Detection of damage to structures has recently received considerable attention from the viewpoint of maintenance and safety assessment. In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the whole building, but it has not been established as a practical method until now. It is reasoned that this is perhaps due to restrictions on the experiment, use of improper method, and lack of inspection opportunity for the structures. In addition, in the case of largescale structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom, and this can also be a considerable problem for the analysis. A practical method for the detection of structural damage using the first natural frequency and mode shape of building is proposed in this paper. The effectiveness of the proposed method is verified by numerical analysis and experimental tests. From the results, it is observed that the severity and location of the damage can be estimated with a relatively small error by using modal properties of building. Copyright © 2004 John Wiley Sons, Ltd.
THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS Struct Design Tall Spec Build 13, 1–8 (2004) Published online in Wiley Interscience (www.interscience.wiley.com) DOI:10.1002/tal.227 STRUCTURAL DAMAGE ASSESSMENT OF BUILDING STRUCTURES USING DYNAMIC EXPERIMENTAL DATA HEUNG-SIK KIM1 AND YOUNG-SOO CHUN2* Department of Architecture, Honam University, Kwang-ju, Korea Department of Structural Eng., Korea National Housing Corporation, Kyeonggi-do, Korea SUMMARY Detection of damage to structures has recently received considerable attention from the viewpoint of maintenance and safety assessment In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the whole building, but it has not been established as a practical method until now It is reasoned that this is perhaps due to restrictions on the experiment, use of improper method, and lack of inspection opportunity for the structures In addition, in the case of large-scale structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom, and this can also be a considerable problem for the analysis A practical method for the detection of structural damage using the first natural frequency and mode shape of building is proposed in this paper The effectiveness of the proposed method is verified by numerical analysis and experimental tests From the results, it is observed that the severity and location of the damage can be estimated with a relatively small error by using modal properties of building Copyright © 2004 John Wiley & Sons, Ltd INTRODUCTION The trend of constructing bigger and higher buildings demands greater safety caution for these structures A diagnosis of structural integrity of these buildings involves an assessment of whether they can serve safely, and its current assessment techniques rely on a visual inspection or localized destructive and non-destructive tests In this case, the quality of the assessment is influenced by the experience and knowledge of each investigator Furthermore, the investigators are faced with problems in assessing an unapproachable element and in an area where direct visual inspection is difficult In addition, the result of a localized inspection does not represent the condition in whole structures, and it is necessary to inspect a considerable area to represent the condition of the building at large After all, these constraints imply that current assessment techniques are time-consuming, labour-intensive, and costly These problematic issues have stimulated a search for a better method, and recently many research attempts to accomplish this purpose have been continuing using dynamic characteristics of vibration tests of the building (Goh et al., 1995; Li et al., 1999; Hassiotis and Jeong, 1993) Structural damage to buildings can occur due to cracking, ageing of materials etc and is indicated by a change in physical and modal parameters of structural system These parameters can be used as an index of such damage detection This concept has recently been applied in many research studies for damage detection of various structures (Stephens and Yao, 1987; Goh et al., 1995; Liu, 1995; Bicanic and Chen, 1997; Li et al., 1999; Hassiotis, 2000) In this case, most of these methods require limited information on measured modal parameters such as natural frequency or mode shape for the * Correspondence to: Young-Soo Chun, Department of Structural Engineering Korea National Housing Corporation, 175 Kumi-dong, Pundang-gu, Sungnam-shi, Kyonggi-do, 463-500 Korea Copyright © 2004 John Wiley & Sons, Ltd Received October 2002 Accepted November 2002 H.-S KIM AND Y.