Structural Damage Detection Using Local Damage Factor

Structural Damage Detection Using Local Damage Factor SHANSHAN WANG QINGWEN REN Department of Engineering Mechanics, College of Civil Engineering, Hohai University, Nanjing, Jiangsu 210098, P. R. China

PIZHONG QIAO Department of Civil and Environmental Engineering, Washington State University, Pullman, WA 99164-2910, USA ([email protected]) (Received 13 January 2006; accepted 16 May 2006)

Abstract: Damage in a structure alters its dynamic characteristics. Significant research has been conducted in damage detection and structural health monitoring using dynamics-based techniques. But simultaneously determining the presence, severity, and location of damage using the existing damage detection methods can still prove challenging. In this study, a new practical method of structural damage detection called Local Damage Factor (LDF) is presented, which is capable of determining the presence, severity, and location of structural damage at the same time. By including the dynamic characteristics of the intact local structure in the LDF method, the influence of structural nonlinearity, imperfections, and system noise is considered, so that the accuracy of damage detection is improved. Furthermore, a modified LDF (MLDF) method is proposed, which can detect damage without requiring benchmark data for the intact local structure. As a demonstration, the proposed LDF and MLDF methods are applied to damage detection in a 3-D steel frame structure, and the experimental results indicate that both methods can effectively determine the presence, severity, and location of a crack cut into one of the pillars in the frame with a saw. The LDF method is effective in a way that can eliminate both the nonlinear severity effect of structure itself and the ambient noise inherent in the intact structure, whereas the MLDF method is advantageous in that it does not require information about the intact local structure, which is often unavailable for damage detection. The proposed LDF method of in situ damage detection is illustrated using the concrete columns in a wharf structure. The successful detection of damage in the 3-D steel frame, as well as the wharf, demonstrates that the proposed local damage factor technique can be effectively and efficiently used in damage detection and structural health monitoring of structures.

Key words: Damage detection, dynamic testing, nonlinear severity, structural health monitoring

1. INTRODUCTION Effective detection of structural damage is one of the most important factors in maintaining safety and integrity of the structures and avoiding loss of human life due to the catastrophic failure of undetected structural damage. Changes in the physical properties of a structure due to the existence of damage can alter its dynamic responses, such as the natural frequency,

Journal of Vibration and Control, 12(9): 955–973, 2006 c 2006 SAGE Publications Figures 1, 3, 5–20 appear in color online: http://jvc.sagepub.com

DOI: 10.1177/1077546306068286

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vibration signal response, and mode shapes. These parameter changes can be extracted to predict damage information, such as the presence, severity, and location of damage within the structure. Thus, these parameter changes obtained, from dynamic tests, provide a viable means of damage detection and structural health monitoring. Due to the simplicity of its implementation, the dynamic response-based damage detection method attracts most attention. Significant research (Doebling et al., 1998; Carden and Fanning 2004) has been conducted into dynamic response-based damage detection methods. Early damage detection methods were generally based on the frequency changes, because frequency measurements can be conducted quickly, and are often reliable. Salawu (1997) reviewed the studies of using frequency response for damage detection. One advantage of this approach is the global nature of the identified frequencies, allowing the measurement points to be customized. However, many of these studies require either a theoretical model of damage or a set of sensitivity values to be computed before the physical measurements. In addition, the changes in natural frequency alone may not be sufficient for a unique identification of the location of structural damage. For example, cracks with the same crack length but at two different locations may cause an identical frequency change. On the other hand, the mode shapes provide more information for damage detection, and can be used to determine the location of damage within a structure. Pandey et al. (1991) introduced curvature mode shapes as a candidate for identifying and locating damage in a structure. By using a cantilever as well as a simply supported analytical beam model, it was shown that the absolute changes in the curvature mode shapes were localized in the region of damage and hence could be used to detect damage in a structure and determine its location. The changes in the curvature mode shapes increase with increasing size of damage, and this information can be used to determine the severity of the damage. Wahab and Roeck (1999) conducted an experimental damage detection study using the curvature mode shapes of a real structure. Jun and John (1999) observed that the traditional mode shapes are not sensitive to damage. Recently, Hamey et al. (2004) applied experimentally determined curvature mode shapes to locate various types of damage in laminated composite beams. The major drawback of the traditional mode shape-based methods is the need for a large number of measurements to acquire accurate mode shapes. In recent years, many alternative methods using dynamics-based techniques have been developed in the area of damage detection. Chinchalkar (2001) proposed a numerical method for determining the location of a crack of varying depth in a beam when the lowest three frequencies of the cracked beam are known. Lu et al. (2002) developed two efficient methods for detecting multiple damage locations in beam structures. Ren and Roeck (2002) proposed a damage identification scheme to establish the relationship between the damage and the changes in the structural dynamic characteristics. Pothisiri and Hjelmstad (2003) presented a global damage detection and assessment algorithm based on a parameter estimation method using a finite element model and the measured modal response of a structure. Kim and Stubbs (2003) developed a nondestructive crack detection scheme to locate a crack and estimate the crack size using changes in the modal parameters of bridges. Barroso and Rodriguez (2004) used a new damage index to determine the location and severity of damage. Most recently, Wang and Qiao (2006) developed two damage detection algorithms (the simplified gapped smooth method and generalized fractal dimension method) for locating damage in beam-type structures based on the uniform load surface. Carden and Fanning

