 like also to talk about the support for the case studies. I was unfortunately not able to come to the Munich workshop. So that's why something additional from my side, of course, I had a chance on also to follow what has been happening in the Munich workshop, but also last Friday. And today in the morning, we got the fact sheet, which is summarizing the output. Thank you for the presentation. Also, Ronald, what has been coming out. I would like to talk a little about the frameworks categorizations. And I have another point, maybe another categorization, because we are adding to the conclusion that we cannot put it all into one. And I would also like to talk about the domains. This is rather something in the background. We may come up with one or the other idea. And it is about the case studies now. And this caused action. But I think in the end, it's about much more. And of course, we are developing ideas throughout working and presenting and discussing. I, since we have all these frameworks and categorizations, which are rather comprehensive, I would also like to talk about the basics. So what are straight ways to determine the probabilities we need for a very basic decision analysis? And maybe that should be, hi, Helmut, very kind. And I think this is also something we need to know. And we need to have in mind. And to me, this is always the way of starting an analysis to make it simple, to have a start to know exactly what's going on. And then building complexity, that's the third point. So the domains of structural health monitoring or value of structural health monitoring, we have been collecting with the literature study. And we have put in here in the fact sheet. But that's also in other publications. So of course, it's about the operation of structures and portfolio of structures. So various decisions, surface life extension, structural utilization, modification. I think this was also very represented by Matteo. Then it's about code making and code calibration or standard calibration. So here decisions, for instance, about target reliability levels for design and assessment. This is very important for the reliability based approaches in the codes and standards, which are then itself a basis for the semi probabilistic approaches where we have safety factors and load combination factors. So here, structural health monitoring can make a difference in terms of that uncertainties can be reduced, which then influences the target reliability levels. It can be about early damage warning. So this could be decisions about evacuation measures, risk mitigation, repair, for instance. It could be, structural health monitoring could be about the structure prototype development designed by testing. So that was observed in the offshore wind industry around the year 2005, six, seven, eight, where many ideas evolved about the foundation design in considerable depth, water depth. And here, prototypes are built. Prototypes were instrumented. And I think it would be really interesting to accompany such a prototype development with SHM and clearly formulate the decisions. Of course, this SHM has implicitly helped to develop the foundation types. And then, so you have observed that I was speaking for points 1, 2, 3, and 4 about decisions which are associated to the structures or the structural system. But it's also about the SHM system. So SHM system development, SHM system design. So how should the SHM system work? How long should it be operated? On what location should it be operated? What precision should it have? And of course, there are many more parameters, lifetime, and so on. Something adding to the perspective of where SHM could be of value and in which areas we may find interesting case studies, regardless of the structural type here. This is what we have seen and what I found interesting when reading the fact sheet and going through the presentations. This is our value of information flow chart as already presented. It could be something else. So we have the icosar paper. But the framework comes from another paper. It's a framework on decision analysis. And here we can distinguish the system states. One system state is, of course, the intact system. And here we are producing benefits. I found, OK, anyway, I think this is also a very important thing, that we have infrastructures which are producing benefits and why not including it also in the decision analysis. And then we have the lines we are thinking in terms of risk analysis. So that's the exposure events, direct consequences, indirect consequences, direct consequences about constituent or opponent damage and failure states. And then the indirect consequences is about the functionality. I think this is also very important to keep in mind in the perspective of what states we should model here. It's the functionality. We need to address when we calculate the probability of a system failure. So it's the system failure and it's the relevant consequences. We need to calculate the probability of the relevant states for the consequence. We don't need to calculate all possible system damage and failure states, just the ones where we have consequences. OK, and this is the icosaw paper I'm talking about. So I think in every system state, when we classify the system states according to here the risk analysis part and here the intact system, we can acquire information. And we can have a decision on what the optimal locations are. So there's two locations here. And then, of course, there's costs associated with each of the SHM systems. But let's come to the basics. What we need for a value of information analysis is a choice of information, a choice of actions, and then probabilistic models of the chances of the information and the chances of the system states and the associated utilities, which may be also a chance. So this is the basics. And there can also be a very basic example. We consider a bridge. And it is estimated that with the probability of 20%, there's a damage. So that's the system state x2. We have two action options. That's the most basic options to do nothing or to lower the load bearing class. This costs 20 and provides less benefit. And then we have associated to the system states and the actions, the costs and benefits. So we have for the intact