Week 7 - Lecture 35 : System-Level Prognostics, Health Management Integration, and Case Studies

So friends, we are there on the fixed lecture of seventh week and that is prognostics and health management a systems approach. Okay. In this lecture, we'll see um how diagnostics can be implemented in machine learning. Um we'll not be exactly discussing machine learning, but a sort of connection between diagnostics and machine learning. So um let me introduce first um diagnostics and prognostics, both can be done online or offline. That we have shown and discussed there actually. Uh and objective is to know or detect any deviation from the normal operation actually. So in that sense diagnostics is a present situation what is going on and what what will happen, but the prognostics is predicting the future. So there is one difference. Okay? And they have overlapping actually. Uh data-driven machine learning techniques are emerging tool for because physics of failure on the contrary they require a lot of scientific uh uh scientific depth into failure. Each failure has got its own characteristic. So machine learning and data-driven technique, they are basically tracking in time and trying to tell what is going on and that looks more much better an option. Prognostics using physics-based failure approach can be useful for reducing the uncertainty. That means one module which was predicting based on data. Now, other one physics of So, if they join together and they can reduce the uncertainty in declaring the results, that will be a good idea. But for that physics of failure approach have to come to real-time situation, especially a lot of electronics have been done. So, I think electronics is going to be the first area where POF working with the data data-driven approach. And for complex system, the the domain is very vast. So, so probably the in complex system, signals are being monitored. So, use the process parameter or you know, signatures which are there in the control room for prognostics number one and number two, go for data-driven approach. That means at local level in the area are the signal coming on the health of the machines also. And in that case, the fault tree event tree knowledge is part knowledge is available. It has to be further expanded. For we have as I mentioned earlier, expert system-based approach. So, fault tree event tree can directly translate into rule-based approach and wherever quantified rules or qualitative rules are not available, linguistic informations or vague situations are there. Even fuzzy approach can do a good job. Sign diagram Though I have it did not form part of my lecture, but then during while discussing some example, I'll definitely discuss this. And then nails base classifier. It is a classifying approach where and here I have done in this lecture, I have done this you know, use of this approach nails base approach for classifier that is yes or no uh variable for a common cause failure mechanism. And since there were some example available in generic source, I have adopted that thing for our common cause failure analysis. So, now uh major elements of diagnostic algorithm. So, one is identifying the objective and scope. Then uh domain expert, I am repeatedly uh talking about don't domain experts involvement into the to elicit the knowledge and the model uh is a key to success of diagnostics uh the way it was there for even prognostics also. Then we have to have a a regime for data pre-processing, machine learning. Uh we have to select proper machine. Uh that is the machine learning approach. Um it could be ANN, it could be statistical approach. Uh but we the results define what kind of approach we're going to use. And for that lot of iteration of simulations are are required. Uh the especially for rule-based approach, there is there is a strategy called inference engine. Uh if X is equal to Y, Y is equal to Z, then the consequence. So, uh for for for making it working in a machine learning model uh requires a inference engine approach. So, we should have a proper inference engine approach. Uh and then training of machine learning approach. Um maybe if you have a data set of X, so uh 0.8 X we can use for training and 0.2 X we can use it for um recall test uh because we have to validate the model actually. And apart from this, some new vectors have to be brought and unless until we put it in the use, we will not know whether our training is complete or not. So, it is a like a human keeps learning all through his life in the operational ecosystem, machine also has a one because new event has come. So, if it is not able to match onto a our vector module, then new event should be recorded and this the machine learning algorithm should ask whether you want to train this algorithm. We if we train it, it becomes part of our vectors, trained vectors. So, how the framework works and we are talking about the supervised learning only. So, first as we mentioned in the previous slide, scope and objective, then just to just to underline the point, domain expert and machine learning team, they should work together for data pre-processing and feature extraction. And domain expert should be on the same page with the machine learning equipment. Okay, whatever features we are extracting, they are they are they are relevant and they can be fruitfully utilized. And then preparation of vectors, that means labels. So, for every vector there will be a label. And but if this is ready, then then we have a machine learning algorithm. Okay. So, training goes on actually. So, once you have a trained ML, then test vector should be subjected. And finally, we have the trained machine machine learning diagnostic framework. These steps are important to have a robust model of diagnostics in a plant. And this this should