Proposal of Bridge Features for Advanced Bridge Health Monitoring System（橋梁ヘルスモニタリングシステム高度化のための橋梁特徴量の提案）
Principal Investigator: Dr. Gen HAYASHI,
Asst. Professor, Osaka Metropolitan University
研究代表者 大阪公立大学大学院工学研究科 助教 林 厳
1．Introduction
Constructed in the 1960s and the 1970s, a significant inventory of Japanese bridges
are now aging. Consequently, the number of bridges in service for extended periods is
projected to increase significantly in the future[1]. The 2014 revision of the periodic
bridge inspection guidelines man dated a five-year inspection for each bridge in Japan.
According to inspections conducted across Japanese bridges up to 2018, approximately
59% of them exhibited some form of damages, which is expected to increase with theongoing ageing of these structures. The deteriorating of these bridges is a global issue,
with numerous instances of structural damage and bridge collapse owing to
misjudgment in the inspection process having been reported. In 2019, Nanfangao
Bridge[2] experienced a collapse, followed by the collapse of the Musota Aqueduct
Bridge[3] in 2021. Against this background, vibration-based structural healthmonitoring (VSHM), which utilises the vibration response of bridges as astraightforward and effective diagnostic tool, has gained momentum[4,5,6,7,8].
Truss bridges and arch bridges are susceptible to significant impacts on the overall
stability of the structure by damages. Therefore, extensive research has been conductedon them. Varing the bridge response, damage to the main members is anticipated,leading to investigations into methods that use features such as natural frequencies
identifiable from the response acceleration due to vehicular and ambient vibrations. For
truss bridge, Kim et al. [9,10] conducted vibration experiments by cutting members ofreal bridge after service. For arch bridge, vibration experiments and numericalsimulation was conducted on model bridges[11,12,13]. These studies suggest thepossibility of anomaly detection at the member rupture level, highlighting the potential
advantages of VSHM for redundant bridge structures.
The estimation of the damage location and extent is vital for an efficient VSHM. Lee
et al. proposed an entropy-based method for locating damage in truss bridges using acontinuous wavelet transform[14], thus demonstrating the potential for both damage
detection and multiple damage location estimation. Zhang et al. demonstrated that therunning load from a single truck can be integrated with the bridge weigh-in-motion－ 147 －

(BWIM) algorithm, utilising the rotation angle of the bearings for estimating the vehicle
weight and detecting damage in PC girder bridges[15]. Huseynov et al. theoretically andempirically illustrated the possibility of estimating the damage location and identifying
the damage level for singular damage instances by using influence lines from therotation angle along the bridge axis obtained via tiltmeters installed at various bridge
locations[16].
Despite efforts in damage detection using the vibration characteristics and rotation
angles independently, few studies have sought to combine these techniques forenhancing the sophistication of bridge health monitoring. Furthermore, bridges withnumerous joints, such as truss and arch bridges, may have multiple members damaged
within areas that are difficult for visual inspection. However, past studies have focusedon multiple damage detection methods that require multi-point observations forlocation estimation. It is crucial to understand the mechanical behaviour of the bridgewith damages, particularly when the number of sensors is limited, for a straightforward
structural monitoring method.
To address these challenges, this study explores the applicability of VSHM to a modelLangar arch bridge in terms of vibration characteristics and rotation angle under thecondition of anomaly detection with a limited number of sensors. This approach has
rarely been adopted previously. First, a finite element (FE) model of the target bridge
was developed in which the simulated damages by varying the damaged member,
location, and level. The variations in the mechanical behaviour and vibration
characteristics of the steel arch bridge with damage were analysed. The changes innatural frequencies and rotation angles were then quantitatively evaluated.
Subsequently, various damage scenarios involving different combinations of single-andmultiple (two-location) damage instances were analysed. The aim was to clarify themechanisms driving changes in the mechanical behaviour and natural frequencies ofthe bridge and investigate the potential for damage detection with a small number of
sensors.
2．Research methods
2.1. Target bridges
The subject of this study was a 1/15 scale model of a 75-m-long Langer arch bridge, as
depicted in Figure 1, 2. Dimensions of the bridge model are 5000 mm in length, 567 mm
in width, and 893 mm in height, and comprised stiffening girders, arch ribs, crossgirders, hangers, and gusset plates made of SS400 (JIS G 3101) plates. The crosssectional shapes and dimensions of these components are presented in Table 1.

