# Image Analysis Applications for Building Inter-Story Drift Monitoring
## 1 Introduction  
Structural health monitoring is capable of sensing structural damage by detecting minor variations in structural vibration characteristics or deformation, providing a chance for early warning and the minimization of further damage. The health of structures such as buildings and bridges can be degraded not only by the natural aging of materials, inter-material bonding, and connections but also by over-weighting, natural hazards such as earthquakes, or improper renovations. The degradation of the structure may induce a change in the natural frequencies and vibration modes of the structure or induce slight deformation of the structure. Most of the changes in the vibrational characteristics and deformation of structures are typically not observed by humans, yet they can be detected by thesensing systems used for structural health monitoring, minimizing the risk of severe damage or the collapse of structures. Structural health monitoring techniques are being developed for monitoring current buildings, bridges, and other civil structures [1; 2; 3]. Many of the structural health monitoring systems on buildings and bridges use accelerometers not only to identify the structural natural frequencies and vibration modes [4; 5; 6] but also have been used recently for dynamic response estimation, including displacement and internal forces [7; 8]. In addition to accelerometers, different types of sensors or sensing methods, such as film-based strain gauges [9; 10], optical fiber sensors [11; 12; 13], acoustic emission [14; 15; 16], cameras [17; 18; 19; 20; 21; 22], or even global navigation satellite systems [2], are being developed and employed for structural health monitoring. A variation in the system stiffness or vibration modal shapes could indicate a certain level of structural damage [6; 23; 24]. Several studies have investigated improving the accuracy of the identification of damage [25; 26], reducing the noise induced by sensors or environmental interference [26], minimizing sensing synchronization errors [27; 28; 29], and reducing the number of sensors required to capture the necessary vibration modes or failure modes [30]. Experience has shown that the collapse of many buildings from earthquakes is initiated by the failure of a weakened story [31; 32; 33]. Inter-story responses are the movement of the ceiling with respect to the floor, as shown in the colored planes in Figure 1. Large inter-story responses and residual displacement [34; 35; 36] could indicate large deformation of structural and imply a risk of structural damage or failure [37]. For better and wider applications of structural health monitoring, more sensor options are required, in addition to the ability to monitor different types of failure, with different levels of accuracies and costs, to address practical limitations and requirements. While an accelerometer is good at capturing vibrations, which are relatively high frequency responses, it does not sense slow structural responses such deformation induced by settlement, material creep, or gradual deformations or displacements. While displacement sensors such as linear variable differential transducers (LVDT) are relatively accurate for measuring displacements, they require additional supporting fixtures that are sometimes difficult to install due to limited interior space, limiting their practical applications. Figure 1: The ceiling and floor of a certain story of a building. Due to the relatively high cost of hardware, even a relatively small number of accelerometers or LDVTs with minimal data acquisition systems could be much higher than the cost many the building owners would like to invest. As digital imaging technology has been dramatically developing in recent years, several researchers have investigated the use of image analysis for measuring structural deformation and vibration responses [38]. In structural laboratories, image analysis techniques have been developed and employed to measure displacements [29], deformations [39], settlement and shrinkage [40], and cracks [41; 42].