在无完整模型时，通过频域分析识别非线性系统输入输出间的因果关系。
A method for identifying causality in the response of nonlinear dynamical systems
- 基于输出预测与噪声测量的最优融合，提取因果成分。
- 无需高保真模型，即可在频域中量化输入输出因果性。
- 适用于广泛非线性动力系统，特别适合缺乏基准模型场景。
预测受随机宽带激励的非线性动力系统响应在结构动力学、神经科学等领域至关重要。构建数据驱动模型需系统输入与输出的实验测量，但模型误差与噪声难以区分。本文提出一种新方法，在存在输出噪声的情况下，无需高保真模型，仅凭输入输出测量即可在频域内识别系统的因果成分。该方法将现有模型的输出预测与实际噪声输出进行最优组合，以反推系统输入；算法参数用于平衡信号并计算非线性相干度，作为因果性度量。该方法适用于一大类非线性动力系统，目前尚无此类问题在缺乏完整基准模型下的解决方案。
原文摘要 · Abstract (English)
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires experimental measurements of the system input and output, but it can be difficult to determine whether inaccuracies in the model stem from modelling errors or noise. This paper presents a novel method to identify the causal component of the input-output data from measurements of a system in the presence of output noise, as a function of frequency, without needing a high fidelity model. An output prediction, calculated using an available model, is optimally combined with noisy measurements of the output to predict the input to the system. The parameters of the algorithm balance the two output signals and are utilised to calculate a nonlinear coherence metric as a measure of causality. This method is applicable to a broad class of nonlinear dynamical systems. There are currently no solutions to this problem in the absence of a complete benchmark model.
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