In the construction of the paper machine map seven features were used: wire width, wire trim width, speed, minimum and maximum grammages, present technical production capacity and the year the machine was (re)built. For the pulp lines five features were used: bleaching type, fibre type, main pulp grade type, market capacity as a percentage of the total pulp production and the total pulp production capacity itself. The units, ranges and mean deviations of the components are given in table 5.1. The different types of bleaching, fibre and main pulp grade are listed in table 5.2.
|Paper machine data|
|Wire width (mm)||0 - 10160||1200||420|
|Wire trim width (mm)||0 - 9450||1200||400|
|Speed (m/min)||0 - 2800||310||130|
|Grammage, min ( )||0 - 999||50||28|
|Grammage, max ( )||0 - 9999||180||120|
|Capacity ( )||0.1 - 525||36||13|
|(Re)built (year)||1863 - 1996||14||7.1|
|Pulp line data|
|Main pulp grade code||1,2,3,4,5||1.3||0.28|
|Market pulp capacity (%)||0 - 100||26||5.7|
|Total capacity ( )||1 - 1075||73||35|
|OV||2||other virgin fibre|
|Main pulp grade|
|PW||5||process waste paper|
Three different-sized 1-dimensional SOMs were trained for both the paper machine and pulp line data and their quality was measured using four different quality measures. The results are depicted in table 5.3. It can be seen that as the size of the map increases the quantization error measure ( , equation 3.4) decreases, as does the energy function (E, equation 2.5). This is a natural consequence of having more neurons available for quantization. On the other hand the topographic error ( , equation 3.2) does not follow this trend, but is smallest for the smallest map (paper machines) or the second smallest (pulp lines). The topograhic quantization error ( , equation 3.5) combines these errors.
From the errors it is apparent that the pulp line data can be expressed much better with the 1-dimensional map than the paper machine data. The biggest paper machine map folds to make better use of its neurons, and the two criterias (topology preservation and resolution) become contradictory goals, as in figure 2.4. The best paper machine map was the one with 20 neurons. Both to use equal sized low level maps and since the 20x1-sized pulp line map was relatively good, the 20x1-sized maps were selected for further analysis.
|Paper machine maps|
|Pulp line maps|
The vector component values in the map units can be seen from the component plane representations in figure 5.2. By visual inspection of the paper machine map the three first components wire width, wire trim width and speed, have a strong correlation, as do the next two components minimum and maximum grammage. In the pulp line map none such global correlations can be seen. The mean deviations of vector components with respect to the values in their best-matching weight vectors are listed in the fourth column of table 5.1.
Figure 5.2: The component planes of the paper machine (a) and pulp line (b) maps. The name of the component on the right and the corresponding values in the map units from 1 to 20 in the middle. All components are presented with a grayscale with black representing the maximum value and white the minimum.
The clustering of the maps was based on visual inspection of the u-matrixes shown in figure 5.3 supplemented by the knowledge of the distribution of component values. From the paper machine map 6 clusters were extracted corresponding to different types of machines. The clusters and their descriptions are shown in table 5.4. The first cluster correspondes to new, high capacity machines with high speed and high value for wire width. The second cluster includes slightly older big or average sized machines. The fourth cluster resembled the second with the difference that the machines are a bit smaller and about 5 years older. The third cluster consists of machines with big paper weight. The two last clusters got the largest number of hits. They correspond to smallest and oldest paper machines. Based on the properties of the clusters, the paper machines can be divided into three different types:
The pulp line map can be divided into five clusters listed in table 5.4. The pulp lines in the first cluster make bleached pulp and use waste paper for fibre. The second cluster corresponds to pulp lines making unbleached pulp with varying fibre and main grade types. The third cluster has pulp lines which produce bleached pulp mostly from wood or other virgin fibres with chemical main grade. The fourth cluster consists of pulp lines with high capacity and an average market ratio. The pulp was bleached, fibre mostly wood and grade mostly chemical. The last cluster consisted of pulp lines with high market ratio. All in all, there are three major pulp line types:
Figure: The u-matrix presentations as of the paper machine (a) and pulp line (b) maps, with the map unit on the x-axis and the value of u-matrix on y-axis. Clusters on map are separated by peaks in the u-matrix. Clusters are listed in table 5.4.
|Paper machine map|
|1||1,2||454||Wide wire and high speed, small paper weight, high capacity, new machines.|
|2||3-6||1024||Average sized machines, over ten years old on the average.|
|3||7-9||467||Narrow wire, slow speed, big paper weight, small capacity.|
|4||10-12||1033||Average wire width and speed, over 15 years old on the average.|
|5||13-16||2648||Small machines, over 15 years old on the average.|
|6||17-20||3139||Small and old machines.|
|Pulp line map|
|1||1-4||557||Pulp made from waste paper.|
|2||5-11||993||Unbleached pulp, both fibre and grade vary.|
|3||12-15||762||Bleached pulp, wood or other virgin fibres, chemical main grade.|
|4||16-18||303||Bleached pulp, mostly wood fibre and chemical main grade, average market ratio, high capacity.|
|5||19,20||364||Big market ratio, mostly wood fibre and chemical main grade.|