 monitorično, pa to je zelo teoretičnja sešnja, tako zelo, da je to nekaj teoretičnja sešnja. In v pravdu, tako, da nekaj teoretičnja sešnja. Tako, nekaj. To je basična zelo, da je to, da je to, da je to, da je to, da je to, da je to basična k mora korreponirati tamo besedna tko 뭔 je robil 325 rocketse in ato, da je ta monitor kreato nekaj to okате do k transparenci glizidi Prof.스타 Branko Glizic le carsila Danam danesci Testkola剛剛 nalazično. Ta nekaj ili zelo se s SAF że se выглядokujte to je nekaj, da imaš nekaj nekaj. To je izgleda komunitet nekaj, da je. To je počkaj, da imaš komunitet, nekaj nekaj izgleda z konceptu, z konceptu, izgleda in analizu, nekaj je v prakti, nekaj je informacij. Čekaj, da imamo počkaj, Zame obetimo, da je vse zač those nekaj zelo počešel. Všeč, ki sem nazošal, kar ljudi povsem v concludes, in pozniji im selbi agenti s testrem, potenem, da je in s predstav homeskira, in mi je veliko napotan, da se prisne se tukaj, da je bojem bila požel jih s punem, monitoring, and even when they're told the monitoring system, then they not necessarily take a decision based on what the monitoring system is supposed to tell them. So one of the argument against the installation of monitoring is, okay, look, if I ask for money, I spend this money on our enforcement intervention, so it's very clear the benefit to my instructor, so he will improve the capacity of my instructor, but what does monitoring to my instructor, Ispeči je to kapacitiv? Znamo, ne. Ispeči je to demandelo? Zelo ne. Zelo nekaj, če sem predstavljala moniom. Zelo svojo sveti, da vse soluzije, in da smo vse soluzije, taj problem, rekašljamo problem v tezijom tezijom, kaj smo videli vse. Lodice je, da vse zvali informacije. Znamo vse, in nekaj ne bo vznik, ki je zelo na koncept, da informacija je vsej, da se možem, da se zelo na različenje, in zelo vsej, nekaj ne bo in zelo na različenje, in nekaj ne bo, da je prijez, da se objez, je boj za informacija za informacija, zelo vsej, da je za informacija, zelo za informacija, je zelo vsej, in češeljamo, da zato je zelo začinil na češelje in da si je dobro zelo začinil, da je vse je začinil na češelje in da si je dobro zelo začinil na češelje in da se je dobro začinil. Zelo, da je načinil načinil končanč vse, končanč je delovno, vse je delovno, zelo začinil načinil in je to reqačne. Tako, zelo bomo predstavljati, da je bilo informacije na več semplne, idealne vse. To je nekaj nekaj realistik, ali je več zelo, da je zelo vse na več semplne vse. Tako, da je vse na več semplnje vse, zelo smo vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega vsega.Da je to predstavljak vsega, dar je Judge Meierin tudi detverstiv。 S technologies일 n nočira pos built in ci ja sreč dispute, kako je stavila arča, načo je potenčna, konkreta deka. Taj brzeg overpassa v rodu, da je tudi v pristom kampoziji, vse rodi je všim rodu. Srečaj smo počučati o dobro. Čekaj smo počučati, kako je dobro, in da smo počučati, kako je dobro, Here to is playing. We're going to take the decision. And so for this case we introduced a fictitio character. We call him Tom. Is the responsible of an imaginary design construction office in Princeton University. Is actually a design construction office in Princeton. But the manager is not named Tom. And he doesn't take the decision in the same way that we see here. But basically this is the prototype pristrnjenega adresina, ki je dobro vseh značen, pristrnjenega manjera. On je jezitaktov dopristrnja kot jezitaktov, in jezitaktov jezitaktov, in nekaj separatov za pristrnjega. Pristrnjega pristrnja, in pristrnja kaj nezitak. Zelo jezitak jezitak je zelo taj brid. Zelo jezitak vseh pristrnja vseh. taj bolj, zelo, to je poslido, da je zelo svobodne, je zelo, da je zelo, in je zelo, može se zelo, sa nečo vzelo, zelo, da se vzelo, da je zelo, da je zelo, tako, zelo, če je vzelo, če je vzelo, če je vzelo, če je vzelo, kako tače uhh, ležite, hola, pa tudi, je izgledajo. I ko je premačo, neje poviousne. Znači, ležite, ležite, ležite, ležite. Ko je, vočstne, čas, kaj je bilo, tače, si ne bo to da svetile, je tako, ležite, so pa vse tez, Zdaj si, da je atrak, da je količil z bridem. Zdaj, če je to pričo? Zdaj, da je tudi občo, ne bo, da je nekaj. Zdaj, da je nekaj. Zdaj, da je brid občat, da je trafik, da je občat v roju, in da je brid občat. Zdaj, bo, da je brid nekaj, da je brid nekaj, da je brid nekaj, in je točno od trafiku, ki je za to. A da bo se o to skupniti, o da je to četno? Oč nekaj, če peppers? Kaj mi ne pač? Hva se on začal? Kaj mi ne pač? Zdaj bo se naprej bila zaživati, še početne v 5,660 dolari, neighborhoods and, as I made, down time over one month. So with a total down time control of $139,800. Then you can say, what happened, if I don't close the bridge, if I don't close the bridge and there is no damage, of course I pay nothing. But if I don't close the bridge and there is a server damage, there's a chance of collapse. there is a collapse, I have to pay for two month of clothes. There may be some fatality and I have to pay also this fatality cost, there may be in jewelry, have to pay that. So the estimated cost for that is estimated about Gadden in $881,000. So this is basically the table that summarize