Estimating the reliability of predictions in locally weighted partial least‐squares modeling

It is important to predict the reliability of the estimation results given by adaptive soft sensors. In this study, a locally weighted partial least‐squares (LWPLS) method, which is a just‐in‐time‐based adaptive soft sensor, is analyzed, and the reliability of LWPLS modeling is predicted as the standard deviation of the estimated values of an objective variable y. The relationship between the minimum of Euclidean distance (MinED) and the standard deviation of y errors (SDYE) is constructed using training samples, giving the proposed y‐error model. For the test samples, the MinED from a query to the training samples is input into the y‐error model, allowing the SDYE for the query to be predicted. The proposed LWPLS model can estimate the y values with associated error bars, which indicate the reliability of the estimated y values. The effectiveness of the proposed method is demonstrated through two case studies using datasets from industrial plants. Locally weighted partial least squares (LWPLS) is used as an adaptive soft sensor. The reliability of predictions in LWPLS modeling is estimated. Standard deviation of Euclidean distance from a query to training samples is input. Standard deviation of errors in an objective variable is output for the query. The proposed method is evaluated using two datasets from industrial plants.