 Once again, Dimitri, how do they introduce me? I came from, I'm coming from Lloyd's Register Foundation Center for Safety and Reliability Engineering in Aberdeen, Scotland, so it's geographically and politically still just in Europe. Okay, where I'm coming from, and in other words, what is the motivation and challenges of the study? Perhaps I should really return to the title. What I'm going to present is a framework, or really an initial sketch, perhaps of a framework rather than theory, of optimization of structural health monitoring, sensing system topology, in other words, sensor location, most for maximizing the value of information from such schemes. And the motivation is as follows. Of course, the topic of optimal sensor location is not new. There has been a lot of frameworks proposed over a couple of decades now, mostly related to, or starting from some information theoretic approaches, mostly related to measurements of dynamic signals, so very suitable for say, or related to strong to vibration based damage detection method. They basically amount to placing sensors in such place, in such a place of places where you will not lose too much vibrations from modes of interest or frequency range of interest and so on and so forth. So that's okay, those are useful approaches and depends what you want to really achieve from your measurements. But first of all, what about other types of sensors, right? SHM is not only about vibration based, there are other types of measurements, not necessarily leading to any context of model analysis and so on and so forth. So that's one challenge or one motivation for what I'm trying to achieve. And second one is really, is this information or optimization of sensor location really kind of spot on in terms of what you want to achieve in terms of damage detection, right? Is it really, are you able to reliably linked say information from vibration based method to something which is related to damage as such. So what objective is to formulate an initial really outline of a framework for optimal sensor placement, which would assess the structural condition or manage risk of structural failure, based on minimizing the failure risk against the cost of data collection, in other words, maximizing really the value of information from what we measure. So okay, so in damage detection, we want to, NSHM excluding perhaps applications where you want to assess performance, but kind of quite often activity is try to detect damage. So we really need to look a little bit in terms of how we conceptualize damage in structurally engineering. So reliability of structural failure theory, which assumes basically the reliability of a structural system is a function of reliability of individual members. Failure occurs when a mechanism is formed, perhaps plastic, perhaps brittle mechanism, due to local failures of one or more structural members of cross sections, due to buckling of the member, for example, plastic information cracking, fatigue crack, which leads to catastrophic consequences, and so on, so forth. And this is illustrated here on the simple example of a rigid frame with hinges, right? There are typically several probable modes, how this structure can fail. It can fail in finite number of modes because hinge can suddenly form somewhere in the middle of the column or so, but we normally exclude such cases because they are typically of low probability. So there will be a number of possible failure modes for the system, other than over by capital F. This is event occurrence of an if failure mode. So for this frame, we will have so-called beam mode, so-called sway mode, and so-called combined mode where the structure forms itself because plastic hinges, let's assume it's a steel structure, right, which is properly designed and deducted and so on. So those modes will happen where plastic hinges, sufficiently large plastic hinges do overcome redundancy in the system will form. And I will call small f even local failure of JF member or cross section, right? So here you have, for example, F1 would be plastic hinge formed here. In this corner, another F, small f, F2 plastic hinge formed here. Another corner and say F3 plastic hinge formed in the middle of the beam and so on and so forth. Now, probability of system failure as such is the union of probabilities of all the relevant failure modes, right? So in this case, it would be a function of probability of this mode and this mode and this mode. And I was trying already to explain, highlight, because these are known facts, probability on the other hand of each of the failure modes, each failure mode will depend where at the same time, most local failures, in this case, plastic hinge formation occur. So they have to happen at the same time. So what would be my approach from how we, how we normally conceptualize, I think that's how we do failure is to use structural health monitoring or damage detection skills to update those probabilities of local failure. I mean, it's quite obviously to return approach to damage detection, right? First point, damage detection as such, then localization and then some form of severity assessment at level three. So while I interpret the severity assessment as updating, as finding localizing damage and finding what is the extent in terms of probability. So data from monitoring systems can be used to update probabilities of local member cross section failures here, p of small, f of j. Subsequently, these local failures probabilities can be used to update system failure mode probabilities and then overall system failure probabilities. So from here, obviously, we can find update PFA. Well, it's difficult to inform that that's another story, right? Because both events are quite often not exclusive and so on and so forth. So there might be challenges there. And from those, we are able to find probability of failure. Otherwise, I'm approaching from the point of view of quantifying the value of SHM in, say, preposterior analysis. Otherwise, how are you going to quantify this value of information from SHM if you don't know the probabilities of failure? Consequences called that it is another challenge, but it's sort of another thing, really. So subsequently, those local probabilities can be used to update probabilities of modes of failure and when overall system failure. Consequences cost can be assigned, as a superb task, to failures to calculate overall risk, including cost of monitoring. You see, for example, preposterior analysis. And memories can be minimized via optimal sensor placement. And or... The presentation is about optimizing sensor placement, but obviously a very similar approach can be used for optimal scheduling of monitoring, even choice of monitoring system to use and even the algorithm you process your data with. And of course, all of those optimization problems are very increasingly complexity, but can be treated as together. So how would such an optimization of system look like? So let's say we have a truss, perhaps a bridge, and so on. In this case, this is not redundant structure. This is a very serious system, but that's perhaps not that important. You can think of placing different types of sensors in different places. Not often are shown, right? In some cases, this is perhaps an accelerometer, this is a strain gauge, and so on and so forth. Of course, sensors can be placed in many other places. They can be placed even inside the structure. For example, to measure ground motion or you can have a wind system here on the approach to the bridge, and it will be technically of all the possible locations of sensors you can describe the topology by such a vector, which will have binary vector, which will have one, if you do place sensor in your chosen location and zero if you don't. You monitor the collected data from the sensors, multiple sensor systems, those could be strength accelerations and also four of many other signals can be collected. Some signals with environmental conditions like temperature will likely be necessary and so on. So these are the time series from individual sensors. They will form a vector m of t. You hardly use