be generic to the extent possible, that means it should be so much its applicability could should be for electronics component, mechanical components, civil component. So, the model should be generic and you know, available for rule-based approach. In fact, it should accommodate different techniques also. So, this machine learning algorithm it should be embedding the most of the machine learning tools and methods which are there. And here we can use a inference strategy to use this tool and training can be performed and trained model is available here. And finally, it is validated and certified to be used in the field. So with this now let us see we are talking about fault tree, event tree and all that, you know. So how then the fault tree, event tree we know top event. Probably if you may not know this event is called top event. This is called or gate. These are the links and these are called inter-intermediate event because finally when we start developing we will have to use this tool like a domain expert. And then this is or gate. So how it translates? A or B or C happens then intermediate event occurs. Okay? But this is or gate. But and gate D and E should happen to activate this intermediate module event. Okay? So So now and finally it will go to the because this is or gate. Any one of the thing get activated, it will go to the top event. So top event gets activated. So now we are talking in terms of machine learning and processing the data. So basic event, or gate and and gate. Just for the understanding purpose. And So once you arrive here, it can be that goal found, you know, technique. So that means machine learning learning algorithm will stop at this point. If we connect this particular node to an event tree, then it will try to understand the consequences also. That means this input will go to the event tree top and there we are event we have identified. But these root causes also we have identified. So now if you consequence vector, that means what is the level of risk or consequences that can be done in the event tree. So let us see one example here. We have this a generator. Okay? And this diesel generator can fail because of the These are the modes of failure, you know. So, we see in our FMEA anyone, mode of failure is important. So, mechanical mode actuation system failure, lube oil failure, starting signal failure, control and protection system. Lube oil has come twice, okay. So, this we can ignore. Now, for mechanical failure, it could be bearing failure, that is diesel generator bearing failure, crankshaft failure, piston failure, and cylinder failure. Now, I have indicated a basic event here. That means I do not want to go down, but bearing failure I I'll go down to further details, inner case, outer case. If it is a of course roller bearing. If it is a hydrodynamic bearing, then I'll have one shaft running under fluid, and there is a fluid is separating the stationary part with the dynamic part. So, lubrication will come into the picture there. So, the details will depend on what kind of component or interfaces coming that can lead to failure. Crankshaft failure, then then piston piston ring failure. These are the component they see because they are a reciprocating components, and they frictions are reduced by lube oil lubricating oil, you know, oil which is used for So, but then if the oil quality quality is not good, piston ring failure occurs. Cylinder failures, they are more rugged compared to anything. So, normally you don't see cylinder failure unless and until some some catastrophic phenomena is happened. Similarly, now you see here. These are or any one of them fail, then we have diesel failure because everywhere it is connecting through or gate. But here you see actuation system. There are two system which are there to start a diesel generator. Air start, compressed air start, or electrical motor start. So, these two are there. Unless until both fails, this will not go on top. Okay? So, if suppose air start fails has failed, the electric start is available and system is success. And it the event will remain here. And that is the advantage of redundancy. Here there is a there is a not redundancy, there is a diversity. The air start and so this is much higher level of redundancy. Because similar component they are redundant, but different component or system working on different principles, air systems and they are truly diverse systems, you know? And their probability of failure is less. Because their dependence is also not there on each other. Now, starting signal. Starting signal for starting this we require a starting signal. So, under voltage signal if it is not working, relay is not working, control signal, relay signal, and solenoid. Solenoid is the final actuation device, which will put it the things on this. So, starting signal, diesel starting signal I should say. Control and protection system, these events I have not developed because for understanding we had this lube oil, no lube oil, fuel pump, and oil. Don't you think it is provided a very elegant mechanism for developing our diagnostics? Components into sub intermediate level, and then finally basic component level. So, with this itself you can create your rule base, okay? And production rules for diesel generator. And if we implement during a situation when class four power are, you know, offside power failure has occurred, what diesel has not come. And this particular format was available in a expert system which is supporting the uh, you know, plant in charge or shift engineer. Automatically, one of the failed component will come on top. Diesel generator is failed because of starting air problem. So, easy to know. Then, I'll focus on other one is available. Yeah, it it's so and you'll find that if it is not started