Inside-out: Statistical methods for Computed Tomography validation of complex structures in Additive Layer Manufacturing

Lead Research Organisation: University of Warwick
Department Name: Statistics


Additive layer Manufacturing (ALM) is a "3D printing" technique which develops products directly from their digital design data by the layer-wise addition of material. It is widely regarded as having great promise, especially for its capabilities to respond cost-effectively to changing customer demand and its ability to create objects with complex internal structure. At present a major difficulty holding back ALM is the problem of determining the extent to which the digital design has been correctly realized by the process: direct verification typically involves lengthy analysis of individual manufactured objects using Computed Tomography (CT) scans, tending to vitiate the advantages of ALM for general purposes. The purpose of this project is to explore methods by which this quality assurance process may be carried out more rapidly. The investigation will be carried out by a close collaboration between engineers and statisticians at Warwick using statistical techniques including random fields, false discovery rate methods, and ideas from stochastic geometry.

Planned Impact

Who Will Benefit from the Research
With its focus on enabling the rapid and accurate quality assessment of complex Additive Layer Manufactured (ALM) components, and increasing their acceptance in the High Value Manufacturing (HMV) sectors, the beneficiaries will be the UK HMV industry, providers of ALM and Computed Tomography (CT) technologies, the UK government and society (e.g. consumers of energy, users of air transport, healthcare users) and the environment.

How Will They Benefit from the Research
Economic Impact: The UK has a healthy High Value Manufacturing sector, and a particularly strong aerospace manufacturing presence. UK aero engine manufacturing is 2nd in the World, with key players, including BAE Systems, Bombardier, EADS, and Rolls-Royce, worth £23.5bn in 2011-12, and predicted to reach £26.2bn in 2016-17. The UK's biomedical sector, and especially the orthopaedic and implantables market is worth over £400m (UK) and over £10bn globally, and is expanding at a Compound Annual Growth Rate (CAGR) of over 7%, with key players such as S&N, Zimmer, Stryker, Biomet. Both sectors will benefit from the ability to cost-effectively deliver new products with enhanced customer benefit (advanced fuel injectors and combustion systems with improved fuel performance, customised biomedical implants for improved fit and longevity). Increased uptake in these and other sectors will benefit ALM and CT Original Equipment Manufacturers (OEMs) through increased revenues. It has been estimated that, by overcoming the current limitations of ALM and gaining market acceptance, penetration could be expected to expand from 8% to 92% by 2020, a market worth £66bn globally [1].

Social and Environmental Impact: This research will enhance the capability of ALM technologies, which are inherently resource efficient, encouraging their use in HVM and thus displacing more traditional resource intensive and inefficient manufacturing processes. This is thus in alignment with the global strategies (e.g. Kyoto Treaty) to reduce environmentally damaging emissions through our increasing use of resources. The research supports the development of leaner, fuel efficient turbofan aero engines and gas turbines for energy generation. This will contribute toward the reduction of the negative environmental impact of air travel and energy generation, and will facilitate the continued globalisation of society, and the economic and social benefits that that brings, without detriment to the environment. The UK government will benefit in being aided in attaining its targets on climate change, and through economic savings in hospital care achieved through better provision of orthopaedic treatment (better outcome, faster recovery times, less trauma, fewer revisions and complications) made possible by customised orthopaedic implants. When full market penetration is reached, the savings to the healthcare sector within Europe are estimated to exceed £2.5bn annually. Social benefits will be in a greener environment, sustainable globalisation, and a higher quality of life and health.

1. Wohler, T. Wohlers Report 2012 - Additive Manufacturing and 3D Printing State of the Industry. 2012


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Barnes Clair (2017) Perches, Post-holes and Grids in arXiv e-prints

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Brettschneider J (2020) DetectorChecker: analyzing patterns of defects in detector screens in Journal of Open Source Software

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Dodwell T (2021) A data-centric approach to generative modelling for 3D-printed steel in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Kueh A (2016) Modelling the penumbra in Computed Tomography1. in Journal of X-ray science and technology

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Warnett J (2016) Towards in-process x-ray CT for dimensional metrology in Measurement Science and Technology

