## 4 Distribution of the Subspace-Based Damage Detection Techniques
### Distribution of the Papers on SSI-COV Approach  
Table 12 in Appendix A shows the studies with focus on the SSI-COV approach. From the data presented in this table, a total of 25 studies used SSI-COV in various structures including beams and 2D frames, 3D frames structures and buildings, and bridges. Some of these studies integrated SSI-COV approach with preprocessing or postprocessing stages [159; 160; 161; 162; 163]. In order to smoothen input signal and yield reliable modal parameters, [PERSON] et al. [159] adopted singular spectrum analysis (SSA), for preprocessing of the response signal, and a stabilization diagram for postprocessing of the extracted modal parameters, respectively. The experimental test was carried out for the validation of the proposed algorithm using the long-term monitoring data of Canton Tower high-rise slender structure. It was found that the use of SSA as a pre-processing tool for SSI-COV improved the identifiability of modes using a stabilization diagram. To estimate the tension forces of the cables in cable-stayed bridges, [PERSON] et al. [72] adopted hierarchical clustering algorithm to identify natural frequencies of each stay cable in Veterans' Glass City Skyway Bridge. The agreement between the estimated results and the measured tension forces was good. Due to the need for the removal of bias and variance errors in the modal parameter estimation, [PERSON] et al. [161] used first-order sensitivity of the modal parameters and stabilization diagram to remove bias errors. A simulation model and measured vibration data of a beam and a mast structure were used for the verification purpose. The practicability of the proposed method was confirmed in a real-world application. In order to improve the identifiability of the weakly excited modes [PERSON] et al. [162] introduced component energy index (CEI) and an alternative stabilization diagram to identify spurious and physical modes. A simulation model of a seven-DOF mass-spring-dashpot (MSD) system and the experimental model of a metallic frame structure subject to wind load were used for verification of the proposed scheme. Good performance was observed especially for the measurement data with low SNR. In order to identify structural changes in presence of environmental variation, [PERSON] and [PERSON] [163] proposed a fuzzy clustering algorithm to extract state parameters from real and numerical poles. Data from Z24 Bridge and Republic Plaza Office Building in Singapore were used for experimental verification of the method. The inflicted damage on the Z24 Bridge was successfully identified using the proposed method. The shifts in modes of the Plaza Office Building in Singapore were also clearly captured. Several studies on SSI-COV were concerned with discrimination environmental and operational effect during the identification process by improving the inherent performance of the SSI-COV algorithm. [PERSON] et al. [164] presented an efficient and fast SSI-COV damage detection that is robust to changes in the excitation covariance. Three numerical applications were presented. It is reported that the new approach can better detect and separate different levels of damage. Several researches on SSI-COV dealt with improving the damage detection process by introducing a damage sensitive and noise-insensitive features [165; 166; 167; 168; 71]. To discriminate changes in modal parameters caused by damage from those occurred due to environmental factors, [PERSON] et al. [165] designed a damage detection algorithm using null space residual, \(\chi\)2 test and a statistical nuisance rejection. A vertical beam made of steel and aluminum was tested under controlled ambient temperature for verification of the presented scheme. The relevance of the presented algorithm was illustrated using a laboratory-scale test structure. [PERSON] et al. [170] proposed the use of subspace residual as damage feature and \(\chi\)2 tests to discriminate the effect of noise from estimated modal parameters.