Feasibility Study of Earthquake-Induced Damage Assessment for Structures by Utilizing Images from Surveillance Cameras

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Introduction
Seismic hazards pose a substantial risk to the safety of structures located in earthquake-prone regions [1,2] and can cause severe social and economic losses in densely populated cities [3,4].After an earthquake, a rapid and accurate assessment of the true seismic damage to structures is crucial for post-disaster relief [5][6][7].Te seismic fragility and vulnerability models are often used to evaluate the probabilistic seismic risk of structures [8].To improve the accuracy of prediction, an updated empirical model for structural seismic vulnerability assessment was proposed using the survey data obtained from the Yushu earthquake [9].Additionally, as an alternative to the traditional seismic vulnerability model, a surrogate model based on an artifcial neural network was also investigated [10].To assess the damage condition of a structure after an earthquake, it is necessary to collect the on-site data and establish the relationship between the collected data and the damage status of the structure [11,12].Existing methods for on-site seismic damage assessment can be broadly divided into two types depending on the type of data collected: assessment based on visual inspection and assessment based on vibration monitoring [13].
Traditional visual inspection-based assessment methods primarily rely on the observable characteristics of the damage structures post-earthquake to evaluate the extent of the damage [14,15].Te most common form is manual inspection, in which the structural damage is assessed by trained specialists on site [16,17].However, the manual inspection process can be inefcient, costly, and dangerous, and the assessment results can be highly subjective depending on the personal decisions of surveyors [18].In light of these limitations, researchers have proposed acquiring images of post-earthquake structures by using imaging devices (such as handheld cameras [19], unmanned aerial vehicles [20], and satellites [21]) to reduce costs and improve the efciency of seismic damage assessment.A robot with a vision system was applied to estimate the residual displacement of structural joints via engineered landmarks in non-line-of-sight conditions [22].Other researchers utilized the deep learning-based computer vision technology to evaluate the structural damage [23,24].An improved convolutional neural network was proposed for identifying and locating the seismic damage from the images of reinforced concrete columns [25].While techniques for visual inspection-based assessments have signifcantly advanced over time, the correlation between the external appearances of a structure and its actual condition remains somewhat unclear [11].Additionally, the impact of structural surface decorations or coating on the evaluation results is a factor that cannot be overlooked.Tis potential infuence has yet to be thoroughly researched.
In contrast to visual inspection approaches, vibration monitoring-based methods operate on a clearer physical mechanism [26,27], primarily performing the structural damage assessment based on the damage indexes extracted from the structural vibration response [28,29].In general, the vibration responses of structures are obtained by a monitoring system through sensors (such as accelerometers, displacement sensors, and inclinometers) distributed along the structure [30,31].A time-varying system identifcation approach based on the adaptive unscented Kalman fltering was presented and employed to identify the time-varying stifness of prefabricated segmental columns under earthquake excitations by using the measured accelerations and displacements [32].A modal assurance distribution-based instantaneous dynamic parameter identifcation method was proposed for the structural integrity assessment [33].However, practical applications are often limited due to the high cost of installation and maintenance of such monitoring systems [34,35].Tus, there are a large number of buildings that are not instrumented by monitoring systems.On the other hand, vision-based vibration measurement is expected to solve the above problems due to its low cost and high efciency [36,37].Te vibration responses of a structure are usually recorded by stationary or movable cameras outside the monitored structure [38,39].While less expensive overall, there are still costs associated with the installation and maintenance of cameras [40,41].
