Hierarchical measurement strategy for cost-effective interpolation of spatiotemporal data in manufacturing

High-resolution spatiotemporal data is crucial for characterizing, modeling, and monitoring the space–time dynamics of complex systems in manufacturing. However, the acquisition of such data is generally expensive and time-consuming. Spatiotemporal interpolation aims to predict the values at unmeasured locations using measured data, and emerges as a promising solution to cost-effectively characterizing spatiotemporal processes. Since the interpolation performance is largely influenced by the available measurement data, an intelligent measurement strategy is an important prerequisite to the success of interpolation methods. In this paper, a hierarchical measurement strategy is developed to achieve a balance between interpolation precision and measurement cost in spatiotemporal interpolation. A hierarchical decision-making problem is formulated to determine the observation times and measurement locations at each observation. To expedite the solution search process, hierarchical genetic algorithm is adopted and implemented using high-performance computing. Moreover, a new form of the covariance function is developed using a Bessel additive periodic variogram to more accurately model the periodic spatial variations in spatiotemporal processes. Case studies using real-world data collected from ultrasonic metal welding are reported to demonstrate the effectiveness of the proposed method.