 I'm Sebastian Töhnz and I'm German, I'm sorry. So welcome, welcome to the training school on the value of structural health monitoring information. That's exactly the topic of the course that we are having. We have been starting late 2014, basically we have started in 2015. There have been quite some activities. Mainly workshops, conference sessions, papers we have been working on. But this is the first training school on this topic of the value of structural health monitoring information. So what are we after? We are after the employment of Bayesian decision theory to the topic of structural health monitoring. And the most powerful tool we have in Bayesian decision theory is free posterior decision analysis. Which means that I have pre-posterior knowledge. Which means in the context of structural health monitoring that I can model my structural health monitoring data. And if I can model them, I can find out what I can do with these data before I have it. And if I can find out how to utilize these data, I can optimize my SHM system and my data before implementation. So this is what we are after and are asked to be able to perform a value of information analysis after the completion of the course. You should also be able to select appropriate decision analysis types. Meaning addressing pre-posterior decision analysis, that's one type. But there are also analysis types on how do I perform a analysis once I have my decision scenario and the decision tree. So this goes to the implementation of the analysis. And then we are building upon the Bayesian decision analysis on probabilistic models. And here we provide the background that you can develop and apply probabilistic models. And these probabilistic models, they are basically about modeling the relevant uncertainties we have where we have limited precision in our models. When I'm talking about the precision of models, then we can take a mechanical model. If you go to reality, there will be some differences between our mechanical model and the predictions we have. And what we observe in reality. And the difference between these two is for instance called a model uncertainty. And then we also provide the basics of structure reliability analysis and measurement information modeling. So this is basically the two models we are connecting. It's the structure performance, how the structure behaves, and how does the measurement system perform and how they are interlinked. Okay, there's much more to tell. But maybe a few words to the setup. You all have got this document that received this document. And we are already in day two here. So this will be our day-to-day. There will be two more lectures. I'm doing the introduction and descriptive statistics. Jochen sitting behind. We'll take the second part, probability theory fundamentals, and then probabilistic modeling will be done by Professor John Daz-Kazerov from Albuquer University, from the Norwegian Technical University. So this will be our frame basically for every day. Three lectures. It's quite intense, I presume. There are many, many topics. And in the afternoon you will have some time to basically work on your own. We will provide exercises you can go through in the afternoon. You can do a self-study. You can do reading. You can do programming. You can ask us if you want a certain topic to have more exercises on or to be elaborated again. So we will flexibly organize. So, and day two, that will be tomorrow, Tuesday. It's a tree of us again, but in different order and on different topics. And we have in the evening a train scooter. And on day three, I think this is the most important day. On the previous days we are building the funeramentals, the basics, and here we are going into the decision analysis for different perspectives. The Bayesian decision analysis, then specifically on value of information and two lectures. And I'm very happy that Karl Meilings, sitting over there, joined from the US, from Carnegie Mellor University, together with Matteo Potsi, who will be on Skype. He could not be here today and tomorrow and the day after tomorrow. But I'm very happy that we have also a lecture from you here. And we will close then this on the training school on, there's closing remarks written. It's of course not the closing of the training school, but it's the closing of the lectures. And the day four, we have all these, okay. And that's the day four, that's the Thursday. We start to work on your report task. We will find out what it exactly will be and how we organize. And then you have support us from the working groups of the course section. Okay, so this is an overview before starting the introduction lecture. We have quite many, but I think it's worth that each of you says a few words. Of course the name, the affiliation and maybe a few words about value of information, what you expect and what your background is, maybe. Okay, who wants to start? I start. Good. Someone has to say, I'm Adrienne Tamour. I'm a lecturer in England at the University of Best of England, which is in Bristol. And I'm a senior lecturer doing bridge monitoring, and mainly work with mainstream arched bridges, but monitor other types of bridges as well. Hi, I'm Iris Consida. I'm a civil engineer and a researcher at the University of Bristol, England, working on monitoring bridges and other types of structures, especially using XLR filters. Thanks a lot. Maybe if you complete the first one, we'll tell you. I'm Iris Helger from Portugal. I work as a major consultancy for the Irish Institute of Portion, where we have some investments on monitoring, and we are looking forward to applying these in realities. I'm interested mainly from the practical point of view, and it's a quite vulnerable action, also, to train schools. And as I said before, I'm a Ph.D. student of the Laboratory of Risk Ants and Health Sciences at Porto de Milano. I have a background in civil engineering, but now I'm studying at the Energy Department. I work at condition-based