Co-evolving data driven models and test data sets with the application to forecast chaotic time series
Co-evolving data driven models and test data sets with the application to forecast chaotic time series
复制标题
共同进化数据驱动模型和测试数据集以及预测混沌时间序列的应用
DOI：
10.1109/cec.2011.5949592
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
W. Punch
中科院分区：
文献类型：
--
作者：
M. Mirmomeni;W. Punch
介绍了几种具有混沌特性的非线性动力学的建模和预测方法。在这些方法中，数据驱动的方法，如自回归（AR）模型、非线性自回归（NAR）模型、径向基函数（RBF）网络和多层感知器（MLP）神经网络，已被证明是混沌动力学建模和预测的有力方法。然而，这些模型的结构需要在训练阶段之前就知道，这是一个非常复杂的问题。在本研究中，我们引入了一种用于混沌动力学建模和系统辨识的协同进化方法。该算法由两个共同进化的种群组成：候选数据驱动模型和测试数据集，这些数据集从非线性混沌系统中提取新信息或从中获得期望的行为。候选模型的适应度是它们通过预测这些数据集的未来值来解释迄今为止所进行的测试所观察到的目标混沌系统的行为的能力；候选测试数据集的适应度是它们使模型在预测中不一致的能力。为了验证该算法的性能，考虑了三个案例研究。首先，我们将该方法应用于近似一个在零附近具有复杂行为的静态函数。然后，我们使用该算法预测混沌文献中的两个基准时间序列：太阳黑子数（SSN）和麦基-格拉斯（MG）时间序列。仿真结果表明了该方法在复杂非线性系统建模和预测方面的有效性。
Several approaches have been introduced for modeling and prediction of nonlinear dynamics which have chaotic characteristics. Among these methods, data driven approaches such as Auto Regressive (AR) models, Nonlinear Auto Regressive (NAR) models, Radial Basis Function (RBF) networks, and Multi Layered Perceptron (MLP) neural networks have proven themselves to be powerful approaches in modeling and prediction of chaotic dynamics. However, the structure of these models should be known before the training phase, which is a very complicated problem. In this research, we introduce a co-evolutionary approach for modeling and system identification of chaotic dynamics. The proposed algorithm is composed of two co-evolving populations: candidate data driven models, and test data sets which either extract new information from the nonlinear chaotic system or elicit desirable behavior from it. The fitness of candidate models is their ability to explain behavior of the target chaotic system observed in response to tests carried out so far by predicting the future values of these data sets; the fitness of candidate test data sets is their ability to make the models disagree in their predictions. To check the performance of this algorithm, three case studies are considered. First, we apply this method to approximate a static function which has complicated behavior near zero. Then, we use this algorithm to predict two bench mark time series in chaos literature: Sunspot Number (SSN) and Mackey-Glass (MG) time series. Simulation results depict the power of proposed method in modeling and predicting complicated nonlinear systems.