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Damage diagnosis of steel girder bridges using ambient vibration data
Engineering Structures 28 (2006) 912–925 www.elsevier.com/locate/engstruct
Damage diagnosis of steel girder bridges using ambient vibration data Jong Jae Lee a,∗ , Chung Bang Yun b a Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA 92697, USA b Smart Infra-Structure Technology Center, Korea Advanced Institute of Science and Technology, Yusong-gu, Daejeon, 305-701, Republic of Korea
Received 24 March 2005; received in revised form 7 September 2005; accepted 28 October 2005 Available online 20 December 2005
Abstract This paper presents an effective method for damage estimation of steel girder bridges using ambient vibration data. Modal parameters were identified from the ambient vibration data using the frequency domain decomposition technique, and were utilized as the feature vectors for damage diagnosis. Conventional back-propagation neural networks (BPNNs) were incorporated to assess damage locations and damage severities based on the modal parameters. To alleviate ill-posedness in the inverse problem, the potentially damaged members were screened using the damage indicator method based on modal strain energy (DIM-MSE). The effectiveness of the proposed method was demonstrated by means of a numerical example analysis on a simply supported bridge model with multiple girders, and by a field test on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea. c 2005 Elsevier Ltd. All rights reserved. Keywords: Damage diagnosis; Bridge structures; Ambient vibration; Modal strain energy; Neural networks
1. Introduction Bridge structures are exposed to various external loads and may deteriorate over time in unexpected ways. Structural failures resulting from such deterioration can inflict a heavy cost in terms of repair or human life, or both. Accordingly, in recent years, there has been increasing interest in methods for predicting and estimating the location and extent of damage in bridge structures. The use of system identification approaches for structural damage detection has been expanded in recent years, due to the improvement of structural modeling techniques that incorporate response measurements and the advancements in signal analysis and information processing capabilities. Damage estimation methods based on the vibration data can be classified into two groups, based on the structural model involved: signal-based methods and model-based methods [1,2]. Signal-based methods detect damage by comparing structural responses before and after damage, though not using the information on the structural model. Damage is defined ∗ Corresponding author. Tel.: +1 949 231 2759; fax: +1 949 824 9389.
E-mail addresses: [email protected] (J.J. Lee), [email protected] (C.B. Yun). c 2005 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2005.10.017
by means of damage indices, which may be determined using the results of an experimental modal analysis [3–6], a time–frequency domain analysis [7–10]. Signal-based damage estimation methods are generally appropriate for detecting damage locations, but they are not effective for estimating damage severities. In this study, a damage indicator method based on modal strain energy (DIM-MSE), which is a kind of signal-based damage detection method, is utilized to identify the potentially damaged regions. The basic scheme is to compare the strain mode shapes (the second derivative of the mode shape) before and after damage. Accordingly, the method is very sensitive to damage, as well as noise. Using experimental data to improve the mathematical model of the structure, model-based methods can estimate damage severity, as well as damage location. This is possible since structural damage results in changes of the dynamic characteristics of structures [11–14]. Various techniques have been developed for estimating the stiffness changes due to damage. Recently, soft computing techniques, such as neural networks and genetic algorithms, have been increasingly used, because of their excellent pattern-recognition capability [15–18]. In this study, conventional back-propagation neural networks (BPNNs) are utilized for element-level damage estimation.
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With realistic bridge structures, the degree of freedom (DOF) could be very large. The more complex a structural system is, the more difficult the numerical calculation for damage detection is. In addition, for large structures, measuring and identifying all the structural members is very difficult, and the accuracy of such estimates is rarely reliable. One solution for this problem is to use the substructural identification technique [18]; accordingly, a structure can be examined substructure by substructure. Some subsections of a structural system may be more critical for structural safety than others. For the local identification of critical parts, substructural identification is employed to overcome the problems associated with many unknown parameters or DOFs in a large structural system. Another solution is to use a multi-stage approach for damage detection in large structures [19]. A multi-stage diagnosis strategy aims at the successive detection of the occurrence, location, and extent of the structural damage. This approach has many advantages, such as high computational time efficiency and high estimation accuracy. In a multi-stage approach, an assessment of damage severity is performed on the potentially damaged members identified in the previous stage. Accordingly, a damage assessment is undertaken on a small number of members. This can make the estimate results more accurate. This study presents an effective method that uses ambient vibration data for damage detection of steel girder bridges. Modal parameters were identified from ambient vibration data, using the frequency domain decomposition technique, and were utilized as the input feature vectors for damage diagnosis. A two-step identification strategy was incorporated to enhance the effectiveness of the damage detection method. At first, a damage indicator method based on modal strain energy (DIMMSE) is utilized to screen the potentially damaged members. Then, conventional neural networks with back-propagation algorithm are used for a more detailed damage assessment. Only the potentially damaged members identified in the first stage need to be considered in this networks configuration. In addition, only a few modal components measured in the potentially damaged regions are necessary to assess the damage locations and severities more accurately. Fig. 1 shows the flowchart of the proposed method. Theoretical backgrounds on the modal parameter identification method and the damage detection methods that are utilized in this study are briefly addressed. Then, a numerical example analysis is presented to demonstrate the effectiveness of the proposed two-step identification strategy. Finally, the proposed method is also applied in a field test on the Hannam Grand Bridge in Seoul, Korea. Note that modal parameters were directly calculated from analysis model in a numerical example, and artificial measurement noise was added to the calculated modal parameters to simulate realistic cases. 2. Theoretical background 2.1. Modal parameter identification using ambient vibration data Experimental modal analysis has drawn much attention from structural engineers, for updating the analysis model
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Fig. 1. Flowchart of the proposed method.
Fig. 2. A schematic illustrating a plate’s N x by N y sub-regions.
and estimating the present state of structural integrity. Forced vibration tests, such as impact tests can be carried out for this end; however, such tests are generally restricted to small-scaled structures, because they can be difficult and expensive to carry out on large structures, such as bridges. Accordingly, ambient vibration tests under wind, wave, or traffic loadings may be more effective alternatives. In this study, modal parameters were identified using the frequency domain decomposition technique [20,21], which is a frequency domain method that does not use input information. The frequency domain decomposition (FDD) method was originally used to extract the operational deflection shapes in mechanical vibrating systems. It utilizes the singular value decomposition for the spectral matrix of output responses, as shown in Eq. (1). The natural frequencies are estimated from the peaks of the power spectral density functions in the peak picking method and are evaluated from singular value (SV) functions of the spectral matrix in the FDD method. S yy (ω) = U(ω)s(ω)V(ω)T
(1)
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Fig. 3. Mode shape curvature from mode shape data.
Li et al. [26] presented two novel damage sensitive parameters to determine the damage locations for plate-like structures, based on the continuity condition and the residual strain mode shape technique. In this study, a damage indicator method based on modal strain energy for plate-like structures is incorporated to detect damage of a steel girder bridge. The damage index for the sub-region j k in Fig. 2 is m m ∗ fi j k fi j k (2) β jk = i=1
i=1
where fi j k =
Fig. 4. Architecture of back-propagation neural networks.
where S yy (ω) ∈ R Nm×Nm is the spectral matrix for output responses y(t) ∈ R Nm , s(ω) ∈ R Nm×Nm is a diagonal matrix containing the singular values of its spectral matrix, and U(ω), V(ω) ∈ R Nm×Nm are corresponding unitary matrices. Nm is the number of measuring points. The general multi-DOF system can be transformed to the single DOF system close to its natural frequencies by means of singular value decomposition. Then the mode shape can be estimated as the first column vector of the unitary matrix of U(ω), since the first singular value may include the structural mode close to its natural frequencies. However, in the closely spaced modes, the peak of the largest singular values at one natural frequency indicates the structural mode, and an adjacent second singular value may indicate the close mode. 2.2. Damage indicator method based on modal strain energy The damage indicator method based on modal strain energy (DIM-MSE), which constructs indices from various modal parameters, has been extensively adopted as one of the most effective methods for damage localization. Strain (or curvature) mode shape is sensitive to damage, because of its local behavior [22], and it has been utilized to locate damage sites in beams or frame structures [3,5,23,24]. When strain mode shape is used to identify damage in complex structural systems, such as plate-like structures, issues such as the establishment of an intuitive and effective damage sensitive index and the achievement of an accurate strain mode shape will be of great interest. Cornwell et al. [25] extended the damage indicator method based on modal strain energy for beam-like structures to include the detection of damage in plate-like structures that are characterized by a two-dimensional curvature [25].
