 Actually at first I would plan to show the only the bands network that I have in mind now to Determine the how long the should the mere strain measurement last But I think because here I have Sebastian Son and then show to author of the thesis that I like the most so I would like to show my reason Result research so you can give me some feedback We appreciate that So this presentation Okay, so it about using Scala data in remaining fatigue life of Monopai support structures It's at the title. I make it up for the PhD seminar in Brussels. That's a week to go. I think and so The problem with the with the Monopai foundation is that's a scour and corrosion of the of the foundation by it may happen and Is it effect the remaining lifetime of the support structures? So the idea how to predict the the time to go to inspect So the message I want to deliver is that by updating wind speed distribution It is possible to update the remaining lifetime of the Monopai foundation I will make that clear by showing you how I update the wind speed distribution and how I estimate the remaining lifetime based on the measurement of the wind speed and the stretch range as Strain measurement or some train measurement data and I show the application with some results So to update wind speed distribution I I need to use the the measurement of 10 minutes mean wind speed together with the No, this is just about the wind speed solution. Sorry. So I assume that the terminus speed distribution is following the whiteboard solution And I know the parameter of that distribution from the desired stage and I assume that the shape parameter is deterministic while scale parameter is Normally distributed with unknown mean and unknown standard deviation Then this scale parameter can be updated using the several years of wind speed measurement data after structure going to operation So just to summarize we have the scale parameter following the normal distribution Mu the mean in normal and then the sigma following in Virgama 2 and then the joint distribution in The posterior density function of Mu and signal so the same so it's a Conjugate distributions and the predictive is following the students the distribution for the scale parameter Yeah, I'm following that I can update the wind speed distribution over time using the measurement data Wind speed 10 minute Is from Skada, so it's on the on the window back But that wind speed data will not be used alone. Are you together with the concurrent measure strain data? at the point that I am interested in or You can say well, maybe for the fall or moon by foundation the dangerous point location in not on air, but near the mud light Location so win we need to use kind of Because virtual sensing approach actually just a method to extrapolate the stress that you you got from measurement at some Location above water for the location under the water so by doing that you also have the derived the strain data or here I you directly the measure strain data adjust for illustration so from the mere strain we get the stress and then we have the stretch range Set range and then from the wind speed data we We fit the wind speed The 10 minute wind speed of each year into one wide-build distribution with the The shape and parameters The same as the one we have from design stage so I give the same shape parameter and I try to use the the bed fist Approach to find the scale parameter for that here so by doing that I can have the different value of scale parameters for each year for different years yes so by relating the Wind speed and this straight range together I can calculate the fatigue damage using minor rule and then calculate the failure probability and estimate the remaining lifetime using the Tachist reliability in day So this is the limit state function that I said I have the the uncertainty in the Minor rule I have here summation over T years of in operation up to the year that we are interested in this is J from 1 to and you 10 this is So I separate the the wind distribution into different beans so like I separate them into different beans and I calculate fatigue damage from each bean of wind speed That's why I have that summation and inside just this is a from the straight range distribution in that beam and This is the probability of that beam That the limit function that I have so I saw that the missus function using form to have the reliability index and this is About a random ribose I have I have the uncertainty in the measurement Instead concentration factor in a sand cuff in straight range and This is just the the scale parameter of the wind speed distribution Yes this is the way I Estimated remaining lifetime so we all know Using the target safety level But this is about how to determine the target safety level and about the application I Need to have the data of 10 minutes minimum speed. I need to have strain data. I need to have pitch rpm to Clean the the measure data to get rid of some heroes from the instrument Identify the operational case and then I need to have the geometry code detail of the joint That's the four types of information I need And this is the updated distribution of the winds of the scale parameter of wind speed contribution Using three years of measurement the continuous one either one before updating and The prior one is the one using the updated one either one