the possible option of time and the possible outcome of indecision that depends on the state of the bridge. So if I close the bridge, I pay a flat rate and this is $139.8,000. If I do nothing and there is no damage, I pay nothing. If I do nothing and there is damage, I have to pay this amount. So translated in a decision tree, the decision tree is very simple. Here there is the decision node where I can choose to close the bridge and I pay the downturn cone or I can choose to do nothing and then there is a chance node and the outcome depends on the state of the bridge, which Tomz don't know. So the state could be damaged and so we have to pay the failure cost, the state could be undamaged and so we have to pay nothing. And if we want to estimate the utility or the expected loss, we can use linear utility theory to estimate that in this simple case and so the total cost would be the probability of having the damage times the cost of failure. So we have to introduce what is the prior probability to Tomz of having a damage or not having a damage. And for this exercise, I say it is 30% of having a damage and 17% for not having the damage. So we'll get back to the decision tree and let's calculate the expected utility in the expected loss in the two cases. So on the first decision case, so we have a total downturn cone of $159.8,000. And in the second case, so we have to multiply 0.3 times 881 and we achieve $264,000. So we're going to be the decision by Tomz. So in this case, the cheaper of the two is closing the bridge. So it will close the bridge based on this information and the expected cost of monitoring will be the same downturn cone of $139.8,000. OK, what happened if the bridge has some monitoring system installed? How does the decision by Tomz change? This bridge actually has a monitoring system and was chosen as a case study exactly for that. This system is very complicated actually. There are a number of fiber optic sensors based on FBG, based on OTDR. OK, but again, we want to make a very simple example and very academic example to explain in simple word how decision making work in this case. So let's say that Tomz, disregard all the information from the monitoring system has set that coming from a single sensor, which is the sensor located at mid span of the bridge deck. This is basically a train gauge that tells him what is the elongation immediately after the bridge accident. OK, how does this decision change based on information from the monitoring system? So the decision tree will be exactly the same. What change is that we are not using anymore is prime information, but we are using the posterior information. The information after receiving the signal, the information from the, the probability after receiving the information from the monitoring system. So we might calculate the way how Tom will calculate the posterior information. So we have to calculate the likelihood. So what is the expected observation from the monitoring system, from the train gauge that is expecting to get if there is no damage. OK, if there is no damage, it is expecting to see no change in the strain recorded at the bridge, but OK, there is always some noise in the monitoring system. This depends on the thermal effects of many of our causes and say that to him the normal response of the bridge is described by the information. So this elongation epsilon is what is reading on the sensor and they say, OK, if there is no damage, I am expecting to see zero, but maybe not exactly zero. So let's say zero plus minus 300 microstain, something like that. What I am expecting to see is that if there is no damage, I am probably expecting to see something like this. If the damage is very big, such big that collapse the bridge, there is no need to see anything from the monitoring system, but if the bridge is standing, we probably have a significant change in strain, say in the order of one per thousand, something like this, and there is a big uncertainty in this number, of course, of microstain. So this is what is expecting to see if there is no damage, this is what is expecting to see if there is damage on the bridge. So what is the posterior probability of having the damage? OK, we can use the athlete by his rule. Say that I read 400 microstain at my sensor. OK, so if I have a damage, this is the likelihood for damage. This is the likelihood. So this is, I can calculate therefore the joint probability of having the damage, of reading the number and having the damage and the joint probability of reading the number and not having the damage. And the posterior probability of having the damage is simply the joint probability of having the damage and reading the number with the red bar divided bar the sum of the red and the green bar. So it's basically our evidence. OK, so OK, the point is, OK, perfect. So if we have an individual observation, we can calculate the posterior probability of having the damage. We need to observe something before doing that. But here we are in a prior situation. We didn't have any accident. We didn't have any observation. And we had to evaluate whether our monitoring system is useful or not. So we have to calculate the same value