However, the kernel norm adds up all the singular values of the matrix. If one or more of the singular values of the matrix is too large, the kernel norm overestimates the rank of the matrix and may not recover the true low-rank matrix with high probability. To overcome the above problems, scholars have tried to use different non-convex functions to approximate the rank of the matrix [PERSON] et al. (2020); [PERSON] et al. (2020); [PERSON] et al. (2020); [PERSON] et al.