 So, the first presentation is held by Piotr Maria Pinam and Ufuk towards understanding and quantifying the value of SHM and inspection data for seismic risk management of buildings. So, please go ahead. All right. Good morning, everybody. The title was already and the offers were already mentioned, so I will just go very quickly to the next slide because we don't have much time. The outline of the presentation is that in introduction there will be a little bit information about of two types of seismic structural health monitoring that we propose or envisage. Then the value of information for seismic building monitoring will be cast as a preposterior risk-based decision-making problem and a framework for that will be shown. Events of the preposterior framework will be discussed in terms by my co-authors, first damage detection techniques in the probabilistic framework, then utilizing both inspection and monitoring data for the purpose of what we want to achieve, and at the end some information if time allows about modeling of consequences and cost for seismic risk assessment, and finally I will try to wrap up with a set of conclusions. So first, two types of seismic structural health monitoring and to start with not yet two types, which is the title of that part, but types of seismic monitoring arrays we can have in that situation. Now, typically when we hear structural health monitoring, we think about putting sensors on the structure, right? So they are shown here on the building, well, on foundations too. That's very important in the seismic context because obviously the forcing to the building is through the foundations, right, through ground motions. But that's not all that we can think in terms of instrumenting the whole system, and always occurs very some monitoring of nearby faults which originate, where the excitation to the structure originates, as well as there will be typically sensors in the wider area, perhaps whole city, perhaps even whole region and so on. And this is all useful to measure attenuation, characteristics, hazard exposure and so on. If you think about it, in seismic monitoring, there are several sensors on the building and then obviously sensors there, but it's not really on the presence of sensors far away from the building. It's not only restricted to seismic monitoring situation. You can have this, for example, a transportation network of a city equipped with several weight in motion measurement stations, which allow you to characterize better properties of the loading and so on, but acting on a given bridge or perhaps a collection of bridges or similar situations. So this is just to emphasize that there is more sources of information that we normally typically assume exist. Two types of seismic SHM or perhaps uses of data from such monitoring exercises. First one would be used for quick post event actual damage detection. I think Helmut was saying yesterday that it focuses on performance. It's true for systems which deteriorate slowly due to say for example fatigue, corrosion and so on. For seismic I would say that we are still interested in damage, which will occur suddenly without much accumulation over time as such. Basically this type of monitoring, this type of system will be, depending on the output from them, decision will be to either evacuate the building after a strong motion event or quickly resume normal uninterrupted building usage. The two different scenarios which you can see, if you get your decisions evacuated or not evacuated wrong, the consequences are as follows. If you evacuate when there is actually no damage, so we are here, that entails unnecessary losses to business interruption, rent income, cost of alternative accommodation and so on, where you don't really have to do that. On the other hand, the wrong decision when you do not evacuate when there has actually been damage sustained by the building, it means that typically after the main shock you will have a series of aftershocks, the building will be weakened already by the main shocks and therefore if people are still in the building equipment or whatever content is there, they may die because of you allowing them to stay there. Another type of monitoring, it's not related to damage detection as such and it's based on collection of data for updating hazard and vulnerability models. So this is typically a modeling of those faults and so on and why their areas, where you measure fault activity, you measure wave propagation, typically over extended period of time to capture larger numbers of seismic event and you can update probabilistic hazard models in this case. There is also a place for sensors on the building where you will be able to calibrate your, for example, computer models of the building or generally speaking, your vulnerability models related to a given model, given building. Downside is that those will be very likely many events, so statistically you can process them, but they will be low moderate intensity and so on, so not really, well there will be problem of extending this type of data to strong event. So we started to thinking about how to cast this decision making about whether you use monitoring or not as a preposterior risk based decision making problem. Yesterday there was more than one presentation about the theory behind those type of decision making processes, so I won't go through it. And what we did, it's a well known technique, we just applied it to a particular problem, so I will talk about what is relevant, what is different in, well what is specific about it compared to general theory. So you start with basically the decision either to do not monitor or do nothing, that doesn't cost anything, right? Or monitor, there will immediately be some cost. This is a very simplified decision tree with only two branches at each note. In practice you will have much more decisions here, while monitoring it could be several options, several techniques with associated costs and so on. There is place also for example things like enhanced