Damage Detection and Condition Monitoring of Pre-stressed Concrete Bridges by using Vibration-based Health Monitoring Techniques

: Damage detection plays a vital role in bridges as the structural performance of the bridges decreases progressively throughout their service life due to many deterioration processes. Although damage detection is performed mainly through periodic visual inspection, due to its immense drawbacks, researchers have focused increasing attention to the potential of using vibration-based structural health monitoring (V-SHM) techniques to detect damages and monitoring conditions of the structures. The fundamental theory of the V-SHM is that structural damages will change mass, stiffness and damping properties of structures leading to detectable changes in their dynamic characteristics such as natural frequencies, mode shapes and modal damping ratios. The applicability of V-SHM techniques to detect the existence of damage in pre-stressed concrete bridges by experimentally identifying their dynamic characteristics is reported in this study. Eigensystem Realization Algorithm (ERA) was used for experimental modal analysis of the bridges by using the free vibration records extracted from field vibration measurements. Numerical modal analysis for the bridges was performed using finite element models of the bridges to obtain the dynamic characteristics of the intact structures. The identified dynamic characteristics from both experimental and numerical approaches were used in obtaining an indication of the possible level of existence of damages in studied pre-stressed concrete bridges. Three global damage identification (DI) criterions are defined and evaluated to further corroborate that these bridges have not undergone appreciable damages, as the evaluated DI criterions are within acceptable tolerances for no damage state, accommodating noisy data.


Introduction
Pre-stressed Concrete (PC) bridges are an essential component in Sri Lankan transportation network. These bridges are susceptible to damages due to the increase in traffic volume of the road network and adverse dynamic loading conditions in challenging environmental conditions. The structural performance of PC bridges decreases progressively throughout their service life due to deterioration processes such as fatigue, creep, reinforcement/pre-stress tendon corrosion and adverse loading. Hence, damage identification is required to maintain the infrastructure in a serviceable state and diagnose damage at an early stage so as to avoid disastrous failures.
Bridge damage detection is performed mainly through periodic visual inspection, which is often subjective. Invisible damages cannot be easily identified by visual inspection alone. To address these drawbacks, researchers have focused the attention increasingly on Vibrationbased Structural Health Monitoring (V-SHM) technique due to it being a non-destructive method of evaluation non-reliant on subjective human input such as visual inspection.
Structural Health Monitoring (SHM) is defined in [1] as "at the simplest level, recurrent visual observation and assessment of structural condition (cracking, spalling and deformations) could be viewed as SHM, yet the aim of present -day research is to develop effective and reliable means of acquiring, managing, integrating and interpreting structural performance data for maximum useful information at a minimum cost while either removing or supplementing the qualitative, subjective and unreliable human element", which sums up the definition of SHM quite well.
The fundamental theory behind vibrationbased damage identification technique is that damage induces changes in physical properties of the structures resulting in detectable changes in modal properties such as natural frequencies [2], mode shapes [3] and modal damping ratios [3]. This implies that modal parameters vary according to the extent of damage and identifying the differences/trends in the variation of modal parameters with damage may give reliable insights to measure the level of damage of structures.
The research data presented here will be beneficial to understand the feasibility of adopting the V-SHM techniques to detect structural damages by identifying the dynamic characteristics including natural frequency, mode shapes and modal damping ratios of the studied PC bridges.
Hence, this research was carried out to identify the damage level of two existing single span PC bridges by using the V-SHM techniques. Field vibration measurements of the two single spanned PC bridges were taken under normal service conditions by using a wired accelerometer setup. Experimental modal identification was done by Eigensystem Realization Algorithm (ERA) and numerical modal parameter identification was done by the finite element models created using commercially available finite element software package 'SAP2000'. For one of the PC bridges, the measurements recorded in two consecutive years (2017 and 2018) were analyzed and results were reported while the results presented for the other bridge was based on measurements recorded in 2017 only. The identified dynamic characteristics from both experimental and numerical approaches were used to establish the level of existence of damages in the studied PC bridges. To this end, three damage identification (DI) criterions were defined and evaluated. From the damage assessment process, which involves four levels, i.e., damage detection, damage localization, damage quantification and damage consequence (assessment of remaining service life of the structure) [4], the study presented herein is focused on damage detection of PC bridges only.

