Uncertainty Quantification Based on Conformal Prediction for Industrial Time Series With Distribution Shift

Abstract

Conformal prediction (CP) is known to theoretically guarantee prediction interval coverage under the exchangeability assumption. However, industrial time series collected from real-world industrial processes often violates this assumption due to temporal dependencies and distribution drift. Therefore, an uncertainty quantification framework is proposed for industrial time series, with the prediction interval composed of two one-sided intervals. Specifically, it adopts CP as the basic framework and integrates entire and local nonconformity score information to adjust the confidence levels of two one-tailed intervals over time. This enables the proposed method can adapt quickly to distribution shifts and provides effective prediction intervals. Two experiments show that the proposed method improves the efficiency of prediction intervals while guaranteeing coverage. Specifically, under a nominal confidence level 95%, the proposed method achieves an average empirical coverage of 95.0% with a 6.29% reduction in prediction interval width in the wastewater dataset. While in the actual sintering production dataset, it achieves a similar improvement, with a 95.6% coverage and a 15.70% reduction in width, compared to the best-performing benchmark model.