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.

翻译：预测受随机宽带激励的非线性动力系统的响应，在结构动力学和神经科学等一系列科学领域中具有重要意义。建立数据驱动模型需要对系统输入和输出进行实验测量，但很难确定模型中的不准确性是源于建模误差还是噪声。本文提出了一种新方法，用于在存在输出噪声的情况下，从系统测量数据中识别输入输出数据的因果成分，并将其作为频率的函数，而无需高保真度模型。该方法将使用现有模型计算出的输出预测，与含噪声的输出测量值进行最优组合，以预测系统输入。算法中的参数用于平衡两个输出信号，并用于计算一个非线性相干度量作为因果关系的指标。此方法适用于一大类非线性动力系统。目前，在缺乏完整基准模型的情况下，尚无其他解决方案可解决此问题。