structural control and condition research interests … · structural control and condition ......
TRANSCRIPT
Structural Control and Condition Assessment
Ananth Ramaswamy
Professor, Indian Institute of ScienceBangalore, India
3rd Asia Pacific Summer School on Smart Structures Technologies, University of Tokyo, Japan 15thJuly-04th August 2010.
Research InterestsA. Material and Structural Behavior:
Steel fiber reinforced prestressed concrete beams and RC beam column joints.
Performance of non metallic rebars for RC.
Material characterization of self compacting concrete (SCC) with admixtures (fly ash, silica fume) & related fracture studies.
Creep and shrinkage in normal and heavy density concrete
Repair of structural concrete using GFRP / CFRP / SCC with fibers - Concrete beam and column repair against mechanical & extreme thermal loads
Field application of repair
B. Vibration control and condition assessment of structures Studies on thermal
distortion and vibration control in laminate composites having piezomaterial as layers.
Studies on vibration control of seismically excited buildings, bridges and the possibility of adaptive vibration control for repair.
Thermal Distortion and Vibration Control in Laminate Composites having Piezo Layers
Composite laminates used in space applicationsare often exposed to: i) thermal gradients that cause distortions ii) unacceptable levels of vibrations (jitter).
Use of piezo layers as patches (sensing and actuation) to control these deformations has been explored.
Piezo Electric Material – Constitutive Equations:
.3,2,1,6,..2,1,
)(
)(,,
,,
lkandqpwhere
effectDirectTPEeD
effectConverseTEeQE
klT
klpTkpk
Epk
Tkpq
TEpqp
σ, ε, Ek, Dk, ΔT represent the stress, strain, electric field, electric displacement and raise in temperature, respectively.
Q, є, e, λ and P represent the elastic moduli, dielectric tensor, piezo electric coefficient, thermal stress coefficient and pyroelectric coefficient. The superscripts indicate quantities held constant while quantifying the variable .
Piezoelectric Shell Laminate and curvilinear coordinate system.
Piezo Electric Material – Constitutive Equations:
Laminate having layers with different orientation
Laminate with arbitrarily located Piezo Layers
Piezo electric sheet
Analogy between mechanical and electrical quantities
Implicit Layering
Explicit Layering
Layering Procedures in FEM
0)....(0
dtdoneWorkEPEKt
Using Hamilton’s Principle
Where:
v
ktkp
tplkl
tkpkp
tkppq
tq dvTPETEEeEQEHEP }2{
2
1),(..
dvwwvvuuEK llllll
v
)(2
1..
pv
wvu
v
wsvsuswbvbub
qdsdvqvPvPuP
dswTvTuTdvwfvfufdonework
2
1
''
][][ ,,,,,,
In a finite element framework:
*][][][
}{]][[}{}{*}{
][]][[][*][
}]{[*}{}*]{[}]{[}]{[
1
1
KMC
FKKFFF
KKKKK
KFdKdcdM
dddd
dddd
dddd
addddd
ssss
ssss
a
Adopting a constant gain negative velocity feedback control: )(][)( tGt sca
*}{}*]{[}]]{[]][][[[}]{[ 1 FdKdKKGKCdM dcddd sssa
Extra Damping
Optimization Problem:
0
)( dtRQyyJ aTa
T Minimize
*}{}*]{[}]]{[]][][[[}]{[ 1 FdKdKKGKCdM dcddd sssa
Subject to:
System Performance based on measurement y=Cod weight Q
Control force applied (φa) weight R
Extra Damping
MATLAB / SIMULINK Feedback control Algorithm
}]{ˆ[}]{[}]{[ ad BuBXAX
][][]'[][
][]0[][ 11
dddddd CMKM
IA
1][
]0[][
ddMB
][][
]0[]ˆ[ 1
addd KMB
Using the state-space formulation x={d, d’}
Where:
State matrix Disturbance matrix Control matrixThe measurement equation (output matrix): {y}=[Co]{X}
Using the feedback law: }]{[][][}]{[}{ 1 XSBRXG Tca
Where [S] satisfies the Riccatti equation:
0]][[][][]ˆ[]][ˆ][[]][[][][ 001 CQCSBRBSASSA TTT
}]{[}]){][ˆ[]([ dc uBXGBAX The closed loop system dynamics is given by:
Graphite Epoxy Laminate with Surface Bonded Piezo Patches, FE Model, Properties.
Simply Supported PlateBansal, A. and Ramaswamy, A. (2002) “FE Analysis of Piezo-laminate Composites under
thermal loads”, Journal of Intelligent Material Systems and Structures, v.13, No.5, 291-301
Deformation under Thermal Gradient of 100oC, deformation under active compensation, sensor voltage.
Thermal Distortion - uncontrolled
Thermal distortion-under applied voltage
Plexi-glass beam with surface bonded PVDF, properties.
uncontrolled
Controlled
Sensor Potential
Vibration control of seismically excited structures
Ground motion induced vibrations in building and bridge structures can result in both excessive structural deformation that results in member / structural failure and occupant discomfort due to high floor accelerations.
Conventional ductility based designs, accompanied by plastic hinge development and mechanism occurrence methods may result in maintenance difficulties.
Structural control methods offer a via media that can lead to resolving the above concerns.
Passive and Hybrid Vibration control of Buildings
Parameters considered include-models for building (cantilever, plane frame, torsionally coupled building) , loads (Seismic, Wind), control strategy, material nonlinearity, limits on number of sensors and actuating devices, functional constraints in sensor/actuator.
Multi-objective ‘Pareto optimization’ Supervisor model for adaptive control when material
nonlinearity included.
