The 14 th World Conference on Erthque Engineering IDENTIFICATION AND MODIFICATION OF FRAME STRUCTURE P. Roso 1 1 Ass. Professor, Center of Mechnics nd Structurl Dynmics, Vienn University of Technology, Austri Emil: pr@llmech.tuwien.c.t ABSTRACT : The pper presents identifiction nd upgrde of structure under erthque lods on the bse of optimiztion. The mesured frequency spectrum of the structure determines the numericl model design. The structure is excited by ground ccelertion. Liner nd nonliner dynmic nlysis in time domin is relized. The identifiction of the model prmeter is solved s n optimiztion problem. The objective is the error index minimiztion between mesured response in rel structure nd clculted response of the numericl model. The hybrid optimiztion lgorithm is pplied. In order to improve erthque resistnce of the structure the pssive control help of tuned mss dmper is designed. Three-storey frme is investigted. Experimentl nd prllel numericl nlyses re relized. Accelerogrms from the Friuly-erthque re pplied. KEYWORDS: Identifiction, frme, optimiztion, pssive control, tuned mss dmper
The 14 th World Conference on Erthque Engineering 1. INTRODUCTION Dynmic behvior nd resistnce of civil structures under erthque lods hs high importnce. This is fter thousnds yers experience not question. To nlyze concrete structure two different wys re vilble: experimentl nd numericl. The civil engineering prctice needs correct informtion bout current stte of building structures. The experimentl nlysis nswers this question. The numericl models nd nlyses enble simultion of vrious lods nd structurl behvior. Advntge of this wy is the nondestructive testing nd possibility of esy model modifiction. Combintion of experimentl nd numericl nlysis profits from dvntges of both. The result of this combintion is numericl model rel prmeters nd fesibility for upgrde. Over lst yers severl methods hve been evolved in this re. The identifiction nd upgrde of structure illustrted on three-storey frme exmple is presented in the pper. The methodology is chosen to be universl for liner nd nonliner cses. 2. EXPERIMENTAL ANALYSIS - MEASUREMENT The three-storey frme is investigted [1]. Nowdys re vilble dtbses providing informtion nd ccess to strong motion records (e.g. COSMOS Virtul Dt Center, Europen Strong Motion Dtbse [2] etc.). Figure 1 Accelerogrm from Friuli erthque The record of Friuli erthque is pplied s excittion. The response of the structure is mesured. The time history is output of the mesurement. The output prmeters of experimentl nlysis hve to be comptible output prmeters from numericl nlysis. From this reson we did not use insted frequency response functions displcement nd its derivtions.
The 14 th World Conference on Erthque Engineering Figure 2 Three-storey frme Figure 3 LbVIEW control progrm Experimentl setup consists of PC LbVIEW control progrm, Sher, Ntionl Instruments nlogue digitl converter, Brüel&Kjer ccelerometers nd chrge mplifiers. 3. NUMERICAL MODEL, ANALYSIS In dynmics simple models low number of degrees of freedom re preferble. They hve to include complex informtion of the rel structure nd hve to be ble to simulte the sme behvior s the rel structures. The geometry of the structure nd nlysis in frequency domin determines the model design. Figure 4 Response spectrum
The 14 th World Conference on Erthque Engineering 3.1. Model 1(1) 2(1) 3(1) x 1(2) m1 2(2) m2 3(2) m3 c1 c2 c3 Figure 5 3-Degree of Freedom Model 3.2. Anlysis Dynmic equilibrium equtions of elstic multi-degree-of-freedom (MDOF) system ground excittion re Mx + Cx + Kx= Me (3.1) The equtions governing the response of the inelstic MDOF system ground excittion re ( ) Mx + Cx + fs x,x = M e u g (3.2) M mss mtrix C dmping mtrix K stiffness mtrix fs ( x,x ) lterl force vector, e is influence vector x t, x t, x t displcement-, velocity- nd ccelertion- vector u g () () () () t is the ground ccelertion Chopr [3] proposed modl nlysis concept for elstic nd inelstic MDOF systems s well, lthough modl nlysis in clssicl form is not vlid for n inelstic system. The dynmic response of n MDOF sy stem is expressed in terms of modl contributions N x = φ q = Φq = 1 u g = 1,2,, N (3.3) x ( t ) displcement vector, Φ modl mtrix, q( t ) vector of modl coordintes. Substituting (3) in equtions (1), (2) nd premultiplying by gives N independent equtions T Φ L q + q q xg (3.4) 2 2ζ ω + ω = m 2 ζ ω + FS L m = m q + q xg (3.5) ω nturl frequency, ζ dmping rtio, L nd m re elements of L T = Φ Me (3.6)
