Most distributed parameter systems (DPSs) are unknown, including unknown parameter, boundary and even structure, and have a strongly nonlinear spatiotemporal nature. In order to achieve desirable modeling accuracy, the models from the commonly used DPS modeling methods often have a high order, which makes them difficultly used for prediction and control. Here, a novel low-order spatiotemporal least squares support vector machine (LS-SVM) method is proposed for modeling unknown and nonlinear DPSs. Generally, the information of a certain sensor may be represented by information of its neighboring sensors due to the spatial correlation between them. Making use of this feature, a kernel-space based spatial correlation analysis method is developed for deleting redundant spatial kernel functions, from which a low-order model can be achieved and it is without loss of any spatial information. On this basis, a LS-SVM model is constructed to represent the nonlinear temporal dynamics. Integration of the without-redundant spatial kernel functions and the LS-SVM temporal model, a low-order spatiotemporal model is created to reconstruct the spatiotemporal dynamics of the nonlinear DPSs. Additional analysis and proof show that: (1) the proposed method has the same modeling performance with the without-order-reduction spatiotemporal modeling method; and (2) it has better modeling performance than the model with the same order achieved by the without-order-reduction one. Using case studies, the effectiveness of the proposed method and its superior modeling ability compared to several common methods are demonstrated.

大多数分布式参数系统（DPS）是未知的，包括未知参数、边界甚至结构，并且具有很强的非线性时空性质。为了达到理想的建模精度，常用的DPS建模方法中的模型往往具有较高的阶数，这使得它们难以用于预测和控制。在这里，提出了一种新的低阶时空最小二乘支持向量机 (LS-SVM) 方法来对未知和非线性 DPS 进行建模。通常，某个传感器的信息由于它们之间的空间相关性，可以用其相邻传感器的信息来表示。利用这一特点，提出了一种基于核空间的空间相关性分析方法，用于删除冗余空间核函数，从中可以实现低阶模型，并且不会丢失任何空间信息。在此基础上，构建了 LS-SVM 模型来表示非线性时间动态。整合无冗余空间核函数和 LS-SVM 时间模型，创建低阶时空模型来重建非线性 DPS 的时空动态。额外的分析和证明表明：（1）所提出的方法与无阶约简时空建模方法具有相同的建模性能；(2) 与无阶约简实现的同阶模型相比，具有更好的建模性能。通过案例研究，证明了所提出方法的有效性及其与几种常用方法相比的优越建模能力。