Dynamic Optimization of Structures Subjected to Earthquake

Transcription

1 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 Dynamc Optmzaton of Stuctues Subjected to Eathquake Aleza Lavae and Aleza Lohasb Abstact To educe the oveall tme of stuctual optmzaton fo eathquake loads two stateges ae adopted. In the fst stategy, a neual system consstng self-oganzng map and adal bass functon neual netwoks, s utlzed to pedct the tme hstoy esponses. In ths case, the nput space s classfed by employng a self-oganzng map neual netwok. Then a dstnct RBF neual netwok s taned n each class. In the second stategy, an mpoved genetc algothm s employed to fnd the optmum desgn. A 7-ba space tuss s desgned fo optmal weght usng exact and appoxmate analyss fo the El Cento (S-E 940) eathquake loadng. The numecal esults demonstate the computatonal advantages and effectveness of the poposed method. Index Tems Optmzaton, genetc algothm, eathquake, neual netwoks, self-oganzng map, adal bass functon. I. INTRODUCTION Optmum desgn of stuctues s usually acheved by selectng the desgn vaables such that an objectve functon s mnmsed whle all of the desgn constants ae satsfed. Stuctual optmzaton eques that the stuctual analyss to be pefomed many tmes fo the specfed extenal loads. Ths makes the optmal desgn pocess neffcent, especally when a tme hstoy analyss s consdeed. Ths dffculty wll be esonated when the employed optmzaton method has the stochastc natue such as evolutonay algothms. In the ecent yeas, tadtonal and evolutonay seach technques wee employed to optmal desgn of stuctues subjected to esponse spectum and eathquake loadngs. Salajegheh and Heda [] ncopoated neual netwok technques n the optmzaton pocess to pedct stuctual tme hstoy esponses. They employed wavelet back popagaton neual netwok. In the ecent yeas, neual netwoks ae boadly utlzed n cvl and stuctual engneeng applcatons. In ths nvestgaton, n ode to elmnate the dawback, the dynamc esponses of the stuctues have been appoxmated usng a self-oganzng neual system. S. Gholzadeh and E. Salajegheh ntoduced an ntellgent neual system (INS) fo effcent appoxmaton of tme hstoy stuctual esponses n Ref. []. In INS, the nput and taget spaces ae dvded nto some subspaces as the data located n each subspace have smla popetes. These popetes ae taken as sgnfcant natual peods of the stuctues. Classfcaton of nput space s acheved by usng compettve neual netwoks. Then a dstnct adal bass functon (RBF) neual netwok s taned fo each subspace Manuscpt eceved Octobe 30, 04; evsed Febuay 7, 05. Aleza Lavae and Aleza Lohasb ae wth Depatment of Cvl engneeng, College of engneeng, Booujed Banch, Islamc Azad Unvesty, Ian (e-mal: Shetab@gmal.com, A_lohasb@yahoo.com). usng ts assgned tanng data. Also, the authos ncopoated the INS n the optmzaton pocess n Ref. [3]. The numecal esults showed geat computatonal effcency wth a man lmtaton of dffcultes fo detemnng the numbe of data clustes. In the pesent study, self-oganzng map (SOM) neual netwoks ae used to classfcaton of the nput space. The numecal examples show that by usng SOM neual netwoks the mentoned lmtaton of detemnng data clustes s completely vanshed. The SOM s a neual netwok algothm developed by Kohonen [4] that foms a two dmensonal pesentaton fom mult dmensonal data. The SOM neual netwoks lean to classfy nput vectos accodng to how they ae gouped n the nput space. They dffe fom compettve neual netwoks n that neghboung neuons n the SOM lean to ecognze neghboung sectons of the nput space. Thus, SOM lean both the dstbuton (as do compettve layes) and topology of the nput vectos they ae taned on. The man am of ths pape s to mpove the INS by substtutng the compettve netwok wth self-oganzng map neual netwoks. The esulted neual system s called self-oganzng neual system (SONS). Theefoe, SONS conssts of an ntellgent classfyng unt and a set of paallel RBF neual netwoks whch ae locally taned on the nput space. Illustatve example shows the computatonal advantages of SONS compang wth sngle RBF neual netwok. In the compute mplementaton phase of SONS, the nput space ncludes natual peods