System Identification of Heritage Structures Through AVT and OMA: A Review

In this review article, the past investigations carried out on heritage structures using Ambient Vibration Test (AVT) and Operational Modal Analysis (OMA) for system identification (determination of dynamic properties like frequency, mode shape and damping ratios) and associated applications are summarized. A total of 68 major research studies on heritage structures around the world that are available in literature are surveyed for this purpose. At first, field investigations carried out on heritage structures prior to conducting AVT are explained in detail. Next, specifications of accelerometers, location of accelerometers and optimization of accelerometer networks have been elaborated with respect to the geometry of the heritage structures. In addition to this, ambient vibration loads and data acquisition procedures are also discussed. Further, the state of art of performing OMA techniques for heritage structures is explained briefly. Furthermore, various applications of system identification for heritage structures are documented. Finally, conclusions are made towards errorless system identification of heritage structures through AVT and OMA.

• The accelerometers are low cost and highly sensitive.
• The accelerometer does not require any power source.
• The accelerometer can operate on wide frequency spectrum.

Accelerometers
Accelerometers are the sensors which converts acceleration into signal variable output like current, voltage etc. Specific characteristics of accelerometers such as range (difference between maximum measured response to minimum measured response), Resolution (Smallest value of increment recorded by response), type, sensing frequency (maximum value of frequency of response that is measured), working environment, and size (Physical dimensions of the accelerometers), play a vital role in acquiring accurate response of the heritage structure during AVT [Taleb, Bouriche, Remas et al. (2012)]. The significant characteristics of accelerometer have to be finalised before conducting an AVT [Prawin, Rao and Lakshmi (2015)]. Further, the selected accelerometer should be able to detect frequency as low as 1-2 Hz and sensitivity of 1v/g or higher is desirable for AVT on heritage structures [Atmaturkur, Pavic, Reynolds et al. (2009)]. There are many type of the accelerometers available in the market, from which piezoelectric type (for example Wilcoxon WR731A, BK Type 4506, PCB 393B12 etc.) and force balance type (for example EpiSensor FBA ES-T SA-107LNC etc.) accelerometers were commonly used for performing AVT on the heritage structures [Turek, Ventura and Placencia (2002); Bayraktar, Birinci, Altunişik et al. (2009) ;Foti, Diaferio, Giannoccaro et al. (2012) ;Min, Kim, Park et al. (2013); Gentile, Saisi and Cobboi (2015)].

Locations of accelerometers
Number of accelerometers and their locations are extremely significant as they have to record the response of the heritage structure wholly. While performing AVT, if the accelerometer networks are not covering the whole geometry, then the results will be unreliable and will not illustrate the exact response of the structure under ambient vibrations [Atamturkur and Sevim (2011)]. Effective accelerometer locations can be selected based on, (1) engineering judgement, (2) past experience, (3) initial numerical models and modal analysis, (4) optimization algorithms and (5) combination of above said all parameters. El Borgi et al. [El Borgi, Smaoui, Casciati et al. (2005)] used an initial finite element model for judicial placement of the accelerometers on a Palace structure and found that a total of 70 critical accelerometer locations were required for acquiring full response of the structure. Studies conducted by Atmaturkur et al. [Atmaturkur, Pavic, Reynolds et al. (2009)] on several Gothic Churches and concluded that the finite element modelling and modal analysis helps in the placement of accelerometer than engineering experiences and optimization algorithm. Pachón et al. [Pachón, Compá n, Fdo et al. (2014)] and Compan et al. [Compan, Pachón, and Cá mara (2017)] suggested that the response of the largest modal displacement determined by modal analysis on the initial finite element model must be taken into consideration for planning locations of reference accelerometers. Conde et al. [Conde, Ramos, Oliveira et al. (2017)] followed recommendations provided in previous research works on heritage bridges and used numerical models for placement of accelerometers Prabhu and Atmaturkur [Prabhu and Atmaturkur (2012)] developed an algorithm for effective accelerometer locations on heritage structure. In their study, Effective Independence Method (EIM) [Kammer, (1991)] was modified to determine the optimized location of accelerometers on heritage structures and named as Modified Effective Independence Method (MEIM). A total of 781 candidate accelerometer locations were selected on Gothic Revival-style masonry cathedral initially and after applying MEIM, the optimum number of location reduced to 120 accelerometer locations at a loss of 10% initial dynamic information. More algorithms on optimization of location of accelerometers can be found in Rao et al. [Rao, Lakshmi and Krishnakumar (2014)] and Yang et al. [Yang and Lu (2017)]. Some of the studies showed that the accelerometers cannot be placed on the desired locations due to various constraints including complex geometry and inaccessibility. In this concern, Tab. 1 summarises few practical problems and solutions achieved by researchers regarding placement of accelerometers. Researchers were not allowed to enter in some part of the tower, because of on-going retrofitting work.
Researchers put the accelerometers in nearby locations of prohibited areas.
2. Atamturktur, Pavic, Reynolds et al. (2009) Authors found that curved surfaces were difficult for placing the accelerometers in desired horizontal direction.
Authors used steel screw plates for placing the accelerometers in exact direction. 3. Foti, Diaferio, Giannoccaro et al. (2012) The study dealt with an area occupied by staircase situated at left side of the tower.
The authors placed accelerometers only on the side where staircase was absent at the right side of the tower.