In an efort to curb costs, researchers have turned their attention to the ubiquitous indoor surveillance cameras.Te feasibility of using these devices to capture inter-story seismic responses has been demonstrated, indicating a promising new direction for cost-efective and efcient earthquake damage assessment [40,42,43].However, it is still challenging to assess structural seismic damage based on the acquired seismic response of inter-stories only from the pixels obtained from the videos recorded by the cameras, because the seismic response of the structure is usually a nonstationary signal.
To quantify the severity of damage of a structure, the selection of an appropriate damage index is essential.Commonly used damage indices are calculated based on the inter-story drift ratio [44], vibration mode [33,42], or natural frequency [45].However, for structural seismic damage assessment based on surveillance cameras, the unit of structural displacement is the pixel rather than the meter.Te pixel needs to be calibrated to the physical length of a given target in the image [46].It is impractical to perform calibration for all responses after an earthquake, and thus, the inter-story drift ratio-based damage indices (such as maximum or residual inter-story drift ratio) cannot be directly available and used for damage assessment [44].In addition, videos captured by diferent cameras distributed along the structure are often not precisely synchronized.Te asynchronous acquisition is detrimental to the extraction of structural vibration mode, and therefore, the vibration mode-related damage indices also cannot be used for damage assessment [33,42].Natural frequency-based damage indices are not afected by signal amplitude and can be obtained from only one vibration signal.Consequently, damage indices based on natural frequencies might be a viable approach in structural seismic damage assessment using surveillance cameras.
Te commonly used natural frequency-based seismic damage index is the natural frequency shift before and after an earthquake, and it has been utilized for structural seismic damage assessment [45].However, the acquisition of the natural frequency shift often requires modal testing and analysis of the structure before and after the earthquake, which is time-consuming and costly.In recent years, the advancement of modern signal processing techniques and system identifcation theory has brought time-frequency analysis technology into the spotlight [47].Tis technique, which estimates the shift in natural frequency based solely on a structural nonstationary seismic response, has been increasing usage thanks to its innovative approach and promising results [48].Tese methods mainly can be divided into wavelet transform-based methods and Hilbert transform (HT)-based methods [49,50].For the methods based on the wavelet transform, the frequency shift is typically identifed by extracting the frequency ridges from the wavelet scalogram [51,52].However, the selection of wavelet bases has a large impact on the analysis results.To mitigate the potential impact of suboptimal wavelet selection, adaptive time-frequency analysis methods like empirical mode decomposition (EMD) [53,54], based on Hilbert transform (HT), were introduced.Tese methods frst extract single-component signals from the original multicomponent signal.Subsequently, the shifts in various orders of natural frequency are obtained by using HT.However, the EMD is not sufcient or rigorous enough in mathematical proofs.Furthermore, a new method called empirical wavelet transform (EWT) [55] was proposed, and it was enhanced by the synchroextracting transform (SET) [56] to identify the natural frequency of a time-varying system by using accelerometers [57].Drawing inspiration from the previous research [57], this study estimates the shift in structural natural frequency by using a SET-enhanced EWT method.Tis approach utilizes pixel-based inter-story structural responses as captured by surveillance cameras.
Tis study presents a novel approach to assess structural damage induced by earthquakes by combining the capabilities of surveillance cameras with computer vision and time-frequency analysis technologies.Te structural seismic 2 Structural Control and Health Monitoring responses were extracted from the video by using a markerfree computer vision technique.Te damage state was assessed according to the shift in structural natural frequency, which was estimated by using a time-frequency analysis technique.Te accuracy and feasibility of the approach were verifed through a shake table test conducted on a small-scale steel model.Ten, the practicality of the approach was further confrmed using the experimental data from a full-scale reinforced concrete model.Te rest of the study is organized as follows: Section 2 presents the theoretical foundation of the proposed method.Sections 3 and 4 describe the experimental setups and results of the small-scale model and full-scale model shake table experiments.Section 5 shows the conclusion and future work.