2.
Literature Review V-SHM techniques can be categorized as nonphysical and physically based methods. Nonphysically based approach uses a system model to study a physical structure and predict the responses. The physically based detection method identifies the damage by comparing the modal parameters between the healthy and damaged structural model. A well-known classification for the damage identification methods, presented by [4] defines four levels of structural health monitoring.
Level 1: Damage detection -determination that damage is present in the structure. Based on the features used for damage identification, the damage detection methods can be classified as natural frequency based methods, mode shape and curvature based methods, and damping change based methods. The simplicity of natural frequency based methods makes it attractive as a means of damage detection. Moreover, natural frequencies can be conveniently measured and used as a parameter for modal validation [5]. However, mode shapes are more sensitive to local damages and this enables them to be used directly in multiple damage prevalence scenarios [5]. Furthermore, they are less sensitive to environmental effects when compared with natural frequency [5]. Modal damping ratio is also a very sensitive indicator. By means of observing damping changes one has the ability to detect the nonlinear, dissipative effects that cracks produce [6].
Eigensystem Realization Algorithm (ERA) [7] is a high precision system realization method which uses the time domain response of multiinput and multi-output (MIMO) data to identify modal parameters. That is, modal parameters extracted from ERA utilize multiple synchronous outputs (time domain data) simultaneously to arrive at a high precision estimate for the modal parameters. In this study, as several sensors were used for synchronous measurement of the acceleration of the bridge, ERA was one of the most appropriate methods to extract modal parameters. This method exhibits important features, such as the robustness of the algorithm requiring only simple numerical operations, numerical stability, the ability to use data from more than one test simultaneously to efficiently identify closely spaced eigenvalues, and moderate computation requirements, which encouraged the use of ERA in this study.

Methodology
The methodology consists of both experimental and numerical analysis to identify the modal parameters including natural frequencies, mode shapes and damping ratios. The experimental part of the study involved the measurement of structural response induced under normal service condition of two bridges and identification of dynamic characteristics (natural frequencies, mode shapes and damping ratios) by analyzing the acceleration data obtained from the field vibration measurements. For one of the bridges, results were analyzed and reported for two consecutive years. The experimental modal parameter identification was done by analyzing the extracted free vibration records using the Eigensystem Realization Algorithm [7].
In the numerical study, the eigenvalue analysis of the finite element models of the two PC bridges was conducted using a commercially available software package (SAP2000) to obtain the dynamic characteristics of the structures.

Description of the Bridges
Two single spanned PC bridges, bridge No 43/10 and bridge No 13/3, were selected for this study as shown in Figure 1 and  Table 1.The bridge 13/3 consists of 14 pre-stressed concrete girders while bridge 43/10 consists of 19 prestressed concrete girders.

Accelerometer Positioning
The accelerometer sensors ("Guralp Fortis" 0~200 Hz) were placed at optimal locations (maximum modal amplitude locations of the first two modes) to capture the first two mode shapes of the bridges effectively by experimental modal analysis. The sensor setup for bridge 13/3 and bridge 43/10 are shown in Figure 3 and Figure 4, respectively.
These accelerometers were connected to a data logger ("Tokyo Sokki Kenkyujo DC-204Ra") to record and save the resultant acceleration-time history data from vibration caused by vehicles passing through the bridge, for further analysis.

