optimization course rome 05_05_2015_fp

Optimization and

Performance-Based Design (PBD)

(service / ultimate / extreme scenarios)

Francesco PetriniStroNGER s.r.l.

Corso di OTTIMIZZAZIONEFacolta’ di Ingegneria Civile e Industriale

Sapienza Universita’ di Roma

Roma, 06 Maggio 2015

Object of the course

2Corso di Dottorato: Introduzio ne all'o7mi zzazione struttural e Roma, 06 Maggio 2015

Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.

• Introduction of basic and advanced ideas and

aspects of structural design without to much

stress on the analytical apparatus but with

some insigth on the computational

techniques.

Object of this lecture

• To show some of the issues related with the optimization of real complex structural systems

• Examples of practical design cases where the optimization has been conducted with respect to specific performance requirements

– Offshore wind turbines (general)

– High rise buildings

• Regarding the behaviour under wind (service)

• Regarding the robustness under fire (ultimate)



INTRODUCTION • Who I am

• Background concepts (optimization and PBD)

4FB

WHO I AM

5

Education, Milestones, Research topics (2005-2015)

Jul

20

09

Au

g2

00

9

Oct

20

04

Ma

r 2

00

6

No

v 2

00

8

PhD StudentPG

Assistant

Ma

r 2

00

9A

pr

20

09

MS

c d

eg

ree

(la

ure

a)

Jan

20

07

Jan

20

09

P.E

.

Ma

r 2

00

5

No

v 2

00

5

Jan

20

05

Jan

20

06

Jan

20

08

(Sapienza University of Rome)

Jun

20

05

Ph

D d

eg

ree

Jan

20

10

Post-Doc Research Associate

Ma

r 2

01

2

Associate Researcher

Ma

y2

01

1

Jan

20

11

Ap

r2

01

2

Jan

20

13

Jan

20

12

Jan

20

14

Jun

20

14

No

v2

01

3

Jan

20

15

(Sapienza

University

of Rome)

Research Spin-off

Company. Co-founder and Director

Structures of the Next Generation:

Energy harvesting and Resilience

No

v2

01

2

Ma

r 2

01

4


Aerodynamics and Aeroelasticity

PBD for Wind

PBD for Wind, Earthquake, Fire, Blast

Resilience

Energy Harvesting


Ma

r 2

01

5

People networking and design consulting (2005-2014)O

ct 2

00

4

Oct

20

07

Ma

r 2

00

6

No

v 2

00

8

PhD StudentPG

Assistant

Ma

r 2

00

9A

pr

20

09

Design Consultant

(a long-span suspension

bridge)

Design Consultant

(precast connections)

Design Consultant

(offshore wind turbines)

Jan

20

07

Jan

20

09

Ma

r 2

00

5

No

v 2

00

5

Jan

20

05

Jan

20

06

Jun

20

07

Jan

20

08


Jun

20

05

ASCE E&S ’10 (USA)

Jan

20

10

Post-Doc Research Associate

Ma

r 2

01

0

Au

g2

01

0

Spin-off

company

IABMAS’12

(Italy)

SS ChairMa

r 2

01

1


Ma

y2

01

1

ICASP’11

(Swizerland)

MS ChairJan

20

11

Ap

r2

01

2

Jan

20

13

PMC’12

(USA)

SS Chair

Jan

20

12

Jun

20

13

Jan

20

14ICOSSAR 2013

(USA)

MS Chair

Jun

20

14

No

v2

01

3IN-VENTO 2014

(Italy)

SS Chair Jan

20

15

(Sapienza

University

of Rome)

Spin-off company

Jun

20

12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25 30 35

P(Av > av*|Vm(zdeck))

Vm(zdeck) [m/s]

My approach to the research

1. Advanced

Numerical analysis

2. Probabilistic/heuristic

approach

3. Real structural

systems

Tools: FEA software (ANSYS, ABAQUS, ADINA, OpenSees, Strand7), programming languages

(MATLAB, Mathematica).

Trying to address the structural engineering problems under a multi-scale, systemic vision.