2 2 2 bk+1 a j +1 ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2φ + + 2ν + 2 (1 − ν) ∂ x∂ yi dxdy aj bk ∂x2 ∂ y2 ∂x2 ∂ y2 2 2 2 b a ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi + + 2ν + 2 (1 − ν) dxdy 0 0 ∂ x∂ y ∂x2 ∂ y2 ∂x2 ∂ y2
(3) and m is the number of modes to be utilized. φi (x, y) is the i th mode shape of the undamaged state and v is the Poisson ratio. An analogous term fi∗j k can be defined using the damaged mode shape, φi∗ (x, y). The above equation was derived by comparing the fractional strain energies at location j k of a plate before and after damage. More detailed derivations are explained in Ref. [25]. In this study, mode shape curvatures (or strain mode shapes) were computed by numerically differentiating the identified mode shape vectors. At first, the mode shapes are identified from the acceleration data, and then the coarse mode shapes are interpolated into the finer ones using a cubic polynomial function. This is done because the number of sensors used for the mode shapes is limited, and the damage indicator method based on modal strain energy for plate-like structures requires many data points for better resolution. Fig. 3 illustrates the procedure used to calculate the finer mode shape curvatures from the coarse mode shape data. The effect of measurement noise on the mode shapes can be amplified in the mode shape curvatures, since they are calculated from a second derivative. To overcome the noise-sensitive characteristics of the mode shape curvatures, it is recommended to use sufficient records of measurement data, since the effects of noise can be largely alleviated through averaging. To remove the noise amplification in differential operations, the mode shape curvatures can be directly obtained from the dynamic strain data. As the technologies on smart sensors, such as optical fiber sensors, are being rapidly developed, the use of dynamic strain data to accurately calculate the strain mode shapes for the damage
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Fig. 5. A bridge model and the element numbers for girders.
detection of bridge structures is an increasingly promising approach. 2.3. Neural networks technique In recent years, there has been increasing interest in the use of neural networks to estimate and predict the extent and location of damage in complex structures. The neural networks technique, which can be categorized into a model-based damage detection method when it is trained by simulation data, can be an effective tool for the damage assessment of bridge structures. The neural networks technique has the advantage of quick estimation, since it does not require much computation time at the operational stage, once the networks have been properly trained. Another advantage of the neural networks technique for damage estimation is that it is useful in cases that have various types of input data. Moreover, it can effectively deal with the modeling errors that come from the discrepancies between the actual structure and the corresponding numerical model, by incorporating the error-insensitive input data. In this study, the mode shape differences between before and after damage are used as the error-insensitive input data to the neural networks [27]. A popular neural networks model called multi-layer perception neural networks [28–30] was used to identify the element-level stiffness parameters. The networks consist of an input layer, two hidden layers, and an output layer, as shown in Fig. 4. Sigmoid functions are utilized as nonlinear activation functions for all layers. The input layer contains the measured mode shape properties (i.e., the mode shape differences between before and after damage) and the output layer consists of the element-level stiffness indices to be identified as Si = kid /ki0
(4)
where k is element stiffness. Subscript i denotes the element number and superscripts 0 and d represent intact and damaged states, respectively. In this study, the element-level damage severity is defined as αi = 1 − Si .
(5)
The input/output relationship of the neural networks can be nonlinear, as well as linear, and its characteristics are determined by the synaptic weights assigned to the connections between the neurons in two adjacent layers. A systematic way of updating the weights to achieve a desired input/output relationship based on a set of training patterns is referred to as a training or learning algorithm. In this study, the conventional back-propagation algorithm is adopted. Noise injection learning (NIL) was also employed, to reduce the effect of measurement noise [31]. In the NIL algorithm, the training is carried out using the artificially contaminated training patterns with noise of a prescribed level. The generalization capability of the neural networks under noisy conditions can be remarkably enhanced through this algorithm. Noise can be added to the training patterns as x˜ = x + ν N(0,σ )
(6)
where x˜ is a noise-injected input vector and x is an exact input vector. The term ν N(0,σ ) refers to Gaussian random noise with zero mean and standard deviation σ . The noise level σ is application specific. The noise described in the above equation indicates that signal-to-noise (S/N) ratios for all sensor locations are not equal, since the sensors mounted on different locations naturally suffer different uncertainties, even though the imposed noise level is nearly equal. Accordingly, a sensor with a low-amplitude signal will be exposed to a relatively high level of noise.
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Fig. 6. First three mode shapes of a bridge model.
Fig. 7. Effect of noise: σ = 0.5%.
3. A numerical example analysis
one or two element(s). Measurement noise was considered by adding noise into the mode shape, as follows:
3.1. An example bridge structure
φ˜ i = φi + φin NS 1 n φi = φ 2 × N[0, σ ] NS i=1 i
A numerical example analysis was performed on a simply supported bridge model, with multiple girders, to demonstrate the effectiveness of the proposed method for the damage detection of steel girder bridges. The bridge is composed of 10 steel girders, diaphragms, and slabs. It is modeled using beam elements for the steel girders and diaphragms, and shell elements for the concrete slabs in SAP2000 software, as shown in Fig. 5. The first three modes, which are to be used as the input data for damage detection, were calculated for the intact case, as shown in Fig. 6. Damage estimations were carried out for 20 damage scenarios, as described in Table 1. The first 10 damage scenarios are cases with a single damage location (DS1–DS10), while the other 10 cases have two damage locations (DM1–DM10). Damage was simulated by reducing the bending stiffness of the specified element(s): a 30% reduction of bending stiffness in
(7) (8)
where φ˜ i and φi represent the mode shape with and without noise at location i , respectively. The term φin refers to the imposed noise. The term NS refers to the number of sensors, and N [0, σ ] is a random number with zero mean and standard deviation σ . The noise in Eq. (7) has the same amount of uncertainty for all locations according to σ value, regardless of the individual sensor location i . In this study, three different values of σ (0.1%, 0.5%, 1.0%) are investigated. For each σ , 100 noisy mode shapes were randomly generated for intact and damage cases according to Eqs. (7) and (8), respectively. To illustrate the effect of noise imposed by Eqs. (7) and (8), 10 example cases of the randomly perturbed first modes for σ = 0.5% are shown in Fig. 7. The noise with an equal
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Table 1 Success rate (SR) in screening using DIM-MSE (out of 100 cases) Single damage Damage case
El. No
SR (%)
Multiple damage Damage case
El. No.
SR (%)
El. No.
SR (%)
14 15 16 17 18 38 39 40 41 42
100 100 100 100 100 98 100 100 100 100
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
100 100 100 100 100 100 100 99 100 100
87 53 62 53 77 82 45 57 81 105
95 100 100 100 100 100 100 100 100 100
14 15 16 17 18 38 39 40 41 42
43 51 86 95 83 21 42 74 96 80
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
26 55 71 74 73 73 51 63 41 45
87 53 62 53 77 82 45 57 81 105
22 93 24 96 92 40 57 64 63 69
14 15 16 17 18 38 39 40 41 42
28 34 49 69 48 22 28 45 77 57
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
33 32 47 44 43 41 38 36 24 34
87 53 62 53 77 82 45 57 81 105
19 67 15 70 68 33 44 43 49 48
(a) 0.1% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10 (b) 0.5% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10 (c) 1.0% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10
amount of uncertainty has different effects on the mode shapes: the noise level of σ = 0.5% can be very high at the nodal points with small amplitude of the mode shape and relatively low at the points with large amplitude of the mode shape. The noise level of σ = 0.5% for the first mode shape rises to 4% of the exact mode shape at the nodal points, as shown in Fig. 7. 3.2. Screening using a damage indicator method based on modal strain energy At first, a damage indicator method based on modal strain energy (DIM-MSE) for plate-like structures was utilized for screening potentially damaged members of a bridge model. Twenty elements with the higher damage indices out of 120 elements were selected as the potentially damaged members. This screening criterion corresponds to the confidence level of z = 1.0 for the standard normal distribution, where z is the standard normal random variable. Table 1 summarizes the results of the screening process. The success rate (SR) is defined as the number of successful identifications during the
screening process out of 100 randomly perturbed cases for each damage case. When an actually damaged member was among the 20 potentially damaged members identified, the first step for screening was considered successful. The success rate in the screening process is closely related to the noise level, as shown in Table 1: the actually damaged member(s) was (were) successfully identified when the noise level was small (σ = 0.1%), and the SR decreased as the noise level increased. For example, the SR for Damage Case DS-1 was 43% when σ = 0.5%. This means that an actually damaged member (Element 14) was included in the identified 20 potentially damaged members 43 times (simulation cases) out of 100 times (simulation cases). An SR of 43% may seem to be a disappointing result; however, it is very difficult to consistently recognize an actually damaged member, or members, with the presence of a significant noise level. Moreover, the screening process naturally yields an SR of 16.7% to each element under random noise at an intact state, when 20 elements randomly selected out of 120 elements are assumed to be damaged. Therefore, it is more reasonable to investigate the trend of an
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(a) Cases with single damage: DS-1, 3, 5, 7, 9. Fig. 8. Probability of damage occurrence using 100 records with the noise of σ = 0.5%. (The exact locations of damage are marked with arrows (↓).)