Gentile and
Saisi (2014) The authors studied that the cross section of every floor was different in the tower.
The researchers placed the accelerometers at the point where cross sections were changing. 5. Diaferio, Foti and Giannoccaro (2015) Authors found that it was too difficult to place the accelerometers in exact orthogonal position in tower due to irregular geometry of the floors.
Authors designed proper rectangular blocks to place the accelerometers orthogonally.
6. Gentile, Saisi and Cobboi (2015) Authors faced difficulties in placing the accelerometers inside the Church structure due to summer season.
Authors placed accelerometers only on outer side of the walls and performed the test. 7. Ceravolo, Pistone, Fragonara et al. (2016) The study dealt with some areas with no proper accessibility in the building for placement of accelerometers.
The authors used optimization algorithms to choose other appropriate locations which can cover the whole structure.
Location of the accelerometers is crucial parameter in AVT, which has to be achieved incorporating practical solutions to the field problems. Tab. 2 highlights the geometry of test structure and the details of accelerometer locations used in past investigations.

Description of accelerometer locations
The authors selected a total of 20 locations for placement of accelerometers. To cover the whole structure, they performed AVT in two deployment of accelerometers. In the first deployment, thirteen locations (shown in Fig. 1 with green colour) were used. In the second deployment, seven locations (shown in Fig. 1 with red colour) were used. The placement of accelerometers covered both horizontal orthogonal directions. The accelerometers which are placed on the right top corner (shown Fig. 1 as number 7, 12) were acted as reference acclerometers.

Description of accelerometer locations
For the objectives the authors have selected fifteen locations (shown in Fig. 2 with red colour) for the placement of seismometers on the third floor. They placed nine seismometers in longitudinal direction and six seismometers in lateral direction. The entire study was condected in a single deployment.

Description of accelerometer locations
The authors selected a total of eight locations (shown in Fig.  3) for placement of accelerometers. Further, thirteen uniaxial accelerometers were employed in horizontal orthogonal directions. Among them, four accelerometers were placed at 5 th floor. Further, 7 th , 9 th and 10 th floors had three accelerometers each. The accelerometers at the 10 th floor were used as reference accelerometers as shown in Fig. 3.

4.
Diagram showing structural geometry and accelerometer location

Description of accelerometer locations
The study was conducted choosing 48 different accelerometer locations. A total of ten accelerometers were used for AVT following redeployment of accelerometers for seven times to capture the vibration of whole structure. A pair of reference accelerometers were placed at 5.8 m height of left most Go-ju column (as highlighted inside the box, Fig. 4). At first, four pairs of accelerometers were deployed at the left most Go-Ju column at the elevations of 0.4 m, 4.0 m, 5.8 m, and 8.8 m and vibrations were recorded. Reinstallation and same test procedures were sequentially conducted for the remaining Go-Ju columns from the left to the right direction, (i.e. deployment 1 st to 4 th in Fig. 4). The same above said procedures were adopted for placing accelerometers at all Guigo-Ju columns twice at elevation of 5.8 m and 8.8 m respectively (i.e., 5 th and 6 th deployment in Fig. 5). Further the vibration measurment of Pung Ju columns were recorded placing the accelerometers at elevation of 8.8m (i.e., 7 th deployment in Fig. 6).

