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Efficient multidimensional regularization for Volterra series estimation

机译：用于Volterra级数估计的有效多维正则化

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摘要

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models.
机译：本文提出了一种有效的非参数时域非线性系统辨识方法。它显示了如何在不进行长时间无瞬变测量的情况下有效地估计截短的Volterra系列模型。该方法是针对线性时不变系统的脉冲响应估计而开发的正则化方法的新扩展。为了避免长时间测量或大量估计参数的情况下过多的内存需求，还提供了一种实用的基于梯度的估计方法，从而得出与所提出的Volterra估计方法相同的数值结果。此外，基于线性时变（LTV）系统瞬态消除的新颖思想，可以通过一种特殊的正则化方法消除模拟输出中的瞬态效应。结合所提出的方法，本文提出了级联水箱基准的非参数Volterra模型。比较和研究了从简单的有限冲激响应（FIR）模型到带有或不带有瞬态去除的3度Volterra级数的不同方案的结果。显然，当在验证数据集上进行测试时，所获得的模型可以捕获系统动态，并且其性能与白盒（物理）模型相当。

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