Tag Archives: dynamics

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.

References:

[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.

Reduction in usefulness of reductionism

decorative paintingA couple of months ago I wrote about a set of credibility factors for computational models [see ‘Credible predictions for regulatory decision-making‘ on December 9th, 2020] that we designed to inform interactions between researchers, model builders and decision-makers that will establish trust in the predictions from computational models [1].  This is important because computational modelling is becoming ubiquitous in the development of everything from automobiles and power stations to drugs and vaccines which inevitably leads to its use in supporting regulatory applications.  However, there is another motivation underpinning our work which is that the systems being modelled are becoming increasingly complex with the likelihood that they will exhibit emergent behaviour [see ‘Emergent properties‘ on September 16th, 2015] and this makes it increasingly unlikely that a reductionist approach to establishing model credibility will be successful [2].  The reductionist approach to science, which was pioneered by Descartes and Newton, has served science well for hundreds of years and is based on the concept that everything about a complex system can be understood by reducing it to the smallest constituent part.  It is the method of analysis that underpins almost everything you learn as an undergraduate engineer or physicist. However, reductionism loses its power when a system is more than the sum of its parts, i.e., when it exhibits emergent behaviour.  Our approach to establishing model credibility is more holistic than traditional methods.  This seems appropriate when modelling complex systems for which a complete knowledge of the relationships and patterns of behaviour may not be attainable, e.g., when unexpected or unexplainable emergent behaviour occurs [3].  The hegemony of reductionism in science made us nervous about writing about its short-comings four years ago when we first published our ideas about model credibility [2].  So, I was pleased to see a paper published last year [4] that identified five fundamental properties of biology that weaken the power of reductionism, namely (1) biological variation is widespread and persistent, (2) biological systems are relentlessly nonlinear, (3) biological systems contain redundancy, (4) biology consists of multiple systems interacting across different time and spatial scales, and (5) biological properties are emergent.  Many engineered systems possess all five of these fundamental properties – you just to need to look at them from the appropriate perspective, for example, through a microscope to see the variation in microstructure of a mass-produced part.  Hence, in the future, there will need to be an increasing emphasis on holistic approaches and systems thinking in both the education and practices of engineers as well as biologists.

For more on emergence in computational modelling see Manuel Delanda Philosophy and Simulation: The Emergence of Synthetic Reason, Continuum, London, 2011. And, for more systems thinking see Fritjof Capra and Luigi Luisi, The Systems View of Life: A Unifying Vision, Cambridge University Press, 2014.

References:

[1] Patterson EA, Whelan MP & Worth A, The role of validation in establishing the scientific credibility of predictive toxicology approaches intended for regulatory application, Computational Toxicology, 17: 100144, 2021.

[2] Patterson EA &Whelan MP, A framework to establish credibility of computational models in biology. Progress in biophysics and molecular biology, 129: 13-19, 2017.

[3] Patterson EA & Whelan MP, On the validation of variable fidelity multi-physics simulations, J. Sound & Vibration, 448:247-258, 2019.

[4] Pruett WA, Clemmer JS & Hester RL, Physiological Modeling and Simulation—Validation, Credibility, and Application. Annual Review of Biomedical Engineering, 22:185-206, 2020.

Slow start to an exciting new project on thermoacoustic response of AM metals

We held the kick-off meeting for a new research project this week.  It’s a three-way collaboration involving three professors based in Portugal, the UK and USA [Chris Sutcliffe, John Lambros at UIUC and me]; so, our kick-off meeting should have involved at least two of us travelling to the laboratory of the third collaborator and spending some time brainstorming about the challenges that we have agreed to tackle over the next three years.  Instead we had a call via Skype and a rather procedural meeting in which we covered all of the issues without really engendering any excitement or sparking any new ideas.  It would appear that we need the stimulus of new environments to maximise our creativity and that we use body language as well as facial expressions to help us reach a friendly consensus on which  crazy ideas are worth pursuing and which should be quietly forgotten.

Our new research project has a long title: ‘Thermoacoustic response of Additively Manufactured metals: A multi-scale study from grain to component scales‘.  In simple terms, we are going to look at whether residual stresses could be designed to be beneficial to the performance of structural parts used in demanding environments such as those found in reusable spacecraft, hypersonic flight vehicles and breeder blankets in fusion reactors.  Residual stresses are often induced during the manufacture of parts and are usually detrimental to the performance of the part.  Our hypothesis is that in additive manufacturing, or 3D printing, we have sufficient control of the manufacture of the part that we can introduce ‘designer stresses’ which will improve the part’s performance in demanding environments.  The research is funded jointly by the National Science Foundation (NSF) in the USA and the Engineering and Physical Sciences Research Council (EPSRC) in the UK and is supported by The MTC and Renishaw plc; you can find out more at Grants on the Web. The research will be building on our recent research on ‘Potential dynamic buckling in hypersonic vehicle skin‘ [posted July 1st, 2020] and earlier work, see ‘Hot stuff‘ on September 13th, 2012.  While the demanding environment is not new to us, we will be using 3D printed parts for the first time instead of components made by conventional (subtractive) machining and taking them to higher temperatures.

The thumbnail shows measured modal shapes for a subtractively-manufactured plate subject to the three temperature regimes: room temperature (left), transverse heating of the centre of the plate (middle) and longitudinal heating on one edge (right) from Silva, A.S., Sebastian, C.M., Lambros, J. and Patterson, E.A., 2019. High temperature modal analysis of a non-uniformly heated rectangular plate: Experiments and simulations. J. Sound & Vibration, 443, pp.397-410.

 

Potential dynamic buckling in hypersonic vehicle skin

The skin of an aircraft is supported on the inside by a network, or mesh, of ribs and stringers running approximately at right angles to one another; so that the skin is effectively a series of rectangular plates supported around their edges.   In hypersonic flight, above five times the speed of sound, these rectangular plates are subject to vibration and to high temperatures that vary spatially and with time.  The combined vibratory and thermal loading causes the plates to buckle out of plane which has two possible detrimental consequences: first, it causes the formation of fatigue cracks leading to catastrophic failure; and, second, it might influence the formation of the boundary layer in the flow over the skin of the aircraft and affect the aerodynamics of the aircraft.  In my laboratory, we have built a test-rig that allows us to subject rectangular plates to random mechanical vibrations up to 1000Hz and, at the same time, to temperature distributions upto 1000K that vary in time and space.  Earlier this year, we published an article in which we showed, by experiment, that an edge-reinforced rectangular plate behaved as a dynamic system in response to thermal loading.  In other words, when a constant temperature distribution is applied, the shape of the plate varies with time until an equilibrium state is achieved.  In addition, we found that the post-buckled shape of the plate is not proportional to the energy supplied but dependent on the in-plane temperature distribution.  Probably, both of these observed behaviours are a result of differential thermal expansion of the plate and its reinforcements.

The image shows point-wise temperature and displacement measurements (centre) at the centre and edge of a reinforced plate (top) subject to a localised strip of heating over time as shown by the temperature distributions (bottom).

This is the fourth in a series of posts on recent work published by my research group.  The others are: ‘Salt increases nanoparticle diffusion‘ on April 22nd, 2020; ‘Spatio-temporal damage maps for composite materials‘ on May 6th, 2020; and, ‘Thinking out of the box leads to digital image correlation through space‘ on June 24th, 2020.

Source:

Santos Silva AC, Lambros J, Garner DM & Patterson EA, Dynamic response of a thermally stressed plate with reinforced edges, Experimental Mechanics, 60:81-92, 2020.