Question

6. Apply concurrent deviation method to determine the value of coef-
ficient of correlation from the data given below.
x : 100 110 110 120 122 125
y : 120 140 160 160 130 110
[Ans: -.58]
Sum of the products of the deviations of the variables x and y from​

Answer 1

Answer:

Modal characteristics of engineering structures can be determined via dynamic observation in scope of system identification and they can be used for a variety of purposes, including model updates, damage assessment, active control, and original design re-evaluation. This paper presents the use of an autoregressive with eXogenous inputs (ARX) model to assess the impact of horizontal displacements in the Oymapinar Dam in Antalya province, Turkey, during the first reservoir filling stage. Besides, displacements in the dam after the filling stage are predicted. There is a high linear correlation between the displacements of the body of the dam and the first filling phase of the reservoir. An ARX model of the dam without damage is created using displacements predicted from a 3D finite element model of the dam and the changes in water level. The displacements in the dam observed in the first filling phase are recalculated using water level changes for damaged or undamaged cases, observed displacements, and the parameters of the undamaged ARX model. The standard deviations of the residuals calculated from the ARX model of the undamaged dam are statistically compared for different confidence intervals using the standard deviations of residuals of the ARX model of the undamaged or damaged dam’s observations, and it was determined that there was no dangerous damage to the dam. In addition, the observed displacement values were extended in different scales and standard deviations of these displacements are calculated using the ARX of the undamaged dam model. These standard deviations and the one calculated from undamaged model of the dam were compared, and it was determined that 55 mm of displacement could be dangerous for the dam. Finally, the displacements in the dam for different water levels in the operation phase (after filling) were predicted using the ARX model and were found to be consistent with the measured displacement values.