Abstract
Distributed parameter systems (DPSs) are widespread in industrial processes, such as thermal processes, fluid processes, and transport-reaction processes. They are described by partial differential equations (PDEs), where the input, output, and parameters may vary in time and space. Although DPS modeling is challenging, it is essential for system optimization, controller design, and fault detection. Time-space separation-based methods have been proven effective for spatiotemporal modeling of one-spatial dimensional (1-D) DPSs. However, many industrial processes have two or more spatial dimensions. The spatially distributed nature, complex spatiotemporal coupling, and a limited number of sensors make high-spatial dimensional (high-D) DPSs modeling more difficult.The detailed explanations of these difficulties are as follows:
1. How to separate the time and multiple spatial variables? In high-D DPSs, the coupling presents between time and space and between different spatial dimensions. The separation of variables is critical to the accuracy of the reduced-order model (ROM).
2. How to achieve online modeling for high-D DPSs with strong time-varying dynamics? With the continuous data collection in a streaming environment, how to efficiently update the existing model to track the system dynamics is an important task.
3. How to reduce the number of sensors? The accuracy of time-space separation-based methods severely depends on the number of sensors. However, limited sensors are allowed in industrial processes due to cost, installation, and other restrictions.
This thesis focuses on the multi-dimensional spatiotemporal modeling of DPSs. In response to the above problems, the following three perspectives are investigated:
1. Modified HOSVD for Spatiotemporal Modeling of High-spatial Dimensional DPSs
A framework based on high-order singular vector decomposition (HOSVD), which is a multilinear generalization of SVD, is proposed for spatiotemporal modeling of high-D DPSs. First, a modified HOSVD is designed and used for the separation of time and multiple spatial variables. The spatially distributed nature of high-D DPS is well preserved, and the interactions between spatial basis functions (BFs) across different modes are considered. Sequentially, the system dynamics derived from PDE can be decomposed into several low-order nonlinear ordinary differential equations (ODEs) through Galerkin projection. Then, the typical nonlinear machine learning techniques can be used to learn the system dynamics in a low-dimensional temporal domain. Finally, the spatiotemporal output can be reconstructed through time-space synthesis.
2. Incremental HOSVD-based Online Spatiotemporal Modeling for High-spatial Dimensional DPSs
An incremental HOSVD-based spatiotemporal learning scheme is proposed for online modeling of high-D DPSs with strong time-varying dynamics and nonlinearities. First, under the framework of time-space separation, the high-D BFs and corresponding temporal model can be constructed through modified HOSVD. Then, as the system evolves, an incremental learning scheme is developed to update the high-D BFs and re-identify the temporal model recursively. In this way, the spatiotemporal model can be effectively inherited and adjusted to track the system dynamics. Finally, previous and future spatiotemporal outputs can be reconstructed and predicted through time-space synthesis. This is the first attempt to consider both the high-D spatially distributed nature and online tracking in DPS modeling.
3. Spatiotemporal Modeling for DPSs under Sparse Sensing
An information completion and learning strategy is proposed for spatiotemporal modeling of DPSs under sparse sensing. During the offline initialization phase, the initial full spatial BFs are constructed first in the full sensing environment under the framework of time-space separation. Subsequently, during the normal operation phase of fewer sensors, the sparse BFs are obtained and further used to complete the lost spatial information with the help of the initial full BFs, which are then recursively calibrated by the incremental technique. By iteratively repeating these two steps, the sparse spatiotemporal output can be completed in a streaming data environment. Finally, the proper spatiotemporal model can be constructed through time-space synthesis. This method is applicable to both 1-D and high-D DPSs. It can effectively reduce the sensor number as well as sampling cost without decreasing the modeling accuracy.
Systemic simulations and experiments have been conducted to validate the effectiveness of all proposed methods.
| Date of Award | 4 Aug 2021 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Hanxiong LI (Supervisor) |