－ 148 －

Gb2

Gb3

Gb4

Gb5

Gb6

Gb7

b girder

Cb0

Cb1

Cb2

Cb3

Cb4

Cb5

Cb6

Cb7

Cb8

Ca0

Ca1

Ca2

Ca3

Ca4

Ca5

Ca6

Ca7

Ca8

Ga1
625

Ga2
625

Ga3
625

Ga4
625

Ga5
625

Ga6
625

a girder

Ga7
625

567

Gb1

625

5000

(a) Bottom plane viewa girderHanger(Upper)

Hua2

Damage location
Hua4
Hua3

Hla1
625

Hua6
Hua7

893

Hua1

Hua5

Hla2
625

Hla3
625

Hla4
625

Hla5
625

Hla6
625

Hla7
625

625

5000

(b) A side Plane view
Figure 1 Dimensions of the target bridge and damage location. (Unit: mm)Table 1 Dimensions of members

Figure 2 Joints of langer arch bridge
Connections between members were made with M6 bolts via gusset plates for thehanger members and stiffening girders/arch ribs and M8 bolts via those for theconnections between the arch ribs and stiffening girders.
2.2. FE model
Figure 3 presents an analytical model of a bridge constructed using Abaqus/Explicit
2022 [17]. All the members were modelled by beam elements, with the boundary
conditions set as the pin and roller supports. Since the actual modelled bridge was bolted
via gussets shown in Figure 2, the connections between the members were assumed
fully connected. The element divisions were 250 for arch ribs and stiffening girders, 30－ 149 －

Figure 3 Analytical model and loading position
for cross girders, and 20–40 for hanger members, depending on their lengths. The
damage analysis was performed by reducing the cross-sectional area of each joint. The
element divisions of damage were three. The material properties of the members wereas follows: elastic modulus of 200 kN/mm2, Poisson’s ratio of 0.3, density of 77 kN/m3,
and total weight of 65 kg, which were identical to those of the model bridge. The sectionof the gusset plate connected to the hanger members were modelled by adjusting thecross-section of the beam element to match the dimensions of the gusset plate. The
gusset plates between the stiffening girders and arch ribs were represented byincreasing their elastic modulus to 370 kN/mm2.
2.3. Damage scenario
The damage was set at the coloured positions indicated in Figure 1. The damage waspresumed to be localised corrosion of the hangers and internal corrosion at various
points on the cross and stiffening girders.
The damaged members were the connecting points of the stiffening girder (G), hanger
members (Hl: lower, Hu: upper), and cross girder (C), as illustrated in the coloured
sections of Figure 1. Damage labelling follows the pattern ’member name (G, Hl, Hu, C)+ girder name (a, b) + damage location (0-8) shown as Figure 1.
The damage scenarios are presented in Table 2. For the single-damage scenarios,
there were 180 cases (60 locations 3 levels = 180 cases). Damage levels of 25, 50, and
75% were applied to 60 locations across the stiffening girders,× hanger members, andcross girders. For the multiple-damage scenarios, 78 patterns were selected from the 13
locations that were most prone to damage among the single-damage cases, and thesewere combined, as shown in Table 2. This resulted in 702 cases (78 × 9 damage patterns).