visual inspection, something along the lines of BORP program in the San Francisco area, Building Operation Resumption Program, where you effectively pay consultancy so that in case of your building potentially building damage, they quickly send people for visual inspections. Other options to manage risks, and this was already covered in some presentations yesterday, for example to strengthen structure, and again a number of options are possible. Combinations of those options, monitoring plus some strengthening, using visual inspections and monitoring, indeed Ufuk will be talking soon about how to merge those types of data are also possible, right? Then once you decide to monitor your system, you will either detect damage with certain probability, sorry, not detect damage, zero is for DD damage detection, zero means negative outcome, or it will detect damage, right? So this is DD1. Well, in perfect words, damage detection means either false, sorry, true positive or false positive, right? Based on the indication from system, you will be making decisions either to not evacuate building or evacuate building. Again, this is a very simplified situation, there may be other decisions to be made at that point, for example, whether you want to quickly, reasonably quickly, of course, because it's a question of minutes or anything like that, repair the building, or perhaps, I don't know, demolish it even, and so on. The real state of nature, so this is DS0 or 1, DS4 from damage actually sustained, DS4 sustained is here. Each of those situations, decisions and chance outcome entails certain costs or consequences, generally speaking, or costs, right? As I said, if you evacuate building, there will be business interruption. If you do not evacuate, but the building later collapses, there will be cost of, or consequences will be lives lost in that situation. Now, I realized while reading around the topic that some nearly 10 years ago there was a cost action on building robustness, and several people in this room were part of it, so I here assumed that damage means failure immediately, right? So you can think about it that I'm not, I'm considering the situation that the building is not robust. If you want it, you can end here another chance event from damage to failure to account for robustness. I will skip that probably slide because of lack of time, but Dimitri was explaining how to analyze those types of trees. You go back and at each, well, chance event, you calculate expected cost, so this will be probability times consequences or times cost, effectively risk, right? And at each point, at each decision note, you try to minimize risk. Now, we talk about here as the formula here, right, which is lengthy and perhaps not immediately obvious if, but the basic idea is to choose the path, right, from here or from here and so on, which will result in least cost, including cost of monitoring and minimizing at the same time the risk. And that finally answers the question whether you are on this part of the tree or this part of the tree based on risk. Yes, and with that, I will pass on to Maria. Detection, which can be expressed in terms of the likelihood function of a chosen damage feature, which could be a model parameter, for example, the frequency, the period, or other. And in terms of the prior probabilities, the prior probabilities can be calculated as, I estimate it better, as we will see from the fragility curves. Here are the usual likelihood function that is the probability that damage is not detected given damage exists or the probability of damage being detected given damage exists. And the same here, damage not being detected given damage do not exist and the probability of damage being detected when it does not exist. The fragility curves, these are plots of the conditional probabilities of exceeding a given damage state at various levels all over the ground motion. This depends from the hazard of the seismic zones. So the fragility curves are plots like this, where there is a parameter which expresses the level of ground motion, which could be the ground acceleration or spectral acceleration, for example. And on the vertical axis, there is the conditional probability of exceeding a given damage level, a damage state. Here are represented four different damage states from collapse to minor damage. These plots usually are defined in terms of a damage parameter, which could be, for example, the interest rate drift or the number of buildings collapsed with respect to the total number of buildings of that type. And this parameter needs not to be the same damage feature, which is used for which the likelihood functions are calculated. The likelihood of hood function. Of course, when we are in the pre-imposterior analysis, there is not a monitoring system on the structure. And so these functions cannot be estimated based on the data recorded on the structure. They have to be estimated using numerical models or using a statistical model. And this, this is my opinion, is the really weak point of all the procedure because there is a lot of uncertainty in this. But I would love to hear what is the idea of people who are more involved than me in the estimation of likelihood function on this. OK, this is the face of likelihood, what could be the likelihood functions of, I don't know, for example, the period, the model period. We have this distribution of the damage parameter in a reference configuration where the distribution is due to, well, the variability is due, for example, to environmental sources. And this is the same distribution for the damaged configuration. So there is an increase of the period due to damage and the variation of the distribution, the variation of the variability of the parameter. From these curves, we can estimate the probability of not detection. That is the probability that damage is not detected. And this is true. Damage does not exist, which is the white area here. Or, for example, the probability of false alarm, which is the area here under the curve