High-fidelity characterization and effective monitoring of spatial and spatiotemporal processes are crucial for high-performance quality control of many manufacturing processes and systems in the era of smart manufacturing. Although the recent development in measurement technologies has made it possible to acquire high-resolution three-dimensional (3D) surface measurement data, it is generally expensive and time-consuming to use such technologies in real-world production settings. Data-driven approaches that stem from statistics and machine learning can potentially enable intelligent, cost-effective surface measurement and thus allow manufacturers to use high-resolution surface data for better decision-making without introducing substantial production cost induced by data acquisition. Among these methods, spatial and spatiotemporal interpolation techniques can draw inferences about unmeasured locations on a surface using the measurement of other locations, thus decreasing the measurement cost and time. However, interpolation methods are very sensitive to the availability of measurement data, and their performances largely depend on the measurement scheme or the sampling design, i.e., how to allocate measurement efforts. As such, sampling design is considered to be another important field that enables intelligent surface measurement. This paper reviews and summarizes the state-of-the-art research in interpolation and sampling design for surface measurement in varied manufacturing applications. Research gaps and future research directions are also identified and can serve as a fundamental guideline to industrial practitioners and researchers for future studies in these areas.

Online tool condition monitoring (TCM) is a pivotal capability in many manufacturing applications including ultrasonic metal welding (UMW). Effective and efficient TCM can facilitate predictive maintenance, improve product quality, and enhance productivity. Existing online TCM systems based on conventional machine learning models often require a large amount of labeled data, the collection of which is cost-prohibitive, time-consuming, and labor-intensive. Such models fail to satisfy the requirements of cost-effectiveness and agility posed by modern, reconfigurable UMW systems. As such, data-efficient TCM methods with excellent generalization ability are of vital importance. To this end, we develop a novel similarity-based meta-representation learning (SMRL) method for domain generalization. SMRL effectively learns high-level meta-knowledge that is shared among different welding scenarios or domains. Therefore, the model trained in source domains can be generalized to other domains without access to labeled data in the training phase. Case studies are performed using four welding scenarios with varied welding materials and welding parameters. It is demonstrated that the proposed method is superior to the baseline methods, including neural network, hierarchical neural network, model-agnostic meta-learning (MAML), and hierarchical MAML. Compared with the baseline methods, SMRL offers an average improvement of 15.44%–31.62% in TCM accuracy. These results show that SMRL is readily applicable to industrial applications to enable cost-effective and data-efficient TCM.

Limited resources motivate decomposing large-scale problems into smaller, “local” subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of “local hardness,” i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin glasses and related frustrated spin systems. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem. These errors are intimately connected to global critical threshold instabilities, characterized by gapless, avalanchelike excitations that follow scale-invariant size distributions. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the computationally much more expensive global minimization. We leverage these findings to introduce a heuristic contraction-based algorithm for globally studying spin-glass ground states. The local solvers further display sharp imprints of the phase transition from the spin-glass to the ferromagnetic phase as the distribution of spin-glass couplings is shifted, as well as characteristic differences for the infinite-range model, implying the existence of specific classes of local hardness. Our findings shed light on how nature may operate solely through local actions at her disposal.