Sixth World Conference on Structural Control and Monitoring

Transcription

1 Sixth World Conference on Structural Control and Monitoring Proceedings of the 6th edition of the World Conference of the International Association for Structural Control and Monitoring (IACSM), held in Barcelona, Spain 5-7 July 4 Edited by: J. Rodellar Uniersitat Politècnica de Catalunya-BarcelonaTech, Spain A. Güemes Uniersidad Politécnica de Madrid, Spain F. Pozo Uniersitat Politècnica de Catalunya-BarcelonaTech, Spain A publication of: International Center for Numerical Methods in Engineering (CIMNE) Barcelona, Spain

2 Structural Damage Identification based on irtual Structure Construction of irtual Structure for Damage Identification * Jilin Hou, Łukasz Jankowski, and Jinping Ou Abstract This paper presents a damage identification method using irtual structure. The main concept is based on irtual Distortion method (DM), which belongs to a fast structural reanalysis method and employs the irtual distortions or irtual forces to simulate the structural modifications. In this paper, the structure with irtual mass, damping or stiffness is defined as irtual structure. Firstly, the frequency response of the irtual structure is constructed by DM method; Secondly, the natural frequencies of irtual structure with additional masses or stiffness are estimated; At last, the estimated natural frequencies of the irtual structure are used for damage optimization of the structure. A numerical beam model is used to describe and erify the proposed method. I. INTRODUCTION Structural health monitoring (SHM) is an important researched field in ciil engineering. Thereinto structure damage are usually identified using the information such as structure mode (frequency and mode shape) [], flexibility matrix [], time domain response [3] and frequency response [4]. Howeer due to the complexity of structures, limitation of the sensors and the insensitiity to the local damage, damage identification for large structures is not easy to be performed accurately in ciil engineering. Adding control parameters [5], such as mass [6], stiffness [7], support, load or thermal loading, proide efficient way for damage identification. Howeer, in real application sometimes it is not easy to add mass or stiffness on structures perfectly. Therefore this paper proposes a method for structural damage identification by the construction of irtual structure using irtual Distortion Method (DM). DM [8,9] belongs to a fast structural reanalysis method which employs irtual distortion or irtual force to simulate structural changes. The damage or modified parameters can be structural stiffness, mass or damping. ia DM, the responses of modified structure are constructed using the responses of the original structure and certain irtual distortions (irtual forces), and so the whole analysis of the modified structure model is aoided. DM is used ersatilely on structural parameter identification, like stiffness [8,9], mass [], moing mass [], and damping identification []. This paper employs DM to construct irtual structure for damage identification. The paper is structured as follows. The next section describes and deries the theory of the proposed approach. While a numerical example of a plane beam is utilized to test the proposed method. The effectieness and aailability of the approach is demonstrated at the assumed Gaussian measurement noise leel of 5 % rms. II. THE CONSTRUCTION OF ICTUAL STRUCTURE BY DM Assume that a structure contains n d degrees of freedom (Dofs). Denote by the mass, stiffness, and damping matrix of its original real structure respectiely, equation of the motion of the structure in frequency domain can be written as: MX CX KX BF () Y = H BF () where F is input excitation with dimension of n f, n f is the number of the excitation; Y is the measured response of structure with the dimension n y ; n y is the number of the sensors, then sensors could be acceleration, elocity, displacement, strain and so on; B is the matrix of load displacement, with dimension of n d n f ; H is the impulse response matrix with dimension of n d n f, of which H is the response of the ith sensor to excitation applied on the jth Dof of the structure. ij Denoted by ΔM, ΔC, ΔK the modification of the mass, damping and stiffness matrix of the original real structure, then equation of motion of the modified structure in frequency domain is as follows: M+ ΔM X C+ ΔC X K+ ΔK X BF (3) where is the response of the modified structure. By moing the modification terms to the right-hand side of (3), which is expressed as the equialent form: *Resrach supported by the support of the National Basic Research Program of China (973 Program) (3CB3635), of National Science Foundation of China (NSFC) (5857, 5866), of the Fundamental Research Funds for the Central Uniersities (China) (DUT3LK3), of Special Financial Grant from the China Postdoctoral Science Foundation (T555), and of the Project of National Key Technology R&D Program (China) (BAKB, BAKB3,6BAJ3B5). Financial support of the Polish National Science Centre Project AIA (DEC/5/B/ST8/97) and of Structural Funds in the Operational Programme-Innoatie Economy (IE OP) financed from the European Regional Deelopment Fund, Project Modern material technologies in aerospace industry (POIG...--5/8), is gratefully acknowledged. Jilin Hou is with the Dalian Uniersity of Technology, Dalian, 64, P. R. of China (corresponding author to proide phone: ; hou.jilin@hotmail.com). Łukasz Jankowski is with Institute of Fundamental Technological Research, Polish Academy of Sciences, -6, Warsaw, Poland Jinping Ou is with the Dalian Uniersity of Technology, Dalian, 64, P. R. of China, and Harbin Institute of Technology, Harbin 59, P. R. of China 73

