 Govdjo. I'm Maria Pinale Mungeli, I'm affiliated with Politechnico di Milano, Department of Architecture, Built Environment and Construction Engineering. As requested, the first slide is a very short presentation of the, my research group, and which is made up of the person listed there, profesor, reserčer, asocijator, P.H.D. studenti. Sreče imamo našeljne koalaboracije, tudi v universtriju Udine in Vydivstar, in v Parisu, kaj sem tudi srečen, tudi srečen srečen srečen. Tukaj tukaj tukaj tukaj tukaj tukaj tukaj tukaj tukaj tukaj vseči je kvalitavno zelo, da je naša zelo, ter je zelo, da je stavila seboj, da je vzelo, da je vseči vseč i kultura, da je vseči vseči in vseči vseči. V nekaj roli smo povalili vsišenju zelo, da povali seboj zelo, da sem bilo povali sve, da se te bljenje povali, na odličenju. Našljena je zelo, da je točnja, začal je, da je zelo, da se odličenja je odličenja. Zelo je, da je zelo. Točnja je odličenja, da je zelo, da je zelo, da je odličenja ima vse skupne, vse skupne, da ne predlje, da ne predlje, da ima vse skupne, struktur. This change in the form shape of the structure will make the shape irregular at the location of the stiffness loss. The idea is to detect this irregularity by fitting the operational shape, the shape of the structure with a smooth function. We used a spline, a cubic spline function because it has a mathematical characteristic, which is called Gibbs Phenomenon, which makes the interpolation very bad, close to a curvature discontinuity, since the loss of stiffness and uses discontinuity of curvature, the interpolation with the spline function will become as much worse, as much higher is the stiffness loss. So we define the damage feature as the difference, sorry, out of point here. The damage feature is as the difference between the recorded, the deformed shape and its interpolation with the spline function. We can do this in terms of the total deformed shape, or we can do this in terms of operational deformed shapes, that is for each value of frequency if we work in the frequency domain. So here are some very nice operational shapes calculated for a numerical model, and for each of these we can calculate this error, and in order to have one value of the error for each location, we can sum up the errors for all the operational shapes in the frequency range of interest. So this is the basic idea of the method and the presentation of the damage feature. The problem is that, of course, this damage feature will exhibit variations even if there is no damage at all. This is due to some random sources, the usual random sources. So usually we may have three situations. Yesterday someone talked about that there are mainly three types of monitoring, short, periodical, and long-term monitoring. The main difference in the application of methods like this is that it is in the volume of data that are available. In a short monitoring we may have a test before in the original configuration and another test in the inspection phase. So we have a very limited amount of data, very limited amount of sample, and there is no way we can find the distribution of the damage feature nor in the original configuration, neither in the damaged configuration. If we have a periodical monitor, we may hope to find the distribution of the damage feature in the original configuration, but not in the damage, in the inspection phase, because in the inspection phase, for example, we have, when we need a prompt alert after a catastrophic event or even not catastrophic, an earthquake, for example, and we want to know if the structure is safe or not. We don't have the time, of course, to collect as many information as the one needed to find the distribution, probability distribution in the damaged configuration. So we have just a value, and in that case we have to define a threshold and say, OK, the structure is damaged if the threshold is exceeded, but what is this threshold? How can we fix this threshold? It would be nice to fix it basing on cost-benefit analysis, but for most civil structure is not quite easy to have a cost model to fix the threshold. In our application, we just fixed an accepted probability of false alarm, which is the area here. If the damage feature exceeds this threshold, this means that the probability that we give a false alarm is very low, and we fixed the value of the probability of false alarm that we accept. In which we have more data, of course, is the long-term monitoring. We may recover the distribution of the damage feature, both in the undamaged configuration. In this case, we can estimate both the probability of false alarm and the probability of missing alarm. That is the probability that we don't give an alarm and the structure is damaged. In that case, we can fix the threshold as a tradeoff between the two values of the probability. Very quickly, we applied this method on a lot of numerical models because, as was just said, there are not many data available on really damaged structures, but also on a really damaged structure. This is the bridge in Italy, the Donio Bridge, which was artificially damaged with progressively increasing severity by cutting the slab, as you can see here, cutting the slab at the beginning at half of this section then all these sections and so on. Here are the results of the application. Vibration tests were carried out in the original configuration and after each damaged state. Here you can see the results of the application of this method. The circle, the location is the one of the damage and the bars here are the values of the damage index, the damage parameter. That is the variation of the interpolation error. For the lower intensity of damage, we have some false alarms, but for the higher intensity of the damage, the localization is quite clear. In the last damaged scenarios, they induced damage also in another section, this section and also in another section close to the other one. Actually, the method finds the damage in a section at the middle between the two. Also, we tried to apply the method by considering as the original configuration the one with the damage is just one section and the method was able to find the damage at the other section. Considering that here we had very few data, we adjusted data, one set of data in the original configuration and one after each test, the damage scenario was a very good result. This is another application, but it was carried out on a numerical model of this bridge for which we simulated several damage scenarios. In this case, we considered two damaged sections and the method works. Here is another application where we assumed that there is a permanent monitoring, so we assumed that we can recover, we assumed because this is a real instrumented structure. The factor building, which was instrumented by USGS, is densely instrumented. It has four accelerometer per floor, a tish floor. Actually, it is possible to recover the distribution of the damage parameter in the original configuration, but the damage scenarios were all artificially modeled by a numerical model because this building was never damaged. Also in this case, here you can see the blue bar is the real location of damage and these curves represent the damage parameter. The method finds always the damaged location, even if there is noise in the recorded signal. In this case, we investigated the capability of the method not to detect, but to follow the severity of damage. We found that actually the damage parameter increased with the severity of damage. There is certainly a link between the two, but at the moment it is not possible from the value of the damage parameter to recover the values of the loss of stiffness. The wish list, yesterday someone proposed to propose a wish list and I immediately borrowed the idea because I like it very much. The first is actually not a wish but a dream, I think. Now, because what I think is really needed for all this method of damage detection and this was just said by Geert, are data. A lot of data recorded on real damage structures because otherwise we will continue to check our models on our methods on numerical models and usually they work very well. They always work very well. The difficult thing is to let them work with real structures. So the dream is to have a living lab structure. Of course, this is not a dream for this course but can be an idea for future networking. Yesterday Dr. Wenzel was saying, we are here, we can propose something like that. A structure. A structure that we can monitor with any sensor we like. We can ask producers of sensors if they want to install their sensors. I think they will be interested because they can check the performance of their instrument sonarial structure and will be really a treasure for researchers to check their model. I am almost finished. Then another wish would be a cost model to define the threshold because one of the problems to define to say, okay, the structural damage, one of the ingredient, the main ingredient is the threshold, which has to come out from a cost benefit analysis. And then the last thing, yesterday the value was defined as the difference between the life cycle benefits and what this requires that we can model the structural performance. And these for structure suggested to fatigue may be possible, difficult ma possible. But if I think to imaginary structure subjected to an earthquake, these are really, really difficult things to do. So I think this will be one of the main problems to assess the value of structural monitoring for this kind of structure. Thank you.