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(2004) recently reviewed the state of the art in vibration-based condition monitoring with particular emphasis on structural engineering applications. Although research efforts have been made to improve the accuracy of damage detection, simultaneously determining the presence, severity and location of damage using existing methods is still in problematic. Furthermore, existing damage detection methods pay little attention to the random effects of the environment and testing equipment. In this study, a new damage detection index called the local damage factor (LDF) is introduced. The difference of local damage factors between the intact and damaged cases is utilized to assess the damage in a structure, and the LDF method can determine the presence, severity and location of structural damage. Further, a modified local damage factor (MLDF) is proposed as well, which does not require information about the intact local structure to be able to detect the damage. A 3-D steel frame structure is evaluated by dynamic testing to demonstrate the proposed LDF and MLDF methods, and their relative advantages are discussed. Finally, the application of the LDF method to in situ damage detection of concrete columns in a wharf structure is presented.

2. THEORETICAL BACKGROUND In this section, the theoretical background of the proposed local damage factor (LDF) and modified LDF methods is introduced. In a dynamic structural system, x(t) is one random vibration signal in the entire structure and y(t) is the other random vibration signal in the local structure or component of a structure. All the random processes considered are stationary and erratic. The correlation between x(t) and x(t + τ ) or between y(t) and y(t + τ ) is known as the auto-correlation, and is expressed by

1 Rx x (τ ) = lim T →∞ T

x(t)x(t + τ )dt

(1a)

y(t)y(t + τ )dt

(1b)

0

1 T →∞ T

R yy (τ ) =

T

T

lim

0

Similarly, the correlation between x(t) and y(t + τ ) is known as the cross-correlation, and is given by 1 T →∞ T

T

Rx y (τ ) = lim

x(t)y(t + τ )dt

(2)

0

The auto-spectral density Sx x (ω) or Syy (ω) is obtained by using the Fourier transform of the auto-correlation function Rx x (τ ) or R yy (τ ) as Sx x (ω) =

1 2π

Syy (ω) =

1 2π

+∞

−∞

+∞

−∞

Rx x (τ )e−iωτ dτ

(3a)

R yy (τ )e−iωτ dτ

(3b)

958 S. WANG ET AL. In the same way, the cross-spectral density Sx y (ω) is obtained by using the Fourier transform of the cross-correlation function Rx y (τ ) as Sx y (ω) =

1 2π

+∞

−∞

Rx y (τ )e−iωτ dτ

(4)

From equations (3) and (4), the generalized coherence function is defined as γ x y (ω) =

Sx y (ω) Sx x (ω)Syy (ω)

(5)

The value of the generalized coherence function indicates the severity of nonlinearity between the local structure and the entire structure. Damage in a structure usually reduces the stiffness of local structure where the damage occurs, and it correspondingly increases the nonlinear severity between the local structure and the entire structure. Therefore, structural damage can be detected by considering the value of the generalized coherence function, which corresponds to the nonlinear severity or local stiffness reduction. By considering the nonlinear effect of both the structure itself and the testing system, the system effect coefficient (SEC) is defined as SEC = 1 − γ ix y (ω)

(6)

where γ ix y (ω) is the generalized coherence coefficient between the intact (healthy) local structure and the entire structure. Thus, the SEC indicates the nonlinear severity between the intact local structure and the entire structure, which is primarily caused by the effects of the structure itself and of testing system noise. If there is damage present in the local structure, a new damage indicator, the local damage factor (LDF), is then introduced, and is defined as LDF = 1 − γ dx y (ω) − SEC