really, of course, data as such. You extract features, maximum strengths, perhaps natural frequencies, perhaps some other features. So this is Eren. And again, this is what we think really, really what you get from your monitoring system to failure of your system. I think that those features very soon for additional marking it's always done from features to some other parameters which relate to failure. The other point is here that I think the critical link is that it will enable the term... But those parameters which you extract from measurements they have to enable the termination of reliability with respect to the failure modes, which I previously shown. Now, certain things do not really relate that well, right? Failure modes are typically be described by traditional engineering mechanics by strengths, stresses, and their results, perhaps moments, perhaps axial forces and so on and so forth, right? I think there is a challenge because the features or even parameters which we try to... and detected as such are not often suitable or immediately suitable to go to failure modes and have probability span of failures. So, critical but challenging and currently I think underdeveloped link. Obviously, well, as I already emphasized if you want to use your system to provide complete information of what you are doing, you need damage localization and security assessment from your system unless it might be a viable strategy in some cases you just want to detect damage and then send people in with some entity to do some inspections. I think it's going to be a full solution and clearly your system has to go beyond just damage detection as to localize damage and assess security. In critical analysis we will need probabilities and some modeling of damage detection method performance for individual members or cross sections to find those probabilities, right? Next here is the... so here I have on the horizontal axis DM, the measured parameters which relate well, hopefully well to the... damage probability, to failure probabilities and here I have the actual values of those parameters happening in the structure because it's, for example, longer than so on and there is a joint probability distribution function here sketched this way. Conditional probabilities of our parameters... our measured parameters conditional on the actual parameters having certain value will look as follows and this is what you can establish in the lab to study, right? You can... test your method in this way but we would like to have this method if it's going to work well it has to be accurate that means mean value of the parameters that you measure or establish for measurements will have to be same as as the actual parameters and small standard variations so perhaps this distribution is not really that small, right? but this will give you a pre-decision. If you set up threshold for TM so certain threshold for the values of measured parameters and threshold TA for the actual values everything above that is actual occurrence of damage, right? So for example, stress has exceeded yielding stress or something like that Now here are the values of measured stress. Typically you don't want any damage detection you don't want to detect damage you want to detect the fact that the system is tending towards damage, right? So the threshold for detection will have to be smaller than the actual, as shown here than the actual threshold for those parameters to get back. Now by integrating this probability distribution function which might be a challenge but typically you will have a vector of parameters in a structure so by integrating those probabilities in all those four regions defined by the TM and TA threshold you will get probabilities of two positives in your detection false negatives and false positives which you need for pre-posterior analysis later. So after that decisions can be considered with for the pre-posterior analysis you will have no monitoring case or on the strong central times in this morning, right? And you will have another description for if monitoring system configuration of an if monitoring system is described by this vector which shows you the position Michael had a nice kind of stack of those those decision trees related to different systems and so on, so imagine that there is another decision tree like that for another configuration of the system and so on and so forth and then out of all those you can find one that will minimize your overall cost those building remarks so a framework for optimizing sensing system topologies for maximizing value of information has been outlined for assessment of structural condition or managing risk of failure based on minimizing the failure risk against the cost of data collection basic premise is to use measurements to create features but not into parameters that relate to local member or cross section failures for example information of plastic images because that would be a symptom of the probability of failure in the traditional I know about the other ways of approaching it but in the traditional structural engineering or reliability engineering structural reliability engineering context and framework these parameters from measurements may be used to update local members cross section failure probabilities system failure load probabilities and finally total system failure probabilities assigning cost sequences or cost to failures and using pre-posterior analysis to calculate the risk reductions associated with each candidate sensing topology or perhaps cost increases and choosing the topology that is optimal in this sense there are of course a number of challenges I haven't done in numbers and so on just assisted the framework the framework challenges for application to really complex structural systems will include determination of all relevant failure mechanism and associated probabilities so this is really that picture here or this is a simple structure it's not so much about SHM it's a well known challenge in failure analysis as such the only thing to expect here in this framework on top of this challenge you will have some other challenges constructing teachers from measured signals that correlate well with reaching maximum capacity in crucial members cross section this is called SHM or damage detection activity called challenge and so on challenge that has I think not yet been definitely on crackdown or anything like that so this is a challenge I think that again I have no so much practice or experience with that I think when optimization problem itself might be very challenging right so efficient computation algorithm for solving the optimization problem are useful as always we have to be pragmatic here we have to be pragmatic and here we have to be pragmatic and just get rid of cases which are hopeless which either have well are not going to be optimized focus on the first insight or failure modes which are highly unlikely and so on and somehow start with a smaller top of possible solutions all right so that's it I would just like to thank Lloyd's Register Foundation who kind of support financially the operations of our Safety Reliability Centre in Aberdeen and last but not least thank the second of your time I believe most of you of whom I have emailed addresses I myself are organizing a mini symposium on structural health monitoring at NeuroDyne Conference next year around September abstract argue September 12th this year right I have received already some abstract so thank you very much I would like to warmly encourage you to submit more abstracts now Alvaro who ran the whole conference in Porto two years ago conference okay so three years that was in SHM symposium just in case if you need any information you can just google it very easily taught me that SHM strength two years ago in Tokyo was really a conference in Porto was really a conference within a conference with 150 papers which brings me to the topic I notice that the symposium is targeting the Stanford workshop Stanford workshop has recently been announced the overlap but this is in Europe and is about SHM and so on so I think the choice is obvious thank you very much