We propose an automatic approach for manifold nonlinear autoregressive with exogenous inputs (mNARX) modeling that leverages the feature-based structure of functional-NARX (F-NARX) modeling. This novel approach, termed mNARX+, preserves the key strength of the mNARX framework, which is its expressivity allowing it to model complex dynamical systems, while simultaneously addressing a key limitation: the heavy reliance on domain expertise to identify relevant auxiliary quantities and their causal ordering. Our method employs a data-driven, recursive algorithm that automates the construction of the mNARX model sequence. It operates by sequentially selecting temporal features based on their correlation with the model prediction residuals, thereby automatically identifying the most critical auxiliary quantities and the order in which they should be modeled. This procedure significantly reduces the need for prior system knowledge. We demonstrate the effectiveness of the mNARX+ algorithm on two case studies: a Bouc-Wen oscillator with strong hysteresis and a complex aero-servo-elastic wind turbine simulator. The results show that the algorithm provides a systematic, data-driven method for creating accurate and stable surrogate models for complex dynamical systems.

翻译：我们提出了一种基于流形非线性自回归外生输入（mNARX）建模的自动化方法，该方法利用了函数型NARX（F-NARX）建模中基于特征的结构。这种新方法称为mNARX+，在保留mNARX框架关键优势（即能够建模复杂动力系统的表达能力）的同时，解决了其核心局限性：严重依赖领域专业知识来识别相关辅助量及其因果排序。我们的方法采用数据驱动的递归算法，自动构建mNARX模型序列。该算法通过根据模型预测残差的相关性依次选择时间特征，自动识别最关键辅助量及其建模顺序，从而显著减少对先验系统知识的需求。我们通过两个案例研究验证了mNARX+算法的有效性：一个具有强迟滞特性的Bouc-Wen振荡器，以及一个复杂的气动-伺服-弹性风力发电机模拟器。结果表明，该算法为复杂动力系统提供了一种系统化、数据驱动的创建精确稳定代理模型的方法。