Minimum Synthesis and Learning Algorithm for A Hybrid Nonlinear Predictor

现在一天，我们有很多问题、环境破坏、环境污染、经济危机、人口问题、自然灾害、自然保护等等。如果要解决这些问题，这是分析这些现象的过程非常重要的。这些现象可以按照时间系列的规定进行。他们主要是非线性的时间系列。因此，非线性预测可能是非常重要的。（1）本研究项目中的非线性预测器，我们开发了混合非线性预测器，将神经网络和前馈线性预测器结合起来。由于神经网络有线性输出单元，大多数非线性部分和一些线性部分可以被神经网络预测。剩余的部分是由线性预测者预测的。（2） Learning Algorithms An Improved learning algorithm has been proposed，哪个单独优化了神经网络和该顺序中的线性预测器。一个增强的学习算法已经被提议用于噪音非线性时间序列预测。（3）时间序列预测的非线性分析是过去样本x（n-1）=[x（n-1），x（n-2），..，x（n）]到下一个示例x（n）。When the past samples x（n y D21 y D2-1） and x（n y D22 y D2-1） are similar， however， the next samples x（n y D21 y D2） and x（n y D22 y D2） are far from each other， then， nonlinearity of this time series is high.一个衡量标准，谁可以评估这个财产已经被引入？（4）对真实非线性时间序列的预测：拟议的方法已应用于许多真实非线性时间序列，包括混沌、某些湖泊、雾产生的水水平，以及其他。拟议的混合非线性预测用常规方法进行了良好的性能比较。

Now a day, we have a lot of problems, environmental disruption, environmental pollution, economic crisis, population problem, natural disaster, nature conservation, and so on. In order to solve these problems, it is very important to analyze progress of these phenomena. These phenomena can be regarded as time series. Mainly they are nonlinear time series. So, nonlinear prediction becomes very important.(1) A Nonlinear PredictorIn this research project, we have developed a hybrid nonlinear predictor, which combines a neural network and a feed-forward linear predictor. Since the neural network has linear output unit, most of nonlinear part and some linear part can be predicted by the neural network. The remaining part is predicted by the linear predictor.(2) Learning AlgorithmsAn improved learning algorithm has been proposed, which separately optimize the neural network and the linear predictor in this order. An enhanced learning algorithm has been proposed for noisy nonlinear time series prediction.(3) Nonlinearity Analysis of Time SeriesPrediction is the mapping from the past sample x(n-1)=[x(n-1),x(n-2),..,x(n-N)] to the next sample x(n). When the past samples x(nィイD21ィエD2-1) and x(nィイD22ィエD2-1) are similar, however, the next samples x(nィイD21ィエD2) and x(nィイD22ィエD2) are far from to each other, then, nonlinearity of this time series is high. A measure, which can evaluate this property has been introduced.(4) Prediction of Real Nonlinear Time SeriesThe proposed method was applied to many the real nonlinear time series, including Chaos, water levels of some lake, fog generation, and so on. The proposed hybrid nonlinear predictor demonstrated good performance compared with the conventional methods.