How can a human Neural Network be used to reduce complexity in signal analysis?

[serbring]

Hi all,

I have 40 signals recorded on a vehicle. Some signals are analog and some are digital with 4 different states. One signal (I call it A) is really important to me, it is positive and all the other signals lead to its variability. For example, when there is a state change in a couple of signal there might be a peak in the signal A. Of course the condition might be more complex than this and probably the patterns that lead to peaks might be different for each acquistion. I need to know which signals variation lead to the peaks of signal A. Is there any systematic method to do it? In case my problem is not clear for you, I will provide you more details.
Any suggestion, paper or topic to study is really welcome

thanks

 

[berkeman]

Hi all,

I have 40 signals recorded on a vehicle. Some signals are analog and some are digital with 4 different states. One signal (I call it A) is really important to me, it is positive and all the other signals lead to its variability. For example, when there is a state change in a couple of signal there might be a peak in the signal A. Of course the condition might be more complex than this and probably the patterns that lead to peaks might be different for each acquistion. I need to know which signals variation lead to the peaks of signal A. Is there any systematic method to do it? In case my problem is not clear for you, I will provide you more details.
Any suggestion, paper or topic to study is really welcome

thanks

One method is through a Monte Carlo simulation... https://en.wikipedia.org/wiki/Monte_carlo_simulation

Do you have models for how each component signal affects other signals (including A)?

 

[Baluncore]

Maybe an application for a neural network.

Predict the signal A from all other available signals. Use the difference between predicted and actual A to improve the prediction.

 

[serbring]

Maybe an application for a neural network.

Predict the signal A from all other available signals. Use the difference between predicted and actual A to improve the prediction.

Hi, Thanks for your reply, I can use the neural network for the definition of a model but how to use it for understand which signal conbination lead to the peaks?

One method is through a Monte Carlo simulation... https://en.wikipedia.org/wiki/Monte_carlo_simulation

Do you have models for how each component signal affects other signals (including A)?

Thanks for the reply, I know the montecarlo simulation, but how may I use it for the pattern identification? I do not have a model.

JFY, with the exception of signal A, that is a force in a vehicle component, the other are related to the vehicle working parameters, so the digital signals are from switches (e.g. engaged gear, brake conditions, etc), instead anolog signals are for example the steering wheel angle and the vehicle speed. I need to know which driving events lead to the force peaks in the vehicle component.

 

[berkeman]

I do not have a model.

Oh, so you don't have any models yet, and that's what you are trying to figure out? You want the transfer function from all of your other input signals to the signal A?

 

[Chestermiller]

I think maybe that this should be moved to a mathematics forum, which I will do as soon as I'm done with my response.

You have a main time-dependent response signal, and about 40 other time-dependent forcing signals that you have measured, and you want to find out how each of the forcing signals contributes to the response signal. Is this correct?

Here are some questions:
1. Do each of the forcing signals contribute separately to the response signal, or is there non-linear interaction between them.
2. Is there a time delay between the forcing signals and the response signal?
3. Is the response signal affected directly by each of the forcing signals, or does it depend on their derivatives as well?

I'm not an expert on this kind of thing, but I have some ideas, depending on the answers to the above questions. Consider getting the correlation between the variations of the response signal and the variations in each of the forcing signals. Also consider this correlation as a function of the time interval, if you index the response signal behind the forcing signal by a varying amount of time.

Chet

 

[Chestermiller]

I should also mention that, if you are doing what I suggested in my previous post, you should normalize by the square root of the forcing self-correlations and the response self-correlation so that the individual forcings can be compared on a common basis.

Chet

 

[Baluncore]

I can use the neural network for the definition of a model but how to use it for understand which signal conbination lead to the peaks?

The coefficients in your NN, once optimised, are the coefficients of a scattering matrix that defines the system.
Search the matrix for the highest coefficients in A.

An alternative technique would be to compute correlation coefficients between signal A and the other signals.

 

[serbring]

Oh, so you don't have any models yet, and that's what you are trying to figure out? You want the transfer function from all of your other input signals to the signal A?

Actually I don't know, how a transfer function might be helpful. How would you use it in my case?

I think maybe that this should be moved to a mathematics forum, which I will do as soon as I'm done with my response.

You have a main time-dependent response signal, and about 40 other time-dependent forcing signals that you have measured, and you want to find out how each of the forcing signals contributes to the response signal. Is this correct?

Not really, I'm more interested to extract which driving event (turning, braking, braking and turning, accelerating, etc) leads to higher forces. Consider for each acquisition I have more than an event repetition and I have different acquisitions in similar conditions.

Here are some questions:
1. Do each of the forcing signals contribute separately to the response signal, or is there non-linear interaction between them.
2. Is there a time delay between the forcing signals and the response signal?
3. Is the response signal affected directly by each of the forcing signals, or does it depend on their derivatives as well?I'm not an expert on this kind of thing, but I have some ideas, depending on the answers to the above questions.

