Control performance assessment (CPA) is vital to ensure the safety of control systems. However, most multivariate CPA methods are limited to the system with explicit knowledge. Recently, it has been recognized that high predictability of closed-loop outputs implies poor control performance. This paper proposes a probabilistic CPA (PCPA), which is compatible with the above promising idea. This paper constructs a modified Gaussian process regression (GPR) model to quantitatively​ estimate the prediction uncertainty of outputs with only routine closed-loop data as input and focuses on the prediction variance of interest. As a non-parametric and probabilistic method, the proposed framework can handle the nonlinearity and random uncertainties inherent in complex control systems. Combined with the varying window size strategy, a novel performance metric, called disruption resistance (DR) here, is designed to characterize different control performance. The evaluation confidence and uncertainty can be revealed with concurrent analytics of GPR and Gaussian process classification when performing the performance assessment. This gives rise to a reliable and pragmatic PCPA framework, which shows more accurate and comprehensive results in the application to both simulated and real industrial processes.

控制性能评估（CPA）对于确保控制系统的安全至关重要。但是，大多数多元CPA方法仅限于具有明确知识的系统。最近，已经认识到闭环输出的高可预测性意味着较差的控制性能。本文提出了一种概率CPA（PCPA），它与上述有前途的想法兼容。本文构建了一个改进的高斯过程回归（GPR）模型，以仅以常规闭环数据作为输入来定量估计输出的预测不确定性，并关注感兴趣的预测方差。作为一种非参数和概率方法，提出的框架可以处理复杂控制系统中固有的非线性和随机不确定性。结合可变窗口大小策略，新颖的性能指标，此处称为抗破坏性（DR）旨在表征不同的控制性能。进行绩效评估时，可以同时进行GPR和高斯过程分类分析，从而揭示评估的置信度和不确定性。这产生了一个可靠且实用的PCPA框架，该框架在应用于模拟和实际工业过程中均显示出更加准确和全面的结果。