Real Time Integral-Based Structural Health Monitoring

Transcription

1 Real Time Inegral-Based Srucural Healh Monioring The nd Inernaional Conference on Sensing Technology ICST 7 J. G. Chase, I. Singh-Leve, C. E. Hann, X. Chen Deparmen of Mechanical Engineering, Universiy of Canerbury, Chrischurch, New Zealand

2 Inroducion Srucural Healh Monioring SHM compares a srucures condiion relaive o a baseline sae Need o deermine exisence, locaion and degree of damage - Visual and localized inspecion mehods are complicaed and ime consuming Curren SHM Techniques Modal parameer esimaion - insensiive o localized damage and sensiive o noise - more suiable o linear srucures Flexibiliy based mehods - compuaionally inense, no suiable for real-ime

3 New mehod - Measuremen Measure ground and srucural Acceleraions Esimae srucural displacemen and velociy by inegraion Correc esimaed response using low frequency displacemen measuremen -GPS, Fibre-Opics or Sorey-Drif Exensomeers

4 Parameer Idenificaion Assume shear building model wih Bouc-Wen hysereic srucure bu sill quie general Idenify srucural siffness, permanen displacemen from esimaed daa magniude of each floor good damage measure Linear leas squares fi allows real-ime implemenaion Inegral formulaion Robus o he presence of noise

5 Non-Linear Srucural Model Equaion of Relaive Moion: M& x + Cx & + K e x + K h z = Mx & g && x,x,x & & x& g Permanen displacemen is represened by x z M = Mass Marix C = Damping Marix Ke = Elasic Siffness Marix Kh = Hysereic Siffness Marix x x& & x& && x g z = Displacemen = Velociy = Acceleraion = Ground Acceleraion = Hysereic Displacemen

6 Hyseresis loop 3 Typical Bouc-Wen Hyseresis Loop Force N Displacemen m

7 Inegraion and Drif Inegrae o esimae displacemen and velociy 6 4 Noisy Clean Acceleraion dd Acceleraion m/s/s Time s Displacemen Esimae m m Double Inegral Displacemen Esimae Wih No Noise Time s

8 Fiing Approach DOF Rearranged Equaion of Moion: k p d + Z = mx && mx & cv g where: k = k + k p e h Z = kh z x v d = Esimaed Velociy = Esimaed Displacemen Wish o idenify k p and Z in a piecewise sense using linear leas squares Fied k p is allowed o vary a inervals of Fied Z is allowed o vary a inervals of z

9 Fiing Approach Fiing Approach DOF DOF Fiing Example: =s, z =.5s, Sampling a 4Hz = cv mx mx cv mx mx cv mx mx cv mx mx Z Z k d d d d g g g g p && && && && && && && && Z Z k p is found by leas squares fi Esimaion of bi-linear facor α gives he permanen displacemen z x α = p h k k k h Z z x = where

10 Inegraion Correcion Use measured displacemen every. s correc error in double inegraion Problem: : Using direcly measured acceleraion and going backwards o correc velociy and displacemen doesn work! Acceleraion is no precisely he double differeniaion of correced displacemen causes havoc wih he mahemaics!

11 Double inegrae acceleraion Evaluae error every.s 3 Fi C coninuous spline Inegraion Correcion - Algorihm spline hrough ε, i =,, K, o ge 4 Ge correced displacemen measuremen = && x + ε 5 Creae new velociy and acceleraion measuremens d x& correc = x ' approx d && + ε d && xcorrec = x + ε ' approx d && Measured acceleraion x approx ε, ε., ε. i x correc ε approx = && x + ε Numerical differeniaion approx Noe ha in sep 3: a C spline significan error in correced acceleraion, and a C spline very noisy esimae of correced acceleraion Therefore C is bes rade off

12 Esimaion Accuracy x Comparison Comparison of of of True True True and and and Esimaed Esimaed Displacemens Acceleraions Velociies Esimaed Esimaed Real Real Acceleraion Velociy m/s m/s/s Displacemen m Time s Esimaed velociy and acceleraion are calculaed using numerical differeniaion

