Tag Archives: image decomposition

From strain measurements to assessing El Niño events

Figure 11 from RSOS 201086One of the exciting aspects of leading a university research group is that you can never be quite sure where the research is going next.  We published a nice example of this unpredictability last week in Royal Society Open Science in a paper called ‘Transformation of measurement uncertainties into low-dimensional feature space‘ [1].  While the title is an accurate description of the contents, it does not give much away and certainly does not reveal that we proposed a new method for assessing the occurrence of El Niño events.  For some time we have been working with massive datasets of measurements from arrays of sensors and representing them by fitting polynomials in a process known as image decomposition [see ‘Recognising strain‘ on October 28th, 2015]. The relatively small number of coefficients from these polynomials can be collated into a feature vector which facilitates comparison with other datasets [see for example, ‘Out of the valley of death into a hype cycle‘ on February 24th, 2021].  Our recent paper provides a solution to the issue of representing the measurement uncertainty in the same space as the feature vector which is roughly what we set out to do.  We demonstrated our new method for representing the measurement uncertainty by calibrating and validating a computational model of a simple beam in bending using data from an earlier study in a EU-funded project called VANESSA [2] — so no surprises there.  However, then my co-author and PhD student, Antonis Alexiadis went looking for other interesting datasets with which to demonstrate the new method.  He found a set of spatially-varying uncertainties associated with a metamodel of soil moisture in a river basin in China [3] and global oceanographic temperature fields collected monthly over 11 years from 2002 to 2012 [4].  We used the latter set of data to develop a new technique for assessing the occurrence of El-Niño events in the Pacific Ocean.  Our technique is based on global ocean dynamics rather than on the small region in the Pacific Ocean which is usually used and has the added advantages of providing a confidence level on the assessment as well as enabling straightforward comparisons of predictions and measurements.  The comparison of predictions and measurements is a recurring theme in our current research but I did not expect it to lead into ocean dynamics.

Image is Figure 11 from [1] showing convex hulls fitted to the cloud of points representing the uncertainty intervals for the ocean temperature measurements for each month in 2002 using only the three most significant principal components . The lack of overlap between hulls can be interpreted as implying a significant difference in the temperature between months.


[1] Alexiadis, A. and Ferson, S. and  Patterson, E.A., , 2021. Transformation of measurement uncertainties into low-dimensional feature vector space. Royal Society Open Science, 8(3): 201086.

[2] Lampeas G, Pasialis V, Lin X, Patterson EA. 2015.  On the validation of solid mechanics models using optical measurements and data decomposition. Simulation Modelling Practice and Theory 52, 92-107.

[3] Kang J, Jin R, Li X, Zhang Y. 2017, Block Kriging with measurement errors: a case study of the spatial prediction of soil moisture in the middle reaches of Heihe River Basin. IEEE Geoscience and Remote Sensing Letters, 14, 87-91.

[4] Gaillard F, Reynaud T, Thierry V, Kolodziejczyk N, von Schuckmann K. 2016. In situ-based reanalysis of the global ocean temperature and salinity with ISAS: variability of the heat content and steric height. J. Climate. 29, 1305-1323.

Out of the valley of death into a hype cycle?

Fig 5 from Middleton et al with full captionThe capability to identify damage and track its propagation in structures is important in ensuring the safe operation of a wide variety of engineering infrastructure, including aircraft structures. A few years ago, I wrote about research my group was performing, in the INSTRUCTIVE project [see ‘INSTRUCTIVE final reckoning‘ on January 9th, 2019] with Airbus and Strain Solutions Limited, to deliver a new tool for monitoring the development of damage using thermoelastic stress analysis (TSA) [see ‘Counting photons to measure stress‘ on November 18th, 2015].  We collected images using a TSA system while a structural component was subject to cycles of load that caused damage to initiate and propagate during a fatigue test. The series of images were analysed using a technique based on optical flow to identify apparent movement between the images which was taken as indication of the development of damage [1]. We demonstrated that our technique could indicate the presence of a crack less than a millimetre in length and even identify cracks initiating under the heads of bolts using experiments performed in our laboratory [see ‘INSTRUCTIVE update‘ on October 4th, 2017].  However, this technique was susceptible to errors in the images when we tried to use low-cost sensors and to changes in the images caused by flight cycle loading with varying amplitude and frequency of loads.  Essentially, the optical flow approach could be fooled into identifying damage propagation when a sensor delivered a noisy image or the shape of the load cycle was changed.  We have now overcome this short-coming by replacing the optical flow approach with the orthogonal decomposition technique [see ‘Recognising strain‘ on October 28th, 2015] that we developed for comparing data fields from measurements and predictions in validation processes [see ‘Million to one‘ on November 21st, 2018] .  Each image is decomposed to a feature vector and differences between the feature vectors are indicative of damage development (see schematic in thumbnail from [2]).  The new technique, which we have named the differential feature vector method, is sufficiently robust that we have been able to use a sensor costing 1% of the price of a typical TSA system to identify and track cracks during cyclic loading.  The underpinning research was published in December 2020 by the Royal Society [2] and the technique is being implemented in full-scale ground-tests on aircraft structures as part of the DIMES project.  Once again, a piece of technology is emerging from the valley of death [see ‘Slowly crossing the valley of death‘ on January 27th, 2021] and, without wishing to initiate the hype cycle [see ‘Hype cycle‘ on September 23rd, 2015], I hope it will transform the use of thermal imaging for condition monitoring.

Logos of Clean Sky 2 and EUThe INSTRUCTIVE and DIMES projects have received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreements No. 685777 and No. 820951 respectively.

The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.