Feed forward (open loop) control
Feed‐back (Closed loop) control
• Choice of control devices and sensors
•Idealization of Structure (Building Model)
•Choice of control algorithm
Control devices
Passive Control Base Isolation with
elastomeric bearings Sliding bearings Friction bracing systems Visco-elastic dampers. Orifice dampers Liquid column dampers Tuned Mass dampers
(TMD)
Active Control Active Mass driver (AMD)
Semi-active Control ER / MR dampers
Hybrid Control(Combination of passive and active/semi-active control) TMD +AMD or MR/ER
dampers
Passive System – Base Isolation
Viscous Fluid DampersVisco‐elastic dampers
X‐braced friction damperPassive systems ‐ Can be introduced at basement level, as a bracing system between columns and floors.
Tuned Mass Dampers
Hybrid Mass Dampers
Structural Model Idealizations
Cantilever BuildingShear Building Model•Rigid floors•Inextensible columns•Symmetric buildings•Response is predominantly in one‐direction•Same ground excitation on all points of building
Torsionally Coupled Building Model
•Principal axis along x and y•Centre of mass and resistance are not coincident, do not lie along same vertical line and result in variable eccentricities on each floor. •All floors have different radii of gyration and have differing ratio of torsional to lateral stiffness ratio•Response is predominantly in one‐direction•Same ground excitation on all points of building
Structural Model Idealizations Fuzzy Logic Control SystemsFLC design
• Establishes a nonlinear map between I/O data.• Sensitivity to system parameter uncertainties and noisy data is less.• Easy to establish control rules (if one knows the system well).
I/O parameters Design of the input output scaling parameters
I/O Membership Functions Choice of membership function Parameters that define membership function Number of membership function
Fuzzy Rule Base It is always left to the experts to define the rule base Number of rules
Fuzzy Logic Control Systems: Problems
Defining these parameters are a real challenge in FLC design and are always left to experts. One can use evolutionary search methods to search for optimal parameters to a FLC.
[System]Name='fuz_arb'Type='mamdani'Version=2.0NumInputs=2NumOutputs=1NumRules=25AndMethod='min'OrMethod='max'ImpMethod='min'AggMethod='max'DefuzzMethod='centroid'
[Input1]Name='Velocity'Range=[-1 1]NumMFs=5MF1='NL':'zmf',[-1 -0.7]MF2='NS':'gbellmf',[0.35 2.2811088413887 -0.5]MF3='ZE':'gbellmf',[0.15 2.2811088413887 0]MF4='PS':'gbellmf',[0.35 2.2811088413887 0.5]MF5='PL':'smf',[0.7 1]
[Input2]Name='Accleretion'Range=[-1 1]NumMFs=5MF1='NL':'zmf',[-0.8 -0.5]MF2='NS':'gbellmf',[0.15 6.25 -0.5]MF3='ZE':'gbellmf',[0.35 6.25 0]MF4='PS':'gbellmf',[0.15 6.25 0.5]MF5='PL':'smf',[0.5 0.8]
[Output1]Name='Control'Range=[-1 1]NumMFs=7MF1='NL':'gbellmf',[0.2667 2.2811088413887 -1]MF2='NE':'gbellmf',[0.0667 2.2811088413887 -0.666666666666667]MF3='NS':'gbellmf',[0.2667 2.2811088413887 -0.333333333333333]MF4='ZE':'gbellmf',[0.0667 2.2811088413887 0]MF5='PS':'gbellmf',[0.2667 2.2811088413887 0.333333333333333]MF6='PO':'gbellmf',[0.0667 2.2811088413887 0.666666666666667]MF7='PL':'gbellmf',[0.2667 2.2811088413887 1][Rules]1 1, 1 (1) : 11 2, 1 (1) : 11 3, 1 (1) : 11 4, 2 (1) : 11 5, 3 (1) : 12 1, 1 (1) : 12 2, 1 (1) : 12 3, 1 (1) : 12 4, 2 (1) : 12 5, 3 (1) : 13 1, 1 (1) : 13 2, 3 (1) : 13 3, 4 (1) : 13 4, 5 (1) : 13 5, 5 (1) : 14 1, 7 (1) : 14 2, 7 (1) : 14 3, 7 (1) : 14 4, 6 (1) : 14 5, 5 (1) : 15 1, 7 (1) : 15 2, 7 (1) : 15 3, 7 (1) : 15 4, 6 (1) : 15 5, 5 (1) : 1
ACCELERATION
VELOCITY
NL NE ZE PO PL
NL NL NE NS NS ZE
NE NE NS ZE ZE ZE
ZE NS ZE ZE ZE PS
PO ZE ZE ZE PS PO
PL ZE PS PS PO PL
Build-FLC
ACCELERATION
VELOCITY
NL NE ZE PO PL
NL NL NE NS NS ZE
NE NE NS ZE ZE ZE
ZE NS ZE ZE ZE PS
PO ZE ZE ZE PS PO
PL ZE PS PS PO PL
Fuzzy Logic: Rule Base & MFs
Fuzzy Rule Base
I/O Membership Functions
J6 and J7 were objectives optimized in a multi-objective Genetic algorithm framework with constraints imposed on the actuator stroke, actuator acceleration
Simulink model for a three storey single bay structure with an active mass driver at the top
Implementation Issues Integration time step = 0.0005s Sampling time = 0.001s ADC & DAC 12 to 16 bits, Saturation of sensor +/- 3volts. Sensor noise RMS 0.01v(.03% of span)-
Gaussian rectangular pulse process of width equal to sampling time of ADC.
