GPS-X Technical Reference

419 Miscellaneous
RESIDUAL PLOTS
For a selected measured time series data, a number of residuals as show in Table 15-2 are
estimated. The calculated residuals are used for plotting against time or observed data. A
histogram of the standardized residuals is also made available for evaluating the model fit.
Table 15-2 – Types of Residuals
No. Criteria Equation
1 Residuals (O i − P i )
2 Absolute Residual |O i − P i |
3 Squared Residual (O i − P i ) 2
4 Relative Residual
(O i − P i )
O i
5
Absolute Relative
Residual
|O i − P i |
O i
6 Squared Relative Residual ( O 2
i − P i
)
O i
7 Standardized Residuals
(O i − P i )
√ 1 n ∑ n i=1
(O i − P i ) 2
Histogram of Standardized Residuals
A histogram of the standardized residuals are plotted to check the assumption that the
errors are normally distributed. The histogram of standardized residual may also help to
inspect if the residuals are randomly scattered about zero and to approximately 95 percent
of the residuals lie between +2 and -2. A histogram produced for the BOD dataset is as
shown in Figure 15-5.
Residual Plots against Measured Data
The estimated residuals can be plotted against the measured data point to see trends and
biases in model outputs. A typical output of this type of plot is as shown in Figure 15-6.
Residuals Plots against Time
For identifying trends in estimated residuals, the time plots of the residuals may be
useful. The model predictability may be affected some specific time based events and
these plots may be of help to identify time periods of special events (rain fall, plant
maintenance etc.) where the plant operation conditions are not captured adequately in the
model. A typical output for this type of plot is as shown in Figure 15-7.
GPS-X Technical Reference