MULTIVARIATE ANALYSIS OF THE DISPLACEMENTS OF A
CONCRETE DAM WITH RESPECT TO THE ACTION OF ENVIRONMENTAL CONDITIONS
Sheila Regina Oro
Federal University of Technological - Paraná, Brazil
E-mail: sheilaro@utfpr.edu.br
Anselmo Chaves Neto
Federal University of Paraná, Brazil
E-mail: anselmo@ufpr.br
Tereza Rachel Mafioleti
Federal University of Technological - Paraná, Brazil
E-mail: mafioleti@utfpr.br
Suellen Ribeiro Pardo Garcia
Federal University of Technological - Paraná, Brazil
E-mail: suellenrp@utfpr.edu.br
Cláudio Neumann Júnior
Itaipu, Brazil
E-mail: neumann@itaipu.gov.br
Submission: 07/12/2015
Revision: 31/12/2015
Accept: 27/01/2016
ABSTRACT
A review of the concrete dam’s structural performance is a complex issue
comprised of many dimensions. This article proposes a method to assist in
monitoring the displacements of structures and foundations of dams, considering
the action of environmental conditions. Multivariate techniques are used to
analyze the data pendulums, extensometer bases and multiple rods extensometer,
along with environmental variables of the concrete surface temperature, ambient
temperature and the reservoir water level. Specifically applies to Canonical
Correlation Analysis to evaluate the influence of environmental variables in
the displacement of structures and foundations. Factor Analysis identifies the
factors inherent to the variability of the data. This technique makes it possible to order the variables considering the
action of factors. This applies also to Cluster Analysis on the data of dates
of measurements, according to the similarities present in the observations.
Then, Discriminant Analysis evaluates the formed groups for uniformity. The
results demonstrate that the method can distinguish the dam responses and identify
the effects of variations in environmental conditions over the displacements of
structures and foundations.
Keywords: structural monitoring; concrete dam; multivariate analysis
1. INTRODUCTION
The
concrete dam structures are subject to changes caused by the incidence of
phenomena, such as displacements, strains, stresses, pressures, etc. (CARVALHO;
ROMANEL, 2007).
This occurs because these structures have strong interaction with
environmental, hydraulic and geomechanical factors, as the temperature of the
concrete, the hydrostatic pressure and the effect of time (LI;
WANG; LIU, 2013). Therefore,
these factors should be taken into account during structural evaluation.
Structural
Monitoring is accomplished by visual inspection, geodetic measurement using
vertical and/or horizontal displacements, bathymetric surveys and monitoring
instrumentation (CRUZ,
2006). The
instruments used in this monitoring include pendulums, extensometer bases,
triple orthogonal meters, flow meters, piezometers, multiple rod extensometers (MATOS,
2002).
The
instrumentation data set is useful for assessing the safety of dam’s
performance, especially if the current measures are compared with the entire
series data through statistical and structural identification tools (DE
SORTIS; PAOLIANI, 2007). Reports on
instrumentation and visual inspections are useful in this case because they
cover all aspects of the dam since its construction up to the operational phase
(KUPERMAN
et al., 2005).
Detailed
analysis of instrumentation data requires a combination of knowledge,
especially of Engineering, Mathematics and Statistics, and should be done by an
experienced technical team, with the assistance of computational resources (VILLWOCK
et al., 2013).
This
work presents a helper method in the structural monitoring of concrete dams,
combining multivariate statistical techniques to: (1) quantify the influence of
environmental conditions on displacements of structures and foundations; (2)
identification of the most relevant sensors with respect to the variability of
the data; (3) grouping of the dates of measurements, according to the
similarities.
The
text structure is composed of six sections, with Introduction being the first
one. The second section presents the review of the literature on the use of
statistical techniques in the structural monitoring of concrete dams. Section 3
discusses the theory related to multivariate techniques of Canonical
Correlation Analysis, Cluster Analysis, Discriminant Analysis and Factorial
Analysis. The proposed method is described in the fourth section. Then, the
results obtained in applying the method are conferred and discussed. The last
section grants the conclusion of the article and suggestions for future
research.