3 Δ Δ ( ) Δ ( ) MX CX KX BF MX CX KX (4) In this method, only local structure is modified. Denote by n m, n c, n k respectiely the number of Dofs of the modified mass, damping, and stiffness respectiely, and let Δm, Δc, Δk be the corresponding physical matrix of local structure, which are square T T T T T T matrices with respectie dimension of n m, n c, n k. Then ΔM T ΔmT, ΔC T ΔcT, ΔK T ΔkT, where T, T and T are the m m c c k k relatie transfer matrices from local coordinate to global coordinate. They hae the respectie dimension of n m n d, n c n d, n k n d. z Set, z T X, z T X, z T X, Z m c k z z ectors z, z, z respectiely are n m, n c, n k. Then (4) can be written as:, which are the responses along modified Dofs.The dimension of column, T Let h =HT, h =HT T and T m m c Y Δ Y H T T Δm H T T Δc H T T Δk Z (5) c k m c k h =H T, which are the impulse response matrices corresponding to the Dofs of modified mass, damping and stiffness respectiely, with respectie dimension of n y n m, n y n c, n y n k. Let h h h h, Δ m c k Here measured response Δm Δc Δk the response related to modified dofs (or response,then (5) can be written as: k Y, Δ Y Δ Z Y is diided into two parts Y and Y, i.e. Y =[ Y ; Y ], where Y s s Z ) with dimension of (n m +n c +n k ), and sensors with of dimension of (n y -(n m +n c +n k )). Y can be expressed by (7). Y h (6) s m c k are Y are the response of the rest PZ (7) where P is the obsere matrix of local modified structure with dimension of (n m +n c +n k ) (n m +n c +n k ), and it is required to be reersible matrix in this method. h The frequency response is also diided into two parts corresponding to the measured response: h =. It can be h computed using (8), ; s s s U =h Q U =h Q (8) where Q is measured excitation matrix where the excitation is applied on the modified Dofs. The dimension of Q is (n m +n c +n k ) (n m +n c +n k ). Q is the excitation applied on the i-th modified Dof of the j-th group excitations. ij Substitute (7) and (8) into (6), there is Y, Δ Y UQ Δ P Y (9) Y, Δ Y UQ Δ P Y s s s The response Y, Δ is computed using the first equation of (9),see (),then response Y, Δ can be computed by s substituting () into the second equation of (9), see (): Y, Δ I U Q Δ P Y (), Δ Δ Δ () Y Y U Q P I U Q P Y s s s 733

4 A. Finite Element Model (FEM) of Beam III. NUMERICAL EXAMPLE A simply supported beam is used for numerical erification, see Fig.. The length is cm; the cross-section is 4 cm.4 cm. Young s modulus of the beam is 6 GPa, and the density is 895kg/m 3. The FEM model of the beam is diided into elements. The beam is diided to 5 substructures, and each substructure contains 4 elements, see Fig..The mode shape and natural frequency are respectiely shown in Fig. and Table I. The assumed damage extents of the 5 substructure are shown in Fig.3, and the corresponding natural frequencies of damaged beam are shown in Table I. Figure. The FEM of beam ω = 9.38 ω = ω 3= ω 4= Figure. The first 4 orders of structural modes TABLE I THE NATURAL FREQUENCIES (HZ) Order 3 4 Intact Damaged damage extent.6.4. element Figure 3 The damage extent B. The construction of ictual structure by DM Added irtual mass In this section, irtual mass is added on the middle of substructure, see Fig.4. Two acceleration sensors are placed on the middle of substructure and 3. Hammer excitation is applied on the middle of substructure and 3 respectiely, see Fig. 5, and the corresponding responses are respectiely shown in Fig.6 and Fig

