The status of control valves directly influences the routine operation of industrial process. Stiction nonlinearity is one of the widely known failure modes of a valve, which may hazard the performance of the control loop. This leads to a clear demand for quantifying valve stiction timely and accurately, in order to determine further strategies for valve maintenance. In this paper, a new quantification approach based on a Bayesian approach on the Riemannian manifold which incorporates a Hamiltonian Monte Carlo expectation-maximization (HMCEM) scheme into a Riemannian parameters estimation is proposed to quantify the valve stiction. The key idea is to describe the relationship between process variables and controller output as the shape sample on the Kendall’s shape space (complex projective space), which is always exhibited like a limit cycle due to valve stiction. Assisted by the probabilistic model with Bayesian prior distribution on the associated Riemannian parameters, the proposed method can realize the quantification of apparent stiction more accurately. Furthermore, the proposed method is capable of providing the estimated interval for valve stiction, not just a single estimation value. The availability of this method has been justified through a simulated numerical example and its applications to a steam turbine plant and to real benchmark industrial data.

中文翻译：

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使用黎曼流形上的贝叶斯方法量化控制回路中的阀门粘滞

控制阀的状态直接影响工业过程的日常运行。静摩擦非线性是众所周知的阀门故障模式之一，它可能会危及控制回路的性能。这导致了对及时准确地量化阀门粘滞的明确需求，以便确定阀门维护的进一步策略。在本文中，提出了一种基于黎曼流形上的贝叶斯方法的新量化方法，该方法将哈密顿蒙特卡洛期望最大化（HMCEM）方案结合到黎曼参数估计中来量化阀门粘滞。关键思想是将过程变量和控制器输出之间的关系描述为 Kendall 形状空间（复投影空间）上的形状样本，由于阀门的粘滞，它总是表现得像一个极限循环。在相关黎曼参数上具有贝叶斯先验分布的概率模型的辅助下，该方法可以更准确地实现表观静摩擦的量化。此外，所提出的方法能够提供阀门粘滞的估计间隔，而不仅仅是单个估计值。该方法的有效性已通过模拟数值示例及其在汽轮机工厂和实际基准工业数据中的应用得到证明。所提出的方法能够提供阀门粘滞的估计区间，而不仅仅是单个估计值。该方法的有效性已通过模拟数值示例及其在汽轮机工厂和实际基准工业数据中的应用得到证明。所提出的方法能够提供阀门粘滞的估计区间，而不仅仅是单个估计值。该方法的有效性已通过模拟数值示例及其在汽轮机工厂和实际基准工业数据中的应用得到证明。