Figure 6 3D Frequency distribution of the systematic measurement error. Similarly, a measurement error of 2P is likely to occur when the tracked marker passes through the regions where the view and reflection angles approach to the limit values. During the rotation, the markers move on a circular path, which should be fully captured in each one of the 2D images analyzed. For the outermost markers, the horizontal and the vertical view angles approach to critical values twice a cycle. As the distance from the center of rotation increases, the contribution of 2P component gradually becomes more important, probably because those markers are closer to the boundaries of the field of view where calibration errors and artifacts due to projection on the plane of rotation become more dominant. Unfortunately, the 2P components exhibit a spatial distribution along the blade that is similar to the expected deformation. Therefore, the 2P component of the error cannot be easily eliminated by using simple filters and constitutes the major part of the error. The maximum value of the 2P part can reach ±30 mm and is experienced by the outermost marker. This error can be reduced further by using more sophisticated camera calibration techniques and data comparison algorithms. Figure 7 The locations and corresponding labeling of the markers used in error estimation. The overall measurement error is the summation of random and systematic errors. Its maximum value can reach up to 35 mm and experienced by the outermost marker. As getting closer to the center of rotation it linearly decreases. Depending on the results of these analyses the average measurement error can be reported as ± 25 mm. Although such an amount of error corresponds to approximately 10 % of the measured deformation amplitudes (shown in Figure 5), it is only effective within a narrow frequency range. Therefore, it is not expected to have a negative effect on the identification of important turbine modes. 263
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