Spatiotemporal Modeling for Nonlinear Distributed Thermal Processes Based on KL Decomposition, MLP and LSTM Network

Abstract

Estimation of absolute temperature distributions is crucial for many thermal processes in the nonlinear distributed parameter systems, such as predicting the curing temperature distribution of the chip, the temperature distribution of the catalytic rod, and so on. In this work, a spatiotemporal model based on the Karhunen-Loève (KL) decomposition, the multilayer perceptron (MLP), and the long short-term memory (LSTM) network, named KL-MLP-LSTM, is developed for estimating temperature distributions with a three-step procedure. Firstly, the infinite-dimensional model is transformed into a finitedimensional model, where the KL decomposition method is used for dimension reduction and spatial basis functions extraction. Secondly, a novel MLP-LSTM hybrid time series model is constructed to deal with the two inherently coupled nonlinearities. Finally, the spatiotemporal temperature distribution model can be reconstructed through spatiotemporal synthesis. The effectiveness of the proposed model is validated by the data from a snap curing oven thermal process. Satisfactory agreement between the results of the current model and the other well-established model shows that the KL-MLP-LSTM model is reliable for estimating the temperature distributions during the thermal process. INDEX TERMS Spatiotemporal modeling, nonlinear distributed thermal processes, Karhunen-Loève decomposition, multilayer perceptron, long short-term memory.

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