**7. Results**

In the cluster Analysis, the patterns are the rods of the extensometers, and its readings along the months which are compared in order to determine the clusters. The dendrogram on figure 7 shows the formation of the clusters for these data.

Considering the first cut, there are two clusters left. The first cluster, here denominated "cluster 1", is formed by the rods of the extensometers that are considered extremely important to the monitoring of the dam. They are rods of extensometers installed in the axis of the block upstream the dam and inclined 60º towards upstream.

Notice that there is a formation of two additional clusters in the second cut. The first one denominates "cluster 2" which most of its rods of the extensometer installed in the balsatic rocks B, C and D (A and B are called the deepest rocks; C and D are called the superficial rocks), and on the lithological contacts B/C and C/D. The second cluster, denominated "cluster 3" has most of the rods of the extensometers installed in the joints (between the rock layers) A and B and on the lithological contact A/B.

This was the quantity of clusters which are been considered (3 clusters), since it was possible to obtain technical justification for its formation. In a larger subdivision, such justification was not observed.

Notice that at this point it was possible to cluster the instruments according to the relevant geological characteristics of the foundation mass, even though they weren't explicitly showed to the technician. However, on cluster 2, three rods of extensometers installed in joint B were observed, and in cluster 3, three rods of extensometers installed in the basaltic rocks B and C and in the lithological contact B/C were observed.

94 Multivariate Analysis in Management, Engineering and the Sciences

and it was also supervised by him.

**7. Results** 

was not observed.

(Maria Teresinha Arns Steiner). This study was part of a project guide by the third author (Andrea Sell Dyminski), called "*Analise de Incertezas e Estimação de Valores de Controle para o Sistema de Monitoração Geotécnico-estrutural na Barragem de Itaipu"* (Estimation of Control Values for the System of Geotechnic-structural Monitoring in the Itaipu Dam). All the research process counted with the collaboration of the fourth author (Anselmo Chaves Neto)

As mentioned before, the aim of this paper is to identify the instruments that are the most significant to the analysis of the behavior of dams. There are no records of the existence of methods that perform the ranking of the instruments of monitoring dams. In order to achieve this aim, it is necessary to select, cluster and rank geotechnical-structural instruments of an electric power plant looking forward to maximizing the effectiveness and efficiency of the readings analysis, in our case the Itaipu Hydroelectric Power Plant. In case of needing to intensify the reading this hierarchy could be useful to define which instruments to choose.

The choice of instrumentation is performed with no previous knowledge about the location, features, or characteristics of the instruments. In this way, it is possible to think of applying the methodology when making decisions about the automation of the additional instruments. Approaches that are similar to this can be used in many other cases because there are hundreds of large Civil Engineering construction works that rely on systems of

In the cluster Analysis, the patterns are the rods of the extensometers, and its readings along the months which are compared in order to determine the clusters. The dendrogram on

Considering the first cut, there are two clusters left. The first cluster, here denominated "cluster 1", is formed by the rods of the extensometers that are considered extremely important to the monitoring of the dam. They are rods of extensometers installed in the axis

Notice that there is a formation of two additional clusters in the second cut. The first one denominates "cluster 2" which most of its rods of the extensometer installed in the balsatic rocks B, C and D (A and B are called the deepest rocks; C and D are called the superficial rocks), and on the lithological contacts B/C and C/D. The second cluster, denominated "cluster 3" has most of the rods of the extensometers installed in the joints (between the rock

This was the quantity of clusters which are been considered (3 clusters), since it was possible to obtain technical justification for its formation. In a larger subdivision, such justification

Notice that at this point it was possible to cluster the instruments according to the relevant geological characteristics of the foundation mass, even though they weren't explicitly

instrumentation in Brazil which the data must have an appropriate treatment.

figure 7 shows the formation of the clusters for these data.

layers) A and B and on the lithological contact A/B.

of the block upstream the dam and inclined 60º towards upstream.

**Figure 7.** Dendrogram showing the formation of the clusters in different types of cuts (Ward's method).

Figure 8 shows the graphic of all the rods of the extensometer during the period of study. The lines were colored according to the cluster of which the rods belong to (black, blue and yellow for clusters 1, 2 and 3, respectively). It is possible to note the distinction between the clusters. This distinction of clusters is not easily recognized when there is no previous knowledge about these three clusters. The task would not be possible if a larger cluster of data hat to be analyzed, hence, the importance of this type of analysis.