Description 1: We have investigated issues of image quality for CT scanners, and published an analysis (Kueh et al, 2016) demonstrating that "penumbra" effects (consequences of the x-ray source not being a point source) are larger than would be expected; we provide evidence that this arises from scattering and can be mitigated by careful filter design.
2: The model for the variance - mean relationship was confirmed in broad detail. However there are several significant features of interest which are now being investigated by an EPSRC-funded research student.
3: We have developed a procedure for rapid assessment and location of collections of small defects in 3D-printed objects. A paper describing this methodology is now in preparation.
4: We have developed an analysis of spatial statistics for dead pixels in detector screens. A paper describing this methodology is nearing completion (preliminary working papers: Brettschneider et al, 2014, 2017), and we have now produced a (Turing Institute funded) web-based data-collection app to draw together information from other users of detector screens.
5: Warnett et al (2016) reports on ongoing investigation of industrial uses for real-time tomography devices developed in the context of airport baggage searches.
6: Using nonlinear geometric mean values, Kendall (2015) has developed non-parametric methods for studying hurricane trajectories.
Exploitation Route As noted in item 2 above, we have developed a web-based data-collection system to facilitate cooperation by users to gain better understanding of how pixels in detector screens degrade, based on the paper in preparation which will set out the initial analysis on which this exercise would be based. We have spoken about this at a forthcoming two-day meeting in Manchester (June 2019) on "Measuring errors in X-ray CT for industrial applications", and also at the XCT Fringe Meeting (10 June 2019) prior to the Advances in Xray Imaging workshop (11 June 2019) at Harwell Science and Innovation Campus, and are developing contacts with participants at these meetings.
Sectors Manufacturing, including Industrial Biotechology

Description Our group met for steering committee meetings at six-monthly intervals with representatives from Nikon UK, EOS, and Renishaw. We discussed our early research results with them in detail at these meetings. The work reported on in Kueh et al (2014) attracted specific attention from Nikon, who inform us that it bears on significant design issues for their CT scanners. Our work on Dead Pixels is now freely available via the (Turing Institute funded) web app at ; we are preparing a short associated paper to be used to enable users to participate in further research via this web app.
First Year Of Impact 2019
Sector Manufacturing, including Industrial Biotechology
Impact Types Economic

Description Turing Fellowship
Amount £1 (GBP)
Funding ID TU/B/000100 
Organisation Alan Turing Institute 
Sector Academic/University
Country United Kingdom
Start 09/2017 
End 09/2019
Title Dataset to support article : 'Modelling the Penumbra in Computed Tomography' 
Description These data files correspond to the data discussed in Kueh et al (2016). A 3mm ceramic rod was placed centrally on the manipulator in an approximately vertical alignment such that the magnification was x4.45. Images were taken at a constant voltage of 140kV, at each of the following 7 different exposure/power settings: 0.177s/44W, 0.25s/30.6W, 0.354s/21W, 0.5s/14.6W, 0.708s/9.6W, 1s/6.4W, 1.415s/4W. Three images were taken for each parameter set, and these are placed within their respective folder (labelled by magnification) as TIFF files. Code which imports these files into the R environment is provided in Import.R. 
Type Of Material Database/Collection of data 
Year Produced 2016 
Provided To Others? Yes  
Impact Nikon UK report that the work represented by this dataset and accompanying article is being influential in design considerations for their X-ray scanners. 
Title Dataset to support article : 'Perches, Post-holes and Grids' 
Description This dataset corresponds to the data discussed in Barnes & Kendall (2017). The "Planning in the Early Medieval Landscape" project (PEML) project , funded by the Leverhulme Trust, has organized and collated a substantial quantity of images, and has used this as evidence to support the hypothesis that Anglo-Saxon building construction was based on grid-like planning structures based on fixed modules or quanta of measurement. This dataset was created and analyzed to provide some statistical contributions to the debate concerning this hypothesis. In practice the PEML images correspond to data arising in a wide variety of different forms (post-holes, actual walls, indications of linear structure arising from hedge and road lines, etc). Ideally one would wish accurately to reduce each image to a measurement-based dataset that could be analysed statistically to bear on the historical debate. In practice it does not seem feasible to produce a single automatic method which can be applied uniformly to all such images; even the initial chore of cleaning up an image (removing extraneous material such as legends and physical features which do not bear on the planning hypothesis) typically presents a separate and demanding challenge for each different image. Moreover care must be taken, even in the relatively straightforward cases of clearly defined ground-plans (for example for large ecclesiastical buildings of the period), to consider exactly what measurements might be relevant. This dataset supplies data corresponding to pilot statistical analyses concerning three different situations. These establish not only the presence of underlying structure (which indeed is often visually obvious), but also provide an account of the numerical evidence supporting the deduction that such structure is present. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
Impact The accompanying article will appear in a book describing the outputs of the "Planning in the Early Medieval Landscape" project 
Description Talk to Sixth-Formers, London 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact I was invited to present a talk on my research, accessible to students of GCSE Maths level and higher, by the Training Partnership. I was told around 850 students attended. I spoke on Probability and Geometry and discussed issues arising during the progress of grant EP/K031066. I answered questions after the talk during a lively discussion with all the students moderated by the chair.
Year(s) Of Engagement Activity 2015