Prof.ramaswamy July17 APSS2010

8/20/2019 Prof.ramaswamy July17 APSS2010

1/20

Structural Control and Condition Assessment

Ananth Ramaswamy

Professor, Indian Institute of ScienceBangalore, India

3rd Asia Pacific Summer School on Smart StructuresTechnologies, University of Tokyo, Japan15thJuly-04th August 2010.

Research Interests A. Material and Structural Behavior:

Steel fiber reinforced

prestressed concrete beamsand RC beam column joints.

Performance of non metallicrebars for RC.

Material characterization ofself compacting concrete(SCC) with admixtures (fly ash,silica fume) & related fracturestudies.

Creep and shrinkage in normaland heavy density concrete

Repair of structural concreteusing GFRP / CFRP / SCC withfibers - Concrete beam andcolumn repair againstmechanical & extreme thermalloads

Field application of repair

B. Vibration control and

condition assessment ofstructures Studies on thermal

distortion and vibrationcontrol in laminatecomposites having piezomaterial as layers.

Studies on vibrationcontrol of seismicallyexcited buildings, bridgesand the possibility ofadaptive vibration controlfor repair.

Thermal Distortion and VibrationControl in Laminate Composites havingPiezo Layers

Composite laminates used in space applications are often exposed to:

i) thermal gradients that cause distortions

ii) unacceptable levels of vibrations (jitter).

Use of piezo layers as patches (sensing andactuation) to control these deformations hasbeen explored.

Piezo Electric Material – ConstitutiveEquations:

.3,2,1,6,..2,1,

)(

)(

,,

,,

lk and q pwhere

effect Direct T P E e D

effect ConverseT E eQ

E

k l

T

kl p

T

kpk

E

pk

T

kpq

T E

pq p

σ, ε, Ek , Dk , Δ T represent the stress, strain, electricfield, electric displacement and raise in temperature,respectively.

Q, є, e, λ and P represent the elastic moduli,dielectric tensor, piezo electric coefficient, thermalstress coefficient and pyroelectric coefficient. The

superscripts indicate quantities held constant whilequantifying the variable .

Piezoelectric Shell Laminate andcurvilinear coordinate system.

Piezo Electric Material – ConstitutiveEquations:

Laminate having layers with different

orientation

Laminate with arbitrarily located Piezo Layers

Piezo electric sheet

Analogy between mechanical andelectrical quantities


2/20

Implicit Layering

Explicit Layering

Layering Procedures in FEM

0)....(0

dt doneWork E P E K t

Using Hamilton’s Principle

Where:

v

k

t

k p

t

plkl

t

k pkp

t

k p pq

t

q dvT P E T E E e E Q E H E P }2{2

1),(..

dvwwvvuu E K llllllv

)(2

1..

pv

wvu

v

wsvsuswbvbub

qdsdvqvPvPuP

dswT vT uT dvwf vf uf donework

2

1

''

][][ ,,,,,,

In a finite element framework :

*][][][

}{]][[}{}{*}{

][]][[][*][

}]{[*}{}*]{[}]{[}]{[

1

1

K M C

F K K F F F

K K K K K

K F d K d cd M

dd dd

d d dd

d d dd

ad dd dd

ssss

ssss

a

Adopting a constant gain negative velocity feedbackcontrol: )(][)( t Gt sca

*}{}*]{[}]]{[]][][[[}]{[ 1 F d K d K K GK C d M d cd dd sssa

Extra Damping

Optimization Problem:

0

)( dt RQy y J aT

a

T Minimize

*}{}*]{[}]]{[]][][[[}]{[ 1 F d K d K K GK C d M d cd dd 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 Bu B X A X

][][]'[][

][]0[][

11

dd dd dd C M K M

I A

1][

]0[][

dd M B

][][

]0[]ˆ[ 1

ad dd K M

B

Using the state-space formulation x={d, d’}

Where:

State matrix Disturbance matrix Control matrix

The measurement equation (output matrix): {y}=[Co]{X}

Using the feedback law: }]{[][][}]{[}{1 X S B R X G T ca

Where [S] satisfies the Riccatti equation:

0]][[][][]ˆ[]][ˆ][[]][[][][ 001 C QC S B R BS AS S A T T T

}]{[}]){][ˆ[]([ d c u B X G B A X

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


3/20

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 seismicallyexcited structures

Ground motion induced vibrations in building andbridge structures can result in both excessivestructural deformation that results in member /structural failure and occupant discomfort due to highfloor accelerations.

Conventional ductility based designs, accompanied byplastic hinge development and mechanismoccurrence methods may result in maintenancedifficulties.

Structural control methods offer a via media that canlead to resolving the above concerns.