(7)

where γ dx y (ω) is the generalized coherence coefficient between the damaged local structure and the entire structure. Based on equations (5) to (7), the LDF can be rewritten as LDF =

i S xy

i (ω) Sxi x (ω)Syy

−

d S (ω) xy d (ω) Sxdx (ω)Syy

(8)

i where Sxi x , Syy , and Sxi y are the auto-spectral densities and cross-spectral density of the intact d structure, while Sxdx , Syy , and Sxdy are the auto-spectral densities and cross-spectral density of damaged structure. If damage is present in the structure, it changes the value of the LDF; hence, the LDF can be used as a damage indicator (index) for detection of structural damage. As indicated in equation (8), the system effect coefficient of the intact structure is included in the calculation


of the LDF. Thus, the LDF can filter out the nonlinear effects of the structure itself and of testing system noise. However, calculation of the LDF requires the use of data from the intact structure, which may not be available for an already damaged structure. To overcome the requirement for the data from the intact structure in calculating the LDF value, a modified local damage factor (MLDF) is introduced: MLDF = 1 −

γ dx y (ω)

=1−

d S (ω) xy d (ω) Sxdx (ω)Syy

(9)

As indicated in equation (9), the MLDF method is based on the generalized coherence coefficient between the damage local structure and the entire structure, and thus information related to the intact structure is not required. Although the MLDF method is convenient and does not need any information about the intact structure as a benchmark, it is unable to take the nonlinear severity effects of the structure itself and the testing system noise into consideration. Therefore, it may lead to reduced accuracy in damage detection, if the effects of system nonlinearity and testing noise are significant. In the following sections, the magnitudes of both the LDF and MLDF values are used as damage indices to determine the presence, location, and severity of damage.

3. DAMAGE DETECTION OF A FRAME STRUCTURE 3.1. Experimental Procedures

The objectives of the experimental study are two-fold: to validate the proposed concept of the Local Damage Factor (LDF) in damage detection in a real structural application, and to demonstrate the advantages and disadvantages of the LDF and modified LDF (MLDF) methods in damage detection. A three-dimensional (3-D) steel frame structure (shown in Figure 1) is considered in this study. The frame consisted of four vertical pillars, each 12 × 12 × 500 mm, welded to a flat top plate measuring 346 × 346 × 22 mm. The pillars form a square with sides of length 300 mm. A conceptual sketch of the 3-D frame structure is given in Figure 2, which also shows the location and direction of the excitation force, and the location of the transducers measuring the vibration response. Structural damage in the frame structure is simulated by saw-cutting cracks with different depths across the whole width of a pillar. A crack in one of the pillars, located about 100 mm below the steel top plate is shown in Figure 3. Four accelerators are used as the transducer; the location of the crack and arrangement of the transducers are shown in Figure 4. In particular, two transducers are mounted near the crack (about 20 mm above and below the crack, see Figure 4), and are used primarily to determine the location of the crack. In this study, four cases of undamaged and damaged pillars (local structures) are experimentally investigated: (A) intact (undamaged); (B) 6 mm deep crack; (C) 10 mm deep crack; and (D) through-depth (12 mm deep) crack, in which the pillar is fully separated to simulate a fully damaged local structure. The excitation equipment is an electromagnetic vibration system controlled by a COMET shaker control system. The data acquisition and analysis are performed using a dynamic an-

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Figure 1. Steel test frame.

Figure 2. Sketch map of frame structure.


Figure 3. Crack in the pillar.

Figure 4. Dimensions (mm) of structure and arrangement of transducers.

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alyzer with a parallel multi-channel function. Before the experiment, the natural frequency along the excitation force direction is measured using the resonance method. The first natural frequency of the structure was determined to be 15.66 Hz. The excitation force is introduced as random vibration with bandwidth between 10 Hz and 30 Hz and a constant 0.3 (m/s2 )2 /Hz acceleration PSD level. 3.2. Experimental Results and Discussion