2. STRUCTURAL SECURITY
The
interest in perfecting techniques for structural monitoring of dams has grown
in recent decades mainly due to the need for greater security in order to avoid
the consequences of disasters caused by structural problems (MEDEIROS;
LOPES, 2011).
The
methods used to monitor the structural safety of dams usually consist of
comparing loads and safety factors used in the projects of dams with the
behavior of all structures over the years (KUPERMAN
et al., 2005).
The
selection of data, during the process of monitoring the behavior of structures,
involves the choice and type of method, number and location of the sensor, and
hardware acquisition/storage/data transmission. This process is specific to
each application. Economic issues play an important role in making these
decisions. The time interval in which data should be collected is another point
that should be considered (FARRAR;
WORDEN, 2007).
In
situations that have uncertainties inherent in the system adopted, the
statistical analysis is indicated Farrar and Worden (2007) to sort an amendment
of the parameters as from the structural condition change (failure) or
modification of environmental and/or operating conditions.
As
the data may represent measures of different natures and scales, it is
important to standardize the data to enable the damage identification process.
Accordingly, Figueiredo et al. (2011) points out that standardization of data
is an inherent procedure for data acquisition, feature extraction and
statistical modeling in structural monitoring process, such as to remove the
effects of operational and environmental variables with the extracted
resources.
In
addition, Farrar and Worden (2007) it is stressed the need to identify and
minimize sources of variability in the data acquisition process and in the
monitored system. However, not all sources of variability can be eliminated,
for example, the variation caused by various environmental conditions such as
temperature, humidity, loading and boundary conditions. Therefore, it is
necessary to make appropriate measures so that these resources can be
quantified statistically.
According
to the literature, the statistical modeling of the structures monitoring data
has been applied, mainly, to achieve classification, association, forecast
values and outliers detection. Among multivariate statistical techniques, the
most used for this purpose are discriminant analysis, canonical correlation,
multiple linear regression and principal component analysis. Reports and
discussions of these applications can be found at (BUZZI,
2007; CHENG; ZHENG, 2013; DENG; WANG; SZOSTAK-CHRZANOWSKI, 2008; DE SORTIS;
PAOLIANI, 2007; FIGUEIREDO et al., 2011; GUEDES; DE FARIA, 2007; JIN-PING;
YU-QUN, 2011; LI; WANG; LIU, 2013; MATA, 2011; MATA; TAVARES DE CASTRO; SÁ DA
COSTA, 2013; MUJICA et al., 2014; XU; YUE; DENG, 2012).
3. THEORETICAL
A
collection of n observations of p distinct random variables, taken from
the same item, compose a multivariate sample, which can be represented in
matrix form (Eq. 1), where each Xj
vector containing the n observations
of the variable j, for all j = 1, 2, ..., p.
|
(1) |
Multivariate
analysis provides methods and techniques for the theoretical interpretation of
jointly sample. The main purposes that justify the use of multivariate analysis
methods and techniques are: data reduction and structural simplification;
sorting and grouping; investigation of dependence between variables; forecast;
construction and hypothesis testing.
The
following are the theoretical aspects of multivariate techniques called
canonical correlation analysis, factor analysis, cluster analysis and
discriminant analysis used in this study.
The
Canonical Correlation Analysis is an interdependence analysis technique that
allows researchers to identify and quantify the associations between two groups
of variables (X and Y). The basic idea is to find the linear
combination of variables X and linear
combination of variables Y that
produce the highest correlation between the two groups (JOHNSON;
WICHERN, 2007).
The
first group (X) is composed of p
decision variables, also called, explanatory variables (independents). While
the second (Y) is formed by q
response variables (dependents on explanatory).
The
vectors X and Y have covariance matrices and, respectively, and the relationship
is summarized in the cross-covariance matrix between these vectors, that is.
Given
that U and V are linear combinations of the vectors in X and Y (Eq. 2),
respectively, the canonical problem is to obtain the vectors of coefficients a
and b that maximize the correlation between U and V (Eq. 3). The vectors a and b, in this case, are solutions of a system of equations (Eq. 4). The linear combinations U and V, in this case, are called canonical variables.
|
(2) |
|
|
|
(3) |
|
(4) |
Where
λ is the largest eigenvalue of the
matrix or, equivalently, of the matrix .
