Environmental Engineering Reference
In-Depth Information
1.5
data 1
linear
quadratic
cubic
1
0.5
0
- 0.5
0
1
2
3
4
5
6
7
8
residuals
Linear: norm of residuals = 0.356
Quadratic: norm of residuals = 0.13793
Cubic: norm of residuals = 0.081693
0.2
0.1
0
- 0.1
- 0.2
1
2
3
4
5
6
7
8
Fig. 10.3 Results for the example fitting problem, using the 'Basic fitting' tool under MATLAB
®
In the 'Basic Fitting' box various options are available: polynomial fitting for
polynomials of degrees 1-10 and spline interpolation. Residuals can be shown as
bar plots, line plots or scatter plots, either in a subplot or a separate figure. Equations
can be shown in the curve plot, residual norms in the residual plot. The user may
select the number of significant digits of the fitting and may center and scale
x
-axis
data. If more than one data-set is depicted in the figure, fitting can be performed for
all data-sets separately. Moreover, there is the option to save the results of the fitting
procedure to the workspace.
Using the options shown in Fig.
10.2
for the example data-set, one obtains the
plot, given in Fig.
10.3
.
The upper subplot of Fig.
10.3
shows the linear, quadratic and cubic best fits
together with the original data. The lower subplot depicts histograms of the residual
vectors for all three fits and lists the norm of the residuals. The coefficients of the
polynomials are obtained by using the
button in the 'Basic Fitting' box.
10.3 Exponential Curve Fitting
In environmental systems exponential fits are often more appropriate than polyno-
mial fits. See the next sub-chapter for an argument, why exponential curves can be
expected as outcome of batch experiments. Generally, there may be some reason
that the solution has the exponential form:
