Subspace-based Damage Detection Methods on a Prestressed Concrete Bridge F. Hille1, M. Döhler2, L. Mevel2, W. Rücker1 Division Buildings and Structures, BAM Berlin, 12200 Berlin, Germany 2 INRIA, Centre Rennes - Bretagne Atlantique, Campus de Beaulieu, 35042 Rennes, France email: [email protected], [email protected], [email protected], [email protected] 1

ABSTRACT: For the last decades vibration based damage detection of engineering structures has become an important issue for maintenance operations on transport infrastructure. Research in vibration based structural damage detection has been rapidly expanding from classic modal parameter estimation to modern operational monitoring. Methodologies from control engineering especially of aerospace applications have been adopted and converted for the application on civil structures. Here the difficulty is to regard to the specific environmental and operational influence to the structure under observation. A null space based damage detection algorithm is tested for its sensitivity to structural damage of a prestressed concrete road bridge. Specific techniques and extensions of the algorithm are used to overcome difficulties from the size of the structure which is associated with the number of recorded sensor channels as well as from the operational disturbances by a nearby construction site. It can be shown that for concrete bridges the proposed damage detection methodology is able to clearly indicate the presence of structural damage, if the damage leads to a change of the structural system. Small damages which do not result in a system change when not activated by loading, do not lead to a modification of the dynamic response behavior and for that cannot be detected with the proposed global monitoring method. KEY WORDS: Subspace methods; fault detection; monitoring techniques; concrete bridge. 1

INTRODUCTION

At present, in Germany but also in other European countries the majority of the federal highway bridges are made of prestressed concrete. Especially the bridge structure designs of the 50s, 60s and 70s used this economically efficient construction type despite a general lack of experience at that time. So in the course of the last 50 years several sources for a reduction of their durability and even their load carrying capacities have been discovered. Therefore, in the last decades the effort for maintenance and repair of the prestressed concrete road bridges increased dramatically [1]. One of the major shortcomings of the early prestressed concrete design was an inadequate amount of constructive reinforcement besides the load carrying prestressing tendons. The lack of constructive reinforcement lead to a lack of robustness of the whole structure and in case of failure of prestressing tendons the risk of a sudden collapse of whole bridge deck parts could not be neglected. Because of several material and design based deficiencies the probability of tendon deterioration processes was distinctive. On the load side, the trend to an increase of heavy load vehicle traffic has not stopped until now. In Germany, an increase of the truck weight limit from 40t to 60t is discussed and the first so called “Gigaliner” vehicles are tested on federal roads and bridges [2]. So bridge structures and especially prestressed bridges are exposed to natural degradation processes and in same time the operational loading and the associated dynamic stressing of the bridge structures is increasing. It is obvious that the bridge owners must respond to the increased uncertainty about the load bearing capacity of the bridges. To provide an unrestricted operational availability as well as to protect the

high investment costs the early detection of structural damage is of great interest. In dependence of expected degradation processes and damage scenarios currently the detection and evaluation of the degree of damage and structural safety of bridge structures is accomplished by visual inspections. Besides the difficulty to inspect all relevant structural components in a necessary interval, this approach is generally based on the knowledge and experience of the inspecting person. To overcome those disadvantages, several especially vibration based approaches for automatic identification of structural damage in early stages have been developed in recent years [3],[4]. The majority of the currently used dynamic methods for early damage detection performs modal system identification and compares the obtained modal parameter of the actual state (eigenfrequencies, mode shapes and modal damping values) with those of the undamaged state. Therefore, those methods are explicitly dependent on the sensitivity of the used parameters to local damage. However, despite intensive efforts in research and development for a lot of real applications in civil engineering with ambient excitation and a limited number of sensor points, the sensitivity of modal damage indicators is often not satisfying. One major reason for this is the fact that mostly the generally analyzed first few vibration modes of a system are only to a small extent affected by local damage. , Also varying temperature and other environmental influences may have a far greater impact on the dynamic properties of a system as structural damage in early stages [5]. Until now, the separation of detected changes in identified modal parameters according to their causes is quite difficult to be performed satisfying.

