利用Volterra核的张量分解对并行Wiener- Hammerstein系统进行建模
Modeling Parallel Wiener-Hammerstein Systems Using Tensor Decomposition of Volterra Kernels
AI总结：
本文提出通过张量分解Volterra核来识别并行Wiener-Hammerstein系统，利用块结构特性提升建模精度，在噪声环境下实现准确重构。
摘要：
通过块导向方法可以在非线性系统识别中提供灵活性和可解释性。并行Wiener-Hammerstein系统是多个Wiener-Hammerstein分支的总和，由静态非线性元件夹在动态线性块之间组成。虽然并行Wiener-Hammerstein模型比单分支模型更具描述能力，但其识别需要定制化的系统识别方法。本文通过分解非线性系统获得的Volterra核进行识别，展示了并行Wiener-Hammerstein块结构如何导致Volterra核的联合张量分解，具有块循环结构的因子。Volterra核与张量方法的结合是解决并行Wiener-Hammerstein系统识别任务的有效途径。在仿真实验中，能够在噪声条件下准确重建底层块。
英文摘要：
Providing flexibility and user-interpretability in nonlinear system identification can be achieved by means of block-oriented methods. One of such block-oriented system structures is the parallel Wiener-Hammerstein system, which is a sum of Wiener-Hammerstein branches, consisting of static nonlinearities sandwiched between linear dynamical blocks. Parallel Wiener-Hammerstein models have more descriptive power than their single-branch counterparts, but their identification is a non-trivial task that requires tailored system identification methods. In this work, we will tackle the identification problem by performing a tensor decomposition of the Volterra kernels obtained from the nonlinear system. We illustrate how the parallel Wiener-Hammerstein block-structure gives rise to a joint tensor decomposition of the Volterra kernels with block-circulant structured factors. The combination of Volterra kernels and tensor methods is a fruitful way to tackle the parallel Wiener-Hammerstein system identification task. In simulation experiments, we were able to reconstruct very accurately the underlying blocks under noisy conditions.
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