A Statistical Modelling and Convex Relaxation Approach for Product Quality Analytics

Abstract

Massive continuous stream data in multi-stage processes provide a data foundation for product-oriented quality determination and intelligent decision-making. However, quality analytic models based on historical data are difficult to consistently stable in complex multi-stage manufacturing processes, so quantifying the model uncertainty becomes an important challenge. In this paper, we propose a multi-output conformal risk control method to realize robust interval estimation of product quality and adaptive calibration of the model. The proposed method first uses a multi-output regression model as the basic model. Then it minimizes the multi-output prediction region as the conformal risk control objective on the calibration set with a given global confidence level. The model adaptive calibration is realized by fine-tuning the prediction intervals through parameters, and finally, the fine-tuning coefficients for each quality indicator are solved by the convex relaxation method. Taking the hot rolling process as an example, the proposed method is used for the prediction of the mechanical properties of thick plates. The experimental results prove that the proposed method can provide interval estimation with a global coverage guarantee for multiple quality variables, and it can be adaptively calibrated by the new data, which can provide real-time and effective information for intelligent decision-making.