**1. Introduction**

Metrology is considered a fundamental tool in the context of Industry 4.0, where reliable data are needed to realise data-driven manufacturing strategies [1–3]. As far as metrology is moving from the lab to the shop floor where the manufacturing of goods takes place, it is breaking the stigma of non-productive activity and gaining a position as an enabling technology that adds value to every step of the production process [4]. This perception is becoming more evident in Industry 4.0, where measurement data from several sensors are required, including dimensional data, for the monitoring of complete manufacturing processes and real-time adjustment of process parameters, including the creation and use of metrological digital twins [2,5–9].

Massive integration of 3D optical sensors within manufacturing processes is occurring nowadays, replacing traditional Coordinate Measurement Machines (CMM) within the automotive, aerospace and power generation industries, among the leading industries in the adoption of MBD [10]. However, while the delivery of millions of points in a matter of seconds is assumed by 3D optical sensors, the process of automatically converting dense data into meaningful information and assuring the quality of these data remains a challenge [11].

This research article presents a practical approach to addressing both challenges. While the process of converting dense data into meaningful information is solved through

**Citation:** Kortaberria, G.; Mutilba, U.; Gomez, S.; Ahmed, B. Three-Dimensional Point Cloud Task-Specific Uncertainty Assessment Based on ISO 15530-3 and ISO 15530-4 Technical Specifications and Model-Based Definition Strategy. *Metrology* **2022**, *2*, 394–413. https:// doi.org/10.3390/metrology2040024

Academic Editor: Simona Salicone

Received: 22 July 2022 Accepted: 22 September 2022 Published: 27 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

a Quality Information Framework (QIF)–Model-based Definition (MBD) based measurement post-processing strategy, the assurance of the quality of the data that relies on the establishment of metrological traceability is assessed by the combination of the ISO 15530-3 and ISO 15530-4 technical specifications through which the establishment of metrological traceability, which requires (a) evaluation of the measurement uncertainty and (b) the realisation of an unbroken chain of calibrations to relate a measurement result to a reference value [12], is realised. Thus, the article introduces a task-specific uncertainty assessment of a dense point cloud type of data acquisition in the absence of reliable numerical simulation models for optical systems.

Considering the evaluation of the measurement uncertainty, the *Guide to the Expression of Uncertainty in Measurement* (GUM) JCGM 100:2008 [13] establishes general rules for evaluating and expressing uncertainty in measurements that are intended to be applied to a broad spectrum of measurements. The GUM-proposed general measurement procedure seems to be clear and easy to adopt but it can be extremely difficult to implement when a complex measurement system is evaluated. As stated by Dury et al., in the broad study about 3D optical systems characterisation performed in the National Physical Laboratory (NPL) "National FreeFrom centre" [11,14–16], there are many potential uncertainty error sources such as the light condition, measurand surface properties, system orientation and resolution, ambient temperature, measurement volume, chromatic effects, etc. that complicate to a high extent the reliable characterisation of those systems.

Compared with traditional CMMs, 3D optical systems are a relatively new technology, and their measurement error sources are still being researched. Even though the German guideline for optical 3D measuring systems, the VDI/VDE 2634 series (parts 2 and 3) [17,18], attempts to provide a procedure for comparing the performance of different systems for the acceptance and re-verification of these systems, it does not consider all the potential uncertainty sources while operating in unfavourable environments. Therefore, the lack of measurement procedures to fully understand how 3D optical systems behave under different measurement scenarios limits to a high extent the development of mathematical modelling for those systems [11], and therefore, the development of a digital metrology twin.

