So I'm now about a year into my MSc project and progress is, well, good :-)
I'm pretty much finished and I'll probably be publishing some papers based off my work if my supervisor has his way.
So what have I done? Well I've used the Fuzzy-Transform (F-transform) in a way, which as far as I can see, has never been done before. I've also managed to predict the range of an electric vehicle successfully, which is nice!
Hopefully once I've published any papers that will come out of my project I will be able to share what I've done a little more publicly, but for now I'm afraid things have to stay secret!
Showing posts with label Control engineering. Show all posts
Showing posts with label Control engineering. Show all posts
Friday, 3 August 2012
Tuesday, 10 April 2012
Stay on target!
OK so I'm now into the implementation phase of my MSc project - see my previous post on the fuzzy transform for what I was doing a while ago. Because my end-result is for a device to go into a vehicle I need to work in an embedded environment (my target environment) to accurately determine the capability of my system. If you're interested the target platform I'll be using it's called the Olimexino-STM32 and it's made by Olimex.
Over the last few weeks I've found that there's an active community developing small systems using this and other devices, which is useful since it means there are other people doing things that I can learn from and also ensure that I don't inadvertently replicate anything that's already being worked on.
As part of my project I need to do some prediction work, one way of doing this is the method of least squares, and I've described an approach to it in the linked PDF: Using least squares with a linear system
Whether this is the approach I'll end up with is debatable, as the fuzzy transform may still have a few treats in store for me!
'Using least squares with a linear system' by Iain Cunningham is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Over the last few weeks I've found that there's an active community developing small systems using this and other devices, which is useful since it means there are other people doing things that I can learn from and also ensure that I don't inadvertently replicate anything that's already being worked on.
As part of my project I need to do some prediction work, one way of doing this is the method of least squares, and I've described an approach to it in the linked PDF: Using least squares with a linear system
Whether this is the approach I'll end up with is debatable, as the fuzzy transform may still have a few treats in store for me!
'Using least squares with a linear system' by Iain Cunningham is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.
Tuesday, 10 January 2012
I feel all fuzzy inside...
Just kidding.
I've not been around much recently as I've been working hard at my MSc project. For part of this I've had to implement something called a "Fuzzy Transform", this was initially presented by Irina Perfilieva and has been developed by the Institute for Research and Applications of Fuzzy Modeling (IRAFM) at the University of Ostrava in Ostrava in the Czech Republic.
The way in which I'm presently using the Fuzzy Transform is one that provides a numerical analysis method that is a cross between fuzzy logic and a filtering function (a filtering function is used to remove noise [unwanted information] from a signal; such functions are in use everywhere in our modern world, from cellphones to missile guidance systems). It's a numerical method, because it doesn't try to "guess" what gave rise to the original data (methods that try to work out what gave rise to the data in the first place are "estimators" and tend to use "mathematical models" to represent whatever is generating the data from a given input); if you wanted to you could feed in a totally random stream of numbers and a numerical method would have a good go at approximating the numbers "with arbitrary accuracy" (this means "as well as you make it", see below).
One of the things that the fuzzy transform provides as well as the filtering capability of the filtering function is an ability called "Universal Approximation", this means that provided any series of data a correctly set-up fuzzy transform can be used to approximate the data. Universal Approximators are useful since they allow you to do all kinds of fun stuff, such as pattern matching (for example, character recognition and face recognition), data compression and forecasting... but more on this later.