-S CHUN identification of structural damage or quantification of such damage However, up to now, no method has been able to provide this function reliably for large structures, and it is more so for the case of building structures It is reasoned that this is perhaps due to restrictions on the experiment, incorrect method, and lack of inspection opportunity for the structures In addition, for the case of large-scale structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom (DOFs), and this can also be a considerable problem for the analysis Thus, this study, as an attempt at such analysis, takes a practical approach to use only first modal vibration characteristics of buildings to overcome the difficulties of the field experiment, proposes a method for damage detection by simple modelling of the buildings for each storey, and verifies its usefulness DAMAGE DETECTION ALGORITHM The damage detection algorithm used in this research is a method to detect local damage using the change of stiffness of each storey of a multi-storied building based on the modal information as measured and obtained in the field It requires first natural frequency and mode shape only as the input data Here, local damage refers to not each element level but each storey level, and structural damage is indicated by the decrease in stiffness of each storey due to damage to each element Thus, it is assumed that any change in storey stiffness is solely due to change in the sum of column or wall stiffnesses at that storey, and the stiffness of each storey of the damaged building can be represented by the product of a damage index and stiffness of each storey of the undamaged building as shown in Equation (1) NL Ki* =  a i Ki (1) i =1 Here, represents the damage index of ith storey, Ki, K*i is the contribution of the ith storey on the global stiffness matrix of the undamaged and damaged structure respectively, and NL is the number of elements of the structures with n degrees of freedom can provide information not only on the location of the damage but also the severity of the damage The damage index, ai, is obtained using the following algorithm First, the eigenvalue problem of an undamped free vibration equation of undamaged structure with n-DOF can be written as follows (Clough and Penzien, 1993): ( K - l j M )f j = (2) Here, lj is the eigenvalue (= wj2) of the jth vibration mode, and fj is the corresponding natural mode shape of the system Equation (2) can then be rewritten as [K ]{f j } = w 2j [ M ]{f j } (3) It is assumed that damage is not accompanied by a change in mass However, a change in stiffness produces changes in the eigenvalues and eigenvectors Therefore, the eigenvalue problem of the damaged structure is given by [K *]{f *j } = w *j [ M ]{f *j } (4) The left-head side of Equation (4) can be rewritten by substituting Equation (1) as in Equation (5): [K *]{f *j } = [ D*][K ]{a i } Copyright © 2004 John Wiley & Sons, Ltd (5) Struct Design Tall Spec Build 13, 1–8 (2004) DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA where Èf1*jf 2*j ◊ ◊ ◊ ◊ ◊ ◊ f *N ◊◊◊◊◊◊ Í * Í f1*j ◊ ◊ ◊ ◊ ◊ ◊ f2*jf3*j ◊ ◊ ◊ f Nj Í [ D*] = Í f1*j ◊ ◊ ◊ f2*j ◊ ◊ ◊ Í O M O M Í * ÍÎ f1 j f2*j È K1 ÍK Í ÍM Í Í0 Í0 [K] = Í Í0 ÍM Í Í0 Í0 Í ÍÎ K2 - K2 M K2 M 0 0 M - K3 - K3 M 0 ◊◊◊ ˘ ˙ ◊◊◊ ˙ ˙ ◊◊◊ ˙ OM ˙ ˙ * ˚˙ f Nj (6) ◊◊◊◊◊◊ ◊◊◊◊◊◊ O ˘ ˙ ˙ M ˙ ˙ ˙ ◊◊◊◊◊◊ ˙ ˙ ◊◊◊◊◊◊ ˙ O M ˙ ˙ K N -2 K N -1 ˙ - K N -1 ˙ ˙ K N ˙˚ {a i } = {a , a , a , ◊ ◊ ◊ ◊ ◊ ◊ , a N } T (7) (8) Finally, Equation (9) for the solution of the damage index, aj, is obtained by a i = w *j [ A][ M ]{f *j } (9) where [A] = {[D*][K]}-1 As shown in Equation (9), the proposed algorithm makes the damage detection of the structure in each storey possible with data on only one minimum mode If information on several modes can be obtained by experiment, an expanded equation as shown in Equations (4) and (5) is possible An optimization problem can then be solved for improvement in the accuracy of damage detection DAMAGE DETECTION PROCESS AND NUMERICAL EXAMPLE Based in the proposed algorithm and the definition of damage to structures, a detailed method and process for the detection of building damage is introduced and the usefulness of such a method is verified using a numerical example The example building chosen for the illustration of the proposed method is a residential building with shear-wall dominant systems, which is widely used in Southeast Asia and is a 20-storey straight linear flat apartment as shown in Figure 1(a) The story height is 2600 mm for all storeys For the sake of simplification of the analysis, it is assumed that all walls in the building are uniform This example assumes that a perfect analysis model has been set for the building before damage occurs The procedure for damage detection is straightforward and easy to implement, as described in the following Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004) H.-S KIM AND Y.