Ground Balance Theory

[Aziz]

Hi all,

please feel free to test other VRM soil model functions G(t). If you find something better, then let us know please.
I have to make all the VRM analysis once again with the new G(t). I've got more measurement data as well. So this is a work for many many weeks and month.


It is indicating, that many VRM soil models mentioned in scientific publications and patents will get truly busted. (It is well known, that all the ground balance solutions don't work really well enough. But the new G(t) makes your life not easier - quite the opposite happens. )


Aziz,
the "Armchair (Data) Prospector"(c)(r)(tm) *LOL*

[Aziz]

1A Premium Service Continues

Hi all,

and this is what I get if I take the original formula 17 mentioned in the scientific publication above.
Note, that I have set p=0 (no phase) and exponent b=-1 to we get the original formula.
When I solve the best fit for all four measurements with the original time code (no correction made), I get a Sum of Errors² of 133297.5. This is quite large. If I search for optimal time code & phase correction for all four measurements together, the error decreases to 48972.1. This is still large.


These numerical simulation experiments on measurement data indicate, that the original formula isn't much correct. That's the reason, why we use the variable exponent form (b) and a phase shift term (p). The new G(t) is fullfilling the requirements and is showing its power by delivering very very nice curve fittings.

BTW, the time code of such measurements is very very important. It must be consistent for all measurements. So don't trigger your oscilloscope on the flyback decay signal. Use a very stable digital logic source for the timings (at TX switch-off). The system time delay in the TX clock stages, TX mosfet driver, TX mosfet and front-end amplifier delay must be taken into consideration and the time code needs some correction of course. BTW, that is my variable p-ofs in this case (see Excel sheet). But the variable p (phase shift) can inherently do a time code correction as well if you don't use p-ofs.

But what's when the new G(t) isn't correct? Well, we have to find a better soil model function.

Cheers,
Aziz

[Aziz]

Hi all,

I want to clarify something so you don't get confused about the interpretation of the latest results.

We have tried a simplified form of VRM response earlier (approximation):
G1(t) = a*(t+p)^b

And we have tried the improved form of VRM response, which is derived from the above mentioned scientific publication:
G2(t) = a*( (t+p)^b - 1/(t+p+w) )

The parameters a and b of each soil model function can't be compared together. These are like apples and pears. Completely different things. Now the crucial point is, that you can be quite fooled when using the Excel Solver. If the parameter w in G2(t) gets large, the second term of G2(t) approaches to zero. And then the G2(t) becomes the G1(t). So you have to be very careful, whether the Excel Solver is delivering G1(t) parameters or G2(t) parameters. G1(t) has usually a larger negative exponent b, whereas the G2(t) exponent is around -1.0 +/-x.

G2(t) is delivering reasonable exponents, which is the most common & accepted interpretation of the decay rate exponent in VRM science. So don't get confused about exponents anymore.

Cheers,
Aziz

[Carl-NC]

Hmmm... not working and not sure why. Will work on it some more tomorrow.

[Carl-NC]

How about adding buttons next to the file links that would load and display individual images inline? It is much easier to read a thread with embedded images rather than switching between several browser tabs.

This is an excellent idea, so I look around and found a mod that should do this. I've attached your plots to this post and they should show up as links, but now with a button that converts them into images. Testing....

[Aziz]

And this is what I get, when I make both p and b variable. The time base correction (phase shift) is inherently in the parameters p. But they differ now.


The error gets slightly smaller and I get very nice best fit curves. But you can easily be get fooled when solving both p and b parameters together. The Excel Solver might not find for you the best solution. Noise in the measurement data and inappropriate starting values for the parameters can force the solver to a local minimum error.

Cheers,
Aziz

[Aziz]

Hi Aziz, here are the two Excel files with the latest measurements (post #519): [ATTACH]27186[/ATTACH]

What is 'w' and how did you determine the values?

Thomas

Hi Thomas,

thanks for new measurements. I'll look at it soon.

