发表机构
Norwegian University of Science and Technology; Statkraft Energi AS; SINTEF Energy Research（挪威科技大学; Statkraft能源有限公司; SINTEF能源研究）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于高斯过程的闭环多输入单输出系统传递函数估计方法，给出可辨识性条件并证明零噪声收敛，通过蒙特卡洛模拟验证，兼顾偏差与误差权衡。
AI 中文摘要
本文将从基于复高斯过程回归的传递函数估计从单输入单输出设置扩展到闭环多输入单输出（MISO）系统。在闭环MISO系统中，准确估计各个传递函数具有挑战性，因为反馈和测量信号之间的相关性会掩盖每个输入的贡献。我们为MISO系统构建了基于高斯过程的估计器，提供了每个系统模块可被单独识别的解析条件，并证明了在零噪声极限下估计器收敛于真实传递函数。此外，我们展示了如何利用依赖外部激励的传统闭环偏差处理技术来构造合适的回归量。蒙特卡洛模拟支持解析可辨识性结果，并突出了由部分内生信号构造外生回归量所引入的闭环偏差与误差之间的权衡。所提出的工作为MISO系统的现有估计方法提供了一种富有表现力的非参数替代方案，同时提供了估计不确定性的概率表征。
英文摘要
This paper extends complex Gaussian process regression-based transfer function (TF) estimation from the single-input single-output setting to closed-loop multiple-input single-output (MISO) systems. Accurate estimation of individual TFs in closed-loop MISO systems is challenging as feedback and correlation between measured signals can obscure the contributions of each input. We formulate a Gaussian process-based estimator for MISO systems, provide analytical conditions under which each system module can be separately identified, and show that the estimator converges to the true TFs in the zero noise limit. Moreover, we demonstrate how conventional closed-loop bias handling techniques relying on external excitation can be employed to construct appropriate regressors. Monte Carlo simulations support the analytical identifiability results and highlight the trade-off between closed-loop bias and error introduced by constructing exogenous regressors partly from endogenous signals. The presented work offers an expressive, nonparametric alternative to existing estimation approaches for MISO systems, while providing a probabilistic characterization of the estimation uncertainty.
