Functional Soft Sensor Based on Spectra Data for Predicting Multiple Quality Variables

In many complex chemical processes, such as ethanol fermentation process, prediction of the multivariate quality variables based on spectra data presents a great challenge because the dimensions of the spectra far exceed their sampling number. To address this problem, the dimension reduction of the predictors is necessary. It can be conducted either by regressing on components or by smoothing methods with basis functions. Based on the functional data analysis methods, this work introduces a novel wavelet functional partial least squares (WFPLS), which combines both of the foregoing dimension-reduction approaches. The high-dimensional spectra can be well fitted by fewer wavelet basis functions in the proposed method. Using the proposed WFPLS method does not require the measured data to be linear and to be sampled on a regular basis. It will be proved that the proposed WFPLS method can be finally transferred into the traditional PLS method in computation. By comparison with the existing prediction methods, the advantages of the proposed method are well demonstrated via a numerical case and an ethanol fermentation experiment.