This article presents a fully automated algorithm for the extraction of parameterized macromodels from frequency responses. The reference framework is based on a frequency-domain rational approximation combined with a parameter-space expansion into Gaussian radial basis functions (RBFs). An iterative least-squares fitting with positivity constraints is used to optimize model coefficients, with a guarantee of uniform stability over the parameter space. The main novel contribution of this work is a set of algorithms, supported by strong theoretical arguments with associated proofs, for the automated determination of all the hyperparameters that define model orders, placement, and width of RBFs. With respect to standard approaches, which tune these parameters using time-consuming tentative model extractions following a trial-and-error strategy, the presented technique allows much faster tuning of the model structure. The numerical results show that models with up to ten independent parameters are easily extracted in few minutes.

中文翻译：

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迈向全自动高维参数化宏观建模


本文提出了一种从频率响应中提取参数化宏模型的全自动算法。该参考框架基于频域有理近似与高斯径向基函数 (RBF) 的参数空间扩展相结合。使用具有正性约束的迭代最小二乘拟合来优化模型系数，并保证参数空间上的均匀稳定性。这项工作的主要新颖贡献是一组算法，由强有力的理论论证和相关证明支持，用于自动确定定义模型阶数、布局和 RBF 宽度的所有超参数。对于使用遵循试错策略的耗时的试验性模型提取来调整这些参数的标准方法，所提出的技术允许更快地调整模型结构。数值结果表明，可以在几分钟内轻松提取具有多达十个独立参数的模型。