[1] Middleton CA, Gaio A, Greene RJ & Patterson EA, Towards automated tracking of initiation and propagation of cracks in Aluminium alloy coupons using thermoelastic stress analysis, J. Non-destructive Testing, 38:18, 2019.

[2] Middleton CA, Weihrauch M, Christian WJR, Greene RJ & Patterson EA, Detection and tracking of cracks based on thermoelastic stress analysis, R. Soc. Open Sci. 7:200823, 2020.

Alleviating industrial uncertainty

Want to know how to assess the quality of predictions of structural deformation from a computational model and how to diagnose the causes of differences between measurements and predictions?  The MOTIVATE project has the answers; that might seem like an over-assertive claim but read on and make your own judgment.  Eighteen months ago, I reported on a new method for quantifying the uncertainty present in measurements of deformation made in an industrial environment [see ‘Industrial uncertainty’ on December 12th, 2018] that we were trialling on a 1 m square panel of an aircraft fuselage.  Recently, we have used the measurement uncertainty we found to make judgments about the quality of predictions from computer models of the panel under compressive loading.  The top graphic shows the outside surface of the panel (left) with a speckle pattern to allow measurements of its deformation using digital image correlation (DIC) [see ‘256 shades of grey‘ on January 22, 2014 for a brief explanation of DIC]; and the inside surface (right) with stringers and ribs.  The bottom graphic shows our results for two load cases: a 50 kN compression (top row) and a 50 kN compression and 1 degree of torsion (bottom row).  The left column shows the out-of-plane deformation measured using a stereoscopic DIC system and the middle row shows the corresponding predictions from a computational model using finite element analysis [see ‘Did cubism inspire engineering analysis?’ on January 25th, 2017].  We have described these deformation fields in a reduced form using feature vectors by applying image decomposition [see ‘Recognizing strain’ on October 28th, 2015 for a brief explanation of image decomposition].  The elements of the feature vectors are known as shape descriptors and corresponding pairs of them, from the measurements and predictions, are plotted in the graphs on the right in the bottom graphic for each load case.  If the predictions were in perfect agreement with measurements then all of the points on these graphs would lie on the line equality [y=x] which is the solid line on each graph.  However, perfect agreement is unobtainable because there will always be uncertainty present; so, the question arises, how much deviation from the solid line is acceptable?  One answer is that the deviation should be less than the uncertainty present in the measurements that we evaluated with our new method and is shown by the dashed lines.  Hence, when all of the points fall inside the dashed lines then the predictions are at least as good as the measurements.  If some points lie outside of the dashed lines, then we can look at the form of the corresponding shape descriptors to start diagnosing why we have significant differences between our model and experiment.  The forms of these outlying shape descriptors are shown as insets on the plots.  However, busy, or non-technical decision-makers are often not interested in this level of detailed analysis and instead just want to know how good the predictions are.  To answer this question, we have implemented a validation metric (VM) that we developed [see ‘Million to one’ on November 21st, 2018] which allows us to state the probability that the predictions and measurements are from the same population given the known uncertainty in the measurements – these probabilities are shown in the black boxes superimposed on the graphs.

These novel methods create a toolbox for alleviating uncertainty about predictions of structural behaviour in industrial contexts.  Please get in touch if you want more information in order to test these tools yourself.

The MOTIVATE project has received funding from the Clean Sky 2 Joint Undertaking under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 754660 and the Swiss State Secretariat for Education, Research and Innovation under contract number 17.00064.

The opinions expressed in this blog post reflect only the author’s view and the Clean Sky 2 Joint Undertaking is not responsible for any use that may be made of the information it contains.

Spatio-temporal damage maps for composite materials

Earlier this year, my group published a new technique for illustrating the development of damage as a function of both space and time in materials during testing in a laboratory.  The information is presented in a damage-time map and shows where and when damage appears in the material.  The maps are based on the concept that damage represents a change in the structure of the material and, hence, produces changes in the load paths or stress distribution in the material.  We can use any of a number of optical techniques to measure strain, which is directly related to stress, across the surface of the material; and then look for changes in the strain distribution in real-time.  Wherever a permanent change is seen to occur there must also be permanent deformation or damage. We use image decomposition techniques that we developed some time ago [see ‘Recognizing strain‘ on October 28th, 2018], to identify the changes. Our damage-time maps remove the need for skilled operators to spend large amounts of time reviewing data and making subjective decisions.  They also allow a large amount of information to be presented in a single image which makes detailed comparisons with computer predictions easier and more readily quantifiable that, in turn, supports the validation of computational models [see ‘Model validation‘ on September 18th, 2012].

The structural integrity of composite materials is an on-going area of research because we only have a limited understanding of these materials.  It is easy to design structures using materials that have a uniform or homogeneous structure and mechanical properties which do not vary with orientation, i.e. isotropic properties.  For simple components, an engineer can predict the stresses and likely failure modes using the laws of physics, a pencil and paper plus perhaps a calculator.  However, when materials contain fibres embedded in a matrix, such as carbon-fibres in an epoxy resin, then the analysis of structural behaviour becomes much more difficult due to the interaction between the fibres and with the matrix.  Of course, these interactions are also what make these composite materials interesting because they allow less material to be used to achieve the same performance as homogeneous isotropic materials.  There are very many ways of arranging fibres in a matrix as well as many different types of fibres and matrix; and, engineers do not understand most of their interactions nor the mechanisms that lead to failure.

The image shows, on the left, the maximum principal strain in a composite specimen loaded longitudinally in tension to just before failure; and, on the right, the corresponding damage-time map indicating when and where damage developing during the tension loading.


Christian WJR, Dvurecenska K, Amjad K, Pierce J, Przybyla C & Patterson EA, Real-time quantification of damage in structural materials during mechanical testing, Royal Society Open Science, 7:191407, 2020.