Damage detection of shear building structure based on FRF response variation

Transcription

1 , pp Damage etection of shear builing structure base on FRF response variation Hee-Chang Eun 1,*, Su-Yong Park 1, Rae-Jung im 1 1 Dept. of Architectural Engineering, angwon National University, Chuncheon , orea heechang@kangwon.ac.kr, sesinia@naver.com, 63zelkova@hanmail.net Abstract. This work stuies the amage etection of a shear builing structure from the change in the frequency response function (FRF) response before an after attaching an aitional mass on the existing structure. The proper orthogonal moes (POMs) corresponing to the first proper orthogonal values (POVs) are extracte from the FRF ata in the neighborhoo of the first resonance frequency at two ifferent states. The POM set at the first measurement is taken as the baseline atum, an it is compare with the other set extracte from the moifie structure, in which aitional mass was attache at all floors. It is shown that amage exists at a location to represent an abrupt change in the ifference of the POMs at two ifferent states. Furthermore, the metho oes not require baseline ata in the intact state. The valiity of the propose metho is illustrate in numerical examples an experimental works. eywors: amage etection, moe shape, resonance frequency, frequency response function, proper orthogonal ecomposition, shear builing. 1 Introuction Most of the amage etection methos require knowing funamental information for a structure without amage in orer to establish a baseline for amage etection. The methos are not very suitable for practical structures, for which baseline ata cannot be reaily obtaine. Practically, the structural performance shoul be evaluate only by the measure ata at the amage state. During the past several ecaes, a significant amount of research has been conucte in the area of structural amage etection [1], []. Hola an Schabowicz [3] presente a survey of state-of-the-art non-estructive iagnostic techniques of testing builing structures. Büyüköztürk et al. [4] provie the current state-of-theart non-estructive test methos an their application to civil engineering an other engineering materials an structures. Sung et al. [5] an oo et al. [6] provie amage etection methos of a five-story full-scale shear builing by moal flexibility matrices obtaine from acceleration responses. Utilizing the change in the * Corresponing author. ISSN: ASTL Copyright 013 SERSC

2 first moe shape slopes an the sensitivity of moal parameters, Zhu et al. [7] presente a amage etection metho for shear builings. Morita an Teshigawara [8] presente the parameter ientification metho an amage estimation metho using the results obtaine from the shaking table test of a three-story large-scale steel structure. Escobar et al. [9] presente the transformation matrix metho for amage etection in frame builings. Vinayak et al. [10] hanle the amage etection from moal parameter changes using a neural network approach. Xu et al. [11] ientifie the amage locations an severities using the statistical moment-base amage etection metho. Xu et al. [1] provie a structural parameter ientification an amage etection metho using a isplacement measurement time series. The metho was carrie out using a isplacement-base neural network emulator an a parametric evaluation neural network. Most approaches for the amage etection of shear builing structures require baseline ata for the intact state an have been limite to a theoretical approach like sensitivity analysis. The change in the FRF response before an after attaching the aitional mass on the existing structure at measurement is utilize as the amage inex in this stuy because it represents the change of the ynamic responses ue to the aitional mass. The POM is extracte from the FRF response ata collecte in the neighborhoo of the first resonance frequency to be collecte by the accelerometers. It is shown that amage exists at a location to represent an abrupt change in the ifference of the POMs at two ifferent states without baseline ata at the intact state. The valiity of the propose metho is illustrate in numerical examples an experimental works. Damage etection algorithm The ynamic behavior of a structure is assume to be linear an approximately iscretize for n DOFs an can be escribe by the equations of motion where M,, an C enote the ( t) M u& + Cu& + u = f (1) n n analytical mass, stiffness, an amping matrices at measurement, respectively, an u = [ u u L ] T. ( t) 1 u n f is the n 1 loa excitation vector. In orer to establish the relationships between the FRF an moal parameters for successful moal testing, the substitution of leas to where ( ) = ( W) j t u = Ue W an j t f = Fe W into Eqn. (1) U W F () inicates the ynamic stiffness matrix, = -W M + jwc +, W -1 enotes the excitation frequency at measurement, an = -1 H W = W is the FRF matrix of the finite element moel, whose elements can be the receptances. j. ( ) ( ) Copyright 013 SERSC 19