-S CHUN (a) (b) Figure Example building and condensed model (a) Typical floor plan of the example building (b) Condensed model (numbers indicate condensed DOFs) Step First, according to the assumption previously introduced in Section 2, the sample building is converted into a simple n-DOF system corresponding to n storeys as shown in Figure 1(b) In this numerical example, the stiffness of each storey can be obtained by applying a unit load at each storey But, in a real problem, static condensation is performed to eliminate all rotational DOFs (Guyan, 1965) and then, to narrow the gap between the condensed model with n-DOF lumped massspring system and the actual structure, system identification is performed First, full-scale measurements are carried out for the building, and by applying the random decrement technique on a time window of acceleration responses at each floor of the building, output-only modal analysis is conducted Then, by using the damage detection approach in Section 2, the stiffness terms of the simple model are identified and then used to update the stiffness matrix of the complete model Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004) DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA Table Damage scenarios Classification Case Case Case Case Damage element Degree of damage Vibration mode used 2-storey 10-storey 17-storey 5-storey, 15-storey 20% decrease in stiffness 20% decrease in stiffness 20% decrease in stiffness 20% decrease in stiffness First mode First mode First mode First mode Step Parameters such as natural frequency and mode shape are needed for the damage detection and are obtained by experiment In this numerical example, the damage at a particular storey is introduced by decreasing the stiffness of the finite element model, and the modal information of the building before and after damage is obtained by an eigenvalue analysis In this case, the change in modal information is assumed to be data measured from the field test, and the damage at a particular storey follows an assumed damage scenario In this example, four damage scenarios were constructed to indicate a change in modal characteristics with respect to the severity of damage and the location of damage and to verify the usefulness of the proposed detection method Generally, most previous research has used a case of severe damage in order to make the usefulness of the proposed method more visible and also applied a very unrealistically high mode for the natural frequency and mode shape Nevertheless, the internal damage of an aged building can be much less in reality, and the detection of such damage is considered to be more useful in a practical sense In addition, the number of vibration modes that can be obtained by an actual measurement is very limited in the case of a building, and the validity of such measurements is also very restricted For those reasons, this example uses only the first mode and a lightly damaged structure Table summarizes the damage scenario Step As previously mentioned in Section 2, the decrease in stiffness is computed reversely In this case, the accuracy of damage detection can vary according to the number of vibration modes used, the location and the severity of damage, etc Therefore, the usefulness of the proposed method can be examined with respect to the reversely computed amount of decrease in the stiffness In order to find out the detection result with respect to the location of damage, a 20% decrease in the stiffness at the 2nd, 10th, 17th and 5–15th storeys was applied according to the damage scenario, and the location and severity of damage were computed following the proposed algorithm Table exhibits the modal data for each model per the case scenario, and Table depicts the damage detection result Table shows the result of the simulation, that the proposed damage detection method can predict the damage at each storey of a building regardless of the damage location if the accuracy of the modal data obtained from the field test is assured EXPERIMENTAL VERIFICATION An experimental model was constructed as shown in Figure in order to verify the usefulness of the proposed damage detection method experimentally The experimental model is a reduced model of the major structural member of the sample building as shown in Figure The experimental model building has five storeys, and the size of wall of the model is 50 cm, cm and 100 cm for the width, thickness and height, respectively It was constructed using concrete of fck = 300 kgf/cm2, and kgf of Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004) H.-S KIM AND Y.-S CHUN Table Modal data of numerical example Classification Case Case Case Case Frequency (rad/s) First mode 1·0000 0·9943 shape 0·7008 0·6447 Frequency (rad/s) First mode 1·0000 0·9942 shape 0·6842 0·6276 Frequency (rad/s) First mode 1·0000 0·9941 shape 0·6906 0·6336 Frequency (rad/s) First mode 1·0000 0·9943 shape 0·6936 0·6379 2·622 0·9828 0·9658 0·5850 0·5219 0·9432 0·9152 0·4558 0·3871 0·8820 0·8437 0·3162 0·2435 0·8005 0·7528 0·1694 0·0755 0·8805 0·8418 0·2974 0·2245 0·7982 0·7499 0·1504 0·0754 0·8751 0·8361 0·3005 0·2269 0·7921 0·7435 0·1520 0·0762 0·8739 0·8357 0·2941 0·2220 0·7928 0·7453 0·1487 0·0746 2·638 0·9826 0·9654 0·5674 0·5039 0·9425 0·9142 0·4374 0·3685 2·652 0·9824 0·9606 0·5730 0·5089 0·9376 0·9089 0·4419 0·3723 2·619 0·9829 0·9658 0·5785 0·5159 0·9433 0·9154 0·4503 0·3821 Table Damage index of numerical examples