 loading I can start already so yesterday we were asked to do a small presentation in which we would emphasize how to determine the likelihood of our problem in order to do the posterior analysis and to find out the value of information and since that moment we have been working all the evening then we have been sent to a dinner and this morning we have been given very very interesting lecture and after that we had coffee break and during that coffee break I had the option to have coffee which would have been nice given the previous hours of my life or to do a presentation and I did that so I tried to put together in five minutes 15 slides and let's see how it goes I don't promise anything okay so this is the case study I've been developing the last months within the framework of this cost action it was inspired by the case study that presented Sebastian although his study was focused on decisions made during operation and the maintenance phase and I used the same idea but changed the decision context to the design phase so in this case is a risk-based design of an offshore wind turbine support structure using value of information and we are again regarding the possible dynamic amplification with the 1p and 3p regions and the associated reduction in the fatigue life that the rotor excitation may cause to the structure so I will not go in detail in this it was is the same as what Sebastian presented we have an uncertain we can determine with high uncertainty the first natural frequency especially at the design phase and we need to design in this small frequency region in order to avoid the resonance hazard so how to do that for onshore turbines it was suggested to leave a certain safety margin with the boundaries of this region but for offshore first the rotors are getting larger and therefore this region smaller and smaller and second uncertainties in the estimation of the soil parameters in particular are much uncertain of shore is more expensive to inspect and therefore the as uncertainty associated with the estimation of the first natural frequency of the structure is larger at the design stage offshore so here we I propose a risk base or to solve this following a risk-based methodology and this is more or less the idea that I addressed in this case study so we have a probabilistic decision scenario we have an uncertain design performance of the structure and we have two ways of overcoming or to to manage that uncertainty we can either invest in design so to make it more reliable in this regarding fatigue I refer to the term robustness as a way of measuring if you say if you think of a crack propagating the thicker the section is the more robust would be you would have more time to detect that truck for example or second alternative is to invest in acquiring more information so we suppose there is going to be a trade-off between those two investments and an optimal solution can be found in between originally this was the Bayesian network I developed just trying to think as many factors that could be involved and then I would simplify to make it tractable so this was originally I will not go through this so much I don't know how much time is allocated for these presentations thank you very much okay you decide you can press the button like in the X-factor so yes in the end this is the Bayesian network that I have they have solved so let's go element by element we have a design set so that series of designs have been proposed I will show in next slide I think how I determine or how I yeah what parameters determine one design I have true state of the soil stiffness the soil stiffness and the design yield a probability of failure in between I skipped a few things so given one design and an uncertain soil characterization we would have an uncertain first natural frequency characterization and in the end it would lead to a estimation of the probability of failure but I skipped this part in the Bayesian network and I went directly for the probability of failure so given that there would be a risk associated with each design each design is also associated with a certain cost and additionally there is possibility to test the soil so here originally I have a prior soil characterization I can perform tests obtain more information about the soil and update the probability or the characterization of the probability density function of soil and these tests are have some cost associated as well so it's relatively similar to the problems we have been seen during the lectures maybe there are some further or more interrelations than the basic ones but the idea is not much more difficult I will skip this these are the designs so this is our wind turbine has a fixed hub height it has a fixed water depth and a fixed penetration depth the turbine is the reference and real 5 megabyte turbine and also the position or there's a site in the in the North Sea is fixed so I could have the environmental loading data so given that this diameter and thickness is fixed also by the wind turbine manufacturer I leave a very simplistic design to just fix the diameter and thickness at this height and I assume a linear transition up to this point and a constant diameter and thickness until the bottom so given those assumptions we only have to determine two design parameters and I have modified them or created sensible range that would cover what I would consider a realistic range of designs so I have six designs in which the thickness is keeps a ratio d over t equals a hundred and additionally I have considered the same diameters and I have modified the thickness by adding three millimeters so in the end I have 12 designs and I will do a risk-based decision analysis so the first step was to develop or create an FIA model in MATLAB and to determine or to map the relation between the first natural frequency and the soil characteristics note that this is wrong in this picture I didn't have time to change but this should be the spring constant I modeled the soil structure interaction with linear springs so in the end I came up with this plot in which the relation between the first natural frequency and this the spring that models the soil structure interaction is mapped and as you see it's a nonlinear relation this omega min and omega max are the the values that in which the operational range happens so this would be actually the first the 1p region yes and this would be between omega max and 3 omega min would be the actual what is called the soft stiff region so the the region in which we can make designs so here to do the dynamic time integration I wanted to do it as simple as possible although not too unrealistic so I didn't want this to get into elastic simulations or anything as such so I decided to go for an integration of the rotational sampling into the wind spectrum so into the carbon spectrum I integrated the rotational sampling so I can reproduce the excitations of the blade and the full rotor so the three blades I also have the wave modeled by John Swap and I have 11 sea lamp states modeled by a wave or following a wave probability distribution so these are 11 fatigue design cases that I took from this report in which they use similar or they use the same turbine and similar characteristics and so I chose the same position just to take the same data and this is the very basic equation of motion and I assume that the first mode of vibration was the one that covered most of the energy that would model the dynamic vibration of the structure so I integrated the equation of motion in the time domain assumed only the first mode of vibration is relevant and I calculated for one-hour time series the fatigue damage using a pilgrim minor sum and I have scaled to the fatigue life in this case I consider a service life of 20 years so at the end I end up with a fatigue life damage estimation and since I have an FE model to compute this time integration the probabilistic modeling how to map that together what I did was to generate realizations of the soil and for each realization of the soil I would run the model one hour so basically for each design I get to have one fatigue life estimation for each soil realization I generated and in the end I can map the fatigue light damage with the first natural frequency for each of the designs so basically now I have the mapping that I wanted so I map something that I can relate to consequences with performance of the structure so basically I mapped between dynamic amplification hazard to fatigue which can be mapped also with consequences and I just need probabilistic definition of the soil in order to get a probabilistic definition of the first natural frequency and therefore unexpected fatigue life damage and unexpected probability of failure so this is the prior PDF of the soil and given that prior I end up with a prior PDF of the first natural frequency for each design here I just put it six of them so given that I can obtain the probability of failure per design and estimate the utility the estimated utility and find an optimum prior design given the constraints of the model so this is this was the first part but now if we go back to the Bayesian network so we keep clear what we have solved we have solved this part of the Bayesian network which is the prior knowledge or the prior informed risk-based decision problem now we need to model the value of information part so the most challenging part is to be able to to map between inspections on your decision parameter so to be able to to represent the likelihood function and this Bayesian network is only used in discrete CPT so I also need to discretize this likelihood function so this is not Bayesian data is just built on let's say even join likelihood but the idea is that in the vertical axis we can have an indicator of the soil stiffness that come up with the soil stiffness and if I discretize as I have discretized the prior information so I have the soil can be soft can be medium or can be stiff I can also integrate I can represent the likelihood function as a conditional probability table so I end up with this conditional probability table yes and this would be the posterior PDF of the soil stiffness so yeah I didn't have time to put more slides in five minutes but yes I think if we are to discuss something here is the most or the part I found more most challenge and I haven't fewer outs completely