SR for all the elements, rather than the specific value of an SR for a certain element. Fig. 8 shows the probability of damage occurrence as calculated from the screening process, using 100 noisy data sets, each with a noise level of σ = 0.5%. At first, 20 elements with higher damage indices out of the 120 elements were selected as potentially damaged members for each record. Then, the frequency of damage alarming (i.e. the number of being identified as a potentially damaged member) was calculated for every elements. Finally, 20 elements with higher frequencies of damage alarming were selected as potentially damaged members. Dashed lines in Fig. 8 divide the 20 potentially damaged elements from the remaining elements. The probability of damage occurrence, i.e. the frequency of damage alarming for 100 data sets, corresponds to the result of the success rate, as shown in Table 1(b). From these results, it can be concluded that a comparison of the damage alarming frequency for all elements provides a reliable indication, while the specific values of the success rate provide only ambiguous results.
3.3. Damage assessment using neural networks The neural networks technique with a back-propagation algorithm was used to localize the damaged members and to assess the damage severities. Only the potentially damaged members that were identified in the previous stage need to be considered in this networks configuration. In addition, only a few modal components measured at the identified potentially damaged regions are used to assess the damage locations and severities more accurately. Fig. 9 shows some example cases for damage assessment. In Fig. 9, a single measurement record with a noise level of σ = 0.5% was used as the input to the networks. At first, 20 potentially damaged members were determined by the probability of damage occurrence calculated from 100 noisy records, as shown in Fig. 8. Then, a more detailed identification was performed on the potentially damaged members using the 100th record of noisy data, assuming that the latest data set is being continuously stored in the measurement system. The damaged member(s) was (were) reasonably identified when the actually damaged member(s)
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(b) Cases with multiple damage: DM-1, 3, 5, 7, 9. Fig. 8. (continued)
was (were) selected as the potentially damaged member(s) in the first step, whereas the estimated results still showed lots of false alarms and fairly large errors as shown in Fig. 9, since they were calculated based on the single set of noisy data. The results of DM-1 and DM-3, shown in Fig. 8(b), demonstrate that it is very important to not miss the actually damaged members during the first stage. Averaging is the easiest and the most effective means to enhance the accuracy of the screening process, as well as the estimate of the second stage. Fig. 10 shows some typical results using the averaged data of 10 and 20 noisy records. Twenty members with large value of damage index were considered at the second stage. The results of the damage assessment using the averaged data set yielded much better results as the number of data sets increased: the false alarms were alleviated and the estimated damage severity for the actually damaged member was close to the true value (30%) with less than 10% error. The effects of the measurement noise were remarkably reduced, since the averages of 10 and 20 sets of measurement data with 0.5% noise level can be regarded as a single record with 0.16% and 0.11%
noise level, respectively. From these results, it can be concluded that averaging a sufficient amount of measurement data should precede the damage diagnosis, to not miss the actually damaged members and to enhance the estimation accuracy. The accuracy in the screening process can be improved more when the averaging is performed on the input data, and the frequency of damage alarming is used as an occurrence indicator. 4. Field tests on a steel girder bridge 4.1. Description of experiments Field tests of damage estimation were performed on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea (Fig. 11), which is to be replaced during bridge renovation. The span is simply supported, with a length of 22.7 m. It is composed of nine steel plate girders and a concrete slab. Originally, it had 10 girders, but the 10th girder was removed during the construction of the newly built bridge next to it. Ambient vibration tests were carried out for the vertical accelerations on the bridge deck. The vibration
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(a) DS-1.
(b) DM-7. Fig. 9. Examples of damage assessment using neural networks (σ = 0.5%). (The exact locations of damage are marked with arrows (↓).)
was mainly induced by the traffic loads on the adjacent new bridge and by the train and vehicle loads under the test bridge. Seven sets of measurements were carried out on Girders 1 to 7, as shown in Fig. 12. For each set of measurements, vertical accelerations were measured at 11 equally spaced points on the slab just above each girder. Reference signals to correlate each experimental set were obtained at seven points (R1–R7). Fig. 12(c) shows a typical case of the acceleration time history obtained from the ambient vibration test. Acceleration signals were measured for more than 2 h for each damage case with the sampling frequency of 100 Hz. The number of samples used to calculate the Fourier transform is 8192. Averaging was performed about 200 times with overlapping for each damage case, to alleviate the non-stationary characteristics of the ambient vibration tests and to reduce the measurement noise. Fig. 13 shows the inflicted damage scenarios imposed by torch cuts on the main girders of the bridge for the present damage detection study. Modal parameters for each damage state were identified using the frequency domain decomposition method [19,20]. Table 2 shows the modal properties calculated from the initial finite element (FE) model and those estimated from the experiments for each damage case. The measured first natural frequencies do not show a close correlation to the
imposed damage. This indicates the difficulty in using resonant frequencies as damage indicators for large civil engineering structures, where the environmental and operational effects such as temperature, humidity and traffic volume may not be ignored. Accordingly, the natural frequency information was not used in the damage detection procedure. In Table 2, the modal assurance criteria (MAC) values are also shown, which represent the closeness between the calculated and the experimental mode shapes. The first three modes gave close results to the test results: above 97% in MAC value. Therefore, the first three mode shapes were used as inputs for the damage estimation. The mode shapes were used to calculate the strain mode shape (the second derivative of mode shape) for the screening process, and the mode shape differences between before and after damage, which are found to be less sensitive to the modeling errors, were used as the input to the neural networks [27]. 4.2. Screening using a damage indicator method based on modal strain energy In the first step, a damage indicator method based on modal strain energy (DIM-MSE) for plate-like structures was used to screen potentially damaged members of the test bridge. The
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(a) Using average of 10 records: DS-1.
(b) Using average of 20 records: DM-7. Fig. 10. Damage assessment using averaged data (σ = 0.5%). (The exact locations of damage are marked with arrows (↓).) Table 2 Natural frequencies and modes of Hannam Grand Bridge for various damage cases Modes
1st mode
2nd mode
3rd mode
Calculated (intact)
4.071 Hz
4.452 Hz
5.626 Hz
4.247 Hz (99.79) 4.188 Hz (99.38) 4.196 Hz (99.90) 4.218 Hz (99.51)
4.876 Hz (97.86) 4.903 Hz (99.45) 4.780 Hz (99.35) 4.757 Hz (99.56)
5.771 Hz (99.71) 5.823 Hz (99.64) 5.778 Hz (99.57) 5.799 Hz (99.73)
Measured
Intact Damage I Damage II Damage III
Measured mode shapes (Intact case)
Note: Values in parentheses are the MAC values (%).
first three modes for all of the intact and damaged cases, which are measured at 77 points with dimensions of 7 (girders) by 11 (sensor locations), were interpolated into the finer mode shapes using a cubic polynomial function, to numerically calculate the mode shape curvatures. Fig. 14 shows the damage
indices calculated from DIM-MSE. The bright locations correspond to the potentially damaged regions. The damage locations were identified with good accuracy for all damage cases, while there were some false damage alarms at several locations.
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(a) Overview of old and new bridges.
(b) Northern-most span of old bridge (L = 22.7 m).
(c) Section view of old bridge. Fig. 11. View of Hannam Grand Bridge in Seoul, Korea.
