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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
Behavior prediction models and control charts for safety control of concrete dams
with the process. Cook’s distance is calculated according to equa-
tion [22].
(22)
D
i
=
r
i
2
h
ii
p(1-h
ii
)
A value of indicates that the i-th point of analysis has some influ-
ence and should be investigated and, if necessary, eliminated from
the series. Throughout the analysis, some values exceeded Cook’s
distance. After these values were eliminated, an improvement in
the coefficient of multiple determination was noticed.
4.5 Analysis of results
Figure [4] shows the displacements measured by the direct pendu-
lum, as well as the displacements calculated from the regression
model given by equation [23], together with the coefficient of mul-
tiple determination. Figures [5] and [6] show the charts for Control
Type I and Type II, respectively.
(23)
y^ = – 0,24 + 1,26E(– 07)h
4
–1,20sen
(
(
(
(
(
2πt 365
)
)
)
)
)
+
0,12cos
2πt 365
– 0,22sen
2 2πt 365
0,33sen
2πt 365
cos
2πt 365
7,22[1 – exp(– 10
-3
t )] +1490[1 – exp(– 10
- 5
t )] +
13290[1 – exp(– 10
- 6
t )]
In Figure [4], one can see that there is a good adherence between
the values read and the estimated values, even when the readings
were taken at longer time intervals. Moreover, during the filling of
the reservoir, between 1984 and 1986, and in 2008, when readings
were taken at higher frequencies, one finds greater adherence to
the regression curve.
Figure [5] shows that some points exceed the 1.96 and -1.96 limits,
especially around May/24/2000. A similar situation was also found
in Control Chart Type 2, shown in Figure [6], where the curve of the
regression values exceeds the lower limit. As stated earlier, this
situation indicates a scenario with two possibilities: measurement
error or change in dam behavior.
The construction of the second stage of the Tucuruí dam began in
1998 and was completed in mid-2006 [17]. These brought about
several changes, such as demolition of cofferdams, as can be
seen in Figure [7]. Certainly, such modifications caused these mo-
mentary changes in the behavior of the block under analysis which
coincide with the period identified in both control charts.
5. Conclusion
Readings taken in overly-spaced time intervals results in “jumps”
in time series, which reduce the precision of the prediction mod-
els. Even though, it was possible to achieve a good adjustment
between the predicted and measured values and clearly detecting
a process change, i.e., a change in structural behavior. In this re-
search, the change in the structural behavior of the block was due
to the construction of the second step of the plant, in which coffer
dams had to be demolished. Possibly, other process changes such
as those brought about by foundation settlement and instrument
break-down could also be identified in this type of analysis.
The “jump” problem in the time series could be solved by having
an online monitoring system, such as those employing of optical
Figure 5 – Control chart for the residuals of the direct pendulum, Control Type I