SERIES Concluding Workshop Joint with US-NEES, JRC … hybrid... · Towards Faster Computations and Accurate Execution of Real-Time Hybrid Simulation Khalid M. Mosalam, Professor,

Towards Faster Computations and Accurate Execution of Real-Time Hybrid Simulation

Khalid M. Mosalam, Professor, PI of nees@berkeley

Selim Günay, Project Scientist, nees@berkeley

Structural Engineering, Mechanics, and Materials

Department of Civil and Environmental Engineering

University of California, Berkeley

SERIES Concluding Workshop – Joint with US-NEES, JRC-Ispra, May 28-30, 2013

1

SERIES Concluding Workshop – Joint with US-NEES, JRC-Ispra, May 28-30, 2013 2

National Science Foundation (NSF) & Network for Earthquake Engineering Simulation (NEES)

Acknowledgment:

California Department of Transportation (Caltrans) & Pacific Earthquake Engineering Research (PEER) Center

US Department of Energy (DOE) & California Institute for Energy and Environment (CIEE)


Outline

3

Background

Development I: A standalone RTHS system for integration time steps as small as 1 milisecond

Development II: Use of an efficient equation solver in RTHS to reduce computation time

Development III: Novel use of a three variable control (TVC) for RTHS on a shaking table configuration


Background

Analytical Simulation

Hybrid Simulation (HS)

=

Experimental Simulation

+

4


Background u2

u1

m2

m1

Objective of analytical simulation: Solve the equations of motion using numerical integration methods

g

2

1

1

21

2

1

2221

1211

2

1

2

1u

m

m

u

u

cc

cc

u

u

m0

0m

f

ff

pfucum

m u c u f p

Analytical Simulation:

5


Background

Bottom spring replaced with a test specimen

Analytical substructure

u2

u1

m2

m1

u2

u1

m2

m1

g

2

1

2

1

2221

1211

2

1

2

1u

m

m

u

u

cc

cc

u

u

m0

0m

a

ea

f

ff

Experimental substructure

Measured

Computed

(-)

6


HS Classification

Background

7

HS duration = N×Δt

Real-time Hybrid Simulation

u2

u1

m2

m1

HS duration > N×Δt

Slow Hybrid Simulation

Shaking Table Configuration Actuator + Shaking Table Configuration

mkc

mkc

Bus


on a shaking table &

connected to an actuator

Actuator Configuration

u1

m, Im

u2


Background

Requirement for Real Time HS (RTHS):

Loading rate = Computed velocity

Slow HS is sufficient for most cases when rate effects are not important.

RTHS is essential for rate-dependent materials and devices, e.g. viscous

dampers or friction pendulum isolators.

8


Uniaxial shaking table

Test specimen: Insulator

Controller

DAQ & Computational platform (DSP)

Development I: RTHS System

9

RTHS system capable of executing an integration time step of 1 millisecond

Step 1 (Computations)

Step 2 (Computed displacements)

Step 3 (Command displacements)

Step 4 (Force feedback)






10




11 0 10 20 30 40 50 60 70-1.2-0.6

00.61.2

X a

cc. (g

)

19.489619.489719.489819.4899 19.49 19.490119.490219.490319.4904

0.8

1

1.2

Y a

cc. (g

)

0 10 20 30 40 50 60 70-1.2-0.6

00.61.2

Time (sec)

Z a

cc. (g

)

Conventional Shaking Table Simulation

≡

0 10 20 30 40 50 60 70-1.2-0.6

00.61.2

X a

cc. (g

)

19.489619.489719.489819.4899 19.49 19.490119.490219.490319.4904

0.8

1

1.2

Y a

cc. (g

)

0 10 20 30 40 50 60 70-1.2-0.6

00.61.2

Time (sec)

Z a

cc. (g

)

Analytical substructure

Step 1 (Computations): Substructuring Corresponding

RTHS

+ 0 10 20 30 40 50 60 70-10

-5

0

5

10

Dis

pla

cem

ent (in)

550 kV Switch Test

0 10 20 30 40 50 60 70-100

-50

0

50

100

Velo

city

(in

/sec)

0 10 20 30 40 50 60 70-4

-2

0

2

4

Time (sec)

Accele

ratio

n (

in/s

ec2)



m

k c gu

k=F/u

F, u

m, c

m, k and c represent the mass, spring and damping constants for a SDOF system representing the steel support frame


12

Step 1 (Computations): Equation of Motion


m k c guf

gumfkucvma

Force f includes the inertial and damping forces acting on the insulator since the

hybrid simulation is conducted in real time.


