# How Can Fault Detection Be Modeled in a Water Tank System?

I am assigned to work on a project where I am required to perform multiple types of data analyses on process data using Python or Matlab. The analyses chosen must relate to at least one process objective (e.g., fault detection). I am required to choose one basic linear technique and one more advanced technique.

I was thinking to consider model a simple system like a water storage tank with two pumps and two valves aimed at maintaining a certain set point. I am uncertain about where to begin. Should I start by modeling water tank system using differential equations that describe the rate of change of water level in the tank to generate data representing normal operating conditions. Then I would introduce faults in the form of sensors biases to generate faulty data. I am not aware on how one can model bias to accurately represent the behavior of a sensor. Also, how can I apply regression techniques to predict the water level if I lack actual measurements?

Were I to do this I would probably generate the data using excel. There is not that much data required. First generate "normal data" and then apply various systematic biases and random biases to create miscreant data. This choice of model will give you no particular requirements for speed of response which is often important in the real world.

I perhaps misunderstand the assignment. Is this an exercise in sensor design or feedback control?

The project is not focused on sensor design or feedback control.Instead, the goal is to perform data analysis on process data using Python or Matlab. The chosen data analysis techniques should be related to at least one process objective, such as fault detection.Since I couldn't find a suitable process dataset on Kaggle, I decided to model a simple, non-reactive system such as a water tank with a pump, inlet valve, outlet valve, and two sensors high level sensor and low level sensor.

My approach (I am not sure if its correct)
1) Solve the ODE modelling the tank without introducing any sensor bias to generate normal data.

2) Introduce sensor bias and solve the ODE again to generate faulty data. I am not sure how to model that

3) Apply classification algorithm to classify data as normal or fault.

So is the purpose of this excercise to develop an algorithm that can automatically classify, afer the fact, whether the accumulated data represents normal operation of the system or a system fault? I am curious as to why this is a useful exercise. Would you not want a real time system to do this? Is this designed to lighten the load on insurance adjusters? Just askin'........

So yes you need to create a simulacrum of the normal system using MATLAB or Excel and create normal data. Then you need to randomly reasonably screw up the system to create schizophrenic data and use these to "black box test" your fault detection. Preferably the person who screws up the system should be different from (and not familiar with) the designer of the fault detection.

I totally agree with you in how is this useful. I am purposely inducing random faults and trying to model that. But I am curious to know from you how would one go about to simulate the normal state/fault state of a real tank system? Do we manipulate variables that we think might affect the system (valve opening, pump power, flow rates) and subject them to the level constraints?

I totally agree with you in how is this useful. I am purposely inducing random faults and trying to model that. But I am curious to know from you how would one go about to simulate the normal state/fault state of a real tank system? Do we manipulate variables that we think might affect the system (valve opening, pump power, flow rates) and subject them to the level constraints?
Yes.

How about a tank where the water level must be maintained between high and low limits?
1) the limits could be sensed with float switches, pressure measurement at the bottom of the tank, pressure measurement measurement at the top of the tank (if the tank is air-tight)
2) pumps that come on to either add or remove water to maintain the water level

3) you will have to find a way to recognize the "normal" water level changes as it relates to the pump and valve operations
4) introduce random faults of sensors and/or pump flow (sensor reading not changing when it should, changing too fast, pump flow lower than "normal", etc.)

5) compare current sensor readings with "normal" readings to detect that servicing is needed

Now that I've done the first 5% of your project... HAVE FUN!
(you'll have to be creative. )

Cheers,
Tom

This reminds me a little bit of the simulations NASA runs to investigate and optimize crew response. I don't know how they selected the failures used for test analysis. As witnessed by both Apollo12 (lightning strikes) and Apollo 13 (abusive previous ground handling overvoltages) the actual failure modes were far weirder than any of their sims. So the difficult part of this testing paradigm is creating a relatively complete and comprehensive set of multiple failure modes ( which is sort of impossible on its face). Probably one should look at comprehensive failure rate data for the various system components and weight the random injected failures appropriately. I'll bet you will discover faults that will boggle the mind. Non-linear dynamic system!
This part of the assignment is, IMHO, a very good learning exercise and far more important than the actual design of the detection system (although they are sort of "mirror image" processes). If you are having trouble gettimg started, just divise the simplest tank system you can think of and play with it for a while. Try to keep it flexible and make it more complicated as needed. Sounds like good geeky STEM fun.

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