# Application of the Random Decrement Technique in Damage Detection under Moving Load
## 1 Introduction  
Generally, modal parameters are identified by measuring input excitations and output responses. These modal parameters are then used as damage indicators in the damage detection process. For simplicity, it is assumed that if the input excitation is considered as zero, the output response behaves as a free response [1]. There are situations in which inputs come from ambient or random excitations and cannot be ignored. In such cases, it is necessary to use output-only modal identification methods. However, these types of methods also have some limitations. One of the common drawbacks of output-only methods is considering the input as zero-mean and random white noise. Utilizing acceleration data to detect the damage location could effectively decrease the cost of Structural Health Monitoring (SHM). Accelerometers can be implemented in any desired location of structure to record the acceleration response with a wide range of frequencies. Generally, SHM methods using acceleration data can be categorized into four groups: 1-transformer-based methods, such as Wavelet or Hilbert-Huang transformers [2; 3; 4; 5; 6; 7]; 2-averaging-based methods, such as Random Decrement (RD) or Moving average based approaches [8; 9; 10; 11]; 3-filtering-based methodologies, such as Kalman filter [12; 13]; and, finally, 4-source separation methods such as Blind Source Separation approach [14; 15; 16; 17]. This paper presents a RD-based approach that belongs to the second group. The RD technique is one of the promising output-only time-domain methods introduced by [PERSON] in 1968 [18]. Since then, the RD technique has been received a large amount of attention in Structural Health Monitoring (SHM) when a complete knowledge of random input to the under-operationstructure is not available. RD technique is a special averaging method that has no mathematical basic developed for general cases [19; 20]. A general review of the application of the RD technique in Operational Modal Analysis (OMA) is presented in this paper. For the first time, the RD technique was used to calculate a so-called auto-RD function from one output signal [18]. However, it was later extended to multi-output signals. To find RDSs for multi-output signals, it is necessary to select the main signal first; then, the RDSs for the other signals can be consequently found according to the main signal. The RDSs for the main signal and other signals are called auto-RDS and cross-RDS, respectively [1]. It is proved that auto-RDS can significantly decrease noise content; however, cross-RDS incorporates some sort of noises due to its special triggering condition. To overcome this problem, vector triggering RD technique is employed, which can calculate the auto-RDS for all signals simultaneously [21; 22; 23]. The application of OMA using RDS was properly addressed in both time and frequency domains by [PERSON] and [PERSON] [24]. Later, [PERSON] et al. [10] employed RD technique in time and frequency domains for acceleration data and compared the OMA results. The infrastructure, such as a bridge, receives various ambient excitations, most of which are non-stationary in nature. Although the RD technique was proved to work well for stationary input excitations, some researchers used it for non-stationary excitations [19; 25; 26]. [PERSON] et al. [25] used the RD technique to find the free response of the bridge under traffic loadings. [PERSON] et al. [27] combined the RD technique with empirical mode decomposition and found the modal parameter for a bridge under non-stationary operational excitation. [PERSON] et al. [28] employed the mode separation technique along with the RD technique and determined the modal parameter of cables in a cable bridge. A complete systematic procedure for designing and implementing SHM using the RD technique on an arbitrary system was well-illustrated by [PERSON] et al. [11]. Using more sensors in RD technique could lead to more accurate results, but it would be more time-consuming as well.