# Time Domain Damage Identification Approach of the Newly Hollow Floor Structure with TRMD
## 1 Introduction  
Recently, a structure system with a reinforced concrete hollow floor has been widely used in practical engineering [1, 2]. It is well known that structural control techniques are intended to mitigate structure responses under ambient dynamic excitation in consideration of the safety and serviceability issues of structures [3, 4, 5, 6]. Based on the cavity characteristics of the reinforced concrete hollow floor structural system, which is widely used in buildings at present, a tuned rolling mass damper that could be placed in the hollow floor has been proposed. The concept of the tuned rolling mass damper was first introduced as a ball vibration absorber for horizontal movement by [PERSON] [7]. Then, [PERSON] and [PERSON] [8] proposed a new tuned rotary mass damper that consists of a container (outer shell) and a cylinder-type weight (rotary mass) as a passive-type vibration control system and conducted a field experiment on a lamppost for a highway bridge [9]. The tuned rolling mass damper (TRMD) proposed by [PERSON] et al. [10, 11] in this paper consists of a ball rolling along an arch path located in hollow modules to absorb the structural kinetic and potential energy when subjected to ambient excitations. Furthermore, compared with the traditional vibration control system--the tuned mass damper (TMD) as an additional energy absorbing device [12]--the most significant advantage of the installation of theTRMD in hollow modules embedded in slabs lies in its capacity to maintain architectural integrity. [PERSON] and his research team [10; 11] carried out theoretical and experimental research into the hollow floor structure with TRMD. The advantage of the newly combined TRMD and the hollow floor structural system, as shown in Figure 1, is that the damping device TRMD not only suppresses structural responses but also effectively solves the conflict between the setting of the control device and the function of the building, which does not occupy the use space of the building or affects the use function of the structure. However, newly hollow floor structures with TRMD will also inevitably suffer different degrees of damage under the combined effects of natural disasters, human factors, and the aging of building materials during their long-term service. Therefore, damage identification and structural health monitoring of this newly controlled structure deserve our attention. Vibration-based structural damage identification methods have been the research focus in the field of structural damage identification [13]. The basic concept of vibration-based structural damage identification is to establish the function relation between structural response indicators and the inherent physical characteristics of the structure. Compared with the frequency domain vibration-based structural damage identification method, which adopts frequency [14], mode shapes [15], and frequency response function [16] as the structural indicators, the time domain damage identification method, which employs dynamic response as the structural indicator [17; 18; 19; 20], has advantages for the newly hollow floor structure with TRMD. Firstly, because the time domain damage identification method directly uses measured vibration data, the signal process and transformation between the time domain and frequency domain avoid leading to no data conversion, signal distortion, or error. In addition, the dynamic response data that are employed for damage identification can be obtained directly from the sensing system and data acquisition system in the structural control system. Therefore, it is quite promising to combine with the structural control system and structural health monitoring system to control and detect the safety of the structure. This paper presents a time domain method for structural damage detection of controlled building structures equipped with TRMD. Firstly, the simplified model and motion equation of a controlled structure with TRMD are derived considering the interaction force between the main structure and the damper.