Cluster 1, which is composed by rods of extensometers installed on the upstream of the dam, clearly shows the effects of summer and winter. The clusters 2 and 3 are separated due to the absolute measures. This separation can be justified by the fact that they are indifferent conditions, which is more superficial in cluster 2, and deeper in cluster 3. Once the readings of the most superficial rods and the readings of the deepest rods are summed up, these measures are larger.

Table 2 shows the most important rod for each of eight factors, for instances, the rod dominating each factor. Notice that in table 2 the factor 2 is dominated by the rod equip1\_1, equip1\_2, equip4\_1, equip4\_2, equip6\_1, equip6\_2, equip8\_1, equip8\_3, equip21\_1, equip21\_2, equip25\_3, equip26\_2 e equip31\_1. This factor has 10 of the 11 rods that are part

of cluster 1, it means that there is an external phenomenon influencing them. As mentioned before, these rods reflect the effects of the summer and winter. In the same way, each factor is dominated by a set of rods and there is an external phenomenon that explains each set of rods or factor, even though it is not easy to interpret them.

Itaipu Hydroelectric Power Plant Structural Geotechnical Instrumentation

Temporal Data Under the Application of Multivariate Analysis – Grouping and Ranking Techniques 97

A community is the portion of the variation of the extensometer rods which is explained by its factors. A low community within a rod indicates that the same is not greatly affected by the factor because a community is the sum of contributions of each rod in each square factor. Thereon, in this case the influence mainly comes from a random factor. Notice that none of the extensometer rods showed lower community than 0.71, it means that none of the random variations are over 29%. A community that is equal to 0.71 indicates that the 71% of the rods extensometer variations is ascribed to the factors and that only 29% of those variations is random, it means that these correlated rods are working properly. A low

Table 3 shows 25 rods of extensometers with the highest communalities. In case of reading intensification, these rods are the recommended ones. The highlighted rods are part of the system of automatic data acquisition of Itaipu. 24 of the 74 rods that were analyzed were automated by the engineers' team of Itaipu. The method of ranking that was proposed

(without the previous clustering of the rods) indentified 14 of the 24 automated rods.

Communality 0,988861 0,981763 0,976523 0,975655 0,972231 0,971971 Rod equip29\_1 equip21\_2 equip23\_1 equip22\_1 equip3\_1 equip1\_1 Communality 0,971798 0,970804 0,970397 0,968213 0,968083 0,967029 Rod equip22\_3 equip11\_1 equip1\_2 equip23\_2 equip4\_1 equip21\_1 Communality 0,966632 0,965999 0,965522 0,964925 0,963139 0,960121 Rod equip4\_2 equip29\_2 equip34\_3 equip6\_1 equip6\_2 equip22\_2 Communality 0,957609 0,953036 0,950395 0,949394 0,949108 0,948646 Rod equip14\_3 equip25\_1 equip33\_2 equip24\_2 equip24\_1 equip5\_1

After forming three clusters, the ranking of the rods was performed within each cluster with the help of the Factor Analysis. The hierachization within each group can also be used to identify rods used on readings intensification. The advantage of application of ranking within each group is that a separation of the rods with similar behavior is firstly obtained then the indicated rods will well represent the variability of the cluster. Note that the rods of the automated extensometers are, mostly, among the first in the ranking of each cluster.

As mentioned above, a low communality of a rod indicates that this rod is not strongly influenced by the factors and, in this case, the influence comes from random factors. In the application of Factor analysis within each cluster, there are rods of extensometers with communities between 0,6 and 0,7, in other words, random variation between 30% and 40%.

Furthermore, in order to identify the 24 rods that are the most relevant, we opted, in first place, to identify the 8 best ranked rods from each cluster. In this case, there would be 15 out of the 24 automated rods. This number of rods coinciding with the automated ones in Itaipu

community would indicate a need of investigating the rods.

**Table 3.** Shows the 25 rods of extensometers with the highest communalities.

It is indicated that the investigation on the rods is performed in this case.