3 The element ( H ) i, j in the matrix H inicates a isplacement response at station i an a isturbing force at station j. Taking Eqn. (1) as the ynamic equation of motion at the amage state an expressing the aitional mass matrix as D M, the ynamic equation of the moifie structure can be written as where ( U + DU) F m = (3) m inicates the moifie ynamic stiffness matrix ue to mass aition, ( M + DM) + WC m = -W j + result gives where. Inserting Eqn. () into Eqn. (3) an arranging the D U = ( DH)F (4) D H represents the variation in the FRF matrix because of mass aition uner the same external force an D = - W ( M + DM) The element Hij -1-1 [ + jwc + ] ( W ( DM) ) H. D represents the FRF variation in a isplacement response at station i an a isturbing force at station j. The equation shows that the FRFs are affecte by the mass change, an the FRF variation before an after placing aitional mass on the amage-expecte structure can be utilize as an inex to etect amage neglecting a little change of resonance frequencies ue to mass aition. 3 Experimental verification by a shear builing structure The valiity of the propose metho was consiere in a four-story, one-bay by one-bay steel frame scale-moel structure, shown in Fig. 1. A photograph showing the typical beam-column connection an bracing system is shown in Fig.. The four vertical columns were comprise of continuous steel angles L in height an were bolte to a concrete founation with imensions of b w t = mm. The concrete founation consists of four steel flanges bolte to each column, an the column was fastene to a massive concrete founation. Four steel shim sheet squares represente the slab an measure approximately mm, an. 08kg were place on the flanges of the steel beams. Cross bracing was externally ae within each story along two faces. All cross bracing members were mae using 38 3mm wie steel strips, each measuring approximately 505 mm in length. An impact hammer was use to excite the frame an hit the mispan point of the beam at the fourth floor in the bracing irection. This experiment was carrie out using an accelerometer set to impact a fixe point of the fourth floor. The accelerometer set is compose of four accelerometers. Five measurement channels were utilize for ata acquisition, incluing a channel for the impact hammer. The experiment was conucte using DYTRAN moel 3055B1 uniaxial accelerometers along with a miniature transucer hammer Brüel & jaer moel 804 to excite the system. The ata acquisition system was a DEWETRON moel DEWE-43. The 0 Copyright 013 SERSC

4 FRFs relative to the reference location of the stationary accelerometer were measure. The measure ata were collecte as a FRF, which is efine as the ratio of the response of a system to its excitation force. Fig. 1. Four-story steel frame structure. Fig.. Steel frame moel structure The FRF is expresse as a function of the cross an auto spectra, which can reaily be obtaine from most multi-channel ata acquisition systems. The cross spectrum is compute by multiplying the Fourier spectrum of a measure response by the complex conjugate of the Fourier spectrum of a known input: xy * ( w) F ( w) F ( w) where G ( w) enotes the cross spectrum, ( w) xy G = (6) x y F the Fourier spectrum of a measure response, an * is the complex conjugate. The auto spectrum is compute by multiplying the Fourier spectrum of the input by the complex conjugate of itself. where ( w) yy yy * ( w) F ( w) F ( w) y y x G = (7) G represents the auto spectrum. The FRF is then efine as the ratio of the cross an auto spectra. yy ( w) ( w) G xy H ( w) = (8) G Copyright 013 SERSC 1

5 where H ( w) is the FRF. A mass ea loa of 1. 68kg an a steel shim sheet of. 08kg were uniformly place on each floor of the frame. On each floor, the floor mass was stuck to the center of the floor using a magnet. The experimental work consiere two amage cases by the removal of one bracing at the secon an fourth floors. Two ifferent measurement ata sets from the amage frame an the moifie frame ue to mass aition were collecte. The former ata set is regare as the baseline ata an is compare with the latter ata set to fin the response change. A FRF ata set before attaching aitional mass was collecte an save to compare it to the other FRF ata set. Aitional mass corresponing to 6.4% of the floor mass, incluing the steel shim sheet, was place on all floors by magnets, an the other FRF ata set was collecte from the moifie structure. (a) (b) Fig. 3. Curves of FRF magnitue of the builing moel: (a) before placing the aitional mass, (b) after placing the aitional mass at the secon floor, (c) after placing the aitional mass at the fourth floor Figure 3 illustrates the plot of FRF amplitue versus frequency at each floor of the builing structure. It is shown that the amplitue of FRF at the fourth floor is the highest of all floors. An the first resonance frequency in the plots was rarely (c) Copyright 013 SERSC

6 change epening on the aitional mass an was observe in the neighborhoo of 11.90Hz. A little variation in the resonance frequency ue to the aitional mass was neglecte. The POMs were extracte from thirteen FRF ata sets in the frequency range of Hz, incluing the first resonance frequency. The POM corresponing to the first POV was consiere. Figure 4 presents the POMs corresponing to the first POV an the variation in POM isplacement before an after placing the aitional mass. The POM curves at both states exhibit very similar tenencies an o not provie amage information, as shown in Figs. 4(a) an (b). The plots in Fig. 4(c) an () show that the abrupt change in the POM variation in the floor correspons to the floors loosing one bracing. As another experimental stuy, the amage etection of a builing structure with a nonuniformly istribute floor mass was consiere. The masses were 1.9, 1.9, 1.68 an 1.68 kg for the first, secon, thir an fourth floor, respectively. Two cases of amage, in which one bracing at the secon an fourth floors were lost, were stuie. The aitional mass of 0. 4kg was place by magnets as the previous POM POM after aitional mass before aitional mass before aitional mass after aitional mass (a) 0. (b) 3 x x POM ifference 0-1 POM ifference (c) Fig. 4. POM an its ifference between two states (uniform mass istribution): (a) POM (amage at the secon floor), (b) POM (amage at the fourth floor), (c) POM ifference (amage at the secon floor), () POM ifference (amage at the fourth floor) () Copyright 013 SERSC 3

