基于时空FOA-Elman的分布参数系统建模——时空建模
Time/Space Separation Based FOA-Elman Modeling for Non-Linear Distributed Parameter Processes—Spatial-Temporal Modeling
摘要: 本文针对具有无穷维时空特性和复杂非线性特性的分布参数系统，提出了一种基于数据驱动的建模方法。系统的时空输出可以由分布在空间中的有限个传感器获得，同时假设系统输入为有限维时间变量。首先利用Karhunen-Loève (K-L)分解对系统进行模型降维，得到主元特征向量，之后提取得到系统的一组主导空间基函数，利用时空分解获得系统时间系数，随后结合时间系数与系统激励构成输入输出信息，利用FOA算法优化Elman神经网络结构参数，后用优化的Elman神经网络辨识出系统时域NARX模型，最后进行模型重构，得到预测输出。仿真表明，上述建模方法能够对分布参数系统取得良好的建模效果。
Abstract: In this paper, because of infinite-dimensional nature and complex nonlinearities of the distributed parameter systems, a new data-driven modeling method has been proposed. The spatiotemporal output of the system is measured at a finite number of spatial locations; at the same time it is assumed that the input of the system is a temporal variable. Firstly, Karhunen-Loève (K-L) decomposition is used for dimension reduction to get PCA eigenvectors, which can be utilized to extract the nonlinear basis functions in dominant space. After using time-space separation to get the temporal coefficients, then combining the temporal coefficients and the excitation input signal as input and output information, the NARX model can be identified by using Elman neural network whose structure parameters have been optimized by FOA. Finally, model has been reconstructed and the predicted output gotten. Simulation result shows that the proposed modeling method can achieve good performance for distributed parameter systems.
文章引用：杨仁建, 范瑛琦. 基于时空FOA-Elman的分布参数系统建模——时空建模[J]. 计算机科学与应用, 2019, 9(2): 328-338. https://doi.org/10.12677/CSA.2019.92038

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