Many industrial thermal processes belong to distributed parameter systems (DPSs), which have two coupled nonlinear blocks. Dual least square support vector machines (LS-SVM) has been proposed to model such systems. However, due to the use of two LS-SVM, this method often leads to heavy computation and long learning time, which does not suit for online application. In this study, a dual extreme learning machine (ELM)-based spatiotemporal modeling method is proposed for such two nonlinearities embedded DPSs. Firstly, the KL method is applied to reduce the dimension of the original system and obtain the spatial basis functions (BFs). Then, dual ELM is designed to match the two nonlinear structures. Finally, through the reconstruction of space–time synthesis, the approximate spatiotemporal distribution model of the original system is obtained. In addition, simulations on a curing process is studied to confirm the effectiveness of the proposed method.

中文翻译：

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基于双极限学习机的非线性分布式热过程时空建模

许多工业热过程属于分布式参数系统 (DPS)，它具有两个耦合的非线性模块。已提出对偶最小二乘支持向量机 (LS-SVM) 对此类系统进行建模。但是，由于使用了两个LS-SVM，这种方法经常导致计算量大、学习时间长，不适合在线应用。在这项研究中，针对这两个非线性嵌入式 DPS，提出了一种基于双极限学习机 (ELM) 的时空建模方法。首先，应用KL方法对原系统进行降维，得到空间基函数（BFs）。然后，对偶 ELM 被设计为匹配两个非线性结构。最后，通过时空合成的重构，得到原系统的近似时空分布模型。