Page 379 - Mechatronics for Safety, Security and Dependability in a New Era

Ch73-I044963.fm Page 363 Friday, July 28, 2006 1:57 PM
Friday, July 28,2006
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Ch73-I044963.fm
1:57 PM
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their filtering result would be poor. Using Kalman filtering only at level sections of the stem profile and
backward approximation are poor solutions since they follow the original measurement too closely, im-
proving the diameter estimate only locally. Although the filtering methods give good results, because of
their lack of robustness they should not be used if smoothing methods are applicable.

ONLINE SMOOTHING
The simplest solution is to smooth the diameter profile by computing the average of the measurements
inside a window, i.e. a portion of the diameter profile containing an equal amount of measurements on
each side of the current measurement. The window is centered at the measurement that is being esti-
mated. A second approach is to fit a polynomial to the values inside the window. Like in the averaging
method, some measurements are considered before and after the current measurement. Polynomial fit-
ting may give hugely erroneous results if the number of fitting points is small compared with the order
of the polynomial. This may occur if many fitting points are removed because of level sections in the
diameter profile. The basic polynomial fitting method can be improved by assigning different weights to
different measurements. A large weight is assigned to points that are situated after large drops in the
diameter profile, which is justified by the characteristics of the measurement process. A Kalman filter
can be also used to smooth measurements. The model for the tapering of the stem and changing of the
noise were implemented like in the Kalman filter online filtering method.
Online smoothing methods are better and more robust than the online filtering methods discussed earlier,
because in smoothing it is possible to use measurements before and after the point to be estimated. Thus
smoothing should be used instead of filtering whenever possible. The simple average yields good results
both when the whole stem and when the cutting points are considered. The result is most of all due to the
fact that the averaged profiles are smooth and resemble the true stem profiles. Windowed weighted
polynomial fitting is good in the sense that it gives profiles that pass near the bottoms of large drops in
the diameter profile. Polynomial fitting suffers from the unpredictable behavior of polynomials when
there are not enough fitting points. The algorithm discards measurements that are on level sections of the
stem profile. This leads essentially to extrapolating the diameter when long level sections are encoun-
tered, fn the methods where the amount of measurements to be taken into account can be changed,
increasing the window size is advantageous, fncreasing the number of measurements improves the ro-
bustness of the algorithms and makes it possible for them to take forthcoming changes in the diameter
earlier into account. Like in filtering case, also in smoothing the quality of the results given by the Kal-
man filter depend on the quality of the stem tapering model. The better robustness of the smoothing
approach when compared with the filtering approach may compensate some flaws of the model.

OFFLINE SMOOTHING

The first algorithm that was used was linear approximation of incorrect measurements. The method
searches the first and last point of each level section. The first point is connected with a line to the point
that follows the last point of the level section and the line is used as the diameter estimate instead of the
original measurement. This method can be generalized by fitting a polynomial to all the measurements
in the least squares sense. The measurements that are situated on the level sections of the profile are not
taken into account since they can be considered erroneous.

The next method added to the previous one weighting of the points that follow large drops in the diame-
ter profile. As stated before, the points following large drops are closer to the true diameter of the stem,
because the delimbing knives have most likely been in contact with the stem at these points. In the algo-
rithm the weighting factor is decreased in order to take into account the increasing uncertainty as
measuring continues after the drop. If a level section is detected, the weight is returned to the normal