risk assessment. Hi, I'm Amacler. I'm a Ph.D. student in the University of North, and I work on the special temporal intimidation of monitoring for concrete structures, as if in marine environments. Hi, I'm Benjamin from France. I'm working as a Ph.D. student in the same laboratory as Romain. I'm working on the monitoring of marine life for 14 minutes a night, and the structure, the reliability of those marine life. I'm Sufie Mahfoud, I'm an Assistant Professor at the University of Belamon. I'm going to the Earth Cook Engineering, but I started recently in structural health monitoring, and I, one of my expertise is in the field of decision analysis, so I'm trying to see how the tool can be applied to a structural health monitoring unit. Hi, my name is Moonka. I'm from Slovakia. I'm a Ph.D. student. I just started this September, and my supervisor and the group of these other Ph.D. students, they did some monitoring of famous regis in our capital city, and I would like to learn something more about the value of this information. I'm Mita, I'm a Ph.D. professor at the University of Belamon. I'm working with a structural health monitoring unit at the University of Belamon. This is much of a structure that will be exactly the same. Hi, my name is Tomo Zegir. I'm a researcher at the University of Ciena. I'm a Nehola architect, and I work on the construction of the most specific area of this topic. Hello, I'm Toma Kobiacki. I'm a Ph.D. student at the University of Technology in Poland. And I've been working on the application of health care technology to monitor structures. But also I'm working in an industry in a company which implements structural health monitoring systems from a variety of structures in Poland. Hi, my name is Andréle Roukolo. I'm a Ph.D. student from the Polytechnic University in Belamon. I have a background in civil engineering, and I work on structural monitoring of authorities like our staff or British and so on. And so I'm interested in value information. Hi, I'm D. Francesco. I'm a Ph.D. student at the University of Surrey. I just started as well. I've got background in mechanical engineering, and I'll be looking at the T models and you'll see what I've got. I'm from the University of Belgium. I'm currently finishing my Ph.D. on structural robustness without further ado. Hello, everyone. I'm Marco Ciberra. I came from Polytechnic for the Torino. And I got lucky as a civil engineer, but I just started officially four days ago. My Ph.D. in aerospace and so on. And I'm focusing on structural engineering and air wings and civil aircrafts. Hello, I'm Dominic. I'm working at the University of Belgium in the bridge department. And I'm dealing mainly with assessment of existing bridges using bridge waiting options. So I'm interested in the structure of that monitoring and value of information. My name is Slav. I'm coming from the same university as Dominic from the University of Zagreb. My main field are timber structures. But I have some experience in monitoring of wall structures and heritage buildings. I want to implement the knowledge from here to these kind of structures. My name is Wabi. I work at all of the University in Denmark on life cycle assessment and life cycle courses and performance of bridges. My name is Jochen Krüder. I'm from the University of Science and Technology in Frontenheim, Norway. I'm a professor there in Instruction Engineering in general. But my special interest is to answer the modeling in engineering. The current project related to this topic environment is reliability assessment of moving lines and short platforms, bigger ones. And also assessment of concrete bridges or broad bridges. It's also named the topic and much more interesting. Hello, my name is Wabi. I'm from the Netherlands. You know, a research institute. I work in the department of the structural library. And we assess the civil infrastructure of networks in the Netherlands in general, some regions that are still not spent so long. And with respect to work and asset management and maintenance and condition based asset management but also assertion. I have much interest in that value of information that we're going more accepted also as mentioned. I've recently completed my PhD at Carnegie Mellon University. My advisor was Dr. Theo Pazzi in the beginning of her later this week which is related to my research topic which was using value of information to optimize the placement of sensors and more sustainability. Hi, I'm Lisa Jeves. I'm also from the Netherlands a research institute. I work in the department of structural library as well. And I work in general all kinds of different regions and roads types. Hello, I'm Chiara. I'm a PhD student from the University of Las Vegas in Southern Italy. My research topic is the structural engineering. And especially the results for the damage to the detection and the localization on possible concrete structures. Hi, I'm Lisa Leper-Pistone. I'm running a bit of expertise in interest in the structure of monitoring bridges offshore structures and railways. My name is Claudia Neves and I'm a PhD at KTH.com. I've been pretty much still working with machine learning techniques applied to monitoring bridges. So pretty much developing algorithms that can look at measurements on a bridge and from there we can automatically assess if the bridge is damaged or not. But of course we have these kind of false diagnosis and so at this point I would like to turn my research into the value of information. I am Leper-Lemon Jairie. I'm an associate professor of political science. And part time is I think professor of architecture in France. And I work mainly on structural and specific field is damaged detection and localization. And since I've been participating in this construction now I'm starting to work on management of the emergency and the value of information from structure monitoring for the management of seismic emergency. Hello everybody. I'm I came from Spain. And I recently