Passive and Hybrid Vibration control ofBuildings

Parameters considered include-models for building(cantilever, plane frame, torsionally coupled building), loads (Seismic, Wind), control strategy, materialnonlinearity, limits on number of sensors andactuating devices, functional constraints insensor/actuator.

Multi-objective ‘Pareto optimization’

Supervisor model for adaptive control when materialnonlinearity included.

Feed forward

(open loop)

control

Feed‐back

(Closed loop)

control

• Choice of controldevices and

sensors•Idealization ofStructure (BuildingModel)

•Choice of controlalgorithm

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 passiveand active/semi-activecontrol) TMD +AMD or MR/ER

dampers


4/20

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 Building

Shear 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).


5/20

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 arealways left to experts.One can use evolutionary search methods to search for optimal parametersto a FLC.

[System]

Name='fuz_arb'

Type='mamdani'

Version=2.0

NumInputs=2

NumOutputs=1

NumRules=25

AndMethod='min'

OrMethod='max'

ImpMethod='min'

AggMethod='max'

DefuzzMethod='centroid'

[Input1]

Name='Velocity'

Range=[-1 1]

NumMFs=5

MF1='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=5

MF1='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=7

MF1='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) : 1

1 2, 1 (1) : 1

1 3, 1 (1) : 1

1 4, 2 (1) : 1

1 5, 3 (1) : 1

2 1, 1 (1) : 1

2 2, 1 (1) : 1

2 3, 1 (1) : 1

2 4, 2 (1) : 1

2 5, 3 (1) : 1

3 1, 1 (1) : 1

3 2, 3 (1) : 1

3 3, 4 (1) : 1

3 4, 5 (1) : 1

3 5, 5 (1) : 1

4 1, 7 (1) : 1

4 2, 7 (1) : 1

4 3, 7 (1) : 1

4 4, 6 (1) : 1

4 5, 5 (1) : 1

5 1, 7 (1) : 1

5 2, 7 (1) : 1

5 3, 7 (1) : 1

5 4, 6 (1) : 1

5 5, 5 (1) : 1

ACCELERATION

V

E

L

O

C

I

T

Y

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

V

E

L

O

C

I

T

Y

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


6/20

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 widthequal 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-Floor M=3.6x105kgK=650MN/m

C=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 widthequal 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 AMDOptimal HMD

Pareto Optimal Performance (J1- Inter-story drift) vs.

(J3-absolute acceleration) for 10 story shear building

model

A


7/20

Time History & PSD for inter-story drift for Kobe

EQ Excitation at Point “A”

Hybrid Control System for SeismicallyExcited Torsionally Coupled Building

8-story building, 15m and 24m, mass mi=3.456X10

5 kg,

mass moment of inertia Ii=2.37104X103 Kg-m2,

stiffness in x-direction k xi=3.404X105 kN/m, in y-

direction k yi=4.503X105 kN/m, torsional stiffness

k i=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 ofthe building (Fur et al. 1996)

Torsionally Coupled Model

HMD SystemTMD System

Peak Inter-story Drift (J1) Vsrotation (J

2

) and Acceleration (J3) (TMDSystem)

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

/ J

3

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 TorsionallyCoupled 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 TorsionallyCoupled 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.


8/20

Remarks

GA-FLC and PSO based control systemsare seen to be effective. However, theireffective implementation requires thatthe control scheme be placed on a chip,so as to reduce process times.

Adaptive trained supervisor based ANNsystems can detect changes in thesystem and alter the parameters of theFLC to offer improved control.

Base isolation is an effective means to isolating structures

from ground motions

But base isolation show severe displacement under nearsource excitation

One means to protect is to combine base isolation withdamping mechanism

Semi-active devices are effective in damping as theyprovide better control than active devices with lesserenergy input

We combine base isolation with semi-active MR damperto protect building against near source ground motions

Motivation

MR Damper: Bouc-Wen Model

0f c x z

1n n z 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 relation

Nonlinear input/output map is needed for prediction of voltage oncerequired 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

5

-1.5 -1 -0.5 0 0.5 1 1.52500

2000

1000

0

500

2000

-25 -20 -15 -10 -5 0 5 10 15 20 25-2500

-2000

-1000

0

1000

2000

2500

F o r c e ( N )

F o r c e ( N )

F o r c e ( 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 Membership Functions Choice of membership function

Parameters that define 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 arealways left to experts.One can use evolutionary search methods to search for optimal parametersto a FLC.


9/20

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.