Methodology
Te schematic diagram of the proposed structural seismic damage assessment strategy is shown in Figure 1, where u l (l � 1, 2, 3, ...) is the meter displacement of the lth story with respect to the ground; δ l (l � 1, 2, 3, ...) is the inter-story meter displacement of the lth story; Δx j l (l � 1, 2, 3, ..., and j � 1, 2, 3, ...) is the inter-story pixel displacement of the jth feature point of the lth story extracted from the video; CFOV refers to the camera feld of view; and ROI indicates the region of interest.First, images were captured using the existing indoor surveillance cameras during an earthquake.Next, the structural inter-story pixel displacement responses were extracted from the videos using computer vision techniques.Ten, the natural frequency shift of the structure was estimated by using the timefrequency analysis techniques.Finally, the structural damage was assessed according to the calculated damage index.It is worth noting that surveillance cameras mounted on ceilings, walls, or other locations are all applicable to this method.For the sake of presentation, it is assumed that the camera is mounted on the ceiling throughout the following.

Structural Inter-Story Pixel Displacement Response
Extraction.Te schematic diagram of structural inter-story seismic response extraction is shown in Figure 1.First, a rectangular box was used to manually select the ROI in the frst frame of the video.Te ROI is defned as a region of the image that involves distinctive feature points fxed to the foor.Te purpose of the ROI selection is to ensure that subsequent tracked feature points are not lost due to occlusion.Ten, the feature points in the ROI are detected.Considering that there are no pre-installed marker points in practice, a typical marker-free feature detection algorithm (i.e., Harris corner detection algorithm [58]) is adopted.More specifcally, the features in the ROI are automatically detected based on the magnitude of the pixel gradient in diferent directions.Finally, the pixel displacement of diferent feature points is automatically computed based on the diference between the ROI in adjacent frames using a classic optical fow algorithm (i.e., Kanade-Lucas-Tomasi algorithm [59]).Te structural interstory pixel displacement of the lth story Δx l (t) can be obtained by averaging the motions of diferent feature points according to the following equation: where m is the number of detected feature points, and t is the time variable.Te whole response extraction process is automated except for the selection of ROI and does not require any specifc markers.

Structural Natural Frequency Shift Estimation.
Te fowchart for the estimation of structural natural frequency is shown in Figure 2. First, the single-mode responses are extracted from the acquired multimode inter-story response by using the SET-enhanced EWT method.Ten, the natural frequency of the structure is estimated from the instantaneous frequency of the extracted single-mode response by using the HT and the Savitzky-Golay fltering (SGF) [60].After the above signal processing, the natural frequency of the structure can be generally extracted from the seismic response of the structure.Te details of the estimation process will be introduced in the following section.

Extraction of the Single-Mode Response.
EWT is a widely used adaptive signal decomposition method.Te traditional EWT method consists of two steps: (1) determining the frequency boundaries between the diferent single-mode signals and (2) constructing the fltering bank to extract the single-mode signals [55].However, it is diffcult to use only the traditional Fourier spectrum to determine the fltering boundary for the nonstationary signal.
To tackle this issue, the SET is introduced to determine the fltering boundaries.Te SET is based on the short-time Fourier transform (STFT) and can generate an energyconcentrated, time-frequency representation of the signal [56].Te EWT allows us to determine frequency boundaries between diferent modes based on the resulting timefrequency representation derived from the SET [57].
For an n degree of freedom shear-type building during a strong earthquake, the equation of motion can be expressed as follows: where M(t), C(t), and K(t) represent the time-variant mass, damping, and stifness matrices of the structure during the earthquake, respectively.and € u(t) denote the displacement, velocity, and acceleration response vectors of the structure.f(t) is the external earthquake excitation vector.
Transforming (2) into spatial modal coordinates yields where are generalized mass and generalized load of the ith mode shape, φ i (t) is the ith mode shape, q i (t) is the ith modal coordinate,  and ω 0i (t) and d 0i (t) are the ith natural frequency and damping coefcient of the structure, respectively.According to the modal decomposition theory, the interstory multimode pixel displacement at the lth story Δx l (t) extracted from the video can be expressed as follows:

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where l � 1, 2, . .., n.Te value of u 0 is constantly equal to 0. s l is the unit conversion factor from pixel to meter for the lth story.φ li (t) is the coefcient at the lth degree of freedom of the ith mode shape.
According to the analytic signal theory, the analytic signal Q i (t) of the q i (t) can be expressed as follows: where A i (t) and ω i (t) are the instantaneous amplitude and frequency of the ith modal response, H[ ] denotes the HT, and j is the imaginary unit.Furthermore, the analytic signal ΔX li (t) of the Δx li (t) can be expressed as follows: According to the defnition of the instantaneous frequency (i.e., the derivative of phase versus time), the instantaneous frequency of the ith modal response q i is equal to the instantaneous frequency of Δx li .
Te STFT expression G(t, ω) of the multimode signal Δx l can be expressed as follows: where  g( ) represents the fast Fourier transform.Te instantaneous frequency trajectory IFT(t, ω) for the G(t, ω) can be obtained as follows: Te energy-concentrated, time-frequency representation Te(t, ω) obtained by using the SET can be expressed as where δ(ω − IFT(t, ω)) is defned as According to (9), an energy-concentrated, timefrequency representation can be obtained, and the frequency boundaries between diferent modes can be determined.Te fltering boundaries for each single-mode signal in the EWT can be defned by an interval Additionally, a transient phase with a width of 2τ i is defned for each ω i ′ .More details can be found in reference [57].
Te corresponding empirical scaling function and the wavelet function can be determined as Structural Control and Health Monitoring where τ i � cω i ′ , 0 < c < 1, and β( ) is the auxiliary function for the Meyer wavelet [55].
Ten, the EWT analysis can be conducted.Te detail coefcients W Δx (i, t) and the approximation coefcients W Δx (1, t) can be obtained as Te single-mode response extracted from the multimode response can be described as

Estimation of the Natural Frequency.
Te ω 0i and d 0i of the structure can be regarded as lower-order polynomials of A i .Specifcally, ω 0i and d 0i behave as a low-pass flter, while q i behaves as a high-pass flter.According to the Bedrosian theorem of the HT, the following can be obtained: where (19) can be rewritten as follows by substituting the frst two derivatives of Q i .
where the frst term ω 2 0i is a low-frequency component, while the second term is a high-frequency component.Te ith natural frequency ω 0i can be estimated by fltering out the high-frequency component from ω i .
Te SGF is a data smoothing technique that utilizes local least-squares polynomial approximation [60].It has been validated in the feld of digital signal processing for its excellent high-frequency noise reduction capabilities, as well as its ability to preserve the shape of the signal [62].In this study, the SGF is applied to flter out the high-frequency components from the ω i to get the estimated ω 0i , which can be expressed as follows: where F(τ) is a polynomial function, r and β i are the order and coefcient, M is the SGF span, and β opt is the coefcient acquired by using the least-square ft.
After obtaining the estimated natural frequency ω 0i , the natural frequency shift is approximated by the ratio of the maximum to the minimum of the acquired natural frequency.

Structural Damage Assessment.
To facilitate the assessment of structural damage, given the minimal contribution of higher-order vibrations in low-rise structures, only the frst modal response is extracted in the following analysis.Te natural frequency shift-based structural damage index [45,50] was defned as where f b 1 is the frst natural frequency of the structure before the earthquake; f a 1 is the frst natural frequency of the structure after the earthquake.Te value of D is less than 1, and the larger the value of D, the more severe the structural damage.
In this study, the damage index can be approximated as where ω 01 (t) is the estimated frst natural frequency of the structure.
A reasonable criterion regarding the correspondence between damage indices and damage states is important for structural damage assessment.To illustrate the feasibility of 6 Structural Control and Health Monitoring the proposed method, a criterion based on the principles of the performance-based earthquake design is introduced [50].Te range of the damage index for reinforced concrete structures is shown in Table 1.

