This paper reconstructs the stability, interpretability, and generalizability of machine learning from a measurement science perspective, focusing on sensor data in Smart Manufacturing and System Health Management (SM&SHM). Based on the well-posedness of differential equations, it contrasts coarse-graining and observation expansion to explain the balance among error, regularization, and resolution. An active observation design using multi-armed bandits unifies data acquisition and learning. Through Spikelet decomposition, the study demonstrates the effectiveness of coarse-graining for time-series analysis and presents a theoretical basis for well-posed learning that integrates domain knowledge.