－ 150 －

Table 2 Damage scenario

2.4. Analysis method
In the damage analysis, both eigenvalue and static analyses were conducted. In
eigenvalue analysis, the focus is on identifying modes that can be measured in modelexperiments actually conducted. The natural frequencies of the first-to third-order
bending modes and first-to second-order transverse modes along the longitudinal axis
were extracted from the effective mass of the analysis results. The static analysis
involved a linear elastic analysis with a concentrated load (20 kN) applied at the centreof the span, as depicted in Figure 3. It was assumed that the rotation angles could bemeasured using triaxial accelerometers and gyro sensors on an actual bridge. Thus, therotation angles around the x axis (longitudinal direction) and z axis (transverse
direction) at the midsection of the cross girder in the span centre (loading point) wereextracted. The unit of rotation angles is degrees (°), with the positive direction being
clockwise.
3．Single damage
3.1. Eigenvalue analysis results
Figure 4 shows the natural frequencies of the first-to third-order bending modes andfirst- and second-order transverse modes in the intact case (INT) obtained from theanalysis, along with the natural frequencies of these modes. Figure 5 shows the modeshapes when Hlb3 was damaged as an example. In this way, it was confirmed that, evenwith the damages, the mode shapes did not change. Figure 6 shows the damage locationand difference between the natural frequencies of the intact and damaged cases. The－ 151 －

Figure 4 Natural vibration modes

Figure 5 Natural vibration modes at single damage
horizontal axis represents the damage location, as shown in Figure 1, and the verticalshows the change in the natural frequency for each vibration mode. A negative value on
the vertical axis indicates a decrease in the natural frequency. Because the trend was
similar in all cases, the damage level for a single damage shown in the figure isrepresented only by the 75% damage case because the difference is only in the natural
frequency.
For the first-order transverse mode, as depicted in Figure 6(a), the natural frequencychanged by only a few Hertz when the near L/4 of stiffening girders (damage locations
1, 2, 6, and 7) were damaged. However, when the cross-girders at the bearing locations(damage locations 0 and 8) were damaged, the natural frequency significantly changed.
This change is asymmetric with respect to the centre of the span, with a greater decrease
observed when the damage is on the pin bearing side. Conversely, the natural frequency
barely changed when the central cross-girders were damaged, and the reduction rate ofthe damage to the cross girders near the roller bearing was smaller than that on the pin
bearing side. In essence the first-order transverse mode is more significantly influenced
by boundary conditions. The natural frequency decreased because of the stiffness－ 152 －

Figure 6 Relationship between damaged location and difference of natural frequencies(Damage level: 75%)
reduction caused by damage to the bridge end parts. This agrees with a previous study
on girder bridges[18], which reported the impact of bridge edge damage on transverse
vibration modes, and a similar trend was also observed for arch bridges.
In the second-order transverse mode, Figure 6(b) shows the effects of damage to boththe hanger members and stiffening girders. Damage to the cross-girders significantly
affects this mode. Unlike the first-order transverse mode, the natural frequencies
exhibited substantial changes when the damage occurred near L/4 (damage positions 1,
2, 6, and 7). This is likely due to a stiffness of near L/4, given that the vibration modecauses twisting of the arch ribs and stiffening girders, as shown in Figure 4. Thus, it issuggested that damage to the cross-girder is more likely to influence the transverse
vibration mode.
For the bending vibration mode, Figure 6(c) and (d) indicate that damage to thehanger members and stiffening girders significantly impacts these modes. This is likely
because the stiffness of the stiffening girder contributes significantly to the verticalvibration. Moreover, that of the arch rib at the location of the damage influences thenatural frequency owing to the substantial deformation of the vibration mode in thehanger members that connect the arch rib and stiffening girder.
In the first-order bending mode, the hanger member at damage locations 4 exhibits ahigher degree of deformation during natural vibration. This is likely because the－ 153 －

