Mitigation of Distribution Shifts for Data-Based Virtual Sensors

The increasing demand for cost-effective monitoring solutions has led to widespread adoption of virtual sensors, which estimate critical system states and parameters using available measurements rather than dedicated physical sensors. However, these data-based solutions face a fundamental challenge: their accuracy often deteriorates significantly when deployed in field conditions that differ from laboratory testing environments. Such distribution shifts are often inevitable due to varying environmental conditions, equipment aging, and different usage patterns across installations. Although virtual sensors are typically trained and validated under controlled laboratory conditions, maintaining their performance for both state estimation and parameter estimation under real-world distribution shifts remains an open problem. This work addresses this challenge by providing two complementary mitigation strategies: an adaptation approach based on importance sampling and a robust design method using uniform training. We demonstrate our approach in an industrial freezer monitoring system, where the goal is to estimate the insulation quality despite the varying operating conditions between laboratory testing and field deployment. The results provide theoretically grounded, yet practical tools for deploying reliable virtual sensing solutions.