Time delay = 1 sampling time Quantization errors
= (Twice span of ADC/DAC)/2no. Of bits
Sample & hold Circuit ADC zeroth order (constant) DAC 1st Order (linear)
A trade-off between the maximum inter-story drift and the maximum floor acceleration represents the “Pareto” optimal Solution.
Ahlawat, A.S. and Ramaswamy, A. (2001)"Multi-objective Optimal Structural Vibration Control Using Fuzzy Logic Control System", Journal of Structural Engineering, ASCE,
127(11), pp.1330-1337
Each-FloorM=3.6x105kg K=650MN/mC=6.2MN-s/m
GA optimized FLC for TMD, AMD and HMD example for a 10 storey shear building
Ahlawat, A.S. and Ramaswamy, A. (2002) “Multi-Objective Optimal Design of FLC Driven Hybrid Mass Damper for Seismically Excited Structures”,
Earthquake Engineering and Structural Dynamics, 31(5), 1459-1479, May Implementation Issues Integration time step = 0.0005s Sampling time = 0.001s ADC & DAC 12 to 16 bits, Saturation of sensor +/- 3volts. Sensor noise RMS 0.01v(.03% of span)-
Gaussian rectangular pulse process of width equal to sampling time of ADC.
Time delay = 1 sampling time Quantization errors
= (Twice span of ADC/DAC)/2no. Of bits
Sample & hold Circuit ADC zeroth order (constant) DAC 1st Order (linear)
SIMULINK Model for Building with Fuzzy Logic Control
0.4 0.5 0.6 0.7 0.8 0.9 10.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
J1
J 3
Hadi and Arfiadi (1998)PRESENT STUDY: Optimal TMD Optimal AMD Optimal HMD
Pareto Optimal Performance (J1- Inter-story drift) vs. (J3-absolute acceleration) for 10 story shear building model
A
Time History & PSD for inter-story drift for Kobe EQ Excitation at Point “A”
Hybrid Control System for Seismically Excited Torsionally Coupled Building
8-story building, 15m and 24m, mass mi=3.456X105 kg, mass moment of inertia Ii=2.37104X103 Kg-m2, stiffness in x-direction kxi=3.404X105 kN/m, in y-
direction kyi=4.503X105 kN/m, torsional stiffness ki=3.84X107 kN/rad, eccentricity ex=0.24 m and eccentricity ey=0.15 m
damping ratios 2% for the first three modes mass of the HMD system = 1.0% of the total mass of
the building (Fur et al. 1996)
Torsionally Coupled Model
HMD SystemTMD System
Peak Inter-story Drift (J1) Vs rotation (J2) and Acceleration (J3) (TMD System)
0.4 0.5 0.6 0.7 0.8 0.9 10.3
0.4
0.5
0.6
0.7
0.8
0.9
1
J1
J 2/J3
Fur et. al 96 J
3
Fur et. al 96 J
2
present study J
3
present study J
2
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
J1
J 2/J 3
Fur et. al (1996) AMD1 J
3
AMD1 J2
AMD2 J3
AMD2 J2
AMD3 J3
AMD3 J2
present study J3
present study J2
Peak Inter-story Drift (J1) Vs rotation (J2) and Acceleration (J3) (HMD System)
Ahlawat, A.S. and Ramaswamy, A. (2003) “Multi-objective Optimal Absorber System for Torsionally Coupled Seismically Excited Structures”, Engineering Structures: Journal of Earthquake Engineering, Wind and Ocean Engineering, 25(7), 941-950.
Ahlawat, A.S. and Ramaswamy, A. (2002)“Multi-objective Optimal FLC Driven Hybrid Mass Damper for Torsionally Coupled Seismically Excited Structures”,
Journal of Earthquake Engineering and Structural Dynamics, 31(12), 2121-2139
Adaptive control System Architecture ANFIS System and Optimal FLC Parameter computation
Performance in Seismically excited nonlinear Plane frame building with Optimal FLC for linear; Nonlinear & adaptive nonlinear
Performance in Seismically excited nonlinear Torsionally coupled building with Optimal FLC for linear; Nonlinear & adaptive nonlinear
An multi-objective optimal design of a FLC driven active and hybrid control system, offering a set of Pareto-optimal designs, is developed Adaptive Control has potential to be deployed in pre or post seismic event retrofit / rehabilitation-useful if online system identification is feasible.
Remarks
GA-FLC and PSO based control systems are seen to be effective. However, their effective implementation requires that the control scheme be placed on a chip, so as to reduce process times.
Adaptive trained supervisor based ANN systems can detect changes in the system and alter the parameters of the FLC to offer improved control.
Base isolation is an effective means to isolating structures from ground motions
But base isolation show severe displacement under near source excitation
One means to protect is to combine base isolation with damping mechanism
Semi-active devices are effective in damping as they provide better control than active devices with lesser energy input
We combine base isolation with semi-active MR damper to protect building against near source ground motions
Motivation
MR Damper: Bouc-Wen Model
0f c x z
1n nz x z z x z A x
0 0 0( ) ; ( )c a c c cab bu u c u c c u
( )c cu u v
Damper Force:
Evolutionary variable:
Voltage dependency:
Filter to input voltage:
Input voltage to output force is a nonlinear relationNonlinear input/output map is needed for prediction of voltage once required control force is known
MR Damper: Simulation Results
Time Displacement (m)
Velocity (m/s)
0 0.25 0.5 0.75 1 -2500
-2000
-1000
0
1000
2000
2500
-1.5 -1 -0.5 0 0.5 1 1.5-2500
-2000
-1000
0
500
2000
2500
-25 -20 -15 -10 -5 0 5 10 15 20 25-2500
-2000
-1000
0
1000
2000
2500
For
ce (
N)
For
ce (
N)
For
ce (
N)
Fuzzy Logic Control SystemsFLC design
• Establishes a nonlinear map between I/O data.• Sensitivity to system parameter uncertainties and noisy data is less.• Easy to establish control rules (if one knows the system well).