differences in the vertical mode vectors of the stiffening girders and arch ribs at thenodal locations of the vibration mode were the largest. Moreover, the deformation of thehanger member prompted a bending vibration mode. This suggests that the stiffness ofthe hanger member contributes significantly to this mode of vibration, resulting in alarger change in the natural frequency when the hanger member is damaged at thislocation, as shown in Figure 6(c).
For the second-order bending mode, the changes in the natural frequency follow asimilar pattern to those of the first-order bending mode in Figure 6(d). The change innatural frequencies is substantial at damage locations 2 and 6, where deformations are
significant.
Furthermore, in the third-order bending mode, a similar trend is observed, withsignificant changes in natural frequencies at damage locations 2 and 6 in Figure 6(e).
The results for Hl and Hu indicate that the damage location within the hanger
member was generally the same, suggesting that the damage location did not
significantly influence the outcome if damage occurred within the same hanger member.
In contrast, the change in natural frequency owing to damage to the stiffening girder
was found to be more significant when damage occurred at a location where the local
vibration of the hanger member was minimal for both bending vibration modes. The
position where the bending vibration of the stiffening girder becomes dominant is foundto correspond to the belly position of the overall mode.
The above results reveal that the natural frequency of each vibration mode iscontingent on both the location and member. However, it is important to note that theresults for damage locations–0-4 and 4-8 (in the width direction of the bridge on the aand b-sides, respectively) and at the target location centred around the middle of thebridge span were nearly identical. It is difficult to identify damage locations solely basedon natural frequencies.
3.2. Static analysis results
The rotation angles around the x- and z-axes for each damage case in the damage
analysis are shown in Figure 7. The horizontal axis represents the damage location, andthe vertical axis represents the rotation angle. In accordance with the Cartesian
coordinate system illustrated in Figure. 3, the rotation angle is positive in the clockwise
direction. It is important to note that as shown in Figure 7(a), the positive and negative
directions of rotation differ for girders a and b. Figure 8 shows an example of thedeformation diagram under static loading with damage to Ga4 and Hla3.

－ 154 －

Figure 7 Relationship between damaged location and rotations (Eigenvalue analysis)

Figure 8 Relationship between damaged location and rotations (Static analysis)
Figure 8(a) shows that the displacement of the stiffening girder under loading was
greater for the damaged a-girder than for the undamaged b-girder. Therefore, it isbelieved that rotation around the x-axis likely tilts in the direction of damage. Thereby
the rotation angle if the damage is located at a-girder becomes positive, while therotation angle if the damage located at b-girder becomes negative. From these results,
it can be observed in Figure 7(a) that the rotation angle can provide an estimation of thedamage location if other members are damaged. However, the rotation angle changes
minimally if the damage is located at positions 3 and 5 of the cross-girder and stiffening
girder at the bridge end.
As shown in Figure 7(b), the damage locations in the longitudinal direction differeddepending on whether the hanger member or stiffening girders were damaged.
Specifically, differences were evident at the damage locations 0-4 and 4-8. The
deformation diagram in Figure 8(b) represents a case in which there is a significant
change in the rotation angle in the longitudinal direction. When a hanger member isdamaged, the deflection immediately below the damaged member location is smaller
than that at the symmetrical location with respect to the centre of the span, thereby－ 155 －

tilting it in the opposite direction of the damaged member.
The results above suggest that the rotation angle could potentially be used to estimate
the location of damage in both the width direction (a- or b-girder) and longitudinally at
the centre of the span (damage locations 0-4 and 4-8). These locations cannot be
ascertained through the natural frequency alone. However, damage to the cross-girders
located at the edge of the bridge seems to have a minimal impact on the rotation angle
response, suggesting that other response values may need to be considered.
3.3. Damage location and damage level
In this section, the effects of varying damage levels from individual incidents on thenatural frequency and rotational angular response are investigated.
Figure 9 presents the natural frequencies of the second-order transverse, first-order
bending, and third-order bending modes, as well as the differences in rotation angles.
In these figures, only damages at positions 0-4 of the A girder were considered. The
damage levels taken into account were 25%, 50%, and 75%.
In Figure 9(a) and (b), the axes indicate the difference in frequency from the intact
case for each natural-order bending mode in the damaged case. Specifically, Figure 9(a)shows the second-order transverse mode on the horizontal axis and the second-order
bending mode on the vertical axis. In Figure 9(b), the second-and third-order bending
modes are on the horizontal and vertical axes, respectively.
Finally, the axes in Figure 9(c) represent the difference in rotation angle relative tothe intact case. The rotation angle in the longitudinal direction (x-axis) is shown on thehorizontal axis, and that in the transverse direction (z-axis) on the vertical axis.
In all figures, the damaged members are represented by the colour of the plot (green
for stiffening girders, orange for hanger members, and blue for cross girders), and thedamage level is indicated by the marker shape (◯ for 25%, □ for 50%, and △ for 75%).
The solid lines in the figure connected the points at the intact condition (0%) and 75%
damage level.