13

Step 1 (Computations): Equation of Motion


1 Step toGo 8)

1iiSet 7)

uγΔtuu 6)

mmpu 5)

ucfukump 4)

f Measure & u Apply 3)

u2ΔtuΔtuu 2)

uγ1Δtuu 1)

1i c,γΔtmm,u,u,u Initialize

iii

tableeffeffi

iiigeff

ii

1-i2

1-i1-ii

1-i1-ii

eff000

~

~

~

14

Development I: RTHS System Step 1 (Computations): Computational Algorithm of Explicit Newmark






Digital signal processor (DSP) I/O module of Pacific Instruments (PI) DAQ system Programming in Reverse Polish Notation (RPN)

15

Development I: RTHS System Step 1 (Computations): Implementation of Computational Algorithm


10 10.2 10.4 10.6 10.8 11-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time(sec)

Dis

pla

ce

me

nt(

inch

)

Command

Feedback

-40 -30 -20 -10 0 10 20 30 40-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Velocity (v) [inch/sec]

Err

or

(e)

[inch]

e = 0.042v+0.513

e = 0.0174v

e=0.042v-0.513

Add the error to the computed displacement

16

Development I: RTHS System Step 1 (Computations): Feed-forward error compensation


10 10.2 10.4 10.6 10.8 11-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time(sec)

Dis

pla

ce

me

nt(

inch

)

Command

Feedback

No correction

Feed-forward error correction

10 10.2 10.4 10.6 10.8 11

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time(sec)

Dis

pla

ce

me

nt(

inch

)

Command

Feedback

17


-40 -30 -20 -10 0 10 20 30 40-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Velocity (v) [inch/sec]

Err

or

(e)

[inch]

e = 0.042v+0.513

e = 0.0174v

e=0.042v-0.513

V=0.0 Correction=0.0

Step 1 (Computations): Feed-forward error compensation






18




19

Step 2: Communication between computational platform & controller

Standard cable for BNC to BNC connectors





20





21

Benefits of 1 milisecond integration capability:

Increase of the application range of Explicit integration

πT

Δt

n

milisec 1 Δt nTmilisec32.0



22

Benefits of 1 milisecond integration capability:

Eliminating approximation introduced by application of a predictor-corrector smoothing algorithm

Predict

Correct

Displacement Integration time step: 10 milisecond

ti ti+1

5 milisec 5 milisec

Integration time step: 1

milisecond

Time


Comparison with conventional shaking table tests

Courtesy of

Southern States

Conventional shaking table test (PEER, 2008) RTHS (UC Berkeley, 2011)

23



Comparison with conventional shaking table tests

Accelerations at Insulator Top

0 10 20 30 40 50

-6

-4

-2

0

2

4

6

Time [sec]

Accele

ration [

g]

-6

-4

-2

0

2

4

6

Accele

ration [

g]

0 10 20 30 40 50

-6

-4

-2

0

2

4

6

Time [sec]

-6

-4

-2

0

2

4

6

Top of support structure: Real-time HS

Top of support structure:

Conventional shaking table

Top of insulator: Real-time HS

Top of insulator: Conventional shaking table

24


$$$

$

$$$

$


Parametric Study

Polymer Porcelain

25


kc

m

≡

kc

m

m(y)

EI(y)

u(y)

u1

≡

mlive = mass

of live parts

y


Strains: Porcelain Insulator

0 1 2 3 4 5 6 7 8 9 10 110

10

20

30

40

50

60

70

80

Support structure uncoupled frequency fss

[Hz]

Peak s

train

[

str

ain

]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

10

20

30

40

50

60

70

80

Ratio of uncoupled frequencies fss

/ fins

0 1 2 3 4 5 6 7 8 9 10 110

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Peak s

train

/ F

ailu

re s

train

1% Damping

3% Damping

5% Damping

26

Development I: RTHS System Parametric Study

F, u

k = F / u

k = 10508 kN/m

[60.0 kips/in.]

F, u

k = 385 kN/m

[2.2 kips/in.]

k = F / u


Displacements: Porcelain Insulator

0 1 2 3 4 5 6 7 8 9 10 110

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Analytical substructure uncoupled frequency fss

Dis

pla

cem

ent

[in.]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Ratio of uncoupled frequencies fss

/ fins

1% damping

3% damping

5% damping

Relative displacement of

insulator w.r.t. ground

27

Parametric Study


F, u

k = F / u

k = 10508 kN/m

[60.0 kips/in.]