Thus,
each pair of canonical variables have unit variance, maximum correlation and is
not correlated with others pairs of canonical variables. The number of pairs of
canonical variables that can be obtained is equal to the lowest value of p and q. In general, we try to get a few pairs of canonical variables
that explain much of the interdependence between the two sets of observable
variables.
The
application of multivariate technique of Factorial Analysis allows the
explanation of the correlations between many variables of a set of data through
a limited number of unobservable random variables, called factors. (JOHNSON;
WICHERN, 2007).
Verification
of the viability of the factor model used is made by applying the Bartlett Test
(Eq. 5), and the quality of fit of the model to the data set is estimated by
the Criterion Kaiser-Meyer-Olkin (KMO). The KMO coefficient (Eq. 6) varies
between 0 and 1. The closer to 1, the better the adjustment factor model to the
data.
|
(5) |
|
(6) |
Where
qij is the element
belonging to the i-th row and j-th column of the matrix, with .
The
factor model (Eq. 7) considers that each variable can be written as a linear
combination of the common factors (Fk)
and specific factors. During the process of obtaining the factors, are
estimated the factor loadings (lji),
the commonalities (hi),
the specific variances (εj)
and the factorial scores (fjk)
that are measurements with explanatory properties of great interest to the
researcher.
The
load factor is a measure of the variable correlation with the factor. The
commonality is the portion of the variance of each original variable from the
extracted factors. The remainder of the variability, which can be owed to other
factors, is measured by specific variance.
|
(7) |
The
factor scores (Eq. 8) are estimates for the values of the factors for each sample
element. They may be used to sort sample components or as input variables for
further statistical analysis.
|
(8) |
The
use of Cluster Analysis seeks to find, within a heterogeneous set of data, a
small number of homogeneous groups, whose variation within the group is
substantially smaller than the total variability of the data set.
Initially,
in the hierarchical agglomerative method, each observation forms a separate
group. At each step of the process, the groups join according to the
similarities, forming new groups, until remains only one group with the total
number of observations included.
Similarity
is a measure of proximity between two groups. One way of calculating this
measure is the Mahalanobis distance (Eq. 9).
|
(9) |
Where
Σ is the complete data set of
covariance matrix X.
Discriminant
Analysis is a technique that enables, starting from independent variable, to
study the profile, performing classification and differentiation of two or more
group elements. The number of groups should be known in advance. The
discrimination is made based on a mathematical rule, which minimizes the
likelihood of incorrect classification errors.
In
the perspective of Mahalanobis (Eq. 10), is calculated the distance () of each observation to the centroid of each group (). Then, the observation is allocated to the nearest
centroid group.
|
(10) |
Where
ΣW is the covariance
matrix within the group between the independent variables.
4. METHODOLOGY
The
evaluation of the responses of a dam structure, considering the instrumentation
data and taking into account interaction with the environment, is a problem composed
of various dimensions. Therefore, it is necessary to use techniques that allow
the joint analysis of monitoring data, reduce the magnitude of the problem and
assist decision-making.
The
multivariate statistical techniques, called Canonical Correlation Analysis,
Factorial Analysis, Cluster Analysis and Discriminant Analysis meet these
requirements and, therefore, constitute the method used in this work.
As
illustrated in Figure 1, the method consists of five steps. The first is the
selection of instruments, the definition of the time period and data
collection. If there is a difference in frequency of the measurement
instruments, it is necessary to equate the periods, using for example, the
monthly average of observations. Furthermore, in this step are identified and
filled in the gaps coming from the absence of readings in the period. The
filling is made with modeling and forecasting time series.
Then,
the Box-Plot and Scatterplot graphics are used to identify the occurrence of
outliers. For each detected outlier, it is need to evaluate its maintenance or
exclusion from the data set. If you choose to exclude it, you must make a new
value forecast, using the same procedure of filling the gaps.
