A spatio-temporal Volterra modeling approach for a class of distributed industrial processes |
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Authors: | Han-Xiong Li Chenkun Qi Yongguang Yu |
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Affiliation: | aDepartment of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong, PR China;bSchool of Mechanical and Electrical Engineering, Central South University, Changsha 410083, PR China;cDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China |
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Abstract: | It is difficult to model a distributed parameter system (DPS) due to the infinite-dimensional time/space nature and unknown nonlinear uncertainties. A low-dimensional and simple nonlinear model is often required for practical applications. In this paper, a spatio-temporal Volterra model is proposed with a series of spatio-temporal kernels for modeling unknown nonlinear DPS. To estimate these kernels, they are expanded onto spatial and temporal bases with unknown coefficients. To reduce the model dimension and parametric complexity in the spatial domain, the Karhunen–Loève (KL) method is used to find the dominant spatial bases. To reduce the parametric complexity in the temporal domain, the Laguerre polynomials are selected as temporal bases. Next, using the Galerkin method, this spatio-temporal modeling becomes a linear regression problem. Then unknown parameters can be easily estimated using the least-squares method in the temporal domain. After the time/space synthesis, the spatio-temporal Volterra model can be constructed. The convergence of parameter estimation can be guaranteed under certain conditions. This model has a low-dimensional and simple nonlinear structure, which is useful for the prediction and control of the DPS. The simulation and experiment demonstrate the effectiveness of the proposed modeling method. |
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Keywords: | Distributed parameter system System identification Spatio-temporal Volterra Galerkin method Karhunen– Loè ve method Laguerre polynomial |
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