I/O parameters Design of the input output scaling parameters
I/O Membership Functions Choice of membership function Parameters that define membership function Number of membership function
Fuzzy Rule Base It is always left to the experts to define the rule base Number of rules
Fuzzy Logic Control Systems: Problems
Defining these parameters are a real challenge in FLC design and are always left to experts. One can use evolutionary search methods to search for optimal parameters to a FLC.
Genetic Fuzzy Logic Control SystemsGAFLC design
• GA can be used to design the knowledge base of FLC• Adaptively redesigns fuzzy rules, MF parameters, I/O scaling.
GeneticAlgorithm
I/O parameters Design of the input output scaling parameters
I/O Membership Functions Choice of membership function Parameters that define the membership function Number of membership function
Fuzzy Rule Base It is always left to the experts to define the rule base
GAFLC Systems
Present GA changes all the above except the number of MFs and number of rules
GAFLC Systems: Rule base design
NL
NL
PL
PS
ZENS
PL
PS
ZE
NS
NL
PLPSZENS
Velocity
Acceleration
Consequent Line
CS
CA
NE
PO
A geometric approach to the FLC design has been taken:
1. The angle of the Consequent line (CA)
2. Spreading of the output MF’s (CS) How it works:
1. CA can take any value between 0-180o(Consequent line rotates about ZE-ZE position).
2. Position of the consequent (output) changes each time CA takes a new value.
3. CS changes the spread of the consequents. With fixed CA, CS increases or decreases the zone for each of the consequent (NL, NS etc.)
Rule base: How it works
Can take into account the symmetry in structural dynamic behavior
Symmetry provides robustness to the FLC design.
How it works:
4. Every consequent is given a weight based on its distance from the origin.
5. Distance of Consequent defines the rule base for a particular antecedent pair.
Adjacent figure show rule base for CA=135, CS=1
Properties:
ZE
GAFLC Systems: MF design
Generalized bell shaped MF is used:
1. Width ‘a’ is changed to create non uniform MF width
2. Slope at 0.5 MF grade-’b’ is changed to get different MF type.
Properties:1. Always symmetric about the
origin. 2. Generalized bell shaped MF
can take any shape based on slope ‘b’ and width ‘a’.
-1
-0.5
0
0.5
1
-1
-0.5
00.5
1
-0.2
0
0.2
0.4
0.6
0.8
Velocity
Accleretion
Con
trol
-1
-0.5
0
0.5
1
-1-0.5
00.5
1
-0.5
0
0.5
VelocityAccleretion
Con
trol
GAFLC Systems: Sample Rule Base Maps
Chichi Earthquake Elcentro Earthquake
One can see the adaptive nature of the rules
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Velocity
De
gre
e o
f m
embe
rshi
p NL NS ZE PS PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Accleretion
De
gre
e o
f m
embe
rshi
p NL NS ZE PS PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Control
De
gre
e o
f m
em
bers
hip NL NE NS ZE PS PO PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Velocity
Deg
ree
of m
embe
rshi
p
NL NS ZE PS PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Control
Deg
ree
of m
embe
rshi
pNL NE NS ZE PS PO PL
-1 -0.5 0 0.5 1
0
0.2
0.4
0.6
0.8
1
Accleretion
Deg
ree
of m
embe
rshi
p
NL NS ZE PS PL
Chichi Earthquake
Elcentro Earthquake
GAFLC Systems: Sample Membership Functions
One can see the adaptive nature of the MFs
Adaptive rule base FLC used with hybrid base isolated structure
Ali, Sk. Faruque and Ramaswamy, A. (2008) “GA optimized FLC driven semi-active control for Phase II smart
nonlinear base isolated benchmark building”, Journal of Structural Control and Health Monitoring, 15, 797-820
The objective was to minimize bearing level displacements while also limiting magnitude of floor accelerations and base shear
The ARB-FLC results in an improved performance and is stable.
The clipped optimal control used in the benchmark took longer to stabilize.
A variable rule base FLC is shown to be
better than a fixed rule base FLC system.
Nonlinear Force – Displacement relationship with MR dampers used.
Problem Definition
Vibration control of a two-span, prestressed concrete box-girder bridge on 91/5 over crossing located in Orange County of southern California forms the benchmark problem-Phase I (Agrawal et al 2005, 2009)
Sensors and Actuators Location
Nine Actuators and six accelerometers are used
ANFIS-Why?
ANFIS changes the position of the MFs w.r.t the input in an optimal way
•No standard method exists for designing the Fuzzy Rule base. It is based on the experience of the designer.•Fuzzy logic Membership Functions (MFs) are fixed type and it does not change with the change in the input parameter. Thus, tuning of the MFs is not done to minimize the error.Consequently, FLC acting alone doesn’t provide an optimal control.
How does ANFIS work ?
Adaptive Nodes
Fixed Nodes
NE = Negative
PO = Positive
N = Neural Network
ANFIS Optimal Position of MFs
Takagi & Sugeno Type Inference Scheme
3 bell shaped MFs for Acceleration and Velocity
Optimal Positions of the MFs are determined using ANFIS
Solution Technique: ANFIS FLC
A Hybrid Control Approach is undertaken using both FLC and ANFIS to control the vibration of the Highway Bridge.
Two separate ANFIS model are trained and tested with a set of near and far field earthquake excitations.