Thus,
it is composed a sample data matrix (X),
with n lines (monthly average) and p columns (sensors of the instrument). If
there are differences of magnitude and in the scale of the observations, owed
to the use of different kinds of instruments, the data must be standardized.
The standardized data matrix (Z) is,
then, used as input to the procedures listed in the following steps.
The
second step is the application of Canonical Correlation Analysis to study the
relationship between the group of sensors, which measure the displacements of
the dam structures and their foundations, and the group of indicators of
environmental conditions.
Then,
in step 3, the Factorial Analysis is used to estimate the influence of
environmental conditions in shifts, perform the ranking of the instruments
according to their importance in the factor model and identify factors that can
be used as criteria for the overall assessment of displacements.
In
the next stage, the scores of factors are subjected to Cluster Analysis for the
formation of homogeneous groups of measurements dates.
In
the last step, Discriminant Analysis tests the formed groups, with reference to
the sensors with higher ranking in the Factorial Analysis.
The
proposed method was applied to a structural monitoring process of a concrete
dam. The data set used consists of the observations recorded in the period
between January 1990 and December 2013, which were obtained through manual
measurements of the installed instrumentation in D7 and D8 key blocks (Fig. 2),
the D portion (Dam Right Side, built in blocks buttresses) of the Itaipu dam,
and the hydrometeorological data from the same period.
Figure 2: Layout of instrumentation installed in key blocks D7
and D8 of the Itaipu dam
Table
1 shows the sensors 42 considered in this study, corresponding to the direct
pendulums, inverted pendulums, extensometer bases, multiple rods extensometers,
thermometers and Limnimetric ruler.
Table 1: Phenomena monitored by instruments and respective
sensors
Phenomena |
Instrument |
Sensor ID |
Radial displacement |
Direct pendulum |
Z1, Z5 |
Radial displacement |
Inverted pendulum |
Z3 |
Tangential displacement |
Direct pendulum |
Z2, Z6 |
Tangential displacement |
Inverted pendulum |
Z4 |
Opening and closing of joints between blocks |
Extensometer base |
Z7, Z9, Z11, Z13, Z15, Z17 |
Horizontal sliding between blocks |
Extensometer base |
Z8, Z12, Z14, Z18 |
Differential settlement between blocks |
Extensometer base |
Z10, Z16 |
Surface temperature of block |
Concrete thermometer – downstream |
Z19 |
Surface temperature of block and water reservoir |
Concrete thermometer – upstream |
Z20 |
Deformations of rocky massive |
Multiple rod extensometer |
Z21, ..., Z40 |
Ambient temperature |
Thermometer |
Z41 |
Water level of the reservoir |
Limnimetric Ruler |
Z42 |
Given
that the frequency of measurements gauged with the different instruments
(sensors) was not the same, it was decided to use the monthly average of the
observations. The implementation of a computational procedure, performed with
the help of Matlab software (Matlab
R2013, 2013),
allowed to create a monthly average observations of each of the 42 sensors and
to identify the existence and location of gaps, corresponding to periods
(months) that measurements were not performed.
It
was found that there are eight incomplete series, totaling 15 deficiencies
resulting from the lack of measurements at some point. There were created two
(sub) series for each sensor that detects the occurrence of gaps: one with
previous observations to the missing data and the other with subsequent
information to the same issue. The forecast of this data was performed using
the forecasting/backforecasting procedure, which consists in modeling each
(sub) series, making value forecast and fill the gap with the average value of
the two forecasts. The ARIMA models were used for the realization of the
forecasts, with the help of Statgraphics software (Statgraphics
Centurion XVI, 2010).
After
completing the sensor data series, we proceeded the analysis of the Box-plot
and Scatterplot graphics of each series, in search of the occurrence of
outliers. Outliers were identified in the data reservoir water level (Fig. 2). The cause of this occurrence was
the incidence of drought (low rainfall) in the months of the summer season of
the years 1999/2000 and 2012/2013. It was decided to keep the values as
observed, to check the influence of this occurrence in the dam’s answers.