In recent years a stochastic subspace based output-only damage detection method was developed, were instead of identifying the modal parameter a  ²-type test is used to analyze changes in the dynamic response of the system [6-8]. Utilizing state space models the method uses Hankel matrices of output covariance estimates to store the system characteristics. Starting with analyzing a reference state of the undamaged structure a residual is created from the left null space of the reference Hankel matrix. Variations in excitation and environmental conditions can be accounted of by computing the residual covariance in the undamaged stage and considering it within the  ²-type tests. The method has been successfully applied to several laboratory and real application from aerospace as well as mechanical and civil engineering [8-10]. This paper presents the adoption of the stochastic subspace based damage detection method to a civil engineering structure. Within the European project IRIS a prestressed concrete bridge in Austria was artificially damaged with two scenarios. For comparing several output-only damage detection methods the dynamic of the structure was measured extensively during the progressive damage test. The paper gives an introduction to the underlying theory of the subspace based damage detection method and presents an additional theory for processing only a reduced number of signals. After describing the test structure, the damaging and the measurement campaign the results of damage detection are presented and discussed. 2

PROGRESSIVE DAMAGE TESTS ON BRIDGE S101

Within the European research project “Integrated European Industrial Risk Reduction System (IRIS)” a prestressed concrete bridge was artificially damaged [11]. The intention was to provide a complete set of monitoring data during a defined loss of structural integrity for testing and evaluation of various SHM methods and applications. Therefore, during the 3-day damaging process the static and dynamic behavior of the structure was measured permanently. The progressive damage campaign was planned and organized by the Austrian company VCE [11]. 2.1

Bridge S101

The S101 was a prestressed concrete bridge from the early 1960th spanning over the 4-lane highway A1 in Austria. The structural system was a three-field frame with a 32m wide mean field and two 12m wide side fields. The superstructures cross section was designed as a 7.2 m wide post-tensioned double T-beam with varying heights (Figure 1). During recurring technical inspections of the bridge several deficiencies as cracks and spellings have been found. Since the crack pattern correlated with the geometric properties of the prestressing a significant deficit of structural reliability was assumed. Because of the subsequently determined limited load bearing capacity it was decided to replace the structure. Before the demolition of the bridge a progressive damage test for measuring and investigating the structural behavior during the degradation processes could be arranged and carried out.

Figure 1. Front and cross-sectional views of bridge S101 [11].

2.2

Damage description

The damage test took place between the 10- 13 December 2008. During the test the highway beneath the bridge was open in one direction. The second direction was closed for traffic because of construction work which in addition took place near the bridge (Figure 2).

Figure 2. Bridge S101 during damage test [11]. In general, two major damage scenarios were artificially induced. First, a significant damage of one of the four columns was inserted by cutting through the column on its lower end. With this action a change in the global structural system was implemented. After a second cut a 5 cm thick slice of the column was removed and the column was lowered for altogether 3 cm until the elastic ductility of the bridge structure was depleted. Afterwards the column was uplifted again to its original position and secured there by steel plates. In a second damage scenario prestressing tendons of one of the beams were cut successively. Since the loss of prestressing by deterioration processes is a typical risk for existing RC bridges it was of specific interest to examine the sensitivity of damage identification routines to that kind of structural degradation. All in all three and a quarter of a wire bundle were cut through. Between each intersection pauses of several hours were kept to let the structural system change into a new

state of equilibrium. For safety reasons the damaging process was stopped after 3.25 tendons were intersected.

bridge. Perturbation of the measurement signals by the undergoing road construction work cannot be ruled out. 3

SUBSPACE-BASED DAMAGE DETECTION

The stochastic subspace-based damage detection algorithm as used in the introduced structural investigations is generally based on the theory of system realization as described in [12]. But instead of extracting modal system parameters the investigated approach exploits a residual, which uses the left null space of Hankel matrix describing the system. The theory has been widely used in the last years and some different approaches have been developed. The introduced work uses the covariance-driven Hankel matrix estimates and a nonparametric ²-type test for damage detection [13-15]. 3.1

Nonparametric detection algorithm

Consider a linear multi-variable output-only system described by a discrete-time state space model in the form:

Xk 1 Yk

Figure 3. Progressive damage of column and tendons on bridge S101 [11].

