Computational Method of Structural Reliability Based on Integration Algorithms

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1 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp Sensors & ransducers 03 by IFSA ttp:// Computational Metod of Structural Based on Integration Algoritms * Cong Cen, Yi Wan College of Pysics and Electronic Information Engineering, Wenzou University, 35035, Cina * el.: , fax: * ccmcm@qq.com Received: 5 June 03 /Accepted: 9 July 03 /Publised: 3 July 03 Abstract: It is very difficult to built reliability design model of structural parts woring in a complex and uncertain environment because of teir dynamic time-dependent caracteristic, an intelligent metod of reliability analysis based on integration algoritm is presented in tis paper, RBFNN and finite element analysis combined wit Monte Carlo numerical simulation is integrated to improve simulation computing precision. And tis metod is applied to reliability analysis of OCS suspension system, matematic model of reliability calculation on OCS system based on integration algoritm is built, and reliability of OCS suspension system are calculated by te metod, and te influence of outside parameter on te wole system is analyzed by te model. OCS suspension system are critical force-bearing parts of OCS system in te ig-speed electrified railway, and fault rate is very ig, teir reliability analysis is important researc subect in railway system, te integration algoritm provides feasible new metod for te reliability analysis and design of OCS system and te oter Structural system. Copyrigt 03 IFSA. Keywords: RBFNN, analysis and design, Monte Carlo, Finite element analysis, OCS.. Introduction e OCS in te ig-speed electrified railway is erected directly and no alternately, various size and structure are in motion and cange under natural environment and complex loads, so frequent trip, electricity supply failure and frequent faults of pantograp and OCS become one of te most equipment faults affecting transportation safety. Improving OCS system stability and reliability plays an important role to improve operation efficiency and decrease operation faults of te igspeed electrified railway, particularly for some location parts, suc as location supporting seat and location pipe, tey are critical force-bearing parts of OCS system in te ig-speed electrified railway and wor in a complex and uncertain environment and are in dynamic canging because of all inds of complex loads suc as pantograp, wind and natural climate, so fault rate is very ig, teir reliability analysis and design are important researc subect in railway system []. In reliability design model, stress-intention distribution model reveals clearly fault cause and te essence of reliability design, but it is difficult to establis stress and intention distribution and oint probability density function in dynamic timedependent environment. In tis paper, an intelligent metod of reliability analysis based on integration algoritm is presented, RBFNN and analysis of finite element combined wit Monte Carlo numerical simulation is integrated to improve simulation computing precision. Matematic model of reliability calculation on OCS system and integration algoritm 5 Article number 77