in the undamaged configuration. And for me, all together. OK, so I will, OK, we have already defined all this. These are all the conditional probability I just mentioned in the previous slide. No, an important thing. In order to define all this probability, we need a threshold, which allows to say if the damage parameter is beyond the threshold, I will say that the structure is damaged. Otherwise, I will say that the structure is not damaged. How to fix the threshold? The threshold can be fixed, for example, this is a proposal, of course, saying that there is an equal cost of the maximum consequences of the probability of false alarm and of missing alarm. And once the threshold is fixed, all the conditional probabilities just mentioned can be estimated and used to calculate the probability of detection or not detection. Good morning, everyone. I'll quickly rush to the next part. Well, as I see the problem of post-surgery safety and damage assessment of structures as follows. Basically, before the event, we have an undamaged structure with pre-event characteristics. Then the earthquake event strikes the building and then it sustains its post-event characteristics. Some of those characteristics can be identified like stiffness and damping. Some of them cannot be identified, but can only be estimated by strength and ultimate limit state. Then the responsibility of the engineer that assesses the safety of the building is to estimate what will be the future earthquake shaking that may excite the building at its site and what will be the post-surgery state of that building after the earthquake and then make a decision on the post-surgery functionality of the structure. Well, in an ideal world, we would have a wonderful model that would capture the response of the structure to that excitation and that model would provide us the actual damage distribution in our analytical framework. However, in order to achieve that, we would need two critical components. One component would be a numerical model and an analytical model to simulate the dynamic response and the displacements sustained under the excitation. And the other model would be a perfect estimate of the likely limit states of the structural components. What would be the limit states that correspond to different deformation levels? Those limit states, for example, for the case of an RC member, would be concrete spelling, concrete cracking and reinforcement buckling. These would be the limit states that would trigger some action by the owner of the building or the engineer responsible from the safety assessment. In these plots, I'm showing these limit states as vertical lines at some deterministic points. But actually, they're usually not like that unless we test the structure in a laboratory. We can only estimate those limit states probabilistically for our structure. And also, we, in our non-ideal world, cannot determine a single unique perfect model for our building, but we can generate a set of plausible models that have equal likelihood of representing the response of the building. And then the key challenge is to identify among those set of plausible models and among those likely range of the limit states, what is the optimal model that represents the behavior of our building? As I see the value of information received from health monitoring and inspection data is to identify posterior likelihoods for different models, starting from a uniform likelihood distribution provided for all models, evaluating the posterior likelihoods for all models, biting out the monitoring data and inspection data, and carrying out a post-archic risk and safety assessment using the set of best performing models based on this posterior likelihood evaluation. A thing I would like to emphasize is to take into account the fact that inspection data would provide an element by element basis severity of the damage, and more importantly, it will also provide some information about the damage mechanism because we have been talking about the severity of the damage quite a lot, but actually the damage mechanism being flexural shear or axial also provides quite important information. The same period elongation that is sustained under flexural deformation may be much less critical than the same period elongation that is sustained under flexural damage mechanism, and this has to be taken into account, and I think taking into account inspection data, jointly with monitoring data, would enable the engineer to achieve that task, and I would like to pass it over to Pietro. All right, so you quickly write it up. Haider asked yesterday whether we should model consequences of failure. Yes, we should. I was supposed to have two slides, but I would just mention that yes, we should, and there are considerable uncertainties there, right? So we look at consequences, their types, and so on. Came up with a few models we used again from the robustness construction previously, and that's from paper that Mario's co-authored and so on. So those construct models for a number of casualties in a building and so on. There are other types of costs you will have to include too. So those constructions actually appears that they do produce something useful if not being perhaps a little bit self-referential at this point, right? But yes, and conclusions. Well, I think we proposed, there are many, we proposed pre-posterior decision-making framework for trying to quantify the value for structural health monitoring. Perhaps I will jump to the last point here, preempting Sebastian's maybe question, what are we going to do with that? As a theoretical, very kind of attempt at this point, we need to pull together and fill all those theoretical concepts with some real data, real example, and so on. Perhaps starting with something that Daniel showed for yesterday for his bridge at Princeton University. But I think as time progresses, we can do better than such simple examples doing some more advanced analysis and so on. So yes, with that, thank you very much for your attention.