ANFIS is trained with velocity and acceleration data as input from east and west abutment ends of the the bridge and corresponding control as output from LQG results to obtain the optimal set of weights.
Acceleration and Velocity data from the central bent column are given as input to the FLC in addition.
Solution Technique: ANFIS FLC
8 hydraulic actuators placed longitudinally between the abutment and deck are driven by ANFIS trained with longitudinal data obtained from LQG model.
From the remaining eight transverse actuators, four (two on each side) are driven by FLC and the rest by ANFIS.
Simulink: ANFIS FLC Control
MR Damper
MR Damper parameters (Tan & Agrawal, 2005) Max Force =1000kN
Bouc-Wen Model
where x(dot) is the relative velocity at the damper location; z is the evolutionary variable, and γ, β , n, A are parameters controlling the linearity in the unloading and the smoothness of the transition from the pre–yield to the post-yield region
Variable input current experimental curves (xmr = 10mm, ω = 0.5Hz)
Variable excitation amplitude test curves (imr = 0A, ω = 0.5Hz)
Optimal DynamicInversion
Schematic of a two-stage dynamic inversion controller
Primary Controller: LQG controller algorithm based on the reduced order benchmark bridge model
IqIq
Qa
d
00 R = 10-5I N×N and N=
number of controllersr
g XKtf^
)(
)(^^
uDXCyLuBXA mr
rmrmr
r
rX
Kg is feedback gain matrix and Xr is the Kalmanestimate of the system. Kg is selected to minimize the cost J1, based on the state feedback law above. The Kalman filter optimal estimator is given by:
L is the observer gain matrix of the stationary Kalman Filter
ODI (Secondary Stage): The controller is designed with a goal to minimize the error between the required force determined by the primary controller and the control force to be supplied by the MR damper in a L2 normed sense:
The controller is designed such that the following stable error dynamics is satisfied.
0))()(())()((2
)}()({))()((
0
tftuPtftuk
tftuPtftu
eke
e
e
To obtain a unique solution, we minimize the cost function formulated as follows:
Subject to the constraint:
Where:
The problem of control singularity may arise if xi, x˙i and zi go to zero simultaneously and hence li goes to zero. So with a user defined tolerance, the voltage is set to zero under these conditions.
Optimal Dynamic Inversion
Ali, Sk. Faruque and Ramaswamy, A. (2009) “Optimal Dynamic Inversion based Semi active Control of Benchmark Bridge using MR Dampers”, Journal of Structural Control and Health Monitoring, DOI: 10.1002/stc.325, 16, 564-585.
Simulink: ODI Control
ANFYS-FLC Control Performance Functions: Peak Values
Performance Index
N. Palm Spring
Chichi El Centro Northridge Turkey Kobe
J1 (Base Shear)
0.8343 0.7878 0.8101 0.7862 0.8619 0.8020
J2 (Base Moment)
0.7556 0.9296 0.7394 0.9284 0.9432 0.7208
J3 (Midspan Disp)
0.8114 0.7541 0.8221 0.7746 0.7243 0.7043
J4 (Midspan Accl)
0.9383 0.8639 0.8473 0.8669 0.8128 0.9040
J5 (Bearing Deform)
0.8499 0.7423 0.6828 0.7756 0.8962 0.5860
J6 (Ductility)
0.7556 0.6633 0.7394 0.6730 0.4204 0.7208
J7 (DissipEnergy)
0.0000 0.5303 0.0000 0.5750 0.3425 0.0000
J8 (Plastic Connec.)
0.0000 0.6667 0.0000 1.0000 0.3333 0.0000
ANFYS-FLC Control Performance Functions: Normed Values
Performance Index
N. Palm Spring
Chichi El Centro Northridge Turkey Kobe
J9 (Base Shear)
0.7474 0.8088 0.6567 0.7634 0.8746 0.7123
J10 (Base Moment)
0.6773 0.7524 0.6301 0.7812 0.5406 0.6808
J11 (Midspan Disp)
0.7018 0.7081 0.6455 0.7405 0.5582 0.6978
J12 (Midspan Accl)
0.8407 0.7554 0.6746 0.7458 0.7946 0.7568
J13 (Bearing Deform)
0.7621 0.7468 0.5091 0.7669 0.9784 0.5428
J14 (Ductility)
0.6773 0.4782 0.6301 0.7144 0.1858 0.6808
ANFYS-FLC Control Performance Functions: Control Parameters
Performance Index
N. Palm Spring
Chichi El Centro Northridge Turkey Kobe
J15 (Peak Force)
0.0076 0.0219 0.0048 0.0221 0.0135 0.0069
J16 (Peak Dev.
Stroke)0.9374 0.8144 0.7196 0.8095 0.9161 0.6620
J17 (Peak Power)
0.0290 0.1058 0.0226 0.1265 0.0572 0.0244
J18 (Total Power)
0.0067 0.0145 0.0034 0.0173 0.0118 0.0044
J19 (No. of Devices)
16.0000 16.0000 16.0000 16.0000 16.0000 16.0000
J20 (Sensors)
6.0000 6.0000 6.0000 6.0000 6.0000 6.0000
J21 (Comp Resource)
22.0000 22.0000 22.0000 22.0000 22.0000 22.0000
ANFYS-FLC Control Performance Functions: Comparison ANFIS v/s LQG
ANFIS
LQG
Performance Index
J1 (Base Shear)
J2 (Base Moment)
J3 (Midspan Disp)
J4 (Midspan Accl)
J5 (Bearing Deform)
J6 (Ductility)
J7 (DissipEnergy)
J8 (Plastic Connec.)