2 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp model are built, reliability of OCS suspension system is calculated by te metod, and te outside parameter influence on OCS suspension system is analyzed by te model. It provides a new way for te design and researc of reliability in complex railway system [].. Stress-intention Interference Model Every components of mecanism part maybe invalid because all inds of complex static loads and dynamic loads lead to internal stress exceed material intensity limit, te failure probability can be obtain by () according to stress-intention interference teory [3, 4]. P f P S 0) f (, s) dds, ( were X, X, X..., X ), D ( 3 i S S X, X, X,..., X ). ( S S S3 S S () f S (, s) is te stress and intention oint probability density of every components, X i is te structural intention, X is te stress. s If X ( X, X..., X n ) is random parameters vector, ten state function is Expressed as: g ( X ) ( X ) S ( X ), () e components will invalidate if g ( X ) 0 according to () and probability and statistics teory, failure probability and reliability can be calculated in a certain amount of random numbers and S. Intensity interference model of structural reliability analysis is sown in Fig.. Fig.. Intensity interference model of structural reliability analysis. 3. Compound Algoritm Matematic Model of Analysis It is difficult to build reliability model of OCS suspension system because tey wor in a complex and uncertain environment. In tis paper, reliability analysis metod of OCS suspension system based on RBFNN and finite element combined wit Monte Carlo is presented, integration algoritm course is as follows [4]: ) Critical factors tat influence te reliability of OCS suspension system are establised, tey are pretigten force P, contact wire tension and wind speed W and ice-covering ticness d. ) N groups of random data are generated according to statistical distribution for selected parameters, maximum stress in dangerous section for eac group of parameters are calculated by te finite element [5]. After selecting te fragment structure unit, caracteristic analysis of typical unit is necessary, relationsip of any point displacement is derived by nodal displacements. { w} [ N]{ u}, (3) were {w} is te column vector of any point displacement in te unit, { u } is te column vector of nodal displacement, [N] is te sape function matrix. e relationsip of unit strain and unit stress and unit balance equation are obtained by (3). { { { } [ B]{ u}, (4) } [ D][ B]{ u}, (5) ( E) P} [ ] { u}, (6) were { } is te strain column vector of any point in te unit, [B] is te unit strain matrix, [D] is te elasticity matrix, [ ] [ B] [ D][ B] dxdydz,{ P} is te force column vector of unit equivalent node. Relationsip between node load and displacement is built by principle of minimum potential energy, namely equilibrium equation of structure. were, U P K, (7) K is te wole rigidity matrix; P is te load array;u is te displacement array. 3) e N groups of data are acted as RBFNN training samples, input-output relation between external parameter and interior stress is built by RBFNN algoritm, te detailed realization of RBFNN algoritm is as follows [6-8]. Let X is input variable and Y is networ output vector: M X x, x,, x,, x ) R, ( m M ( y, y,, y N Y ) z is te idden output (,,, H ), ten output expression is: Z g b X C ), ( 53

3 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp exp X C X C (8) (,, H ), were g (*) is te Gaussian function, W C ( c, c,, c ) is te Gaussian m function central vector, b is te standardized parameter; Z is te output of idden node. It is sown tat te distance between input vector and Gaussian function datum center is nearer by formula (8), because te Gaussian function is radial symmetry, ide node will ave same output for te input of same radial distance from basis function centre C. e output of Radial basis networ is linear combination, namely: E( W) C( ) C( ( C CC( ( C( C( ) (4) E( W) ( ) ( ( ( ( ( ( ) (5) were ( is learning rate and is momentum factor. e structure of RBFNN is sown in Fig.. y H w 0 z W Z, (9) were Z 0, w 0 is te goal unit tresold, W ) ( w0, w, w,, wh,, Z ( z0, z, z,, z H ). e outputs of ide nodes are usually normalized to obtain good speciality of input and output: u z / H en networ output is obtained: Y z ( 0,,,, H), (0) W U (,,, N), () were U ( u0, u, u,, u H ). Let K samples pairs, ten networ goal function is: E K ( d y ), () were d is te networ goal output; y is te networ real output value. Networ learning rules are: E K ( d y ), () ( W( W( ) (3) Fig.. e structure of RBFNN. 4) Material intensity distribution is establised by testing and statistical data in document. 5) of OCS suspension system is calculated by numerical simulation-monte Carlo, Monte Carlo metod is tat state function g is calculated by random sample, and g<0 is udged, te parts is considered failure if maximum stress exceeds limit state[9]. esting total numbers N meets N 00 / P f, if failure total number is L, failure probability Pf is L / N and reliability R is P, f calculation flow cart is sown in Fig. 3. Eigty groups of basic variables are randomly generated according to te mean and variance of basic variables, ten te stress S of eac groups of basic variables are calculated by finite element software ANSYS [0, ], seventy-five groups data are acted as training samples, and five groups data are acted as testing data. In finite element calculating, entity model is turned into PARASOILD format, ten it is lead into ANSYS software and solid9 tetraedron unit is used, 7676 units 6887 nods are obtained by free-dividing meses. Finite element analysis model te base of OCS suspension system is sown in Figs Finite element analysis model te fixing oo of OCS suspension system is sown in Figs