of the stuctues and taget space conssts of coespondng esponses of selected node dsplacements and element stesses aganst the specfed eathquakes. To povde tanng data and to desgn the neual netwoks ANSYS [5] and MATLAB [6] ae utlzed. The employed evolutonay algothm s vtual sub populaton (VSP) method [7]. In the pesent wok, a 7-ba space tuss stuctue subjected to the El Cento (S-E 940) eathquake s desgned fo optmal weght. The numecal esults of optmzaton show that ncopoatng of SONS n the famewok of VSP ceates a poweful tool fo optmum desgn of stuctues aganst the eathquake by spendng low computatonal effots. II. FORMULATION OF OPTIMIZATION In szng optmzaton poblems the am s usually to mnmze the weght of the stuctue, unde some constants on stesses and dsplacements. Due to the pactcal demands the coss-sectons ae selected fom the sectons avalable n DOI: /IJET.06.V

2 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 the pofle lsts. Theefoe, the desgn vaables ae dscete. A dscete stuctual optmzaton poblem can be fomulated n the followng fom that Mnmze f(z) Subject to:,,, m g ( Z) 0 j,,, n S Sa () whee S s the maxmum stess n each element goup fo all loadng cases and Sa s the allowable stess. Smlaly, the dsplacement constants can be wtten as U Ua (3) whee Ua s the lmtng value of the dsplacement at a cetan node. When the stuctue s subjected to the dynamc exctaton, the constants must be teated as the tme functons:,,, m g ( Z, t) 0 (4) III. STRUCTURAL TIME HISTORY ANALYSIS The dynamc analyss consdeed hee s the tme hstoy method. The pocedue nvolves a step-by-step soluton though a tme doman to yeld the dynamc esponse of a stuctue to a gven eathquake. The equatons of equlbum fo a fnte element system subjected to the eathquake may be wtten n the usual fom: MU ( t) CU( t) KU( t) MIU ( t) (5) whee M, C, K and I ae the mass, dampng, stffness and dentty matces; Ut ( ), Ut () and Ut () ae the acceleaton, velocty and dsplacement vectos, espectvely. Fo analyss of the stuctues subjected to eathquake loadng, ANSYS s used. The theoy and soluton pocedues ae based on the fnte-element fomulaton of the dsplacement method wth the nodal dsplacements as the unknown vaables. It uses a step-by-step mplct numecal ntegaton pocedue based on Newmak s method to solve the esultng equatons. IV. DYNAMIC CONSTRAINTS TREATMENT All of the stess and dsplacement constants ae tme dependent. These constants need to be mposed at each pont n the desed tme nteval. The consdeaton of all the constants eques an enomous amount of Zj d R () whee f(z) epesents objectve functon, g(z) s the behavoal constant, m and n ae the numbe of constants and desgn vaables, espectvely. A gven set of dscete values s expessed by R d and desgn vaables Z j can take values only fom ths set. In the optmal desgn of stuctues the constants ae the membe stesses, nodal dsplacements, o fequences. The stess constants can be wtten as whee g( Z, t) tme of t. s the behavoual constant evaluated at the g computatonal effot and, theefoe, teatment wth a vast numbe of tme hstoy esponses s a challengng poblem fo most numecal optmzaton algothms [8]. Vaous numecal technques exst fo teatng such tme-dependent constants [9]. The basc dea of these methods s to elmnate somehow the tme paamete fom the optmzaton poblem. In othe wods, a tme-dependent poblem s tansfomed nto a tme-ndependent one. In the pesent study, the conventonal method [9] s employed. Ths method s qute smple and convenent to mplement whee the tme nteval s dvded nto p subntevals and the tme-dependent constants ae mposed at each tme gd pont. Let the th tme-dependent constant (stess o dsplacement) be wtten as: 0 t T g ( Z, t) 0 (6) whee T s tme nteval ove whch the constants need to be mposed. Because the total tme nteval s dvded nto p subntevals, the constant (6) s eplaced by the constants at the p+ tme gd ponts as: j 0,,, p g ( Z, t) 0 (7) The constant functon g (Z, t) can be evaluated at each tme gd pont afte the stuctue has been analyzed and stesses and dsplacements have been evaluated at each tme pont. If fewe gd ponts ae used, the tme-dependent constants