Damage Identification of Timber Bridges Using ...

Eleventh Asia-Pacific Vibration Conference, 23th – 25th November 2005, Langkawi, Malaysia

Damage Identification of Timber Bridges Using Vibration Based Methods Li Ja, Samali Ba, Choi FCa and Dackermann Ua a

Centre for Built Infrastructure, Faculty of Engineering, University of Technology Sydney, NSW 2007, Australia.

In recent years, a great deal of attention has been paid to the declining state of the aging infrastructure around the world including Australia. The ability to detect damage at their early stage can reduce the costs and down-time associated with repair of critical damage with enhanced safety and reliability of infrastructures. In this paper, development of a dynamic based method for localization and quantification of damage in timber bridges is presented with an analytical verification of the method using a numerical model updated with experimental data. Algorithms of global non destructive evaluation for identifying local damage and decay in timber structures are investigated. The proposed method is based on changes in modal strain energy of a damaged and an undamaged structure. In this study, the investigation focuses on the capability and limitations of the proposed algorithms for detecting damage in a multimember timber structure as well as on the reconstruction of mode shape from limited sensor inputs. As a result of this investigation, a modified algorithm is proposed to overcome the shortcomings of the original method. In addition, a recommendation has been made in order to reconstruct the mode shape from limited sensor inputs. 1.Introduction More than any other types, timber structures are particularly vulnerable to various damages caused by deterioration, aging or traffic overloads. It is highly desirable to use nondestructive evaluation (NDE) to determine the material properties and/or structural capacity of individual members or that of the entire timber structure without impairing the member or the structure. Traditionally, a number of methods have been adopted in the field of NDE for timber, including visual inspection, stress wave, drill resistance, radiography, ultrasonics, and deflection/vibration analysis [1]. Most of these methods are performed on a much localized scale and the evaluation of the entire structure using these methods can be very time consuming and inefficient. Thus, it is desirable to develop method(s) of nondestructive testing for timber structures that can identify damage or decay from a global perspective. However, due to the uncertainties associated with timber properties, coupled with using non-standard structural members and less uniform construction methods, damage detection in timber structures, using global damage detection methods such as vibration based method; impose a great challenge to engineers. On the other hand, development of vibration-based damage identification in the laboratory or in the field in recent years has created opportunities for global NDE of timber structures [2-5]. Among various methods, a method developed by Stubbs based on changes in modal strain energy as an indicator of localized damage or stiffness loss in a structure has been particularly promising [3-10]. In the literature, this method is often referred to as the damage index method. The method was developed for application to a wide range of structural systems. Previous published studies have demonstrated the use of the damage index method to localize and estimate the severity of damage within a structure using a limited number of modal parameters for steel plate girders and highway bridges [5]. Several -1-


analytical studies have been undertaken which verify the performance of this damage localization and severity estimation algorithm [6]. Few limited studies have been carried out on timber beams and timber bridges [7-9] in which the method of damage localization was applied to timber beams. The studies showed the ability of the damage index method to successfully detect and locate the inflicted damage for single damage cases [7-8]. In this paper, the results of a study conducted to investigate the capabilities and limitations of using the damage index method for locating inflicted damage in timber bridges, especially multiple damages, are presented. A numerical model has been developed using Finite Element Analysis. Corresponding to the numerical model, a four-girder prototype bridge has been built and tested in the laboratory to provide data for updating the numerical model. The full experimental damage detection tests on the prototype bridge will be carried out as the next stage of the investigation. 2.Finite Element modelling of timber bridge 2.1 Undamaged model An analytical model was developed using a Finite Element Analysis (FEA) package. The FE model was constructed based on a laboratory timber bridge configuration which was built for experimental investigations (Figure1). The geometric configuration of the bridge model is also illustrated in Figure 1. The specimen’s breath and span length were 2,400mm and 4,500mm, respectively. The model bridge consists of four radiata pine timber beams acting as girders with dimensions of 45 mm (width) and 90 mm (height) and 21 mm thick structural plywood acting as deck.

SHELL63

MATRIX 27

SOLID45

Figure 1. Configuration of the laboratory timber bridge FE model

Figure 2. Cross section of the

Elements of the finite element (FE) model A timber bridge is a complex structural system, thus the selection of suitable elements to represent it is important. A finite element (FE) model was developed using FEA software package ANSYS. A three-dimensional analytical model was built to study the dynamic behaviour of the damaged bridge. For the deck, the eight-noded shell elements (SHELL63) with membrane and plate bending behaviour were chosen. The solid elements (SOLID45) were utilised to model the girders, for which different damage scenarios can be easily created. In order to complete the model, the deck-to-girder connections were modelled using an arbitrary element (MATRIX27) whose geometry is undefined but whose elastic kinematic response can be specified by stiffness, damping, or mass coefficients. The cross section of one of the girders is shown in the Figure 2.