Genetic

Algorithm


I/O Membership Functions

Choice of membership function

Parameters that define the 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 ofMFs and number of rules

GAFLC Systems: Rule basedesign

NL

NL

PL

PS

ZE NS

PL

PS

ZE

NS

NL

PLPSZE NS

Velocity

A c c e l e r a t i on

Consequent Line

CS

C A

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 foreach 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 width2. 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

0

0.5

1

-0.2

0

0.2

0.4

0.6

0.8

Velocity

Accleretion

C o n t r o l

-1

-0.5

0

0.5

1

-1

-0.50

0.51

-0.5

0

0.5

Velocity Accleretion

C o n t r o l

GAFLC Systems: Sample RuleBase Maps

Chichi Earthquake Elcentro Earthquake

One can see the adaptive nature of the rules


10/20

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Velocity

D e g r e e o f m e m b e r s h i p N NS Z P S P

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Accleretion

D e g r e e o f m e m b e r s h i p N NS Z PS P

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Control

D e g r e e o f m e m b e r s h i p

N N NS Z PS PO P

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Velocity


N NS Z PS P

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Control


N N NS Z PS PO P

-1 -0.5 0 0.5 1

0

0.2

0.4

0.6

0.8

1

Accleretion


N NS Z PS P

Chichi Earthquake

Elcentro Earthquake

GAFLC Systems: SampleMembership 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.


11/20

Nonlinear Force – Displacement relationship with

MR dampers used.

Problem Definition

Vibration control of a two-span,prestressed concrete box-girder bridge on91/5 over crossing located in OrangeCounty of southern California forms thebenchmark problem-Phase I (Agrawal et

al 2005, 2009)

Sensors and Actuators Location

Nine Actuators andsix accelerometers

are used

ANFIS-Why?

ANFIS changes the position of the MFs w.r.t the input inan optimal way

•No standard method exists for designing the Fuzzy Rulebase. It is based on the experience of the designer.•Fuzzy logic Membership Functions (MFs ) are fixed typeand it does not change with the change in the inputparameter. Thus, tuning of the MFs is not done tominimize the error.Consequently, FLC acting alone doesn’t provide an optimalcontrol.

How does ANFIS work ?

Adaptive Nodes

Fixed Nodes

NE = Negative

PO = Positive

N = Neural Network

ANFIS Optimal Position of MFs

Takagi & Sugeno TypeInference Scheme

3 bell shaped MFs for Acceleration and Velocity

Optimal Positions ofthe MFs aredetermined using ANFIS

Solution Technique: ANFIS FLC

A Hybrid Control Approach is undertaken using bothFLC and ANFIS to control the vibration of theHighway Bridge.

Two separate ANFIS model are trained and testedwith a set of near and far field earthquakeexcitations.

ANFIS is trained with velocity and acceleration dataas input from east and west abutment ends of thethe bridge and corresponding control as output fromLQG results to obtain the optimal set of weights.

Acceleration and Velocity data from the central bentcolumn are given as input to the FLC in addition.


12/20

Solution Technique: ANFIS FLC

8 hydraulic actuators placed longitudinallybetween the abutment and deck are drivenby ANFIS trained with longitudinal dataobtained from LQG model.

From the remaining eight transverseactuators, four (two on each side) are drivenby 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 evolutionaryvariable, and γ, β , n , A are parameters

controlling the linearity in the unloadingand the smoothness of the transitionfrom the pre–yield to the post-yieldregion

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 algorithmbased on the reduced order benchmark bridgemodel

I q

I qQ

a

d

0

0 R = 10-5I N×N and N=number of controllers

r

g X K t f ^

)(

)(^^

u D X C y Lu B X A mr r m

r mr

r

r X

K g is feedback gain matrix and Xr is the Kalmanestimate of the system. K g is selected tominimize the cost J1, based on the state

feedback law above. The Kalman filter optimalestimator 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 followingstable error dynamics is satisfied.

0))()(())()((2

)}()({))()((

0

t f t uPt f t uk

t f t uPt f t u

ek e

e

e

To obtain a unique solution, we minimize the costfunction formulated as follows:

Subject to the constraint:

Where:

The problem of controlsingularity may arise if xi, x˙i andzi go to zero simultaneously andhence li goes to zero. So with a

user defined tolerance, thevoltage is set to zero under theseconditions.

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.