4.3. Damage assessment using neural networks The conventional back-propagation neural networks technique with a noise injection learning algorithm was used for a detailed damage diagnosis. Only the potentially damaged members identified in the first step were considered in the networks configuration. The number of potentially damaged members to be investigated at the second stage is user-defined, but it should be determined by considering the network complexity and damage missing errors. The larger the number of potentially damaged members we choose is, the lower the damage missing errors is but the more complex the network configuration is. In this study, 20 elements with the higher damage indices out of 70 elements were selected as the potentially damaged members. The mode shape differences between before and after damage, which are found to be less sensitive to the modeling errors [27], were used as the input to the neural networks. The potentially damaged members considered in the second step were as follows:
Damage Case I: 20 Elements (Element 4, 5, 6, 7, 9, 14, 15, 17, 18, 36, 37, 43, 44, 45, 46, 47, 54, 55, 56, 57) Damage Case II: 20 Elements (Element 4, 5, 6, 7, 8, 14, 15, 16, 17, 18, 44, 45, 46, 47, 56, 57, 74, 75, 76, 77) Damage Case III: 20 Elements (Element 15, 16, 17, 18, 23, 24, 25, 26, 44, 45, 46, 47, 54, 55, 56, 57, 64, 65, 66, 67) Fig. 15 shows the results of the damage assessment using neural networks. The numbers of input, 1st hidden, 2nd hidden, and output nodes in the networks are 60–80, 20, 20 and 20, respectively. The number of input nodes is determined by considering the spatial distribution of the identified potentially damaged members and the magnitude of the mode shapes at those points. The results of the damage assessment showed a good estimate for all the damage cases, even though there were many false alarms in the first step. The actually damaged member(s) showed large value(s) of damage severity and the
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(a) Damage locations and element numbers.
(a) Sources for ambient vibration test. (b) Inflicted damage. Fig. 13. Damage scenarios for Hannam Grand Bridge.
(b) Measurement locations (1–77: Roving sensor positions, R1–R7: Reference sensor numbers).
For accurate evaluation of damage assessment, the actual damage locations should be identified first, and then the damage severities of the corresponding structural members are to be assessed. However, in this study, estimation of damage location and severity was carried out together at the second stage to effectively deal with a number of structural members. Thorough inspection of a damaged member is beyond the scope of this study. Various non-destructive evaluation (NDE) techniques can be incorporated for accurate evaluation of structural integrity, after identifying the potentially damaged members with informative damage severities using vibrationbased damage estimation methods. 5. Conclusion
(c) Acceleration time history (at sensor position 39). Fig. 12. Ambient vibration tests.
members with false alarms showed small values, since the noise injection learning algorithm was effectively used to reduce the effect of noise.
In this study, an effective method has been presented for the damage detection of steel girder bridges using ambient vibration data. Modal parameters were identified from ambient vibration data using the frequency domain decomposition technique and were utilized as the input feature vectors for damage diagnosis. The conventional back-propagation neural networks with a noise injection learning algorithm were incorporated to assess damage locations and damage severities based on modal parameters. To alleviate ill-posedness in the inverse problem, the potentially damaged members were screened using the modal strain energy based damage indicator method, in which the mode shape curvatures were calculated from the second derivatives of the identified mode shapes. The effectiveness of the proposed method was demonstrated by a numerical example analysis on a simply supported bridge model with multiple girders, and by a field test on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea.
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(a) Damage Case I.
(a) Damage Case I.
(b) Damage Case II.
(b) Damage Case II.
(c) Damage Case III. Fig. 15. Results of damage assessment using neural networks. (The exact locations of damage are marked with arrows (↓).)
(c) Damage Case III. Fig. 14. Results of screening using DIM-MSE.
In a numerical example analysis, 100 randomly perturbed cases for each damage case were considered. A comparison of the damage alarming frequency for all elements provides a reliable indication, while the specific values of the success rate provide only ambiguous results in the screening process. The
damaged member(s) was (were) reasonably identified when the actually damaged member(s) was (were) selected as the potentially damaged member(s) in the first step, whereas the estimated results still showed fairly large errors because of noise. Using the averaged data of 10 and 20 noisy records, the effects of measurement noise were remarkably reduced. The results of the damage assessment using the averaged data set provided much better results as the number of data sets increased. From these results, it can be concluded that averaging a sufficient amount of measurement data should precede the damage diagnosis, to not miss the actually damaged members and to enhance the estimation accuracy. In the field tests, the first three modes for all of the intact and damaged cases, which are measured at 77 points with dimensions of 7 (girders) by 11 (sensor locations), were interpolated into the finer mode shapes using a cubic polynomial function to numerically calculate the mode shape curvatures. The damage locations were identified with good
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accuracy for all damage cases, while there were some false damage alarms at several locations in the screening process. The results of damage assessment using neural networks with a noise injection learning algorithm showed a good estimate for all the damage cases, even though there were many false alarms in the first step. The actually damaged member(s) showed large value(s) of damage severity and the members with false alarms showed small values, since the noise injection learning algorithm was effectively used to reduce the effects of noise. Acknowledgement This study is supported by the Smart Infra-Structure Technology Center (SISTeC) at KAIST, which is sponsored by the Ministry of Science and Technology (MOST) and the Korea Science and Engineering Foundation (KOSEF). Their financial support is gratefully acknowledged. References [1] Doebling SW, Farrar CR, Prime MB. A summary review of vibrationbased damage identification methods. The Shock and Vibration, Digest 1998;30(2):91–105. [2] Zou Y, Tong L, Steven GP. Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures — A review. Journal of Sound and Vibration 2000;230(2): 357–78. [3] Pandey AK, Biswas M, Samman MM. Damage detection from changes in curvature mode shape. Journal of Sound and Vibration 1991;145:312–32. [4] Kim JT, Stubb N. Model uncertainty impact and damage-detection accuracy in plate girder. Journal of Structural Engineering, ASCE 1995; 121(10):1409–17. [5] Worden K, Burrows AP. Optimal sensor placement for fault detection. Engineering Structures 2001;23(8):885–901. [6] Yam LH, Li YY, Wong WO. Sensitivity studies of parameters for damage detection of plate-like structures using static and dynamic approaches. Engineering Structures 2002;24(11):1465–75. [7] Huang NE, Shen Z, Long SR. A new view of nonlinear water waves: the Hilbert spectrum. Annual Review of Fluid Mechanics 1999;31:417–75. [8] Hou Z, Noori M, St Amand R. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics, ASCE 2000; 126(7). [9] Quek ST, Wang Q, Zhang L, Ong KH. Practical issues in the detection of damage in beams using wavelets. Smart Materials and Structures 2001; 10:1009–17. [10] Loutridis SJ. Damage detection in gear systems using empirical mode decomposition. Engineering Structures 2004;26(12):1833–41. [11] Stetson KA, Harrison IR. Redesign of structural vibration modes by finite element inverse perturbation. Journal of Engineering for Power, ASME 1981;103:319–25.
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[12] Yun CB, Hong KS. Damage assessment of structures by inverse modal perturbation method. In: Proceedings of the 4th east Asia–Pacific conference on structural engineering and construction. 1992. [13] Shi ZY, Law SS, Zhang LM. Structural damage localization from modal strain energy change. Journal of Sound and Vibration 1998;218(5): 825–44. [14] Brownjohn JMW, Xia PQ, Hao H, Xia Y. Civil structure condition assessment by FE model updating: methodology and case studies. Finite Elements in Analysis and Design 2001;37:761–75. [15] Wu X, Ghaboussi J, Garret Jr JH. Use of neural networks in detection of structural damage. Computers and Structures 1992;42(4):649–59. [16] Levin RI, Lieven NAJ. Dynamic finite element model updating using simulated annealing and genetic algorithms. Mechanical Systems and Signal Processing 1998;12(1):91–120. [17] Chou JH, Ghaboussi J. Genetic algorithm in structural damage detection. Computers and Structures 2001;79:1335–53. [18] Yun CB, Bahng EY. Substructural identification using neural networks. Computers and Structures 2000;77(1):41–52. [19] Ko JM, Sun ZG, Ni YQ. Multi-stage identification scheme for detecting damage in cable-stayed Kap Shui Mun Bridge. Engineering Structures 2002;24(7):857–68. [20] Otte D, Van de Ponseele P, Leuridan J. operational shapes estimation as a function of dynamic loads. In: Proceedings of the 8th international modal analysis conference. 1990, p. 413–21. [21] Brincker R, Zhang L, Andersen P. Modal identification from ambient response using frequency domain decomposition. In: Proceedings of 18th international modal analysis conference. 2000, p. 625–30. [22] Yam LH, Leung TP, Li DB, Xue KZ. Theoretical and experimental study of modal strain analysis. Journal of Sound and Vibration 1996;192: 251–60. [23] Yao GC, Chang KC, Lee GC. Damage diagnosis of steel frames using vibrational signature analysis. Journal of Engineering Mechanics ASCE 1992;118(9):1949–61. [24] Ratcliffe CP, Bagaria WJ. Vibration technique for locating delamination in a composite beam. AIAA Journal 1998;36:1074–7. [25] Cornwell P, Doebling SW, Farrar CR. Application of the strain energy damage detection method to plate-like structures. Journal of Sound and Vibration 1999;224(2):359–74. [26] Li YY, Cheng L, Yam LH, Wong WO. Identification of damage locations for plate-like structures using damage sensitive indices: strain modal approach. Computers and Structures 2002;80:1881–94. [27] Lee JJ, Lee JW, Yi JH, Yun CB, Jung HY. Neural networks-based damage detection of bridges considering errors in baseline finite element models. Journal of Sound and Vibration 2005;280:555–78. [28] Haykin S. Neural networks-a comprehensive foundation. New York: Macmillan; 1994. [29] Yun CB, Yi JH, Bahng EY. Joint damage assessment of framed structures using neural networks technique. Engineering Structures 2001;23(5): 425–35. [30] Lee JW, Kim JD, Yun CB, Yi JH, Shim JM. Health-monitoring method for bridges under ordinary traffic loadings. Journal of Sound and Vibration 2002;257(2):247–64. [31] Matsuoka K. Noise injection into inputs in back-propagation learning. IEEE Transaction of Systems, Man, and Cybernetics 1992;22(3):436–40.