Owing
to differences in quantities and measuring scale on the variables, because of
the nature of the sensors, it was necessary to carry out the standardization of
data.
Thus,
it was made the sampling data matrix (Z),
order 288×42, whose lines correspond to the dates (month/year), the columns to
the variables (sensors) and the elements to standardized data.
(a)
(b)
Figure 3: (a) Box-Plot and (b) Scatterplot graphic of the reservoir water level
(RWL) from Itaipu dam, from Jan /90 to Dec /13
The
Canonical Correlation Analysis was used to study the relationship between the
sensors clusters that measure displacement (Z1 to Z18 and Z21 to Z40) and
indicators of environmental conditions (Z18, Z19, Z41 and Z42). As shown in
Table 2, all the eigenvalues were considered significant at a confidence level
of 95% (p-value <0.05). It was decided to discuss the results of the
canonical correlation of higher value.
Table 2: Canonical correlation of
displacement sensors vs. environmental conditions
Eigenvalue |
Canonical Correlation |
Wilks'lambda |
χ2 |
Degree of Freedom |
p-value |
λ1 =
0,973 |
0.986 |
0.003 |
1537.080 |
152 |
0 |
λ2 =
0,717 |
0.847 |
0.114 |
577.122 |
111 |
0 |
λ3 =
0,437 |
0.661 |
0.402 |
242.062 |
72 |
0 |
λ4 =
0,286 |
0.535 |
0.714 |
89.492 |
35 |
0 |
The
canonical correlation between the two groups was 0.986. This measure indicates
the strong influence that the environmental conditions (V1) have on the set of
sensors that measure the displacements of the dam’s structures (U1).
The
correlations between the 38 variables of the first group and four of the second
were estimated. Table 3 lists the
variables with the highest correlations (| ρ | > | 0.8 | and p-value <
0.05), with predominance of multiple rod extensometers (Z23, Z24, Z35, Z38,
Z40) related to temperatures (Z19, Z20 and Z41). Appear, also, three sensors
pendulums (Z2, Z3 and Z5) associated to the block surface temperatures in the
upstream (Z20) and environment (Z41).
Table 3:
Strongly correlated variables
Sensors |
Correlations |
Z35 – Z20 |
-0.913 |
Z24 – Z20 |
-0.910 |
Z24 – Z41 |
-0.889 |
Z23 – Z20 |
-0.888 |
Z23 – Z41 |
-0.872 |
Z5 – Z41 |
-0.855 |
Z40 – Z19 |
-0.855 |
Z40 – Z41 |
-0.843 |
Z3 – Z41 |
-0.829 |
Z2 – Z20 |
-0.820 |
Z35 – Z41 |
-0.815 |
Z23 – Z19 |
-0.814 |
Z24 – Z19 |
-0.812 |
Z38 – Z19 |
-0.811 |
In
the region where is located the Itaipu dam, the range of monthly average
ambient temperatures, observed in the same year, may reach 20° C. The strong
correlation of the sensors with temperature variables confirmed this. The
negative correlation, with dominant presence in the first rows of the table,
indicated an inverse relationship between the variables. That is, in periods of
low temperature, the displacements were larger than those registered in periods
of high temperature were.
Moreover,
the reservoir water level alone showed a small positive correlation with just a
few sensors. Possibly because the low variability in this variable led the
forces acting on the dam almost constant. Another reason may be the need for
the reservoir water level interaction with the temperature to influence the
displacements.
Confronting
the canonical variables U1 and V1, through the Scatterplot (Fig. 3), it was
confirmed the existing linear relationship between these variables, showing the
possibility to predict the dam's structural performance in a given time,
depending on the measuring sensors offsets. It was also noted the distance of a
point compared to the others. This point was referring to measurements made in
July 2000, when it was recorded one of the monthly average lower to room
temperature.
Figure 4:
Scatterplot of the canonical variables U1 and V1
Table
4 presents the most correlated sensors (| ρ |> | 0.9 | e p-value < 0.05)
with the first pair of canonical variables. It is observed that the rod of
multiple rod extensometers Z23, Z24, and Z35 were the more influenced sensors
by temperatures Z20, Z41.
