 from Tongji University. Actually, it's a great honor to be here to see all of you and thanks to Sebastian, also Professor O'Connor, to invite me to be here. And today I would like to introduce some of my work on this structure health monitoring. This work, I worked together with Sebastian, also Michael Farber, actually in the past, about this, actually the role of this SHM in the context, also considering the service life-integrated management. Actually, it's great to listen to this presentation by Matteo and I found that actually the basic idea, almost same, very close to each other. Yes, so first I would like to introduce this motivation of this research work. So generally, as you all know this, we have uncertainties during our service life about this in the performance of structures. So because of that, we need this health monitoring and to monitor the performance to get the information. And then, actually we need quantification because normally existing research, normally on qualification, but in risk and the reliability analysis, normally we need quantifications. And in two aspects, actually one is, I think optimization of this health monitoring and also the value of information, I think Matteo already introduced a lot. That's the general motivation of this work. And then, what we have, actually we have two parts and Matteo also introduced, actually we need this prior. So before the service life, we could assess the service life cost and also generally we have probabilistic modeling of this structure performance for different structures. Normally we have this, already we have this model for this corrosion, also model for fatigue. I think European code already in 2000 and at the end of last century and the beginning of this century we have this code for this corrosion and also many research on fatigue and also many other models. That's what we already have, this prior information. Then afterwards, during the service life we have this annual, even more often or even not so often, these observations from this health monitoring. So it could be regarded as posterior, information or posterior knowledge. So we have two parts prior and the posterior. So generally we can uniform these two things together to this one framework, this generally called Bayesian pre-prosterior analysis. That's the general idea. To formulate this of this work, the general idea of this work is to formulate this one general pre-prosterior analysis framework for this to assess actually the value of information of structural health monitoring things. So the outline of my presentation have several parts. The first is service life cost assessment as introduced in the last slide. And the second part is just to introduce some generic modeling of this probabilistic modeling of this structure performance. And the third part is just assess how to assess the value of information. What's the value of information from these annual observations to consider also the quantitative uncertainties in the data we have and of this deterioration. And then almost in the end, it's some simple example, finding some conclusions. So here we just consider one structure starting from year T zero to the end and end with year we call TS, the end of the service life. And then first we have these two states, normally failure or not failure. If structure fails at the beginning in some years, then directly the cost will be, the failure cost is called C fail. And then at year we say, like we assumed or we define this called TJ, we have some this inspection, one inspection. Then from the inspection results, we could have two actions or two we could make decision based on these inspection results. One is repair, one is no repair. We'll call generic also called do nothing. Then if we in both these two actions, then afterwards, again, we have two possibilities. One is failure, one is no failure. So then this is choose this general decision trees for this the performance of one engineer structures. Then we have different costs from these different results of this performance. Then based on this decision tree, we could formulate this, the service life cost into several parts. Actually here I think we choose five parts. The first part choose the inspection cost. So this PSTJ means that the structure still survive in that year of inspection. Then the second part means the structure failed before this inspection. So we do not do any inspection. And the third part is the this I R means we do repair after the inspection. So we make decision based on this repair then multiply with repair cost. And the first part is we have, we make decisions that we repair as that year as the year of inspection then but finally still failed afterwards before the end of service life. And the last one is we do not repair at the year of inspection but also no failure after the inspection. So this here are small R here means we consider this interest rate. So that's the five parts of this service life cost. So we sum up then this is the equation we calculated. And then the second part I would like to introduce is probabilistic modeling of this structure performance. So we consider this one general engineer structure. So just to formulate one is a time dependent at this limit state function. Here is a very general model for generic very general model for this limit state function considering this iteration of these structures. So here we have this R zero means this initial resistance and ST means time variant of this load from external sources. And this CETA D and CETA S is the model uncertainties. CETA S is model uncertainties of this load and CETA D is model uncertainties of this D. D means degradation or deterioration. Yeah, and also actually there's model uncertainties of this resistance but generally it's smaller than this external load. So normally we just omitted or we just can uniform into one this model uncertainties in the external load. And this Z is a design parameter to calibrate the reliability of these structures into some level according to the code. So here is the deterioration. As I said at the beginning that normally we have this like corrosion like fatigue. It's, but for this generic model we just consider it's accumulation of this deterioration from each year. So from the year, the first year to the year T then it's accumulation of this deterioration. And also the event of failure could be written like this. So this limited state function smaller than zero at time TI. Then here it's just one simple variation networks for this probabilistic modeling of this structure performances. Here just one thing I need to mention here is just on the top is MUD that we consider the uncertainties of these observations from this increment of deterioration. So we use hyperparameter. This means the mean value of these observations or increment of this delta. So that's the hyperparameter we consider in these patient networks. Then again we have one inspection time at year TJ. So the event of detection and also the repair that we set one criteria for this repair or not repair. We make decision. So then we, for this decision making we have to some values or quantifications to define this decision making. So the event of detection, the repair could be written like this. So if the total increment is equal or larger than some given value like DIR then we make repair. If not, then we do nothing at that time. Again the event of failure afterwards. So given the repair event at time TJ then afterwards at time TI this the event of failure could be right like this. And then this again this patient networks could be updated like not updated. Yeah, just rewritten like this considering this repair. Or inspection time, yeah. Then this is the calculation of these probabilities. The first is there are actually five probabilities. The first is the probability of the structures that survive at time at year TI. And the second is failure at time TI. That means we survive at the year before that year. Then from one to TI minus one then finally we failure failed, that structure failed at time at year TI. And the third one is repair at that year. So that means again it still survive at that year then repair because we do inspection then repair at that year. Then this the first one is we do repair but failed afterwards. And the last one is we do not repair but also again it's failed before the end of the service life. That's five probabilities. We