UNIVERSITY OF OXFORD DEPARTMENT OF ENGINEERING SCIENCE Hybrid Testing Simulating Dynamic Structures in the Laboratory Tony Blakeborough and Martin Williams SECED Evening Meeting 28 January 2009

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

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

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 BuffaloBristol University

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 cant capture rate effects Feedback loop can cause errors to accumulate JRC Ispra Lehigh University

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 San Diego outdoor shaking table Minnesota EFT facility

E-Defense, Japan 1200 tonne payload a max = 1.5 g, v max = 2 m/s, u max = 1 m 24 x 450 tonne actuators 15,000 l/min oil flow rates

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

Typical test set-up

Structural Dynamics Lab

Structural Dynamics Oxford Hydraulic installation

The Flight Deck

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

Typical test strategy 1. Solve numerical substructure to give desired actuator displacement at the next main step, 2. Curve fit to the current and the past few displacement points. 3. Use curve fit to extrapolate forward by a time equal to the estimated actuator delay, to give the command displacement, 4. Use same curve fit to interpolate d com values at sub-steps. Send to the inner loop controller, together with the current actuator position d act 5. Repeat step 4 at sub-steps, until the next main step.

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. Newmarks 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

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

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 Explicit Two-step methods Implicit Results

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 Explicit Two-step methods Implicit 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 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 Results

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

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

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

Test B Non-linear, 2DOF system, single actuator

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

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

Comparison of forward prediction schemes RMS errors (%) over a test with constant delay and amplitude error estimates Test ATest BTest C Act#1Act#2 No compensation unstable Exact extrapolation Least squares extrapolator Linear acceleration Laguerre extrapolator unstable

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

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 Test ATest BTest C Act#1Act#2 No update With updating scheme

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

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)

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

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

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

Force control loop

Numerical substructure

Earthquake records El Centro Synthesised EC8 record

Response of Dorka device (El Centro 0.2g)

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

Specimen hysteresis curves EC8 0.2g EC8 0.6g

Large hysteresis loops EC8 0.9gEC8 1.2g

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

Jarret devices

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

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

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

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

Response of Jarret devices EC8 record with a pga of 0.6g Velocity projectionDisplacement projection

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

Human-structure interaction in grandstands EPSRC funded study RA – Anthony Comer

Grandstand rig 15-seater grandstand rig Standard design – typical rake & seat distances Test crowd coordination Effect of grandstand movement on coordination Simulate various natural frequencies and mass ratios

Grandstand rig design Aluminium alloy fabricated rakers and stretchers Light & stiff – lowest internal natural frequency >30Hz Air spring at each corner to take out mean load Electro-mechanical actuator at each corner to control rig Load cell under each spectator

Control problems Force feedback from load cells at actuators suffered large levels of interference from e/m fields emitted by motors Filtering would introduce too much lag for stability Digital displacement feedback available from linear encoders (resolution 3μm) immune from e-m interference Use force control with displacement feedback

Control strategy Three significant degrees of freedom Heave (vertical displacement) Roll Pitch Feedforward Measure loads applied by spectators Resolve into resultant vertical load and roll & pitch moments Apply equivalent forces at actuators to balance force resultants and keep rig stationary Numerical model Simulate vertical and rotational damped springs numerically to control dynamics of grandstand Apply a proportion of vertical resultant load to excite the rig

Response to 130kg male jumping Vertical response only Rotations successfully tared off

Conclusions – grandstand simulation Controlled tests possible on grandstand with spectators jumping and bobbing Can also be used to wobble seated and standing spectators to assess the acceptability of motion (main dynamic use in project) Can be used to simulate human-structure interaction

Split-site testing – hybrid testing over the internet Numerical and physical substructures at separate locations Possibility of testing very large components Possible only over the internet

Network architecture

JANET internet route

Communication interruptions JANET delays ~10ms - OK Inconsistency causes problems Solution Use UK-light – a dedicated link

Oxford-Bristol test

Results of test on Monday

Limitations Physical substructure Limits set by equipment Response times of actuators Control problems at limits of actuator capacity Stiffness of frames Reduce uncertainty Proof testing (strength/performance guarantee) Check individual items Assess design under realistic loading Validate computer models used in design

Architecture of 3 site test – radial model

State of work in split site testing Ethernet not a problem provided use a dedicated link Tests possible and seem to work Future work Increase natural frequencies of systems – currently 3Hz but up to 10 should be possible Investigate different interconnection links At moment there is a central numerical model with physical sites as servers at end of radial spokes – other arrangements are possible Investigate force control Extend to the rest of the world – planning links with EU in FP7 research

Conclusions Simulation of real time behaviour It works for stiffness and rate dependent components Reproduces rate/time dependent effects Useful for more realistic component testing Allows devices to be checked in much more arduous circumstances Copes with non-linear behaviour in both physical and numerical substructures

General conclusions What test at all? Reduce uncertainty Proof testing (strength/performance guarantee) Check individual items Assess design under more realistic loading Validate computer models used in design Challenging activity Push current control techniques and test equipment to limits Trickle down effect – improved techniques help standard testing