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