Quantification of Valve Stiction in Control Loops Using the Bayesian Approach on the Riemannian Manifold

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.