UNIVERSITY OF OXFORD DEPARTMENT OF ENGINEERING SCIENCE Hybrid Testing Simulating Dynamic Structures in the Laboratory Tony Blakeborough and Martin Williams.

UNIVERSITY OF OXFORDDEPARTMENT OF ENGINEERING SCIENCE

Hybrid TestingSimulating 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 Buffalo Bristol 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 can’t 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 amax = 1.5 g, vmax = 2 m/s, umax = 1 m

24 x 450 tonne actuators 15,000 l/min oil flow rates

Real-time hybrid testing

d0(t)

d1(t)

d1(t) – d0(t)

dg(t)

FL(t) FR(t)

FD(t)

dg(t)

Emulated system:

Numerical substructure:

Physical substructure:

Ground displacement

Forces fed back from physical substructure

Computed displacements

Displacement applied by actuator

Displacements

Forces

Dissipator

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

Real-time PC

dSpaceboard Proprietary

controller

Monitoring PC

Actuator 1 Actuator 2

Command GPIB interface

Command

Feedback

FeedbackCommand

Feedback

Structural Dynamics Lab

Structural Dynamics Lab @ 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

Numerical substructure

Outer-loop compensation

Inner-loop (proprietary)

controller

Servo-hydraulic actuator

Physical substructure

Force feedback

Displacement feedback

Transfer system

Input load

dcom dactddes

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 dcom values at sub-steps.

Send to the inner loop controller, together with the current actuator position dact

5. Repeat step 4 at sub-steps, until the next main step.

1des

nd

1com

nd

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

Test system

Simple mass-spring system

All springs in numerical model have bi-linear properties

Increase DOFs in numerical model to test algorithms

Physical substructure Numerical substructure – n-DOF

Base motion

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

Exp

licit

Tw

o-st

ep m

etho

dsIm

plic

it

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

Exp

licit

Tw

o-st

ep m

etho

dsIm

plic

it

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

Exp

licit

Tw

o-st

ep m

etho

ds

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

Exp

licit

Tw

o-st

ep m

etho

ds

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

m2 m1

Base motion

m2 m1Feedback force Actuator

Emulated system

Numerical: Physical:

Test B

Non-linear, 2DOF system, single actuator

m2 m1

Base motion

m2 m1F

Emulated system

Numerical: Physical:

Gapnon-linearity

Test C

Linear, 3DOF system, two actuators

Asynchronous input motions, stiff coupling

m3 m2g2

m3

m2

F2

Emulated system

Numerical:

Physical:

m1g1

g2 m1F1

Numerical:

g1

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 A Test B Test C Test C

Act#1 Act#2

No compensation unstable unstable unstable unstable

Exact extrapolation 1.8 1.5 2.9 2.5

Least squares extrapolator 1.9 2.0 - -

Linear acceleration 1.9 1.6 3.4 2.7

Laguerre extrapolator 1.8 1.7 unstable 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 A Test B Test C Test C

Act#1 Act#2

No update 1.8 1.5 2.9 2.5

With updating scheme 0.9 1.1 2.3 1.8

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

8630kg mass

3m

3m

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 30m 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

Physical substructure

Measure deformation of test specimen

Numerical substructure

Apply measured displacements to

numerical substructure

External earthquake loads

Command actuators to apply forces to

physical substructure

Calculate forcesat interface between physical and numerical substructures

Numerical substructure

Massm

Columns - kc

x

Damper -

Braces - kb

F

gx

g

ubbb

xx

xc

x

x

00

1

01

2 222

g

ubub

xm

x

xm

x

F

00

0

10

0 2222

8630kg mass

3m

3m

Earthquake records

0 2 4 6 8 10 12 14 16 18 20-1

-0.5

0

0.5

1

Time(s)N

orm

alis

ed a

ccel

erat

ion

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Time(s)

Nor

mal

ised

acc

eler

atio

n

El Centro

Synthesised

EC8 record

Response of Dorka device (El Centro 0.2g)