Small-Scale Model Verification
3.1.Experimental Setup.To validate the feasibility of the proposed method, a shake table test for a small-scale model of a two-story steel frame structure was designed.Te experimental setup is shown in Figure 3.To stay within the limits of the loading capacity of the shake table and the available space in the laboratory, the total height of the model is 1.1 m, and the heights of stories one and two are 0.6 m and 0.5 m, respectively.Te cross-sectional dimensions of each column are 3 mm × 20 mm.Each rigid foor has a size of 500 mm × 500 mm × 5 mm and a mass of 10 kg.To simulate the real indoor situation, small-scale models of furniture were fxed on the foors, as shown in Figure 3. Two cameras were rigidly fxed on the ceilings and perpendicular to the foor below.Te resolution and frame rate of the cameras are 640 × 480 pixels and 120 fps, respectively.In addition, to verify the accuracy of the measured response through computer vision techniques, the accurate dynamic response of the model during the experiment was measured at a sampling frequency of 120 Hz using the position-sensing system.Te position sensor markers are fxed on the side of each foor.Te shake table is a Quanser XY Shake Table III produced by the Quanser company.Te cameras are RYS720P Global Shutters from Shenzhen RongyangSheng Electronic Technology Corporation.Te position-sensing system is the NDI Optotrak Certus produced by the Northern Digital Incorporated.Springs are utilized in the experiment to simulate the damage sustained by the structure during the earthquake.Te springs were frstly tightened obliquely on a certain foor of the model.Ten, the springs were suddenly unloaded at a certain moment when the seismic acceleration was large to simulate the stifness degradation caused by the seismic damage.To ensure safety, protective sleeves were installed for each spring.Considering the feasibility of the operation, the springs were installed only on the frst foor, and three different conditions of the structure (DS 1, DS 2, and DS 3) were tested.Diferent conditions of the structure were achieved by changing the number of springs.Te natural frequencies of the structures before and after the seismic load were obtained by using the sweep frequency excitation (Table 2).Te frst natural frequency decreases after the earthquake.Te seismic action applied by the shake table was the earthquake named NGA_no_1105_HIK000, which can be obtained from the website (https://ngawest2.berkeley.edu),as shown in Figure 4. Due to the limitations of the shake table, the peak acceleration of ground motion was adjusted to 0.1 g.

Verifcation of the Structural Inter-Story Response.
Te structural inter-story pixel displacements were obtained through the procedure described in Section 2.1.As shown in Figure 5, the region of the fxed small-scale model of the furniture was set as the ROI, and the feature points in the ROI were automatically detected using the Harris corner detection algorithm.Subsequently, the Kanade-Lucas-Tomasi algorithm was utilized to track the motion of feature points, and the inter-story displacement, in terms of pixels, can be obtained.To verify the accuracy of the structural response measured by computer vision techniques, the displacement was calibrated into meters by multiplying a unit conversion factor s, which can be acquired according to (24).Te diagram of unit conversion is shown in Figure 6, and the P, p, and s in the schematic are 99.52 mm, 148 pixels, and 0.672 mm/pixel, respectively.
where s is the unit conversion factor from pixel to meter, P is the length (meters) of the target, and p is the pixel length of the target.Te position sensor cannot measure the response of the structure during the spring unloading process due to the occlusion by personnel.Tus, the response of the structure without springs was selected to verify the accuracy.Te comparison between the structural responses measured via the computer vision and as measured by the position sensor is shown in Figure 7. Te relative errors of the maximum inter-story displacement of the frst and second stories of the structure are 0.21% and 0.36%, respectively.Furthermore, the main peak frequencies of the inter-story displacement responses obtained by the two approaches are consistent.Te consistency indicates the dynamic response of the structure can be accurately measured using the method described in this study.As observed from the spectrum of the responses, a camera with 120 fps is sufcient to capture the structural response.

