This work deals with accuracy analysis of dynamical systems interconnected in a cascade structure. For a cascade network there are a number of experimental settings for which the dynamic systems within the network can be identified. We study the problem of choosing which excitation and measurement pattern delivers the most accurate parameter estimates for the whole network. The optimal experiment is based on the accuracy assessed through the asymptotic covariance matrix of the prediction error method, while the cost criterion is the number of excitations and measurements. We develop theoretical results under the assumptions that all dynamic systems are equal and with equal signal-to-noise ratio throughout the network. We show that there are experimental settings which result in equal overall precision and that there is an excitation and measurement pattern that yields more accurate results than others. From these results a guideline based on the topology of the network emerges for the choice of the experimental setting. We provide numerical results which attest that the principles behind this guideline are also valid for more general situations.

中文翻译：

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级联网络的最佳激励和测量模式

这项工作涉及以级联结构互连的动力系统的精度分析。对于级联网络，有许多实验设置可以识别网络中的动态系统。我们研究了选择哪种激励和测量模式可为整个网络提供最准确的参数估计的问题。最优实验是基于通过预测误差方法的渐近协方差矩阵评估的准确性，而成本标准是激励和测量的次数。我们在假设所有动态系统都是相等的并且在整个网络中具有相等的信噪比的假设下得出理论结果。我们表明，有一些实验设置会导致相同的整体精度，并且有一种激发和测量模式可以产生比其他模式更准确的结果。从这些结果中，出现了一个基于网络拓扑的指南，用于选择实验设置。我们提供的数值结果证明本指南背后的原则也适用于更一般的情况。