1- the forcing signal can jointly and not linearly contribute to the response signal in function of their state, for example when I drive straight, the steering wheel angle signal does not contribute to the lateral force.

2. Not in general, but there might be a little delay for some forcing signals. I can verify it.

3- Only directly

Consider getting the correlation between the variations of the response signal and the variations in each of the forcing signals. Also consider this correlation as a function of the time interval, if you index the response signal behind the forcing signal by a varying amount of time.

Chet

This is what I have actually done. I computed a moving window correlation between the response signal and each forcing signal. Them I assumed high correlation in case the correlation coefficient is upper than 0.85, low correlation in case the coefficient is lower than -0.85. By doing so I was able to see few events just for a couple of acquisition and for the others I did not see almost anything. For this reason I'm searching for a more robust method or for improving the method I have used so far.

I should also mention that, if you are doing what I suggested in my previous post, you should normalize by the square root of the forcing self-correlations and the response self-correlation so that the individual forcings can be compared on a common basis.

Chet

I haven't normalize the signal! How should I do it? Thanks

The coefficients in your NN, once optimised, are the coefficients of a scattering matrix that defines the system.
Search the matrix for the highest coefficients in A.

An alternative technique would be to compute correlation coefficients between signal A and the other signals.

Interesting the neural network technique! I'll give it a try after the analysis correlation

Thanks to all!

 

[Chestermiller]

I haven't normalize the signal! How should I do it? Thanks

Calculate the autocorrelation of the forcing with itself and the autocorrelation of the response with itself. Take the square root of each of these. Then divide the correlation coefficient of the forcing and response by the two square roots.
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[serbring]

Calculate the autocorrelation of the forcing with itself and the autocorrelation of the response with itself. Take the square root of each of these. Then divide the correlation coefficient of the forcing and response by the two square roots.

Do you mean this autocorrelation https://en.wikipedia.org/wiki/Autocorrelation? If yes, at which lag should I compute the autocorrelation? Just for my reference, do you know any document about this normalization?
Thanks

 

[Chestermiller]

Do you mean this autocorrelation https://en.wikipedia.org/wiki/Autocorrelation? If yes, at which lag should I compute the autocorrelation?

No. It would be with no time delay.

Just for my reference, do you know any document about this normalization?

No. It's just something that makes sense to me so that the contributions of the various forcings can be compared on a common basis.

Chet

 

[serbring]

No. It would be with no time delay.

Chet

That means lag=0, right?

 

[Chestermiller]

That means lag=0, right?

Yes, for the self-correlation in the normalizing factors in the denominator.

Chet

 

[serbring]

Yes, for the self-correlation in the normalizing factors in the denominator.

Chet

Thanks, I'll try it and I'll feedback you.

 

[serbring]

There is a thing that is not fully clear to me. Let's assume two signals like the following:

$$\begin{matrix} \\ y_1=10sin(2\pi*3x); \\y_2=500sin(2\pi*3x); \end{matrix}$$

the two signals have different magnitudes and have a correlation coefficient of 1, doesn't matter the amplitude of the sine. The max value of the autocorrelations of the two signals are 5E4 and 5E6, so the normalized correlation coefficient is:

$$\frac{1}{\sqrt{5E4*5E6}}= 2E-6$$

In that case the correlation coefficient turn to be signal amplitude dependent. Am I understood correctly what you meant? thanks

 

[Chestermiller]

There is a thing that is not fully clear to me. Let's assume two signals like the following:

$$\begin{matrix} \\ y_1=10sin(2\pi*3x); \\y_2=500sin(2\pi*3x); \end{matrix}$$

the two signals have different magnitudes and have a correlation coefficient of 1, doesn't matter the amplitude of the sine. The max value of the autocorrelations of the two signals are 5E4 and 5E6, so the normalized correlation coefficient is:

$$\frac{1}{\sqrt{5E4*5E6}}= 2E-6$$

In that case the correlation coefficient turn to be signal amplitude dependent. Am I understood correctly what you meant? thanks

I guess, because of my inexperience, I have a terminology issue. It looks like what you call the correlation coefficient already includes the normalization that I was suggesting. Sorry for any confusion I may have caused.

Chet

 

[Baluncore]

Is there any systematic method to do it? In case my problem is not clear for you, I will provide you more details.

In my experience there would need to be some understanding of the 40 signals before deciding on a strategy for analysis of those signals. The problem is insufficiently defined to provide a sensible answer.

Actually I don't know, how a transfer function might be helpful. How would you use it in my case?

Your case is so general that it is quite undefined.

The complexity of the problem should be initially reduced by the application of a human Neural Network.