Damage Index Calculation of the Small-Scale Model.
After verifying the accuracy of the measured structural response, the natural frequency of the structure can be estimated from the response using the procedure described in Section 2.2.First, the structural responses in terms of inter-story pixel displacement were obtained via the cameras, as shown in Figures 8 and 9. Ten, the energy-concentrated, time-frequency representation of the response was obtained by using the SET, and the bandwidth of the frst modal response was determined as shown in Figures 8 and 9. Te ranges of the frequency bands for the frst-order modal responses are listed in Table 3. Next, the frst modal response was extracted from the measured response through the EWT.Te extracted frst modal responses are shown in Figures 10  and 11.Lastly, the instantaneous frequency of the frst modal response was calculated using the HT, and the frst natural frequency was then estimated through the application of the SGF (Figures 10 and 11).Te order of the polynomial r was set to 3, and the span M was set to 5999 in the SGF.It can also be seen that the error of the calculated instantaneous frequency of the response due to Gibbs' phenomenon [63], which refers to an overshoot induced by a jump discontinuity, can be also eliminated by SGF.Table 1: Te range of damage index for diferent damage states for reinforced concrete structure [50].To verify the feasibility of the proposed approach, the damage indices were calculated according to the estimated frst natural frequency of the structure.Te results of the calculated damage indices are listed in Table 4 and Table 5. Te error of the damage index is defned as the diference between the damage index estimated by the proposed method and the one obtained by the modal test.Te maximum error of the damage index is 0.097, and the damage indices obtained by using the structural response of the frst and second stories are consistent.Tis indicates that the proposed approach can obtain the natural frequency-based damage index with only one camera.Te error of the damage index is mainly attributed to the measurement error in the pixel displacement and the estimation error in the instantaneous frequency.

Full-Scale Model Verification
4.1.Experimental Setup.To further confrm the practicability and efectiveness of the proposed method, the method was applied to evaluate the damage state of a full-scale reinforced concrete building model.In contrast to the sudden reduction of the structural stifness in Section 3, the seismic damage accumulation of the structure during the earthquake can be considered in this experiment.Te model is from the building nonstructural components and systems (BNCS) project [64] and has fve stories, as shown in Figure 12.Te shake table test of the full-scale model consisted of two phases: base isolated phase and fxed base phase.Te model was severely damaged in the second phase of the test named FB-5: DEN67.Te seismic action applied by the shake table in this test followed the earthquake recorded by the TAPS Pump Station during the Denali earthquake.Te peak acceleration of the ground motion was scaled to be 0.64 g.According to white noise excitation tests, the frst natural frequency of the structure before and after the earthquake is 0.84 Hz and 0.62 Hz, respectively.According to Table 1, the damage index is 0.455, which corresponds to moderate damage.Te camera Q6 (1280 × 720 resolution at 25 fps), which was located on the second foor, was used in this study.More detailed information can be found on the website (https://www.designsafe-ci.org/data/browser/public/nees.public/NEES-2009-0722.groups).

Damage Assessment of the Full-Scale Model.
Te entire assessment procedure for the full-scale model is similar to that for the small-scale model.First, the ROI was selected and the feature points were detected using the surveillance video during the earthquake, as shown in Figure 13.Te structural response was obtained by tracking the feature point, which was observed to remain stationary relative to the foor, as shown in Figure 14.Ten, the energy-concentrated, timefrequency representation of the response was obtained by using the SET, as shown in Figure 14.Te range of the frequency band for the frst modal response is 0.43 Hz to 1.00 Hz.Next, the frst modal response was extracted from the measured response by using the EWT (Figure 15).Finally, the instantaneous frequency of the frst modal response was calculated by using the HT, and the frst natural frequency was estimated through the SGF (Figure 15).Te order of the polynomial r was set to 3, and the span M was set to 1499.Te maximum and minimum of the estimated frst natural frequency were 0.82 Hz and 0.60 Hz, respectively.Te resulting damage index was 0.465, which corresponds to moderate damage and is consistent with the result of the white noise tests [64].Structural Control and Health Monitoring

