# Inter-Story Drift Ratio Detection of High-Rise Buildings Based on Ambient Noise Recordings
## 1 Introduction  
The inter-story drift ratio (IDR) is the ratio between the relative translational displacement between two consecutive floors and the story height [1] and is an important parameter for the structural health of buildings under earthquake or wind loads [2]. The related standards in many countries set limits on the IDR values; for example, Table 12.12-1 of the ASCE 7-16 [1] standard in the United States lists the allowable IDR values for different types of structures in different categories, which range from 0.007 to 0.025. The IDR limit for occupied buildings in Section 4.3.6 of the PIP STC01015 Structural Design Criteria [3] is 1/200. Additionally, the Technical Specification for Concrete Structures of Tall Building of China (JGJ3-2010) [4] limit the IDR values of the frame structure to be smaller than \(1/550\). These restrictions are set to (1) isolate the vertical components from stress cracks or damage to guarantee structural safety; (2) protect the nonstructural components from excessive deformation and damage to guarantee the serviceability of the structure; and (3) guarantee the overall stability of the structure. The IDR is composed of the harmful IDR induced by the deformation of the vertical members and the harmless IDR caused by the rotation of the inferior floor, and harmful IDR can usually reflect the stress of the structural components directly [5]. The IDR is usually obtained based on monitoring the deformation of a structure using trigonometric leveling, digital photogrammetry, GPS, laser scanners, etc. [6]. Most of these methods monitor the changes in the control points on the building surface to obtain the drifts of the structure at floor height and then calculate the IDRs. However, there are many problems with real-time and lifelong monitoring of a high-rise building using the current methods. For optical instruments, e.g., total stations, weather conditions affect the accuracy and lifetime of the instruments [7]. For example, excessive sunlight affects the infrared rays from the total station and changes its path, affecting the accuracy of the total station; heat also prevents measuring light beams from being concentrated, affecting the performance of the total station on hot days [8]. Although the promotion of no-prism total stations eliminates the dependence on reflective devices, a good line of sight between the total station and the measured object is still essential. If the vision is obstructed, the total station cannot work properly [9]. In actual architectural surveying, it is common to be unable to obtain a good line of sight with measured objects due to insufficient space, etc. Many control points are required for covering the area of study to survey the buildings ([PERSON] 2018) [10], which is very cumbersome to operate. A large amount of space is needed, which restricts the scope of application of these methods. For example, the Chinese Code for deformation measurement of building and structure (JGJ8-2016) [11] limit the distance between the instrument and the building to 1.5- to 2-times larger than the building height in some cases. For a 100 m high building, the instrument should be at least 150 m away. It is difficult to find a suitable place in urban areas. Moreover, the total station is fragile and needs a lot of maintenance, which makes lifelong monitoring unaffordable for most projects. GPS is not an option in many application areas, such as indoor settings [12]. An alternative method that can overcome these challenges is ambient noise recordings, which are the continuous seismic waves captured and recorded by seismometers over a wide frequency band. The ambient noise in the low-frequency band (below 1 Hz) is excited due to natural sources, such as oceans and large-scale meteorological conditions; in the intermediate frequency band (1 to 5 Hz), ambient noise is excited either by natural (local meteorological conditions) or cultural (urban) sources; and in the high-frequency band, ambient noise is generated by cultural sources [13].