system state x1 and do nothing and a benefit of 100. If we are lowering the load bearing class, then the benefit is reduced. It's only 70, for instance. And then we have a way of acquiring more information here with structural health monitoring, which costs 10 and has this probability of indication. So 90% probability if the indication was that the system is in the intact state given, it is in the intact state. So a finite precision. And then this very basic example, we can illustrate what types of decision analysis we can perform. When we have information, like the information z2 that the structure has damaged, then it's posterior decision analysis. Prior decision analysis, we have only actions and system states. And pre-posterior decision analysis is when we consider and experiment all possible outcomes in conjunction with the actions and system states. Classical definition of the value of information. So if we combine a prior decision analysis with the optimal expected benefit of a prior decision analysis with the optimal expected benefit out of the pre-posterior decision analysis, then it's the expected value of information. When we work, we can also work with information we have already acquired, z1 and z2, but then it is a conditional value of information. Of course, we are after the expected value of information because that facilitates that we can influence our SHM action in terms of performing a certain SHM strategy. And we are optimizing before we are implementing it. If we have already implemented SHM and have acquired information, then we can rather assess from behind, was it worth it or was it not? But that's not so, well, that's basically too late. OK, so we are after the expected value of information. We can resolve this decision tree very easily and we find that we have, in this case, a value of information of 18.5. The optimal benefit based on the prior analysis is 50, based on the pre-posterior analysis with our SHM strategy. The expected benefit is 68.5. It comes here. This is a chance note. So the probability of z2, 0.25, is multiplied with 40 plus the probability of that we are getting the z1 information that's 0.75 times 0.75 times 78. And if we add that, we arrive at 68.5. And here, this is obtained simply by maximization operation, so this goes here. And we should be aware of what we just did, how we solved it. It's the extensive form analysis. So we are working from this side of the decision tree to our optimal expected benefit on this side. And if you write it down in formulas, then it looks quite the slide looks quite full. Because we have to consider every branch here and do the maximization operations I just mentioned to arrive at the expected benefits b1. We can have it simpler. We can do the normal form analysis. Here we are working from the maximum expected benefit from this side to the consequences on the right-hand side. And when we work through this decision tree, we need decision rules to arrive at the right branches. And that's basically also something which is very, for the analysis, it's not so relevant. But for the implementation and application of the decision analysis and of the results and for implementing the right decisions in the real world, this is very important because someone will be there with an SHM technology. He will get an indication with the system. And then he needs to know what action he has to take. And this is exactly the decision rules we need. But before we come to the decision rules, we should be aware of that these two formulations are equivalent. Yeah, it will arrive at the same optimal expected benefit and that goes here to the Bayesian updating, which is then multiplied with the probability of Z2. Or as we have seen in the last presentation, there's marginalization operation. So that's basically multiplying with the probability of Z1 and Z2. That's equivalent. So if you do this operation, you have done the extensive form. And I think it's very important to know that this may not be necessary when we work with the normal form. But we need the decision rules. So here, the optimal decision rule is that we should do our experiment, our SHM. If we get the outcomes at one, the action should be do nothing. If you get the outcome Z2, then we should do action one, which was lowering the load bearing class. What do I have on the next slide? OK. And that's the proof that we are getting the exact same results with the other formulation. OK. So I think the extensive and normal form analysis is very important for the implementation of this decision process in practice. That's the first point. The second point is about we have here the potential of calculating half the branches. So this is something. And OK, if we have more options, more decision options, the effect may be even larger. The crucial point is to find the optimal decision rules. So we could think of that the scientists doing the extensive form analysis and derive then the decision rules. Also, we could say we are deriving heuristics. But they should be value of information optimal. And the decision analysis in practice can then be done with these heuristics or decision rules. OK. So that's the very basic value of information analysis and in extensive and the normal form we should both be aware of these two analysis types. So something more to basics. System state models. We need basically models of the actual performance and the prediction. And especially the prediction of the performance because we are doing a preposterior decision analysis. And where are these models are coming from? They are coming from observations and databases. Or I should have written and or empirical, physical, or chemical models. So if you just work with observations, we can derive our probabilistic models with the maximum likelihood method. If we combine models and observations, then it's regression analysis and derived methods which are taking basis in regression analysis. So a very basic example here. I think we have seen this in the presentation of Jang Joon. So that was where I also took a little basis in here. So if we have four system states, it can be no failure, no damage. So that's our vector x. And we can derive the probability of these events with the limit state function for failure and survival. So