The earliest work in this domain was introduced by [PERSON], who proposed algorithms for detecting anomalies in process quality control applications [4]. Subsequently, more advanced statistical techniques, such as [PERSON]'s test [5], student's \(t\)-test [6], [PERSON]'s t-squared test [7], and chi-squared test [8] were developed to enhance anomaly detection capabilities. The core principle of statistical-based anomaly detection is that anomalies tend to appear in low-probability regions, whereas normal data instances are typically located in high-probability regions. These algorithms are among the earliest approaches proposed for anomaly detection. Their methodology involves first fitting a statistical model to a given dataset, followed by performing statistical tests on new data to evaluate its conformity to the model. Data points consistent with the model are classified as normal, while those that deviate are identified as anomalies [9]. However, statistical-based methods are limited by the assumption that the data conforms to a specific distribution, such as a Gaussian distribution. When this assumption is not met, their effectiveness diminishes significantly. Furthermore, these methods struggle with high-dimensional data, as conventional statistical approaches are inherently unsuitable for such scenarios. Although dimensionality reduction techniques like Principal Component Analysis (PCA) can mitigate this issue, they are often inadequate for high-dimensional data with nonlinear relationships. These limitations restrict the applicability of statistical-based methods in complex anomaly detection tasks. With the advent of Industry 4.0, researchers and practitioners face an explosion in the volume of data that needs to be processed, often accompanied by nonlinear relations between variables in large datasets. Concurrently, rapid advancements in computational hardware have alleviated the computational complexity constraints, allowing data-driven approaches to become mainstream. Among these, machine learning-based anomaly detection has emerged as a prominent research area. Various machine learning algorithms implement anomaly detection through different methodologies. The distance-based algorithm k-Nearest Neighbors (k-NNs) [10] operates on the core idea that an anomalous data point is far from its k-NN, with the anomaly score computed as the distance between the data instance and its k-NN. Local Outlier Factor (LOF) [11] is another well-known and widely used anomaly detection algorithm, which evaluates the relative density of a data point with respect to its k-Nearest Neighborhood. [PERSON] et al. [12] combined statistical foundations with machine learning kernel methods to propose Kernel Principal Component Analysis (KPCA), addressing the limitations of PCA in handling high-dimensional data with nonlinear relations. [PERSON] et al. [13] successfully applied a clustering-based algorithm, utilizing density-based spatial clustering of applications with noise (DBSCAN), for flight anomaly detection during the aircraft approach phase. Additionally, isolation-based algorithms, subspace-based algorithms, and others have also been proven effective in the domain of anomaly detection. However, while these machine learning methods have somewhat addressed the problem of anomaly detection in multivariate data with nonlinear relations, they still exhibit varying degrees of failure when confronted with higher-dimensional data and data with autocorrelation. With the development of artificial intelligence and neural networks, deep learning-based anomaly detection has gradually become mainstream [14]. This approach can handle massive amounts of data and has relatively lenient requirements for training data. Depending on the labels available in the dataset, one can choose unsupervised, semi-supervised, or supervised learning [1]. Among neural network-based methods, Autoencoder (AE)-based approaches are predominantly used due to their powerful capability in advanced data representation.