2.3

Measurement description

The measurement campaign was carried out by VCE and the University of Tokyo [11]. For vibration measurement a BRIMOS® measurement system containing a permanent sensor grid was used. The grid consisted of 15 sensor locations on the bridge deck, in each location three sensors for measurement in the bridge deck’s vertical, longitudinal and transversal direction. All in all, for vibration measurement 45 acceleration sensors were applied. Figure 4 shows schematically the arrangement of the 15 three dimensional accelerometers. Additionally, for verification of the static response of the structure to the damaging, the vertical displacement of the bridge deck was measured in three characteristic locations.

FXk H Xk

Vk Uk

(1)

where X k is the state vector and Y k the measured output vector of dimension r at time step k , F the state transition matrix and H the observation matrix. The vectors V k and U k denote the state noise and measurement noise processes, which are assumed to be Gaussian white-noise sequences with zero mean. Starting point of the covariance-driven subspace-based detection algorithm is the estimation of output covariance matrices of the measured response time series: N

1 N -i k

Ri

YkYkT-i .

(2)

i 1

where N is the number of data points in the time series. The covariance sequences are then used to construct a block Hankel matrix in the form:

R1 R2

R2 R3

Rq Rq 1

p,q

Rp Figure 4. Schematic draw of the sensor arrangement on the bridge deck [11]. The measurement took place with a sampling frequency of 500 Hz. All values were recorded permanently and stored in files with 165000 data points each. During the three days measurement campaign 714 data files each containing 48 channels were produced. Because of the time of year and because of the cloudy weather the variation of the bridge temperature over the test period was minimal. During the test the highway beneath the bridge was open in one direction. Therefore dynamic excitations from moving trucks can be found in the signals. The second direction was closed for traffic because of construction work which in addition took place near the

Rp

Rp

1

.

(3)

q 1

The indices p and q define the number of considered time shifts and should be chosen in dependence on the assumed system order n , i.e. pr n . Then, usually q is set as q p. In the initial undamaged state S 0T is the left null-space (kernel) of the Hankel matrix

S 0T

(0) p,q (0) p,q

that holds the property:

0

and can be extracted by factorization of singular value decomposition:

(4) (0) p,q

, e.g. using

0

1

U1 U 0

(0) p,q

0

VT

(5)

0

where S 0 U 0 is the kernel and diag( 1 , 0 ) is a diagonal matrix, presenting the singular values in descending order, where the singular values in 0 are considered as zero or close to zero. For the damage detection algorithm the kernel is computed only once from the initial system. The residual vector N is defined as function of the reference matrix

S0T from (4) and the Hankel matrix

p,q

of

the actual system built from the covariance estimates of the measured output as in (2):

N vec S

N

T 0

p,q

.

(6)

It can be deduced from (4) that N has zero mean if changes of the system do not occur, and non-zero mean in the case of changes. Therefore, for the undamaged state the left null space of the Hankel matrix can be used as reference for future residual analysis. Under convenient assumptions, the residual function is asymptotically Gaussian. Then, it manifests itself to damage by a change in its mean value, also corresponding to an increase of the mean of the 2 -test statistics T N

2

where

1

N

,

(7)

.

(8)

is the residual covariance

E

N

T N

The monitoring of the system consists in calculating the 2 test value on the Hankel matrices estimated from newly recorded output data and comparing it to a threshold. A significant increase in the 2 value indicates that the system is no more in the reference state [15]. 3.2

Data reduction by projection channels

Depending on the number of sensors and the chosen system order, the residual function N can be a high dimensional vector. Let the dimension of

1

in (5) be n (corresponding to

the assumed system order), then

((p

1)r

N

has dimension

n)qr . The size of the residual covariance matrix

is hence dependent on r 4 and explodes with a large number of sensors. A way of reducing the size of the underlying Hankel matrix while conserving the structural information is the use of reference sensors or projection channels [16]. Instead of building the output covariances between all sensor data in (2), the covariances are computed between the data from all sensors and the data from a subset of the sensors, the so-called reference sensors or projection channels. Let r 0 be the number of projection channels and at each time lag k the

vector Yk(proj) containing the sensor data of the projection channels of Y k . Then, the resulting output covariances are

Ri(proj)

1 N -i k

N

Yk (Yk(proj) )T . -i

(9)

i 1

and the Hankel matrix in (3) is filled with Ri(proj) instead of

Ri . The damage detection algorithm continues than as in the previous section, but now leading to a residual of dimension ((p 1)r n)qr0 and giving a considerable memory advantage especially for the residual covariance matrix. 4

