Hello Poornima,
I understand that you want to calculate 'Nash–Sutcliffe' efficiency, 'R square', 'RMSE' and 'PBIAS' values for your model in Simulink.
1. Calculation of Nash–Sutcliffe efficiency:
'Nash-Sutcliffe' coefficient is an indicator of the model's ability to predict about the 1:1 line between observed and simulated data.
The formula to calculate the Nash–Sutcliffe efficiency of a model is as follows:
where,
- 'NSE' is the Nash–Sutcliffe efficiency
- '
' is the observed data - '
' is the simulated data - '
' is the mean of the observed data.
2. Calculation of R square value:
'
' is one measure of how well a model can predict the data and falls between 0 and 1. The higher the value of '
', the better the model is at predicting the data. The formula for calculating the '
' value is as follows:
' is one measure of how well a model can predict the data and falls between 0 and 1. The higher the value of '', the better the model is at predicting the data. The formula for calculating the '' value is as follows:
where,
- '
' is the expected output value. - '
' is the calculated value for the model. - '
' is the mean of the y values.
3. Calculation of RMSE value:
To calculate the 'RMSE' (root mean square error) value, the following formula can be used.
RMSE = sqrt(mean((simulatedData - experimentalData).^2));
Here 'simulatedData' represents the simulated data and 'experimentalData' represents the experimental data, obtained from the model in Simulink.
4. Calculation of PBIAS value:
Percent bias (PBIAS) measures the average tendency of the simulated values to be larger or smaller than their observed ones.
The optimal value of 'PBIAS' is 0.0, with low-magnitude values indicating accurate model simulation. Positive values indicate overestimation bias, whereas negative values indicate model underestimation bias.
The following formula can be used to calculate the 'PBIAS' value for a model in Simulink.
where,
- '
' is the simulated data. - '
' is the observed data.
I hope this helps.