BACKGROUND CONCEPTS

9

• Optimization problem formulation

• Optimization issues in complex systems

• Performance-Based Design

Optimization problem formulation

10FP

Objective

Funcrion

Optimization problem formulation

Unconstrained Design space

Constrains

Constrained Design space

We must find the minimum of a certain Objective Function f, depending on certain Design

Variables (DV) x1,…,xn subjected to a number of constrains and by bounding the values of a certain

number of state variables (SV)

nn11

n LSV,,LSV,RXx,0)x(g,0)x(hbeing)x(fmin ≤≤⊆∈≤= K

Constrains Design variables State variablesObjective Functions

Von Mises

stresses



Esposizione formale del problema

.RXe

,0)(,0)(

,0)(,0)(asottoposto

)(min

n

21

11

⊆∈

≤=

≤=

x

xx

xx

x

mm gh

gh

f

MMProcedura

Operativa

Problema vincolato

Funzioni barriera

Problema non vincolato

Esplorazione locale

Optimization problem formulation in ANSYS©



Problema vincolato



Metodi che non eliminano i vincoli

Metodi che eliminano i vincoli

Funzioni penalità

Funzioni barriera

n

2

1

RXe

,0)(

,0)(

,0)(asottoposto

)(min

⊆∈

≤

≤

≤

x

x

x

x

x

mg

g

g

f

M

Spostamenti lungo il bordo

Metodi Quasi-Newton

Aggiornamento dell’Hessiano

Formula di Brayden-Fletcher-Gardoforb-Shanno

Programmazione sequenziale

Equazioni di Newton-Lagrange

Soluzione del subproblema quadratico

Aggiungere ed eliminare vincoli

Stima dei moltiplicatori di Lagrange

( )[ ] 0rPr)(r),T(-1 >+= xgxx f

Fornisce una configurazione ammissibile soltanto a

conclusione della procedura

( )[ ] 0rr)(r),T( >+= xgBxx f

Tutte le configurazioni intermedie sono ammissibili

Strategie attive

……

Problema non vincolato

Polinomio di Taylor

( )2

00jj0ii

n

1i

n

1j ji

0

2

0ii

1 i

00

ο)x)(xx(xxx

)(

2

1)x(x

x

)()()( xx

xxxx −+−−

∂∂

∂+−

∂

∂+= ∑∑∑

= ==

ffff

n

i

).x.......,x,x(21 n

ffff ∂∂∂∂∂∂=∇

∂∂∂∂∂

∂∂∂∂∂

=22

1

2

1

22

1

2

xxx

xxx

nn

n

ff

ff

L

MM

L

H

Gradiente

Hessiano0

xxx −=∂

)()(0

xx fff −=∂

Vettori

perturbazione1°ordine

2°ordine

( )xxx ∂+∂∇=∂ ο)( 0ff

( ) ( )2

0

T

0 ο2

1)( xxxHxxx ∂+∂∂+∂∇=∂ ff

Esplorazione locale

1°ordine gradiente in discesa

Efficiente lontano dal minimo

xx ∂∇=∂ )( 0ff

Si approssima la funzione

0)( 0 <∂∇=∂ xxff

Si ricerca

Per qualunque

perturbazione

kk1k g-xx =+Procedura iterativa k

-1

kk1k gHxx −=+

2°ordine metodo di Newton

Efficiente vicino al minimo

Procedura iterativa

Si approssima la funzione

kk

T

kkkk1k2

1xHxx ∂∂

+∂∇+=+ fff

Si impone la condizione di stazionarietà

0kkk

T

k =∂+∂∇ xHxf

Si assume che l’Hessiano sia invertibile

Ricerca lungo una direzione

Metodo del gradiente

Efficiente se H definito positivo

( ) kkk

T

kk

T

kk1k ggHgggxx −=+Procedura iterativa

Procedura iterativa generale kkk1k α sxx +=+

1) Scelta della direzione di discesa

2) Determinazione del passo

T

kk f∇== gsLa direzione è quella del gradiente

)α(minargαkk

α0

ksx +=

∞<≤

fIl passo rende minima la funzione

obiettivo nella direzione del gradiente

Si approssima la funzione kk

T

k

2

k

T

kk1kα

2

1α gHggg

+−=+ ff

Differenziando e uguagliando a zero 0αkk

T

kk

T

k=+− gHggg

Si ottiene l’espressione per il passo kk

T

kk

T

kkα gHggg=



First order Optimization method (FOOM)

