Statistical processing and analysis of surface topography data for a machine-based evaluation of the measurement uncertainty

Surface measurements in industrial activities are required principally to check tolerances or to characterise the surface functionality of components. There are many engineering application in which surface metrology carry out an important role (e.g. electronics, information technology, energy, optics, etc.), but focusing only on autonomous manufacturing processes, in a perspective of what is called Industry 4.0, the areas of interest are the in-line quality check and the analysis of additive manufacturing processes with the aim of understanding and governing them. To achieve these, it is required that the measurement is acquired and processed quickly, hence, recently the optical instruments have been adopted more and more. Measurement to be reliable has to be coupled with its uncertainty; however rarely areal surface measurements presents this value. Indeed, a standard infrastructure for the traceability of areal surface measurement is still missing. This is probably due to both the complexity of the measurand and the optical instruments, whose interaction with the component is still not completely known. Hence, this project aims to cope with the complexity of such measurands by exploring applicability and limitations of methods for an autonomous, machine-based, statistical evaluation of the measurement uncertainty. First of all, the surfaces are processed in order to remove the form and manage possible non-measured points and/or spikes. The non-measured points are replaced with the values of the fitting surface, extracted during the form removal stage, of the input data. The spikes, instead, are managed with a threshold method that limits the peaks and the valleys at three times the S_q value (Root Mean Square Height of the scale-limited surface). Spikes are not intentionally managed with statistical methods because they are principally due to the instrument systematic behaviour for the most. By contrast, outliers are due to the operator for the most and are rare, and not systematic. Carried out these preliminary operations, the measurements are subjected to the statistical analysis, which considers the repeated measurements of each pixel. Both the Chauvenet's criterion and the modified interquartile range method have been implemented to detect and manage the outliers. However, after an analysis of the result, we decided to proceed without managing them. In fact, without filtering the measurements, outliers are mixed with measurement noise, therefore, the classical methods cannot model this condition. Finally, a possible systematic effect in the measurements of the workpiece is detected through the linear regression taking into account the correlation domain of each pixel. Once correcting this effect, the uncertainty related to the measurements of the workpiece is estimated. As far as the uncertainty is concerned, to achieve the complete uncertainty estimate, the measurements of the calibrated artefacts are required in order to take into account the effect of the instrument. However, because of the pandemic of COVID-19, we could not carry out these measurements but the model equation, inspired to both the ISO 14253-2 and the ISO 15530-3, is provided. This equation, applying the low of uncertainty propagation, allows the estimate of the expanded measurement uncertainty. This MSc project has been conducted in collaboration with the Department of Mechanical Engineering at the Technical University of Denmark.