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 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.

The remaining useful life (RUL) prediction of Lithium-ion batteries (LIBs) is of great importance to the health management of electric vehicles and hybrid electric vehicles. However, fluctuation and nonlinearity occur during battery degradation, resulting in difficulties in both model adaptability and RUL prediction accuracy. To face the challenge, we propose a sequence decomposition and deep learning integrated prognostic approach for the RUL prediction of LIBs. Complementary ensemble empirical mode decomposition and principal component analysis are applied to separate the local fluctuations and the global degradation trend from the battery aging data. The long short-term memory neural network combined with fully connected layers is designed as a transfer learning model. The hyperparameter optimization and finetuning strategy of the model is developed based on offline training data. In addition, to further realize the reasonable and effective LIB second-life applications, the RUL corresponding to different failure thresholds is predicted. The performance of the proposed integrated approach in degradation modeling and RUL prediction is evaluated on three publicly available LIB datasets with different degradation characteristics, as well as compared with other prediction algorithms under the same conditions. The illustrative results demonstrate that the proposed approach can achieve accurate, adaptive, and robust prediction for both capacity trajectory and RUL.

Distributed parameter systems widely exist in many industrial thermal processes. Estimation of their temperature distribution in the entire operating area is not easy as the dynamics are time/space coupled, and there are only a few sensors available for measurement. In this paper, an effective spatiotemporal model is proposed for prediction of the temperature distribution. After the dominant spatial basis functions are obtained by the Karhunen-Loève method under the time/space separation, a kernel-based random vector functional-link network is developed for learning unknown temporal dynamics. After time/space synthesis, the spatiotemporal model can be constructed to effectively estimate the temperature distribution in high learning speed. The generalization performance of this model is discussed using Rademacher complexity. Simulations on two typical industrial thermal processes show that the proposed method has superior model performance than neural networks and least square support vector machine.

Temperature distribution of Lithium-ion battery (LIB) belongs to a nonlinear distributed parameter system (DPS), which is infinite dimensional in space direction. Modeling of such system often leads to the following challenges: 1. Time/space coupled dynamics; 2. Time-varying dynamics; 3. Spatial nonlinearity. For the first two challenges, Karhunen-Loeve (KL) decomposition based data-driven spatiotemporal models have been widely researched and successfully applied to industrial thermal processes. However, this method is a global linear model reduction method that ignores the nonlinear properties of measurements. This will prohibit the model performance of strong nonlinear DPS, which has strong spatial nonlinearity refers to the aforementioned challenge 3. To address this problem, a local properties embedding based modeling method is developed for nonlinear DPS. Firstly, finite dimensional nonlinear spatial basis functions (BFs) that can representative the nonlinear feature of original space are learned by local properties embedding based method. Then, the low dimensional representative can be derived using time/space separation and the unknown temporal coefficients can be identified through traditional neural learning algorithm. Finally, the spatiotemporal temperature distribution can be reconstructed by time/space synthesis. The proposed modeling method can be more effective than traditional KL based method for modeling nonlinear DPS.

The real-time monitoring of temperature distribution in lithium-ion batteries (LIBs) is crucial for their safety and optimal operation in electrical vehicles. An accurate and effective thermal model is needed for online temperature monitoring since limited sensors are available in vehicle application. In this paper, a data-based spatiotemporal modeling method is researched for online estimation of temperature distribution of LIBs. First, Isometric Mapping (ISOMAP) method is used for time/space separation and model reduction. Then, the low-dimensional representation can be obtained in terms of ISOMAP based mapping functions. The unknown temporal dynamics in the low-dimensional space can be approximated using neural network model with parameters trained using extreme learning machine (ELM) algorithm. Finally, the spatiotemporal model of the thermal process can be reconstructed by integrating the neural network model and the mapping functions. The generalization bound of the proposed spatiotemporal model can be analyzed using Rademacher complexity. Simulation results showed that the proposed modeling method can model the LIB thermal process very well.

Global principal component analysis (PCA) has been successfully introduced for modeling distributed parameter systems (DPSs). In spite of the merits, this method is not feasible due to parameter variations and multiple operating domains. A novel multimode spatiotemporal modeling method based on the locally weighted PCA (LW-PCA) method is developed for large-scale highly nonlinear DPSs with parameter variations, by separating the original dataset into tractable subsets. This method implements the decomposition by making full use of the dependence among subset densities. First, the spatiotemporal snapshots are divided into multiple different Gaussian components by using a finite Gaussian mixture model (FGMM). Once the components are derived, a Bayesian inference strategy is then applied to calculate the posterior probabilities of each spatiotemporal snapshot belonging to each component, which will be regarded as the local weights of the LW-PCA method. Second, LW-PCA is adopted to calculate each locally weighted snapshot matrix, and the corresponding local spatial basis functions (SBFs) can be generated by the PCA method. Third, all the local temporal models are estimated using the extreme learning machine (ELM). Thus, the local spatiotemporal models can be produced with local SBFs and corresponding temporal model. Finally, the original system can be approximated using the sum form of each local spatiotemporal model. Unlike global PCA, which uses global SBFs to construct a global spatiotemporal model, LW-PCA approximates the original system by multiple local reduced SBFs. Numerical simulations verify the effectiveness of the developed multimode spatiotemporal model.