Model Validiation
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Transcript of Model Validiation
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3.3 Model validation
A model validation was performed on the Steady State model to evaluate the
significance of the values that were predicted. The model used a Runge-
Kutte method with a time step of 2 months. The techniques applied to
validate the model are considered a “standard” for evaluating whether
modeled values correlate with measured values. There must be three criteria
satisfied for validation of the model. The three criteria include; Residuals of
the predicted concentrations must be randomly distributed, the slope of the
regression line must be significantly close to 1, and the correlationcoefficient must be statistically significant at the 95%confidence level. The
first statistical technique applied was a linear regression analysis. Figure __
below shows a linear regression analysis. For the model to be validated the
slope of the line must be significantly close to 1.
YearMeasured
Calculated
ChiSquare
(mg/m3) (mg/m3) χ^29/15/19
70 50 44.70.62168
1359/15/19
72 58.9 38.910.2730
3639/15/19
73 43 37.30.86983
1939/15/19
74 55 36.19.87419
2059/15/19
85 19 31.4
4.90862
5929/15/19
86 36.1 31.30.75237
2469/15/19
95 30 30.30.00235
5919/15/19
96 3 30.224.4924
9059/15/19 25 30.0 0.83430
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99 3739/15/20
00 24.8 29.90.88460
8769/15/20
01 35.5 29.91.05128
586
Totalχ^2
54.5647847
Figure __: Comparison of Predicted Values to Measured Values
Using a linear least squares regression to fit a trendline to the measured
data, the data is shown as non-linear due to a low r2 value of -1.644. Since
the slope of the line is 0.702 (below 1) the model fails one step in the
validation. A slope less than 1 tells us that the model is under predicting
concentrations.
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Figure ___: Comparison of Predicted Values to Measured Values’
Chi Square analysis of the measured results versus the modeled results
shows that the actual results differ too greatly from the calculated results for
the two to be proven correlated. A sum of the chi squares results in a value
of 54.56. This value isn’t even less than the Chi Square value for a .1%
confidence level (29.59 Chi Square value). The biggest factor in this large
value is an outlier concentration of 3 mg/m3 in the measured data. Without
this outlier, the Chi Square sum drops down to ~30 which is a much more
reasonable number, but still larger than any reasonable confidence level.
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These results indicate that the model does not do a very good job of
approximating the actual concentrations in the records.
A plot of the residuals was the second criteria performed for validation. For
the criteria to be satisfied the residuals most be randomly distributed. As
seen in Figure __ above, the residuals are not randomly distributed. Since the
values are not randomly distributed the model fails the second criteria of
validation.
The third criteria were not performed because the model is assumed to be
invalidated. The Runge-Kutte model was not used to predict concentrations
when selecting different remedial options.