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D

Figure 3. The principal axes of a timber specimen opening damage

B

Figure 4. A typical side view of web

Material properties of the FE model Solid wood and engineered wood products are orthotropic materials with distinctive properties in three mutually perpendicular directions. These directions are longitudinal and parallel to the grain, as well as radial and tangential to the grain as shown in Figure 3. In ANSYS, the orthotropic material properties are defined by the three directional moduli of elasticity (Ex, Ey and Ez), three Poisson’s ratios (xy, yz and xz) and three shear moduli (Gxy, Gyz and Gxz). 2.2 Damaged model Common damages found in timber bridges are termite attacks and decay of timber surface due to moisture. In this paper, these damages are simulated in the FE model by an opening on the web (simulating section loss due to termite attack) and a saw cut from the soffit, simulating decay of a girder. The damage is denoted by its width and depth forming a rectangular opening on the web or a saw cut of one of the girders. The inflicted damage was initially introduced at the midspan of the inner girder G3. This was followed by additional damage at ¾ span of the same girder. The web opening damage continued at ¼ span of the outer girder G1. The final damaged state was reached by introducing cumulative web opening damages and a saw cut near the midspan of girder G1. The details of the damage scenarios are tabulated in Table 1. A typical web opening damage is shown in Figure 4. The FE models were intended to study the changes in modal parameters due to different levels of damage severity. Table 1 Dimensions of inflicted damage Damage Case

Width (mm)

Depth (mm)

1L50H 5L50H 1L50HQC 5L50HQC 1L50HQ2C 5L50HQ2C D14

45 225 45 225 45 225 225

45 45 45 45 45 45 58.5

Opening Area (mm2) 2025 10125 2025 10125 2025 10125 13162.5

Damage girder/ location

G3/midspan G3/midspan G3/midspan, G3/¾ span G3/midspan, G3/¾ span G3/midspan, G3/¾ span, G1/¼ span G3/midspan, G3/¾ span, G1/¼ span G1/ midspan plus all damage above

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Damage sequence

Individual individual cumulative of 5L50H cumulative of 5L50H cumulative of 5L50H-QC cumulative of 5L50H-QC cumulative of 5L50H-Q2C


3.Damage Identification 3.1 The damage index method [3] Since the main load carrying structural elements in a timber bridge are timber girders, the identification will focus on localization of damage on the girders. In this investigation, the damage index method developed by Stubbs [3] was selected to detect the inflicted damage present in the girder of interest in a timber bridge. The method pertaining to damage localization is based on the relative differences in modal strain energy between an undamaged structure and that of the damaged structure. The algorithm used to calculate the damage index for the jth element and the ith mode, i j , is given below. L  // *  L // 2 2 2 // *  ( x ) dx   ( x ) dx    i ( x ) dx i i   * 1  Fij  j 0  0  ij   L L 1  Fij  //  2 2 2 // // *   i ( x ) dx   i ( x ) dx   i ( x ) dx  j  0 0

























(1)

The derivation of Eq. (1) is discussed in [3]. It should be noted that in Eq.(1) the terms i(x) are vectors of mode shape coordinates for each single girder, but denote a matrix describing the mode shape corresponding to mode i for a bridge structure. It was suggested by Peterson [3] that each mode shape coordinate in the mode shape matrix be divided by the Euclidean norm of the matrix to obtain a normalized mode shape matrix. The damage index method was then used to compare the normalized mode shape vector for each girder from each of the damage cases versus the corresponding normalized undamaged mode shape vector. To account for all available modes, NM, the damage indicator value for a single element j is given as NM

j 

 Num

i 1 NM

ij

(2)

 Denom ij i 1

where NUMi j = numerator of i j and DENOMi j= denominator of i j in Eq. (1), respectively. Transforming the damage indicator values into the standard normal space, normalized damage index Zj is obtained: Zj 

 j  βj  βj

(3)

where j = mean of j values for all j elements and j = standard deviation of j for all j elements. A judgment based threshold value is selected and used to determine which of the j elements are possibly damaged which in real applications is left to the user to define based on what level of confidence is required for localization of damage within the structure. 3.2 Modification of the damage index method The damage index method introduced above has been successful in single damage localization but encountered problems during the identification of multiple damage cases [67]. One of the reasons is the fact that Eq (2) accounts for all available mode shapes through the summation of the combination of mode shape curvatures. Although mode shape vectors have been normalized to the Euclidean norm of the matrix, the mode shape curvatures used for the damage index calculation are not normalized. Values of mode shape curvature are dependant on the shapes of each individual mode shape. Instead of reflecting the changes in the curvature due to damage, the summation of non-normalized mode shape curvatures will -4-


distort the damage index in favor of higher modes, which results in false damage identifications. To solve this problem, the following algorithm is proposed in this paper : (1) the mode shape vector is normalized with respect to mass; (2) mode shape curvatures for the ith mode of a given girder are normalized with respect to the maximum value of the corresponding mode. After implementing these modifications, Eq (1) can be re-written as:







  

L 2 2 2  // *  L // // *    i ( x ) dx    i ( x ) dx    i ( x ) dx j 0  0  ij   L L 2 2 2  //  // // *    i ( x ) dx    i ( x ) dx    i ( x ) dx  j  0 0

  // *

  

(4)



//

where  i or  i are normalized curvature vectors. 3.3

Reconstruction of the mode shapes

The effectiveness of damage localization method, introduced above, is closely related to the number of elements of the structure or components. The number of elements to be used by damage detection is dictated by the number of sensors used for the measurement. In order to produce reliable and accurate results, a relatively large number of sensors is required to produce the fine coordinates of the mode shapes. In the numerical simulation, the coordinates can be controlled by mesh density. However, in the field applications or experimental testing, the evaluation of the coordinates of the mode shape vectors is limited by the number of sensors used in the testing which is often far less than what is desired. To overcome this limitation, the techniques for reconstructing mode shapes, to increase the number of coordinates, are proposed. In this paper, two available techniques namely, Shannon sampling theory and Cubic Spline, were used and compared, for reconstruction of the mode shapes. The measured mode shape coordinates can be interpolated using either technique to generate mode shape vectors of greater length. Shannon sampling theory Most researchers believed that Shannon’s sampling theory can provide good results in reconstruction of the mode shape vector [7-10]. The interpolated mode shape should represent the exact reconstruction of the mode shape of interest since the summation is for all n between negative and positive infinity, i.e., for an infinite number of spatially repeated experimental mode shape vectors. Acceptable results can be obtained using several repeats of the experimental mode shape coordinates, i.e., for a finite range of values for n. A more detailed explanation of how to apply Shannon’s sampling theory to reconstruct mode shapes can be found in [10]. Cubic spline Matlab provides easy access to the cubic spline data interpolation using Spline function. A tri-diagonal linear system (with, possibly, several right sides) is being solved for the information needed to describe the coefficients of the various cubic polynomials which make up the interpolating spline.

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4.Results and Discussion As part of the results presented here, the statistically normalized damage indicator values (Zj) for each of the damage cases are plotted against the bridge span length. In principle, the magnitude of the damage indicator values at the location of damage increases with increasing severity of damage. In addition, the confidence in detecting the damage using the damage index method increases with increasing severity of damage. 4.1 Discussions on techniques for reconstruction of the mode shapes It is clear that without sufficient number of sensors, the algorithm will fail to locate the damage (Figure 5a). Considering the practicality of field testing, to reconstruct mode shapes in order to produce sufficiently fine coordinates is essentially part of the damage localisation process. From Figure 5 it is clear that Spline is a better method for mode shapes reconstruction because it has correctly indicated that the mid and quarter spans have suffered the exact same damage while the Shannon theory has failed to do so. In addition, Figure 5(b) also shows that the Shannon theory is likely to produce a false damage report with some extra peaks. Therefore, in the following discussion, the Spline will be the only method to be used for the reconstruction of mode shapes from given data (32 data points for four girders in this study). 4.2 Comparison of modified and original damage index methods for Damage Identifications For cases involving detection of a single damage in a structure, the damage index method and modified damage index method produce similar results. However, for multiple damage scenarios, the modified damage index method is superior to the original algorithm. Figure 6 shows the damage localization results using the two algorithms. It is noted that without the modification, the damage indicator has completely missed the damage at the midspan of girder No 3 and indicated a false damage instead. It is necessary to point out that with the selection of a few lower modes (e.g. only the first two modes) in calculating the damage index, the original algorithm may be able to indicate the correct damage locations in the given scenario, but despite that, the indication of damage severity is incorrect (Figure 7) due to the absence of higher modes. This situation can be worsening, when there is multiple damage with different severity where reliability of damage locations and severity detection depend heavily on the higher modes in the damage index calculation. As seen in Figure 8a, the damage index method may miss the quarter span damage for damage case 1L50HQC if it is calculated based on only the first two modes, since the damage indicator value is too low.

(a) (b) (c) Figure 5 Damage inflicted at midspan and ¼ span (scenario 5L50HQC) and damage index calculated with limited data (a) as is; (b) reconstructed using Shannon sampling theory; (c) Spline.

