Dual Extreme Learning Machines-Based Spatiotemporal Modeling for Nonlinear Distributed Thermal Processes

Jin, Xi; Yang, Hai Dong; Xu, Kang; Zhu, Cheng Jiu

doi:10.1142/s0219876220500267

Cited by 5 publications

(4 citation statements)

References 32 publications

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“…Additionally, numerous identification techniques, such as extreme learning machine (ELM) [19], least-squares support vector machine (LS-SVM) [20], have been applied to the related low-dimensional time-series obtained by MOR. A Dual ELM model is developed for the two nonlinearities embedded in industrial thermal processes [21]. A spatiotemporal LS-SVM model is designed to compensate for modeling errors due to truncation and unknown nonlinear dynamics [22].…”

Section: B Literature Reviewmentioning

confidence: 99%

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SSAE and GRU Based Joint Modeling for Nonlinear Distributed Parameter Systems

Gan

Feng

et al. 2022

IEEE Access

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The modeling and control issues for distributed parameter systems (DPSs) have received a great deal of attention. Because linear model order reduction (MOR) methods may ignore the nonlinear dynamics and lose some details, it is difficult to describe DPS accurately by common modeling methods. To effectively model such systems, a sparse stacked auto-encoder and gated recurrent unit (SSAE-GRU) model is proposed in this paper. Under the time/space separation theory, it is the mainstream way to perform MOR and identification of time series respectively. In the SSAE-GRU model, this practice is still adhered to but joint learning is recommended. SSAE can be used as an excellent MOR technique. A sparse activation strategy that is introduced makes its model space simple and easy to train. GRU has the ability to represent such complex temporal properties because the information stored by previous neurons can be transmitted to the current moment selectively. The joint training method allows them to be responsible and consider the connection between adjacent moments and spatial energy transfer overall. Then, we use L2 regularization in back-propagation to reduce the difficulty of model optimization and prevent overfitting. The modeling scheme is simulated on two typical chemical thermal processes. This article demonstrates the effectiveness of the proposed method as well as outstanding performance compared to existing methods.INDEX TERMS Distributed parameter systems, model order reduction, sparse stacked auto-encoder, gated recurrent unit, joint learning

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Section: B Literature Reviewmentioning

confidence: 99%

“…It is critical to create an appropriate representation and identify the corresponding time series. Some scholars have scientifically proven that time series is decomposed into two nonlinear units with different regularities s i (t) [21], [35]. This law has depicted in Fig.…”

Section: Establish Low-order Temporal Seriesmentioning

confidence: 99%

SSAE and GRU Based Joint Modeling for Nonlinear Distributed Parameter Systems

Gan

Feng

et al. 2022

IEEE Access

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“…Since two coupled nonlinearities are embedded in the general distributed thermal systems [33], the low-order temporal model should be designed according to such structure characteristics. Recent years have witnessed an increasing interest in the topic of extreme learning machine (ELM) [34]- [37], which has the advantage of universal approximation capability and fast learning speed. Therefore, ELM is applied here to approximate the two coupled nonlinear functions, where the derived model is called dual ELM (D-ELM) in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, ELM is applied here to approximate the two coupled nonlinear functions, where the derived model is called dual ELM (D-ELM) in this paper. Since the model structure of D-ELM matches well with the systems, it can achieve better performance [37]. Secondly, an online sequential learning algorithm (OSLA) [36] will be designed for online updating of the spatiotemporal model.…”

Section: Introductionmentioning

confidence: 99%

Dual Extreme Learning Machine Based Online Spatiotemporal Modeling With Adaptive Forgetting Factor

Xu¹,

Tan²,

Fan³

et al. 2021

IEEE Access

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Many industrial thermal processes are large-scale time-varying nonlinear distributed parameter systems (DPSs). To effectively model such systems, dual extreme learning machine based online spatiotemporal modeling with adaptive forgetting factor (AFFD-ELM) is proposed in this paper. This method can recursively update the parameters of the low-order temporal model by using newly arriving data under Karhunen-Loè ve (KL) based space/time separation. In this way, the time-varying dynamics can be tracked real-time very well as output data increases over time. Besides, since the training samples are usually timeliness, adaptive forgetting factor (AFF) is also embedded in this method to improve the online learning effects by adding a reasonable weight to previous data. This online learning strategy makes the process promising for online modeling under continuously samples environment. The proposed method is utilized for online temperature prediction of the curing oven. Simulation results verify the efficiency and viability of the online spatiotemporal model.

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A temporal–spatiotemporal domain transformation-based modeling method for nonlinear distributed parameter systems

Jin

Yang

et al. 2023

Journal of Computational Design and Engineering

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Complex nonlinear distributed parameter systems (DPSs) exist widely in advanced industrial thermal processes. The modeling of such highly nonlinear systems is a challenge for traditional time/space-separation-based methods since they employ linear methods for the model reduction and spatiotemporal reconstruction, which may lead to an inefficient application of the nonlinear spatial structure features represented by the spatial basis functions (BFs). To overcome this problem, a novel spatiotemporal modeling framework composed of nonlinear temporal domain transformation and nonlinear spatiotemporal domain reconstruction is proposed in this paper. Firstly, local nonlinear dimension reduction based on the locally linear embedding (LLE) technique is utilized to perform nonlinear temporal domain transformation of the spatiotemporal output of nonlinear DPSs. In this step, the original spatiotemporal data can be directly transformed into low-order time coefficients. Then, the extreme learning machine (ELM) method is utilized to establish a temporal model. Finally, through the spatiotemporal domain reconstruction based on the kernel-based ELM (K-ELM) method, the prediction of the temporal dynamics obtained from the temporal model can be reconstructed back to the spatiotemporal output. The effectiveness and performance of the proposed method are demonstrated in experiments on the thermal processes of a snap curing oven and a lithium-ion battery.

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Dual Extreme Learning Machines-Based Spatiotemporal Modeling for Nonlinear Distributed Thermal Processes

Cited by 5 publications

References 32 publications

SSAE and GRU Based Joint Modeling for Nonlinear Distributed Parameter Systems

SSAE and GRU Based Joint Modeling for Nonlinear Distributed Parameter Systems

Dual Extreme Learning Machine Based Online Spatiotemporal Modeling With Adaptive Forgetting Factor

A temporal–spatiotemporal domain transformation-based modeling method for nonlinear distributed parameter systems

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