can calculate it or formulate it here. And then now we have monitoring or structure health monitoring and observations. We just say to monitor in some years from this year we just use the symbol T monitor ST. So we're starting from this year and to do this year. So we're starting from this year then to do this annually until the end of this service life. So then we use this patient formulation we can update. Oh, sorry, yeah, see some mathematical equations. So you see some strange symbol here. Yeah. So we use patient formulations that we can update this the mean value, the probabilistic probability distribution of this the mean value of this MUD. So one assumption, this formulation is just based on one assumption that this variable follow normal distribution. If follow other distribution can have other probabilistic calculations. This is if we have else monitoring then the mean value update like this. Then again the service life cost can be updated like this. So it's the function of three parameters. One is monitoring years, then the increment from this annual observations from this monitoring and also the year of inspections. Again, it's have mainly have two parts. One is the first part here you see on the right side of this equation means that we do not have inspection after because it's already filled. That's the first. Then if not filled then we have sorry, we have filled before the monitoring. We still survive before the monitoring. Then it's again have five parts about in the service life cost assessment. Again, it's also these five parts corresponding to that five parts without any monitoring or in the cost assessment I introduced before. Yeah, then the probability and can be updated as this one. So it's have we see as you can see have we see this to put the straffy on the top of this each probability variables. That means it's updated formulation based on this monitoring. So also this is also the probability of survive and also the probability of failure and also the decision of repair and the no repair of something like this. So then it's this is the cost that we do monitoring the service life cost we do monitor that is the expected value. This means this E here means the expected value with this uncertain output of the mean value of this increment of this annual observations. So this is the monitoring cost and the value of information should be this the difference of these two costs. One is the cost of without any observation. So just the cost I mentioned that beginning this the service life cost minus the cost with annual observations from monitoring. So this is the basic actually the idea of this work is to do this very often information actually about very often, et cetera. Then here at last I would like to introduce this the example just to illustrate how to implement or what's the result for general calculations for this some engineer structures. So we assume that the structure has service life we say like 50 years under repair criteria this parameter DIR is said to be 0.2. Then the probabilistic characteristics of these random variables are listed here. So you see only one special things the increment of this data is with this variable this mean value and the mean value of this MUD again it's assumed to have normal distribution here. And the design parameter that is said to be 0.21 just to keep that the beginning of the service life this the structures have the probability at the magnitude around 10 to minus five. So that's the idea of this design parameter. And the values of this interest rate and also the inspection cost and the repair cost and the failure cost is listed as here. So that's the first calculation actually to do this we do this with Monte Carlo simulation to do first calculation for the service life course we just assume that there are no any monitoring structural health monitorings and what's the variation of the service life cost. So it's on the top this blue line it's the variation of service life cost with the variation of in which year we have this inspection so it's like this. So then after the bottom there are five different curves to see the variations of different cost the variation also with the function of this inspection year. So you can see for the first C1 here is the inspection cost. That means just the expected cost of this structure that still survive at this year of inspection then multiply with this inspection cost. So you see it's gradually down but changes very slowly because this value is we assume only to one so it's very small so it's a little down but changes not so much. But for this the second part the failure expected failure cost before this inspection you can see at the beginning it changes almost nothing before like we say the year five but afterwards it's increased greatly that's to this cost. And the C3 you can see it's the expected cost that we will have this repair then it's a little up at the beginning then afterwards a little down. That's the first one it's the trend is similar to C3 it's we make decision that repair but at the time of year of inspection but failed afterwards. Then you see it's a similar C3 but changes greatly more greater than this C3 C4 has changed greatly or more greater than C3 it's also at the beginning it's up then down gradually afterwards. And the C5 you can see the last one that we will not do any repair cost but failed after this year of inspection it's completely different with the second part so you can see it's down very fast at the beginning but finally it's gradually to zero it's almost zero it's like this. So you can see for this service life cost at around 22 or 24 it's reached the minimum it's around this one. This is the service life cost without any these monitoring. So here that's the last one this the service life cost this we just compare these two different costs one is the curve the blue curve actually this is the curve I show in last slide is the service life cost with or without sorry has monitoring and the red one that's the expected cost we have this monitoring. So this X axis for these two curve are different for the blue curve the X axis is the year of inspection and for the red curve this axis represents the year of this starting the starting year of monitoring. So you can see for this blue curve it's around 22 or 23 yeah it's around this it's reached the minimum but for the year of starting year of this monitoring then it's around I remember if I remember correctly it's around year 19 yeah. So it's totally monitoring years the optimized optimal value is 31 years so starting from 19 the year 19 we have this monitoring then will be optimal solution for these structures and this is the difference between these two cost is 2.6 you can calculate for this example it's like this one. So finally I reached the conclusions and the two conclusion one is this approach is just to introduce this for the quantification actually the aim here is how to quantify the value of information and based on these two parts one is service life cost assessment the second is this we just formulate one generic structure performance model to consider this SHM and the second part is just formulate this Bayesian this pre posterior decision theory to see the difference between the cost with without and with this health monitoring cost then to just optimize or to optimal to get optimal this SHM strategy to support this integrated management and actually there are many other many things can be done actually in this part actually like into how actually we could integrate like maybe you're more not maybe I think I believe that you are more expert on this field than me that's there are many different deterioration models and also many different service life costs like deterioration model here is very generic you can integrate this corrosion on also fatigue and also other this different degradation models and another thing I just thinking this day is just because for these networks systems and also for this large doing any near systems one important thing is where to implement this monitoring that's another issue that's for this network that because it's geographically distributed and it's large scale we cannot monitor everywhere and some scholars called importance of this information or importance of these things also can be I think it's also can be graded into this framework that's the general idea yep thank you for your attention that's all