Nonlinear model structure detection and parameter estimation using a novel bagging method based on distance correlation metric
Nonlinear model structure detection and parameter estimation using a novel bagging method based on distance correlation metric
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DOI：
10.1007/s11071-015-2149-3
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发表时间：
2015-05
影响因子：
5.6
通讯作者：
J. R. Ayala Solares;Hua-Liang Wei
中科院分区：
文献类型：
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作者：
J. R. Ayala Solares;Hua-Liang Wei
在过去的几十年里，系统识别在不同的领域得到了应用。特别是，参数化建模方法，如线性和非线性自回归外生输入模型，由于模型结构的透明性已被广泛使用。模型结构检测的目的是通过使用一些依赖度量对一组候选模型项进行排序来识别精简模型，这些依赖度量评估单个候选模型项的包含如何影响期望输出信号的预测。常用的依赖度量如相关函数和互信息在某些情况下可能不能很好地工作，因此，模型参数估计中总是存在不确定性。因此，需要引入一种新的模型结构检测方案来处理参数估计中的不确定性。在这项工作中，实现了距离相关度量，并将其与套袋方法相结合。这两种实现的结合提高了现有前向选择方法的性能，因为它提供了非线性依赖的可解释性和对模型参数估计的深刻的不确定性分析。新方案被称为利用距离相关的bagging正正交回归（BFOR-dCor）算法。在处理几个数值案例研究中，将新的bfor - dor算法与使用诸如误差率、互信息或可逆跳跃马尔可夫链蒙特卡罗方法等指标的基准算法的性能进行了比较。为了便于分析，讨论仅限于可以用参数线性形式表示的多项式模型。
System identification has been applied in diverse areas over past decades. In particular, parametric modelling approaches such as linear and nonlinear autoregressive with exogenous inputs models have been extensively used due to the transparency of the model structure. Model structure detection aims to identify parsimonious models by ranking a set of candidate model terms using some dependency metrics, which evaluate how the inclusion of an individual candidate model term affects the prediction of the desired output signal. The commonly used dependency metrics such as correlation function and mutual information may not work well in some cases, and therefore, there are always uncertainties in model parameter estimates. Thus, there is a need to introduce a new model structure detection scheme to deal with uncertainties in parameter estimation. In this work, a distance correlation metric is implemented and incorporated with a bagging method. The combination of these two implementations enhances the performance of existing forward selection approaches in that it provides the interpretability of nonlinear dependency and an insightful uncertainty analysis for model parameter estimates. The new scheme is referred as bagging forward orthogonal regression using distance correlation (BFOR-dCor) algorithm. A comparison of the performance of the new BFOR-dCor algorithm with benchmark algorithms using metrics like error reduction ratio, mutual information, or the Reversible Jump Markov Chain Monte Carlo method has been carried out in dealing with several numerical case studies. For ease of analysis, the discussion is restricted to polynomial models that can be expressed in a linear-in-the-parameters form.