started with the interview in front of him. I took a life by the open. And the value of information is going to be one of the main parts of my PhD thesis. Hello everyone. I'm Leper-Lemon Jairie. I came from Prague. I'm a PhD student and she took me to the University of Paris Institute. I work in department of structural engineering. So my topic of my research is monitoring and optimizing structural industrial life with towers and chimneys. Hello everyone. My name is Leper-Lemon Jairie. I'm doing a PhD in Vienna, Austria at University of National Resources and Life Sciences with the topic of assessment of concrete bridges and with the addresses of bridges and networks. Hello. I'm Filippo Salopianakis. I'm currently finishing my PhD in Cyprus, the University of Cyprus. My topic is mainly about predicting the time for rehabilitation of bridges for the different type of bridges that exist. So of course the value of information of a major issue. And I'm using the National Bridge Inventory of the U.S. to perform this done. Hello everyone. My name is P. J. Lijeno. I'm a PhD student in the Federal Institute of Materials and Testing and Research in Berlin. And my PhD topic is about quantification of venue information for the towered structures. So I'm dealing with bridges especially as my school has it. Hi everyone. My name is Sima. I'm from Al Gore University working with John Gosko so once again. And I also look at my PhD looking for risk assessments of wind turbines and bridges. So this course will give me a lot of value. Okay. Thank you very much. We got this nice equipment here. So let's start the first lecture. Still there's a lot to talk about for an introduction. Here we have a scheme which we just hopefully better visited in the next slide. Which is one of the results already of the research work we have already performed in post-action. And it has also been published. So this is the references. Here we have it we have it larger but it's not large enough. Yeah. That's a good idea. Thanks Carl. You may zoom in to one or two on this slide. Anyway what you can recognize here is that we have a desktop model and we have the actual structure. So this is one of the basic things we have to be aware of in its reality and in our models and and in our models there's this side here the input is that we change the system by repair action maintenance actions and also renewal of the systems and from our actual structure from our reality the environment the structure will experience exposures and also in terms of risk analysis maybe one environment it may have a limited robustness So these exposures are modded so they find their way to our desktop model and here we have the part where we can collect information here are basically the strategies for monitoring inspections and choice of indicators technologies and they are all going in here being indicators because we have measurement basically referring to our actual structural behavior so it will come over indicators and observations into our models and from the observations there may be basically have to find out there may be decision rules on with what observation we have here which action should we do here meaning repair maintenance and then we can we can optimize in terms of reliability, availability risk reduction life cycle costs and resilience so this part or this scheme will always come back to us I hope in the future and higher resolution and this is again the day one here we are talking about the probabilistic fundamentals and modeling so that's basically the background for this scheme we will focus on the structural reliability that's basically modeling the modeling structure and the performance of the structure and here we have a basic scheme for risk analyzers so we may have exposures that's what we had here also and then we may have direct consequences of damage of the system component but there may also be then consecutively indirect consequences they are arising from the functionality loss of the structure so we are focusing on this part we will talk then also on how to collect information and how to model indicators and observations so that they can actually affect this model and this is basically the part of the third lecture so we are going from structural reliability analyzers that's usually referring to one component to structural systems having more components and then we are talking about the collection of information and modeling this information so that it can be feed in our structural reliability models or the structural reliability models can be updated so that's our second day and the third day is the decision analyzers that's basically the complete frame and we may have an introduction and the Bayesian decision analyzers and then there's already a value of information analyzers from two perspectives so this is the lecture today this is the introduction and we call it descriptive statistics or elementary data analyzers so we look at how we can describe data statistically by means of numerical and the graphical description and also how to how to describe data pairs this will be for few of you this will be very familiar but it provides the background we need here for this lecture so we have one all for that maybe I cannot go through all in detail but I will focus on some very relevant aspects so elementary data analyzers so we the next slide so we have may have here some numbers and this is not good for communication this cloud here so that's why we need some concepts we all know how to describe the data and what these data you have just seen this is a comprehensive strength here but it can be all kinds of other data data basically but also related to natural hazard flutons, sea level data or snow height data for instance so when I'm coming from the data I think this is what we should have in mind here I'm now I already have data now that means I have information and then I can simply describe them with me it's the sample so it comes from the data sample