7 experiment. The POM corresponing to the first POV from the FRF ata in the neighborhoo of the first resonance frequency was calculate. The POMs an the ifference between the POMs before an after attaching the aitional mass are epicte in Fig. 5. The POM curves of the frame structure, which has amage at the secon floor, as shown in Fig. 5(a), o not give any information on the amage location. The corresponing curves show that the amage at the fourth floor in Fig. 5(b) represent an abrupt change at the thir an fourth floors. However, the POM curves cannot be utilize in etecting amage because they o not give consistent results, as in the other cases. The ifference between the POMs before an after attaching the aitional mass near the amage location abruptly changes, as shown in Figs. 5(c) an (). It is expecte that the ifference, rather than the POM curve itself, can be utilize in etecting amage POM POM after aitional mass before aitional mass before aitional mass 0.4 after aitional mass (a) 0. (b) x POM ifference -1 - POM ifference (c) Fig. 5. POM an its ifference between two states (nonuniform mass istribution): (a) POM (amage at the secon floor), (b) POM (amage at the fourth floor), (c) POM ifference (amage at the secon floor), () POM ifference (amage at the fourth floor) The experimental work shows that the abrupt change of the POM ue to the attachment of aitional mass reflects the nature of structural amage. This experiment prove the easiness of the propose amage etection metho by mass aition without any information at the intact state. () 4 Copyright 013 SERSC

8 4 Conclusions This work was starte from the basic iea that the ynamic response ue to the attachment of aitional mass shoul be change. The POM corresponing to the first POV was extracte from the measure FRF response ata in the neighborhoo of the first resonance frequency. The POM of the amage-expecte frame structure, which is regare as the baseline atum, is compare to the other POM from an ientical frame for which aitional mass is attache on all floors by floor. The amage etecte at the region exhibits the abrupt change in the ifference between the POMs at two states. The valiity of the propose metho was illustrate in numerical experiments an frame tests. Acknowlegments. This work was supporte by the National Research Founation of orea (NRF) grant fune by the orea government (MEST) (No ). References 1. Doebling, S., Farrar, C., Prime, M., Shevitz, D.W.: Damage ientification an health monitoring of structural systems from changes in their vibration charteristics: A literature review. Report No. LA-1767-MS, Los Alamos National Laboratory (1996). Paney, A., Biswas, M., Samman, M.: Damage etection from changes in curvature moe shapes. J. Soun Vib. 145, (1991) 3. Hola, J., Schabowicz,.: State-of-the-art non-estructive methos for iagnostic testing of builing structures anticipate evelopment trens. Arch. Civ. Mech. Eng. 10, (010) 4. Büyüköztürk, O., Taşemir, M., Günes, O., Akkaya, Y.: Nonestructive testing of materials an structures. In: Proceeings of NDTMS-011, Istanbul, Turkey (011) 5. Sung, S., oo,., Jung, H., Jung, H.: Damage-inuce eflection approach for amage localization an quantification of shear builings: valiation on a full-scale shear builing. Smart Mater. Struct. 1, (01) 6. oo,., Sung, S., Park, J., Jung, H.: Damage etection of shear builings using eflections obtaine by moal flexibility. Smart Mater. Struct. 19, (010) 7. Zhu, H., Li, L., He, X.: Damage etection metho for scale builings using the changes in the first moe shape slopes. Comput. Struct. 89, (011) 8. Morita,., Teshigawara, M.: Damage etection an estimation of builing through measurements. In: The 13 th Worl Conference on Earthquake Engineering, Vancouver, B.C., Canaa (004) 9. Escobar, J., Sosa, J., Gomez R.: Damage etection in frame builings. Can. J. Civ. Eng. 9, (001) 10.Escobar, J., Sosa, J., Gomez R.: Structural amage etection using the transformation matrix, Computers an Structures. Comput. Struct. 83, (005) 11.Vinayak, H., umar, A., Agarwal, P., Thakkar, S.: NN base amage etection from moal parameter changes. In: The 14 th Worl Conference on Earthquake Engineering, Beijing, China (008) 1.Xu, Y., Zhang, J., Li, J., Xia, Y.: Experimental investigation on statistical moment-base structural amage etection metho. Struct. Health. Monit. 8, (009) 13.Xu, B., Son,g G., Masri, S.: Damage etection for a frame structure moel using vibration isplacement measurement. Struct. Health. Monit. 11, (013) Copyright 013 SERSC 5