8 Static Deformation Analysis for Structural Health Monitoring of a Large Dam 69 0 1000 2000 3000 4000 5000 6000 7000 -50 0 50 PL2Y090 0 1000 2000 3000 4000 5000 6000 7000 -50 0 50 PL2Y115 0 1000 2000 3000 4000 5000 6000 7000 -50 0 50 PL2Y150 0 1000 2000 3000 4000 5000 6000 7000 -50 0 50 PL2Y172.5 Point Deformation (mm) 12/31/2008 1/1/1987 Fig. 8.3 Recorded static radial deformations of Fei-Tsui arch dam along plumb NPL2 line at different heights Figure 8.3 plots the measured static deformation at four locations with different heights of Feu-Tsui dam along profile NPL2. The abscissa of Fig. 8.3 indicates the number of the point (from 1/1/1987 to 12/31/2008, a total of 7,600 data points). The magnitude of the deformation increases as the height of the measurement point increases, and it is relatively insignificant at the height of 90 m. The signatures of the deformations at different heights are very similar to each other. The investigation in this paper is demonstrated by the results of the analysis of the static deformations at these four locations with different heights. 8.3 Modeling Technique The previous study [1] shows that the deformation is mainly affected by the water level and temperature. The proposed approach has two stages with iterations [13]. In the first stage, a least-squares technique is used to curve fit the measured data of static radial deformation as a linear function of the measured water level and temperature. A cost function is formed as J1 D n1 XiDn0 Œa1h.di / Ca2t .di / Ca3 y.di / 2; (8.1) where h(di), t(di), and y(di) are the measured water level, low temperature, and deformation at the ith measurement date di. The unique solution of ai of this linear model can be obtained by minimizing this quadratic cost function. The error between the measured data and the identified least-squares model can be computed as yr .di / Dy.di / ya .di / ; (8.2)
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