This example shows how to use multiple experiments to estimate a mix of model parameter values; some that are estimated using all the experiments and others that are estimated using individual experiments. The example also shows how to configure estimation experiments with experiment dependent parameter values.
You estimate the parameters of a rechargeable battery based on data collected in experiments that discharge and charge the battery.
This example estimates parameters of a simple, rechargeable battery model,
sdoBattery. The model input is the battery current and the model output, the battery terminal voltage, is computed from the battery state-of-charge.
The model is based on the equation
is the battery terminal voltage in Volts.
is the battery constant voltage in Volts.
is the battery polarization resistance in Ohms.
is the maximum battery capacity in Ampere-Hour.
is the battery charge state, with 1 being fully charged and 0 discharged. The battery state-of-charge is computed from the integral of the battery current with a +ve current indicating discharge and a -ve current indicating charging. The battery initial state-of-charge is specified by in Ampere-Hour.
is the voltage drop when charging, expressed as a fraction of the battery constant voltage. When the battery is discharging this value is zero.
Loss are variables defined in the model workspace.
A 1.2V (6500mAh) battery was subjected to a discharge and a charging experiment. This experiment data has been loaded into a preconfigured estimation tool session.
sdoBattery model click Analysis and select the Parameter Estimation... menu item to launch the Parameter Estimation tool. From the Parameter Estimation tool click Open Session and select Open from model workspace and open the
sdoBattery_sdosession session. The measured charge and discharge experiment data are loaded and plotted.
Click the View tab to layout the plots so that the
Experiment plot:Charge_Exp and
Experiment plot:DCharge_Exp are both visible. Click Plot Model Response to see how well the model simulation matches the measured experiment data.
The plots show that the battery initial charge
Q0 is not set correctly for the
Charge_Exp experiment and that the model
Loss parameters need to be estimated.
The previous plot indicates that the
Charge_Exp battery initial charge,
Q0, is not set correctly. Add the initial charge to both experiments.
Charge_Exp and select Edit.... A dialog to edit the experiment opens.
Click Select Parameters to open a dialog to add model parameters to the experiment. Select
Q0 to add to the experiment. Select
Loss as we need to estimate this parameter using only the
Charge_Exp experiment. Click Ok to add the
Loss parameters to the experiment.
Set the battery initial charge
Q0 in the
Charge_Exp to 0, i.e. there is no initial charge.
Similarly add the battery initial charge
Q0 to the
DCharge_Exp experiment and set the initial charge to 6.5., i.e. for this experiment there is an initial charge.
Now that the experiments are updated with the correct initial battery charge click Plot Model Response to simulate the model and compare measured and simulated data.
The experiment plots show that the experiment initial conditions match but the battery response does not. The next step is to estimate the
V model parameters.
The previous plot showed that the model response does not match the measured data and we need to estimate the model
Click Select Parameters to open a dialog to select model parameters.
The upper portion of the select parameters dialog has a section for parameters that are tuned using all experiments. Click Select Parameters and add the
K model parameters to the estimated parameters. Set the
V minimum to 0 and the maximum to 2, similarly set the
K minimum to 1e-6 and maximum to 0.1.
The lower section of the dialog has a section for initial states and parameters that are tuned using individual experiments.
Charge_Exp we tune the
Loss parameter and set its minimum to 0 maximum to 0.5. The battery initial charge
Q0 is fixed to 0 and should not be estimated; uncheck Estimate.
DCharge_Exp from the Experiment combobox to view the parameter settings for the
DCharge_Exp experiment. The battery initial charge
Q0 is fixed to 6.5 and should not be estimated; uncheck Estimate
The experiments and estimated parameters are configured and we a ready to run the estimation. First create a plot to monitor the estimation progress. Click Add Plot and select Parameter Trajectory. This creates a plot that shows how the estimated parameter values change during estimation. Click the View tab to layout the plots so that the experiment and parameter trajectory plots are all visible.
Click the Estimate button to start the estimation. You can modify estimation options by setting the Cost Function combobox and clicking More Options....
While the estimation is running the plots update and a dialog showing estimation progress appears. The progress dialog shows the estimation iterations, the number of times the model has been evaluated (F-count), and the estimation cost at each iteration.
After a number of iterations the estimation converges and terminates. The experiment plots show the measured and simulation data matching well. The
EstimatedParams plot shows the
Loss parameters changing during the estimation; the scale of
Loss are different, right click on the plot and select Show scaled values to see how all the parameters changed from their original values.
To learn how to estimate parameters per experiment using the
sdo.optimize command, see "Estimate Model Parameters Per Experiment (GUI)".
Close the model