5.
Diagram showing structural geometry and accelerometer location

Description of accelerometer locations
The authors chose fifteen locations to record the vibrations of the vault structure. They placed accelerometers in vertical direction on the vault structure in three rows having five accelerometers in each row (as shown in Fig. 7) in a single deplyoment.

Description of accelerometer locations
Authors selected a total of nineteen accelerometers for conducting AVT. At first deployment, authors have placed eight accelerometers around the ring of the dome, in radial and in vertical direction (as shown in Fig. 8 with red colour). In the next deployment, they placed four accelerometers at mid level of the dome only in vertical direction. The reference accelerometer was deployed at the apex of dome structure (as highlighted in box).

7.
Diagram showing structural geometry and accelerometer location

Description of accelerometer locations
Authors selected a total of six locations for the placement of accelerometers. To identify the dynamic characterstic of whole structure they placed the accelerometers on the sides of the deck in vertical and horizontal directions(as shown in Fig. 9).

Description of accelerometer locations
Authors selected a total of 38 locations for the placement of velocity sensors following three deployments to cover the whole structure. In first deployment, 15 velocity sensors were placed on the second floor of the palace (as shown in Fig. 10). In the second deployment, 15 velocity sensors were placed inside the civic tower structure. Among that three sensors were placed on the ground at the base of the tower, four inside the tower at the height of 10.5 m , four on the wooden slab located at height of 29.5 m, and four at the top of the tower i.e., 34.5 m. The last deployment includes partly Margherita Palace and partly the civic tower ( Fig. 11). Three velocity sensors were located at the base of the tower and four at the top of the tower, while the remaining sensors were divided between the first floor and the second floor of the building (as shown in Fig. 12).

9.
Diagram showing structural geometry and accelerometer location Figure

Description of accelerometer locations
Authors selected a total of seven locations for the placement of accelerometers. The accelerometers were placed in vertical direction on the three adjent vaults (as shown in Fig. 15).

Diagram
showing structural geometry and accelerometer location Figure 16: Elevation of tower of Announziata with accelerometer locations [Diaferio, Foti and Giannoccaro (2015)]

Description of accelerometer locations
Authors selected a total of 12 locations for the placement of accelerometers. Eight accelerometers were placed in four corners of first floor (at height of 4.30 m), eight accelerometers were placed on second floor (at height of 12.44 m) and eight accelerometers were placed at top floor (at height of 13.89 m) in both orthogonal horizontal directions (as shown in Fig. 16).

Ambient vibration loads on the historical structures
In general, dynamic loads are the basis of vibration testing while assessing the constructed structures. In case of AVT, wind loads, traffic induced loads, wave induced loads, and other environmental loads are generally being used [Omenzetter, Beshkroun, Shabbir et al. (2013)]. The source of vibration and intensity of the vibration, have major effects for measurement of the dynamic properties of the structures [Wilson, Oyarzo-Vera, Omenzetter et al. (2008)]. Since AVT does not account the input of the external vibration, multiple input vibrations can be used for excitation of the structure at the time of AVT [Cantieni (2009)]. Tab. 3 discusses the excitation sources used by researchers on various heritage structures in their studies.  (2012) Many times it happened that the environmental loads were not enough to trigger all the target modes of the structure. The authors mentioned about the studies used other techniques like impact hammer, external micro-tremors devices to trigger the targeted modes of the structure. The studies also account that the excitation should be given at multiple point of the structure for testing.

2.
Gentile, Saisi and Cabboi (2012) The authors studied the response of the heritage bell tower structure twice by conducting AVT and OMA. In first attempt they used micro tremors and ambient vibrations as excitation sources. In the second attempt they used swinging of bells as source of excitation. Upon analysis, they found that there is slight difference in higher modes. The investigation also concluded that there is slightly increase in frequency due to temperature variation.

3.
Votsis The mentioned studies considered the vibration from human activities, traffic, wind and operational vibrations for exciting the test structure. Authors had considered multiple input excitations because of the fact that the size of the structure was very huge, and single input excitation was not enough to trigger all the necessary modes of the structure.
The authors used a 'free-fall' of concrete block from a truck to induce external vibration on the structure. This impulsive source of vibration should be used in controlled manner so that no damage happens to heritage structure.

