Page 1 ... Pseudo-dynamic testing method (PSD). ⢠applying slowly varying forces to a ... same as the PSD test except that it is conducted in the real time. â¢.
CIE 616
FALL 2004
ADVANCED DYNAMIC TESTING TECHNIQUES IN STRUCTURAL ENGINEERING by Andrei M Reinhorn Xiaoyun Shao
Contents – Introduction of dynamic testing methods – Effective force testing – Pseudo dynamic testing – Real time hybrid dynamic testing
INTRODUCTION – Quasi-static loading test method (QST) – Shaking table testing method (STT) – Effective force method (EFT) – Pseudo-dynamic testing method (PDT) – Real time pseudo-dynamic testing method (RTPDT) – Real time dynamic hybrid testing method (RTDHT)
Quasi-static loading test method (QST) ¾
a test specimen is subjected to slowly changing prescribed forces or deformations by means of hydraulic actuators
¾
inertial forces within the structures are not considered in this method.
¾
purpose is to observe the material behavior of structural elements, components, or junctions when they are subjected to cycles of loading and unloading.
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dynamic nature of earthquakes are not captured
Shaking table testing method (STT) ¾
test structures may be subjected to actual earthquake acceleration records to investigate dynamic effects
¾
inertial effects and structure assembly issues are well represented
¾
the size of the structures are limited or scaled by the size and capacity of the shake table
Other testing methods (STT) • Effective Force Method • Pseudo-dynamic testing • Real Time Dynamic Hybrid Testing (new developement) :
m5x5a
:
m4x4a
Fi
:
m3x3a F
i
:
m2x2a
:
m1x1a
F2
F1
Effective force testing method (EFT)
m 4x4a :
m 3x3a :
m 2x2a :
m 1x1a :
– Real-Time PseudoDynamic Hybrid Testing System – Real-Time “Dynamic” Hybrid Testing System
m 5x5a :
• Effective Force Technique • Hybrid Testing & Computing
Applies the inertial ground motion generated forces through synchronized actuators - NEW
Effective force testing method (EFT) ¾
applying dynamic forces to a test specimen that is anchored rigidly to an immobile ground; perform real-time earthquake simulation
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these forces are proportional to the prescribed ground acceleration and the local structural masses. :
m 5x5a
:
m 4x4a
based on a force control algorithm
m 3x3a :
¾
:
m 2x2a
:
m 1x1a
• Effective Force Technique • Hybrid Testing & Computing – Pseudo-Dynamic Hybrid Testing System – Real-Time “Dynamic” Hybrid Testing System
Fi
F2
F1
Applies forces in substructure through actuators only – real time operation is a benefit but not a must
Pseudo-dynamic testing method (PSD) ¾
applying slowly varying forces to a structural model
¾
motions and deformations observed in the test specimens are used to infer the inertial forces that the model would have been exposed to during the actual earthquake
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Substructure techniques
Real time pseudo-dynamic testing method (RTPDT) ¾
same as the PSD test except that it is conducted in the real time
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Introduce problem in control, such as delay caused by numerical simulation and actuator
• Effective Force Technique • Hybrid Testing & Computing – Real-Time PseudoDynamic Hybrid Testing System – Real-Time “Dynamic” Hybrid Testing System
Fi
Applies forces in substructure through shake table and actuators – real time operation is a must
Real-Time Seismic Hybrid Testing INTERFACE FORCES ACTIVE FEEDBACK FROM SIMULATED STRUCTURE APPLIED BY ACTUATORS AGAINST REACTION WALL
REACTION WALL SIMULATED STRUCTURE
SHAKING TABLES (100 ton)
FULL OR NEAR FULL SCALE TESTED SUBSTRUCTURE
Fig.1. Real-Time Hybrid Seismic Testing System (Substructure Dynamic Testing)
Real time dynamic hybrid testing method (RTDHT) ¾
based on shaking table test combined with substructure techniques.
