Hybrid Testing Simulating Dynamic Structures in the Laboratory

1. Hybrid TestingSimulating Dynamic Structures in the Laboratory Tony Blakeborough and Martin Williams SECED Evening Meeting 28 January 2009

2. Outline • Introduction • Dynamic test methods – why do we need new ones? • The real-time hybrid method • Displacement-controlled tests • Testing strategy and equipment • Numerical integration schemes • Compensation for transfer system dynamics • Recent developments and applications • Tests under force control • Crowd-structure interaction • Distributed hybrid testing in the UK-NEES project • Conclusions

3. Acknowledgements • Numerous colleagues contributed to the work described here, particularly: • Current researchers: Mobin Ojaghi, Ignacio Lamata • Past researchers: Antony Darby, Paul Bonnet, Kashif Saleem, Javier Parra • Collaborators at Bristol, Cambridge, Berkeley, JRC Ispra • We have received financial support from: • EPSRC • The Leverhulme Trust • The European Commission • Royal Academy of Engineering • Instron

4. Testing methods in earthquake engineering • Shaking tables – apply prescribed base motion to models • Can accurately reproduce earthquake input • Normally limited to small-scale models – expensive at large scale • Scaling problems (physical and time) • Control problems SUNY Buffalo Bristol University

5. Testing methods (cont.) • Pseudo-dynamic test facilities: • Slow test, with inertia and damping components modelled numerically, stiffness forces fed back from test specimen • Can be conducted at large scale • Best suited to flexible structures with concentrated masses • Expanded timescale can’t capture rate effects • Feedback loop can cause errors to accumulate Lehigh University JRC Ispra

6. Future trends • Major upgrading initiatives, e.g. NEES (USA), E-Defense (Japan) • Very large shaking tables • Enhancements to pseudo-dynamic methods: • Effective force testing • Real-time hybrid testing • Distributed hybrid testing Minnesota EFT facility San Diego outdoor shaking table

7. E-Defense, Japan • 1200 tonne payload • amax = 1.5 g, vmax = 2 m/s, umax = 1 m • 24 x 450 tonne actuators • 15,000 l/min oil flow rates

8. Real-time hybrid testing

9. Real-time hybrid testing • Advantages: • Avoids physical scaling problems • Avoids time scaling problems • Ideal for testing rate-dependent systems • Economical – only the key parts need to be modelled physically • Now being strongly pursued by NSF NEES programme • Needs: • High-performance hardware and communications • Fast solution of numerical substructure • Compensation of transfer system dynamics

10. Typical test set-up

11. Structural Dynamics Lab

12. Structural Dynamics Lab @ Oxford Hydraulic installation

13. The Flight Deck

14. Typical real-time control loop • Dual time-stepping implementation: • Numerical model runs at main steps ~ 10 ms • Controller runs at sub-steps ~ 0.2 ms • Imperfect transfer system dynamics cause: • Errors in timing and amplitude of applied loads • Inaccuracy and/or instability of test

15. Typical test strategy • Solve numerical substructure to give desired actuator displacement at the next main step, • Curve fit to the current and the past few displacement points. • Use curve fit to extrapolate forward by a time equal to the estimated actuator delay, to give the command displacement, • Use same curve fit to interpolate dcom values at sub-steps. Send to the inner loop controller, together with the current actuator position dact • Repeat step 4 at sub-steps, until the next main step.

16. Numerical integration schemes • We require: • Very fast solution of numerical substructure (~10 ms) • Accuracy, stability, ability to model non-linear response • Explicit integration (e.g. Newmark’s method) • All required data known at start of timestep • Quick, sufficiently accurate • Need short timestep for stability • Implicit integration (e.g. constant average acceleration method) • Requires knowledge of states at end of timestep, therefore iteration (or sub-step feedback) • Unconditionally stable • Two-step methods (e.g. operator-splitting) • Explicit predictor step, implicit corrector

17. Test system • Simple mass-spring system • All springs in numerical model have bi-linear properties • Increase DOFs in numerical model to test algorithms

18. Results Explicit • 10-DOF numerical substructure • Sine sweep input through several resonances • 5 ms main-step • 0.2 ms sub-step • Red = numerical simulation • Blue = hybrid test Two-step methods Implicit