5.
Russo (2016) The author suggested ignoring the excitation of structure from extraordinary sources like fireworks, earthquake or natural calamity. Because of the reason that, the response of the structure will not represent its original service conditions.

Data acquisition
Data acquisition is another important aspect for conducting the AVT accurately. The data acquisition is a procedure of collecting data from the sensing device and stores it to computer system. For recording errorless response of the structure through AVT, following parameters should be selected properly:

Sampling rate
Generally, sampling rate is defined as upper limit of frequency band that can be utilized for analysis of recorded signals. Sampling rate should be selected for testing the structure for each measurement [Brinckner and Ventura (2015)]. In general, sampling rate is the number of samples recorded in unit time and measured in terms of Hertz (Hz) or sample per second (sps). Sampling rate directly affects the quality of data being recorded [Gallino, Gentile and Saisi (2009)]. Generally, there are two methods which are being used for selection for sampling rate [Brinckner and Ventura (2015)]: (a) Maximum significant frequency of the structure (b) Standard frequency for data acquisition system having Nyquist frequency of 50-100Hz for large structures.

Time duration
A proper time duration for recording the data for measurement is another parameter required during excitation of the structure [Brincker and Ventura (2015)]. The measured time duration should be long enough to ensure that all the targeted modes are sufficiently excited [Turek, Ventura and Placencia (2002)]. The time period should be chosen based on Brincker Criterion [Brincker, Ventura and Andersen (2003)] which is been followed in many AVTs conducted on heritage structures [Gentile and Saisi (2007); Ramos, Marques, Lourenç o et al. (2010)]. According to Brincker criterion, if the fundamental frequency of any structure is measured in Hertz, its modal damping factor is , and the recording duration T should be at least = 100 .

Operational Modal Analysis (OMA)
OMA is a common numerical procedure which is used for the processing of collected data acquired from the AVT (having characteristics of white noise) which covers the entire frequency range of modal characteristics of the whole structure [Ewin (1986)] to identify the dynamic characteristics of system. The OMA procedure can be performed in two platforms, i.e., time domain and frequency domain [Brincker, Zhang and Andersen (2000)]. OMA procedure has many techniques, which are used by researchers according The general outcomes of OMA are the dynamic parameters of the system such as frequencies, mode shapes and damping ratios. Over the period of decades, the OMA has proven to be an effective method in dynamic system identification of many complex structures and mechanical systems. Hence, the investigations deal with heritage structures have also adopted OMA procedure and evaluated the complex dynamic parameters in their research studies using abovementioned OMA techniques. Tab. 4 presents the OMA techniques used by research investigations on heritage structures. The following section discusses more details about SSI and FDD techniques on heritage structures.

Stochastic Subspace Identification technique (SSI)
The stochastic subspace identification technique [Van Overschee and Moor (1996)] is a time-domain method that directly works with time data without the need to convert them to correlations or spectra. The stochastic subspace identification algorithm identifies the state space matrices based on the measurements by using robust numerical techniques. The method may be introduced as follows, dynamic behaviour of any mechanical system of n2 masses, which is assembled with springs and dampers can be formulated as.  (2) and (3) for output only vibration in discrete time is +1 = + (4) = + (5) Where, -discrete time state vector which contains the displacement and velocities describing the state of system at time instant and is a output vector of the state space. A-discrete state matrix and C-discrete output matrix which maps the state vector into the measured output. -processed noise due to disturbance and inaccuracy in sensors,measured noise due to inaccuracy. It can be shown that the dynamic model parameters (frequency, mode shape, damping) of a structure under white noise excitation can be identified by measured output response . In case of AVT of the large structures to find the dynamic parameters, all the output can be measured at once, but they are divided into different setups. Assume for N elements of output, the measured response of the structure in form of acceleration are assembled in a data set Y Y = [ y 1 … y N ] N -Discrete time sampling number of responses At first, the data set Y is converted into Hankel matrix for better arrangement of measured response and expressed as Where, are the past and future Hankel Matrix, respectively of data set Y.
Next, data handle technique like orthogonal projection is applied to Hankel Matrix towards eliminating the unnecessary samples to avoid rigourous computation. Upon applying abovementioned technique the Projection matrix ( ) for Hankel Matrix can be defined as the conditional mean of with respect to .
Further, projection matrix ( ) can be factorised into observability matrix (Γ) and Kalman filter state (X) = Γ X (9) In order to calculate observability matrix (Γ), the singular value decomposition (SVD) has been applied to projection matrix ( ) as follows, U-Left singular vector, S-Singular scalar value, V-Right singular vector Where, = ( ) 0.5 is a pre-multiplied weighing matrix, and I is Identity matrix. Now, the observability matrix (Γ) can be calculated as Γ = W −1 1 1 0.5 (11) Finally, from observability matrix (Γ), A and C matrices can be calculated as follows for i blocks of the Hankel Matrix (H) [Eq. (7)]: At last, eigen value decomposition of A will give the eigen values and eigen vectors of the system as follows = ΨΛΨ −1 (13) Φ = CΛ (14) Here, Ψ-Eigen Matrix contains eigen vectors as column, Λ-Diagonal Eigen Matrix, Φmode shape vector. The mode shape of the previously mentioned accelerometer location, defined as the column vector Φ are observed parts of system eigenvectors Ψ and are thus obtained using Eq. (3). In general, the obtained dynamic parameters are compared against model orders in form of stabilization diagram for best understanding. Stabilization diagram accommodates dynamic properties such as, frequency, damping ratio, mode shape in the horizontal axis denoted as x(n,m). The vertical axis accomodates model order denoted as y(n,m). Here, n is a value on vertical axis and m is a considered mode. A modal parameter is identified and considered as stable if it agrees the following stabilization criteria | ( − 1, ) − ( , )| < ∆ (15) Where, ∆ is the threshold value provided for the operation. In stabilization diagram, the modes which are present on vertical lines will be a physical mode. Further, Tab. 5 summarises the key features of SSI technique highlighted in previous studies.

