Quantum statistic based semi-supervised learning approach for industrial soft sensor development

Unlike process variables which can be easily measured online, quality variables are often hard to be collected. Therefore, only a small proportion of soft sensor inputs are attached with quality related output labels. The semi supervised learning mechanism can elegantly incorporate unlabeled input samples for soft sensor improvement and hence has become popular. In this work, a novel mechanism called quantum statistic is incorporated with semi-supervised learning by quantum states. The quantum states are constructed by superposing conventional pure states with composite states and the extended state space as the complements could be more desirable for representing state uncertainties of incomplete labels. Based on that, a quantum statistical based semi-supervised soft sensor is developed. The quantum statistic based model is comprehensively compared with the conventional state-of-the-art method in a numerical example and an industrial process. Results demonstrate that the proposed soft sensor is more effective and stable than the traditional state-of-art method.