Soft Sensor Design Using Multi-State Dependent Parameter Methodology Based on Generalized Random Walk Method

The main problem of developing data-driven soft sensors is the existence of contamination (i.e., outliers) and missing values in the industrial real-time data. In this paper, a new soft sensor modeling method has been extended using a generalized random walk model (GRW) in order to access a robust estimation of parameters in the presence of missing data and outliers. The method termed as generalized random walk-multi-state-dependent parameter (GRW-MSDP) was established based on MSDP models. The model parameters are estimated in multivariable state space by employing the Kalman filter (KF) and fixed-interval smoothing (FIS) algorithms. The Kalman filter has been applied to identify the best state estimation values and reduce the effect of outliers by assigning low weight to them. Although in the optimization of KF hyper-parameters the missing values are not taken into account, the FIS algorithm implements a predictor-corrector type estimator to handle the missing values. The prediction step of FIS can be used for interpolation directly without parameterization. The main privilege of the GRW-MSDP method is the not necessity of data pre-processing for fitting the best models. A simulation case and an industrial debutanizer column are utilized to illustrate the effectiveness and advantages of the proposed method. Results indicate that the non-linearity of the process can be addressed under this modeling method using fewer input variables and the change of the process is also well-tracked when missing values exist in the time series data. In addition, the GRW-MSDP method obtains significant improvements in the smoothing of parameters.