Damage diagnosis of steel girder bridges using ambient vibration data Jong Jae Lee a,∗ , Chung Bang Yun b a Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA 92697, USA b Smart Infra-Structure Technology Center, Korea Advanced Institute of Science and Technology, Yusong-gu, Daejeon, 305-701, Republic of Korea
Received 24 March 2005; received in revised form 7 September 2005; accepted 28 October 2005 Available online 20 December 2005
Abstract This paper presents an effective method for damage estimation of steel girder bridges using ambient vibration data. Modal parameters were identified from the ambient vibration data using the frequency domain decomposition technique, and were utilized as the feature vectors for damage diagnosis. Conventional back-propagation neural networks (BPNNs) were incorporated to assess damage locations and damage severities based on the modal parameters. To alleviate ill-posedness in the inverse problem, the potentially damaged members were screened using the damage indicator method based on modal strain energy (DIM-MSE). The effectiveness of the proposed method was demonstrated by means of a numerical example analysis on a simply supported bridge model with multiple girders, and by a field test on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea. c 2005 Elsevier Ltd. All rights reserved. Keywords: Damage diagnosis; Bridge structures; Ambient vibration; Modal strain energy; Neural networks
1. Introduction Bridge structures are exposed to various external loads and may deteriorate over time in unexpected ways. Structural failures resulting from such deterioration can inflict a heavy cost in terms of repair or human life, or both. Accordingly, in recent years, there has been increasing interest in methods for predicting and estimating the location and extent of damage in bridge structures. The use of system identification approaches for structural damage detection has been expanded in recent years, due to the improvement of structural modeling techniques that incorporate response measurements and the advancements in signal analysis and information processing capabilities. Damage estimation methods based on the vibration data can be classified into two groups, based on the structural model involved: signal-based methods and model-based methods [1,2]. Signal-based methods detect damage by comparing structural responses before and after damage, though not using the information on the structural model. Damage is defined ∗ Corresponding author. Tel.: +1 949 231 2759; fax: +1 949 824 9389.
E-mail addresses: [email protected] (J.J. Lee), [email protected] (C.B. Yun). c 2005 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2005.10.017
by means of damage indices, which may be determined using the results of an experimental modal analysis [3–6], a time–frequency domain analysis [7–10]. Signal-based damage estimation methods are generally appropriate for detecting damage locations, but they are not effective for estimating damage severities. In this study, a damage indicator method based on modal strain energy (DIM-MSE), which is a kind of signal-based damage detection method, is utilized to identify the potentially damaged regions. The basic scheme is to compare the strain mode shapes (the second derivative of the mode shape) before and after damage. Accordingly, the method is very sensitive to damage, as well as noise. Using experimental data to improve the mathematical model of the structure, model-based methods can estimate damage severity, as well as damage location. This is possible since structural damage results in changes of the dynamic characteristics of structures [11–14]. Various techniques have been developed for estimating the stiffness changes due to damage. Recently, soft computing techniques, such as neural networks and genetic algorithms, have been increasingly used, because of their excellent pattern-recognition capability [15–18]. In this study, conventional back-propagation neural networks (BPNNs) are utilized for element-level damage estimation.
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With realistic bridge structures, the degree of freedom (DOF) could be very large. The more complex a structural system is, the more difficult the numerical calculation for damage detection is. In addition, for large structures, measuring and identifying all the structural members is very difficult, and the accuracy of such estimates is rarely reliable. One solution for this problem is to use the substructural identification technique [18]; accordingly, a structure can be examined substructure by substructure. Some subsections of a structural system may be more critical for structural safety than others. For the local identification of critical parts, substructural identification is employed to overcome the problems associated with many unknown parameters or DOFs in a large structural system. Another solution is to use a multi-stage approach for damage detection in large structures [19]. A multi-stage diagnosis strategy aims at the successive detection of the occurrence, location, and extent of the structural damage. This approach has many advantages, such as high computational time efficiency and high estimation accuracy. In a multi-stage approach, an assessment of damage severity is performed on the potentially damaged members identified in the previous stage. Accordingly, a damage assessment is undertaken on a small number of members. This can make the estimate results more accurate. This study presents an effective method that uses ambient vibration data for damage detection of steel girder bridges. Modal parameters were identified from ambient vibration data, using the frequency domain decomposition technique, and were utilized as the input feature vectors for damage diagnosis. A two-step identification strategy was incorporated to enhance the effectiveness of the damage detection method. At first, a damage indicator method based on modal strain energy (DIMMSE) is utilized to screen the potentially damaged members. Then, conventional neural networks with back-propagation algorithm are used for a more detailed damage assessment. Only the potentially damaged members identified in the first stage need to be considered in this networks configuration. In addition, only a few modal components measured in the potentially damaged regions are necessary to assess the damage locations and severities more accurately. Fig. 1 shows the flowchart of the proposed method. Theoretical backgrounds on the modal parameter identification method and the damage detection methods that are utilized in this study are briefly addressed. Then, a numerical example analysis is presented to demonstrate the effectiveness of the proposed two-step identification strategy. Finally, the proposed method is also applied in a field test on the Hannam Grand Bridge in Seoul, Korea. Note that modal parameters were directly calculated from analysis model in a numerical example, and artificial measurement noise was added to the calculated modal parameters to simulate realistic cases. 2. Theoretical background 2.1. Modal parameter identification using ambient vibration data Experimental modal analysis has drawn much attention from structural engineers, for updating the analysis model
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Fig. 1. Flowchart of the proposed method.
Fig. 2. A schematic illustrating a plate’s N x by N y sub-regions.
and estimating the present state of structural integrity. Forced vibration tests, such as impact tests can be carried out for this end; however, such tests are generally restricted to small-scaled structures, because they can be difficult and expensive to carry out on large structures, such as bridges. Accordingly, ambient vibration tests under wind, wave, or traffic loadings may be more effective alternatives. In this study, modal parameters were identified using the frequency domain decomposition technique [20,21], which is a frequency domain method that does not use input information. The frequency domain decomposition (FDD) method was originally used to extract the operational deflection shapes in mechanical vibrating systems. It utilizes the singular value decomposition for the spectral matrix of output responses, as shown in Eq. (1). The natural frequencies are estimated from the peaks of the power spectral density functions in the peak picking method and are evaluated from singular value (SV) functions of the spectral matrix in the FDD method. S yy (ω) = U(ω)s(ω)V(ω)T
(1)
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Fig. 3. Mode shape curvature from mode shape data.