One introduces the following unconstrained objective function:

( ) ( ) ( ) ( ) ( )

++++= ∑ ∑∑∑

= ===

2 31 m

1i

m

1i

iwih

m

1i

ig

n

1i

ix

0

wPhPgPqxPq,Qf

fx

( )λ2

ii

iig

αg

ggP

+=

λ is a large integer so that the function will be very large

when the constraint is violated and very small when it is not

Q is the dimensionless unconstrained objective function,

Px is the exterior penalty functions applied to the design variables,

Pg, Ph, and Pw are penalties applied to the constrained design and state variables,

f0 is the reference objective function value that is selected from the current group of design sets

q is the response surface parameter .

For each optimization iteration (j) a search direction vector d(j) is devised. The next iteration (j+1) is obtained from the

following equation:

( ) ( ) ( )jj

j1j s dxx +=+

( ) ( )( ) ( )1j

1jk

jj rq,Q −−+−∇= dxd

( )( ) ( )( )[ ] ( )( )( )( ) 2

1j

jT1jj

1j

q,Q

q,Qq,Qq,Qr

−

−

−

∇

∇∇−∇=

x

xxx

where sj is the line search parameter, and

The key to the solution of the global minimization of Q relies on the sequential generation of the search directions and on

internal adjustments of the response surface parameter (q).

ANSYS Inc. (2008). ANSYS Theory reference



Sub-problem approximation method (SAM)

• Generazione delle funzioni approssimate

(((( )))) (((( )))) errorexfxf ++++==== ∑∑∑∑∑∑∑∑∑∑∑∑==== ========

++++++++====n

1i

n

1j

jiij

n

1i

ii0xxbxaaf i coefficienti ai e bij si determinano con

una interpolazione ai minimi quadrati

(((( )))) (((( )))) (((( ))))(((( ))))2n

1j

jjj2d

ffΦE ∑∑∑∑====

−−−−==== i pesi Φ vengono associati ad ogni configurazione in base alla loro

ammissibilità o al valore della funzione obiettivo

• Minimizzazione del problema approssimato

Si introducono le funzioni barriera per eliminare i vincoli

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

++++++++==== ∑∑∑∑∑∑∑∑

========

m

1i

i

n

1i

ik0k gGxXpffp,xF

Si determina il minimo imponendo le condizioni di stazionarietà

• Convergenza

ττττ, ρρρρ sono, rispettivamente, le tolleranze delle

variabili di progetto e della funzione obiettivo

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

(((( )))) (((( )))) τff

τff

bj

1jj

≤≤≤≤−−−−

≤≤≤≤−−−− −−−− (((( )))) (((( ))))

(((( )))) (((( )))) n1,2,3,...iρxx

n1,2,3,...iρxx

i

b

i

j

i

i

1j

i

j

i

====≤≤≤≤−−−−

====≤≤≤≤−−−− −−−−



StrumentiNon determinano una

configurazione ottima; il loro utilizzo consente di evitare i minimi locali e

aumentare la conoscenza dello spazio

di progetto

Analisi singola

I valori delle variabili sono introdotte dall’utente

Generazione fattoriale

Si generano 2n configurazioni con n numero delle variabili di progetto; ogni configurazione assume i valori degli

estremi dell’intervallo

“Sweep”

Si generano da 2 a 10 configurazioni per ogni variabile di progetto; si

suddivide l’intervallo rispetto ad una configurazione di riferimento scelta

dall’utente

Generazione casuale

Si generano m configurazioni all’interno dello spazio di progetto

Domain exploration



Optimization issues in complex systems

18FP

In case of real, complex structural systems, main issues in applying the classical mathematical

formulation of the optimization problems are:

• An appropriate (exhaustive) objective function cannot be wrote in analytical terms as

continuous, differentiable mathematical function

• The constrains of the problems cannot be easily implemented

• The uncertainties and interactions affecting the problem cannot be easily implemented

• Both models and actions need to be modeled in detail, this circumstances increases both

computational effort and model uncertainties

Compromessi per l’implementazione del metodo formale:

• La funzione obiettivo si riduce al volume

• Si prendono I valori caratteristici dei carichi e delle resistenze, si modellano I carichi come

statici o quasi statici e non si considerano le interazioni

• Si fanno forti semplificazioni sui modelli con forti compromessi di dettaglio (si cercano di

cogliere solo I comportamenti principali)

Conseguenza

• L’implementazione del metodo formale consente solo di avere una ottimizzazione

preliminare.



