Detecting Nonlinear Oscillations in Process Control Loop Based on an Improved VMD

A novel detector based on improved variational mode decomposition (VMD) is proposed to detect the nonlinearity-induced oscillations. Despite its high adaptivity and frequency resolution, the effectiveness of VMD highly depends on parameters, including mode number <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>, initial center frequency <inline-formula> <tex-math notation="LaTeX">$\omega _{init}$ </tex-math></inline-formula>, and the penalty coefficient <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>. To tackle this problem, an improved VMD is proposed, which involves: 1) the spectrum of phase-rectified signal averaging (PRSA) to determine optimal <inline-formula> <tex-math notation="LaTeX">$K, \omega _{init}$ </tex-math></inline-formula> and 2) the summation of permutation entropy (SPE) to optimize <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>, respectively. The presence of nonlinearity can be monitored by investigating the relationships among different frequencies of the process variable (PV) in the control loops. In addition, the oscillation detector based on the improved VMD is capable of distinguishing multiple oscillations, even when both nonlinear and linear oscillations from different sources occur. The proposed method is completely adaptive and data driven, which acts without <italic>a priori</italic> knowledge. The validity of the raised approach is verified by a set of simulations as well as industrial applications.