There is a nice scientific publication in the internet.
http://www.eos.ubc.ca/research/ubcgi..._eudem2003.pdf
Please have a look at it. And see the formula 17 in page 3 (formula 17 in the brackets).

dM(t)/dt: this is the induced voltage in the coil finally, this is my G(t)
Hx0/log(T2/T1): this is my proportionality factor a, stands for the strength of the VRM response
1/t term: I have used the exponent form t^b but do a time code correction and phase shift (phase offset) -> (t+p)^b
The exponent form is required for varying exponents (b != -1).
1/(t+delta_t): delta_t stands for my variable w, I use the time code correction term -> 1/(t+p+w)

The time base correction is required as the time code might not be really accurate. Therefore I need the variable p. It is also good for detecting phase shifts (if they really exist).

I get finally:
G(t) = a*( (t+p)^b - 1/(t+p+w) )
That's it.

The add-on Excel Solver tool is tweaking and finding all the variables for me. I just set appropriate starting values and push the start button. Often many many times. And often with different starting values. If the best fit error (Sum Err²) can't be minimized further, it is very likely, that the global solution is found.

Cheers,
Aziz

[PiTec]

Uploads are now displayed as a file name, rather than displaying the image embedded in the post. The previous embedded method took up too much bandwidth on the server, and we had a complaint from the hosting company.

How about adding buttons next to the file links that would load and display individual images inline? It is much easier to read a thread with embedded images rather than switching between several browser tabs.

[PiTec]

Hi Aziz, here are the two Excel files with the latest measurements (post #519): decay_curves_04_05.rar

What is 'w' and how did you determine the values?

Thomas

[Aziz]

Hi all,

look, what the numerical simulation analysis brought to us.
I'm referring to the latest data from Thomas I have used last time.

Provided that, that G(t) is accurate enough (= most correct) we can make two experiments:
- Find time base correction (p-ofs) and set p=0 everywhere in the data set and tweak all the green variables to minimize the orange fields (Sum Err² of all four samples).
I get really very nice curve fittings with quite low sum of errors. And the distribution of exponent b makes perhaps sense. So it is obviously varying.
This is what I get:


- Assume, that exponent b never changes and stays at b=-1. Set p-ofs=0 and find all individual phase offsets p by tweaking all the green variable fields. Minimize the orange fields.
Well, I don't get very nice curve fittings anymore. Quite good but I've got seen better results with the first experiment. The Sum Err² is now bigger.
This is what I get:



Provided that, that G(t) is accurate enough, the first experiment is indicating a varying exponent b due to less fitting errors. Interesting experiment - isn't it?

I won't give up to find the answers.

Cheers,
Aziz

[Aziz]

Hi all,

bugger me!, I've got quite fooled with numerical best fit functions like the latest G(t).
It is possible, that you can get more optimal solutions and therefore more parameter sets with less fitting errors. So you don't get reliable and unique parameters (for single optimal solution).

I've started a convergence & stability analysis of the G(t). It is quite interesting, that you can get interesting facts about the numerical simulations.
The interesting questions, which haven't been answered yet are:
- is p varying (is there a phase ofset)?
- is b varying (is the exponent varying)?
- is p & b varying?
- is G(t) correct?

Who knows the (correct & provable) answer?

Cheers,
Aziz

[Qiaozhi]

BTW, why do inline attachments like the two above do no longer show up in the post? They used to do some time ago, now I have click on each attachment to see it. 'Show images' is checked in the general settings.

Uploads are now displayed as a file name, rather than displaying the image embedded in the post. The previous embedded method took up too much bandwidth on the server, and we had a complaint from the hosting company.

[Aziz]

Hate to tell ya but most here are wise to your stories with no product.

Wait a bit. Someone will come up with the WBGB detector!!! And you can forget your GPX!
Maybe a QED-V2-WBGB too.
Who knows.

[PATCHES JUNIOR]

PJ, you probably don't know it. But I have found the holy grail of VRM science.
Candy couldn't. *LOL*

Now let's look at the patent offices, whether someone will need taring & feathering.

Aziz

Hate to tell ya but most here are wise to your stories with no product.

[Aziz]

Hi guys,

I have removed the older Excel sheet pages and it should work now.
Thomas'sDecayDataV2-05lite.zip

Aziz