In Figures 5 and 6, the amplitude/time histories of acceleration transducers No.1 and No. 2 for the intact pillar (Case A) are plotted. By using the vibration data received by these two transducers and equation (6), the SEC of Case A, which indicates the nonlinear severity between the intact local structure and the entire structure, was obtained (see Figure 7). The maximum value of the SEC shown in Figure 7 is about 5%, and occurs at a frequency of 15.25 Hz which is very close to the first natural frequency of the structure as measured by the aforementioned resonance method. For each case, the LDFs are calculated based on Equation (8), and the LDF values of the four cases (Cases A to D) are shown in Figures 8 to 11. As expected, the LDF value of the intact structure (Case A) in Figure 8 is equal to 0, since there is no damage in the structure and the nonlinear severity effects of structure itself (e.g. imperfections) and system noise are eliminated. The LDF distribution of the 6 mm deep crack (Case B) is given in Figure 9, and has a maximum value of about 13%; this occurs at a frequency of 15.20 Hz, which is slightly smaller than the first natural frequency of the intact structure (Case A). The reduction in the first natural frequency in the structure with the 6 mm deep crack pillar is due to the introduction of damage. Similarly, the maximum value of LDF for the 10 mm deep crack (Case C) is around 69%, and also occurs at the first natural frequency of the structure, as shown in Figure 10. Finally, the LDF distribution of the fully separated pillar (Case D) is given in Figure 11; this has a dramatically different pattern to that shown in the other cases. The maximum value of the LDF for Case D is close to 97%, at a frequency of 17.11 Hz, which is not the first natural frequency of the structure. As shown in Figures 8 to 11, the LDF value increases with the increasing severity of the damage. Hence, the LDF method can be used as a damage index and is capable of evaluating both the presence and relative severity of structural damage. The LDF data shown in Figures 8 to 11 were obtained from acceleration transducers No. 1 and 2. In the following, the signal received by the No. 3 transducer, which is located 20 mm above the crack damage (see Figure 4), is used in the data reduction, instead of the signal from the No. 2 transducer, which is 20 mm below the crack. The LDF value calculated using transducer No. 3 for the damaged structure with the 6 mm deep crack in the pillar (Case B) is plotted in Figure 12. It can be seen that the maximum LDF value suddenly changes from 13% (Figure 9) to 3% (Figure 12) as the transducer is relocated from the measuring position below the crack to above the crack. The sudden change in LDF value indicates something abnormal between the transducers No. 2 and No. 3 (i.e. where the crack is). Thus, the damage in the structure can be located by the LDF method through careful positioning and movement of the transducers. It also indicates that the LDF method can be used to evaluate the structural damage with little effort. Figures 8 to 12 demonstrate how the presence, severity, and location of the damage are all evaluated by the LDF method to


Figure 5. Signal received by No.1 transducer.

Figure 6. Signal received by No. 2 transducer.

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Figure 7. SEC value of the intact structure (Case A).

Figure 8. LDF value of the intact structure (Case A) (LDF = 0).


Figure 9. LDF value of the damage structure with the 6 mm deep crack (Case B).

Figure 10. LDF value of the damage structure with the 10 mm deep crack (Case C).

966 S. WANG ET AL.

Figure 11. LDF value of the damage structure with the fully separate pillar (Case D).

Figure 12. LDF value computed by the No. 3 transducer for the 6 mm deep crack (Case B).


Figure 13. LDF value computed from the alternative SEC.

some extent, which is nonetheless relatively simple, straightforward, fast and inexpensive to implement. All the analysis presented above requires information about the intact structure. In some real damage detection situations, however, information from the intact structure may not be available. Thus, neither the SEC in Equation (6) nor the nonlinear severity between the intact local structure and the entire structure can be obtained. In this case, an intact local structure (in this case, one of the other three pillars in the frame), which is similar to the damaged local structure (the damage pillar), is used in equation (6) to obtain the SEC, which is then called the alternative SEC. For example, in this study, the No. 4 transducer mounted on an intact pillar (see Figure 4) is used instead of the No. 2 transducer on the damaged pillar to compute the SEC value. From this SEC value and Equation (8) the LDF value (Figure 13) is obtained for the pillar with the 6 mm deep crack (Case B). From Figure 13, it can be seen that the maximum LDF value is about 14% and occurs at the frequency of 15.20 Hz; comparing with Figure 9, the LDF values in these two cases (i.e. the SEC from the original intact pillar in which damage is later induced (Figure 9) and the alternative SEC from a different, intact, pillar (Figure 13)) are almost identical. Thus, the concept of using the alternative intact pillar to obtain the LDF method is viable for detection of damage within a real structure. The values of MLDF are also calculated for the aforementioned four cases (A to D) using equation (9), and are plotted in Figures 14 to 17. As is to be expected, the MLDF value for Case A is about 5%; the same as the SEC value of the intact structure (Figure 7). Since the MLDF method is not capable of eliminating the nonlinear severity effects of the structure itself and the testing noise, 5% of the MLDF value is thus related to the ambient