Field Vibration Measurement
The vertical vibration measurements of the two single spanned PC bridges were performed during regular service conditions by using a wired accelerometer setup. The sampling rate of the sensor setup was set to 200 Hz. All accelerometers were switched on at the same time when the vehicles were about to enter the bridge. The movement of the vehicles on the bridge induces vibration in the bridge due to the dynamic nature of the load applied. These vibrations usually do not immediately cease after the vehicles exit the bridge but continue to vibrate until the energy is dissipated. This brief period after which the vehicles have exited the bridge but the bridge is continuing to vibrate albeit with diminishing amplitude can be regarded as free vibration. These free vibrations are of interest in this study. A stopwatch was used to determine the time measurements required to extract free vibration data from the vibration records. At the same time, a video was recorded to verify the data later. The accelerometers were turned off a few seconds after the vehicles left the bridge.
For bridge 43/10, the field vibration measurements were conducted in 2017 while for bridge 13/3, they were carried out in 2017 and 2018. Experimental Modal Identification For the experimental modal identification, Eigensystem Realization Algorithm (ERA) was applied on the vibration records obtained from ambient vibration monitoring of the bridges. From these vibration records, data belonging to the free vibration period was extracted so that they could be used in the experimental modal identification with ERA. In Figure 5, a sample of extracted free vibration time histories of bridge 13/3 (obtained in 2017) is illustrated.

3.5
Modal Identification Steps in ERA Field measured vibration records were used as inputs to ERA while natural frequencies and modal damping ratios are the main output. The steps involved in the modal identification process in ERA are illustrated in Figure 6.
Results were subjected to step by step screening process in order to increase the accuracy of the results. Since ERA results usually fluctuate over different system orders, persistent results across system orders were considered as stable robust results. In ERA, physical vibration modes were identified by applying a screening process based on several criterions. The Modal Amplitude Coherence (MAC) [7] and the Extended Modal Amplitude Coherence (EMAC) [8] were used in this study for screening the results which were identified by ERA. Unstable spurious modes were removed by these screening criterions. In the screening process, a stabilization diagram is used to show the stability of identified modes against system order. A sample of stabilization diagrams before and after screeningis shown in Figure 7 and

3.6
Experimental Modal Parameter Identification Natural frequencies were determined for each of the free vibration data samples using the outputs obtained from the ERA analysis. Fast Fourier Transformation (FFT) was applied on the free acceleration-time history data obtained from the field measurements to verify the natural frequency results obtained from ERA.
Modal damping ratios were determined for the two PC bridges using the results obtained through ERA and refined by clustering against system order as well as natural frequencies.
That is, the damping ratios obtained from all data sets were compared with the system order, thereby removing outliers in estimation and arriving at an average value considering the stable range of system orders.
The variation of the damping ratio with system order is plotted in Figure 9 for a particular measurement data set. The variation of damping ratio with natural frequency is illustrated in Figure 10 and Figure 11 for bridge 43/10 and bridge 13/3, respectively.
Mode shapes for the two bridges were obtained for a particular mode for a particular damping ratio.

Numerical Modal Parameter Identification
The numerical modal parameter identification of the two PC bridges considerd was performed by using finite element models (FEM), modelled using commercially available software SAP2000. The required modal characteristics were obtained from the eigenvalue analysis results. Only the superstructure of the studied bridges was modelled including pre-stressed girders and deck. Further details related to the FE modeling are shown in Table 2.
As for the boundary conditions, fixed and pin support conditions were used to represent the support conditions of the bridges on either side of the span.

3.8
Damage Identification Natural frequency, mode shapes and modal damping ratios can be used as major modal parameters of the PC bridges for the process of damage identification. Mode shapes obtained from experimental analysis and numerical modal analysis were compared to identify the damages. Two sets of mode shapes obtained Frequency (Hz) Estimated system order from the ERA analysis and the FEM were compared using the Modal Assurance Criterion (MAC) [9].
where ∅ is the mode shape vector of the respective analysis mode.
The equation (1) was used to obtain the MAC value of a particular mode shape i with respect to a mode shape j. If MAC is equal to 1, it is the perfectly correlated condition and 0 is for no correlation condition. From these MAC values, damage level can be identified.
Modal damping ratio can also be used as an effective and sensitive damage identification modal parameter [10]. Since damping ratios cannot be identified by the numerical model, results from similar bridges (approximately similar in geometrical and structural) or the same bridge but at different time frames can be used for damage detection.

