The document discusses Prof. Giuseppe Carlo Marano's work on parametric identification of nonlinear devices used for seismic protection. It describes using soft computing techniques like genetic algorithms and particle swarm optimization to identify mathematical models of these devices. The techniques are used to minimize the difference between experimental force-displacement data and analytical models of the devices, in order to determine model parameters. Test data from constitutive law and damping efficiency tests on seismic isolation devices is analyzed using linear viscous, generalized viscous, and fractional viscous models. The soft computing methods help reliably identify mathematical models that best fit experimental system response data.
2. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
3. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
4. parametric identification of nonlinear devices for seismic protection using soft computing techniques
BASE ISOLATION
Isolators
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
5. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
6. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
7. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
8. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
9. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
10. parametric identification of nonlinear devices for seismic protection using soft computing techniques
NTC/08 - EN 15129
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
11. parametric identification of nonlinear devices for seismic protection using soft computing techniques
(
mx ( t ) + g x , x, t , Θ = f ( t )
&& & )
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
12. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
13. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Experimental vs analytical responce force
f exp ( t )
(
f a x, x, t ,ϑ
& )
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
14. parametric identification of nonlinear devices for seismic protection using soft computing techniques
f exp ( t ) Design vector
x (t )
ϑ
x (t )
& minimize
tend
∫ abs ( f ( t ) − f ( x, x, t,ϑ ) ) dt
exp
& e
OF ϑ = ( ) tstart
tend
∫ abs ( f ( t ) ) dt
tstart
exp
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
15. parametric identification of nonlinear devices for seismic protection using soft computing techniques
tend
∫ abs ( f ( t ) ) dt
tstart
exp
tend
∫ abs ( f ( t ) − f ( x, x, t,ϑ ) ) dt
tstart
exp
& e
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
16. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
17. parametric identification of nonlinear devices for seismic protection using soft computing techniques
To be identified
&& ( t ) − µ ( 1 − y 2 ( t ) ) y ( t ) + y ( t ) = sin ( ω f t )
y &
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
18. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Searching for a more reliable mathematical models of the investigated
systems…
Mathematical model of Experimental set-up
the system
Simulated system Measured system
response response
Features from the Features from the
simulated response measured response
Minimize the Evaluate
difference correlation
New set of system Reliable model
parameters
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
19. parametric identification of nonlinear devices for seismic protection using soft computing techniques
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
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
20. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
21.
22. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
23. genetic algorhitms (GA)
GA’s are based on Darwin’s theory of evolution
Reproduction Competition
surviving Selection
Evolutionary computing evolved in the 1960’s. GA’s were
created by John Holland in the mid-70’s.
Nuove prospettive del monitoraggio strutturale Giuseppe
Carlo Marano Politecnico di Bari
24. GA scheme
PRIMA GENERAZIONE
Generazione dopo generazione, la
popolazione evolve verso una
soluzione ottima.
GENITORE 1 GENITORE 2
SECONDA GENERAZIONE
Gli algoritmi genetici GENITORE 1 GENITORE 2
TERZA GENERAZIONE
vengono utilizzati per risolvere
una varietà di problemi per cui i
normali metodi di ottimizzazione
risultano poco appropriati (discontinuità, non
differenziabilità, forti non linearità etc.)
GENITORE 1 GENITORE 2
Nuove prospettive del monitoraggio strutturale Giuseppe
Carlo Marano Politecnico di Bari
25. Particle Swarm Optimization
Nuove prospettive del monitoraggio strutturale Giuseppe
Carlo Marano Politecnico di Bari
26. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
27. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Test
Load Velocity
Test Type stroke Cycle
(kN) (mm/s)
(±mm)
7No.
1 20 92 (20%) 3
50
Constitutive law test
2 750 20 230 (50%) 3
3 750 20 460 (100%) 3
4 Damping efficiency test 750 17 460 (100%) 10
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
28. parametric identification of nonlinear devices for seismic protection using soft computing techniques
M is the effective mass
Cα is the damping coefficient
My + Cα y = p
&& & sgn[·] is the signum function
α is the damping law
exponent
K1 is the elastic stiffness
My + Cα y α = p
&& & p is the time-varying force
M is the effective mass
Cα is the damping coefficient
My + Cα sgn [ y ] y + K1 y = p
α sgn[·] is the signum function
&& & & α is the damping law exponent
K1 is the elastic stiffness
K2 and K0 are two constants
My + Cα sgn [ y ] y + ( K 2 y 2 + K1 y + K 0 ) = p
α
&& & & M is the effective mass
C1 is the internal damping coefficient
Cα is the damping coefficient
My + C1 y + Cα sgn [ y ] y + K1 y = p
α sgn[·] is the signum function
&& & & & α is the damping law exponent
K1 is the elastic stiffness
p is the time-varying force
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
29. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Non-classical Identification methods
Algorithm Short description
DEA01 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)
A DEA with adaptive mutation – as in Eq.(8) – and a free-parameter crossover given by Eq.