0.8137 0.8693 0.8619 0.9502
0.8362 0.8565 0.9432 0.9782
0.7651 0.7865 0.8221 0.8669
0.8722 0.8488 0.9383 0.8986
0.7555 0.7611 0.8962 0.9370
0.6621 0.7123 0.7556 0.8516
0.2413 0.2447 0.5750 0.6244
0.3333 0.3333 1.0000 1.0000
Average Maximum
NORMED VALUES
PEAK VALUES
Average Maximum
J9 (Base Shear)
J10 (Base Moment)
J11 (Midspan Disp)
J12 (Midspan Accl)
J13 (Bearing Deform)
J14 (Ductility)
0.7605 0.8006 0.8746 0.8937
0.6771 0.7160 0.7812 0.8780
0.6753 0.7142 0.7405 0.8047
0.7613 0.7645 0.8407 0.7976
0.7177 0.5942 0.9784 0.8211
0.5611 0.6277 0.7144 0.8274
Performance Index
J15 (Peak Force)
J16 (Peak Dev.
Stroke)J17
(Peak Power)J18
(Total Power)J19
(No. of Devices)J20
(Sensors)
J21 (Comp Resource)
Performance Index
0.0128 0.0142 0.0221 0.0230
0.8098 0.7254 0.9374 0.9019
0.0609 0.0657 0.1265 0.1105
0.0097 0.0109 0.0173 0.0150
16.0000 16.0000
6.0000 12.0000
22.0000 28.0000
Average Maximum
ANFYS-FLC Control Performance Functions: Comparison ANFIS v/s LQG
CONTROL PARAMETER VALUES
ANFIS
LQG
ODI Control Performance Functions ANFYS-FLC Control and ODIResults: Base Shear
Northridge EQ
Northridge EQ
ANFYS-FLC Control and ODIResults: Bearing Deformation
Northridge EQ
ANFYS-FLC Control and ODIResults: Curvature at Columns
Northridge EQ
ANFYS-FLC Control and ODIResults: Mid Span Acceleration Remarks
A comparison of the ANFIS based FLC control and the Optimal Dynamic Inversion (ODI) based control on the Highway Bridge Benchmark problem indicates that almost all the performance parameters obtained using the ODI based control scheme is generally better than the ANFYS based FLC control across all earthquakes.
From a real time implementation point of view, ODI is simple to implement as it provides a closed form expression for the control input. Moreover, the ODI based approach is a stable algorithm and its convergence has also been proved.
First order filter used to account for difference between applied and commanded current
The Bouc-Wen parameters (α, γ, β, Co, Ko, and A) are obtained by minimizing the error between the measured and predicted value of the force.
Integral Back-stepping Method
Optimized values of the model parameters at 1Hz frequency
Integral Back-stepping MethodAli, Sk. Faruque and Ramaswamy, A. (2009) “Testing and Modeling of MR Damper and its Application to SDOF Systems using Integral Back-stepping Technique”, Journal of Dynamic Systems, Measurement and Control,ASME, March, Vol. 131 / 021009-1to11.
(1)
(2)
Replacing u(t) from (1) in (2) and writing the closed loop system dynamics (neglecting the external force term) one gets in state space form:
(3)
Equation (3) can be written in the following form:
(4)
(5)
Integral Back-stepping Method
Equation (4) is a second order strict feedback form of the system given by equation (3). To implement integral back –stepping define a variable idum so as to satisfy:
This results in simplifications of the form:
Treating ic to be the real current driver and by selecting the Lyaponouv candidate function as:
Choosing icdeswith kd =1
Integral Back-stepping Method
If simultaneously it will leadto an instability. So if all three are very small switch off
based on a small tolerance.
ic is a state variable and tracking of ides is desirable. Defining an error variable e and related error dynamics as:
ides,x is the derivative of ides with respect to state x
Selecting a second Lyapunov as
The system becomes asymptotically stable when
Integral Back-stepping Method
Model based control algorithms (two-stage optimal dynamic inversion and integrator back stepping) developed for MR damper based control are efficient and offer improvements in performance over FLC based control.
Integral Back-stepping Method
Integral Back-stepping Method Integral Back-stepping Method
Studies on hybrid (MR damper + base isolation) vibration control using Shake Table
MR damper
Voltage-2.5Amplitude: 10 mmFrequency: 0.25 Hz
•Experiments on hybrid base isolated building model using MR damper and sliding bearing have shown the efficacy of genetic algorithm based fuzzy logic control in mitigating the structural responses under near and far field excitations . FLC based algorithms account for structural nonlinearities effectively. •Acceleration in addition to velocity feedback results in improved control performance
Simulink Model
Simple base isolation-based control
FLC rule base
Ali, Sk. Faruque and Ramaswamy, A. (2009) "Hybrid Structural Control using Magneto-rheological Dampers for Base Isolated Structures", IOP Smart Materials and Structures,
doi 10.1088/0964-1726/18/5/055011
Hybrid base isolation based control
Both clipped optimal and optimal FLCs decrease the isolator displacement (J1) but at the cost of an increase in superstructure acceleration (J6). The dynamic inversion and the integrator back-stepping based controllers provide a tradeoff between the isolator displacement and superstructure acceleration responses, offering the engineer a suite of options for selecting a design.
•Basic mechanical properties of the composite material are at variance with the predictions based on the law of mixtures. •Significant enhancement in energy absorption capacity but improvement in ductility limited to the stage prior to the initiation of yielding in the longitudinal rebars. •Further, introduction of fibers in concrete results in a reduction in crack width and spacing
Effect of fibers on mechanical properties of plain, reinforced and prestressed concrete
(3)
(2)
(1)
Fiber
Matrix
Thomas, J., and Ramaswamy, A. (2006) “Width and Spacing of Flexural Cracks in Partially Prestressed T-Beams with Steel Fibers in Partial / Full Depth”, ACI Structural Journal, 103(4), 568-576.