－ 156 －

Figure 9 Relationship between damaged members/ damage degree and natural frequencies / rotational angle
From the discussion on damage experiments on actual bridges in previous studies, it
is known that the bearing conditions (boundary conditions) influence the vibration
frequencies of each natural vibration mode differently. Therefore, the natural vibration
modes selected for this study are those that are less affected by varying bearing
conditions and more sensitive to damage, as revealed from the discussion in the previous
section. Therefore, we focused on the second-order transverse mode, first-order bending
mode and third-order bending mode that the influence of boundary conditions are small.
First, focusing on the relationship between the second-order transverse mode andfirst-order bending mode, we can discern from Figure 9(a) that the damage to Ca2 andCa3 in the cross-girder causes significant changes in the x-axis direction, even thoughsome damage points near the origin may appear indistinguishable. Damage to thehanger members induces variations in the y-axis direction, whereas that to the－ 157 －

stiffening girders causes changes in the direction oriented 45◦. Given these relationships,
it is possible to estimate the damage location.
The relationship between the first- and third-order bending modes, as depicted in
Figure 9(b), implies that the angle to the x-axis differs depending on the location of thehanger member damage. Hence, it may be possible to estimate the damage location
based on this relationship.
Furthermore, the relationship between the rotation angles in Figure 9(c). In thisfigure, the rotation angle was positive around the x-axis and negative around the z-axis
because the damaged member was located at damage locations 0-4 of girder A.
Distinctions among the damage levels were made evident by the near-linearalignment of plots for the three predefined damage levels in this study. This indicatesthat regardless of variations in the damage level, the damage to each member manifests
in a specific natural frequency mode. Furthermore, the degree of change in the natural
frequency increases with the damage level.
Figure 10 presents the results of a damage analysis conducted to further elucidate therelationship between damage level and the change in natural frequency. We focused on
Hla3, for which a slight deviation from linearity was observed upon damage, as shownin Figure 10(a). The analysis was conducted at seven different damage levels: 6.25%,
12.5%, 25%, 37.5%, 50%, 62.5%, and 75%. The axes in the figures shown in Figure 10
represent the difference in the natural frequency relative to the intact condition, similar
to Figure 8(a) and (b).

Figure 10 Relationship between damage degree and natural frequencies in Hla3

－ 158 －

In both Figure 10(a) and (b), it can be observed that the change in natural frequency
maintains an almost linear that it may be possible to predict damage at unknown levels
using natural frequencies.
4．Multiple damage
4.1. Change in natural frequency under multiple-damage
The results of plotting the differences in natural frequencies for each vibration modein the multiple damage cases, as presented in Figure 2, are shown in Figure 11.
Furthermore, the first- and third-order bending modes for single and multiple
damage are shown in Figure 12. For instance, Figure 11(a) illustrates the difference inthe natural frequencies from those of the intact case for the first- and third-order
bending modes. This applies to cases where Ga4, Hlb3, and Ga4+Hlb3 undergo damage
across three damage stages.
From Figure 11(a), it is observed that in the cases of singular damage, either Ga4(green) or Hlb3 (orange), the natural frequency changes linearly with the increasing
damage level, as discussed in the Section3.3. In contrast, in the case of multiple damage
instances, when the damage levels of Ga4 and Hlb3 were both 75% (Ga4:75%,
Hlb3:75%), the change in natural frequency appeared to be the sum of the differencesin natural frequencies between the 75% case for Ga4 damage and that for Hlb3 damage.
In essence, in cases of multiple damage, the natural frequency changes in the coloured
area of Figure 11(a). Therefore, the superposition of the results from singular damage
instances may be utilised to estimate the damaged member and location of the damage.
Figure 12 shows the mode shapes when multiple damages occur. From this figure, it isevident that there is minimal change in the mode shapes even when multiple damages
occur. From this, it can be inferred, as described in Section 3.1, that the members or
positions with significant deformation in each mode shape are the same. In other words,
since the components and positions that have a large effect on the natural frequency ofeach mode are the same as a single damage, the change in natural frequency can beconsidered as the sum of the effects of individual damage on each mode. This trend was
similarly observed for other damages.
Similarly, other members were studied, and the results of the 3D plot are shown in
Figure 11(b). The figure indicates the same trend observed for the Ga4 and Hlb3 damage
cases applies to other combinations of damage cases, with the distributions clustered on
the same plane.