DAMAGE INDICATION ON S101

As mentioned above, measurement values were recorded throughout the whole three day long damage test, including the nights. The data was stored in files with an approximate time length of 330 s. To avoid disturbance of the detection results by noise, the files recorded during damaging activities were excluded. So all in all 660 files, each of 45 acceleration channels were used in the analysis. To monitor the undamaged state for an adequate time period, the measurement campaign started approximately 12 hours before the damage of the column was executed. 4.1

Data analysis

Principally, the data of all channels was first normalized to an equal energy level. The reference state of the undamaged structure was then determined by computing and averaging the reference matrices from the first 9 datasets. With that approach, a possible disturbance by single excitation events is minimized. The size of the Hankel matrix depends on the number of chosen output channels as well as on the time lags, to be accounted for computing the output covariance matrices. A general problem of the analysis of the S101 data was the quite large number of 45 output channels. So it was necessary to use techniques as projection channels as well as a limitation of data correlation to reduce the sizes of matrices computed in the subspace based algorithm. For these reasons, associated with 45 output channels p and q in eq. (3) defining the number of time shifts in the output covariance matrices had to be limited. Further investigations with reduced numbers of projection channels and therefore increased numbers of p and q showed, that the dynamic system is described sufficiently using only 5 output covariance matrices in the block Hankel matrix. The size of the analyzed null space depends on the order of the system and can be generally determined by the rank of the matrix. But because of noise, the singular values won’t drop to exactly zero and the system order must be estimated. For calculation of the residual covariance matrix as shown in eq. (8) it is important to use as much data sets as are required for the covariance matrix to have full rank. To provide a necessary amount of data sets, it is convenient to divide available datasets in a respective number, whereas the number of data points within one residual vector should not be too small to not lose significance.

The residual must also be normalized with respect to the number of samples used for computing the according Hankel matrix as shown in equation (6) and centralized with the mean over all residual vectors. In the test stage, eq. (7) is solved for every data set, which in real time meant an indicator of damage for every 5.5 min.

residual covariance matrix the effects of the excitation by traffic might have been reduced significantly. Influences by solar radiation and/or temperature alternation can be excluded, since during the 3-days campaign misty winter weather with only moderate temperature changes just below freezing was dominant.

4.2

4.3

Results of damage detection

Figure 4 shows a bar plot of 2 -values as damage indicators of all consecutive tests within the three days campaign. The associated analysis used all 45 sensors. For computing the residual covariance matrix 100 datasets of the undamaged state were used. The x-axis of the plot describes the chronological sequence of the damage activities as well as the 6am and 6pm points of time for orientation. Table 1 gives the explanation to the used notation of the damage activities.

x 10

7

4

7

3

4

Damage Indicator

Figure 6 shows the damage indicator during the several steps of the first damage scenario, the cutting and settling of one of the four bridge columns. With exception of the time periods of the direct mechanical destruction processes which were excluded for containing strong noise, the displayed sequence of damage indicators has a consecutive course.

Damage Indicator

x 10

Detection of column damage

3

2

1

2 0

A

B

C

D

6am AB CD EF 6pm

6am G Time

H I 6pm

6am J

K

Figure 5. Course of the damage indicator over the 3-day damage test.

Table 1. Notation of consecutive damage actions. A B C D E F G H I J K

Figure 6. Damage indicator for cutting and settling of one bridge column

Damage Action Begin of cutting through column End of second cut through column Lowering of column –first step (10mm) Lowering of column – second step (20mm) Lowering of column – third step (27mm) Inserting steel plates Uplifting column Exposing cables and cutting of first cable Cutting through second cable Cutting through third cable Partly cutting of fourth cable

One can easily see in Figure 5 that the damage indication is interfered by noise in the ambient excitation of the bridge. The 2 values periodically swell up in the morning and ebb away in the evening. It is assumed, that the traffic going underneath the bridge and/or the construction work nearby the bridge are the source of the noise. With an extension of the measurement time period of the undamaged state to a whole day circle and therefore with the usage of those additional data in the

