marano presentation

Prof. Giuseppe Carlo MARANOTechnical University of BARI, Italy

parametric identification of nonlinear devices for seismic protection using soft computing techniques




Isolators

BASE ISOLATION



NTC/08 - EN 15129



( ) ( ) ( ), , ,mx t g x x t f t+ Θ =&& &



Experimental vs analytical responce force

( )

( )

exp

, , ,a

f t

f x x t ϑ&



( )( ) ( )( )

( )( )

exp

exp

, , ,end

start

end

start

t

e

t

t

t

abs f t f x x t dt

OF

abs f t dt

ϑϑ

−=

∫

∫

&

( )exp

( )

( )

f t

x t

x t&ϑ

Design vector

minimize



( )( )exp

end

start

t

t

abs f t dt∫

( ) ( )( )exp , , ,end

start

t

e

t

abs f t f x x t dtϑ−∫ &



( ) ( )( ) ( ) ( ) ( )21 sin fy t y t y t y t tµ ω− − + =&& &

To be identified



Mathematical model of the system

Simulated system response

Experimental set-up

Measured system response

Features from the simulated response

Features from the measured response

Evaluatecorrelation

New set of system parameters

Minimize the difference

Reliable model

Searching for a more reliable mathematical models of the investigated systems…



Non-classical algorithms: they deal with socially, phisically and/or

biologically inspired paradigms (Perry et al., 2006)

In this field, the most adopted is soft computing algorhitm

Nuove prospettive del monitoraggio strutturale Giuseppe Carlo Marano Politecnico di Bari

GA’s are based on Darwin’s theory of evolution

Evolutionary computing evolved in the 1960’s. GA’s were created by John Holland in the mid-70’s.

genetic algorhitms (GA)genetic algorhitms (GA)

Reproduction Competition

Selectionsurviving


GENITORE 1 GENITORE 2

PRIMA GENERAZIONE

GENITORE 1 GENITORE 2

TERZA GENERAZIONEGENITORE 1 GENITORE 2

SECONDA GENERAZIONE

Generazione dopo generazione, la popolazione evolve verso una

soluzione ottima.

Gli algoritmi geneticivengono utilizzati per risolvereuna varietà di problemi per cui inormali metodi di ottimizzazione risultano poco appropriati (discontinuità, non differenziabilità, forti non linearità etc.)

GA schemeGA scheme


ParticleParticle Swarm Optimization Swarm Optimization



Test Type Load (kN)

Test stroke (±mm)

Velocity(mm/s)

Cycle

1Constitutive law test

7No.50 20 92 (20%) 3

2 750 20 230 (50%) 33 750 20 460 (100%) 3

4 Damping efficiency test 750 17 460 (100%) 10



M is the effective mass C1 is the internal damping coefficient Cα is the damping coefficient sgn[·] is the signum functionα is the damping law exponentK1 is the elastic stiffnessp is the time-varying force

[ ] 1sgnMy C y y K y pα

α+ + =&& & &

[ ] ( )2

2 1 0sgnMy C y y K y K y K pα

α+ + + + =&& & &

[ ]1 1sgnMy C y C y y K y pα

α+ + + =&& & & &

M is the effective mass Cα is the damping coefficient sgn[·] is the signum functionα is the damping law exponentK1 is the elastic stiffnessp is the time-varying force

M is the effective massCα is the damping coefficient sgn[·] is the signum functionα is the damping law exponentK1 is the elastic stiffnessK2 and K0 are two constants

My C y pα+ =&& &

My C y pαα+ =&& &



AlgorithmAlgorithm Short descriptionShort descriptionDEA01 A DEA whose mutation operator is given by Eq.(1) and with binomial crossover as in Eq.(6)

DEA02 A DEA whose mutation operator is given by Eq. (2) and with binomial crossover as in Eq.(6)

DEA03 A DEA whose mutation operator is given by Eq.(3) and with binomial crossover as in Eq.(6)

DEA04 A DEA whose mutation operator is given by Eq.(4) and with binomial crossover as in Eq.(6)

DEA05 A DEA whose mutation operator is given by Eq. (5) and with binomial crossover as in Eq.(6)

DEA06A DEA with adaptive mutation – as in Eq.(8) – and a free-parameter crossover given by Eq.(10)

PSOA01A PSOA whose velocity model is Eq.(11), with inertia weight as in Eq.(13), social and cognitive factors as in Eq.(14)

PSOA02A PSOA in which the velocity updating rule (based on the use of the constriction factor) is given by Eq.(15)

PSOA03A PSOA based on the use of chaotic maps (so-called chaotic PSOA) for both inertia weight and acceleration factors

PSOA04 A PSOA with passive congregation in which the velocity updating rule is given by Eq.(19)

MGARA modified multi-species real-coded genetic algorithm with specialized operators for each subpopulation, see [17] and [18]