－ 159 －

Figure 11 Differential natural frequencies for each vibration mode in multiple
damage cases－ 160 －

Figure 12 Natural vibration modes with multiple damage
4.2. Damaged member/location vs. natural frequency.
Figure 11(c)-(e) present the results of 2D plots on each axis plane derived from the 3D
plot of Figure 11(b). The aim was to investigate the applicability of damage-detection
methods based on changes in the frequencies of the characteristic natural vibration
modes for multiple damage relationship when the level of damage varies. From therelationship observed between the curves, it can be inferred scenarios, as detailed in
Figure 11(a). It is important to note that Figure 11(c)–(e) also show plots of the
combinations of damaged members with varying marker shapes and plane colours.
Figure 11(c) illustrates the relationship between the natural frequencies of thesecond-order transverse mode and the first-order bending mode. Combinations ofdamaged members typically demonstrate cohesiveness of the same colour. Notably, inthe case of combinations of the same members, the influence on the specific vibration
modes is particularly pronounced. The cross girder exhibited a significant impact on thesecond-order transverse mode, while the hanger member had a pronounced effect on thefirst-order bending mode. Consequently, notable changes in the frequencies of thesecond-order transverse mode in the combination of cross girders (C-C) and first-order
bending mode in the combination of hanger members (H-H) were observed.
This is evidenced by the changes in the natural frequencies of the first-order bending
mode for the cross-girder and cross-girder (C-C) combinations and the second-ordertransverse mode for the hanger member and hanger member (H-H) combinations. The
figure also reveals that the stiffening girder and cross girder (G-C) and stiffening girderand hanger member (G-H) combinations exhibited consistency for each pair of damaged
members, although the changes were smaller than those for each identical members.
Moreover, the cross-girder and hanger-member (C-H) combinations are also consistent
within the plane. Nevertheless, it is difficult to classify the damage location using thesemodes alone because the markers frequently overlap in the same damage member
combination.
Figure 11(d) illustrates the relationship between the natural frequencies of the first-－ 161 －

and third-order bending modes. In this figure, there is less overlap between the damage
cases of the stiffening girder and hanger member (G-H) and hanger member and hanger
member (H-H), with damage cases roughly forming three groups for each damage
location. This is likely due to the variation in the natural frequency changes dependingon the damage location of the hanger member in the first-order bending mode and thatand stiffening girder in the third-order bending mode. This makes the estimation of thedamage location relatively straightforward in the case of multiple damage.
However, the damage combinations of Hlb2, Hua3, Hub3, Hlb3, Hua5, Hla6 andHua5 were plotted at similar locations, making it challenging to determine the damage
location. In the damage case of cross girder and cross girder (C-C), the concentration of
the plots near the origin indicates a low sensitivity to damage owing to the smallchanges in both natural vibration modes. In the stiffening girder and cross girder (G-C)
and cross girder and hanger member (CH) damage cases, the plots overlapped, and thedifference in natural frequencies was small. Consequently, it is difficult to classify thedamage to a cross-girder based solely on the bending mode.
Figure 11(e) displays the relationship between the natural frequencies of the secondorder transverse mode and the third-order bending mode. It can be observed that theplots for the damage cases in the stiffening girder and cross girder (G-C) have lessoverlap. This is because of the significant influence of stiffening girder damage on thenatural frequency of the third-order bending mode.
The damage cases for the cross girder and cross girder (C-C), stiffening girder andhanger member (G-H), and hanger member and hanger member (H-H) were found to
exhibit substantial variation in specific directions. Conversely, the damage cases for the
stiffening girder and stiffening girder (G-G) were plotted around the origin, indicatingthat classification using these natural vibration modes alone is challenging.
As discussed above, we found that changes in the natural frequencies of the modes,
characteristic of each member, can be utilised to classify multiple types of damage.
4.3. Damaged member/damage location and angle of rotation
In Section 3.1, it was observed that damages at symmetrical positions show similarchanges in natural frequencies, making it difficult to classify the damages. This section
examines the classification of these damages using rotation angles.
Figure 13 illustrates the change in rotation angle during damage to Hlb2, Hla6, Hlb3,
Hua3, Hub3, and Hua5, which proved difficult to classify based on natural frequency
due to the symmetry of the damage locations. Positions 2 and 6, as well as 3 and 5, aresymmetrical.