4 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp able is testing result after RBFNN is trained, it is clear tat teory values and RBFNN output values is very close from able. e reliability of OCS suspension system are calculated by integration algoritm matematic model, te mean value and deflection coefficient of material intensity limit value of OCS suspension system are obtained according to according to statistics. calculating result of te base of OCS suspension system is 98, calculating result of te fixing oo of OCS suspension system is 9, relative error is only 0.5 % comparison wit calculating result of optimal SVM integration algoritm metod. It is analyzed tat distribution deflection coefficient of external parameter ave an effect on reliability te base of OCS suspension system by te program, relation curve is sown in Figs Relation curve tat distribution deflection coefficient of external parameter ave an effect on reliability te fixing oo of OCS suspension system is sown in Figs Distribution deflection coefficient of pre-tigten force P and contact wire tension ave a great influence on reliability, so reliability optimal design is necessary to reduce failures of OCS suspension system [3]. able. est Result. F (KN) P (N.m) d (mm) W (m/s) eory value (MPa) Forecast value (MPa) Relative error (%) Fig. 3. Flow cart of reliability calculation based on RBFNN and Monte Carlo numerical simulation. Fig. 4. Entity model of te basem of OCS suspension system. Fig. 5. Finite element model of te base of OCS suspension system. 55

5 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp Fig. 6. Wole stress cloud imagery of te base of OCS suspension system. Fig. 7. Finite element model of OCS suspension system. Fig. 8. V.Mises stress cloud imagery of OCS suspension system. Fig. 9. V.Mises stress cloud imagery of OCS suspension system Fig. 0. Relation curve between deflection coefficient of wind speed W and reliability Fig.. Relation curve between deflection coefficient of ice-covering ticness d and reliability. 56

6 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp Fig.. Relation curve between deflection coefficient of pre-tigten force P and reliability Fig. 3. Relation curve between deflection coefficient of contact wire tension and reliability. Fig. 4. Entity model of fixing oo. Fig. 5. Finite element model of fixing oo. Fig. 6. V.Mises stress cloud imagery of fixing oo. 57

7 Sensors & ransducers, Vol. 54, Issue 7, July 03, pp Fig. 7. Relation curve between deflection coefficient of ice-covering ticness d and reliability Fig. 8. Relation curve between deflection coefficient of contact wire tension and reliability Fig. 9. Relation curve between deflection coefficient of pre-tigten force P and reliability Fig. 0. Relation curve between deflection coefficient of wind speed W and reliability. 4. Conclusions statistical data is deficient because te reliability researc of railway OCS system is ust beginning, in addition, tere are complex non-linear relation between eac part internal stress of OCS system and external load, it brings great difficult to reliability researc. In tis paper, an intelligent metod of reliability analysis based on compound algoritm is presented in tis paper, RBFNN and analysis of finite element combined wit Monte Carlo numerical simulation is integrated to improve simulation computing precision. Matematic model of reliability calculation on OCS suspension system and compound algoritm model are built, reliability of OCS suspension system is calculated by te metod, OCS suspension system is critical force-bearing parts of OCS system in te ig-speed electrified railway, and fault rate is very ig, teir reliability analysis is important researc subect in railway system, it is difficult to built reliability model because it wors in a complex and uncertain environment. In tis paper, analysis metod of location installation based on support vector macine and finite element combined wit Monte Carlo is used, and te outside parameter influence on location installation is analyzed by te model. It provides a new way for te design and researc of reliability in complex system of railway. Acnowledgements is wor is supported by tecnology plan proect of Zeiang province in Cina (No. 0C030). e autors are grateful for te anonymous reviewers wo made constructive comments. References []. W. J. Yu, Hig speed electrization railway OCS, Soutwest Jiaotong University Press, Cengdu, 00. []. Y. Wan, A New Intelligent Model for Structural Identification Based on Optimal Macine Learning, Journal of Computers, Vol., Issue 7, 0, pp [3]. J. R. Zang, Structure reliability teory and application for bridge engineering, Public Jiaotong Press, Beiing,

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