continuous and the prior one is a The dashed line so you see it moves to the left. So It's just a little bit. So if we can consider that okay, it's smaller than predicted in the design stage, but It's good estimation for in the design And this is the result of remaining lifetime. I didn't show it in the real lifetime, but it's a ratio of the different life So you can see after three years measurement. We have 1.4 That the solar remaining lifetime is increased a little bit and For the year four or five six. I don't have the data yet. So I assume I have the same mean of the samples yes, and I've reduced the standard deviation using the number of samples there. So you see it's not it's not linear it's starting to reduce but not significant and This is just to show them The effect of load factor I use in the limit is a function. It's designed Well, it's effect. It's very important to the to predict the remaining lifetime and this load factor coming from the straight concentration factor or Factor to consider the corrosion effect or the interpolation factor from the Mirsch location to the underwater location for example And I put everything in just one load factor to consider So come back to the message. I want to deliver that if I you if I can update the wind speed distribution It's possible to update the remaining lifetime at the Monopi foundation Yes So basically That's it But I don't want to stop here yet because I still have two more slides first I want to have some I want to have some feedback on this one and then I will show the the one I really want to well To connect from what I learned here to the problem of determine the duration of strain measurement Like okay, how long should I imagine? Yes The table where you show the distribution. Yes What is So you said K is the stress concentration factor No stress concentration factor x Yes K here the first straight range in each Be in the wind speed we have one distribution of straight range for each be in the wind speed and I consider also uncertainty for that one Where did you take the assumption that this stress is concentration factor? It's not by a normal It's at assumption and Do you mean why the meaning one? The the mean can be larger than one So I take it out and I put it in a load factor here as a deterministic value and I just take one and then I consider For the difference the value is more in the order of three years. Yeah. Yeah That one is for the wind speed distribution Explained that the difference is quite small The reason for that is that I I have 15 years of measurement from the design of similar science I use that statistics to determine the prior information and Because it 15 years compared to three years measurement in operate in construction after construction This Treatment of the prior information that applies to a big area and Compared to that the site specific information So the site specific information my great much more So the mean so do you mean the prior information that I use from similar sites in not really appropriate here I should use Because these observations they don't So it's not that you have the 17 data on the entire area Should actually Not use 17 as a great of the prior but much less because Okay, that information you get when you make an assumption How much your parameters vary in whole an area then you get a little bit Idea what all of magnitude is Mm-hmm. Yeah Do you understand what I mean? So for instance, this end we had in my simple example Also just a function of Relationship between the variances Yeah, and then you suddenly get in prime 0.3 3 less than 1 Okay But I think that's Yes So you subset me to do kind of sensitivity on the number of sample. I should use for the prior information Number Bari Yes I say it's not really important the variation here because the the remaining lifetime in as a factor of the of the reference life It's just 1.4 1.42. It's not really significant if you multiply with 20 years lifetime Something So usually and especially for winter bites the Modern studies in relation to fatigue are tremendous So but in order to reflect this situation Maybe it's worth To have this X And if you are able to At the location where the fatigue damage occurs in that case There should be a significant effect on the fatigue life The So Also think of two two situations There are some of connected in your example They may be disconnected so you can update the wind speed Distribution yes, like you do and then work the rest Design also or you measure Yeah, far from stress or you know what stress, but then you don't need any Continuously Then you can just do a rate for counting and you get the damage and this is subjected them to your measurement uncertainties, maybe The rate for counting should be rather precise Yeah, okay, this is the both separate situations I see you from what you have told us Not in terms of But I understood the model uncertainty The main model certainty there is in the Delta so in the tutorial of Fatigue failure because Yeah, straight derivation like the method that you the virtual sensing for example Then we have uncertainty because we tried to do the structural identification, so But yeah, I don't consider it here And I consider directly that I have the measurement data at that location that I'm interested in So it's not happened Decisive quality is If you can measure