Table 4:
Key correlations between canonical variables and sensors of each group
Sensor |
U1 |
Sensor |
V1 |
Z23 |
-0.924 |
Z20 |
0.989 |
Z24 |
-0.943 |
Z41 |
0.936 |
Z35 |
-0.926 |
|
|
Quality
assessment of the potential of canonical variables was based on the proportion
of variance explained by the canonical variables for each group. The canonical
variable U1 explained 38.7% of the variance observed in shifts, while the
proportion of the variance explained by V1 to the "Environmental
Conditions" group was 65.6%. Thus, the groups "Displacement" and
"Environmental Conditions” were well represented by the first pair of
canonical variables, since the canonical correlation between these groups was
0.986, while the other pairs have lower values.
Therefore,
if the "Environmental Conditions" group was the cause of the
variability observed in the group "Displacement", then U1 can be used
as the best predictor and V1 the most likely criterion for the realization of
the dam's structural performance prediction, in what concerns to offsets.
The
application of Factorial Analysis by principal components resulted in a model
composed of five factors, identified based on the greatest factor loadings of
sensors, able to explain 91.12% of the variance of the set of comments.
The
factors were named according to the sensors more correlated with them, that is,
as the greatest factor loadings. The first factor, due to its positive
correlation with most of the stems of multiple rod extensometers, especially
with Z21, Z22, Z25, Z26, Z29, Z30, corresponds to the "Foundation’s
Movement". This was the most important among factors identified because
accounts for 45.88% of the observed variability in the data set.
The
second factor, named "Horizontal Movement Structure in Normal
Direction", explained 30.83% of the variance and is associated with the
openings and joints between the dam block and the horizontal displacement in
the normal direction (perpendicular to the direction of water flow). The "Horizontal
Movement Structure in the Flow Direction", third factor identified,
accounted for 9.66% of the variability. The dominant variables in this factor
were the temperatures (Z19, Z20, Z41), with the multiple rod extensometers
(Z23, Z24, Z38, Z40) and the horizontal displacements in the direction of water
flow of D8 block (Z3 and Z5).
The
fourth and fifth factors, called "Block D7 Structure Geometry" and
"Hydrostatic Pressure" were related to horizontal displacements in
the direction of water flow of D7 block (Z1) and the reservoir water level
(Z42), respectively. Furthermore, the "Block D7 Structure Geometry"
accounted for 2.41% of the total variability, while the influence of
"Hydrostatic Pressure" was 2.34%.
The
variability in the readings of each sensor, arising from identified factors,
were estimated by commonality. Thus, a commonality low (less than 0.60) would
indicate that the variable would not be sufficiently explained by the model and
could be discarded. The results pointed to the preservation of all sensors
considered in this study.
Using
as a measure of commonality as a measure of importance of each variable to the
factorial model, there was obtained the ranking of the sensors. Therefore, the
most important instruments for the D7 and D8 blocks were respectively rods
extensometer multiple Z33, Z34, Z35 (even borehole) and extensometer bases
(opening) Z7, Z9. Furthermore, the reservoir water level (Z42) was the variable
related to the environmental conditions highest classified.
The
factor, being a latent variable, cannot be measured directly. However, the
values of factors, called factor scores, are estimated based on factor loadings
and the sensor values that dominate this factor. Obtained the factor scores for
each of the 288 dates of the readings, with respect to each factor, took place
the Cluster and the Discriminant analysis.
Using
the method of the group average and the Mahalanobis distance, were identified
three homogeneous groups of dates (Fig. 4), adding 190 elements in the first
(G1), 83 in the second (G2) and 15 in the third (G3). The first group comprised
essentially of the months from November to May, period in which were recorded
the highest temperatures, while most months, with lower temperatures, were
gathered in G2. The third group brought together the dates in which were
recorded the lowest water levels of the reservoir.