The challenge of converting dense data into meaningful information in a matter of seconds involves providing real-time automatic decision-making capability and therefore constantly adjusting process parameters for a zero-defect manufacturing scenario. However, when a 3D optical system is integrated into a manufacturing process and captures millions of points in seconds, "faster data processing" remains a challenge. Thus, the recent publication of the ISO Standard 23952:2020 "Automation systems and integration—Quality Information Framework (QIF)—An integrated model for manufacturing quality information" [19] opens the door to real-time automatic in-line quality control. This Standard suggests a new XML Schema Definition Language that defines, organises and associates the quality and metrology information needed in manufacturing systems and therefore, it allows the effective exchange of metrology data throughout the entire manufacturing quality measurement process—from product design to inspection planning to execution to analysis and reporting. For product definition, QIF includes the ISO QIF part 3: QIF Model-based Definition (MBD) [20–22], which defines a digital data format to convey part geometry (typically called the "CAD" model) and information to be consumed by downstream manufacturing quality processes, such as Product Manufacturing Information (PMI) [21–23]. This means that MBD allows the attachment of Geometric Dimensioning and Tolerancing (GD&T) information to a CAD model, typically with full "smart" associativity, to create a semantic model. This semantic CAD model allows metrology software to automatically create either an inspection plan or decision-making results (angles, distances, GD&T tolerances, etc.) from available 3D point data. Thus, the QIF MBD information model allows converting the captured dense data into meaningful information using automatic data processing methodologies [1,8,21,24,25]. Therefore, in general terms, MBD is a digital-product model that defines the requirements and specifications of the product

and is the cornerstone for Model-Based Enterprise (MBE) since MBE uses MBD to define the product requirements and specifications instead of paper-based documents as the data source for all engineering activities, including the metrology activities during the manufacturing of the product, throughout the product lifecycle [20–23,26–28].

The state-of-the-art of uncertainty assessment to point cloud measurement shows that task-specific uncertainty assessment has not been frequently applied to dense point cloud measurements. Different approaches were suggested for the uncertainty assessment of point clouds, such as the approach introduced by Ding et al., based on spatial feature registration analysis [29]. Senin et al. suggested a method based on fitting Gaussian random fields to high-density point clouds produced by measurement repeats where the fitted field delivers a depiction of the spatial distribution of random measurement error over a part geometry [30]. Yang et al. investigated the point cloud registration step as a major uncertainty source in the laser scanning-aided aircraft assembly process [31]. Zhang et al. also appointed the reconstruction of every point cloud acquisition process as a critical uncertainty source [32]. Forbes et al. presented an uncertainty assessment method associated with the position, size and shape of point cloud data [33]. Another important approach for the uncertainty assessment of point clouds is the mathematical modelling of the measurement instruments, mainly optical systems, employed in the data acquisition process. Mohammadikaji et al. suggested an approach to categorise and model the dominant sources of uncertainty and study the probabilistic propagation of the uncertainties in a 3D inspection using laser line scanners [34]. Zhao et al. suggested the use of a structured light system including the instrument itself, data acquisition, data processing, and other factors as a black model for the uncertainty assessment of 3D point clouds [35]. Some researchers also presented experimental methods to model the systematic errors pertinent to laser scanners [36,37]. Xi et al. suggested various scanner-to-surface distances and inclination angles raise systematic uncertainties for optical sensors [38,39]. Finally, the use of physical artifacts combined with a Design of Experiment (DOE) method was also suggested for the uncertainty assessment of optical systems [40–45].

#### **2. Methods**

## *2.1. Practical Approaches to the Uncertainty Assessment within Production Metrology*

In cases where potential uncertainty sources for a measurement process can be ascertained, it is relatively easy to follow the prescription of the GUM JCGM 100:2008 [13] uncertainty framework. However, this is not the case for CMMs or 3D optical systems, in which it is extremely difficult to understand how every potential uncertainty source affects the final result. In these cases, different approaches were applied to estimate the uncertainty of the coordinate measurement. In the case of CMMs, the prevailing guidance for users is given in the ISO 15530 technical specifications. While part 1 is very informative and tutorial but not intended to provide operative evaluation tools, parts 3 and 4 are the procedures followed by the manufacturing industry for the uncertainty assessment of coordinate measurement [46,47]. While Section 3 defines an experimental comparison method using a calibrated workpiece, Section 4 suggests a computer simulation approach to provide task-specific uncertainty assessment. The project "Evaluating the Uncertainty in Coordinate Measurement" (EUCOM–under grant agreement nº 17NRM03) project within the European Metrology Programme for Innovation and Research (EMPIR) program has performed the research to develop the two missing parts of the ISO 15530 series: part 2 on a repetition and reversal method and part 5 on a method based on prior information and expert judgement.

In the case of 3D optical systems, system manufacturers employ VDI 2634 parts 2 and 3 [17,18] to characterise and run the product acceptance test before product delivery, but this does not mean that complete system characterisation is performed for a robust measurement uncertainty assessment.