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part of the structure (the physical model) is constructed and tested on the shaking table
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The rest part of the structure (the numerical model) is numerically modeled in the compute
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the earthquake effect on the superstructure was calculated as a interface force and applied to the substructure by the actuators (force control based)
Closed Loop Test RESPONSE ANALYSIS (Superstructure)
SUPERSTRUCTURE RESPONSE
CONTROL IMPLEMENTATION
dislacment command
measured force (q)
STRUCTURE RESPONSE
EXCITATION
Specimen (SUBSTRUCTURE)
SUBSTRUCTURE RESPONSE
Pseudo-dynamic Test with Substructure
Closed Loop Test
Summary of dynamic test methods Advantages ¾
Size of the specimen can be large or very large
Disadvantages ¾ ¾
Inertial forces are not true forces and distorted by discrete parameter model, actuators and computers Rate effects are neglected because of quasi-static loading
PDT
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Size of the specimen can be large or very large
RTPDT
¾ ¾
Inertial forces are not true forces and distorted by discrete parameter model, actuators and computers Actuator time delay is introduced
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True inertia forces in assembly
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Size of the specimen is limited
¾ ¾
True inertia forces on the specimen Specimen can be large or very large
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Part of the inertia forces are simulated with errors (same as PDT) Actuator time delay is introduced
STT
RTDHT
¾
Effective Force Testing Equation of motion
a + Cx + Kx = 0 Mx Subscript refers to motion relative to a fixed reference frame (absolute displacement)
x = x + Ix g a
x = x + I x a g
+ Cx + Kx = −M Mx x = P (t ) g eff
Open Loop Control (in concept)
Effective Force Test
Effective Force Test – Hardware Components • Servo-Hydraulic Actuators • Servo-Hydraulic Control System • Elastic Spring • Measurement Instrumentation (DAQ) • Computer – Simulator – Controller
Effective Force Test – Hardware Configuration
Structure
Effective Force Test -Dynamic force control Series elasticity and displacement feedback Target Force
Measured Force
1 / KLC
Command Signal Actuator with Displacement Control
Compensator
Series Load Cell Spring, KLC
Structure
Effective Force Test -Dynamic force control Series elasticity and displacement feedback Actuator Displacement Feedback Desired Force
1/KLC
+
Σ +
C≈
1
GActuator
G Actuator
Actuator Displacement
+
Actuator in Closed-loop Displacement Control
Compensation
Structure Displacement
Σ -
KLC Series Spring
1 ms 2 + cs + k Structure
Achieved Force Desired Force
= CG
ms 2 + cs + k ms 2 + cs + k + K LC (1 − CG )
Ideal: C = 1/G
Achieved Force
Effective Force Test -Dynamic force control The advantages of using the series spring • the actuator can be well tuned and operated in displacement control • it provides for one more parameter than can be altered in the control design (the oil stiffness cannot be) • the term KLC(1-CG) in the transfer function indicates that the smaller the value of KLC the less sensitive is the transfer function to deviations of C from 1/G
Effective Force Test – Effect of Time Delay The dynamic characteristics of hydraulic actuators inevitably include a response delay , which is equivalent to negative damping Experimental
2.0 1.8 1.6
Numerical
Magnitude
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0
2.0
4.0
6.0
Frequency (Hz)
8.0
10.0
Effective Force Test – Predictive Control
1/KLC
+
Σ +
Corrective Displcement
Σ +
+
-
Σ +
T = e-sτ
Predictive Displcement
T0
1 m0 s + c0 s + k0 + K LC 0
Delay Model
Model of StructureSpring System
Actuator
+
Σ -
KLC Series Spring
2
1 ms 2 + cs + k Structure
Smith Predictor
Effective Force Test – Predictive Control 2.0 1.8 1.6
Without compensation
Magnitude
1.4 1.2 1.0
With compensation
0.8 0.6 0.4 0.2 0.0 0.0
2.0
4.0
6.0
Frequency (Hz)
8.0
10.0
Effective Force Test – Software •Simulink® •Realtime Workshop®5 •XPC Target
Pseudo dynamic testing Define a model of the structure system Define the desired excitation – usually base acceleration Calculate the expected response of structure – displacement Use an actuator to apply the desired displacement in the structure Measure the resistance force in the structure (or estimate it from measurements) Repeat the above steps – start from second
+ Cd + R = f Md i i i i
Pseudo-dynamic testing Input excitation fi (desired) -1
∆t ⎞ ⎛ ∆t ⎛ ⎞ a i+1 = ⎜ m+ c ⎟ ⎜ f i+1 -ri+1 -cvi - ca i ⎟ 2 ⎠ ⎝ 2 ⎝ ⎠
vi+1 =vi +
∆t ( a i +a i+1 ) 2
∆t 2 d i+2 =d i+1 +∆tvi+1 + a i+1 2 Impose di+1 on the structure
Pseudo dynamic testing Discretized equation of motion of the structure at time intervals
ti = i∆t
for
, i = 1toN
+ Cd + R = f Md i i i i Equation solved in computer step by step, with Ri as the reaction force measured from the specimen under test. Result is the displacement command of next step that will be applied to the specimen at each node of mass by actuators.
