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-Loeve (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 finite-dimensional 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.
Highlights
In the industrial field, many thermal processes can be characterized by the nonlinear distributed parameter systems (DPSs), in which the input and output states vary both in time and space domain [1]
The KL method is used for dimension reduction and extracting the spatial basis functions, and the multilayer perceptron (MLP)-long short-term memory (LSTM) temporal model is adopted to solve the two inherently coupled nonlinearities based on the temporal coefficients and system inputs
All the results presented above indicate that the proposed KL-MLP-LSTM model can perform better than the other two models in the experiment, which demonstrates its excellent performance in both the time domain and the spatial domain
Summary
Many thermal processes can be characterized by the nonlinear distributed parameter systems (DPSs), in which the input and output states vary both in time and space domain [1]. All the aforementioned temporal models do not consider the intrinsic structure of low-order models As a result, they cannot deal with the situations with two coupled nonlinear dynamics such as the inputs and outputs of many DPS processes with complex nonlinearities. The KL method is used for dimension reduction and extracting the spatial basis functions, and the MLP-LSTM temporal model is adopted to solve the two inherently coupled nonlinearities based on the temporal coefficients and system inputs. In this way, the KL-MLPLSTM can approximate the real DPS situation of the two coupled nonlinear dynamics more accurately.
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