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Figure 14. MLDF value of the intact structure (Case A).

testing noise and the structure itself, rather than any actual damage. For Case B (Figure 15), the MLDF value is about 16%, which is different from 13% of the LDF value (see Figure 9). Again, the higher MLDF value is caused by the nonlinear severity effect of structure itself and testing noise, which cannot be filtered out by the MLDF method. For Cases C and D, the MLDF values are 69% (Figure 16) and 97% (Figure 17), respectively; about the same as for the LDF method, suggesting that the nonlinear severity effect of the intact structure and testing noise may not affect the proposed damage detection methods greatly if the local damage is relatively large and the nonlinear severity effect of the damage dominates the LDF or MLDF spectrum. Thus, the MLDF method has the additional advantages of determining the damage without the need for information from the intact structure and having the same validity as the LDF method in cases of major damage. However, the MLDF method is not capable of eliminating the nonlinear severity caused by the structural imperfection and experiment ambient noise; thus, it may be less effective and accurate when the damage is relatively small and the effects of the structure and ambient noise are significant. In such a case, the MLDF may provide false information which is not related to damage but instead due to structural imperfections and/or testing noise, as shown in Figure 14 for the intact local structure (Case A). The MLDF method was next used to locate the damage by comparing the maximum MLDF values between transducers No. 2 and No. 3. The MLDF from transducer No. 3 for the 6 mm deep crack (Case B) is plotted in Figure 18, and has a maximum value of about 5%, while the maximum MLDF value from transducer No. 2 is around 16% (see Figure 15). The large difference between the MLDF values from these two transducers indicates that a defect exists between them, validating the ability of the MLDF method to locate the damage.


Figure 15. MLDF value of the damage structure with the 6 mm deep crack (Case B).

Figure 16. MLDF value of the damage structure with the 10 mm deep crack (Case C).

970 S. WANG ET AL.

Figure 17. MLDF value of the damage structure with the fully separate pillar (Case D).

Figure 18. MLDF value computed by the No. 3 transducer for the 6 mm deep crack (Case B).


Figure 19. A crack on the concrete pile in the wharf.

4. IN SITU DAMAGE DETECTION OF A WHARF STRUCTURE As an implementation of the proposed LDF method in practice, the heath condition and damage (i.e. cracks) in the concrete piles of a wharf in Ningbo port in China was evaluated. As shown in Figure 19, a typical crack was found in one of the piles under the wharf. To implement the method, a mechanical vibration system called TJQ-4 was used as the shaker to induce a sweep sine wave in the structure. The sweeps took place over a frequency range from 2 to 6 Hz. Only two transducers were applied in the experiment: one transducer was located on the top surface of the wharf, while the other transducer was mounted on the pile somewhere below the crack. Using the data from these two transducers and Equation (8), the LDF value (Figure 20) was computed. The maximum LDF value shown in Figure 20 is about 12.2%, and occurs at a frequency of 3.45 Hz, which is the third order resonance frequency of the wharf (Wang and Ma 2002). Thus, the in-situ structural damage could be detected successfully by using the proposed LDF method.

5. CONCLUSIONS A new structural damage detection method based on the local damage factor (LDF) is presented in this study, and is based on the principle that the nonlinear severity effect between the local and entire structure will increase if the local structure suffers a loss of stiffness due

972 S. WANG ET AL.

Figure 20. LDF value of the damaged concrete pile in the wharf.

to damage. The LDF value is used to determine the presence, severity and location of structural damage, and the accuracy of damage detection is improved by including the influence of structural nonlinearity and system noise. The experimental results for a 3-D frame structure demonstrate the validity and effectiveness of the proposed LDF method, even in cases where the nonlinear severity effects of the structure itself and testing system noise are significant. Further, a modified LDF method is introduced, in which information about the intact local structure is not needed, and this also shows promise in damage detection. The experimental study of the frame structure and in situ demonstration of the technique on a concrete wharf pile indicate that the proposed LDF and MLDF methods could determine structural damage with minor equipment (in this case, a few transducers and a shaker) and are a relatively simple and straightforward approach suitable for effective and efficient damage detection and structural health monitoring of a real structure. Acknowledgments. The authors acknowledge f inancial support from the National Natural Science Foundation of China (NSFC) (Grant No. 50379005) and the Science and Technology Foundation of Hohai University (Grant No. 2002404543). The third author (PQ) acknowledges and is grateful for the support and visiting professorship provided by Hohai University.

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