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I am modeling the internal Resistance of a battery and have proposed the following equation:

$$R_{int}(SOH,SOC,T,Current)=A_1+A_2*SOH+\frac{A_3*T*SOH*asinh(Current*\frac{SOC}{A_4})}{Current*SOC}+\frac{A_5*log(SOH*current*SOC)+A_6+\frac{A_7}{T}}{Current*SOC} $$

Where SOC is the state of charge, SOH is the state of health(how degraded it is), T is the temperature and Current is the current.

The battery experiences enhanced degradation at low SOHs meaning the SOH terms need an additional parameter multiplying them and this is proposed:

$$R_{int}(SOH,SOC,T,Current)=A_1+(SOH<0.75 A_8+1)*A_2*SOH+\frac{(SOH<0.75 A_8+1)*A_3*T*SOH*asinh(Current*\frac{SOC}{A_4})}{Current*SOC}+\frac{A_5*log((SOH<0.75 A_8+1)*SOH*current*SOC)+A_6+\frac{A_7}{T}}{Current*SOC} $$

I get the following plots: SOH=0.7 at 3 currents, 5 temperatures and 10 SOCs

I am getting the following residual curves: not splitting current

and also: enter image description here

we can see the variance is high at low SOCs and that the points that outlie tend to be at low SOC and at either low or high Temperature. What do you suggest regarding both trends and non-uniform variance of the residuals? especially at high/low temps and at low Socs

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