Soft Sensing of a Nonlinear Multimode Process Using a Self Organizing Model and Conditional Probability Density Analysis

A soft sensor based on a self-organizing model and conditional probability density analysis is proposed for a nonlinear multimode process, the operation of which switches between multiple nonlinear modes. The self-organizing model is based on multiple kernel partial least-squares (KPLS) models, with each KPLS model associated with a specific mode. It is assumed that no a priori information is available; that is, neither the number of modes nor mode labels of the training samples are known. During the training stage, both the assigned modes of training samples and model parameters are updated, so that mode assignment and model training can be achieved simultaneously. For the purpose of online estimation, the conditional density p ( y | x ) of the outputs y conditional on inputs x is estimated based on samples assigned into each mode. When a query sample is available, several candidate output predictions are obtained using the trained models. The prediction that yields the most significant conditional probability is assigned as the final estimation. The introduction of conditional density estimation produces an appropriate similarity measure for the nonlinear multimode process. The performance of the proposed soft sensor is validated using a simulation example and an industrial process.