media so that's the value corresponding to the 0.5 quanta we will see in a few moments and also the most frequent value this is called central measures so I'm measuring the average content of my data mean median mode, three different things so and then I have an information about the central content of my data but there's data around and how do I describe them that's dispersion measures so at the sample range that's the easiest measure so the minimum and the maximum that's the most easy measure I have a variance and standard deviation so this sounds probably very familiar to most of you and coefficient of variation so here this measure is basically relating a dispersion measure to a central measure by the variability relative to the sample mean so that's the coefficient of variation so there's a difference so there's often a mistake there's a difference in the variance and the coefficient of variation and there's also shape measures so how do my data look like and then see this in a picture meaning very clean but here is the definitions of skewness and the kurtosis and it looks very similar to what we have here for the sample variance still the resolution it's not so good but there's a square here two there and if we have very similar expression and we have three here so this is the shape measures called skewness and the kurtosis skewness is how misaligned the the shape of the data is and the kurtosis is about the peakiness but we will see so central measures, dispersion measures shape measures and that's our concrete compressive strength here it is unordered here it is ordered and this is a one-dimensional scatter plot so that's already graphical data description so that's the simplest thing we can do with one-dimensional data it's a scatter plot and we then see the range from 24 to almost 40 or a little higher I think it's 25 here we already guessed the mean here of the data graphical description to be added we can do histograms when we do histograms we need basically intervals where we input the data and we count the data in this interval so we define an interval here from 23 to 26 we have one observation here and if you related to the overall observations this will give a frequency and then we can also add the frequencies and then we have the cumulative frequency okay and this is how it looks like okay this is two examples and we have and we can plot the same data with different intervals and we see that here the information content is obviously not as high as here so when we do a histogram we need to have a look at the interval and to see that the interval provides us meaningful way of representation this is a cumulative frequency plot so we had the last column of the table okay so this is some very basic concepts of how to describe the data by means of numerical concepts central dispersion measures, shape measures very similar concepts for the graphical representation so where is that relevant it's relevant for for instance for the distribution of the of concrete aggregates so this is basically a cumulative frequency plot of concrete aggregates and here we have the sizes of the aggregates and then they have different curves and if you mix concrete you need to be aware that you have the right distribution otherwise all things of problems can occur to the mixture but also to the concrete pouring so if the reinforcement is too dense and you have quite some grains which with a high with a large size then concrete gets stuck and doesn't go through the reinforcement okay this was one example where we need obviously the graphical data description is there an example which is even more relevant than this one is the distribution of grain sizes any examples or of course there are many examples on our functions we measure strains and we may have a histogram of the strain observations right or what is more relevant coffee so we have the histogram of the grain distribution of coffee of grinded coffee for a filter holder machine like this I think that's an E61 brewing unit so we have here two peaked histogram we have one peak here so that's microns so that's that's in microns and this is about 70 or 80 microns there is one peak and then there is other peaks and this is two or three different grinding coffee grinders and they all have the same peak here anybody knows where that is relevant for so it's obvious that the peak here it's exactly at the same location only the density is varying there is the same peak you see that the peak is not exactly at one location and the shape is more different than here so the first peak is for taking the pressure out because the pressure here will be around 10 bars the 10 bars water will come and then if the coffee drops out the pressure is zero so the first peak is about taking the pressure away and the second peak here this is about the taste and of course a grinder only functions if this peak is there otherwise you cannot pour it okay this was a relevant example for the application of statistical data description we can also introduce the concept of quantiles so a quantile is calculated with the ordered data by the way I've sent just before the lecture I think I was able to get out the email sending you the lecture slides so you should have it on your computer already and we will try to solve the resolution problem for the next lecture so you take the ordered set of data and then you calculate the quantile with the number of the data or the overall number of the data and the number the ordered number here and then you can assign the quantile and per definition we saw it in one of the first slides the median is defined as the 0.5 quantile value so if you have a quantile plot you can read the median another graphical information is the 2k box plot so this is the most informative plot we are seeing today because it contains quite a few elements here in the plot for instance we we have an indication of the range of the range with the ABA adjacent value and the lower adjacent value that is