Hi everyone!
I spent lots of time to implement DEKF for battery state and parameters estimation simultaneously. However, I need your help! I will be grateful for any your advice.
I use the standard Li-ion battery model with the following state parameters: SOC and two voltages (V1 and V2) corresponding to two RC-branches. The observe equation is
y(k) = OCV(SOC(k)) - V1 - V2 - R0*i(k).
I use current as control.
Parameters are R0, exp(-deltat/R1*C1), R1*(1-exp(-deltat/R1*C1)), exp(-deltat/R2*C2), R2*(1-exp(-deltat/R2*C2)).
I calculated derivatives (Jacobian matrix) for parameters estimation recursively.
Unfortunately, I did not obtain good estimation results for R0 estimation.The problems that I managed to find: parameters covariance matrix updated noticeably during prediction step only; when current is equal to zero, estimated R0 has big noises in these iterations (please, see attached pictures).
The only solution that I found now: predict parameters not in the form of
theta(k+1)- = theta(k)+
but in the form of
theta(k+1)- = alpha*theta(k)+ + (1-alpha)*p, where p is expected parameter value based on mathematical model, alpha is tuning coefficient, unfortunately, I do not understand, how to obtain p in my model or any other because we do not have the explicit mathematical model for params estimation.
Could anyone help me find mistake in my inferences, please? Or provide useful articles where this problem is already solved? I will be very grateful for any advice which will help to find a solution.
If you use your second suggestion then setting alpha=0 gives you p which is rather absurd, since this is what you are trying to find. Your equation defining y(k) has the term R0*i(k) and if i(k) ~ 0 then of course you won't get sensible figures for R0. Make sure during your runs that your that your variables never result in values of i(k) ~ 0, even if this means constraining the value of t.
Best wishes!
Oh sorry, I hurried a little, so, I found mistake in my calculations.
I introduced the verification condition for current values: if current is less than predefined threshold value than parameter will take previously obtained parameter value and ignore DEKF steps; else, parameters values are updated during the main filter steps.
It is obvious that R0 values concentrate around model-value, noises significantly decrease but the result is not still accurate (please, see attached graph).
I am not sure, maybe I have mistake in my derivation of derivatives? If I designate Dx as the total derivative and dx as the partial derivative, I will obtain the following results:
df/dx = [1 0 0; 0 exp(-deltat/R1*C1) 0; 0 0 exp(-deltat/R1*C1)],
df/dthetta = [0 0 0 0 0; 0 V1 i 0 0; 0 0 0 V2 i],
dh/dx = [dOCV/dSOC, -1, -1],
dh/dthetta = [-i, 0, 0, 0, 0],
Dx/Dthetta = df/dx * Dx/Dthetta + df/dthetta,
Dh/Dthetta = dh/dx * Dx/Dthetta + dh/dthetta,
where f is the state function, h is the observe function.
I thought a lot of my problem and what I noticed now. In the attached picture you can see the current values which exceed predefined threshold and R0 values, which are put on them. What is noticeable, the values where current is greater than threshold R0 values tends to model (dot line) value but the values, where current does not exceed threshold confront to filter convergence.
Could you/anyone help to find mistake in my actual inferences, please?
Make sure that the software you use correctly interprets the term exp(-deltat/R1*C1) as exp(-deltat/(R1*C1)). The dimension of C/R is not a time!
Best wishes.
I suppose, this cannot be mistake because I did not use explicit form as exp(-deltat/(R1*C1)). I initialize thetta0 = exp(-1/3), denote this parameter as alpha1 and after that, during each iteration I update parameter alpha1 and use it in the state-equation.
The problem with DEKF was incorrect filter tuning. Correct choose of parameters solve the problem.
yes,according to my experiences, when KF series algorithm is used for battery model parameter identification and SOC estimation, appropriate noise characteristic is really hard to capture, not easy to set P Q & R accurately. So Anna, how is your DEKF now? If there is a huge initial SOC error like 30-50%, can it still work well?
Please, see attached picture, I plot bounds as 3*sqrt(P) to estimate filter goodness and I suppose, filter work is quite well.
Now, I try to find a way to tune DEKF automatically for different data sets. What do you think, is it a good idea?
idea is good, hard to realize I suppose, I can only set it emprically for now
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