Thomas, J., and Ramaswamy, A. (2006) “Load deflection performance of partially prestressed concrete T-beams with steel fibers in partial and full depth”, Structural Concrete Journal of FIB, 7(No. 2), 65-75.
Thomas, J., and Ramaswamy, A. (2006) “Shear Strength of Partially Prestressed Concrete T-Beams with Steel Fibers in Partial/Full Depth”, ACI Structural
Journal, 103(3), 427-435.
Effect of fibers in PSC beams- flexure and shear response
Flexure beamsUltimate moment,
Mu
shear span to depth ratio (a/d)(a/d)2(a/d)1
Deepbeams Shear beams
Arch action controlBeam action controls
After Kani (1967)Fiber addition shifts the failure mode from brittle to ductile failure and is found to be an effective substitute for stirrups in prestressed concrete sections
Thomas, J. and Ramaswamy, A. (2006) “Shear-flexure analysis of prestressed concrete T-beams containing steel fibers over partial or full depth” Structural Engineering International, Journal of the International Association of Bridge and Structural Engineers (IABSE), vol. 16(1), 66-73.
F65FOCWOCF65FFCWFCF65FOCWFCF65FFCWOC
CL
CL
F65FOCWOC
F65FFCWFC
F65FOCWFC
F65FFCWOC
FE modeling PSC beams – influence of bond slip between rebar and concrete ANSYS based FE model
including steel fiber effects and nonlinear phenomenon (bond-slip of longitudinal reinforcements, post-cracking tensile stiffness of the concrete, stress transfer across cracked concrete and load sustenance through the bridging of steel fibers at crack interface with progressive fiber pullout) shows good prediction of load-displacement response.
1
1
3
2
2
3
Hydrostatic axis1 = 2 = 3
Deviatoric axis
Fiber reinforced concrete
Plain concreteThomas, J. and Ramaswamy, A (2006) “Finite Element Analysis
of Shear Critical Prestressed SFRC Beams”, Computers and Concrete, Techno-Press, 3(1), 65-77.
110 mm
FRP ribbon of 15 mm width and 0.67 mm thick
10 mm
10 mm
2 mm
30 mm
FRP strand of 2 mm diameter
Sand coating applied to improve the bond
10 mm
(a) GFRP bar with FRP strand helically wound in opposite direction (G10St)
(b) GFRP bar with FRP ribbons helically wound in opposite direction (G10Ri)
(c) GFRP bar with sand coating (G10Sa)
Surface treatments made for GFRP rebars to improve the bond
Hybrid steel core- FRP shield bar
Stress strain curve of hybrid rebar & GFRP rebar
Non-metallic rebars in reinforced concrete beams-DST project
0
200
400
600
800
1000
1200
0 0.01 0.02 0.03 0.04 0.05
Strain
Str
ess
(MP
a)
Steel 6 mm dia
Steel 8&16 mm dia
GFRP Epoxy
GFRP Polyester
GFRP strip
220
150
25
5.5
Details of GFRP stirrup
Load-displacement response in steel and hybrid reinforced beams
•Hybrid rebars consisting of a GFRP sheathing and steel core used to overcome the problem of steel corrosion and also augment the stiffness of the FRP rebar showed promise.
Saikia, B., Thomas, J., Ramaswamy A. and Rao, K.S.N. (2005)-“Performance of Hybrid Rebars as Longitudinal Reinforcement in Normal Strength Concrete”, Materials and Structures: A RILEM
Journal, vol. 38 (No.284), pp. 857-864
P/2
d
250
420
520
20 Ld
4E
L2
bb
bdbslipb
)xx()xd( iu
ub
slipbci
s1
s2 s3
cc
ct
As1
As2 As3
xu
ds3 ds2
ds1 Fs1
Fs2
Fs3
Cc Tc
(a) (b) (c)
b
xct
D
dcc dct
sisisi AfF •GFRP rebar concrete interface behavior resulting in rebar slip/pullout controls the overall response and failure mode of the beams. A block type rotation failure was observed for GFRP reinforced beams, while flexural failure was observed in geometrically similar control beams reinforced with steel rebars. •The relatively low elastic modulus of GFRP rebars, of the same order as concrete, resulted in large crack widths and deflections.
0
100
200
300
400
500
0 20 40 60 80 100
Mid-span deflection (mm)
Lo
ad
(kN
)
FS1SOC_exptFG1SOC_expt FG1SOC_Eq. (15)FG1GOC_expt FG1GOC_Eq. (15)FG1SFPC_expt FG1SFPC_Eq. (15)FG1GFPC_expt FG1GFPC_Eq. (15)
0 10 0 10 0 10 0 10 0 10 20
0
100
200
300
0 2 4 6 8 10
Crack width (mm)
Lo
ad
(kN
)
FS1SOC_exptFG1SOC_expt FG1SOC_Eq. (13)FG1GOC_expt FG1GOC_Eq. (13)FG1SFPC_expt FG1SFPC_Eq. (13)FG1GFPC_expt FG1GFPC_Eq. (13)
0 1 0 1 0 1 0 1 0 1 2
3ctc
usi
usi
5.0FRP
FRP
Adxd
xDf
E
2.0w
barsofnumber
bdD2Act
3g
3
crc
3
max L
L8
L
a4
L
a3
IE48
PL
g
cr
I
I1
Non-Metallic Rebars in Reinforced Concrete Beams-DST project
Saikia, B., Kumar, P., Thomas, J., Rao, K.S.N., and Ramaswamy A. (2007) “Serviceability Performance in Flexure of Beams with GFRP Rebars”, Construction and Building materials, 21, 1709-1719
Details of creep test setup- cylinder specimen in loaded condition in frame placed in walk-in humidity and temperature control chamber
Studies on creep and shrinkage in normal and heavy density concrete (BRNS project)•Short term tests (various load levels at different ages of curing, relative humidity and temperature).•Prediction of creep and shrinkage test results, and long term forecast of creep and shrinkage levels.•Micro-scale studies (SEM, indenting) of concrete properties•Hygro-thermo-chemo mechanical modeling of creep and shrinkage process
Creep in normal density concrete at different ages of loading a) 45MPa concrete at 60% relative humidity b) 35MPa concrete at 50% relative humidity, c) 25MPa heavy density concrete at 70% relative humidity-long term prediction using B3 model together with short term test data.