F, u

k = 385 kN/m

[2.2 kips/in.]

k = F / u


Development II: Efficient Equation Solver

Computational Platform Options for RTHS

I. Individual Platforms, e.g. programming in RPN on the DSP card, as in Development I

II. Simulink

III. Publicly available computational platforms, e.g. OpenSees

Options I and II:

Faster computation capabilities

Not versatile, case-specific, and problematic for novel users

Option III, OpenSees:

Slower than Options I & II

Well-established, versatile, research-oriented & HS compatible

Use of an efficient equation solver in OpenSees for faster computations



• 3D analytical substructure

• Straightforward OpenSees model

• 12 DOF per element

• Increased matrix bandwidth

• Increased duration of coefficient matrix (keff) factorization

•

eff1 pukeff i

• Problems with real-time execution

An efficient linear solver in OpenSees: “system UmfPack –factorOnce”

Factorization of Jacobian only once at the beginning of the simulation



Complements HS-compatible integrators (including nonlinear substructures): 1) Explicit & 2) Operator Splitting

Explicit Newmark Integration

1) Compute the displacements

iiii

tt uuuu

2

2

1

eff1 pumeff i

2) Compute/measure the restoring force corresponding to

3) Compute the accelerations

4) Compute the velocities 11 1 iiii γγt uuuu

uucfpucm iiiii γtγt 1111

5) Increment i

f 1i 1iu

Constant during integration Factorization is sufficient in the beginning



Complements HS-compatible integrators (including nonlinear substructures): 1) Explicit & 2) Operator Splitting

Operator Splitting Integration

1) Compute the predicted displacements

eff1 pumeff i

2) Compute/measure the restoring force corresponding to

3) Compute the accelerations

5) Compute the velocities 11 1 iiii γγt uuuu

6) Increment i

ii

ttii uuuu 21

2

~2

1

1

~if 1

~iu

iiiiiI γtβtγt uucfpukcm 1~

111

2

11

2

1~

iii t uuu 4) Compute the corrected displacements

Constant during integration Factorization is sufficient in the beginning



0 1000 2000 3000 4000 5000 6000 70000

10

20

30

40

# of DOF

Co

mp

uta

tio

n T

ime

pe

r T

ime

Ste

p [

ms

]

OpenSees: Multiple Factorization

OpenSees: Single Factorization

“system UmfPack –factorOnce”: Available in recent OpenSees versions



N Story M bay

RTHS with 720 DOF using efficient solver

0 10 20 30 40 50 60 70 80 90 100-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Force Feedback

Time [sec]

Forc

e [

kip

]

Pure Simulation

Hybrid Simulation

0 10 20 30 40 50 60 70 80 90 100-0.06

-0.04

-0.02

0

0.02

0.04

0.06Computed Acceleration (Top Node of Experimental Element)

Time [sec]

Accele

ration [

g]

Pure Simulation

Hybrid Simulation

Computed Acceleration

Experimental Element Force

-5 0 5 10

x 10-4

-20

-15

-10

-5

0

5

10

15

20

Curvature [1/inch]

Mo

me

nt

[kip

-in

ch

]

Hybrid Simulation

Pure Simulation


Development III: Three Variable Control (TVC) Implementation

34

Demonstration of the effect of

control-loop errors

Reliability of the HS depends on the accuracy of the force feedback

All errors that contribute to deviation of “correct” force feedback affect the HS

Command Overshoot

Measured

force

Increased

Damping

Overshooting

Displacement

Restoring

Force Restoring

Force

Displacement

Negative

Damping &

Instability

Undershooting or Delay

Displacement

Restoring

Force


Development III: TVC Implementation

35

How to reduce control errors?

Slow HS: Make sure that command is realized by explicit checking

RTHS:

Actuator configuration: Error compensation & tuning

Shaking table configuration: Development III



0 20 40 60 80 100-2

-1

0

1

2

Time (sec)

Dis

pla

cem

ent

(inches)

command

feedbackAlmost perfect displacement tracking

Acceleration mismatch at low periods

Requirement for acceleration and velocity control

0 0.5 1 1.50

0.5

1

1.5

2

Period (sec)

Sa (

g)

Target

Measured

36

Three Variable Control (TVC), developed by MTS, is a well-established displacement-velocity-acceleration control method



