A Novel Roughness-based Metric for Uniformity Modeling and Monitoring in High-Temperature Superconductor Manufacturing

High-Temperature Superconductors (HTS) are widely recognized for their efficiency and minimal energy loss, making them essential in industries such as power transmission, energy storage, and electronics. Nevertheless, the challenge of maintaining a consistent critical current (Ic) along HTS tapes has posed a significant obstacle to their broad commercialization. Quantifying the uniformity of critical current over long HTS tapes is a complex research problem due to the inherent uncertainty of critical current and its dynamic evolution. In this study, we introduce an innovative approach using the Roughness-based Uniformity Metric (RUM) for assessing the uniformity of Ic. By integrating the roughness measure of functional regression with 1D fused lasso, this study aims to achieve two key objectives: (1) accurately measuring the uniformity of the critical current, and (2) automatically monitoring and detecting the drop-out event with statistical control charts. By employing the roughness measure of functional regression for uniformity assessment and applying 1D fused lasso for smoothing, our method enhances the precision in detecting changes in the critical current. We demonstrate the effectiveness of the proposed approach through uniformity modeling and monitoring on three different HTS tapes. The proposed method are also compared with the conventional uniformity metric, e.g., the coefficient variation.