13 Parameer Idenificaion Idenify siffness and permanen displacemen from revised equaion of moion: k p d + Z = m& x ma cv g k = k + p e Z = kh[ z x ] k h v d = Esimaed Velociy = Esimaed Displacemen k p Z = linear siffness = permanen displacemen parameer a = Esimaed Acceleraion Unknown parameers are idenified in a piecewise sense

14 Leas Squares Soluion Leas Squares Soluion Piecewise parameer variaion Piecewise parameer variaion i b i A = 3 Z Z Z k p = 3 i i i d d d A i = i i i g i i i g i i i g cv ma mx cv ma mx cv ma mx && && && b i

15 Algorihm Oupu Algorihm Oupu Leas squares procedure yields soluion vecor: Leas squares procedure yields soluion vecor: 3 Z Z Z k p + = α α k h Z D Can calculae acual permanen displacemen: Can calculae acual permanen displacemen:

16 Fiing Algorihm Overview Measure displacemen and acceleraion daa Esimae properies via inegraion Correc using low frequency displacemen Creae sysem of linear equaions Find unknowns using linear leas squares Calculae permanen displacemens Repea for all ime periods of ineres

17 Resuls Simulaed Daa Single DOF sysem wih linear siffness of 39.58N/m s Period % uniformly disribued noise on all measuremens Siffness idenified over s inervals, permanen displacemen idenified over.4s inervals 45 4 Acual Siffness Fied Siffness x -3 True Idenified 35-3 Siffness N/m Permanen Displacemen m Time s Time s

18 Simulaion - Siffness Accurae idenificaion of siffness Sligh drops in idenified siffness during highly non-linear periods Drop in accuracy a end of record due o lack of response 8 Acual Siffness Fied Siffness 6 4 Siffness N/m Time s

19 Simulaion - Yielding Major rends are accuraely capured Final residual deformaion accuraely capured Resoluion could be increased by reducing he fiing periods x -4 Real Fied - Permanen Displacemen m Time s

20 Real Daa Non-Linear Frame Four sorey srucure designed o demonsrae dynamic response Replaceable plasic hinges /5 h scale srucure subjeced o El Cenro record

21 Seel Frame - Siffness Idenified siffness compares well o pushover analysis resuls Similar behaviour observed for all soreys Discrepancy in final siffness value aribued o srain hardening and srain rae effecs x 5 9 Acual Siffness Fied Siffness 8 7 Siffness N/m Time s

22 Seel Frame - Yielding Iniial and final residual deformaions are accuraely capured Two major yields idenified, boh occur during peaks in displacemen Final residual deformaion idenified o wihin.5% of rue value for all soreys

23 Resimulaion.3 Comparison of Measured and Resimulaed Top Sorey Displacemens Measured Resimulaed.5 Comparison of Measured and Resimulaed Top Sorey Displacemens Measured Resimulaed....5 Displacemen m -. Displacemen m Time s Time s Srucural response is resimulaed using fied parameers, known properies and known ground acceleraion Accurae resimulaion validaes fied parameers

24 Linear Baseline Model Quesion: Can damage be deeced in his non-linear srucure using a purely linear baseline model? x 5 7 Idenified Esimaed 6 5 Siffness N/m Time s Answer: We can idenify he presence of damage bu he magniude and locaion is no clear

25 Final Assessmen The algorihm is able o accuraely idenify siffness and permanen displacemen in a non- linear seel frame srucure The non-linear baseline model used is very versaile and can be used o filer noise and non-lineariy Compuaional simpliciy means easy real-ime implemenaion

26 Shor Term: Fuure Work Fi linearly varying permanen displacemen Idenify yield parameers for Bouc-Wen model Long Term: Monior more complex srucures Idenify more deailed srucural parameers Eliminae need for displacemen measuremen

27 Acknowledgemens Prof Geoff Chase Assoc. Prof XiaoQi Chen Prof. John Mander Dr. Bruce Deam and Ishan Leve Quesions???