Non-classical Identification methods



Objective Function results obtained using a linear viscous

Test Mean Max Min Std

Test 1 0.324322 0.324322 0.324322 0

Test 2 0.363997 0.363997 0.363997 2.8E-16

Test 3 0.272685 0.272685 0.272685 1.68E-16

Test 4 0.297829 0.297829 0.297829 1.68E-16

Objective Function results obtained using a generalized viscous


Test 1 0.254494 0.254494 0.254494 4.26E-14

Test 2 0.332256 0.332257 0.332256 1.39E-07

Test 3 0.264244 0.26426 0.264243 2.99E-06

Test 4 0.28234 0.28234 0.28234 2.45E-09



Mechanical Model: Generalized viscous- linear elastic


Test 10.162356 0.163188 0.162077 0.000298

Test 2 0.203976 0.204116 0.203949 3.45E-05

Test 3 0.153384 0.153388 0.153384 7.23E-07

Test 40.127699 0.127699 0.127699 1.41E-12

Mechanical Model: Generalized viscous- quadratic elastic


Test 10.173636 0.254494 0.158448 0.022962

Test 2 0.208454 0.21712 0.203949 0.006284

Test 3 0.160706 0.26426 0.153025 0.026845

Test 40.12752 0.127699 0.126207 0.00049



Mechanical Model: Linear viscous

ParametersTest Type N.1 Test Type N.2 Test Type N.3 Test Type N.4

v=92mm/s v=230mm/s v=460mm/s v=460mm/s

M (mean) - [kg] 0 0 0 0

M (max) - [kg] 0 0 0 0

M (min) - [kg] 0 0 0 0

C (mean) - [kN/

(mm/s)]6.308518 9.955068 2.950677 3.599261

C (max) - [kN/

(mm/s)]6.308518234 9.955068455 2.95067697 3.599260974

C (min) - [kN/

(mm/s)]6.308518234 9.955068455 2.95067697 3.599260974

C (std) - [kN/(mm/s)] 3.32E-14 0 1.93E-15 3.15E-14



Mechanical Model: Fractional viscous

ParametersTest Type N.1 Test Type N.2 Test Type N.3 Test Type N.4

v=92mm/s v=230mm/s v=460mm/s v=460mm/s

M (mean) - [kg] 1.75E-14 1.45E-11 0 0

M (max) - [kg] 8.74059E-13 7.26404E-10 0 0

M (min) - [kg] 0 0 0 0

M (std) - [kg] 1.24E-13 1.03E-10 0 0

C (mean) - [kN/(mm/s) ^ α] 321.4664 101.8108 20.93332 60.02495

C (max) - [kN/(mm/s)] 321.4663828 102.5398101 22.44238445 60.02544199

C (min) - [kN/(mm/s)] 321.4663828 101.058709 20.75427774 60.01439848

C (std) - [kN/(mm/s)^ α ] 1.05E-10 0.254748 0.284589 0.001661

α (mean) 0.121515 0.456479 0.647184 0.472998

α (max) 0.121514934 0.458176548 0.648755563 0.473033897

α (min) 0.121514934 0.454813372 0.634798957 0.472996579

α (std) 6.82E-14 0.00058 0.002352 5.61E-06



(a)

(b)

(c) (d)



Maxwell C K OF

Test 1 7.3107 139.2401 0.2882

Test 2 4.0123 259.4377 0.1784

Test 3 3.3335 205.6275 0.2869

Generalized Maxwell C K OF

Test 1132.0147 267.8712 0.33

31 1.0006 0.1269

Test 2122.1587 358.5821 0.33

601.0060 0.1240

Test 3 119.2544 277.8710 0.33

331.0017 0.1535

Generalized Voight C K OF

Test 124.1856 0.7847 0.6932

2.0000

0.2300

Test 2 1.0213 1.1889 1.2407 2.0000 0.1816

Test 3 4.7018 52.2115 0.9249 0.4756 0.3079

Voight C K OF

Test 1 6.4963 12.6587 0.2877

Test 2 3.5944 15.5999 0.2049

Test 3 3.0240 12.8350 0.3074



50 mm 70 mm 104 mm



( ) ( )( )1

( ) 1 ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

BWf t k x t kz t

z t x t x t z t z t x t z tη η

α α

β γ−

= + −

= − −& & &&



Test k α β γ η OF

50 mm 2.0812 0.4174 0.0078 -0.0065 1.8350 0.0961

70 mm 2.0522 0.3216 0.0018 -0.0015 2.0297 0.0783

140 mm 3.8513 0.2241 0.0276 -0.0202 1.4126 0.0710

Test k α β γ η OF

50 mm2.579205 0.408575 0.14214 -0.11051 1.064357 0.09611

70 mm2.880737 0.361206 0.030589 -0.02775 1.765703 0.078308

140 mm3.926685 0.219169 0.041263 -0.02879 1.270448 0.07104

400 - 1220 KN vertical load



( ) ( )( )1

( ) 1 ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

BWf t k x t kz t

z t x t x t z t z t x t z tη η

α α

β −

= + −

= − −& & &&



Model K

BW 5 parametrs

b12.0577 0.4237 0.0018 -0.0016 2.3154

BW 4 parametrs b3

1.3588 0.0697 5.8117e-005

2.7033

BW 5 parametrs “forced “

b2

2.0577 0.4237 0.0018 -0.0018 2.3154

marano presentation

Education

mutation operator

binomial crossover

soft computing techniquesprof

bari gas

seismic protection

damping coefficient

damping law exponentk1

internal damping coefficient