This module is a part of “Engine Carbon Brushes Replacement” project. The purpose of the module is a classification of the Cement Mill 10 engine start phases.

Trying to clustering the quality of the start phases was concluded, that is important to clusterize whole working periods because the start phase is a part working period and the difference between start phases is determined by the difference between work periods. It is better way to clusterize whole work period using start phase as one of the classifiers.

As classifiers of work periods were taken four parameters:
a) average current;
b) standard deviation of current;
c) duration of start phase;
d) period of time between previous and analyzed work period.

Before running classification algorithms let’s check whether there are any correlations between chosen classifiers.

There is no any correlation between classifiers.

Classification methods

Classification method will be chosen from hierarchical clustering “ward.D”, “ward.D2”, “single”, “complete”, “average”, “mcquitty”, “centroid” methods and K-Mean clustering method.

The best clustering method and the optimal number of clusters are evaluated by Calinski-Harabasz Index.
For this purpose, all listed algorithms applied to the dataset with the number of clusters from 2 to 20 (step 1). Results are shown in the chart.
(R- code is based on functions published on
https://github.com/ethen8181/machine-learning/blob/master/clustering_old/clustering/clustering_functions.R)

According to the chart, the best result brings K-Mean method divides data for 13 groups.
The biggest CH index k=13 of k-Mean line on the “CH-index” chart. Clusterization all observations by 13 clusters is redundant, I intend to divide data no more than 5 clusters. Actually, CHIndex on k=13 not significantly bigger than on k=5. On “wss” chart, the line of K-Mean represents smallest values and dramatic decline of wss changed by a relatively smooth decline on k=5. CHIndex chart gives the best result on k=5 for a k-mean method. For clusterization will be used a k-mean method with k=5.

Let’s represent the CH Index data in the matrix view:

##     k  ward.D ward.D2 single complete average mcquitty centroid  kmeans
## 1   2  720.23  894.35 791.45   894.35  791.45   894.35   791.45  900.83
## 2   3  694.01 1027.29 511.36   660.28  511.36   511.36   511.36  992.52
## 3   4  753.04 1134.80 411.66   489.87  489.87   489.87   489.87 1146.10
## 4   5  625.20 1290.59 379.02   429.32  429.32   429.32   429.32 1598.59
## 5   6  572.16 1358.47 304.12   607.61  607.61   607.61   349.73 1616.04
## 6   7  758.15 1422.39 277.37   676.25  513.96   513.96   513.96 1620.35
## 7   8  805.09 1405.38 251.00   588.02  459.48   479.79   441.53 1587.46
## 8   9  753.51 1397.33 222.43   576.05  528.33   507.96   410.34 1588.43
## 9  10  690.23 1417.58 206.47   529.27  485.45   466.76   503.63 1520.02
## 10 11  633.83 1459.01 301.92   482.90  438.91   424.42   468.51 1569.59
## 11 12 1147.58 1475.55 274.67   492.24  399.87   386.67   426.57 1524.83
## 12 13 1111.31 1474.68 252.13   605.95  369.58   444.38   392.18 1630.50
## 13 14 1062.90 1471.03 234.14   562.78  370.16   697.08   363.28 1462.92
## 14 15 1053.23 1479.52 227.61   527.00  344.25   650.61   337.56 1464.31
## 15 16 1002.40 1479.82 213.73   944.35  323.17   610.59   315.76 1428.88
## 16 17  971.44 1490.04 202.96   892.55  331.47   576.19   299.01 1536.80
## 17 18  925.84 1499.54 195.32   876.39  408.02   543.25   303.11 1577.76
## 18 19  885.98 1496.22 192.74   830.24  386.01   604.39   286.80 1541.64
## 19 20  867.51 1495.13 184.27   796.67  366.72   574.44   271.96 1552.42

Let’s apply K-Mean clustering method with k=5. The algorithm divided all engine runnings into 5 clusters by following way:

Clusters research

By comparison information gain of all classifiers against clusters, we can see relative weight of all of them (classifiers ) in clustering: 

##                    VarName    weight
## 1               avgCurrent 0.4991753
## 2               stdCurrent 0.2959335
## 3               startPhase 0.1167698
## 4 hoursFromPreviousRunning 0.1000542

The most significant influence in clustering has average current, the less significant influence has time from the previous running.

With the help of radar chart, let’s see distribution of chosen parameters between the groups.

The major group “5” actually represents stable engine work and has a relatively low average current, without significant fluctuations (small std).
The next big cluster “3” also represents stable engine work with more high current than cluster “4” without significant fluctuations (small std).
Group “2” also represents stable work periods with slightly longer time intervals from the previous runnings and a slightly high average of the engine current than cluster 5.
Cluster “1” includes work periods with significantly long start phases.
Cluster “4” - work periods with significant std of the current of both start phase and whole runnings, it is combined with a long time from the previous running.

Let’s see the average current in the groups compared with the average current of start phases of those groups.

Let’s see the average current in the groups compared with the average current of start phases of those groups.

Major groups 5, 3, 2 have a relatively narrow range of current fluctuation and the averages current of start phases (white point) are close to general averages.

In opposed, small group 4 has a wide range of the current fluctuations and the average of the start phase significantly different from the general average.

Now we have a two question:
a) Maybe some processes or events connected to the mill have had a temporary influence and belong to the specific time period and now have no more importance?
b) Maybe the material type has an influence on groups?

According to the chart, obviously, there is no any connection between division by groups and special time period. All groups represented during the whole analyzed time period.

Here is the table of the percent presentation (by work hours) material types in groups: 

##        
##             1     2     3     4     5
##   AM     2.79 11.33 21.32  0.30 37.81
##   AMLS   0.02  0.09  0.02  0.00  0.41
##   empty  0.02  1.33  0.45  0.04  5.46
##   OPC    0.30  2.58  2.56  0.04 13.11

Now it looks like that there is not any connection between material types and groups.

Next chart shows the density of values of current within different types of material. The average current of groups is indicated by vertical black lines.

There isn’t a significant difference between distributions of the currents of the different material types, besides running without a material load.



Next chart shows the density of values of current within different clasters.



Group “1” includes the runnings with longest start phases, and group “4” includes the most unstable runnings.