So, let's take a varying series of data:
This isn't of anything very exciting other than something that provides a nice wiggly line (if you're really interested it's y=sin(x.π)+x with added zero mean, normally distributed noise with variance 0.01). So what happens if we use the fuzzy transform? We get a plot a little like this:
The blue line in the above plot is the result of the Fuzzy Transform, this was obtained by dividing the original wiggly line into 10 horizontally measured sections, or partitions, taking the Fuzzy Transform of the data and then inverting (reversing) the transform; and you can see that it kind of matches the original wavy line, but as well as removing all the noise, the F-Transform has also removed a lot of the shape of the original line (we've lost information). Using 20 partitions gives this:
Which uses the same colours for the noisy data and the approximation as previously and is a better fit, but still leaves a few gaps. While using 30 partitions gives this:
Which again uses the same colours for the noisy data and the approximation as previously and almost exactly matches the original function, which I've plotted below (in green) along with the 30-partition approximation to allow an easy comparison:
So what does this mean? It means that the Fuzzy Transform can approximate the data "with arbitrary accuracy", which we can now see is a way of saying that it can match the data we feed into it (the red line) as closely as we want it to. Why might we not want to try to get an exact match? Well, firstly, the more accurate we make the approximation, the more calculations are required and so it takes longer to get the approximation, and, secondly, if we make the approximation too accurate then it will also start to approximate the noise (the Fuzzy Transform doesn't know where the data has come from, so it can't tell what is "noise" and what is "signal"). This means that we need to find a balance between ease of calculation, and being a good enough approximation, while still "filtering out" the noise.
In the example above, doubling our "effort" by going from 10 to 20 partitions gives quite a large benefit, but putting in another half as much effort again to get from 20 to 30 partitions doesn't give a very big improvement (so if the end use could tolerate the inaccuracy of the 20 partition transform then we'd use that rather than "wasting effort").
Finally, I suppose you want to know how can this be used? Well IRAFM and others have shown how the Fuzzy Transform can be used to detect patterns and relationships that underlie quite complex data. For example, in one paper published in 2008 [subscription required] the Fuzzy Transform was used to provide a model of the GDP of the Czech Republic based on a set of other data, such as unemployment, the rate of inflation, etc. The Fuzzy Transform has also been used to automatically combine multiple images to provide an image that is of better quality overall than the constituent images [PDF]. Pretty impressive, eh?
If you want to learn more about the Fuzzy Transform, or the other things that IRAFM are involved in researching and developing then they have an extensive list of publications that are publicly available in PDF format.
This may be a bit technical, so please ask questions, I'll do my best to explain, or point you to somewhere you can find more information!
I've not been around much recently as I've been working hard at my MSc project. For part of this I've had to implement something called a "Fuzzy Transform", this was initially presented by Irina Perfilieva and has been developed by the Institute for Research and Applications of Fuzzy Modeling (IRAFM) at the University of Ostrava in Ostrava in the Czech Republic.
The way in which I'm presently using the Fuzzy Transform is one that provides a numerical analysis method that is a cross between fuzzy logic and a filtering function (a filtering function is used to remove noise [unwanted information] from a signal; such functions are in use everywhere in our modern world, from cellphones to missile guidance systems). It's a numerical method, because it doesn't try to "guess" what gave rise to the original data (methods that try to work out what gave rise to the data in the first place are "estimators" and tend to use "mathematical models" to represent whatever is generating the data from a given input); if you wanted to you could feed in a totally random stream of numbers and a numerical method would have a good go at approximating the numbers "with arbitrary accuracy" (this means "as well as you make it", see below).
One of the things that the fuzzy transform provides as well as the filtering capability of the filtering function is an ability called "Universal Approximation", this means that provided any series of data a correctly set-up fuzzy transform can be used to approximate the data. Universal Approximators are useful since they allow you to do all kinds of fun stuff, such as pattern matching (for example, character recognition and face recognition), data compression and forecasting... but more on this later.