37

Dsp reference

Ref

eren

ce

gen

erat

or

Fee

db

ack

gen

erat

orDsp measurement

Acc measurement

Dsp cmd

Vel cmd

Acc cmd

Gain for Dsp cmd

Gain for Vel cmd

Gain for Acc cmd

Ʃ

Dsp fdbk

Vel fdbk

Acc fdbk

-

-

-

Gain for D error

Gain for V error

Gain for A error

Ʃ

dP measurementHigh-pass

filter

dP feedback Gain for dP

ʃ dtGain for

integrated D errorClipping

Integral

authority

Ʃ

+

+-

Notch

filters

Valve

cmd

d/dt

d/dt

Low-pass

filter

Dsp

cmd

Vel

cmd

Acc

cmd

Dsp

reference

Low-pass

filter+

ʃ ʃ dt2

d/dt

ʃ dt

d2/dt2

High-pass

filter+

+

Dsp

measurement

Acc

measurement

Dsp fdbk

Vel fdbk

Acc fdbk

Feedback generatorReference generator

Dsp: Displacement

Vel: Velocity

Acc: Acceleration

Dp: Differential pressure

cmd: Command

fdbk: Feedback

TVC Schematic as implemented in nees@berkeley


Three Variable Control

38

Implementation in simulink models both for Shaking Table Tests and Hybrid Simulations


Dsp reference

Ref

eren

ce

gen

erat

or

Fee

dbac

k

gen

erat

orDsp measurement

Acc measurement

Dsp cmd

Vel cmd

Acc cmd

Gain for Dsp cmd

Gain for Vel cmd

Gain for Acc cmd

Ʃ

Dsp fdbk

Vel fdbk

Acc fdbk

-

-

-

Gain for D error

Gain for V error

Gain for A error

Ʃ


filter


ʃ dtGain for


Integral

authority

Ʃ

+

+-

Notch

filters

Valve

cmd

d/dt

d/dt

Low-pass

filter

Dsp

cmd

Vel

cmd

Acc

cmd

Dsp

reference

Low-pass

filter+

ʃ ʃ dt2

d/dt

ʃ dt

d2/dt2

High-pass

filter+

+

Dsp

measurement

Acc

measurement

Dsp fdbk

Vel fdbk

Acc fdbk


Dsp: Displacement

Vel: Velocity

Acc: Acceleration


cmd: Command

fdbk: Feedback


Implementation in simulink models both for Shaking Table Tests and Hybrid Simulations

39

Dsp reference

Ref

eren

ce

gen

erat

or

Fee

dbac

k

gen

erat

orDsp measurement

Acc measurement

Dsp cmd

Vel cmd

Acc cmd

Gain for Dsp cmd

Gain for Vel cmd

Gain for Acc cmd

Ʃ

Dsp fdbk

Vel fdbk

Acc fdbk

-

-

-

Gain for D error

Gain for V error

Gain for A error

Ʃ


filter


ʃ dtGain for


Integral

authority

Ʃ

+

+-

Notch

filters

Valve

cmd

d/dt

d/dt

Low-pass

filter

Dsp

cmd

Vel

cmd

Acc

cmd

Dsp

reference

Low-pass

filter+

ʃ ʃ dt2

d/dt

ʃ dt

d2/dt2

High-pass

filter+

+

Dsp

measurement

Acc

measurement

Dsp fdbk

Vel fdbk

Acc fdbk


Dsp: Displacement

Vel: Velocity

Acc: Acceleration


cmd: Command

fdbk: Feedback


Three Variable Control


Enhancement of Acceleration Feedback with TVC

0 0.5 1 1.50

0.5

1

1.5

2

Period (sec)

Sa (

g)

Target

Displacement Control (STS)

40



Enhancement of Acceleration Feedback with TVC (Tuning for RTHS): No delay between command and feedback

0 0.5 1 1.50

0.5

1

1.5

2

Period (sec)

Sa (

g)

Target


Three Variable Control (Simulink)

41




0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.2

0.4

0.6

0.8

1

1.2

1.4

Period (sec)

Sa (

g)

Target



Enhancement of Acceleration Feedback with TVC (Tuning for RTHS): No delay between command and feedback


Further Enhancement of Acceleration Feedback with TVC (Tuning for shaking table): Delay allowed between command and feedback

43


0 0.5 1 1.50

0.5

1

1.5

2

Period (sec)

Sa (

g)

Target




In Development I, a RTHS system is developed and can execute integration time steps of 1 milisecond.

Towards the objective of improving a general and versatile tool (OpenSees), an efficient solver is utilized in Development II to decrease computation time.

Additional challenge introduced by the control of accelerations in HS on a shaking table is addressed in the Development III by the adaptation of the three variable control for HS.

44

Recap

On-going/Future Development

Physical

Computational


Thank You!

Questions? Comments?

45

Documents

SERIES Concluding Workshop Joint with US-NEES, JRC … hybrid... · Towards Faster Computations and Accurate Execution of Real-Time Hybrid Simulation Khalid M. Mosalam, Professor,