c)
b)a)
The creep coefficient computed for normal concrete using the test data is 1.5 (for loading at 28 days) but the corresponding value for heavy density concrete is nearly 2.5.
Shrinkage in H25 Concrete – 70%RH
Shrinkage in M45 Concrete – 60%RH Shrinkage in M35 Concrete – 50%RH
Shrinkage in normal density concrete a) 45MPa concrete at 60% relative humidity b) 35MPa concrete at 50% relative humidity, c) 25MPa heavy density concrete at 70% relative humidity-long term prediction using B3 model together with short term test data
Shrinkage strains for normal concrete is about 0.0003 while for heavy density concrete it is nearly 0.0025
H25-1year – Needle like structure showing un-hydrated ettringite (higher magnification) M45-1Year – Flower like structure showing
hydrated mono-sulphate hydrate
M45-1YEAR –EDAX ANALYSIS Micro indenting M45 concrete
SEM and micro/nano-indenting to estimate creep
The micro-structural examination of the different concretes, indicates that heavy density concrete has a slower hydration process than seen in normal concrete.
Hemalatha, T., Ramaswamy, A., and Chandra Kishen J.M., (under Review, February, 2010), Phase Identification of Self Compacting Concrete Using SEM and XRD, Journal of Materials in Civil Engineering, MTENG-491.
Fly ash and silica fume addition results in gain in compressive strength of concrete but at a slower rate. The pore structure is denser in these mixes.
Different repair schemes using FRP wraps
FRP fabric used; application procedure on RC beams employed
Repair of beams and beam column joint using Self-compacting concrete with fiber cocktails
Repair of RC beams with GFRP/CFRP fabric wraps and HPFRC-CSIR Project
•In comparison to FRP wraps, cement based repair has been found to offer enhanced ductility in the restored section through the mobilization of the tensile reinforcement in the primary structure and the concrete in compression because of having the advantage of effective bonding with the primary concrete. Additionally inaccessible regions can be repaired through effectively modifying the concrete flow properties.
Ramaswamy, A, and Muttasim Adam Ahmedi (2008) “New materials in structural concrete repair”, Journal of Structural Engineering, SERC,
Chennai, India, v.35 (4), pp. 26-36, April-June
Studies on beam column joints with seismic detailing-possible decongestion of reinforcement in the joint using staggered stirrups and fibers (IGCAR project)•Tests on exterior beam-column joints having seismic detailing-lab scale tests. Effect of staggered ties with addition of fibers studied.•Prototype structure too large to test in lab(1mx1m section). → Size effect studies carried out on plain and fiber reinforced concrete and RC to obtain material properties for model validated on lab scale tests.
With 1% fiber content by volume of concrete, the fibers permitted ties to be spaced at 100mm (instead of 50mm) without loss of strength and stiffness. At 150mm spacing of ties (maximum permitted by IS13920), longitudinal steel in the joint (beam) yielded resulting in larger deformations.
Studies on beam-column joints-cyclic loads with repair
•Load deflection response of beam column Joint under cyclic loading-before and after repair. •Load is shared by rebars within the beam and within the repair material leading to a stiffer stronger joint.
Ramaswamy, A., Adam, M.A. and Ratna Kumar, J. (Under Review, November 2008) “Fiber reinforced self compacting concrete based repair of structural concrete elements”, Construction & Building Materials.
•Load Test of Un-disturbed arch for assessing elastic rebound. Two gradually loaded trucks placed back to back with axles on the crown were used for the test. This indicated full rebound. Some cracks seen on masonry. Therefore it was feasible to repair.
Jaiprasad, R., Srinivasamurthy, B.R., Ramaswamy, A., Jaigopal, S. (2006) “Rehabilitation on 140 Years Old Brick Masonry Arch Bridge Across
Vrishabhavathi Valley in Bangalore, Karnataka-Case Study" printed in Indian Roads Congress (IRC) Journal Volume 67 Part 1, 121-126
FE Analysis of bridge under 70R (IRC) loading- displacements and stresses in interior concrete liner, exterior concrete liner and RC deck and supporting elements were examined to ensure no cracking (minimal tensile stresses) is possible under design loads.
Based on load test and FE analysis a scheme of rehabilitation is identified under 70R-IRC loading. Removal of overburden soil replaced by concrete liner on intrados and extrados of arch and a framing system rising from arch and deck of RC assessed. The existing masonry arch encased in between the concrete liners. The soil is removed in stages and replaced by new system. Carriage way widened from 6m to 8m to include one side pathwayCost of new bridge Rupees 63 LakhsCost of repair to old bridge Rupees35 Lakhs
Thank you