the stress ranges Then you may get rid of both the model uncertainties but if you Related indicator with stress range This is model Here it's another model uncertainty right and some of the some of very sophisticated approaches of determining the safety plan of the scatter data, acceleration data, and so on. They are requiring high, really extensive modeling. But in that case, often the whole answer is unclear of this procedure. And it's claimed to be based on measurements and should be more precise, but it's hard that one can find some model uncertainty. Yeah, that's it. But there are two types of model uncertainty, one in the low-effect, which you can get rid of, as you mentioned. But you can never get rid of the model uncertainty in the resistance of the intrinsic of using the SMP purpose. OK. Yes, thank you. Thank you for your patience. I have just two slides here. So what I want to do is to determine the measurement duration for a stream here in this application. The owner asked me, so how long I should last the measurement campaign? I tried to read by updating directly the straight distribution, but it doesn't work, because the longer you measure, the less you have for the variation. So I can answer by doing that. So I tried to read by the value of information approach to try to summarize some main idea. So we have straight range assumed to follow a wide distribution with scale. This is a normal distribution with unknown mean and unknown standard deviation. The shape is deterministic. And we can update that straight range distribution using the measure stream. And we can predict the meaning of lifetime to be signed for inspection. So this idea I have now in mind is not well prepared. So I would like to have your feedback if it's feasible to do it. So we have straight range. We have the uncertainty in the SMP curve. We can calculate failure probability at the end of the service life to see whether we need to do inspection or not. And then we have the cost of inspection. We need to send a diver there to go down to see the location. And for the straight range distribution, we have this uncertainty in the scale of the wide distribution. And here the number of years of measurement is related to the cost of measurement. And from the number of years of measurement, we have the mean of the scale of all the samples and standard deviation of all the scales value for each year. So actually, I have two utilities here. So that's all I have now in mind to determine the number of years of measurement for the stream. It's the decision for a random variable. Sorry. Number of measurements. It's deterministic. Intermittent. It's a decision. It's a decision. It should be decision. Yes, sorry. Yeah, yeah. Correct, yes. Thank you. Jess, from the audience. So you're inspecting based on a heuristic perspective, based on the failure probability you inspect or not. Do you have a rule? You mean here? Yeah, because you have an arc going into the decision of inspection. So you calculate the failure probability at the end of the service, like life, like at year 20. And then you can see whether it's fail or not. So if it fail, then you should do the inspection. So you have a decision rule? Yeah, so now it's a decision rule here. Yeah, absolutely. Your decision of inspection is not based on the risk, maximization of utility. It's based on the heuristic decision. So you use the probability of failure as a proxy. Yeah. Another question. Because I understand correctly, you estimate some stress table structure based on the strain by the end of the service. But the sensors were installed in this factor after it was built, yes? Yes. Correct. So the part coming from the dead weight and some escalations should be included as a total failure. Because in fact, you are measuring just in different between the zero reading and the actual reading. And in fact, stress table will be and also puts on this what happened before you install the sensor, yes? That's a tough question, isn't it? You can answer me. I don't. I'm not sure that I understand you completely, but. Because in zero reading and information about what was changed in strength, not in what is in fact real strain of the material. So in the configuration of measurement, we have three strains, three string gages installed on the curriculum of the tower inside. So I think what we get is the real strain. But I am not deeply in a structural health monitoring, so I cannot make the distinction between the difference in strain or the real strain. I cannot make it for you now. The comment was related to the fact that when you put the sensors, there is already a strain there. OK. And you cannot measure that strain is already there. Because you put the sensors, you can measure the difference in strength. Oh, OK. Yes. In that case. In that case, yes. Correct. It's just the difference. Yes. The noise system might be a problem. But you can see the fatigue. So you're actually interested in the aptitudes. So the absolute value, if you want to play a role with a one-month fatigue model, if you have a deep model with the absolute value of the stress, it's not like the end result. No, it's a set range, yeah. In this case, it's not that difficult. Yeah. Sorry, I'm sorry. Yes. Are you really in follow-up counting? So it's just the difference. Yeah. Well, yeah. So this is fatigue