Figure 5: Group by the middle connection method, using the
Mahalanobis distance
Discriminant
Analysis, considering the sensors Z7, Z9, Z33, Z34, Z35 and Z42, chosen because
they have the greatest commonalities, tested the classification of 288
observations. Due to the large difference in size of the groups, we considered
the proportionality of the number of observations per group. The results are in
Table 5. The high percentage of correct classification, 94.1%, has confirmed
the discriminating power of the sensors regarded in the analysis.
Table 5. Classification of the dates
of the measurements into three groups
Current Group |
Size of the Group |
Proportion |
Provided Group |
Cumulative percentage |
||
1 |
2 |
3 |
||||
1 |
190 |
65.97% |
178 |
11 |
1 |
93.68% |
2 |
83 |
28.82% |
5 |
78 |
0 |
93.98% |
3 |
15 |
5.21% |
0 |
0 |
15 |
100% |
TOTAL |
288 |
100% |
183 |
89 |
16 |
94.10% |
Two
functions were considered statistically significant, at the confidence level of
99%, to distinguish the observations belonging to each group (Fig. 5). The
first function discriminates High Temperature and Low Temperature groups, while
the second group discriminates the Low Water Level of Reservoir (LWLR) group
from the others.
Figure 6: Dispersion of the elements
according to discriminant functions between groups.
Ranking
functions of observations in groups (Eq. 10) are linear combinations of the
sensors. These functions can be used to classify new dates readings. To do so,
simply calculate the scores of each new element in each group and, then,
allocate it in that with highest score.
G1 = -0,664 + 0,664*Z53 - 1,332*Z52 - 0,075*Z54
+ 0,323*Z9 + 0,134*Z61 - 0,881*Z7 |
|
G2 = -3,398 - 0,446*Z53 + 2,866*Z52 + 0,073*Z54
– 1,284*Z9 + 1,656*Z61 + 2,674*Z7 |
|
G3 = -23,805 +
5,944*Z53 + 1,009*Z52 + 0,544*Z54 + 3,013*Z9 - 10,866*Z61 - 3,636*Z7 |
5. CONCLUSION
The
method proposed in this paper consists in the multivariate analysis of the
displacements of the structures and foundations of a concrete dam, taking into
account the interaction with the environment.
The
results of Canonical Correlation Analysis allow us to infer that these shifts
are strongly influenced by environmental conditions. In general, the
instrumentation registers larger dislocations during periods of low
temperatures. The set of instruments that comprises pendulums, extensometer
bases and multiple rods extensometer can be used to predict the structural
performance of a dam, with respect to displacement, according to the
variability criteria of environmental conditions.
The
dates of the observations recorded by instrumentation, when subjected to Cluster
and Discriminant analyses, can be grouped into "High Temperature",
"Low Temperature" and “Lower Reservoir Water Level”.
Most
of the measurement data variability is due to factors: Foundation’s Movement;
Horizontal Movement Structure in Normal Direction; Horizontal Movement
Structure in the Flow Direction; Block D7 Structure Geometry and Hydrostatic
Pressure.
ACKNOWLEDGMENTS
The authors thank for the contributions of the
following institutions:
- Ceasb - Itaipu Binacional: technical support and
provision of data;
- PROPPG - UTFPR: feasibility of this study by
Ordinance no. 0398/2014;
- PPGMNE - UFPR: theoretical support and encourage the
development of this work.
REFERENCES
BUZZI, M. F. (2007) Avaliação das
correlações de séries temporais de leituras de instrumentos de monitoração
geotécnico-estrutural e variáveis ambientais em barragens - estudo de caso de
Itaipu. Dissertação—Métodos Numéricos em Engenharia: UFPR.
CARVALHO,
J. V.; ROMANEL, C. (2007) Redes neurais temporais aplicadas ao monitoramento de
barragens. Revista Eletrônica de
Sistemas de Informação, n. 10.
CHENG,
L.; ZHENG, D. (2013) Two online dam safety monitoring models based on the
process of extracting environmental effect. Advances in Engineering Software, v. 57, p. 48–56, mar.
CRUZ,
P. T. (2006) 100 barragens brasileiras:
casos históricos, materiais de construção, projeto. São Paulo: Oficina dos
Textos.
