Spatial Interpolation for Periodic Surfaces in Manufacturing Using a Bessel Additive Variogram Model

Abstract

High-resolution spatial data are essential for characterizing and monitoring surface quality in manufacturing. However, the measurement of high-resolution spatial data is generally expensive and time-consuming. Interpolation based on spatial models is a typical approach to cost-effectively acquire high-resolution data. Conventional modeling methods fail to adequately model the spatial correlation induced by periodicity, and thus their interpolation precision is limited. In this paper, we propose using a Bessel additive periodic variogram model to capture such spatial correlation. When combined with kriging, a geostatistical interpolation method, accurate interpolation performance can be achieved for common periodic surfaces. In addition, parameters of the proposed model provide valuable insights for the characterization and monitoring of spatial processes in manufacturing. Both simulated and real-world case studies are presented to demonstrate the effectiveness of the proposed method.

Data-Driven Intelligent 3D Surface Measurement in Smart Manufacturing: Review and Outlook

“…As shown in Figure 2, CLM has the highest resolution among the optical measurement systems, making it a good choice for accuracy-sensitive applications with a relatively small measurement area. It has been widely used for nano-and micro-scale surface characterization studies, e.g., evaluating the effects of machining and polishing techniques on surface topography [41][42][43], analyzing the geometric characteristics of products in additive manufacturing [5], assessing fatigue damage in mechanical structures [44], and monitoring the tool-wear progression in ultrasonic metal welding [9][10][11][12].…”

“…Refer to [66] for a detailed discussion on this topic. Yang et al [11] provided an example for selecting a proper variogram to suit a specific engineering surface interpolation task.…”

“…Spatial and spatiotemporal processes are ubiquitous across all scales in manufacturing. They can manifest themselves in critical product quality characteristics (e.g., surface quality in machining [1][2][3][4], geometric compliance [5,6] and surface finish/texture [7] in additive manufacturing) or degradation of consumable tools (e.g., cutting and lapping tools in machining [8], horn and anvil in ultrasonic welding [9][10][11][12]). Figure 1 shows three examples of spatial and spatiotemporal processes in manufacturing at different scales and highlights the necessity of high-resolution surface measurement.…”

“…The topology of a degraded anvil surface, which was measured using a confocal laser microscopy (CLM), is shown by Figure 1b. Such measurements enabled the first studies on tool-wear characterization and monitoring in ultrasonic metal welding [10,15] and inspired a series of studies on data-driven surface modeling [11,16] and sampling design for spatiotemporal processes, e.g., [9,12]. Prior to these studies, industry practitioners had been using a conservative tool maintenance strategy based on the number of welding cycles, which led to a waste of tool life and/or deteriorated weld quality [15].…”

Enhancing Sustainability and Energy Efficiency in Smart Factories: A Review

“…Lee et al [81,82] used self-organized maps and fuzzy networks to improve the performance of the quality examination. New machine learning and statistical techniques were proposed to achieve a balance between measurement cost and precision or enhance interpolation accuracy for high-resolution 3D measurement tasks [76,[83][84][85]. Applications include high-precision machining and ultrasonic metal welding.…”