A multimode process monitoring strategy via improved variational inference Gaussian mixture model based on locality preserving projections

For multimode process monitoring, accurate mode information is difficult to be obtained, and each mode is monitored separately, which increases the complexity of the system. This paper proposes a multimode process monitoring strategy via improved variational inference Gaussian mixture model based on locality preserving projections (IVIGMM-LPP). First, the raw data are projected to the feature space where samples still maintain the original neighbor structure. Second, a new discriminant condition is introduced to reduce the influence of the initial category parameter on the iteration results in the VIGMM model. Then, the data are updated utilizing modal information, so that the scales of different modes are adjusted to the same level. Next, the deviation vector is introduced to eliminate the multi-center structure of data. Finally, the statistic is built to monitor the process. IVIGMM-LPP establishes one model for monitoring the premise of knowing the mode information, which reduces the complexity of the monitoring process and improves the fault detection rate. The experimental results of a numerical case and the Tennessee Eastman (TE) process verify the effectiveness of IVIGMM-LPP.

Operational Modal Analysis for Vibration Control Following Moving Window Locality Preserving Projections for Linear Slow-Time-Varying Structures

Modal parameters can reflect the dynamic characteristics of the structure and can be used to control vibration. To identify the operational modal parameters of linear slow-time-varying structures only from non-stationary vibration response signals, a method based on moving window locality preserving projections (MWLPP) algorithm is proposed. Based on the theory of “time freeze”, the method selects a fixed length window and takes the displacement response signal in each window as a stationary random sequence. The locality preserving projections algorithm is used to identify the transient modal frequency and modal shape of the structure at this window. The low-dimensional embedding of the displacement response data set calculated by locality preserving projections (LPP) corresponds to the modal coordinate response matrix, and the transformation matrix corresponds to the modal shape matrix. The simulation results of the mass slow-time-varying three degree of freedom (DOF) and the density slow-time-varying cantilever beam show that the new method can effectively identify the modal shape and modal natural frequency of the linear slow-time-varying only from the non-stationary vibration response signal, and the performance is better than the moving window principal component analysis (MWPCA).