referring to the quantiles the 0.75 quantile plus 1.5 times the data range and the range was the minimum at the maximum value so this is how this is defined and there may be even values outside because this is not the maximum of the data and this is not the minimum but it refers to the quantile and the data range so we have here the ABA quantile the ABA quantile is basically the 0.75 quantile and here the lower quantile and we have a median indication here and R is our interquartile range that is where 50% of the data lie so for our concrete compressive strength data the 2k box plot looks like this we have a median of 33 and we have a range indication here we don't have outside values there is no data lying outside and our ABA adjacent value is 39.7 and the lower one is 24.4 so the elements of graphical data description is one dimensional scatter plots it's histograms quantile plots and 2k box plots so these are the main elements there are many more representations but I think this is quite so now let's talk about how to describe the data sets now we have observations of 2 random variables or 2 data random variables is the mathematical concept we will come later today we will get to this later today so we have x observations and y observations and we observed this x value and this y value so let's get a plot what can we take out of this plot here exactly what is the correlation no correlation you already know but here basically I have the same number of observations for x and y if I don't have the same number what am I doing then anybody has an idea that was already on the slide but maybe the resolution wasn't high enough you do a QQ plot so here well this is a table here where you have an observation for x an ordered observation for y and then you calculate the quantiles for each and then you can create a QQ plot so you don't plot the value of the observation but you plot the quantile and then you have a QQ plot a quantile-quantile plot and then you can also conclude the distribution of the data you have at hand so if this was number of cars in one direction and this in the other direction if there's well this is the QQ data this is a straight line and if the plot results in one line the distributions are identical okay so this is for multiple data and then there is also some numerical concepts on how to describe two sets of data so we have here the concept of the sample covariance and the coefficient of correlation it's very similar to one-dimensional data analysis so this is basically the variance if a Y was put to X then you have the variance if you have two data sets X and Y then you have the covariance so CXY CXY is here and if you divide it by the I think this was a symbol for the standard deviation of X and this is the standard deviation of Y you have the correlation we will need this in the lecture tree on day 2 so tomorrow we will come back to this so the basically the covariance has the same information content like the correlation but the correlation is normalized and it's normalized by the standard deviation so what is the range of correlations? yes and if we calculate the coefficient of correlation like this is it linear or nonlinear coefficient of correlation? yes it's the linear coefficient of correlation that's nice ok we complete so there's what is the coefficient of correlation approximately close to one ok this this is right but ok I will draw a straight line as straight as I can draw a line so this is a straight line right or it could lie even here but this looks more like like a curve it would look rather like this so it will be close to one let's say it will be 0.9 if I take the linear coefficient of correlation how can I identify or the point is that I'm identifying the linear dependency of this data here and here so in a mechanical model where do I find the linear dependencies? yeah yeah what example could that be? yeah it's the linear elastic zone and if I'm taking measurements of the deflection and at the load then I would have this relation so that means I can model my dependencies directly with a mechanical model the linear R elastic model but if I don't model the dependencies by this mechanical model I can model them statistically with the correlation so if we do statistical concepts in engineering we should know the underlying models and if you know that there is a mechanical model underlying this this data then we have the explanation for the dependency and if we just see the data and we analyze the correlation like we do it here then we can identify with this coefficient of correlation the linear R dependencies how do I identify the non-linear R dependencies? like the dash line here yes yes ok yeah yeah yeah very good idea to transform it to linear data so you have non-linear data you transform it to linear data and the idea had someone before you and this guy was called Spammin and Spammin introduced the Spammin rank correlation and here with the Spammin rank correlation your linear linear rising data in a way that so mathematically written it's simply that there is a rank operation operator here here and here and by transferring the data into ranks it's a very simple most simple linearization if you yeah that's basically the Spammin rank coefficient of correlation so and then with the Spammin rank coefficient of correlation you will identify the non-linear dependencies and then so this means the non-linear coefficient of correlation will be it's a little scattered so let's say it's 0.95 and the linear coefficient of correlation say it will be 0.85 that will be lower because with this one you are identifying only the linear information content and with this one the non-linear coefficient non-linear coefficient of correlation the non-linear dependencies so let's have a look to these examples and so this is straightforward for the linear coefficient of correlation and it's written on the slide but let's think of this one so suppose it's y-axis and then x-axis here and how large is the