Inference on errors in industrial parts: Kriging and variogram versus geometrical product specifications standard

Abstract

This article focuses on the inference on the errors in manufactured parts controlled by using measurements devices. The characterization of the part surface topographies is core in several applications. A broad set of properties (tribological, optical, biological, mechanical, etc.) depends on the micro-and macrogeometry of the parts. Moreover, parts usually show typical deterministic geometric deviation pattern, referred to as manufacturing signatures, due to the specific manufacturing processes and process setup parameters adopted for their production. In several situations, the measurements may also be affected by systematic errors due to the measurement process, that might be caused, for example, by a poor part alignment during the measurement process. Measurement techniques and characterization methods have been standardized in the International Standard ISO 25178, defining parameters characterizing the surface topography and supplying methods and formula adapt to deal with this issue computationally. In the present article, we consider a type of spatial dependence between measured values at different points that suggest the use of the variogram to identify patterns in the parts. We offer a comparison, based on a real set of measures, between the latter approach and the conventional as a test of the efficient performance of our findings.

Gaussian process regression‐based detection and correction of disturbances in surface topography measurements

“…The ratio between sampled and measured points was set to 0.4% from prior experiences. 79,82 Conventional disturbances management methods and surface topography parameter evaluations have been performed by means of state-of-the-art commercial software, MountainsMap v8.0. 39 The software allows computing standard topographical parameters defined in Section 2.2 and the application of disturbances management technique that are reported in literature, as discussed in Section 1.…”

“…Provided a preliminary plane correction is performed, ordinary kriging can be adopted to predict the whole surface, so that no particular assumptions in the regressive part of the prediction are bounded to describe the shape of the topography. 79,82 As far as the identification of measurement disturbances is concerned, non-measured points are inherently identified. On the other hand, spikes require an identification criterion.…”

“…Conversely, provided that spikes are typically a small fraction of the measured data, subsampling prevents them from negatively affecting the fitting procedure without information loss. 79 The kernel selection can be performed comparing different typical functions, for example, Matèrn, squared exponential, Gaussian, 80,81 with the optimisation criterion aimed at minimising the root mean square error of the residuals. 74 The choice can be validated by exploiting the empirical variogram.…”

“…The choice can be validated by exploiting the empirical variogram. Provided a preliminary plane correction is performed, ordinary kriging can be adopted to predict the whole surface, so that no particular assumptions in the regressive part of the prediction are bounded to describe the shape of the topography 79,82 …”

“…In fact, exploiting the whole original dataset, which presents measurement disturbances, can distort the resulting model to fit the GPR. Conversely, provided that spikes are typically a small fraction of the measured data, subsampling prevents them from negatively affecting the fitting procedure without information loss 79 …”