Pseudo dynamic test—integration algorithm – Both explicit and implicit time-stepping integration algorithm can be applied for solving equation of motion in Pseudodynamic tests. – Explicit methods compute the response of the structure at the end of current step based on the state of the structure at the beginning of the step. • • • • •
Central difference method (Takanashi et al. 1975), Newmark- Beta method (1959), Modified Newmark’s method (1986), The γ-function pseudodynamic algorithm (Chang et al. 1997) Unconditionally stable explicit method(Chang, 2002)
(continued on next)
Pseudo dynamic test—integration algorithm (continued) – Implicit methods require knowledge of the structural response at the target displacement in order to compute the response. – the displacement is dependent on other response parameters at the end of,the step – iteration is required in the algorithm to satisfy both the imposed kinematic conditions and the equilibrium conditions at the end of the time step • Newmark – Alpha method (Hilber et al. 1977) • Hybrid implicit algorithm (Thewalt and Mahin, 1987) • Newton iteration (Shing, 1991)
Pseudo dynamic test—integration algorithm (continued) – implicit iteration algorithm provide improved stability characteristics and permit the used of larger integration time steps – iteration on experimental model is not practical since structure materials are path dependent – explicit methods are easier to implement – Explicit integration methods are preferred for PSD simulation when stability limits are satisfied for the structural model under investigation
ρ Md i +1 + 2 M (d i +1 − d i ) + (1 + α )R i +1 − αR i = f i +1 ∆t 2 ∆ t d i +1 = d i + ∆td i + d i 2
∆t d i +1 = d i + (d i + d i +1 ) 2
Substitute into and solve for
= d i +1
− 2ρ 2 ρ di − d i + M −1 (f i +1 + αR i − (1 − α )R i +1 ) (2 + ρ )∆t 2+ ρ
Pseudo-dynamic testing – substructuring principle • may fabricate only part of the structure whose hysteretic behavior is complex and apply the test to this part • remaining part treated in the computer
Pseudo-dynamic testing – substructuring principle ⎡ M ee ⎢M T ⎣ ea
⎫ ⎡ C ee M ea ⎤ ⎧d e ⎨ ⎬ + ⎢ T ⎥ M aa ⎦ ⎩d a ⎭ ⎣C ea
C ea ⎤ ⎧d e ⎫ ⎧R e ⎫ ⎧f e ⎫ ⎨ ⎬ + ⎨ ⎬ = ⎨ ⎬ ⎥ C aa ⎦ ⎩d a ⎭ ⎩R a ⎭ ⎩f a ⎭
subscripts a and e denote the degrees of freedom within the analytical and experimental substructures.
+ C d + K d = f − M d M ee d e ee e ee e e ea a − C ea d a − K ea d a
+ C d + K d = f − M T d − C T d − K T d M aa d a aa a aa a a ea e ea e ez
Dee de = fe − Dea da Daa da = fa − Dea Tde
Æ Tested part. Calculate displacement command for next step. Æ Interface force: D e a d a Æ Analytical part. Calculate interface state used in interface force.
Dynamic hybrid testing - I • Combined use of earthquake simulators, actuators and computational engines for simulation • Details later in the presentation
Response Feedback
Computational Substructure
Physical Substructure
Physical Substructure Shake Table
Computational Substructure
Ground/Shake Table
Structural Actuator
`
Dynamic hybrid testing - II Well understood
Structural Actuator
Foundatio n Laminar Soil Box Shake Table
Focus of interest
`
Real-time dynamic hybrid testing - II Response Feedback
`
Structural Actuator Has to operate in Force Control Distributed mass
Response Feedback Computation al Substructure Physical Substructur e
Physical Substructur e
Structural Actuator
Shake Table Computation al Substructure Ground/Shake Table
S h a k e t a b l e a c c e l e r a t i o n , u t =
( s ) u1
α
1
F irs t s to ry c o n trib u tio n to s h a k e ta b le a c c e le ra tio n
k − α 3 (s ) 3 ( x 3 − x 2 ) m 2
T h ird s to ry c o n trib u tio n to s h a k e ta b le a c c e le r a tio n
A c t u a t o r F o r c e , F a = − ⎡⎣ 1 − α 1 ( s ) ⎤⎦ m 2 u1 + ⎡⎣ 1 − α 3 ( s ) ⎤⎦ k 3 ( x 3 − x 2 )
F irs t s to ry c o n trib u tio n to a c tu a to r fo rc e
T h ird s to ry c o n trib u tio n to a c tu a to r fo rc e
α1 ( s ) = 0 and α 3 ( s ) = 0
Unified approach to substructure testing • If α ( s) ≠ 0 and α ( s) ≠ 0 , then the control requires a shake table and an actuator to implement the substructure testing. 1
3
• If α ( s ) = 0 and α ( s ) = 0 , then the controller require just an actuator to implement the substructure testing as pseudo-dynamic testing: 1
3
• Note: – In pseudo-dynamic testing, inertia effects are computed. – In dynamic hybrid testing ( α ( s ) ≠ 0 or α ( s ) ≠ 0 ), the actuator should operate in force control. 1
3
Hybrid Controller Implementation (UB-NEES) • Flexible architecture using parallel processing
Optional
Optional
Computationa l Substructure MTS Actuator Controller (STS)
