Tag Archives: image decomposition

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.

Source:

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.

Million to one

‘All models are wrong, but some are useful’ is a quote, usually attributed to George Box, that is often cited in the context of computer models and simulations.  Working out which models are useful can be difficult and it is essential to get it right when a model is to be used to design an aircraft, support the safety case for a nuclear power station or inform regulatory risk assessment on a new chemical.  One way to identify a useful model to assess its predictions against measurements made in the real-world [see ‘Model validation’ on September 18th, 2012].  Many people have worked on validation metrics that allow predicted and measured signals to be compared; and, some result in a statement of the probability that the predicted and measured signal belong to the same population.  This works well if the predictions and measurements are, for example, the temperature measured at a single weather station over a period of time; however, these validation metrics cannot handle fields of data, for instance the map of temperature, measured with an infrared camera, in a power station during start-up.  We have been working on resolving this issue and we have recently published a paper on ‘A probabilistic metric for the validation of computational models’.  We reduce the dimensionality of a field of data, represented by values in a matrix, to a vector using orthogonal decomposition [see ‘Recognizing strain’ on October 28th, 2015].  The data field could be a map of temperature, the strain field in an aircraft wing or the topology of a landscape – it does not matter.  The decomposition is performed separately and identically on the predicted and measured data fields to create to two vectors – one each for the predictions and measurements.  We look at the differences in these two vectors and compare them against the uncertainty in the measurements to arrive at a probability that the predictions belong to the same population as the measurements.  There are subtleties in the process that I have omitted but essentially, we can take two data fields composed of millions of values and arrive at a single number to describe the usefulness of the model’s predictions.

Our paper was published by the Royal Society with a press release but in the same week as the proposed Brexit agreement and so I would like to think that it was ignored due to the overwhelming interest in the political storm around Brexit rather than its esoteric nature.

Source:

Dvurecenska K, Graham S, Patelli E & Patterson EA, A probabilistic metric for the validation of computational models, Royal Society Open Science, 5:1180687, 2018.

Credibility is in the eye of the beholder

Picture1Last month I described how computational models were used as more than fables in many areas of applied science, including engineering and precision medicine [‘Models as fables’ on March 16th, 2016].  When people need to make decisions with socioeconomic and, or personal costs, based on the predictions from these models, then the models need to be credible.  Credibility is like beauty, it is in the eye of the beholder.   It is a challenging problem to convince decision-makers, who are often not expert in the technology or modelling techniques, that the predictions are reliable and accurate.  After all, a model that is reliable and accurate but in which decision-makers have no confidence is almost useless.  In my research we are interested in the credibility of computational mechanics models that are used to optimise the design of load-bearing structures, whether it is the frame of a building, the wing of an aircraft or a hip prosthesis.  We have techniques that allow us to characterise maps of strain using feature vectors [see my post entitled ‘Recognising strain‘ on October 28th, 2015] and then to compare the ‘distances’ between the vectors representing the predictions and measurements.  If the predicted map of strain  is an perfect representation of the map measured in a physical prototype, then this ‘distance’ will be zero.  Of course, this never happens because there is noise in the measured data and our models are never perfect because they contain simplifying assumptions that make the modelling viable.  The difficult question is how much difference is acceptable between the predictions and measurements .  The public expect certainty with respect to the performance of an engineering structure whereas engineers know that there is always some uncertainty – we can reduce it but that costs money.  Money for more sophisticated models, for more computational resources to execute the models, and for more and better quality measurements.