5 excitation excitation acceleration acceleration mass Figure 4. The senor placements and added irtul mass f [N] t [s] Figure 5. Hammer exciation 5 a a [m/s ] a -5 t [s] Figure 6. The acceratation responses to hammer exciation on substruture a a [m/s ] a t [s] Figure 7. The acceratation responses to hammer exciation on substruture 3 Perform FFT on the responses in Fig.6 and Fig.7 and substitute them into (), then the nephogram of the constructed frequency response of irtual structural with attached mass are shown in Fig.8(a) and Fig.8(b).There the depth of the colour reflects the amplitude of the frequency response, so that the darkest points correspond to its peaks, that is to the natural frequencies of the irtual structure. It can be seen that as added mass alue increases, the natural frequencies decrease. When mass alue arries at a certain degree, the frequencies of irtual structure become stable and unchanged with the mass alue increasing. (a) Hammer excitation applied on subtruutrue (b) Hammer excitation applied on subtruutrue 3 735

6 Added irtual stiffness Figure 8. The nephogram of the constructed frequency response of irtual structural with added mass excitation excitation acceleration acceleration spring Figure 9. The senor placement and added spring stiffness In this section, irtual spring stiffness is added on the middle of substructure, see Fig.9. Two displacement sensors are placed on the middle of substructure and 3, and hammer excitation is applied on the middle of substructure and 3 respectiely, see Fig. 9. Similar to added irtual mass, the nephogram of constructed frequency responses of irtual structure with added spring stiffness are computed and they are shown in Fig.(a) and Fig.(b). The depth of the colour reflects the amplitude of the frequency response, so that the darkest points correspond to the natural frequencies of the irtual structure. It can be seen that as the alue of added stiffness increases, the natural frequencies decrease. When added stiffness reaches a certain alue, the frequencies of irtual structure become stable and unchanged with the stiffness alue increasing. (a) Hammer excitation applied on substructure (b) Hammer excitation applied on substructure 3 Figure. The nephogram of the constructed frequency response of irtual structural with adding sping stiffness Added irtual damping In this section, irtual damping is added on the middle of substructure, see Fig.. Two elocity sensors are placed on middle of substructure and 3. Hammer excitation is applied on the middle of substructure and 3 respectiely, see Fig.. Similar to the case of added irtual mass, the nephogram of the constructed frequency response of irtual structural with added damping are computed and are shown in Fig.(a) and Fig.(b). From colour depth of the nephogram, it tells that there is no obious change of the structural frequencies with the damping alue increasing because there is no relation between structural frequency and damping. But phase step happens on frequencies when the added damping reaches a certain alue. excitation excitation elocity elocity damping Figure. The senor placement and added damping 736

7 (a) Hammer excitation applied on substructure (b) Hammer excitation applied on substructure 3 Figure. The nephogram of the constructed frequency responses of irtual structure with added irtul damping C. Damage identification using constructed irtual structure To perform damage identification, first, a sensor is located on the middle of each substructure successiely, and correspondingly model force harmer is successiely used to apply the excitation along the measure senor, see Fig.3. The measured excitation and response are used to construct the irtual added mass, stiffness and damping which are added on each substructure. At last damage extents are identified using the irtual structural mode. f f f 3 f 4 f sensor sensor sensor 3 sensor 4 sensor 5 Figure 3. The placement of senor and hammer exciatiation Added irtual mass In oreder to simulate actual case, 5% Gaussian noise is added to the simulated measured responses. Hammer excitation and acceleration resposne are used to constructe added irtul mass which is added in the middle of the relatie substructure, and the corresponding nephogram of the constructed frequency responses of irtual structure are shown in Fig. 4. Fie irtual added mass wih alues of [ ]kg, are applied on each substructure, see Table II. Fig. 5 shows the frequency responses of substruture with the fie itual added masses. The first order of natrual frequency of the irtual structure is identified using Peak Pick mehtod through the constructed frequency responses correspodning to each irtual added mass. Table II lists the identified frequencies, which are used to identify damage extents. The identified resultes are shown in Fig. 6, which has nice accuracy. Figure 4. The nephogram of constructed frequency responses of irtual structural with added irtual mass 737