Storey number Classification Case Predicted value Actual value Case Predicted value Actual value Case Predicted value Actual value Case Predicted value Actual value 11 12 13 14 15 16 17 18 19 10 20 1·004 1·032 1·0 1·0 0·799 1·015 0·8 1·0 0·991 1·135 1·0 1·0 0·993 1·006 1·0 1·0 0·997 1·026 1·0 1·0 0·986 1·055 1·0 1·0 0·981 1·000 1·0 1·0 0·999 0·998 1·0 1·0 0·971 0·986 1·0 1·0 1·003 0·999 1·0 1·0 0·993 1·003 1·0 1·0 0·996 0·986 1·0 1·0 0·999 0·999 1·0 1·0 0·999 0·995 1·0 1·0 1·000 1·003 1·0 1·0 1·008 1·013 1·0 1·0 1·018 1·000 1·0 1·0 1·009 1·002 1·0 1·0 0·986 1·003 1·0 1·0 0·8123 1·032 0·8 1·0 0·999 1·000 1·0 1·0 0·992 1·005 1·0 1·0 0·998 0·998 1·0 1·0 0·997 0·999 1·0 1·0 0·999 0·989 1·0 1·0 1·002 0·992 1·0 1·0 1·012 0·799 1·0 0·8 1·006 0·998 1·0 1·0 1·080 0·979 1·0 1·0 1·002 0·991 1·0 1·0 1·000 1·023 1·0 1·0 1·002 1·008 1·0 1·0 1·001 1·000 1·0 1·0 0·999 1·016 1·0 1·0 0·811 0·808 0·8 0·8 0·998 0·999 1·0 1·0 0·999 0·999 1·0 1·0 0·989 0·998 1·0 1·0 0·999 1·000 1·0 1·0 1·003 1·003 1·0 1·0 additional steel mass blocks at each storey was added to simulate the lumped mass on the floor of building The damage to the building was modelled by increasing the size of the opening to reduce the stiffness of the experimental model by 20% for the second storey only in order to model the case of entirely known damage Table shows the modal experimental data of the experimental model before and after the damage, and the damage detection result using this data is depicted in Table Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004) DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA Figure Experimental model Table Modal data of experimental model Classification Case Frequency (rad/s) First mode shape 1·0 628·42 0·79 0·93 0·60 0·25 Table Damage index of experimental example Storey number Classification Actual value Predicted value Error (%) 1·0 0·99832 -70·17 0·8 0·8225 +2·8 1·0 1·0132 +1·3 1·0 0·9798 -2·02 1·0 1·0602 +6·0 As previously mentioned in the procedure in Section 2, the condensed model is constructed and each storey stiffness for the undamaged and damaged model building identified by experimental modal data A pre-damage test was therefore conducted on the undamaged model to identify the undamaged storey stiffness and, subsequently, the damage test is conducted on the damaged model A conventional modal testing technique was applied to determine the experimental modal data In traditional modal analysis, the modal data are found by fitting a model to the frequency response function relating excitation forces and vibration response Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004) H.-S KIM AND Y.-S CHUN The damage index, ai, is then computed Table demonstrates that the proposed damage detection method enables damage detection for each storey using only the first natural frequency and mode shape The error is due to an inaccuracy of the modal data obtained from the experiment, and such error can be reduced by optimization if modal data on several modes can be obtained CONCLUSION This investigation proposes a practical method for detecting damage per each storey of a building structure using measured vibration characteristics, and its usefulness is verified by a numerical example and model experiment The major contribution of the proposed method is that it is possible to detect damage using data of only one vibration mode at the minimum and the prediction error due to inaccuracy of the experimental data can be reduced by increasing the number of modes used and optimization The proposed method of this study is a method for detecting a change in stiffness at each storey, and it can be applied to all widely used cantilever-type building structures, for which a modelling for each storey is possible REFERENCES Bicanic N, Chen HP 1997 Damage identification in framed structures using natural frequencies International Journal for Numerical Methods in Engineering 40: 4451–4468 Clough RW, Penzien J 1993 Dynamics of Structures McGraw-Hill: New York Goh CG, See LM, Balendra T 1995 Damage detection of buildings: numerical and experimental studies Journal of Structural Engineering 121(ST8): 1155–1160 Guyan RJ 1965 Reduction of stiffness and mass matrices AIAA Journal 3(2): 380 Hassiotis S, Jeong GD 1993 Assessment of structural damage from natural frequency measurements Computers and Structures 49: 679–691 Hassiotis S 2000 Identification of damage using natual frequencies and Markov parameters Computers and Structures 74: 365–373 Li GQ, Hao KC, Lu Y, Chen SW 1999 A flexibility approach for damage identification of cantilever-type structures with bending and shear deformation Computers and Structures 73: 565–572 Liu PL 1995 Identification and damage detection of trusses using modal data Journal of Structural Engineering 121: 599–606 Stephens JE, Yao JTP 1987 Damage assessment using response measurements Journal of Structural Engineering 113(ST4): 787–801 Copyright © 2004 John Wiley & Sons, Ltd Struct Design Tall Spec Build 13, 1–8 (2004)