13/20

Simulink: ODI Control

ANFYS-FLC Control Performance Functions: Peak Values

Performance

Index

N. Palm

SpringCh ich i El Ce ntro No rth ri dg e Tu rke y Ko be

J1

(Base Shear)0.8343 0.7878 0.8101 0.7862 0.8619 0.8020

J2(Base M oment)

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

SpringChi chi El Cent ro Nor th ri dg e Tur key 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

SpringChi chi El Cen tr o Nor thr id ge Tu rke y Kob e

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)1 6.00 00 16 .00 00 1 6.0 000 1 6.0 000 1 6. 00 00 1 6. 00 00

J20

(Sensors)6.0000 6.0000 6.0000 6.0000 6.0000 6.0000

J21

(Comp Resource)2 2.00 00 22 .00 00 2 2.0 000 2 2.0 000 2 2. 00 00 2 2. 00 00

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 M oment)

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


14/20

ODI Control Performance Functions ANFYS-FLC Control and ODI

Results: Base Shear

Northridge EQ

Northridge EQ

ANFYS-FLC Control and ODI

Results: Bearing Deformation

Northridge EQ


Results: Curvature at Columns

Northridge EQ


Results: Mid Span Acceleration Remarks

A comparison of the ANFIS based FLC control and theOptimal Dynamic Inversion (ODI) based control onthe Highway Bridge Benchmark problem indicatesthat almost all the performance parameters obtained

using the ODI based control scheme is generallybetter than the ANFYS based FLC control across allearthquakes.

From a real time implementation point of view, ODIis simple to implement as it provides a closed formexpression for the control input. Moreover, the ODIbased approach is a stable algorithm and itsconvergence has also been proved.


15/20

First order filter used to

account for difference

between applied and

commanded current

The Bouc-Wen parameters (α, γ,

β, Co, K o, 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. Faruqueand 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 –steppingdefine 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 icdes with k d =1


If simultaneousl y it will lead

to an instability. So if all three are very small switch off

based on a small tolerance.


16/20

ic is a state variable and tracking of i des 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


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

Studies on hybrid (MR damper + base isolation)

vibration control using Shake Table

MR damper

Voltage-2.5

Amplitude: 10 mm

Frequency: 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. Faruqueand 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


17/20

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 limitedto 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 PartiallyPrestressed

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 partiallyprestressed 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 PartiallyPrestressed 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

Deep

beams 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 aneffective 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.

F65FOCWO

CF65FFCWFCF65FOCWFCF65FFCWOC

C L

C L

F65FOCWOC

F65FFCWFC

F65FOCWFC

F65FFCWOC

FE modeling PSC beams – influence of bond slip between rebar and

concrete ANSYS based FE modelincluding 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 axis

1 = 2 = 3Deviatoric axis

Fiber reinforced

concrete

Plain concrete

Thomas, J. and Ramaswamy, A (2006) “Finite Element Analysis

of Shear Critical Prestressed SFRC Beams”, Computers and

Concrete, Techno-Press, 3(1), 65-77.

110mm

FRPribbon 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) GFRPbar with FRPstrand helicallywound in opposite direction (G10St)

(b) GFRPbar with FRP ribbonshelicallywoundin opposite direction (G10Ri)

(c) GFRPbar 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

S t r e s s ( M P

a )

Steel 6mmdia

Steel 8&16mm dia

GFRP Epoxy

GFRP Polyester GFRP strip

2 2 0

150 2 5

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


18/20

P/2

d

250

420

520

20

Ld

4E

L2

b b

bd bslip b

)xx()xd(

iu

u b

slip b

ci

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 Af F •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)

L o a d

( k N )

FS1SOC_expt

F G1 SO C_ ex pt F G1 SO C_ Eq . ( 15 )F G1 GO C_ ex pt F G1 GO C_ Eq . ( 15 )F G1 SF PC _e xp t F G1 SF PC _E q. ( 15 )F G1 GF P C_ ex p t F G1 G FP C_ E q. ( 15 )

0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 2 0

0

100

200

300

0 2 4 6 8 10

Crack width (mm)

L o a d

( k N )

FS1SOC_expt

F G1 SO C_ ex pt F G1 SO C_ Eq . (1 3)F G1 GO C_ ex pt F G1 GO C_ Eq . ( 13 )F G1 SF PC _e xp t F G 1S FP C_ Eq . ( 13 )F G1 GF PC _e xp t F G 1G FP C_ Eq . ( 13 )

0 1 0 1 0 1 0 1 0 1 2

3

ctc

usi

u

si

5.0

FRP

FRP

Adxd

xDf

E

2.0w

barsof number

bdD2Act

3

g3

cr c

3

maxL

L8

L

a4

L

a3

IE48

PL

g

cr

I

I1

Non-Metallic Rebars in Reinforc ed 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 humi dity 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 showinghydrated 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.


19/20

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 inthe 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 MuttasimAdam 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 ofties (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 RatnaKumar, J.

(Under Review, November 2008) “Fiberreinforced 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

VrishabhavathiValley 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.


20/20

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 removedin stages and replaced by new system. Carriage

way widened from 6m to 8m to include one side

pathway

Cost of new bridge Rupees 63 Lakhs

Cost of repair to old bridge Rupees35 Lakhs

Thank you

Prof.ramaswamy July17 APSS2010

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