Modified nonlinear generalized ridge regression and its application to develop naphtha cut point soft sensor

A novel modified nonlinear generalized ridge regression (MNGRR) is proposed to model highly nonlinear system. MNGRR applies nonlinear transformation for independent variables to expand independent variable space. Then, the generalized ridge regression (GRR), which employs a modified differential evolution (MDE) to obtain the optimal ridge parameters according to the predicting error, is applied to remove the multicollinearity among the expanded variables, and thus the model that can describe complex nonlinear system and has good predicting ability is obtained. In practice, MNGRR is applied to develop naphtha 95% cut point soft sensor due to the existence of highly nonlinear relationship between process variables and naphtha 95% cut point in atmosphere distillation unit and the fact that few on-line hardware sensors are available and these are also difficult to maintain. Satisfactory results were obtained. The comparison results show that the performance of MNGRR is better than line regressions, nonlinear ordinary least squares regression and nonlinear traditional ridge regression. Further, MDE uses an adaptive mutation operator to overcome the premature and enhance the probability of obtaining the global optimal solution. The comparison results demonstrated that MDEs on-line and off-line performances are all superior to those of traditional DE (TDE), the probability of obtaining the global optimal solution is larger than that of TDE, and that the parameter sensitivity degree of MDE is lower than that of TDE.