So, let's take a varying series of data:
This isn't of anything very exciting other than something that provides a nice wiggly line (if you're really interested it's y=sin(x.π)+x with added zero mean, normally distributed noise with variance 0.01). So what happens if we use the fuzzy transform? We get a plot a little like this:
The blue line in the above plot is the result of the Fuzzy Transform, this was obtained by dividing the original wiggly line into 10 horizontally measured sections, or partitions, taking the Fuzzy Transform of the data and then inverting (reversing) the transform; and you can see that it kind of matches the original wavy line, but as well as removing all the noise, the F-Transform has also removed a lot of the shape of the original line (we've lost information). Using 20 partitions gives this:
Which uses the same colours for the noisy data and the approximation as previously and is a better fit, but still leaves a few gaps. While using 30 partitions gives this:
Which again uses the same colours for the noisy data and the approximation as previously and almost exactly matches the original function, which I've plotted below (in green) along with the 30-partition approximation to allow an easy comparison:
So what does this mean? It means that the Fuzzy Transform can approximate the data "with arbitrary accuracy", which we can now see is a way of saying that it can match the data we feed into it (the red line) as closely as we want it to. Why might we not want to try to get an exact match? Well, firstly, the more accurate we make the approximation, the more calculations are required and so it takes longer to get the approximation, and, secondly, if we make the approximation too accurate then it will also start to approximate the noise (the Fuzzy Transform doesn't know where the data has come from, so it can't tell what is "noise" and what is "signal"). This means that we need to find a balance between ease of calculation, and being a good enough approximation, while still "filtering out" the noise.
In the example above, doubling our "effort" by going from 10 to 20 partitions gives quite a large benefit, but putting in another half as much effort again to get from 20 to 30 partitions doesn't give a very big improvement (so if the end use could tolerate the inaccuracy of the 20 partition transform then we'd use that rather than "wasting effort").
Finally, I suppose you want to know how can this be used? Well IRAFM and others have shown how the Fuzzy Transform can be used to detect patterns and relationships that underlie quite complex data. For example, in one paper published in 2008 [subscription required] the Fuzzy Transform was used to provide a model of the GDP of the Czech Republic based on a set of other data, such as unemployment, the rate of inflation, etc. The Fuzzy Transform has also been used to automatically combine multiple images to provide an image that is of better quality overall than the constituent images [PDF]. Pretty impressive, eh?
If you want to learn more about the Fuzzy Transform, or the other things that IRAFM are involved in researching and developing then they have an extensive list of publications that are publicly available in PDF format.
This may be a bit technical, so please ask questions, I'll do my best to explain, or point you to somewhere you can find more information!
Friday, 17 June 2011
Ohai2u!
Hello there!
So here we are... I have no idea where this is going to go, or how it will get there, but it should be interesting to find out.
I suppose the first thing I should tell you is a few things about me, for those too lazy to read my account; I live in Warwick in the UK and I am in the middle of a few things, I'll probably write about them now and then:
So here we are... I have no idea where this is going to go, or how it will get there, but it should be interesting to find out.
I suppose the first thing I should tell you is a few things about me, for those too lazy to read my account; I live in Warwick in the UK and I am in the middle of a few things, I'll probably write about them now and then:
- A part-time MSc in Control Engineering. This came about after an argument with a (now ex) girlfriend where we split up for a while, I decided that I would need something to do, and decided, for want of a better expression, to "improve myself" in a way that might make me more useful at work (q.v.). At the time of writing I have about 9 months left to go (which will be taken up with my project, this will involve some Matlab and the report for which will have to be written in LaTeX).
- Teaching myself to play the guitar (this has been going on for about 6 years), one day I expect I'll get around to paying someone for a lesson.
- Relearning to play the cornet (I first learnt at school, a few years ago now).
- Running a photography business.
- Sitting on the board of a high technology company that is in the field of electric vehicle design and engineering. Primarily I'm responsible for all electrical and electronic systems activities, but I also have some input into other areas, such as customer service and information systems.
Something I'm planning to add to the above is that I want to work through, "The Elements of Computing Systems: Building a Modern Computer from First Principles" by Noam Nisan and Shimon Schocken, which is freely available at: http://www1.idc.ac.il/tecs/ so feel free to join in if you'd like to.
Subscribe to:
Posts (Atom)