Li et al. [26] presented two novel damage sensitive parameters to determine the damage locations for plate-like structures, based on the continuity condition and the residual strain mode shape technique. In this study, a damage indicator method based on modal strain energy for plate-like structures is incorporated to detect damage of a steel girder bridge. The damage index for the sub-region j k in Fig. 2 is m m ∗ fi j k fi j k (2) β jk = i=1
i=1
where fi j k =
Fig. 4. Architecture of back-propagation neural networks.
where S yy (ω) ∈ R Nm×Nm is the spectral matrix for output responses y(t) ∈ R Nm , s(ω) ∈ R Nm×Nm is a diagonal matrix containing the singular values of its spectral matrix, and U(ω), V(ω) ∈ R Nm×Nm are corresponding unitary matrices. Nm is the number of measuring points. The general multi-DOF system can be transformed to the single DOF system close to its natural frequencies by means of singular value decomposition. Then the mode shape can be estimated as the first column vector of the unitary matrix of U(ω), since the first singular value may include the structural mode close to its natural frequencies. However, in the closely spaced modes, the peak of the largest singular values at one natural frequency indicates the structural mode, and an adjacent second singular value may indicate the close mode. 2.2. Damage indicator method based on modal strain energy The damage indicator method based on modal strain energy (DIM-MSE), which constructs indices from various modal parameters, has been extensively adopted as one of the most effective methods for damage localization. Strain (or curvature) mode shape is sensitive to damage, because of its local behavior [22], and it has been utilized to locate damage sites in beams or frame structures [3,5,23,24]. When strain mode shape is used to identify damage in complex structural systems, such as plate-like structures, issues such as the establishment of an intuitive and effective damage sensitive index and the achievement of an accurate strain mode shape will be of great interest. Cornwell et al. [25] extended the damage indicator method based on modal strain energy for beam-like structures to include the detection of damage in plate-like structures that are characterized by a two-dimensional curvature [25].
2 2 2 bk+1 a j +1 ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2φ + + 2ν + 2 (1 − ν) ∂ x∂ yi dxdy aj bk ∂x2 ∂ y2 ∂x2 ∂ y2 2 2 2 b a ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi ∂ 2 φi + + 2ν + 2 (1 − ν) dxdy 0 0 ∂ x∂ y ∂x2 ∂ y2 ∂x2 ∂ y2
(3) and m is the number of modes to be utilized. φi (x, y) is the i th mode shape of the undamaged state and v is the Poisson ratio. An analogous term fi∗j k can be defined using the damaged mode shape, φi∗ (x, y). The above equation was derived by comparing the fractional strain energies at location j k of a plate before and after damage. More detailed derivations are explained in Ref. [25]. In this study, mode shape curvatures (or strain mode shapes) were computed by numerically differentiating the identified mode shape vectors. At first, the mode shapes are identified from the acceleration data, and then the coarse mode shapes are interpolated into the finer ones using a cubic polynomial function. This is done because the number of sensors used for the mode shapes is limited, and the damage indicator method based on modal strain energy for plate-like structures requires many data points for better resolution. Fig. 3 illustrates the procedure used to calculate the finer mode shape curvatures from the coarse mode shape data. The effect of measurement noise on the mode shapes can be amplified in the mode shape curvatures, since they are calculated from a second derivative. To overcome the noise-sensitive characteristics of the mode shape curvatures, it is recommended to use sufficient records of measurement data, since the effects of noise can be largely alleviated through averaging. To remove the noise amplification in differential operations, the mode shape curvatures can be directly obtained from the dynamic strain data. As the technologies on smart sensors, such as optical fiber sensors, are being rapidly developed, the use of dynamic strain data to accurately calculate the strain mode shapes for the damage
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Fig. 5. A bridge model and the element numbers for girders.
detection of bridge structures is an increasingly promising approach. 2.3. Neural networks technique In recent years, there has been increasing interest in the use of neural networks to estimate and predict the extent and location of damage in complex structures. The neural networks technique, which can be categorized into a model-based damage detection method when it is trained by simulation data, can be an effective tool for the damage assessment of bridge structures. The neural networks technique has the advantage of quick estimation, since it does not require much computation time at the operational stage, once the networks have been properly trained. Another advantage of the neural networks technique for damage estimation is that it is useful in cases that have various types of input data. Moreover, it can effectively deal with the modeling errors that come from the discrepancies between the actual structure and the corresponding numerical model, by incorporating the error-insensitive input data. In this study, the mode shape differences between before and after damage are used as the error-insensitive input data to the neural networks [27]. A popular neural networks model called multi-layer perception neural networks [28–30] was used to identify the element-level stiffness parameters. The networks consist of an input layer, two hidden layers, and an output layer, as shown in Fig. 4. Sigmoid functions are utilized as nonlinear activation functions for all layers. The input layer contains the measured mode shape properties (i.e., the mode shape differences between before and after damage) and the output layer consists of the element-level stiffness indices to be identified as Si = kid /ki0
(4)
where k is element stiffness. Subscript i denotes the element number and superscripts 0 and d represent intact and damaged states, respectively. In this study, the element-level damage severity is defined as αi = 1 − Si .
(5)
The input/output relationship of the neural networks can be nonlinear, as well as linear, and its characteristics are determined by the synaptic weights assigned to the connections between the neurons in two adjacent layers. A systematic way of updating the weights to achieve a desired input/output relationship based on a set of training patterns is referred to as a training or learning algorithm. In this study, the conventional back-propagation algorithm is adopted. Noise injection learning (NIL) was also employed, to reduce the effect of measurement noise [31]. In the NIL algorithm, the training is carried out using the artificially contaminated training patterns with noise of a prescribed level. The generalization capability of the neural networks under noisy conditions can be remarkably enhanced through this algorithm. Noise can be added to the training patterns as x˜ = x + ν N(0,σ )
(6)
where x˜ is a noise-injected input vector and x is an exact input vector. The term ν N(0,σ ) refers to Gaussian random noise with zero mean and standard deviation σ . The noise level σ is application specific. The noise described in the above equation indicates that signal-to-noise (S/N) ratios for all sensor locations are not equal, since the sensors mounted on different locations naturally suffer different uncertainties, even though the imposed noise level is nearly equal. Accordingly, a sensor with a low-amplitude signal will be exposed to a relatively high level of noise.
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Fig. 6. First three mode shapes of a bridge model.
Fig. 7. Effect of noise: σ = 0.5%.
3. A numerical example analysis
one or two element(s). Measurement noise was considered by adding noise into the mode shape, as follows:
3.1. An example bridge structure
φ˜ i = φi + φin NS 1 n φi = φ 2 × N[0, σ ] NS i=1 i
A numerical example analysis was performed on a simply supported bridge model, with multiple girders, to demonstrate the effectiveness of the proposed method for the damage detection of steel girder bridges. The bridge is composed of 10 steel girders, diaphragms, and slabs. It is modeled using beam elements for the steel girders and diaphragms, and shell elements for the concrete slabs in SAP2000 software, as shown in Fig. 5. The first three modes, which are to be used as the input data for damage detection, were calculated for the intact case, as shown in Fig. 6. Damage estimations were carried out for 20 damage scenarios, as described in Table 1. The first 10 damage scenarios are cases with a single damage location (DS1–DS10), while the other 10 cases have two damage locations (DM1–DM10). Damage was simulated by reducing the bending stiffness of the specified element(s): a 30% reduction of bending stiffness in
(7) (8)
where φ˜ i and φi represent the mode shape with and without noise at location i , respectively. The term φin refers to the imposed noise. The term NS refers to the number of sensors, and N [0, σ ] is a random number with zero mean and standard deviation σ . The noise in Eq. (7) has the same amount of uncertainty for all locations according to σ value, regardless of the individual sensor location i . In this study, three different values of σ (0.1%, 0.5%, 1.0%) are investigated. For each σ , 100 noisy mode shapes were randomly generated for intact and damage cases according to Eqs. (7) and (8), respectively. To illustrate the effect of noise imposed by Eqs. (7) and (8), 10 example cases of the randomly perturbed first modes for σ = 0.5% are shown in Fig. 7. The noise with an equal
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Table 1 Success rate (SR) in screening using DIM-MSE (out of 100 cases) Single damage Damage case
El. No
SR (%)
Multiple damage Damage case
El. No.
SR (%)
El. No.
