# Fault Detection Algorithm Based on Dynamic Global-Local Preserving Projection
## 1 Introduction
[PERSON] designed a local and nonlocal embedding algorithm based on NPE [27]. In this algorithm, the original spatial data structure is extracted by minimizing the nearest neighbor sample distance and maximizing the nonlocal sample distance. [PERSON] combined FDA with GLPP to minimize intraclass scattering and maximize interclass scattering [28]. This method preserves the global and local structures of the data. It also ensures the discriminability of the shadow-casting space and improves fault detection performance. The above methods have achieved satisfactory results in process monitoring. However, they still have limitations for systems with dynamic characteristics. Moreover, data in industrial processes are dynamic. It is closely related to a number of factors such as time, operational control, external conditions, and production materials and processes. And, it is updated and changed using these factors. The dynamic nature of this data is essential for the monitoring, control, and optimization of the production process. Therefore, the dynamic process modeling and monitoring method of mining temporal features has been given considerable attention. Aiming at the system's dynamic characteristics, [PERSON] et al. proposed a dynamic PCA (DPCA) method [29]. The delayed measurement values are introduced to form an augmented matrix, which is then modeled via PCA. [PERSON] et al. proposed a fault detection and diagnosis method based on DPCA residual heterogeneity by combining DPCA and mutual heterogeneity methods [30]. This method can reduce the adverse influence of dynamic characteristics on fault detection. [PERSON] et al. used a sliding window approach to expand the original matrix into a dynamic matrix [31]. This dynamic matrix can effectively characterize the autocorrelation property of time series. [PERSON] et al. used a time series extended-NPE algorithm to establish an information-extraction strategy based on a space and time structure [32]. The dynamic correlation of data with time is obtained by learning the characteristics of time-series data. [PERSON] et al. proposed a method termed time-space nearest neighborhood standardization [33]. The dynamic characteristics of the data are eliminated by locating and standardizing the samples' local neighbors in time and space. A fault-detection algorithm based on DGLPP is proposed in this study to solve the low efficiency of system fault detection using dynamic characteristics. The system's dynamic characteristics are extracted by adding time-delay data to an augmented matrix. The global-local holding projection is used to reduce the dimension and preserve the data's global-local structure. Then, the DGLPP model is constructed, and the corresponding T\({}^{2}\) and SPE statistics are established for fault detection. Finally, the proposed algorithm is applied to the fault detection of the TE process to evaluate its effectiveness. Experimental results show that this algorithm has a higher fault-detection rate than PCA, LPP, and GLPP algorithms. This algorithm effectively captures the dynamic characteristics of the system and preserves the data's relevant structural features. It also improves fault-detection performance and contributes to the dynamic system fault-detection research. This article is organized as follows. In Section 1, the background and research status of the topic are described. Then, the algorithms related to fault diagnosis are introduced in Section 2. In Section 3, the algorithms used in this study are described in detail. The main idea of this study is discussed in Section 4. The proposed algorithm is applied to the TE process for fault detection, and the results are analyzed. Section 5 presents the conclusions of this study.