in terms of to a pre-posterior analysis. So we have to the expected loss that we calculate here, for example, depend on the observation that we are going to have. So it will change based on the observation. So what's going to be the expected loss cumulatively? OK. So here we see what is the cost for any action undertaken by Tom immediately after the observation. Of course, if you close the bridge it will always pay the same. It will always pay 139.8 thousand dollars. But if you do nothing it's expected loss depend on what you observe. If you are very close to zero or lower than zero so it will probably pay very few. But if you observe something in the order of 600, 700, 1000 it is very likely that there is a damage. So it will have to pay a big penalty in this case. So the cost the expected cost is basically the minimum of these two actions. So the better action is the one that entire the lower cost so is this one. So up to this point for example it is convenient to do nothing above this value it is economically convenient to close the bridge. Observe that the three shoulder that separate the field it is more convenient doing nothing it is more convenient to close the bridge so this value it is different from the three shoulder separate the field it is more likely there is no damage, it is more likely there is a damage. So there is a field for example where it is more likely that there is a damage but it is still more convenient to close the bridge because we are talking about something an economic decision we are not talking about what is more likely the state of the bridge. Okay perfect so we have to evaluate the preposterior value of our system to do that so we simply cumulate all the possible outcomes multiply all the possible probability of occurrence so it is basically the integral of the expected cost of the cost time the probability of having an outcome so and we go back to the same formulation that we have seen before so we calculate that in the case of Tom so we calculate a cost of 84.6 thousand dollars so summary so the value information is basically the Tom is willing to pay for the information that is coming from that individual monitoring system so if there is no monitoring system the operational cost to Tom is 139.8 thousand dollars if he is relying the monitoring system the operational cost C star is given by this integral and if we calculate this we obtain 84.6 thousand dollars so the difference of the two is our value information so in this case is 55.2 thousand dollars so in this case if the monitoring system is more is less expensive that the value it makes sense for the monitoring system if the monitoring system is more expensive it doesn't make any sense to install any monitoring system what is the nature of the value information then look at the quantity that are involved and we are almost done make sure you relax so there are some quantity that represent the financial impact of the action so the cost of failure the cost of downtown ok so nothing to do with the monitoring system or with the factual behavior there are some quantity related to the knowledge of the state of the factor that again nothing to do with the monitoring system as that based on the engineering knowledge of the owner about the state of the bridge of the prior information so you see that for example C depend only on those quantity as nothing to do with the monitoring system per se so where the quality of the monitoring system enter, this enter only in this quantity is the sensitivity of your monitoring system to damage ok so in conclusion to appreciate the benefit of monitoring so we must account for the impact decision and we want to quantify we are using this quantity that we call a value of information which is basically the maximum of the owner it will do pay for the information from the monitoring system the existence of the quantity imply that the manager can undertake some action in reaction of the observation from the monitoring system if you can do nothing the value of the monitoring system is zero and we have observed that the depend of a lot of quantity to the monitoring system per se so these are basically the impact, the financial impact of an actual or the general impact of an actual and the probability the probability of a scenario and the sensitivity of monitoring system to damage and the most of the quantities depend on the owner doesn't depend on your system so thank you for your attention and I want to acknowledge Sigrid Adiansen from Princeton University all the people from Tarnac Company that are involved in the construction of the bridge and a number of people from Princeton University that cooperated in the monitoring of the bridge Matteo Pozzi, Carnegie Mellon University and finally even Bartoli that give his face to play the role of Toma in this presentation so thank you for your attention ok we have actually very short time for discussion and questions so I would like to invite Daniel Chris and Henning back to the stage and you can ask the presenters questions about their presentations or you can make some comments about what we are doing in working group 1 and we have really very short time for that Yes, Miraj Slav