Communality 0,943644 Rod equip28\_1

**Figure 8.** Graphic of all rods of the extensometers from the period of study.


**Table 2.** Rods of extensometers that are important to each factor, according to its weights in the Factor Analysis.

A community is the portion of the variation of the extensometer rods which is explained by its factors. A low community within a rod indicates that the same is not greatly affected by the factor because a community is the sum of contributions of each rod in each square factor. Thereon, in this case the influence mainly comes from a random factor. Notice that none of the extensometer rods showed lower community than 0.71, it means that none of the random variations are over 29%. A community that is equal to 0.71 indicates that the 71% of the rods extensometer variations is ascribed to the factors and that only 29% of those variations is random, it means that these correlated rods are working properly. A low community would indicate a need of investigating the rods.

96 Multivariate Analysis in Management, Engineering and the Sciences

rods or factor, even though it is not easy to interpret them.

**Figure 8.** Graphic of all rods of the extensometers from the period of study.

equip34\_2 equip34\_3 equip35\_1 equip35\_2

equip7\_1 equip7\_2 equip7\_3 equip11\_1 equip12\_1 equip12\_2 equip13\_1 equip13\_2 equip14\_1 equip14\_2 equip14\_3 equip19\_2 equip20\_2 equip20\_3 equip22\_1 equip22\_2 equip22\_3 equip23\_1 equip23\_2 equip23\_3 equip24\_1 equip24\_2 equip24\_3 equip25\_1 equip25\_2 equip27\_2 equip28\_1 equip28\_2 equip29\_1 equip29\_2 equip32\_3 equip33\_1 equip33\_2 equip33\_3 equip34\_1

factor2 equip1\_1 equip1\_2 equip4\_1 equip4\_2 equip6\_1 equip6\_2 equip8\_1 equip8\_3 equip21\_1 equip21\_2 equip25\_3 equip26\_2 equip31\_1

**Table 2.** Rods of extensometers that are important to each factor, according to its weights in the Factor

factor3 equip2\_1 equip2\_2 equip3\_1 equip3\_2 equip5\_1 equip5\_2 factor4 equip13\_3 equip18\_1 equip18\_2 equip18\_3 equip19\_1 equip19\_3

factor1

factor5 equip15\_1 equip15\_2

factor7 equip26\_1 factor8 equip32\_1

Analysis.

factor6 equip8\_2 equip20\_1 equip32\_2

of cluster 1, it means that there is an external phenomenon influencing them. As mentioned before, these rods reflect the effects of the summer and winter. In the same way, each factor is dominated by a set of rods and there is an external phenomenon that explains each set of

> Table 3 shows 25 rods of extensometers with the highest communalities. In case of reading intensification, these rods are the recommended ones. The highlighted rods are part of the system of automatic data acquisition of Itaipu. 24 of the 74 rods that were analyzed were automated by the engineers' team of Itaipu. The method of ranking that was proposed (without the previous clustering of the rods) indentified 14 of the 24 automated rods.


**Table 3.** Shows the 25 rods of extensometers with the highest communalities.

After forming three clusters, the ranking of the rods was performed within each cluster with the help of the Factor Analysis. The hierachization within each group can also be used to identify rods used on readings intensification. The advantage of application of ranking within each group is that a separation of the rods with similar behavior is firstly obtained then the indicated rods will well represent the variability of the cluster. Note that the rods of the automated extensometers are, mostly, among the first in the ranking of each cluster.

As mentioned above, a low communality of a rod indicates that this rod is not strongly influenced by the factors and, in this case, the influence comes from random factors. In the application of Factor analysis within each cluster, there are rods of extensometers with communities between 0,6 and 0,7, in other words, random variation between 30% and 40%. It is indicated that the investigation on the rods is performed in this case.

Furthermore, in order to identify the 24 rods that are the most relevant, we opted, in first place, to identify the 8 best ranked rods from each cluster. In this case, there would be 15 out of the 24 automated rods. This number of rods coinciding with the automated ones in Itaipu

would increase with the aid of a specialist for a better interpretation of the results. This specialist would detect that cluster 1, for example, is formed by rods that are extremely important for the monitoring of dams, and that all rods from this cluster should be automated.