Sn.
Reference Remarks 1. Ramos (2006) Authors found that SSI technique is very efficient in finding closely spaced frequency of structural modes of the axisymmetric structure.
Authors found that SSI technique has ability to distinguish between real modes of the structure and the modes that occurred temporarily. Further, the SSI technique was found to be more accurate for the linear dynamic characterisation of the tested monument.

3.
Foti, Diaferio, Giannoccaro et al. (2012) The study concluded that SSI technique is very useful in finding out mode shapes and associated frequency of symmetrical structures.

4.
Diaferio, Foti, Giannoccaro et al. (2014) The author concluded that SSI method did not highlight the peaks corresponding to frequency of structure due to very squat and fixed shape of the test structure.
The study concluded that the SSI technique was very helpful in determining the higher modes of the cylindrical shaped building.

Frequency Domain Decomposition technique (FDD)
The frequency domain decomposition technique [Brincker, Zhang and Andersen (2000)] is a frequency domain method which is based on singular value decomposition (SVD) of the spectral density (SD) obtained from ambient vibration test. The technique is closely related to the complex modal indicator function (CMIF) [Shih, Tsuei, Allemang et al. (1988)] which was based on an SVD of the frequency response function (FRF) matrix and presentation of the singular values as function of frequency. It concentrates all information in one single graph with singular values of the SD matrix. Tab. 6 summarises the features of FDD technique highlighted in previous studies. The theoretical background of FDD method [Brincker, Zhang and Andersen (2000)] for OMA is as follows: At first, the relationship between unknown input x(t) and response y(t) has to be expressed in form of power spectral density function (PSD) Where, ( ) -response power spectral density function, ( ) -input spectral density function, H ( ) -Frequency Response Function (FRF) Matrix, T-Complex conjugate or transpose Next, FRF matrix ( ) has to be reduced into pole/residue form as follows, Here, -Residue, -Poles. The unkown input matrix has to be assumed as in form of white noise, then the input PSD matrix will become a constant matrix ( )=C, further, the Eq. (16) can be written as Where H is complex conjugate transpose. In order to simplify Eq. (18) partial fraction theorem and mathematical manupulations has been performed as follows Where is the k th residue matrix of PSD and contribution to residue from k th mode can be given as Here, -negetaive part of the real poles. In case of lightly damped structure or very low damping, the residue will become propotional to the mode shape vector which is shown below = ∝ ̅ (21) Further, at frequency, limited modes will be contributed significantly. Let the set of mode be Sub( ), thus the response density function for PSD becomes Furthermore, the estimated PSD ( ) is then decomposed into singular value by singular value decomposition ( ) = Where, = [ ,1 ,2 … . . , ] is unitary matrix and is diagonal matrix contains scalar values of k th mode. If k th mode is dominating then there will be only one term in Eq. (22). Thus the estimated mode shape will be: Finally, the mode shapes are estimated from the singular vectors of the SVD of the spectral density matrix. However, we have an SVD for each frequency where the Singular Diagonal matrix is known because the SVD can be carried out for all known frequencies. This also means that if we have the same number of modes as we have sensors, then in principle all mode shapes can be found at one single frequency line. In the spectral density plot of PSD vs frequency, PSD function is identified around the peak is estimate of the mode shape ̂ with the singular vectors for the frequency lines around the same peak. From the Single Degree of Freedom (SDOF) density function obtained around the peaks of PSD function, natural frequency and damping can be estimated for respective mode shapes.  Gentile and Saisi (2007) Authors found that the estimated frequency for the AVT is matching the result of field test performed in year 1992. FDD techniques were found efficient in estimating bending mode shapes of the tower structure.

