Many thermal and fluid processes are distributed parameter systems (DPSs) described by partial differential equations (PDEs). The input, output, and process parameters of the DPS vary in space and time. Time-space separation-based methods have been widely used for modeling and diagnosis of DPSs. However, the exact governing PDEs and boundary conditions of DPSs are very difficult to obtain for many practical industrial processes, and existing data-based methods cannot achieve spatially continuous modeling and precise abnormality localization. In this thesis, a novel spatial construction method is proposed to preserve the spatial information between sensing locations for process modeling of unknown DPSs. In order to maintain the system dimension structure, the proposed spatial construction method is improved for the modeling of high-dimensional DPSs. Based on the proposed spatial construction method, the abnormalities can be detected in time and located accurately.

The difficulties faced in process modeling and abnormality diagnosis can be summarized as follows:

1. The exact governing PDEs and boundary conditions of DPSs are very difficult to obtain for many practical industrial processes, which makes continuous SBFs impossible to be derived by first-principles methods.

2. Traditional data-driven methods usually produce discrete SBFs because of limited sensing. The spatiotemporal dynamics between sensing positions are neglected. Thus, traditional data-driven methods cannot achieve spatially continuous modeling and accurate abnormality localization under limited sensors.

3. Traditional data-based fault diagnosis methods rely heavily on big data for model training. However, only a small number of sensors are used in many practical industrial processes, which makes these big data-based methods perform not well.

This thesis focuses on the intelligent modeling and abnormality diagnosis of unknown DPSs. In response to the above problems, the following perspectives are investigated:

1. Spatial Construction for Online Modeling of Distributed Parameter Systems
For modeling unknown distributed parameter systems (DPSs), a spatial construction method is proposed to preserve the spatial information between sensing locations. With the help of the spatial construction method, continuous spatial basis functions (SBFs) can be constructed to capture the spatial information lost in the time-space separation. The corresponding temporal dynamics can be identified using the generalized radial basis function network with the orthogonal least-squares (OLS) algorithm. After the time-space synthesis, the constructed spatiotemporal model can provide continuous modeling in the spatial domain with satisfactory performance. Convergence analysis proves that the proposed method can guarantee bounded errors. Finally, the experiments on a linear thermal process and a nonlinear catalytic process validate the effectiveness of the proposed method under limited sensors and its robustness when one of the sensors fails.

2. Spatial-Construction-Based Abnormality Detection and Localization for Distributed Parameter Systems
A spatial-construction-based fault diagnosis method is proposed to detect and locate the abnormality for unknown distributed parameter systems (DPSs). To accurately locate the abnormality, the continuous spatial basis functions (SBFs) are derived by the proposed spatial construction method from empirical data. Theoretical analysis proves that the B-spline curve is a proper solution to the spatial construction problem. Two new statistics are constructed based on the derived continuous SBFs and the improved independent component analysis algorithm. The abnormality can be detected timely according to the reference signals derived by the central limit theorem and hypothesis testing. With the continuous SBFs, the probability distribution of statistic contribution can be constructed to reveal the actual position of the abnormality. The proposed method can timely detect and locate the abnormality under fewer sensors without the knowledge of PDE and boundary conditions. The internal short circuit experiment on a lithium-ion battery demonstrates the effectiveness and superiority of the proposed method.

3. Spatiotemporal Entropy for Abnormality Detection and Localization of Distributed Parameter Systems
The spatiotemporal entropy is proposed to detect and locate thermal abnormalities of LIB packs under limited sensing. Based on the Karhunen-Loeve (KL) decomposition, the spatial entropy and temporal entropy can be constructed from different scales, and then appropriately integrated into the comprehensive spatiotemporal entropy. The kernel density estimation is employed to derive the detection threshold of the spatiotemporal entropy, based on which the abnormality detection can be achieved. The entropy contribution function is designed for abnormality localization based on the spatial basis function (SBF) variations in different modes. The physical meaning of the spatiotemporal entropy is explained from the perspective of the system disorder degree, energy concentration, and information theory. Experiments on the Li-ion battery pack under different fault conditions demonstrate that the proposed method can timely detect and precisely locate the abnormal cells at the early stage.