一种非双曲型非线性离散系统次最优建模方案

A Suboptimal Modeling Scheme from Scalar Series for Non-hyperbolic Nonlinear Discrete System

研究非线性系统建模是一个NP-hard问题,若系统因稳定流与不稳定流平行均属于非双曲线型时,上述研究将变得更加明显。对同一中搜索算法,Total Error性能明显优于Marginal Error。当不同的算法和策略混用时,后次迭代以前次迭代的结果集为基础往往优于以全基函数集为基础的迭代。结合以上特点,模型选取的最小描述长度(Minimal Description Length)准则,给出了一种新的全局误差(Total Error)次最优选取算法。算法结构清晰,易于实践。多次试验中,对不同的受扰序列,总体时间开销均小于公认最有效的Shaking方法。既然非线性序列的模型选取是一个NP-hard问题,故方法也不能确保所选模型为最优模型,尽管在有限次的试验中总能成功获得最优模型。

Constructing models of nonlinear time series itself is typically NP - hard. The situation will get worse if nonlinear system is non -hyperbolic, which means that the stable manifold of nonlinear system is parallel to its unstable manifold. Based on the minimal description length criteria, It is been pointed out that the marginal error algorithm is not optimal to the discrete system, sometimes even unadapted, from the viewpoint of over - fitting and under -fitting. A modified algorithm named total error algorithm is proposed and analyzed. The thought and structure of the algorithm are plain, so the algorithm can be easily implemented in practice. For noisy series in different non - hyperbolic nonlinear system, the whole time spending in many experiments is less than the Shaking method which is acknowledged to be the most effective at present. Since modeling nonlinear series are NP - hard, similar to other method, the method in this paper can not guarantee that the result is necessarily the optimal, though the best model has been obtained for implemented limited experiments.