Itaipu Hydroelectric Power Plant Structural Geotechnical Instrumentation

Temporal Data Under the Application of Multivariate Analysis – Grouping and Ranking Techniques 99

The identification of the months with more significant readings for an external effect (in this case, the effect of summer and of winter on the readings of the rods of the extensometers), can be useful, for example, in the projection of the values of control. Admitting that there are differences in the readings of the rods for the months related above, only the readings performed in these months would be used to define specific values of control for these months.

The application of this methodology is suggested for other instruments and other periods, and the implementation of it in order to define values of control and for anomaly detection. Once the process of ranking is repeated in several periods (every 2 years, for example.) it can show the appearance of new rods which are indicated for performing readings intensification or the appearance of rods that could no longer be indicated (these should be

This manuscript shows a methodology that uses some techniques of the field of Multivariate Analysis, which aim is to select, cluster and rank geotechnical-structural instruments of a Hydroelectric power plant, in our case, the Itaipu hydroelectric power plant, in order to

maximize the efficiency and effectiveness of the analysis of the readings.

Final factorial score Month Final factorial score Month 1,755 January/98 -0,761 April/02 1,217 August/95 -0,816 July/03 1,153 January/95 -0,821 Febrary/03 1,091 Febrary/95 -0,821 June/00 0,992 June/95 -0,856 June/02 0,914 March/95 -0,877 May/03 0,902 April/95 -0,904 Febrary/00 0,877 November/96 -0,924 May/00 0,794 May/95 -0,934 May/02 0,781 July/95 -0,965 April/00 0,776 April/97 -0,971 April/04 0,749 October/95 -1,050 April/03 0,741 November/95 -1,061 June/03 0,710 September/95 -1,135 May/00 0,709 Febrary/96 -1,152 March/03 **Table 4.** Shows final factorial scores of the months in which the readings of the 72 rods of the

15 first 15 last

extensometers were performed.

**8. Further research** 

investigated).

**9. Conclusions** 

This type of analysis was not found in literatures, for this reason the contribution of this study is relevant. It is recommended that this Analysis (process of hierarquization) is repeated periodically (according to the needs indicated by the specialists in this field – in this case, by the engineers' team of Itaipu) what could be done, for example, every two years. This can show the appearance of new rods that are indicated by the performing of readings intensification (that should be investigated), the same could occur with rods that would no longer be indicated.

When there are rods within the clusters with low communalities, it is recommended that they are investigated. Low communality indicates a high percentage of randomness in the data and that can be an indicator of problems with the rods.

These identifications of similar rods can also be used in projecting the control values. In this case, the values of control for each rod can be associated to the readings of the rods that belong to a same cluster.

The final factorial score performs the hierachization of the attributes. In this case the patterns are vectors of which the components (attributes) are the readings of the rods of the extensometers in a certain month. Therefore, the final factorial score performs the hierachization of the months showing whether there is any month that is rather relevant and that deserves greater attention.

Table 4 shows the first 15 months with a higher final factorial score and the last 15 months with lower final factorial scores, considering the 72 rods of extensometers. The values of the 15 first months with a higher final factorial score reveal that all the months are important; there is no month that is rather relevant. Only the month of December does not appear in the first 15 months. Notice that 1995 was the most relevant year and in analyzing the ambient temperature during the period of study it was possible to verify that this occurred due to the high temperature variation. The values of the last 15 months with least final factorial scores revealed that the months of April, May, and June are the most important one, identifying the effects of summer.

As mentioned, cluster 1 shows the effect winter/summer in its readings. For this reason the final factorial score was calculated in order to perform a ranking of the months for cluster 1, to show whether there is any month or some months with greater relevance.

The first 15 months with a higher final factorial score and the last 15 months with least final factorial scores were observed considering only the 11 rods of the extensometer of cluster 1. The values of the 15 first months with higher final factorial scores reveal that the months of September, October, and November are the most relevant ones, identifying the effects of winter. The values of the last 15 months with least final factorial score reveal that the months of March, April, May and June are the most important ones, identifying the effects of summer.

The identification of the months with more significant readings for an external effect (in this case, the effect of summer and of winter on the readings of the rods of the extensometers), can be useful, for example, in the projection of the values of control. Admitting that there are differences in the readings of the rods for the months related above, only the readings performed in these months would be used to define specific values of control for these months.


**Table 4.** Shows final factorial scores of the months in which the readings of the 72 rods of the extensometers were performed.