SR (%)
14 15 16 17 18 38 39 40 41 42
100 100 100 100 100 98 100 100 100 100
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
100 100 100 100 100 100 100 99 100 100
87 53 62 53 77 82 45 57 81 105
95 100 100 100 100 100 100 100 100 100
14 15 16 17 18 38 39 40 41 42
43 51 86 95 83 21 42 74 96 80
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
26 55 71 74 73 73 51 63 41 45
87 53 62 53 77 82 45 57 81 105
22 93 24 96 92 40 57 64 63 69
14 15 16 17 18 38 39 40 41 42
28 34 49 69 48 22 28 45 77 57
DM-1 DM-2 DM-3 DM-4 DM-5 DM-6 DM-7 DM-8 DM-9 DM-10
14 15 16 16 16 16 27 27 27 27
33 32 47 44 43 41 38 36 24 34
87 53 62 53 77 82 45 57 81 105
19 67 15 70 68 33 44 43 49 48
(a) 0.1% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10 (b) 0.5% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10 (c) 1.0% noise DS-1 DS-2 DS-3 DS-4 DS-5 DS-6 DS-7 DS-8 DS-9 DS-10
amount of uncertainty has different effects on the mode shapes: the noise level of σ = 0.5% can be very high at the nodal points with small amplitude of the mode shape and relatively low at the points with large amplitude of the mode shape. The noise level of σ = 0.5% for the first mode shape rises to 4% of the exact mode shape at the nodal points, as shown in Fig. 7. 3.2. Screening using a damage indicator method based on modal strain energy At first, a damage indicator method based on modal strain energy (DIM-MSE) for plate-like structures was utilized for screening potentially damaged members of a bridge model. Twenty elements with the higher damage indices out of 120 elements were selected as the potentially damaged members. This screening criterion corresponds to the confidence level of z = 1.0 for the standard normal distribution, where z is the standard normal random variable. Table 1 summarizes the results of the screening process. The success rate (SR) is defined as the number of successful identifications during the
screening process out of 100 randomly perturbed cases for each damage case. When an actually damaged member was among the 20 potentially damaged members identified, the first step for screening was considered successful. The success rate in the screening process is closely related to the noise level, as shown in Table 1: the actually damaged member(s) was (were) successfully identified when the noise level was small (σ = 0.1%), and the SR decreased as the noise level increased. For example, the SR for Damage Case DS-1 was 43% when σ = 0.5%. This means that an actually damaged member (Element 14) was included in the identified 20 potentially damaged members 43 times (simulation cases) out of 100 times (simulation cases). An SR of 43% may seem to be a disappointing result; however, it is very difficult to consistently recognize an actually damaged member, or members, with the presence of a significant noise level. Moreover, the screening process naturally yields an SR of 16.7% to each element under random noise at an intact state, when 20 elements randomly selected out of 120 elements are assumed to be damaged. Therefore, it is more reasonable to investigate the trend of an
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(a) Cases with single damage: DS-1, 3, 5, 7, 9. Fig. 8. Probability of damage occurrence using 100 records with the noise of σ = 0.5%. (The exact locations of damage are marked with arrows (↓).)
SR for all the elements, rather than the specific value of an SR for a certain element. Fig. 8 shows the probability of damage occurrence as calculated from the screening process, using 100 noisy data sets, each with a noise level of σ = 0.5%. At first, 20 elements with higher damage indices out of the 120 elements were selected as potentially damaged members for each record. Then, the frequency of damage alarming (i.e. the number of being identified as a potentially damaged member) was calculated for every elements. Finally, 20 elements with higher frequencies of damage alarming were selected as potentially damaged members. Dashed lines in Fig. 8 divide the 20 potentially damaged elements from the remaining elements. The probability of damage occurrence, i.e. the frequency of damage alarming for 100 data sets, corresponds to the result of the success rate, as shown in Table 1(b). From these results, it can be concluded that a comparison of the damage alarming frequency for all elements provides a reliable indication, while the specific values of the success rate provide only ambiguous results.
3.3. Damage assessment using neural networks The neural networks technique with a back-propagation algorithm was used to localize the damaged members and to assess the damage severities. Only the potentially damaged members that were identified in the previous stage need to be considered in this networks configuration. In addition, only a few modal components measured at the identified potentially damaged regions are used to assess the damage locations and severities more accurately. Fig. 9 shows some example cases for damage assessment. In Fig. 9, a single measurement record with a noise level of σ = 0.5% was used as the input to the networks. At first, 20 potentially damaged members were determined by the probability of damage occurrence calculated from 100 noisy records, as shown in Fig. 8. Then, a more detailed identification was performed on the potentially damaged members using the 100th record of noisy data, assuming that the latest data set is being continuously stored in the measurement system. The damaged member(s) was (were) reasonably identified when the actually damaged member(s)
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(b) Cases with multiple damage: DM-1, 3, 5, 7, 9. Fig. 8. (continued)
was (were) selected as the potentially damaged member(s) in the first step, whereas the estimated results still showed lots of false alarms and fairly large errors as shown in Fig. 9, since they were calculated based on the single set of noisy data. The results of DM-1 and DM-3, shown in Fig. 8(b), demonstrate that it is very important to not miss the actually damaged members during the first stage. Averaging is the easiest and the most effective means to enhance the accuracy of the screening process, as well as the estimate of the second stage. Fig. 10 shows some typical results using the averaged data of 10 and 20 noisy records. Twenty members with large value of damage index were considered at the second stage. The results of the damage assessment using the averaged data set yielded much better results as the number of data sets increased: the false alarms were alleviated and the estimated damage severity for the actually damaged member was close to the true value (30%) with less than 10% error. The effects of the measurement noise were remarkably reduced, since the averages of 10 and 20 sets of measurement data with 0.5% noise level can be regarded as a single record with 0.16% and 0.11%
noise level, respectively. From these results, it can be concluded that averaging a sufficient amount of measurement data should precede the damage diagnosis, to not miss the actually damaged members and to enhance the estimation accuracy. The accuracy in the screening process can be improved more when the averaging is performed on the input data, and the frequency of damage alarming is used as an occurrence indicator. 4. Field tests on a steel girder bridge 4.1. Description of experiments Field tests of damage estimation were performed on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea (Fig. 11), which is to be replaced during bridge renovation. The span is simply supported, with a length of 22.7 m. It is composed of nine steel plate girders and a concrete slab. Originally, it had 10 girders, but the 10th girder was removed during the construction of the newly built bridge next to it. Ambient vibration tests were carried out for the vertical accelerations on the bridge deck. The vibration
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(a) DS-1.
(b) DM-7. Fig. 9. Examples of damage assessment using neural networks (σ = 0.5%). (The exact locations of damage are marked with arrows (↓).)
was mainly induced by the traffic loads on the adjacent new bridge and by the train and vehicle loads under the test bridge. Seven sets of measurements were carried out on Girders 1 to 7, as shown in Fig. 12. For each set of measurements, vertical accelerations were measured at 11 equally spaced points on the slab just above each girder. Reference signals to correlate each experimental set were obtained at seven points (R1–R7). Fig. 12(c) shows a typical case of the acceleration time history obtained from the ambient vibration test. Acceleration signals were measured for more than 2 h for each damage case with the sampling frequency of 100 Hz. The number of samples used to calculate the Fourier transform is 8192. Averaging was performed about 200 times with overlapping for each damage case, to alleviate the non-stationary characteristics of the ambient vibration tests and to reduce the measurement noise. Fig. 13 shows the inflicted damage scenarios imposed by torch cuts on the main girders of the bridge for the present damage detection study. Modal parameters for each damage state were identified using the frequency domain decomposition method [19,20]. Table 2 shows the modal properties calculated from the initial finite element (FE) model and those estimated from the experiments for each damage case. The measured first natural frequencies do not show a close correlation to the
imposed damage. This indicates the difficulty in using resonant frequencies as damage indicators for large civil engineering structures, where the environmental and operational effects such as temperature, humidity and traffic volume may not be ignored. Accordingly, the natural frequency information was not used in the damage detection procedure. In Table 2, the modal assurance criteria (MAC) values are also shown, which represent the closeness between the calculated and the experimental mode shapes. The first three modes gave close results to the test results: above 97% in MAC value. Therefore, the first three mode shapes were used as inputs for the damage estimation. The mode shapes were used to calculate the strain mode shape (the second derivative of mode shape) for the screening process, and the mode shape differences between before and after damage, which are found to be less sensitive to the modeling errors, were used as the input to the neural networks [27]. 4.2. Screening using a damage indicator method based on modal strain energy In the first step, a damage indicator method based on modal strain energy (DIM-MSE) for plate-like structures was used to screen potentially damaged members of the test bridge. The
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(a) Using average of 10 records: DS-1.