DENG,
N.; WANG, J.-G.; SZOSTAK-CHRZANOWSKI, A. (2008) Dam Deformation Analysis Using the Partial Least Squares Method.
Proceedings in 13th FIG Int. Symp. on Deformation Measurements and Analysis
& 4th IAG Symp. on Geodesy for Geotechnical and Structural Engineering.
Lisbon.
DE
SORTIS, A.; PAOLIANI, P. (2007) Statistical analysis and structural
identification in concrete dam monitoring. Engineering
Structures, v. 29, p. 110–120.
FARRAR,
C. R.; WORDEN, K. (2007) An introduction to structural health monitoring. Philosophical Transactions of the Royal
Society A, v. 365, p. 303–315.
FIGUEIREDO,
E.; PARK, G.; FARRAR, C. R.; WORDEN, K.; FIGUEIRAS, J. (2011) Machine learning
algorithms for damage detection under operational and environmental
variability. Structural Health
Monitoring, v. 10, n. 6, p. 559 – 572, nov.
GUEDES,
Q. M.; DE FARIA, É. F. (2007) Modelo
estatístico de controle do deslocamento monitorado na barragem casca da UHE
Funil. Proceedings in XXVII SEMINÁRIO NACIONAL DE GRANDES BARRAGENS. Belém,
PA, jun.
JIN-PING,
H.; YU-QUN, S. (2011) Study on TMTD Statistical Model of Arch Dam Deformation
Monitoring. Procedia Engineering, v.
15, p. 2139 – 2144.
JOHNSON,
R. A.; WICHERN, D. W. (2007) Applied
Multivariate Statistical Analysis. 6. ed. Pearson.
KUPERMAN,
S. C.; MORETTI, M. R.; CIFU, S; CELESTINO, T. B.; RE, G.; ZOELLNER, K. (2205) Criteria to establish limit values of
instrumentation readings for old embankment and concrete dams.
LI,
F.; WANG, Z. Z.; LIU, G. (2013) Towards an error correction model for dam
monitoring data analysis based on cointegration theory. Structural Safety, v. 43, p. 12–20.
MATA,
J. (2011) Interpretation of concrete dam behavior with artificial neural
network and multiple linear regression models. Engineering Structures, v. 33, p. 903–910.
MATA,
J.; TAVARES DE CASTRO, A.; SÁ DA COSTA, J. (2013) Time–frequency analysis for
concrete dam safety control: Correlation between the daily variation of
structural response and air temperature. Engineering
Structures, v. 48, p. 658 – 665.
Matlab
R2013 (2013). Math Works.
MATOS,
S. F. (2002) Avaliação de instrumentos
para auscultação de barragem de concreto. Estudo de caso: deformímetros e
tensômetros para concreto na Barragem de Itaipu. Dissertação—Curitiba, PR:
UFPR.
MEDEIROS,
C. H.; LOPES, M. G. M. (2011) O Risco da
Classificação de Barragens por Categoria de risco, com Base em Método de
Ponderação de Fatores. Sessão Técnica apresentado em XXVIII Seminário
Nacional de Grandes Barragens. Rio de Janeiro.
MUJICA,
L. E.; RUIZ, M.; POZO, F.; RODELLAR, J. (2014) A structural damage detection
indicator based on principal component analysis and statistical hypothesis
testing. Smart Materials and Structures,
v. 23, n. 2, p. 25014 – 25025, Fev.
Statgraphics
Centurion XVI (2010). StatPoint Technologies.
VILLWOCK,
R.; STEINER, M. T. A.; DYMINSKI, A. S.; CHAVES NETO, A. (2013) Itaipu Hydroelectric Power Plant Structural
Geotechnical Instrumentation Temporal Data Under the Application of
Multivariate Analysis - Grouping and Ranking Techniques. In: Multivariate
Analysis in Management, Engineering and the Sciences. [s.l.] InTech, 2013. p.
81–102.
XU,
C.; YUE, D.; DENG, C. (2012) Hybrid GA/SIMPLS as alternative regression model
in dam deformation analysis. Engineering
Applications of Artificial Intelligence, v. 25, p. 468–475, abr.