0 5 10 15 20 25-12

-10

-8

-6

-4

-2

0

2

4

6

8

Time (s)

Forc

e (k

N)

Detail - EC8 synthesised earthquake tests

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8-15

-10

-5

0

5

10

Time (s)

For

ce (

kN)

Force demand

Measured force

Error

3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

-60

-40

-20

0

20

40

60

Time (s)

For

ce (

kN)

Force demand

Measured force

Error

0.2g pga

1.2g pga

Specimen hysteresis curves

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2-15

-10

-5

0

5

10

15

Specimen displacement (mm)

Spe

cim

en f

orce

(kN

)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8-40

-30

-20

-10

0

10

20

30

40

50

Specimen displacement (mm)S

peci

men

for

ce (

kN)

EC8 0.2g EC8 0.6g

Large hysteresis loops

-1.5 -1 -0.5 0 0.5 1 1.5 2-60

-40

-20

0

20

40

60

Specimen displacement (mm)

Spe

cim

en f

orce

(kN

)

-3 -2 -1 0 1 2 3 4-80

-60

-40

-20

0

20

40

60

80

Specimen displacement (mm)

Spe

cim

en f

orce

(kN

)

EC8 0.9g EC8 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

1.8 2 2.2 2.4 2.6 2.8

-4

-2

0

2

4

6

8

Time (s)

For

ce (

kN)

Brace demand

Measured force

Error

-2 -1 0 1-10

-5

0

5

10

Specimen displacement (mm)

Spe

cim

en f

orce

(kN

)

-100 -50 0 50 100-10

-5

0

5

10

Specimen velocity (mm/s)

Spe

cim

en f

orce

(kN

)

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

Response of Jarret devices

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8

-5

0

5

Time (s)

For

ce (

kN)

Force demand

Measured force

ErrorEl Centro record with a pga of 0.2g around the peak at 3.3s

21 21.5 22 22.5 23

-2

-1

0

1

2

Time (s)

For

ce (

kN)

Force demand

Measured force

Error

.... and at end of record

Response of Jarret devices

0 5 10 15

-20

-10

0

10

20

Time (s)

Forc

e (

kN

)

Force demand

Measured force

Error

0 5 10 15-6

-4

-2

0

2

4

6

Time (s)

Dis

pla

cem

ent

(mm

)

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

Response of Jarret devices

-10

0

10-200 -150 -100 -50 0 50 100 150 200

-15

-10

-5

0

5

10

15

20

Displacement (mm)

Velocity (mm/s)

For

ce (

kN)

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

Response of Jarret devices

-10

-5

0

5

10-200 -150 -100 -50 0 50 100 150 200

-15

-10

-5

0

5

10

15

20

Velocity (mm/s)

Displacement (mm)

For

ce (

kN)

-6 -4 -2 0 2 4 6

-200

0

200

-15

-10

-5

0

5

10

15

20

Velocity (mm/s)Displacement (mm)

For

ce (

kN)

EC8 record with a pga of 0.6g

Velocity projection Displacement 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 studyRA – 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

40 45 50 55-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Time (s)

Forc

e r

esultant

Vertical force (N)

Pitch moment (Nm)

Roll moment (Nm)

40 45 50 55-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Equiv

ale

nt

dis

pla

cem

ent

(mm

)

Vertical

Pitch

Roll

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

0 1 2 3 4 5 6 7 8 9 10-6

-4

-2

0

2

4

6sine 5mm command to bristol rig from oxford

time (s)

disp

lace

men

t (m

m)

achieved bristol (measured ox)

command oxford

0 1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

0.3

0.35network "delay" sine 5mm command to bristol rig from oxford

time (s)

Del

ay (

s)

Oxford-Bristol test

Results of test on Monday

0 5 10 15 20 25

-15

-10

-5

0

5

10

15

time s

disp

lace

men

t m

m

Achieved displacements

achieved bris(ox)floor 1

achieved oxford floor 2achieved oxford floor 3

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