(b) Using average of 20 records: DM-7. Fig. 10. Damage assessment using averaged data (σ = 0.5%). (The exact locations of damage are marked with arrows (↓).) Table 2 Natural frequencies and modes of Hannam Grand Bridge for various damage cases Modes
1st mode
2nd mode
3rd mode
Calculated (intact)
4.071 Hz
4.452 Hz
5.626 Hz
4.247 Hz (99.79) 4.188 Hz (99.38) 4.196 Hz (99.90) 4.218 Hz (99.51)
4.876 Hz (97.86) 4.903 Hz (99.45) 4.780 Hz (99.35) 4.757 Hz (99.56)
5.771 Hz (99.71) 5.823 Hz (99.64) 5.778 Hz (99.57) 5.799 Hz (99.73)
Measured
Intact Damage I Damage II Damage III
Measured mode shapes (Intact case)
Note: Values in parentheses are the MAC values (%).
first three modes for all of the intact and damaged cases, which are measured at 77 points with dimensions of 7 (girders) by 11 (sensor locations), were interpolated into the finer mode shapes using a cubic polynomial function, to numerically calculate the mode shape curvatures. Fig. 14 shows the damage
indices calculated from DIM-MSE. The bright locations correspond to the potentially damaged regions. The damage locations were identified with good accuracy for all damage cases, while there were some false damage alarms at several locations.
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(a) Overview of old and new bridges.
(b) Northern-most span of old bridge (L = 22.7 m).
(c) Section view of old bridge. Fig. 11. View of Hannam Grand Bridge in Seoul, Korea.
4.3. Damage assessment using neural networks The conventional back-propagation neural networks technique with a noise injection learning algorithm was used for a detailed damage diagnosis. Only the potentially damaged members identified in the first step were considered in the networks configuration. The number of potentially damaged members to be investigated at the second stage is user-defined, but it should be determined by considering the network complexity and damage missing errors. The larger the number of potentially damaged members we choose is, the lower the damage missing errors is but the more complex the network configuration is. In this study, 20 elements with the higher damage indices out of 70 elements were selected as the potentially damaged members. The mode shape differences between before and after damage, which are found to be less sensitive to the modeling errors [27], were used as the input to the neural networks. The potentially damaged members considered in the second step were as follows:
Damage Case I: 20 Elements (Element 4, 5, 6, 7, 9, 14, 15, 17, 18, 36, 37, 43, 44, 45, 46, 47, 54, 55, 56, 57) Damage Case II: 20 Elements (Element 4, 5, 6, 7, 8, 14, 15, 16, 17, 18, 44, 45, 46, 47, 56, 57, 74, 75, 76, 77) Damage Case III: 20 Elements (Element 15, 16, 17, 18, 23, 24, 25, 26, 44, 45, 46, 47, 54, 55, 56, 57, 64, 65, 66, 67) Fig. 15 shows the results of the damage assessment using neural networks. The numbers of input, 1st hidden, 2nd hidden, and output nodes in the networks are 60–80, 20, 20 and 20, respectively. The number of input nodes is determined by considering the spatial distribution of the identified potentially damaged members and the magnitude of the mode shapes at those points. The results of the damage assessment showed a good estimate for all the damage cases, even though there were many false alarms in the first step. The actually damaged member(s) showed large value(s) of damage severity and the
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(a) Damage locations and element numbers.
(a) Sources for ambient vibration test. (b) Inflicted damage. Fig. 13. Damage scenarios for Hannam Grand Bridge.
(b) Measurement locations (1–77: Roving sensor positions, R1–R7: Reference sensor numbers).
For accurate evaluation of damage assessment, the actual damage locations should be identified first, and then the damage severities of the corresponding structural members are to be assessed. However, in this study, estimation of damage location and severity was carried out together at the second stage to effectively deal with a number of structural members. Thorough inspection of a damaged member is beyond the scope of this study. Various non-destructive evaluation (NDE) techniques can be incorporated for accurate evaluation of structural integrity, after identifying the potentially damaged members with informative damage severities using vibrationbased damage estimation methods. 5. Conclusion
(c) Acceleration time history (at sensor position 39). Fig. 12. Ambient vibration tests.
members with false alarms showed small values, since the noise injection learning algorithm was effectively used to reduce the effect of noise.
In this study, an effective method has been presented for the damage detection of steel girder bridges using ambient vibration data. Modal parameters were identified from ambient vibration data using the frequency domain decomposition technique and were utilized as the input feature vectors for damage diagnosis. The conventional back-propagation neural networks with a noise injection learning algorithm were incorporated to assess damage locations and damage severities based on modal parameters. To alleviate ill-posedness in the inverse problem, the potentially damaged members were screened using the modal strain energy based damage indicator method, in which the mode shape curvatures were calculated from the second derivatives of the identified mode shapes. The effectiveness of the proposed method was demonstrated by a numerical example analysis on a simply supported bridge model with multiple girders, and by a field test on the northernmost span of the old Hannam Grand Bridge over the Han River in Seoul, Korea.
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(a) Damage Case I.
(a) Damage Case I.
(b) Damage Case II.
(b) Damage Case II.
(c) Damage Case III. Fig. 15. Results of damage assessment using neural networks. (The exact locations of damage are marked with arrows (↓).)
(c) Damage Case III. Fig. 14. Results of screening using DIM-MSE.
In a numerical example analysis, 100 randomly perturbed cases for each damage case were considered. A comparison of the damage alarming frequency for all elements provides a reliable indication, while the specific values of the success rate provide only ambiguous results in the screening process. The
damaged member(s) was (were) reasonably identified when the actually damaged member(s) was (were) selected as the potentially damaged member(s) in the first step, whereas the estimated results still showed fairly large errors because of noise. Using the averaged data of 10 and 20 noisy records, the effects of measurement noise were remarkably reduced. The results of the damage assessment using the averaged data set provided much better results as the number of data sets increased. From these results, it can be concluded that averaging a sufficient amount of measurement data should precede the damage diagnosis, to not miss the actually damaged members and to enhance the estimation accuracy. In the field tests, the first three modes for all of the intact and damaged cases, which are measured at 77 points with dimensions of 7 (girders) by 11 (sensor locations), were interpolated into the finer mode shapes using a cubic polynomial function to numerically calculate the mode shape curvatures. The damage locations were identified with good
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accuracy for all damage cases, while there were some false damage alarms at several locations in the screening process. The results of damage assessment using neural networks with a noise injection learning algorithm showed a good estimate for all the damage cases, even though there were many false alarms in the first step. The actually damaged member(s) showed large value(s) of damage severity and the members with false alarms showed small values, since the noise injection learning algorithm was effectively used to reduce the effects of noise. Acknowledgement This study is supported by the Smart Infra-Structure Technology Center (SISTeC) at KAIST, which is sponsored by the Ministry of Science and Technology (MOST) and the Korea Science and Engineering Foundation (KOSEF). Their financial support is gratefully acknowledged. References [1] Doebling SW, Farrar CR, Prime MB. A summary review of vibrationbased damage identification methods. The Shock and Vibration, Digest 1998;30(2):91–105. [2] Zou Y, Tong L, Steven GP. Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures — A review. Journal of Sound and Vibration 2000;230(2): 357–78. [3] Pandey AK, Biswas M, Samman MM. Damage detection from changes in curvature mode shape. Journal of Sound and Vibration 1991;145:312–32. [4] Kim JT, Stubb N. Model uncertainty impact and damage-detection accuracy in plate girder. Journal of Structural Engineering, ASCE 1995; 121(10):1409–17. [5] Worden K, Burrows AP. Optimal sensor placement for fault detection. Engineering Structures 2001;23(8):885–901. [6] Yam LH, Li YY, Wong WO. Sensitivity studies of parameters for damage detection of plate-like structures using static and dynamic approaches. Engineering Structures 2002;24(11):1465–75. [7] Huang NE, Shen Z, Long SR. A new view of nonlinear water waves: the Hilbert spectrum. Annual Review of Fluid Mechanics 1999;31:417–75. [8] Hou Z, Noori M, St Amand R. Wavelet-based approach for structural damage detection. Journal of Engineering Mechanics, ASCE 2000; 126(7). [9] Quek ST, Wang Q, Zhang L, Ong KH. Practical issues in the detection of damage in beams using wavelets. Smart Materials and Structures 2001; 10:1009–17. [10] Loutridis SJ. Damage detection in gear systems using empirical mode decomposition. Engineering Structures 2004;26(12):1833–41. [11] Stetson KA, Harrison IR. Redesign of structural vibration modes by finite element inverse perturbation. Journal of Engineering for Power, ASME 1981;103:319–25.
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