Expectation-maximization Algorithm with Monte Carlo Implementation on Complex Projective Space for Control Valve Stiction Quantification

As a vital actuation facility, control valves are ubiquitously employed in many real industrial applications. Valve stiction is the most frequent root-cause for malfunction of control loops. Recent two decades have witnessed an increasing interest in effective strategies for valve stiction detection and diagnosis. However, how to quantify stiction from the prospective of probabilistic interpretations is still an open issue. In this paper, we propose a novel quantification method for valve stiction based on Monte Carlo expectation-maximization (EM) algorithm for parameters on Riemannian manifold. The transformation stage projects the raw time series signals onto the complex projective space, which is a special kind of manifolds. Then, assisted by adopting Monte Carlo scheme, the expectation of joint log likelihood function for latent variable on the associated tangent space could be approximated, which can effectively extract the shape variations caused by valve stiction. Compared with traditional methods, the proposed method is available to provide the probabilistic interval at a high confidence level for valve stiction. Results from simulated steam plant case study and the benchmark International Stiction Data Base (ISDB) illustrate the superior performance of proposed method.