2.
Casarin and Modena (2008) The investigation showed that FDD technique was able to find the natural frequency of targeted modes. However, only few higher structural modes were detected. 3. Cimellaro, Piantà , and De Stefano (2012) Authors found that FDD techniques were very exact in extracting modes when input data is in the form of white noise. But FDD technique was unable to extract closely spaced frequency of structural modes.

4.
Lacanna, Ripepe, Marchetti et al. (2016) Authors found first six structural modes by using FDD technique within frequency range of 0 to 6 Hz. The authors also conclude that FDD technique allowed to measured detailed mode shapes of the Baptistery.

5.
Conde, Ramos, Oliveira et al. (2017) The investigation showed that FDD technique was able to find first six vibrational modes and associated frequencies of arch bridge structure. The estimated frequencies were well spaced and varied in range of 4.67 Hz to 12.45 Hz. [Foti, Diaferio, Giannoccaro et al. (2012)] The researchers carried out modal extraction from recorded AVT data by FDD and SSI techniques. Stabilization diagram by SSI technique of the output results [as shown in Fig.  17(a)] which shows that well aligned poles are formed between the frequency ranges 2-6 Hz. The same results are obtained from the spectral density matrix plot obtained from FDD technique [ Fig. 17(b)] shows five mode shapes were in same frequency ranges 2-6 Hz. The results from both the methods are presented in Tab. 7 for clarity.

The tower of the Provincial Administration Building in Bari, Italy
(a) Stabilization diagram by SSI technique (b) Spectral density matrix by FDD technique Figure 17: Experimental results obtained from AVT and OMA [Foti, Diaferio, Giannoccaro et al. (2012)] Fig. 18(a)] and Power Spectral matrix of the FDD technique is given in Fig.  18(b). Further, modes and frequencies estimated by both the methods are presented in Tab. 8 for clarity.

Comparison of SSI and FDD techniques
For the dynamic parameter estimation of heritage structures two major representative techniques i.e. SSI technique and FDD technique were elaborated in previous sections. These two techniques are highly complex and mathematical in nature. Though the methods are equally compatible, many studies showed that the results from both the techniques for same response dataset are not same, this may due to unwanted noise, geometrical configuration of the structure, mathematical algorithm followed by both the methods. Some of the studies are elaborated in Tab. 9 which compares the differences found in dynamic parameter estimation by both techniques for same response dataset with advantages and disadvantages.
The investigation showed SSI technique can able to estimate all the modal frequencies and damping ratio of the palace building.
Authors found that FDD technique was able to estimate only natural frequencies, mode shapes and damping ratio could not be estimated.

2.
Magalhã es, Cunha, Caetano et al. (2010) Authors found that the time taken for estimating the dynamic parameters from dataset by SSI technique was 1/4 th that was taken by FDD technique.
Authors found that the time taken for processing the dataset for estimating dynamic parameters was longer compared to SSI technique.