non-linear coefficient of correlation and estimation yes, okay there may be something in it but it's not the symmetry or maybe it goes to the symmetry symmetry that's right any other opinions it looks like a function it should be close to one but this is linearization operation by Spurman maybe it's worth to consider other linearization operations but what Spurman does or what the Spurman rank coefficient of correlation does is it only identifies B-unique dependencies so only for one x-value there's one y-way but if you have symmetry or if you have a curve like like this you don't have a B-unique dependency so here you would need other statistical measures to identify the dependencies you cannot do this with the linear coefficient of correlation or the non-linear coefficient of correlation and again for the coefficient of correlation we need a relevant example what could that be any ideas what else that could be I can't with you I will repeat it could be wind speeds and measurements at wind turbines here we have a complex interrelation from the wind speeds and then by aerodynamics it's transferred to the structure and to the turning of the wind turbine energy production and then there's all kinds of mechanical systems introducing loads in the structure so here the models are very complex and you cannot know from the beginning what the correlation of the data will be and what effects will dominate over the other effects I think this is a very good example so here statistical data analysis is sometimes really necessary and we will see also in lecture 3 of day 2 even with simple probabilistic models and some random variables have full correlation some are defined as being uncorrelated but what is the correlation of the limit state then so this is not so easy we can do this lecture 3 on day 2 ok I give you a relevant example so it's the relationship between the stock population and the birth rates so there has been a data analysis on the number of stock breeding pairs and the birth rates thousands per year birth rate in a region and there is scientific publication about it and we see it's correlated there is a dependency but there's also here again we have the number or here we have the number of stock breeding pairs and here we have the land area so there's also a dependency of if the land area was large then the number of the stock breeding pairs is large and of course there is the birth rate which is also dependent on the land area right so I think this illustrates what we have been discussing about before we are engineering we have for instance mechanical models where we know that if two sets of data are reproduced by a mechanical model then we know by the mechanical model what the correlation dependency should be but we see already with the example of wind turbines this is also an engineering system but it's a very complex system much more complex than a building or a bridge because it's basically a machine here we already see that we cannot really know in advance the dependencies of the data which we get and then for this kind of data analysis the underlying dependencies are unclear and we cannot conclude basically on the dependencies by the data analysis we know that there is a dependency but we don't really know where it comes from unless we have a model for reproducing this data so the most important things for the data pair description is that we have numerical measures the sample covariance which is closely related to the variance we have the coefficient of correlation which can be simply calculated out of covariance what we had in the lecture we cannot identify nonlinear dependencies which are very unique nonlinear R-definances with the Spurman rank coefficient of correlation and we have these scatterplots and qqplots to compare the data or the distributions so we need the elementary data analysis that we have a common understanding on how to describe the data and to communicate we have here in the room quite some SHM engineers or SHM researchers but the essential thing in the cost action on the topic of information is that we cover both the SHM engineering and modeling and the structural engineering and modeling we need both and this is what the lectures are about at least between these two domains we need to communicate this goes to the data analysis but this goes to more specific concepts than like the probability of indication for instance with the probability of indication you have that's basically the probability related to the damage size and how good you are able to identify this damage size with your structural health monitoring system and I would and if you have the probability of indication then there is a very clear way of how to update the structure performance and this is a more specific way of communication between these two fields the SHM engineering and the structural engineering so yeah I think that's the contents okay and then we we have the task for this lecture in the afternoon and that's basically going through the self-assessment of chapter 3 in the book of Mayor Favre Statistics and Probability Theory of Engineering Decision Support so please in the afternoon there will also be a lecture around and it can be I think in this room and we will tell you whether there is other rooms available so that you may work can we just ask about this book where do we get the book how do we get access to the chapters right? don't have it, I should say that this is around a lecture plan or a training school plan of environmental habits here I will okay so that's the basic contents it starts for this lecture it starts easy but there will be a lot more and a lot easier things may come a little complex so maybe we we go to our how we could discuss something something else so we have the data analysis I've shown you the scheme if you load the lecture slides you should also have in the afternoon a closer look to the scheme so this was the first slides here and let's talk about the basic elements of information