may be volated between the gd ponts. Use of a fne gd can captue these ponts. V. OPTIMIZATION METHOD Thee ae two majo steps n compute mplementaton of the optmal desgn pocess of stuctues: the analyss step and the optmzaton step. As mentoned pevously, the tme hstoy dynamc analyss of stuctues s pefomed usng Newmak s method. The optmzaton method employed hee s an mpoved genetc algothm (GA). GA has been qute popula and has been appled to a vaety of engneeng poblems [0]-[3]. The stochastc natue of GA makes the convegence of the method slow. Specally, employng GA to fnd optmum desgn of stuctues wth many degees of feedom leads to the tme consumng cycles. In ths pape, to educe the computatonal buden of the optmzaton pocess, VSP s employed. In ths method all the necessay mathematcal models of the natual evoluton opeatons ae mplemented on the small ntal populaton to access optmal soluton on teatve bass. As shown n Ref. [7] the computatonal wok by VSP s less than the standad GA. Despte the seous educng effects of VSP on the optmzaton tme, the computatonal buden of the pocess due to mplementng the tme hstoy dynamc analyss s vey hgh. Theefoe, usng neual netwoks to educe the compute effot s vey effectve. VI. SELF-ORGANIZING NEURAL NETWORKS The self-oganzng map (SOM) s a neual netwok 8

3 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 algothm developed by Kohonen [4] that foms a two dmensonal pesentaton fom mult dmensonal data. In othe wods, the SOM s non lnea pojecton methods fom a hgh dmensonal nput space to a low (two o one) dmensonal gd space, whee t s ease to classfy and vsualze the data. The SOM neual netwoks lean to classfy nput vectos accodng to how they ae gouped n the nput space. They dffe fom compettve neual netwoks n that neghbong neuons n the SOM lean to ecognze neghbong sectons of the nput space. Thus, SOM lean both the dstbuton (as do compettve layes) and topology of the nput vectos they ae taned on. The topology of the data s kept n the pesentaton such that data vectos, whch closely esemble one anothe, ae located next to each othe on the map. Ths knd of neual netwoks has been found vey useful fo the undestandng of the mutual dependences between the vaables, as well as of the stuctues of the data set. In contast to tadtonal methods, such as pncpal component analyss, the SOM gd can also be ceated fom hghly devatng, nonlnea data. The neuons n the laye of an SOM ae aanged ognally n physcal postons accodng to a specfc topology such as gd, hexagonal, o andom topology. A typcal stuctue of SOM netwoks s shown n Fg.. dffeence between SONS and INS les n the classfyng unt. The detals of SONS ae explaned as follows: Fstly, the geneated nput-taget tanng pas ae classfed based on the natual peods of the stuctues. Input space classfcaton s mplemented by usng a SOM neual netwok. Now t s possble to tan an RBF netwok fo each subspace usng ts tanng data. By consdeng the mentoned stategy, the sngle RBF netwok taned to cove all the nput space s substtuted wth a set of some paallel RBF netwoks as each of them s taned to cove one specfc pat of the classfed nput space. A smple schema of SONS tanng flow s shown n Fg.. Fg.. The flow of self-oganzng RBF (SONS) tanng. Fg.. A typcal stuctue of SOM netwoks. Tanng of SOM netwoks s based on Kohonen selfoganzaton algothm. A SOM netwok dentfes a wnnng neuon usng the same pocedue as employed by a compettve laye. Howeve, nstead of updatng only the wnnng neuon, all neuons wthn a cetan neghbohood N(d) of the wnnng neuon ae updated, usng the Kohonen ule. Specfcally, all such neuons N(d) ae adjusted as follows: w ( k ) w ( k) α[ v ( k) w ( k)] (8) j j j j whee W j s the weght of SOM laye fom nput to neuon j, v j s j th component of the nput vecto, α s leanng ate and k s dscete tme. Hee the neghbohood N(d) contans the ndces fo all of the neuons that le wthn a adus d of the wnnng neuon. Thus, when an nput vecto s pesented, the weghts of the wnnng neuon and ts close neghbos move towad the vecto. Consequently, afte many pesentatons, neghbong neuons have leaned vectos smla to each othe. VII. DETAILS OF