we have here our resistance part. Basically, it's the most simple limit state function is r minus s. So let's say this is the r part. So we have r here. But it's degrading with damages, with deterioration. So that's d. Then there may be a model uncertainty here multiplied to d. Here we have a model uncertainty for our resistance. And that's the design variable. So when we are doing a design, we are creating a resistance to the known loading. So that's z here. And that's minus the loading. So model uncertainty for the loading model and the loading model s. So and then failure and no failure. So I've written here survival. So that's equivalent to this f with the dash here. It's then simply defined with this limit state function. And there may also be a limit state function for the damage. So this is the basic system states. It can be even more basic if we do not account for, for instance, the damage part. Action models are required. They can influence the system state models or just cause costs and have an influence on the consequences. If we do a posterior decision analysis, then we need to know the precision of our SHM information. So a model for the information z is required. So what we need at least here is the type of the information. Where does it go? Where does it connect to the system states? The precision. So what is the probability here that this information is right and the costs? For a pre-procedural decision analysis, we need a more complex model of our SHM, or the information requirements strategy, here. So we have a vector of outcomes dependent on the system states. So what is the most basic approach here for the determination of the probability of no indication, given a damage, or the probability of indication, given a damage? So that's the basic NDT, non-destructive testing or non-destructive evaluation reliability modeling. That's the probability density here on this axis and on this axis. There is the signal or the indicator when we want to also include damage detection procedures or indicators which have been derived to inform about the structural condition. Then we should say indicators here. And they will have a distribution, independency of the damage size. And of course, there's also a reference state or an undamaged state of the system where we also have a distribution of the indicator. And here we can also determine the probability of no indication, given no damage, and the probability of indication given no damage. And that must then be, so we have conditional probabilities. We can calculate for conditional events, but we need to marginalize. And that's basically done by integrating over the damage states. So then we arrive at the probability of detection here. And the probability of any detection gives us the events. So our Z may be defined as Z1 and Z2 in our example. And Z1 is then the event of no indication, and Z2 is the event of indication. So when we add complexity, then we just go to the frameworks and the categorizations. So this is about system modeling, for instance. So I think this was also considered in the Munich workshop that we can work with the system model. And then we also have the system functionality model that can quantify the indirect consequences. And of course, we have it reflected also here. So this is adding system modeling, structural system modeling. Decision scenario is also an important thing. I think this is very good described here on the left-hand upper side. And then it's, again, also SHM system modeling. So our PUD may not just be one-dimensional, but it can be multidimensional. We have been working with Michael Döller on such an approach. So because damage detection information is on structural system level, in contrast to inspections, which are on structural component level. Yeah, temporal modeling. We can think of different times. Here we have our decision tree I introduced at the very beginning. And then there can be depending on a model. When we look, for instance, at the system states, we have a model which goes for the complete service life. It's modeling the system states. And then, independently of where it is monitored and how long, we may have information coming to that system state here, or at t equal to 2. They may come at the same point in time, but they may also come from a previous branch in t equal to 1. And yeah, well, I presented this in the workshop at DTU, a kind of demonstrator, but it may be a little too complicated. So but what we have looked at here and what we also published in the ICOSAR 2017 is that we look at a wind park. And so we have the intact state. And here we have also modeled the functionality. So that means power production. And of course, so that's a cost-benefit analysis. If you just look at the cost-benefit analysis, then it's very evident if you can operate it longer. And not so many actions need to be done for service life extension. Then it's very evident from the cost-benefit analysis. If you can operate it longer, you will have higher benefits. But it's not so easy because we also need to have an eye on the risks. And that's what we have done for this ICOSAR paper. Developed a system model where we are modeling the damages of the components which may lead or which are dependent or influence the failure of the components. So that's the red dash here. But it can also be that there is a damage of the complete wind turbine structure. And then the operation may be interrupted. Or it can even affect the complete wind park and the operation is interrupted, which also influences then the probabilities that there is a complete failure of one wind turbine. Or there is a complete failure in terms of the consequences. So there's a complete production loss. So this is symbolized here with these red support structures and turbines. And then we may look at three SHM strategies, component loading monitoring, hotspot monitoring, and wind turbine load loading monitoring. And the relative values of information are then here. So the first two strategies, it's around 30% that there is a gain of an expected benefit, a gain of utility, around 30% for the first two strategies. The strategy number three leads to a negative value of information. So the conclusion is that the service life can be extended from 20 to 25 years