analysis and we do this we do together some of you know but most of you don't so what do we need if we want to if we want to assess the value of structural health what elements do we have give me elements and events what else do we need okay thank you for this point this is a very very important point but it's a little different so we need basically how to say we need an SHM system and analysis data analysis but we don't need data so this was my comments or my saying in the very beginning we have a pre-posterior decision analysis a value of information analysis a pre-posterior decision analysis I want to make this point very clearly but we may take something else out of the data but okay we don't need the SHM data but we need to know to model what SHM data we may obtain distributions okay we need distributions and you thought of the SHM yeah okay we need to somehow predict the SHM data but this will be answered so that's why our prediction will be a distribution so that's probability distributions we have to be aware of the first line the event that leads to consequences this is the one side of the analysis and now we switch to the other side which is the structural health monitoring this is the more or less traditional way to think for engineers first thing about the measurements but we have to be aware that we have to represent an event that leads to consequences the prediction of this outcome of the event is associated with uncertainties and the results of the SHM should be related to these uncertainties that's important yes thank you Jochen this is the way the stats we will take today tomorrow and the day after tomorrow but let's be a little more basic probability distributions we find here for the SHM outcomes we need outcomes but of course our probability distributions are also for the events here so this is basically the day of today our underlying probabilistic models and there these probability distributions as one major mean of probabilistic modeling they are underlying the complete analysis so we need SHM and event outcomes what else do we need actions ok what else so let's think in the direction that we would like to maybe we need one more event here so I said there are many of you who have been talking with SHM systems and data but the basic other discipline we know is what the structure, the structure system so ok we have now four main points we need in a value of information analysis now I'm asking how can we work with all these elements but yeah so how can we connect this probability tree probability tree yes something that goes in the right direction pardon yeah or a decision tree yeah so we need to define decision scenario out of it so that we have our system we know what we can do this can be repair or maintenance actions and to the structure system there may be an event which causes consequences like the failure so any structure assessment design is against failure that's our limit state functions ok so we have structure system actions we can describe the structure performance with events and consequences then we have SHM and how is that connected now to these elements SHM should give me information about the condition of the structure yeah if we understand which element could be more probable than yeah yeah ok this is the right key words SHM is connected to the structure system performance and should somehow give more information about the events with the consequences yeah this is very good ok so and this basically goes in a decision tree and we should also introduce here the decision scenario where the decision tree is part of it and then we could also ask ok we do a decision analyze but what are we deciding we may be deciding if it's like SHM system or we may be deciding between SHM and different SHM strategies so this is our decisions ok maybe the ones who know stay a little quiet because to engage all the others who may not know already we decide with the value of information analysis about the SHM system so this is very straight forward and this is the value of SHM information about what else do we decide yeah where was it yeah ok but you already know oh no this is the actions ok so we are deciding about action with SHM data and what the best SHM system would be available for this decision anybody knows what that is so if I would like to model actions or SHM then I use a rectangular node and that's a decision node so that means that we have other nodes about the structure system performance and the SHM outcomes this is chance nodes this is associated to probabilistic models and this is related to the decisions I've now built the very basic decision tree for value of information analysis we have here SHM system or strategy also the data analysis all the elements we need to obtain information so this is the SHM outcomes so this is our that describes how we do the SHM with what technology as I said and what data analysis is rather describing and different kinds of strategy and then it's the SHM outcomes so that could be an indication of damage then the actions so this is our decision node here and this is the structural performance and that's the value of SHM analysis this is what we are after so this is a question about the consequences what can be consequences we note that we don't see the consequences here in the decision tree that's the actions and the probabilities there's branches and it's events so here there are events and they should be related to the consequences what can be consequences for decision analysis so we can also brainstorm on that you already have an idea you say one but what can be consequences you mean money or fatality or the environmental consequences can be monetary risks this is what we are it's structure engineers mostly are dealing with it's the monetary consequences of the failure of the structure but what happens also if the structure fails what consequences do we have? yes it's injuries, it's lots of lies so there can be very high consequences ok so if