started, both have failed. Why both of both the things have failed? Is there any common cause other than that? So, or these are the independent causes. Relay, solenoid. Solenoid has not got actuated. Coil must have got burned. You know, so those things further we can develop. And maybe it this same fault tree might run into 20 25 pages covering all the component into their root level actually. Okay. So, now um the fault tree event tree we have seen. There is one special case I'm discussing here. That is Bayesian theorem. Bayesian theorem provides a very good diagnostic approach and it is basically trying to in probabilistic way, we are trying to understand whether the one mechanism is there or not there. Uh, how it is there? So, we know that Bayesian theorem has got a priori evidence and priori means already available information. And um so, what happens if we do not have data, then limited evidences, then priori which is available in the let us say uh, diesel generator failure probability. It is there in the generic domain. I have some evidences for collected for 1 year. So, I'll use Bayesian approach to uh, combine these two sources uh, you know, to provide the estimate of diesel generator. So, so here the um the this algorithm is like this. Probability of A into B, we all know that. If they are dependent event, uh, then probability of Suppose they are independent event, then probability of A into B, that is A intersection section B is equal to probability of A intersection probability of B. But if they are dependent event, then it can be written as probability of A intersection B is equal to probability of A into probability of B given A. That means we have some knowledge of A also. At the same time probably this same thing can be written like this also probability of B intersection probability of into probability of A given B. If we solve this thing we for probability of B given A is equal to probability of B probability of A given B and probability of A because I'm just reorganizing the terms here. So this is known as base theorem. And this theorem whether it is updating the reliability data or trying to solve a problem where two sources of information and want to reduce the uncertainty even it is used for estimating the uncertainty also. So let us see one example here. I have one electronic electronic system. Okay, and I want to analyze that thing. And what are the factor which affect the quality of the electronic board performance. Okay. So so I have and I know which are the factors they might adversely affect the electronic board operation. So I have this quality. quality military grade component that means the component fabrication itself has followed some standard method. So they are the highest quality. Then then there there could be low quality component. That means from from local manufacturer we have we have got it. So one is military one is low low grade component and one is medium grade component. Why medium grade component? Because this component we bought from the open door open market but we subjected them for qualifying testing. Okay? Sometimes it could be even milk testing. We are we are subject So, it is a medium grade. And that is quite quite correct, also. That we have done our own verification and all that. But, definitely it will not be a milk grade component, and it will not be lowest component. So, medium. So, these are the categories of its quality level that we can give. And depends on where we what kind of thing we use. So, this is data table for this particular Now, electronics get affected by we know that temperature. Okay? Humidity and human factor. Human factor maybe in calibration, installation, and repeated in out maintenance. So, it gets affected. Now, let us see Now, I think these abbreviations I I have not given. So, please listen very carefully. It is ground benign. The temperature that means the instrumentation rack where the electronic board was installed, it is ground benign. Ground benign means 22° C temperature and humidity 55%. So, that is ground benign and that is the ideal condition for electronics to operate. So, ground So, other one is ground benign temperature high. That means it was not 22. It was higher. Okay? So, I have put H there. Okay? And then ground benign temperature medium. I have put here. So, that means it was not ground benign, but there are some some variations. And with that I have made some qualifier for accounting for temperature increase or decrease not being either being ground benign low or high. High Low doesn't And humidity. Humidity, also, ground benign humidity is you know that 55%. Ground benign condition. But, if it is H, H means high humidity. 70%, 80%. Definitely, component Electronics, what is lubrication for bearing quality lubrication quality for bearing for for electronics it is temperature and humidity. If we are not able to maintain proper temperature and humidity then the electronics failure will be more frequent actually. Then ground benign high humidity H stands for humidity here and another H stands for high. Please listen to me very carefully because all abbreviations are not given. So H stands for high also H stands for humidity basically ground benign humidity. It says humidity is 60 55% which is correct required humidity is there. And then one more factor is human factor. Human factor can induce in the test maintenance operation or you know even qualification some error. So if you have experienced stuff we we feel it's okay. If experience is low one more barrier if it is a skilled that means in between that so we have that and last column it is called response column. Okay response column is common cause factor judgement. You can imagine that I collected this data from 15 experts or 15 industry and they have given their opinion why