Damage Identification Criterions
Three damage identification (DI) criterions based on (1) natural frequency, (2) mode shapes and (3) modal damping ratios are defined in this study to predict the prevalence of damages in the bridges. These DI criterions are global metrics, i.e. no damage localization is possible using theses indices.
The DI criterion based on natural frequencies is defined as, Where fd and fu are the natural frequencies identified from the experimental modal identification and numerical modal identification, respectively.
The DI criterion based on MAC value (mode shape representation) of a particular mode shape is defined as, where MACd is the MAC value computed using equation (1) for a particular mode shape.
The DI criterion based on modal damping ratios is defined as, where ζ d and ζ u are the modal damping ratios computed from the experimental modal identification at two different time frames.

Results and Discussion
Results of both bridges are summarized in Table 3 and Table 4. All modes of vibrations which were stably identified using ERA which have the least co-efficient of variance were considered for the mode shape identification. By using the finite element models, numerically identified values for the natural frequency and its corresponding mode shapes were found. FFT of free vibration records were also obtained for each and every vibration measurement. Results obtained from FFT and ERA for the two modes are shown in Table 3. Frequency identifications from all three methods, namely FFT, ERA and FEM analysis, for one set of field measurement are plotted in the same figure  Figure 12) to verify the accuracy of the identified modes. Due to the malfunctioning of an accelerometer sensor (third sensor from the left, Figure 4) in the investigation of bridge 43/10, the data from that particular sensor was not used in the analysis.
Mode shapes obtained from both experimental and numerical analysis are shown in Table 4. For bridge 43/10 and bridge 13/3, natural frequencies were identified stably using ERA and FFT and corresponded with the numerical model, which implies successful model validation.
For both bridges, the symmetric vertical bending mode and asymmetric vertical bending modes were identified with higher stability. The Modal Assurance Criterion (MAC) calculated between mode shapes identified from both experimental and numerical approaches for both bridges bear witness that the numerial models for both bridges are well correlated with the physical structures and the bridges are devoid of appreciable damage. The modal damping ratios were also stably identified for both bridges through this experimental approach and they can be used for damage detection of the same bridges in the future.
Furthermore, the DI criterions defined in section 3.9 were evaluated for the two bridges and tabulated in Table 5. The experimental modal analysis results used to compute the DI criterions were obtained from the ERA analysis while the numerical modal analysis results used to compute the DI criterions were obtained from the eigenvalue analysis using commercially available software package "SAP 2000". The latter results were used to represent the parameters of the intact structure except in the case of the computation of DI d where the reference base values were taken from the identification conducted in 2017 for bridge 13/3.

Considering the bridge 43/3, the DI criterions
DIf and DIs are within the tolerance for no damage state, accommodating noisy data. As such, it can be inferred that the bridge is devoid of appreciable damages. Since no multiple investigations were conducted for the bridge 43/3, the DI criterion based on damping ratios could not be computed.
For the bridge 13/3, investigations were conducted for consecutive years and, as such, all the three DI criterions defined in Section 3.9 were computed. All the DI criterions are within acceptable tolerances for no damage state, accommodating noisy data, implying no appreciable damage.   Upstream are defined and evaluated to assess the presence of damage in the two bridges. The variation of the DI criterions over the years would be worthwhile to investigate, to identify the effect of noise in the measurements and subsequently identify the presence of damage.
The experimental modal parameter identification results and the modal analysis results from the numerical model are within acceptable tolerances. Therefore, it is prudent to state that the two vibration modes were successfully identified for both pre-stressed concrete bridges, affirming that this technique can be applied to identify modal parameters experimentally.
The evaluated DI criterions further affirm that the bridges have not undergone appreciable damage. The defined global DI criterions based on natural frequencies, mode shapes and modal damping ratios can be used to identify damages in future investigations.
For damping based damage identification methods, stable damping ratio identifications are a necessity which require high quality structural vibration response measurement using highly sensitive sensors together with stable damping identification techniques. This study proves the capability of stable damping identification; hence it can be recommended to be used for damage detection. Damage location identification is possible with mode shapebased methods and since an accurate depiction of the mode shape requires the establishment of modal amplitudes at as many locations as possible, this necessitates the use of properly located higher number of sensors for field vibration measurements.
Identified results in this study can be applied for damage detection of the same bridges in future, as well, to get an understanding on damping characteristics of the bridges with similar configurations.