19. Results Explicit • In frequency domain • 10-DOF numerical substructure • Sine sweep input through several resonances • 5 ms main-step • 0.2 ms sub-step • Red = numerical simulation • Blue = hybrid test Two-step methods Implicit

20. Results • 50-DOF numerical substructure • Sine sweep input through several resonances • 25 ms main-step (15 ms Newmark) • 0.2 ms sub-step • Implicit schemes unable to compute in real time • Red = numerical simulation • Blue = hybrid test Explicit Two-step methods

21. Results • 50-DOF numerical substructure • Sine sweep input through several resonances • 25 ms main-step (15 ms Newmark) • 0.2 ms sub-step • Implicit schemes unable to compute in real time • Red = numerical simulation • Blue = hybrid test Explicit Two-step methods

22. Actuator dynamics • Both timing and amplitude errors exist, and may vary during test • Delay of the order of 5 ms is unavoidable • Delay has an effect similar to negative damping  instability

23. Compensation schemes Two components: • Forward prediction scheme • Aims to compensate for known or estimated errors through scaling and extrapolation • Exact polynomial extrapolation • Least squares polynomial extrapolation • Linearly extrapolated acceleration • Laguerre extrapolator • Delay estimation • Delay and amplitude error estimates are updated as test proceeds

24. Validation experiments – Test A • Linear, 2DOF system, single actuator

25. Test B • Non-linear, 2DOF system, single actuator

26. Test C • Linear, 3DOF system, two actuators • Asynchronous input motions, stiff coupling

27. Effect of forward prediction Hybrid test Test A, with fixed delay estimate, exact polynomial extrapolation Analytical response Synchronization plots:

28. Comparison of forward prediction schemes RMS errors (%) over a test with constant delay and amplitude error estimates

29. Delay updating results Delay estimates produced by updating scheme in Test C:

30. Effect of delay updating • RMS errors (%) over a test with with third order exact extrapolation • Tests A and B used 0.5 ms sub-steps • Test C used 0.2 ms sub-steps

31. Developments and applications • Tests under force control • Dorka and Jarret Damper • Crowd-structure interaction • Grandstand simulation rig • Distributed hybrid testing • Oxford-Bristol-Cambridge

32. EU NEFOREE project comparison of testing methods Single storey test building designed by Prof Bursi at Trento Parallel tests on shaking table, reaction wall and real time hybrid substructuring Two dissipative devices to be tested - Dorka shear device and Jarret dampers Natural frequency Unbraced 2.6Hz 2% damping Braced 8.6Hz 5% damping (Dorka)

33. Seismic testing of dampers NEFOREE – EU study Shaking table set-up (elevation) Hybrid test of device

34. Dorka and Jarret devices Dorka shear panel: shear diaphragm in SHS - hysteretic damping Jarret dampers: Non-linear visco-elastic devices

35. Control problems • Two actuators – equal but opposite forces • Dorka cell - very stiff specimen • Significant rig/specimen interaction • LVDT noise 30mm rms produced significant forces • Not possible to run under displacement control Solution • Run test in force-control • Two MCS controllers – one for magnitude and other for force imbalance • Displacement feedback into numerical model

36. Force control loop

37. Numerical substructure

38. Earthquake records El Centro SynthesisedEC8 record

39. Response of Dorka device (El Centro 0.2g)

40. Detail - EC8 synthesised earthquake tests 0.2g pga 1.2g pga

41. Specimen hysteresis curves EC8 0.2g EC8 0.6g

42. Large hysteresis loops EC8 0.9g EC8 1.2g

43. Conclusions – Dorka device Real time hybrid tests successful Simulated behaviour in 8Hz frame with 5% damping Stiff specimen required force feedback loop Device robust enough for use

44. Jarret devices

45. Response to square wave input 0.15g alternating sign (square wave) ground acceleration of period 2s

46. Response of Jarret devices El Centro record with a pga of 0.2g around the peak at 3.3s .... and at end of record

47. Response of Jarret devices Force & displacement response of to the EC8 record with a pga of 0.6g

48. Response of Jarret devices Force against displacement and velocity for the EC8 record with a pga of 0.6g

49. Response of Jarret devices Velocity projection Displacement projection EC8 record with a pga of 0.6g

50. Conclusions – Jarret device Tests successfully completed Realistic tests at low velocities Problems at higher velocities due to extreme non-linear response in velocity Student just starting work on this – possibly use velocity feedback with improved displacement measurements