A Modeling Approach With Spatial Basis Functions Learning and Temporal Dynamic Online Modeling for Time-Varying Distributed Parameter Processes

Xinjiang Lu,Jie Xu,Chao-Jun Zhou

doi:10.1109/access.2019.2942084

Xinjiang Lu, Jie Xu + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2942084

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Abstract

Currently, most of existing data-driven modeling methods for distributed parameter systems (DPSs) are offline and do not take the intrinsic structure of streaming data into account. This often makes them difficult to model strongly nonlinear and time-varying DPSs. To overcome this, a novel modeling method that integrates the advantages of both manifold-learning-based spatial basis functions learning and temporal dynamic online modeling is proposed. In this method, the original spatiotemporal data are first mapped into high dimensional space using nonlinear mapping function, from which manifold learning is developed to obtain spatial basis functions. This allows the strongly nonlinear relationship on space able to be constructed due to nonlinear mapping, and maintaining the intrinsic data structure due to manifold learning. In addition, the online least squares support vector machine (LS-SVM) is developed to construct the temporal dynamics model. This may make time-varying dynamics of DPSs able to be captured. By integrating spatial basis functions and the online LS-SVM temporal model, a spatiotemporal model is constructed, which allows for the reconstruction of time-varying and nonlinear dynamics of DPSs. The catalytic rod simulation and heating experiments not only demonstrate the effectiveness of the proposed method, but also the better modeling ability as compared to several common modeling methods.

Highlights

Changes in the status of input, output, and process parameters for a number of industrial processes, such as thermal, fluid, and chemical processes, are generally related to time, and space [1]–[5]
A great deal of distributed parameter systems (DPSs) are time-varying since their parameters and even the model structure change over time
For the known model structures, partial differential equations (PDEs) are usually transformed into ordinary differential equations (ODEs) to generate finite-dimension models [13]

Summary

INTRODUCTION

Changes in the status of input, output, and process parameters for a number of industrial processes, such as thermal, fluid, and chemical processes, are generally related to time, and space [1]–[5]. Liu and Li [40] used the locally linear embedding (LLE) method to reconstruct spatiotemporal output data, which enables the preservation of the intrinsic structure of the data as achieving the spatial basis functions These manifold learning methods for modeling of DPSs only pay attention to the linear relation between local neighbor points on space, where nonlinear variations among local neighbors are ignored. Simulation and experiments demonstrate the effectiveness of the proposed method, and the better modeling ability as compared to several common modeling methods

PROBLEM DESCRIPTION

CONFIGURATION OF PROPOSED MODELING METHOD

EXPERIMENT VALIDATION

CATALYTIC ROD EXPERIMENT

CONCLUSION