The 14 th World Conference on Erthque Engineering M T = Φ M Φ (3.7) (, ) T (, ) F = F q q = φ f q q (3.8) S S S F S is nonliner hysteric function of the -th modl coordinte q. Solution of equtions (3.4) lterntively solution of equittions (3.5) result the output of numericl dynmic nlysis. 4. PARAMETER IDENTIFICATION The identifiction of the model prmeter is defined s n inverse problem. The inverse problem is solved help of optimiztion procedure. The objective is the error index minimiztion between mesured response in rel structure nd clculted response of the numericl model. Objective mi ( ) mesured response min ci v clculted response function v vribles of optimiztion nt number of time increments nt ( i= 1 mi nt i= 1 ci 2 mi ( v )) 2 (4.1) To improve the efficiency the mesured response is nlyzed. Appernce of nonlinerities is checed nd liner lterntively nonliner numericl nlysis procedure is chosen. Prmeters of liner cse re elements of stiffness-, mss- nd dmping- mtrices. Prmeters of nonliner cse re elements of mss- nd dmping- nd chrcteristics of biliner hysteresis (detils in mtrices [8]). 4.1. Optimiztion procedure The hybrid optimiztion lgorithm is pplied. Before the genetic lgorithm (GA) strts, the sensitivity nlysis the mesured response is executed. As result of sensitivity nlysis only prt of time history is needed. Using sensitivity in connection GA improves the efficiency of optimiztion. Flowchrt of hybrid optimiztion procedure: I. Sensitivity nlysis II. GA: II.1 Initil popultion cretion II.2 Evlution of initil popultion Genertionl loop II.3 II.8: II.3 Fitness vlue clcultion for ech member of the popultion II.4 Selection of individuls for breeding II.5 Crossover of individuls II.6 Muttion pplying II.7 Evlution of the objective function II.8 Replce the popultion offspring
The 14 th World Conference on Erthque Engineering Detils of GA re explined in bsic boos of Rechenberg [4] nd Goldberg [5] nd in contributions of Toropov et l. [6] or Wng et l [7]. The ppliction is shown in [8]. Hysteresis of our frme exmple s result of experimentl nd numericl nlysis is presented in fig.7. The minimum vlue of error is 0,1%. F[N] 10 0-10 -5 5 0 x [mm] Figure 6 Objective - Optimiztion history Figure 7 Force-deformtion reltion 5. MODIFICATION OF THE STRUCTURE - UPGRADE In order to improve erthque resistnce of the structure the pssive control help of tuned mss dmper is designed. The optimiztion problem definition: minimiztion of dynmic response. bjective: min x(, m ) (5.1) O ( ) TMD TMD Vribles of optimiztion re dded stiffness TMD nd mss m TMD. The hybrid lgorithm introduced in prt 4. is pplied. Comprison of fig.4 nd fig.9 shows chnges by nturl frequency. Figure 8 Three-storey frme TMD Figure 9 Response spectrum of frme TMD
The 14 th World Conference on Erthque Engineering CONCLUDING REMARKS The presented methodology llows cretion of usble liner nd nonliner models of structures in dynmics. The fetures of these models re low number of degrees of freedom nd physiclly good interpretble system prmeters. The identified model is usble for next nlyses, for monitoring of the structure nd for structurl upgrde design. The hybrid optimiztion is relible procedure for structurl prmeter identifiction, upgrde of structure nd improvement of structurl behvior under erthque lods. REFERENCES [1] Adm, C., Heuer, R. nd Pirrott, A. (2003). Experimentl dynmic nlysis of elstic-plstic sher frmes secondry structures. Experimentl Mechnics, 43, 124-130. [2] Ambrseys, N., Smit, P., Berrdi R., Rinlds, D., Cotton, F. nd Berge, C. (2000). Dissemintion of Europen Strong-Motion Dt. Europen Commission, DGXII, Science, Reserch nd Development, Bruxelles. [3] Chopr, A.K. (2007). Dynmics of Structures, 3rd Edition. Prentice Hll, New Jersey. [4] Rechenberg, I. (1973). Evolutionsstrtegie Optimierung technischer Systeme nch Prinzipen der biologischen Evolution, Frommnn Holzboog, Stuttgrt. [5] Goldberg, D. E. (1989). Genetic Algorithms in Serch, Optimiztion nd Mchine Lerning, Addison Wesley Publishing Compny, New Yor. [6] Toropov, V. nd Yoshid, F. (2004). Appliction of dvnced optimiztion techniques to prmeter nd dmge identifiction problems. CISM course Udine, Springer. [7] Wng, G..S., Hung, F.K. nd Lin, H.H. (2004). Appliction of Genetic Algorithm to Structurl Dynmic Prmeter Identifiction, in Proceedings of 13 th WCEE, Vncouver. [8] Roso, P. (2005). Dynmic System Identifiction of Civil Structure using Genetic Algorithm, in Proceedings of 6th World Congress of Structurl nd Multidisciplinry Optimiztion, Rio de Jneiro. ACKNOWLEDGEMENTS The uthor wishes to thn collegues Prof. C. Adm nd Prof. R. Heuer from Vienn University of Technology for experimentl frme model cretion.