－ 162 －

Figure 13 Rotation angle at multiple damage
In the figure, the horizontal axis represents the rotation angle at the x-axis, thevertical axis represents the rotation angle at the z axis, and the colours of the markers
indicate different combinations of damage.
Focusing on Hla6-Hua3 (green), both damages involved in a girder, resulting in them
being plotted in the region where the rotation angle at the x-axis was significant. On theother hand, in the case of Hla6-Hub3 (pink), where damages involved in both a and b
girder, the rotation angle at the x-axis was smaller compared to the green plots and wasplotted near the centre. This trend is also evident in the relationships between Hla6Hua5 (blue) and Hlb2-Hua5 (light blue), as well as between Hlb2-Hlb3 (white) andHlb2-Hua3 (yellow). The plots of Hla6-Hlb3 (red) and Hla6-Hub3 (pink), as well as Hlb2Hlb3 (white) and Hlb2-Hub3 (brown), appear to overlap; this is because damages haveoccurred in the same hanger members.
Hla6-Hua5 (blue), both damages were within the positions 4 to 7, causing the rotation
angle at the z-axis to increase in the positive region. Both Hlb2 and hlb3 (white)corresponded to damage positions 1 to 4, causing the rotation angle to increasing
significantly in the negative direction. Furthermore, in cases such as Hla6-Hub3 (green),
Hlb2Hua5 (light blue), Hla6-Hua3 (pink), where damages occurred in both positions 1
to 4 and 4 to 7, it is observed that they are distributed around the central region. Fromthese trends, the plots in Figure 13 were dispersed into positive and negative regions ofx or y-axis, allowing for the classification of each damages.
Indeed, from the above analysis, it can be concluded that even in cases of multiple
damages, it is feasible to pinpoint the location of the damaged members by utilising therotation angle in addition to the natural frequency. Therefore, this method offers a morecomprehensive approach for assessing and identifying the severity and location of－ 163 －

damage within a structural system such as a bridge.
5．Conclusion
In this study, damage analysis was conducted on a steel langer arch bridge model,
setting single and multiple damages, to investigate the applicability of natural
frequency and rotation angle as features that can detect multiple damages, aiming toutilize a small number of sensors in vibration health monitoring. The changes in themechanical behaviour and vibration characteristics owing to damage were analyticallyclarified. The results were as follows:1)

By setting damage in the structural model and analysing the subsequent changes
in natural frequencies and rotation angles, these features were observed to besensitive to the location and severity of damage.

2)

The stiffening girder is sensitive to the third-order bending mode, the hanger
member is sensitive to the first and second-order bending modes, and the crossgirder is sensitive to the first and second-order transverse modes.

3)

It was also observed that the natural frequencies and rotation angles changed
almost linearly with the extent of the damage, suggesting that it is possible toestimate the level of damage by monitoring these changes.

4)

In the case of multiple damages, the changes in natural frequencies and rotation
angles followed a plane, showing the superposition of the effects of each individual
damage. This shows that it is possible to estimate the location and extent ofmultiple damages by analysing these changes.

5)

Even in cases of multiple damages, the combination of changes in natural
frequencies and rotation angles can help pinpoint the location of damaged members
to some extent.