if there was information with a sufficient precision throughout the operation of the wind park. OK, and that's rather the end of my presentation. I would, in my perspective, and maybe I'm not fully aware of what exactly is the progress of the case studies. But I think it's a good starting point to describe the case study with the value of information flow chart we have developed in the Munich workshop. And then it's not about just one demonstrator. I think there should be a demonstrator for all the case studies, and that should be worked on with, I think, working group one, two, and three should be here in the lead with the, or should do most of the work, not being in the lead. We have the OK study leaders. So I think there should be a variety of individual demonstrators. Daniel has been working on one, and this will also be an ICOSAR publication. I think this is a very good example for working with Bayesian networks. But it may not be the only tool. And so we should work on many demonstrators. Then adding complexity. What can we do? Temporal modeling, system modeling. I think this is the most important point. And then stepwise performing the case study and disseminate the case study. Thank you for your attention. Do we have any questions? I have a question. Because of the application for the case studies, do we have all the information that we need to apply this framework in the case studies? For example, the probability of detection even down the door, even not down the door. Do we have them? How well do we get them for the case studies? I think this is a critical point. This is something we will start working out today. So we will be starting with the case study and collect the information. And we check how to apply this to the framework. And we will observe very, very many obstacles. And we try to come over these obstacles. So we choose not today, but in the next. So now we are in the state where we choose some case studies, but not basically the information we have. We just choose the title. Yes. The latest presentation, the list of not all case studies must exactly follow your approach. Because it's not possible in some cases to follow that. So they might be spot monitoring and due to the case one has might also validate the analysis to prepare for the final information. I don't know if it's going to be possible to follow these lines strictly. Because I realized from the question she asked how to follow in my case study or something this one. I think this is a very critical point or also a very good point. I would think that we should address the basics. So when we, what I've just presented I think the most important point would be the basics. This is what we have to address. Not exactly with the approach, but we need to have the basic in terms of the SHM strategy, in terms of actions, in terms of the outcomes and the system states. I think this must be consistently described. And then we have very many things around and the frameworks and also very diverse, many more approaches for determining this likelihood than I just outlined. So I just outlined the most straightforward one. But there's different ways of modeling this likelihood in many more ways. But here, very clear, this must come from a working group one, two entry or basically one entry. But one should also keep in mind working group five, which is the practical implementation in the information among all these working groups. The case studies and then from the case studies you get something out which you summarize in some kind of recommendations. Sure. I think we are the group. I don't criticize them, I just think about them because I have some of the game shows and you think you have a workshop or something. It's very interesting, but we have put somehow everything together. Yes. The case studies can be seen as a reality check. So the case study is not something that comes to disturb theoretical concepts. It's actually a reality check for theoretical concepts because they talk about engineering and science. So we want to do something that can be applied. Now the last workshop in Munich was to develop this framework. It was presented before. And this workshop is about taking this practical case ideas and try how we can link these ideas to this framework. And we will come over obstacles, that's for sure. But there I have to be critically reflected because the theoretical concepts should accommodate for practical examples. So that would be very interesting today. I'm really looking forward or a small group of discussions I don't think you would come up with a unified pattern for all the case studies because it's impossible. If you are checking service integrity maybe you can apply the framework because it is and you will have a deformation. If you are applying this thing to study a visual restructuring in a seismic region you will never come up with the right interpretation. So it's a... Well, you can come up with that. The uncertainties will be much, much higher because you just have to know that and you have to know to do that. So I'm not sure. I'm sure we will not be able to be unified. If we find it's not, maybe not, but we have to wait. But I like the idea to structure the project and the connection between the working groups. Otherwise, one example is for them to be like something, like the idea to have it somehow as connected as possible and under a framework as possible. Not not not being the same but we will see. The basics, the last thing maybe as a tool can be useful to have a decision-making a basic decision-making Sure. We will work with the application with this very information for management of seismic emergencies and one of the problems for me an expert told us was that to build the intelligent. So maybe if we have, I don't know, an excertified decision tree where we can change things for the dummies like me for the very information to be to be very useful. Okay. Thank you. I had a similar thought. Sure. We should distribute at least an excert sheet. Yeah. And maybe something more flexible where we can define a limited amount of states for each node and a limited amount of nodes but more flexible than an excert sheet. Well, I don't know which one is that one. Yeah. Something that we can use. Yes. Yes, yes. Yeah. Thanks.