Gentile and
Saisi (2011) Authors found that SSI technique was unable to estimate 1 st torsion mode at frequency 2.014 Hz for tower structure.
Authors concluded that Singular Value plot from FDD technique identified a torsion mode at frequency 2.014 Hz for tower structure. 4. Aguilar, Torrealva, Ramos et al. (2012) Investigation showed that an improved identification of nine natural frequencies from SSI techniques for 19 th century hotel building.
Authors found that only two natural frequencies were estimated by FDD techniques for same set of response data of 19 th century hotel building. 5. Diaferio, Foti and Giannoccaro (2015) The investigation concluded that the SSI technique is able to evaluate all the higher structural modes of the test tower structure.
FDD technique was unable to estimate higher structural modes of the test tower structure.
Authors found that the estimation of structural mode was difficult due to unclear peaks in specral density plot. 7. Altunişik, Genç , Günaydin et al. (2018) The authors found that the first three natural frequency of tower was in range of 4.452-7.011 Hz in SSI techniques for Bastion structure. The second mode frequency observed for bastion was higher in SSI technique.
The authors found that the first three natural frequency of tower was in range of 4.452-6.967 Hz in FDD techniques for Bastion structure. The second mode frequency was 0.77% lower in FDD technique.
Authors have found first four natural frequencies clearly for the bridge structure.
The investigation showed that FDD technique was unable to capture the second and third mode frequency of the bridge structure.

Applications of system identification through AVT and OMA
AVT and OMA techniques are not just restricted only for determining system identification. There are numerous applications in the field of civil infrastructure design and assessment where the results of the AVT and OMA can be used. As far as heritage structures are concerned, there are many practical applications such as (1) finite element model updation, (2) seismic vulnerability assessment, (3) damage identification, (4) assessment of retrofitting of structural elements and (5) structural health monitoring for heritage structures, are investigated by researchers. The following section discusses the abovementioned applications briefly.

Finite Element model updation
Finite Element (FE) model updation is a simple procedure for calibrating the existing numerical model incorporating the results obtained from AVT and OMA. An existing FE model can account only the initial geometric and material properties. But in the case of heritage structure it becomes at most necessary to update the numerical model regularly for present day condition towards successful conservation. In general, FE model updation can be achieved by adjusting the physical properties, mechanical properties, boundary conditions, masses, restrained properties, joint properties and geometry of the elements in the numerical model to match against the results obtained from AVT and OMA [Pau, De Sortis, Marzellotta et al. (2005); Gentile, Saisi and Cobboi (2015); Lacanna, Ripepe, Marchetti et al. (2016)]. A common procedure followed in the literature studies for FE model updation for heritage structures is presented in Fig. 19. Ramos et al. [Ramos, Aguilar, Lourenç o et al. (2013)] used four mechanical parameters such as Young's modulus of masonry, stiffness of the soil near to the structure, normal and shear stiffness of the contacting elements to update the model of Mogadouro Clock Tower, Purtugal using Douglas-Reid method [Douglas and Reid (1982)]. Votsis et al. [Votsis, Kyriades, Chrysostomou et al. (2012)] used sensitivity analysis [Mottershead, Link and Friswell (2011)

Dynamic health monitoring
Dynamic monitoring systems are valuable for predicting long-term structural evaluation. These systems (consist of accelerometers, data acquisition system) are installed on the heritage structures for tracking changes in the global frequency with respect to time, as well as for acquiring the data required for the subsequent implementation of damage notification tools [Gentile, Saisi and Cabboi (2012)]. The main objective of dynamic monitoring system is to correlate the variation of natural frequencies with damage and environmental effects ]. The different phases involved in dynamic monitoring are, (1) model updating, (2) [Gattulli, Lepidi and Potenza (2016)] conducted monitoring of Basilica of S. Maria Di Collemaggio in June 2011. A total of 16 wireless sensors were installed all over the structure. The monitoring was aimed for investigating causes of collapse, performance of scaffoldings and long term dynamic response of the structure and updation of FE model. The study concluded that dynamic monitoring was effective tool for damage identification and evaluation of performance of structure during operational condition.

Repair and retrofitting
The AVT and OMA can be performed before and after the repair and retrofitting of the structure. Many studies states that AVT and OMA can be safely used to observe the restoration effects by determining dynamic response of heritage structures. Fig. 20 shows the common procedure adopted by literature studies for the assessment of repair and restoration of heritage structures. Few noticeable studies on the assessment of repair and rehabilitations of heritage structures using AVT and OMA can be seen from Tab. 11.  The investigation showed the results from AVT and OMA before and after the restoration work was found to be very close. The first five natural frequencies of the repaired case of the vault were identified in the frequency range of 9.371-27.850 Hz, which was more than pre-restored case of the structure. It was concluded that the increased frequencies were due to increase in the rigidity of the structure due to restoration work.