Acknowledgment
This research received support from the JFE 21st Century Foundation in 2022
through their funding scheme.
References[1] Road Bureau, Ministry of land, infrastructure and transport document 2 frommeeting no. 1 of experts on highway bridge preventive maintenance held october24, 2007.
[2] M. Greenwood, What Caused Taiwan’s Nanfang’ao Bridge to Collapse?, 2019.
[3] Wakayama City, Publication of the investigation committee report concerning the－ 164 －

damage to the musota aqueduct bridge and the aqueduct bridge maintenance andmanagement manual, 2022.
[4] C.-W. Kim, F.-L. Zhang, K.-C. Chang, P. J. McGetrick, Y. Goi, Ambient and vehicleinduced vibration data of a steel truss bridge subject to artificial damage, Journalof Bridge Engineering 26 (2021)[5] D. M. Siringoringo, Y. Fujino, Estimating bridge fundamental frequency fromvibration response of instrumented passing vehicle: Analytical and experimental
study, Advances in Structural Engineering 15 (2012) 417 – 433.
[6] A. Furukawa, T. Matsuo, K. Nishikawa, A study on damage detection of the steel
truss bridge based on the spectral element method using high frequency excitation,
Journal of Japan Society of Civil Engineers, Ser. A1 (Structural Engineering &Earthquake Engineering (SE/EE)) 68 (2012) I_523–I_532.
[7] K. Maes, G. Lombaert, Monitoring railway bridge kw51 before, during, and after
retrofitting, Journal of Bridge Engineering 26 (2021).
[8] A. Ruffels, I. Gonzalez, R. Karoumi, Model-free damage detection of a laboratory
bridge using artificial neural networks, Journal of Civil Structural Health
Monitoring 10 (2020).
[9] K.-C. Chang, C.-W. Kim, Modal-parameter identification and vibration-based
damage detection of a damaged steel truss bridge, 636 Engineering Structures 122(2016) 156–173.
[10] C.-W. Kim, K.-C. Chang, S. Kitauchi, P. J. McGetrick, A field experiment on a steel
gerber-truss bridge for damage detection utilizing vehicle-induced vibrations,
Structural Health Monitoring 15 (2016) 174 – 192.
[11] A. Ruffels, I. Gonzalez, R. Karoumi, Model-free damage detection of a laboratory
bridge using artificial neural networks, Journal of Civil Structural Health
Monitoring 10 (2020) 183 – 195.
[12] F. Magalhães, A. Cunha, E. Caetano, Vibration based structural health monitoringof an arch bridge: From automated oma to damage detection, Mechanical Systems
and Signal Processing 28 (2012) 212–228. Interdisciplinary and Integration Aspects
in Structural Health Monitoring.
[13] S. Donomoto, T. Yamaguchi, T. Kitahara, Damage detection method 650 of steelarch bridge using SOM, Journal of Japan Society of Civil 651 Engineers, Ser. A2(Applied Mechanics (AM)) 73 (2017) I_813–I_820.
[14] S. G. Lee, G. J. Yun, S. Shang, Reference-free damage detection for 654 truss bridge
structures by continuous relative wavelet entropy method, 655 Structural Health
Monitoring 13 (2014) 307–320.

－ 165 －

[15] L. Zhang, E. J. OBrien, D. Hajializadeh, L. Deng, S. Yin, Bridge damage
identification using rotation measurement, Journal of Bridge Engineering 28(2023).
[16] F. Huseynov, C. Kim, E. OBrien, J. Brownjohn, D. Hester, K. Chang, Bridge
damage detection using rotation measurements – experimental 661 validation,
Mechanical Systems and Signal Processing 135 (2020).
[17] M.Smith, ABAQUS/Standard User’s Manual, Version2022, Dassault Systèmes
Simulia Corp, Providence, RI, 2022.
[18] G. Hayashi, R. Oura, A. Hiraoka, T. Yamaguchi, Vibration characteristics and loadcarrying capacity of multiple steel plate girder bridges with corroded girder ends,
Structure and Infrastructure Engineering (2023) 1–14.

－ 166 －