DEA06
(10)
A PSOA whose velocity model is Eq.(11), with inertia weight as in Eq.(13), social and
PSOA01
cognitive factors as in Eq.(14)
A PSOA in which the velocity updating rule (based on the use of the constriction factor) is
PSOA02
given by Eq.(15)
A PSOA based on the use of chaotic maps (so-called chaotic PSOA) for both inertia weight
PSOA03
and acceleration factors
PSOA04 A PSOA with passive congregation in which the velocity updating rule is given by Eq.(19)
A modified multi-species real-coded genetic algorithm with specialized operators for each
MGAR
subpopulation, see [17] and [18]
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
30. parametric identification of nonlinear devices for seismic protection using soft computing techniques
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 Mean Max Min Std
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
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
31. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Mechanical Model: Generalized viscous- linear elastic
Test Mean Max Min Std
Test 1
0.162356 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 4
0.127699 0.127699 0.127699 1.41E-12
Mechanical Model: Generalized viscous- quadratic elastic
Test Mean Max Min Std
Test 1
0.173636 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 4
0.12752 0.127699 0.126207 0.00049
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
32. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Mechanical Model: Linear viscous
Test Type N.1 Test Type N.2 Test Type N.3 Test Type N.4
Parameters
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/
6.308518 9.955068 2.950677 3.599261
(mm/s)]
C (max) - [kN/
6.308518234 9.955068455 2.95067697 3.599260974
(mm/s)]
C (min) - [kN/
6.308518234 9.955068455 2.95067697 3.599260974
(mm/s)]
C (std) - [kN/(mm/s)] 3.32E-14 0 1.93E-15 3.15E-14
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
33. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Mechanical Model: Fractional viscous
Test Type N.1 Test Type N.2 Test Type N.3 Test Type N.4
Parameters
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
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
34. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
35. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
36. parametric identification of nonlinear devices for seismic protection using soft computing techniques
(a) (b)
(c) (d)
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
37. parametric identification of nonlinear devices for seismic protection using soft computing techniques
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
132.0147 267.8712 0.33 1.0006 0.1269
Test 1 31
122.1587 358.5821 0.33 1.0060 0.1240
Test 2 60
119.2544 277.8710 0.33 1.0017 0.1535
Test 3 33
Generalized Voight
C K OF
24.1856 0.7847 0.6932 2.0000 0.2300
Test 1
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
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
38. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
39. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
40. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
41. parametric identification of nonlinear devices for seismic protection using soft computing techniques
50 mm 70 mm 104 mm
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
42. parametric identification of nonlinear devices for seismic protection using soft computing techniques
f BW ( t ) = kα x (t ) + ( 1 − α ) kz (t )
& & & (
z ( t ) = x ( t ) − β x (t ) z (t )
η −1
z (t ) − γ x (t ) z (t )
&
η
)
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
43. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
44. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
45. parametric identification of nonlinear devices for seismic protection using soft computing techniques
400 - 1220 KN vertical load
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 mm
2.579205 0.408575 0.14214 -0.11051 1.064357 0.09611
70 mm
2.880737 0.361206 0.030589 -0.02775 1.765703 0.078308
140 mm
3.926685 0.219169 0.041263 -0.02879 1.270448 0.07104
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
46. parametric identification of nonlinear devices for seismic protection using soft computing techniques
f BW ( t ) = kα x (t ) + ( 1 − α ) kz (t )
z (t ) = x(t ) − β x(t ) z (t )
& & & ( η −1
z (t ) − x(t ) z (t )
&
η
)
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
47. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
48. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Model K
BW 5 b1 2.0577 0.4237 0.0018 -0.0016 2.3154
parametrs
BW 4 1.3588 0.0697 5.8117e- 2.7033
parametrs b3 005
BW 5 2.0577 0.4237 0.0018 -0.0018 2.3154
parametrs b2
“forced “
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy
49. parametric identification of nonlinear devices for seismic protection using soft computing techniques
Prof. Giuseppe Carlo MARANO
Technical University of BARI, Italy