Probabilistic density-based regression model for soft sensing of nonlinear industrial processes

Process nonlinearity is a challenging issue for soft sensor modeling of industrial plants. Traditional nonlinear soft sensing methods are not achieved through the probabilistic manner, which only give single point estimation for output variables but do not provide the prediction uncertainty. To meet the probabilistic soft sensor requirement, a novel density-based regression method, which is called weighted Gaussian regression (WGR), is proposed in this paper. By taking the weights of training samples into consideration, a local weighted Gaussian model (WGM) is first built to model the joint density P(x, y) of input and output variables around the query sample. Then, the output variables can be estimated by taking the conditional distribution P(y|x). The new method can successfully approximate the nonlinear relationship between output and input variables. Moreover, WGR can provide more detailed information of uncertainty for the prediction. The effectiveness and flexibility of WGR are validated through a numerical example and an industrial debutanizer column process.