# Image Analysis Applications for Building Inter-Story Drift Monitoring
## 4 Results  
A comparison of the actual applied inter-story drift and the measured inter-story \(u\) is shown in Figure 6. The errors between the actual applied and measured inter-story responses \(u\) at the peaks are generally smaller than 0.1 mm. The maximum 0.1 mm error is equivalent to 0.1 pixels of positioning error in image point tracking and is equivalent to a 0.025% inter-story drift ratio, or a 1-mm accuracy if the specimen is scaled to full scale, which is relatively small. While this accuracy is not comparable to conventional displacement devices such as an LVDT, which normally achieves an accuracy of 0.05 mm, the accuracy of the proposed method is capable of measuring significant inter-story responses in practical applications. The measured responses are shown in Figure 7 for the 1-Hz test, where the inter-story responses are relatively small. The displacement of \(u\) is \(\pm\)1.8 mm, while the displacement of \(v\) is \(\pm\)0.4 mm, and the  
Figure 6: Comparison of the actual applied and measured inter-story displacements and the errors. (**a**) Measured and actually applied (controlled) inter-story displacement \(u\). (**b**) Error of measured inter-story displacement \(u\) (image measured). torsion is even smaller at \(\pm\)0.08 degrees. Comparing the differences between the responses measured by the proposed method/prototyped device and the industrial 3D image measurement, the maximum displacement errors along \(u\) and \(v\) observed in these tests are within \(\pm\)0.3 mm and \(\pm\)0.5 mm, respectively. The error along \(u\) gradually reduced to 0.1 mm during the later period of the steady state response. The displacement \(v\) resulted in larger errors than \(u\) mainly because it is along the depth direction of the camera, which is the direction that a typical camera has little sensitivity. If the error along the depth direction does not meet the requirement, more than one camera could be considered. The description is added in the revised manuscript. In the 3-Hz test (Figure 8), the inter-story responses are almost ten times larger than those in the 1-Hz test, mainly because the excitation is closer to the natural frequency of the specimen (i.e., 2.2 Hz). The observed natural frequencies generally matched its numerical modal analysis. Along the \(u\)-direction, the inter-story drifts reached maximum amplitudes of 4.32% (i.e., the ratio of 17.3 mm to 400 mm) and \(-\)3.93% (i.e., the ratio of \(-\)15.7 mm to 400 mm) in the transient state (from 0 to 3 s), and gradually remained at a 4.5-mm amplitude in the steady state (after 4 s). The differences between the responses measured by the proposed method/prototyped device and the industrial 3D image measurement are up to 0.5% (i.e., the ratio of 2 mm to 400 mm) at major peaks in transient responses and approximately 0.13% (i.e., the ratio of 0.5 mm to 400 mm) during the steady state response. Along the \(v\)-direction, in addition to an error larger than 0.5% (i.e., the ratio of 2 mm to 400 mm), a phase difference is also observed. In both tests, image blurs can be observed in the photos taken by the prototyped device due to the rapid movement of the tracking points. The image blurs are especially significant in the 3-Hz test when the relative velocities of the tracking points are high. Figure 9 shows example images of one of the tracking points on the lower floor (indicated by a red box in Figure 9a). The images shown in Figure 9b,c are a sub-region of the photos. At time \(t=\) 1.514 s when the relative displacement \(u\) just went through a peak, the tracking point is clearly visible in the photo. Within only three image frames (approximately 0.1 s), the image became significantly blurred (Figure 9b). The image became clear again at the negative peak, yet when going back to positive from negative, the images once again became blurred. While Figure 9 shows two relatively severe cases, the image blurring occurred in almost every cycle of motion during the transient responses.