SELF-ORGANIZING NEURAL SYSTEM Detals of SONS and INS ae smla. The man One of the most mpotant dffcultes of INS mplementaton s the detemnaton of the numbe of data clustes. Ths dffculty s allevated by usng SOM neual netwok n the famewok of SONS. In ode to tan the classfyng unt of SONS a geneal gd of SOM neuons wth andom topology s consdeed. Afte tanng, the confguaton of ntal gd captues the shape of dstbuton of data n the nput space. In ths egad, the neuons tend to clusteng and theefoe the numbe of clustes can be smply detemned mean of exact vectos component. VIII. ERROR MONITORING In ode to evaluate the accuacy of appoxmate stuctual esponses pedcted by neual netwoks, two evaluaton metcs ae used: the elatve oot mean squae (RRMS) eo and R-squae (R ) statstc measuement [4]. The RRMS eo between the exact and pedcted esponses s defned as follows: whee, λ and RRMSE ~ ae the th - ( ) ( ) (9) component of the exact and pedcted esponses, espectvely. The vectos dmenson s expessed by. 9

4 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 To measue how successful fttng s acheved between exact and appoxmate tme hstoy esponses, the R-squae statstc measuement s employed. Statstcally, the R s the squae of the coelaton between the pedcted and the exact esponses. It s defned as follows: R-squae ( ) ( ) whee, s the mean of exact vectos component. IX. APPROXIMATION OF TIME HISTORY RESPONSES BY SONS (0) The nput space conssts of some natual peods of the selected stuctues and the coespondng tme hstoy esponses of nodal dsplacements and element ntenal stesses aganst eathquake ae consdeed as the taget space components. At fst, a SOM netwok s taned to classfy the nput space based on the natual peods. To appoxmate tme hstoy esponses of stuctues located n each subspace, a dstnct RBF netwok s taned usng the data located n t.. 00 kg/m, weght densty s 7850 kg/m3. Cosssectonal aea of the membes ae selected fom the ppe, wth adus to thckness less than 50, sectons avalable n Euopean pofle lst. The optmzaton s caed out by the VSP usng followng stuctual analyss methods: ) Exact Analyss (EA). ) Appoxmate analyss by a sngle RBF neual netwok (RBF). 3) Appoxmate analyss by SONS neual netwoks (SONS). TABLE I: SPECIFICATIONS OF VSP METHOD Populaton sze 30 Cossove method One, two and thee ponts cossove Cossove ate 0.9 Mutaton ate 0.00 Maxmum geneaton 5 The 7-ba tuss s shown n Fg. 3. The mass of 0000 kg s lumped at nodes of to 4. The tuss s subjected to 5 s of the eathquake ecod, shown n Fg. 4. X. MAIN STEPS OF OPTIMIZATION The fundamental steps n the optmzaton pocess by VSP usng SONS fo eathquake loadng ae as follows: ) Selectng some paent vectos fom the desgn vaables space. ) Evaluatng the tme hstoy esponses of the stuctue employng SONS. 3) Evaluatng the objectve functon. 4) Checkng the constants at gd ponts fo feasblty of paent vectos. 5) Geneatng offspng vectos usng cossove and mutaton opeatos. 6) Pedctng the stuctual tme hstoy esponses fo the offspng populaton usng taned SONS. 7) Evaluatng the objectve functon. 8) Checkng the constants at gd ponts; f satsfed contnue, else change the vecto and go to step (f). 9) Checkng convegence; f satsfed stop, else go to step (e). - Selectng the majoty paent vectos fom the pevous soluton and some andom desgn vaables as a VSP. Repeatng steps (e) to (k) untl the pope soluton s met. As the sze of populatons n VSP s small the method s apdly conveged. It can be obseved that dung the optmzaton, the dynamc analyss of the stuctues s not needed. In fact, the necessay esponses ae found by the taned SONS. Fg Ba space steel tuss. XI. NUMERICAL EXAMPLE One llustatve example s optmzed fo mnmum weght. The tme of optmzaton s computed n clock tme by a pesonal Pentum IV 000MHz. The eathquake ecods ae appled n x decton. Young s modulus s Fg. 4. The El Cento eathquake ecods (S-E 940). Due to smplcty and pactcal demands, the tuss membes ae dvded nto 9 goups based on coss-sectonal aeas, shown n Table II. 30

