Casestudie Breakdown prediction Contell PILOT - Transumo

accurately predetermined. Suggested is a size of 100 to 150 values. (Daßler95] p.
25)
Figure 4-2 pictures that the ring memory module communicates with three
succeeding ones. First step of analysis is the curve selection. The basic idea is to
describe the stored measurement values within the ring memory by finding a
mathematical function (called regression). The curve selection module determines
this function by using the method of least squares. 36 The acquired function is used to
predict upcoming values by the succeeding module. (Daßler95] p. 25-26)
These predicted values are used to recognize changes in trend. As soon as a
change is recognized, the ring memory is cleared. This is especially important
because old values that were stored before the change, falsify the results. An
identification of changes is done by comparing actually measured values to their
corresponding predictions. In case of exceeding a certain threshold (see below), a
new trend is assumed. (Daßler95] p. 58-60)
The biggest problem of a reliable prediction is the already mentioned noise because
a high noise could lead to an assumption of a new trend, although the behavior stays
the same. That is why the noise has to be determined. The first step is a calculation
of an envelope. This envelope normally includes all peaks. To exclude potential high
peaks from envelopes, the following algorithm is used: (Daßler95] p. 61)
1. Select the first five measurement values
2. Determine ( f b
) as a line of best fit for these values
3. Calculate the distances between f
b
and measurement values
4. Calculate the mean distance above the line ( d
a
)
5. Calculate the mean distance below the line ( d
b
)
6. Assign d
a
and d
b
to the measurement point right in the middle,
Assign
f ( X
max
) + d to the maximum value ( X
max
)
b
a
Assign
f
X )
b
( X
min
) − db
to the minimum value (
min
7. If end is not reached, deselect the first selected value, add the next one and
go to 2.
36 Section 5.4 contains a detailed description of regression and the method of least squares
50