2.
Osmancikli, Uç at, Tarum et al. (2012) The bell-tower of Hagia Sophia Church, Turkey The authors performed AVT and OMA for Hagia Sophia Bell Tower in prerestored and restored condition. The authors found that the first and second bending modes of the restored tower had close frequency values as prerestored case. The mode shapes of the tower for restored and pre-restored cases were approximately the same. The average modal damping ratios of the tower were also decreased from 2.69% to 0.6%. Further it was concluded that the restoration was effective.

3.
Ercan (2018) The "Grand House", Turkey The author conducted AVT and OMA masonry structure before and after retrofitting. The study showed that the 1 st modal frequency had increased three times as compared to initial condition. The author also concluded that the AVT and OMA are most reliable method to evaluate the impact of retrofitting of the heritage structures.

Conclusion
This review paper summarised detailed procedures, methodologies, instrumentation, and application of AVT and OMA carried out by research community for past 20 years on heritage structures for successful system identification. Further, the paper has appraised various outcomes of these investigations and highlighted the applications of system identification. Following are some of the major conclusions drawn from this paper: • AVT and OMA are found to be most reliable procedure for system identification (identifying mode shapes, frequency, damping etc.) of heritage structures. Further, the results determined from AVT are quite dependable with minimum errors. • It is learnt that primary survey is an essential step prior to performing AVT. The primary investigation includes understanding the historical data, whole geometry, and material characteristics. An apt primary survey will be a leap step in understanding the response of the structure under operational conditions as well as sources of the errors. • Investigations showed that knowledge of excitation sources along with geometry of the structure will help in selecting suitable instrumentation. Adding to this, the accelerometers should be sufficiently sensitive in order to capture the smallest response of the structure. Further, the accelerometer locations should be chosen such that whole structure to be covered in order to get full response. If there are not enough number of accelerometers available, multiple deployment technique should be used carefully. Some time it is not possible to put accelerometers on prerequisite positions, in that case one can choose the location nearer to actual position. • The investigations showed that the natural sources like wind, traffic, operational excitation sources are useful for exciting the structure for vibration measurement. Sometime, these excitations are not enough for exciting the whole structure for targeted modes. In such cases, the better way to excite the structure for essential mode is to use impact hammer in different directions on different locations. Another artificial method is to use micro-tremor which generates the vibration of low level, which can be useful for excitation of the structure. • The literature shows that two major OMA techniques (time domain as well as frequency domain) should be performed simultaneously and the results of the methods should be compared and validated.
7 Future scope • Genrally, the results of AVT and OMA are used to update the FE model such that the dynamic characterstics of FE model should match with the response estimated by AVT and OMA. However, during FE model construction, the material characterstics are generally assumed which perhaps can be harvested from some non-destructive tests (NDTs) such as ultrasonic pulse velocity, rebound hammer, flat jack test etc. so that the accuracy of the response of the structure is improved alongside of AVT and OMA and updated FE model. At present very few studies have practised NDTs along with AVT and OMA which may be considered as mandatory. • Many heritage structures are being controlled and maintained within permissible vibrations by active/passive vibration control systems. The implementation of these control systems will be effective if they are designed using the results obtained from AVT and OMA. Till now, no applications are found in this avenue. • The complex geometry of heritage structure always demands optimized placement of sensor network. Only few studies were found and more studies will pave clear direction to achieve best sensor network to capture the reponse of whole structure. • The advent of wireless sensors and their effectiveness to be explored for AVT and OMA in case of heritage structures. • Present OMA techniques are highly complex mathematical in nature. This put practising engineers to undergo rigorous computations. Simplified algorithms for OMA will be effectively useful for practising engineers towards system identification. • No studies are found in AVT and OMA incorporating Soil structure iteraction with heritage structures. Conducting such studies can be very effective in predicting seismic vulnerability of heritage structures. • There are strong requirements of understanding environmental effects like tempreture variation, humidity, rain etc. while evaluating the life and deterioration of heritage structures. Persuing such studies with AVT and OMA will provide a new scope for the maintainance schemes and plans for heritage structures.
• There is strong need of a common platform where all the AVT and OMA data on different heritage structures shall be stored and maintained, which will help the research community for progressing in field of the study.