Knowledge based recursive non-linear partial least squares (RNPLS)

Soft sensors driven by data are very common in industrial plants to perform indirect measurements of difficult to measure critical variables by using other variables that are relatively easier to obtain. The use of soft sensors implies some challenges, such as the colinearity of the predictor variables, the time-varying and possible non-linear nature of the industrial process. To deal with the first challenge, the partial least square (PLS) regression has been employed in many applications to model the linear relations between process variables, with noisy and highly correlated data. However, the PLS model needs to deal with the other two issues: the non-linear and time-varying characteristics of the processes. In this work, a new knowledge-based methodology for a recursive non-linear PLS algorithm (RNPLS) is systematized to deal with these issues. Here, the non-linear PLS algorithm is set up by carrying out the PLS regression over the augmented input matrix, which includes knowledge based non-linear transformations of some of the variables. This transformation depends on the system's nature, and takes into account the available knowledge about the process, which is provided by expert knowledge or emulated using software tools. Then, the recursive exponential weighted PLS is used to modify and adapt the model according to the process changes. This RNPLS algorithm has been tested using two case studies according to the available knowledge, a real industrial evaporation station of the sugar industry, where the expert knowledge about the process permits the formulation of the relationships, and a simulated wastewater treatment plant, where the necessary knowledge about the process is obtained by a software tool. The results show that the methodology involving knowledge regarding the process is able to adjust the process changes, providing highly accurate predictions.