5 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 Goup No TABLE II: ELEMENT GROUPS OF THE 7-BAR TRUSS Elements Because of the nsgnfcant ntenal stesses of of goup 9 unde the eathquake exctaton, a mnmum coss-sectonal aea of.54 cm s assgned to them. Fo all the element goups, allowable stess s chosen to be 00 kg/cm. Also, fo the top node of the stuctue, the allowable hozontal dsplacement s chosen to be cm. In ode to satsfy the pactcal demands, 8 types of cosssectonal aeas ae consdeed fo the tuss whch ae dsplayed n Table III. Fg. 6. Input data dstbuton on nput space and cente of clustes. The esults of testng the sngle RBF and SONS neual netwoks ae only shown fo node dsplacement and axal stess of goup 7 n Fgs. 7 to 0. No TABLE III: AVAILABLE CROSS-SECTIONAL AREAS Aea (cm) Fg. 7. 7: R-squae of appoxmate dsplacement of node. In the begnnng, 300 stuctues ae andomly geneated based on coss-sectonal aeas and ae subjected to the eathquake ecod. The fst, thd and ffth natual peods ae selected to be nput space components. The coespondng node dsplacement and axal stesses of element goups to 8 ae chosen as taget space components. Fom whch 0 and 80 samples ae employed to tan and to test the pefomance genealty of the netwoks, espectvely. A sngle RBF netwok s taned fo pedctng node dsplacement and axal stess of each element goups. The fst step n desgnng SONS s to classfy the nput space. At fst, a 5 3 gd of SOM neuons wth andom topology s consdeed. Afte tanng the SOM netwoks, as shown n Fg. 5, t s obseved that the neuons ae gouped n thee man clustes. Fg. 8. RRMSE of appoxmate dsplacement of node. Fg. 9. R-squae of appoxmate stess of goup 7. Fg. 0. RRMSE of appoxmate stess of goup 7. Fg. 5. Input data dstbuton on nput space and a 5 3 gd of SOM neuons. To elmnate edundant computatons, a gd of 3 SOM neuons wth andom topology s adopted fo ths example. Thus, all the nput data s dvded nto thee clustes. Input data dstbuton and cente of clustes s shown n Fg. 6. It s smple to fnd out fom Fgs. 7 to 0 that SONS possesses the bette pefomance genealty compang wth the sngle RBF netwok. The aveage R-squae and RRMSE fo sngle RBF and SONS fo all tanng samples ae , and , 0.873, espectvely. Mean R- squae and mean RRMSE of pedcted stuctual esponses n all the clustes ae dsplayed n Table IV. In ths example, the total tme spendng to data geneaton and neual netwoks tanng s equal to 460 mn. Now employng the sngle RBF and SONS netwoks, the 7-ba tuss s desgned fo optmal weght. The esults of optmzaton usng exact and appoxmate analyss ae dsplayed n Table V. As shown n ths table, the optmum desgn obtaned usng exact analyss n bette than othe 3

6 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 solutons but t s vey extensve n tems of the optmzaton ove all tme. Tme hstoy esponses of optmum desgns obtaned usng appoxmate analyss ae compaed wth the coespondng actual ones. A bef summey s dsplayed n Table VI. The compasons eveal the appopate confomance between all of the appoxmate and coespondng actual esponses. But the pefomance of SONS s bette than that of the sngle RBF netwok. TABLE IV: MEAN R-SQUARE AND RRMSE OF TEST DATA FOR THREE MAIN CLUSTERS Stuctua Cluste Cluste Cluste 3 l esponse R-squae RRMSE Rsquae RRMSE R-squae RRMSE Node dsp Goup Goup Goup Goup Goup Goup Goup Goup Av TABLE V: OPTIMUM DESIGNS OBTAINED BY VSP USING EXACT AND APPROXIMATE ANALYSIS Element Goups No. Optmum aeas (cm ) EA RBF SONS Weght (kg) Geneatons Tme (mn) TABLE VI: MEAN R-SQUARE AND MEAN RRMSE OF OPTIMUM DESIGNS Stuctual paametes SONS RBF R-squae RRMSE R-squae RRMSE Node dsplacement Goup Goup Goup Goup Goup Goup Goup Goup Aveage The optmum desgn attaned usng SONS s bette than that of the obtaned usng the sngle RBF netwok. It s mpotant to note that, n ths example the tme of optmzaton employng neual netwoks, ncludng data geneaton and tanng the neual netwoks s about 0.8 tme of exact optmzaton. XII. CONCLUSIONS A obust optmzaton pocedue has been developed fo the optmal desgn of stuctues subjected to eathquake usng dscete desgn vaables. In the pocedue, a combnaton of the evolutonay algothm and neual netwoks has been utlzed. The employed evolutonay algothm s vtual sub populaton (VSP) method. The VSP method has elmnated the shotcomngs of