As can be seen in Figure 6, the 3 steps of the column settlement action are very distinctive in influencing the computed damage indicator. Obviously, the dynamic system has changed to quite some extend and the altogether 27mm of elastic settlement can be detected clearly. Although not distinctivly visible in Figure 6, also the cutting of the column (A+B) caused an increase of the indicator of approximately 75%, though it has to be mentioned, that the absolute effect is superimposed by the traffic excitation noise. Figure 7 shows a detail of that time period. x 10

5

8 7 6

Damage Indicator

0

E

Time

1

5 4 3 2 1 0

A

B Time

Figure 7. Detail of damage indicator for cutting through one bridge column The column remained in the settled condition for approximately one day and was then uplifted again in its

former position. The effect of the uplifting is again clearly visible in Figure 5 by a drop of the damage indicator. However, the indicator did not drop completely to its origin value which is certainly due to the fact, that the lowering of one column will have led to cracking within the concrete structure to some extend and therefore also to a change of the dynamic signature of the system. 4.4

Detection of tendon damage

x 10

6

10

Projection channels

With the application of projection channels as described above, the computing costs of the analysis of the damage indicators could be reduced massively. So the analysis of all 45 channels requires an extent of memory space which commonly is not provided on desk top computers. Several constellations of projection channels were tested and, as can be seen of Figure 9 almost equal information about the damage indication compared to Figure 5 could be achieved by only four well chosen projection channels (one vertical and one 3D sensor). The computing time was cut to a fifth compared to a complete sensor analysis. 3.5

x 10

7

3

2.5 Damage Indicator

As one can see in Figure 5 the cutting of the prestressing tendons did not lead to a significant change in the damage indicator after the single cutting steps. Nevertheless, a distinctive increase of the indicator could be observed at the end of the measurement. Figure 8 shows the last time period in detail. It is expected that a change of the bridges structural system took place with a time delay after cutting the fourth tendon partly.

4.5

2

1.5

Damage Indicator

1

0.5

5 0

J

6am AB CD EF 6pm

6am G Time

H I 6pm

6am J

K

K Time

Figure 9. Damage indicator on S101 with four projection channels and the location of the chosen sensors

Figure 8. Detail of damage indicator at the end of the tendon cutting process. For a prestressed concrete structure the loss of pre-stressing is a major damage which comes along with a significant loss of its load bearing capacity. One reason that the cutting of the tendons does not affect the proposed damage indicator is that the overall prestressing is designed for combinations of dead and traffic loads. Since the bridge deck S101 has a quite slender cross section, the dead load is not that high in comparison with the traffic loading. An additional dead load reduction comes from the removal of the asphalt surface before the damage test. Also it has to be recalled that the prestressing was designed with adequate safety margins. Also, because of the bound between tendons and concrete, the cutting results only in local loss of prestressing. For the specified reasons it is assumed, that the cutting of the tendons during the damage test did not lead to a significant change of the structural system, because the loading of the structure was not high enough to activate the damage right after its insertion. The increase of the indicator at the end of the test series might be the result of a delayed rearrangement of the structural system by a reduction of stresses under generation of cracks in the concrete of the bridge deck. Though, an evidence of that assumption, for instance by an increase of the measured bridge deck deflection, could not be found.

5

CONCLUSIONS

In this paper, the statistical subspace based damage detection test was successfully applied to output-only vibration data from a progressive damage test of the S101 Bridge, a prestressed concrete bridge. The link between the structural changes due to the artificially introduced damage cutting/lowering of one column and the behavior of the respective 2 test values at each test stage was clearly shown. For a second damage scenario, the cutting of single prestressing tendons, an early stage change of the dynamic response behavior could not be indicated. It is presumed that due to the absence of operational loading during the test the locally acting damage did not activate a significant change of the overall structural system. Under the assumption of an adequate preliminary monitoring of the undamaged structure and taking into consideration the preceding assertion about damage activation, this fully automated method proves to be feasible for Structural Health Monitoring of civil engineering structures. Moreover, a significant increase of the efficiency of the damage detection test was achieved by the use of projection channels. Future work will focus on the robustness of the damage detection test to significant changes in the ambient excitation.

ACKNOWLEDGMENTS This work was partially supported by the European projects FP7-NMP CP-IP 213968-2 IRIS and FP7-PEOPLE-2009IAPP 251515 ISMS. We also thank VCE for providing the data from S101 Bridge. REFERENCES [1]

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