failure. Yes. So let's say it's the probability of fatigue damage. What do we do after the fatigue damage? I say if the failure probability larger than 5 to the 10 power of minus 4, for example, then I consider it's failure. That's not what we can do. Then if it will fail after 20 years, then there are problems now at the foundation. And I should send the diver there to inspect to see whether it's because of the scar or because of the corrosion or something. Yes, fatigue damage. Then you need to repair. You don't need to inspect. Yes, we will need to do something. We will need to do something, yes. But it will give us. It's an IO with an action. So you have information and the concept of the information. But to you, I think you should think of the issue of repair and action. OK. Yeah. Yes. How do you repair what you are going to repair? I think it's going to be related to problems. So you really don't have real feedback between that limited function and what you are inspecting or the decision for repairing based on that inspection. You cannot update that ever. You cannot update the damage based on what you see. No, yes. But after you repair it, then the new measurement will give you the feedback, give you new state. But if you don't repair it, you just go for inspection and then you mess it up again. In that case, we cannot update using only that minor rule. We need to incorporate also the Paris law for correct propagation. Yes. That I want to show you. But I see that Pablo already discussed with Professor Schor about it, using the two information together. This makes the way you're explaining the inspection is representing the way you're explaining. Representing it is sort of a diagnostic thing, really. But what you're saying was that the probability of failure determine whether you're going to inspect it. Yeah. But if you have a link for beta inspection, it really means that when you decide on the inspection, you know if you have a failure. That's what you imply by this graph. Yes. And if you know that you haven't failed in a month, there's no need to do inspection. You want to learn from the inspection of the failure, but the... Yeah, or maybe I just correct it to repair action. But on the other hand, it should be, yes. You read this info diagram, you make a measurement. The measurement is the mean and the separation of samples. Yes, of this. And you measure the result. Yeah. But they're not used. It's okay. If you have no link going from those results to any position, then there's no... In this info diagram, you are not using them. They will not affect the scale parameter here? No, it will affect the scale parameter. But if you think of the decision here, right now the only decision is on inspection. And the decision on inspection, the only information you will have available is whether it fails or not. That's not what you have available. What you want to say is that if you have the information about the mean and the separation of the samples. Yes. That means you have to put an arrow from those to the decision that you're going to take. So you have to add an arrow from those samples to the inspection. But when you put it inside of the inspection, you have to have information from your monitoring system. But the inspection option here is to the foundation, not for the stress. To? To the foundation, to the... So if the structure will fail after 20 years, then now I will send the diver to the site to check for the scour or corrosion or crack at the critical point underwater. So and repair it, of course. If it was... The way you will set the diver, okay. But you still have the information from the... You have the available information from the... Strange measurement. Yes. But you should add this link from this measurement and statistics to the inspection. So you mean I should have a grab propagation model inside this one to connect from that one to the inspection there? I just had a link there. Saying that when you do the exposition, you know about... Like the decision based on what you're measuring. And you're measuring straight or straight? Yeah, on straight. When you're making this model, how far are you from this 20 year horizon that you're measuring? No, I am at year 3 or year 4 of the survey. But if you think the structure will fail after 20 years, the state of the structure right now might be not the best, maybe it doesn't make sense. But maybe for a scour that makes the stress higher than predicted, then we should correct that one to maintain their service life. Temporary modelling, which we don't see here, maybe the challenge is here to make in perspective of the value of information analysis, we will need a complete decision scenario. And with the clear, also temporary model, the information analysis will meet, I think this is what we have got. And the information side is also the outcome, but the action is missing. And I think this is the basic thing in relation to a value of information analysis that some of the action is missing and that clear decisions narrow. This is what we are discussing here now. What decision is done at one point in time? And from start you may just consider one point in time of your complete temporary modelling. And then you go with the temporary dimension. This is the way forward. There is a more abstract sense. Any more points? Thank you very much. Thank you.