Conclusion and Future Work
Tis study presents an efcient and efective strategy to accurately assess post-earthquake structural damage.Te approach was developed based on computer vision and time-frequency analysis techniques and applied to data from existing surveillance cameras.Te relative seismic response of inter-stories was extracted from the video by using a marker-free computer vision-based method.Subsequently, the natural frequency shift of the structure was estimated by using HT-based time-frequency analysis.Te damage index related to the frst natural frequency shift was then calculated and used for the damage assessment.Te feasibility of the approach was verifed via shake table experiments.Te main conclusions are as follows: (1) Te inter-story seismic response of the structure can be accurately acquired by using surveillance cameras and computer vision techniques under favorable illumination conditions.Te relative error of the maximum inter-story displacement of the structure is less than 0.4%.(2) Te natural frequency shift of the structure can be estimated by employing the SET-enhanced EWT method, HT, and SGF.Te error of the damage index using the estimated frequency shift was less than 0.1.(3) Te damage state of a structure can be directly evaluated solely by analyzing the relative pixel displacement response of the structure with natural frequency-based damage assessment theory.
Te proposed strategy for assessing structural damage induced by earthquakes capitalizes on existing surveillance cameras to achieve accurate assessment.Tis method can serve as an alternative solution for post-earthquake structural damage assessment in situations where sensor monitoring systems are not in place.Despite the encouraging results, there are still some open research challenges in future research.Tese challenges include the following: (1) Te quality of the images collected in the experiment is good, but the images acquired in the actual seismic scenario are adversely afected by factors such as insufcient illumination and occlusion.Tus, the computer vision-based algorithms to extract structural inter-story pixel displacement need further improvement.(2) Te external images of the structure hold rich information about structural damage.Consequently, the integration of visual inspection-based assessments with vibration monitoring-based assessments represents the next crucial area of exploration.(3) Due to laboratory constraints, the feasibility of the proposed method is verifed only in one-dimensional shake experiments, and the potential applicability of the proposed method in two-and three-dimensional seismic scenarios will be pursued in future studies.(4) Te development of advanced algorithms for pixel displacement measurement and instantaneous frequency estimation will also be a focus of future research to further reduce the damage index error.

Figure 1 :1Figure 2 :
Figure 1: Te schematic diagram of the proposed structural seismic damage assessment strategy.

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Figure 3 :
Figure 3: Te experimental setup of the shake table test for the small-scale model: (a) side view of the model; (b) front view of the model; (c) the position sensor; (d) overall diagram of the experimental setup.
Te load-bearing components are intact, and some non-load-bearing components are slightly damaged 0.00∼0.10Slight damage Individual load-bearing components have slight residual deformation, and individual non-load-bearing components are obviously damaged 0.10∼0.20 Moderate damage Most of the load-bearing components have slight residual deformation, and some of them are obvious 0.20∼0.50Heavy damage Most of the load-bearing components are seriously damaged or partially collapsed 0.50∼0.75Collapse Most of the load-bearing components are collapsed 0.75∼1.008 Structural Control and Health Monitoring

Figure 8 :
Figure 8: Te acquired structural inter-story pixel displacement responses of the frst story and their energy-concentrated time-frequency representation from SET: (a, b) DS 1; (c, d) DS 2; (e, f ) DS 3.

Figure 10 :
Figure 10: Te extracted frst modal response of the frst story and the estimated frst natural frequency of the structure: (a, b) DS 1; (c, d) DS 2; (e, f ) DS 3.

Figure 14 :
Figure 14: Te acquired structural inter-story pixel displacement response (a) and its energy-concentrated time-frequency representation from SET (b).

Table 2 :
Te settings of structural conditions in the small-scale model experiment.

Table 3 :
Te range of the frequency bands for the frst-order modal responses.

Table 4 :
Te results of the damage index calculation using the response of the frst story.

Table 5 :
Te results of the damage index calculation using the response of the second story.