8 6 amplitude m m m 3 m 4 m ω[[] Figure 5. The constructed frequency response with 5 irtual added mass on substruture TABLE II THE NATURAL FREQUENCY (HZ) Identified natural Substructure Mass frequency damage extent.5 number Figure 6. The identified damage extents Actual Identified Added irtual stiffness Similarly to performance of irtual added mass alue, if elocity sensor is used instead of displacement sensor, then irtual stiffness can be constructed, which are added respectie in the middle of the substructures. The corresponding nephogram of the constructed frequency responses of irtual structure with added stiffness are shown in Fig. 7. From Fig. 7, 4 added stiffness 738

9 are selected and the corresponding frequencies are obtained, which are used to identify damage extents. The identifed results are shown in Fig. 8. It proes that damage extents can be identified accurately with both irtual added mass and irtual added spring stifness. Figure 7. The nephogram of the constructed frequency response of irtual structural with added spring stiffness damage extent.5 number Figure 8. The identified damage extents Actual Identified I. CONCLUSION This paper proposed a damage identification method by constructing irtual structure. The added irtual mass and stiffness proide more mode data for damage identification, and thus the identification accuracy is increased. REFERENCES [] L.R. Zhou, G.R. Yan, J.P. Ou. Response Surface Method Based on Radial Basis Functions for Modeling Large-Scale Structures in Model Updating. Computer-Aided Ciil and Infrastructure Engineering. 3, 8(3), 6. [] Z. Duan, G. Yan, J. Ou, B.F. Spencer. Damage Localization in Ambient ibration by Constructing Proportional Flexibility Matrix, Journal of Sound and ibration, 5, 84(): [3] P. Kolakowski, M. Wiklo, J. Holnicki-Szulc. The irtual Distortion Method - a ersatile reanalysis tool for structure and systems. Structural and Multidisciplinary Optimization, 8, 36(3):734 [4] R.M. Lin, D.J. Ewins. Model updating Using FRF Data. 5th Int. Seminar on Modal Analysis. Leuen, Belgium, 99, 4-6. [5] K. Demz, Z. Mroz. Damage identification using modal, static and thermographic analysis with additional control parameters. Compute & Structures,, 88( ): [6] H. Dinh, T. Nagayama, Y. Fujino. Structural parameter identification by use of additional known masses and its experimental application. Structural control and health monitoring,,9(3): [7] N. Nalitolela, J. Penny, M. Friswell. A mass or stiffness addition technique for structural parameter updating. Modal Analysis: The International Journal of Analytical and Experimental Modal Analysis. 99, 7(3): [8] P. Kołakowski, M. Wikło, J. Holnicki-Szulc. The irtual distortion method a ersatile reanalysis tool for structures and systems, Structural and Multidisciplinary Optimization. Papers 36 (3), 7 34 (8). [9] J. Holnicki-Szulc, J. (ed.), Smart Technologies for Safety Engineering, John Wiley & Sons, Chichester, (8). [] G. Suwala, L. Jankowskiy. A model-free method for identification of mass modifications. Structural control and health monitoring., 9(): 63. [] Q. Zhang, Ł. Jankowski, Z. Duan. Simultaneous identification of moing masses and structural damage, Structural and Multidisciplinary Optimization. In press,, 4:97 9. [] A. Świercz, P. Kołakowski, J. Holnicki-Szulc. Damage identification in skeletal structures using the irtual distortion method in frequency domain, Mechanical Systems and Signal Processing. 8, (8), Zhou LR, Yan GR, Ou JP. Response Surface Method Based on Radial Basis Functions for Modeling Large-Scale Structures in Model Updating. Computer-Aided Ciil and Infrastructure Engineering. 3, 8(3), 6 739