the standad GA such as tappng nto local optma and much effot n the phase of compute mplementaton. Moeove, pefomng the stuctual optmzaton usng the exact tme hstoy analyss fo eathquake nduced loads mposes a huge computatonal buden to the optmzaton pocess. That s, n each desgn pont of the desed eathquake the stuctue should be analyzed to evaluate the necessay esponses. To educe the compute effot of the optmzaton pocess due to the pefomng tme hstoy analyss, a new neual system s employed. In the neual system, a specfc combnaton of self-oganzng map (SOM) and adal bass functon (RBF) neual netwoks s employed to access hgh qualty appoxmaton of stuctual tme hstoy esponses. The neual system s called self-oganzng neual system (SONS). In fact, SONS ncludes two opeatonal phases; classfcaton and paallelzaton. In the classfcaton phase the nput space s classfed employng a SOM neual netwok. In the paallelzaton phase, a dstnct RBF neual netwok s taned fo each class. In the pesent pape, RBF neual netwok and SONS s employed to appoxmate the necessay tme hstoy esponses of stuctues. A smple method s employed to teat wth dynamc constants. In ths method the tme nteval s dvded nto some subntevals and the constants ae mposed at each tme gd ponts. The numecal esults of optmzaton show that n the poposed methods, the tme of optmzaton ncludng tanng tme s educed to about 0. of the tme equed fo exact optmzaton; howeve, the eos ae small. Fnally, t s demonstated that the best soluton has been attaned by VSP method usng SONS. REFERENCES [] E. Salajegheh and A. Heda, Optmum desgn of stuctues aganst eathquake by wavelet neual netwok and flte banks, Eathquake Engneeng and Stuctual Dynamcs, vol. 34, pp. 67 8, 005. [] S. Gholzadeh and E. Salajegheh, An ntellgent neual system fo pedctng stuctual esponse subject to eathquakes, n Poc. the Ffth Intenatonal Confeence on Engneeng Computatonal Technology, 006, p. 63. [3] E. Salajegheh, J. Salajegheh, and S. Gholzadeh, Stuctual optmzaton fo eathquake loadng usng neual netwoks and genetc algothms, n Poc. the Eghth Intenatonal Confeence on Computatonal Stuctues Technology, 006, p. 49. [4] T. Kohonen, Self-Oganzaton and Assocatve Memoy, nd edton, Spnge-Velag, Beln, 987. [5] ANSYS Incopoated, ANSYS Release 8., 004. [6] The Language of Techncal Computng, MATLAB, Math Woks Inc, 004. [7] E. Salajegheh and S. Gholzadeh, Optmum desgn of stuctues by an mpoved genetc algothm usng neual netwoks, Advances n Engneeng Softwae, vol. 36, pp , 005. [8] X. K. Zou and C. M. Chan, An optmal eszng technque fo sesmc dft desgn of concete buldngs subjected to esponse spectum and tme hstoy loadngs, Computes and Stuctues, vol. 83, pp , 005. [9] J. S. Aoa, Optmzaton of Stuctues Subjected to Dynamc Loads, Stuctual dynamc systems computatonal technques and optmzaton, Godon and Beach Scence Publshes,

7 IACSIT Intenatonal Jounal of Engneeng and Technology, Vol. 8, No. 4, August 06 [0] J. D. Mathas, X. Balandaud, and M. Gedac, Applyng a genetc algothm to the optmzaton of composte patches, Computes and Stuctues, vol. 84, pp , 006. [] V. Govndaaj and J. V. Ramasamy, Optmum detaled desgn of enfoced concete contnuous beams usng genetc algothms, Computes and Stuctues, vol. 84, pp , 005. [] G. A. Gazonas, D. S. Wele, R. Wldman, and A. Mohan, Genetc algothm optmzaton of phononc bandgap stuctues, Intenatonal Jounal of Solds and Stuctues, vol. 43, pp , 006. [3] S. F. Hwang and R. S. He, Impovng eal-paamete genetc algothm wth smulated annealng fo engneeng poblems, Advances n Engneeng Softwae, vol. 37, pp , 006. [4] X. Jang, S. Mahadevan, and H. Adel, Bayesan wavelet packet denosng fo stuctual system dentfcaton, Stuctual Contol and Health Montong, 006. A. Lavae s an academc membe n the Depatment of Cvl Engneeng, College of engneeng, Booujed Banch, Islamc Azad Unvesty, Ian. He stated teachng cvl couse n Azad Islamc Unvesty snce 008. Hs eseach nteests ae n optmzaton, genetc algothm, eathquake, neual netwoks, and hazad assessment. He s a membe of Amecan Concete Insttute (ACI) and membe of Constucton Engneeng Dscplnay Oganzaton (Level n Desgn and Contol) n Ian. 33