you think of a bridge let's say the bridge is severely damaged it's not collapsing but it's severely damaged what consequences do we have in this situation? economic consequences if it connects to for example the shop and the production center so there will be road closures there will be traffic diversions so this causes economic consequences and then the repair action also causes consequences ok and if we we have a few in the room who are working with offshore structures what can there's another very basic type of consequences for offshore structures what is that? yes it goes to the environment there are environmental consequences ok thank you for that we have decision analysis should include the consequences which are relevant in the decision scenario I think this is also a very important orientation this is without our analysis we are doing but we need a sorted decision scenario to properly model or properly develop models also the consequence models ok thank you very much for the question I don't understand why from the start there is not a structural response also before the actions I mean I have the outcomes from the structural health monitoring then I do not need the structural response and then the actions and then again structural response yes ok it just illustrates the decision scenario and not what you do after and before that's in your models also in your decision you always have the option to do nothing that means to remain at the state as you have been before you can have a decision then you make different decisions you do nothing and that means you don't change it therefore you always consider that option too yes but I cannot understand how you can decide not to do anything if you cannot have a model of this you always have it all together you have it all together it's just illustrating the decision scenario of course your SCGM outcomes influence the structural performance and so basically the reliability so SCGM may reduce the uncertainties so there will be a reliability increase against failure it could be a risk reduction and basically only if you know what the risk reduction is if you have quantified it you can decide what actions you should take so it's not contradicted by this decision tree it's just illustrating the decision analysis as I said contains many elements but it does not contain the consequences and the temporal modeling the scenario you described it's in the model step another question where should we define for example some type of SCGM should we define the threshold values for each action if we measure reflection for example if you are at some bridge first one action is do nothing second one weight restriction third one strengthening fourth one replacement how do you define the thresholds without this okay but that's why I'm asking should we define thresholds no no no let's think how do you define thresholds on structural performance that's why I'm asking exactly and the structural performance and we're defining the threshold because you have a structural performance but if you have reliability requirement or a design check requirement in deterministic terms and then we get out the threshold okay and now we do the same but we are modeling explicitly the event of failure but we describe just the event of failure and we have our SCGM outcomes and so you can imagine that we work with a probabilistic threshold somehow in our models okay I understand that for example let's say how if if it defines the action how can the action be before the same thing for example yeah okay we have to have a few steps to take so this threshold determination is deterministic we would first need to go to probabilistic and we need to model the probabilistic events here this is one step and then it's a decision analysis and we didn't talk about it but I heard it how do we identify the optimal decision so we would like to find the best SCGM system and also the most appropriate action but how do we identify it what's it right here right or we could call it an objective function yes and what goes in there yes please go ahead yes but this is only one ingredient it's the money it's the consequences it's a more general chance it can be quantified all the consequences can be quantified yes it's right I just want to introduce the oil skill salt and detergent money how do you quantify salt and detergent how much is it for example you pay for insurance and for insurance now you are technically very very conservative but this should depend on the country yes so you already know you already know how it is done but what are the underlying models and how they should be scientifically it goes to the life quality index so the that's a way of being able to determine or to assign a more monetary number of human life but we don't go into this let's stay with the consequences let's say we have money or we have a number of fatalities but we still don't know how that's not complete for identifying our best decision what is the other ingredient yes it's the probabilities so it's the probabilities of the consequences and this is what our objective function is about and this is how you identify the actions if you so lately work with thresholds coming back to your question then you circumvent the decision analysis and you will never know was it optimal in terms of expected consequences or not and of course you can take out of the expected consequences also cost estimates but you need to be aware that we always work with the probabilities times the consequence and this is our optimal decision about and this is a pre posterior decision analysis so we always have the situation so talking about the basic element of the decision scenario we are here and we have to decide now about the future about the service life of a structure 25 years for a wind turbine 50, 100 years for a bridge so and we can do this with a pre posterior decision analysis in a very consistent manner and we can even optimize before going out and implement okay I think