ESGI 128 Blogs: Analog Devices and Vehicle Damage
Analog Devices Problem
Day 1
We started the day with registration and coffee – an opportunity to meet the other attendees, and discuss which problems we were thinking of working on. Following an opening address from UL president Desmond Fitzgerald, five industry representatives presented their problems individually. Each seemed interesting and intriguing, with opportunities to make use of many different areas of expertise, from statistics and computer science, to applied maths and physics. The problem which caught our attention was that presented by Analog Devices – relating to the time-to-failure of an electronic device, and how this depends on the operating voltage. It seemed we could make use of our knowledge of physics – particularly to learn more about the method of failure, and also our experience of statistical modelling to extract useful information from their experimental data. Once we selected this problem, we had the opportunity to discuss it in more depth with the company representative, which cleared up many of our initial questions. From here we discussed our previous experience in relevant areas and began looking into the literature for useful methodologies.
Day 2
Having thought about the main issues over the previous evening, the morning of the second day started with a group meeting to discuss ideas for solving the problem proposed by Analog Devices. The group discussed some statistical approaches as well as the physics of the device to investigate its lifespan. One of the first tasks we tackled was to recreate the analysis provided by the Analog representative. It quickly became clear that Analog’s current statistical approach did not make use of all available information when analysing failure times from a sample of devices. In particular, information from censored observations was being ignored – these are devices which did not fail during the testing period (approx. 6 months). To make use of this data we needed techniques from an area of statistics called “survival analysis”. As there are a variety of different survival models that one could consider, we also began to read literature on model averaging techniques which can estimate survival based on multiple models. By the end of the day, we had a clear sense of what needed to be done for the remainder of the week.
Day 3
On Wednesday we continued with the work we had been doing the previous day. We made advances in our model predictions, incorporating the censored data, and implementing model averaging. The afternoon was broken up with a keynote talk, given by Jacqueline Christmas from the University of Exeter. She gave a fascinating account of her work on improving safety at sea by measuring and predicting sea waves. She described different methods of measuring sea waves – such as buoys, and radar, and the complications that come with each. The day ended with the conference dinner, in the Pavillion. It was a nice opportunity once again to chat and get to know others better.
Day 4
Today we finalised our analyses for the problem and collated our lifetime predictions (from each model, and the model average). Once this was done we prepared a presentation of our results to discuss with the Analog representatives. The group is content with the solution being offered, with our contribution incorporating model averaging, others working on comparing models which incorporate thresholds to those without, as well as some study of the fundamental physics of “treeing” (the primary failure mechanism) within the device.
Day 5
Friday morning was spent with each group presenting their solutions to their respective problems. Each team came up with unique and interesting answers to each of the problems, which incorporated mathematical modelling, optimisation techniques and statistical solutions. Overall, the study group was a great opportunity for students to learn new mathematical and statistical tools which can be applied to interesting real world problems. In addition to this, the study group encourages team work between mathematicians, statisticians, engineers, physicists and computer scientists, from all around the world, who may not always have the opportunity to work together. Looking forward to the next study group!
Aoife O’Neill1, Eimear Keyes2, and Maeve McGillycuddy2
1University of Limerick
2University College Cork
Vehicle damage problem
The problem
The problem concerned estimating vehicle collision damage using motion data. This problem has come about in recent years due to decreasing profitability in Irelands insurance market leading to an average increase of 38% on insurance policies. A major contributing factor to this is thought to be losses due to undetected fraudulent claims. Our group was asked to develop a software tool that can accurately reconstruct vehicle collisions, given data from a GPS and an accelerometer (x,y,z). We also considered adjusting the model in the future with the addition of Gyroscopes. The main function of this model was to determine the zone of impact of the crash and to determine the severity.
Our approach
Our initial approach was to split our efforts into three groups. The first looked at the accelerometer data and used a method based on pattern recognition to aid the derivation of several plots. These plots were used to further understand the other two methods. The second group used the accelerometer data to model the impact force using a visual reconstructive of the forces. The third group used a trajectory reconstruction approach to model the path of the vehicle using the accelerometer data. This was compared to the GPS data to construct a more accurate model. The modelled trajectory along with the impact forces were then overlaid on a suitable map (google maps), to recreate the incident as realistic as possible.
Final Model/Recommendations
The final model combines both the trajectory and the forces acting on the vehicle to give an accurate reconstruction of a given incident. For each of the test cases it accurately estimates the observed data. We do recommend however, the addition of a gyroscope or another accelerometer in future. This would provide addition information for the orientation of the vehicle, which would allow for more accurate reconstructions. In summary therefore, the zone of impact can be determined with the data provided and the severity can be determined if correlated to magnitude of impact. A model and software product can easily be built to perform these.
by Dónal Murphy1
1University of Limerick