common cause failure probability will be no or yes for which combination. So now you see I have got all the information with me and now I want to understand the probability of common cause failure. No means no common cause failure will occur or yes means there is a probability of yes there is a probability. We have to read this statement also. When I say yes is a response factor yes this is common cause failure will will be there and no no common common cause failure will be there. So for us no is important. We do not want common cause failure you know. So now let us go ahead and try to see how we have modeled this problem. But now we go to the base theorem we understood. Now, we let us go to What is we see now we have common cause failure of electronic complex critical parameter common cause is rare event. Still the past data are set record shows as follows. Consider the classification of A in the class label. That means A is showing you the label that is response factor. And B is the matrix that we are trying to like we said no I chose the vector five. So, B indicates the four parameter commercial ground banana tea ground banana H humidity and experience. And A is the response variable. Last column we saw that, you know. So, data type and then assumptions are features are independent equally significant for common cause and data sets considered in the. So, independent and equally applicable that is a assumption that will be using this term for for simplifying the our model. How we do that actually? So, now if I convert this whole problem into my problem is B is a class label yes or no. Okay, B is a class and labels are yes or no. Okay? Now, A is equal to A1, A2 there are factors here for A. Are for example five. We have medium ground banana tea same thing I'm repeating here. Now, for PA we have these possibilities probability of A given B, probability of A2 given B, probability of A3 given B and this is how we are trying to estimate the prior probability probability B. Okay? So, but probability B for A1, A2, A3, A4. Okay? Now, probability of probability of B is equal to probability of B probability A I given B for this I. They are all I actually, you know? And probability of A divided by so, the Bayesian algorithm. Now, P B A I is posterior probability. That means this is our posterior probability. Probability B prior probability, okay? And probability A evidence or likelihood estimate that we have with us, okay? So, the final theorem is B cap. That is probability of B we are trying to see. We had a, you know, maximum maximum likelihood estimator for our problem. So, uh probability Y into pi I is equal to 1 to N. That means all multiplication of A I thing whatever we have. The equation is called naive classifier, okay? And now, if I translate it into the problem for my quality metrics, I have common cause failure, yes. How many yes are there? Mil rate got one, medium two, and low three. So, total six yes are there. Uh similarly, uh probability of yes 1 by 6, 2 by 6, 3 by 6, straight forward, 100%. Common cause failure no, four. Four, medium four, and two. So, 10. So, now we have probability of no is equal to 4 by 10, 4 by 10, 2 by 10, 100%. So, if I add all, it will become 100%. Now, example input we have A medium same vector that is vector vector phi I have chosen here. Now, probability of yes is equal to 6 upon 16, okay? Uh because there were so many yes that we counted actually. Uh and probability of no uh is 10 out of That means in the last column, total number of yes and total number of no. So, uh that that we have over here. And uh uh we estimated this probability. Now, let us say some feature we take. Uh quality medium 2 by 6, 5 by 6. The temperature this thing, and we came to this uh probability. Yes ka probability and no ka probability. Now, we'll bring in that conditional element of this. So, common cause failure yes is nothing but individual 2 by 3, 3 by 6, and 6 by 16 that we estimated. Okay? Uh probability of uh yes per year um because uh I'm trying to predict that per year what was the observation of each individual that data came from. Uh for no per year, this is uh this is we got yes ke liye. Now, for no also we got 0.034. So, that means probability of yes is equal to 0.026 which came from here, and this is summation normalization we we have done. So, 0.44. Probability of no uh no common cause failure will will be there 0.57. So, this is a higher probability. Uh we will use this uh thing. So, no probability failure is higher. Okay? Uh analysis predict predict the reference value. So, for common cause failure based on the um expert elicitation technique collecting opinions, and we try to assess what are the probability. Of course, 0.57 is high, but this was an example for demonstration. Okay? Normally, I'll tell you uh common cause failure maximum 0.1. It is now there is a consensus, and it is less than that. But, this method was uh has less to do with the quantification, but more to do with the how you can arrive. This is an alternate mechanism which is available other than the statistical uh or empirical methods that have been given in the books and all that. And, uh, for this book, uh, I have used this, uh, example of, uh, naive Bayes approach. Uh, this particular, uh, this particular, uh, website and, uh, McAfee, uh, https and all. Uh, and, uh, I think I should thank them because this was a, uh, beautiful example that was given which I could adopt it for my common cause failure analysis for, uh, presenting to you. Because otherwise we think common cause failure contribution, uh, involves, uh, a lot of complication, a lot of data, data is not available. International organization are working on that. But, if we use like fuzzy logic an important input, I think it will be a great deal that we, we have.