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Figure 6 Damage localisation with original algorithm (left) and modified algorithm (right) using all 7 mode shapes - the damage scenario 5L50HQC (same damage inflicted at midspan and ¼ span)

Figure 7 Damage localization with (a) original algorithm (b) modified algorithm using only the first 2 mode shapes - the damage scenario 5L50HQC (Same damage inflicted at midspan and ¼ span)

(a) (b) (c) Figure 8 Damage localization with various algorithms and mode shapes) - the damage scenario 1L50HQC (¼ span damage is much less severe than that at midspan) (a) original algorithm with 2 modes (b) original algorithm with all modes (c) modified algorithm with all modes On the other hand if the method uses all modes for the index calculation, the results will miss the very severe damage at midspan as well as indicating a false damage (Figure 8b). On the contrary, by using all available modes the modified algorithm produces precise damage detection results (Figure 8c). Figure 9 shows the comparison of damage detection results for the damage scenario 5L50HQ2C by using the original algorithm and the modified algorithm. For girder No 3 with the same multiple damage as in 5L50HQC, the results for each algorithm is similar to its counterpart in 5L50HQC as previously discussed, i.e. the modified algorithm is superior to the original one. For girder No 1, which possesses a single damage, both algorithms successfully produced correct damage identification results.

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(a) (b) (c) (d) Figure 9 Damage localization using original algorithms : (a) at girder No 1 (b) at girder No 3 and using the modified algorithm (c) at girder No 1 (d) at girder No 3 - the damage scenario 5L50HQ2C 5.Conclusions The modal strain energy based damage identification algorithm is capable of detecting single damage in a timber structure but will experience some problems when faced with multiple damage detection. A modified algorithm has been proposed to overcome the problems associated with the original algorithm. The results of numerical investigations have shown that the modified algorithm is capable of overcoming the problems associated with reliable detection of multiple damages in terms of damage location and severity. With this development it is possible to combine the modified algorithm with other algorithms to quantify the severity of damage. The study also found that the Cubic Spline method is a suitable technique for reconstructing mode shape vectors with finer coordinates. The experimental verification of the modified damage identification method will be conducted on a four girder timber bridge in the laboratory as the next stage of this investigation. 6.References [1] Emerson, R. N., Pollock, D. G., Kainz, J. A., Fridley, K. J., McLean, D.I., and Ross, R. J. (1998). ‘‘Non-destructive evaluation techniques for timber bridges.’’ Proc., 1998 World Conf. on Timber Engineering (WCTE), Lausanne, Switzerland, 670–677. [2] Farrar CR & Doebling SW. (1997) Lessons learned from applications of vibrationbased damage identification methods to a large bridge structure. Proceedings of the International Workshop on Structural Health Monitoring, California, pp.351-370. [3] Stubbs, N., Kim, J. T., and Farrar, C. R. (1995). ‘‘Field verification of a non-destructive damage localization and severity estimation algorithm,’’ Proc., 13th Int. Modal Analysis Conf., Nashville, Tenn., 210–218. [4] Stubbs, N., and Kim, J. T. (1996). ‘‘Damage localization in structures without baseline modal parameters.’’ AIAA J., 34(8), 1644–1649. [5] Bolton, R., Stubbs, N., Park, S., and Choi, H. (1998). Analysis of lavic road overcrossing field data, Texas A&M University Press, Engineering Technology, Lubbock, Tex. [6] Park, S., Stubbs, N., Bolton, R., Choi, S., and Sikorsky, C. (2001). ‘‘Field verification of the damage index method in a concrete box-girder bridge via visual inspection.’’ Int. J. Comput. Aided Civil and Infrastructure Eng., 16, 58–70. [7] Peterson, S. T., McLean, D. I., Symans, M. D., Pollock, D. G., Cofer, W. F., Emerson, R. N., and Fridley, K. J. (2001a) ‘‘Application of dynamic system identification to timber beams: I.’’ J. Struct. Eng.,127(4), 418–425. [8] Peterson, S. T., McLean, D. I., Symans, M. D., Pollock, D. G., Cofer, W. F., Emerson, R. N., and Fridley, K. J. (2001a) ‘‘Application of dynamic system identification to timber beams: II.’’ J. Struct. Eng.127(4), 426–432.

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[9] Peterson ST, McLean DI & Pollock DG. (2003) Application of dynamic system identification to timber bridges. Journal of Structural Engineering, 129(1), 116-124. [10] Stubbs, N., and Park, S. (1996) ‘‘Optimal sensor placement for mode shapes via Shannon’s sampling theorem.’’ Microcomput. Civ. Eng.,11, 411–419.

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