Optimization issues in complex systems

Structural design and structural optimization

Topological

Optimization

Design

Optimization

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START

Refinement of the design

configuration with the goal of

obtaining satisfaction performances

in economical way

Shape optimization

(Options definition)

Parameters optimization

(Options refinement)

Feasible configuration selection

(Option selection)

Yes

Definition of the morphological

configuration of the object

Performance evaluations of the

candidate, feasible configurations



Classical structural optimization

Topological

Optimization

Design

Optimization

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START




in economical way

Shape optimization





(Option selection)

Yes







Final design optimization by PBD

Topological

Optimization

Design

Optimization

PBD

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START




in economical way

Shape optimization





(Option selection)

Yes







Performance-Based Design (PBD)

23FP

Fundamental requirements

(desired structural

attributes)

Non technical requirements,

expressing qualitatively a

fundamental goal

Set of criteria to assure that the

requirements are satisfied

Methods of evaluation to

measure the satisfaction of each

criterion

Commentary to explain the

rationale of each provision

- Safety

- Serviceability

- Integrity of subsystems

• mechanical

• electrical

• illumination

- Robustness

- Durability

e.g. building structures

remain stable under

extreme loads

e.g. design flexural strength

shall exceed the maximum

moment due to design loads

e.g. analysis and test

methods

Fundamental requirements

(desired structural

attributes)

Non technical requirements,

expressing qualitatively a

fundamental goal

Set of criteria to assure that the

requirements are satisfied

Methods of evaluation to

measure the satisfaction of each

criterion

Commentary to explain the

rationale of each provision

- Safety

- Serviceability

- Integrity of subsystems

• mechanical

• electrical

• illumination

- Robustness

- Durability

e.g. building structures

remain stable under

extreme loads

e.g. design flexural strength

shall exceed the maximum

moment due to design loads

e.g. analysis and test

methods

Il Performance-Based Engineering consiste in azioni quali la selezione dei siti, gli sviluppi concettuali,

predimensionamento e progetto, costruzione e manutenzione, dismissione e/o demolizione di una struttura, in modo

da assicurare che questa sia in grado di fornire prestazioni con un certo grado di affidabilità ed in maniera economica,

durante tutto il suo ciclo di vita.

Performance-Based Engineering (PBE)

Performance - Based Codes organization

Rosowski, D.V. and Ellingwood, B.R., (2002). “Performance-Based Engineering of wood frame housing: Fragility

Analysis methodology”, Journal of Structural Engineering, 128(1), 32-38.



Probabilistic approach to PBE

)θq( PDFs uncertain parameters

dRθ∈ Uncertain parameters vector

Mathematical models: θ( )θh

Probability Integral

θ)dθ)q(θh()]θE[h(J ∫==Expected value

( )θh

( )

θ)dθ)q(θ(Iθd)θq(P(F)Jd

R

F

θg

∫∫ ===≤0

Failure

Probability

= Stochastic = Deterministic

Failure

Failure

threshold

Input Output

(response r)

)q(θ1

1θ)q(θ2

2θ

P(M1)

P(M2)

P(Mk)

)q(r1

1r

b =

)q(r2

2r

nθ

),θq(θ mn

mθ

SYSTEM

Input Output

(response r)

)q(θ1

1θ)q(θ2

2θ

P(M1)

P(M2)

P(Mk)

)q(r1

1r

b =

)q(r2

2r

)q(r2

2r

nθ

),θq(θ mn

mθ

nθ

),θq(θ mn

mθ

SYSTEM

( ) ( )( )( )

∈

∉==

θg if θ

θg if θθIθh F

1

0

Failure domain( )θg

1)(1

=∑=

k

i

iMP

Der Kiureghian, A., (2008). “Analysis of structural reliability under parameter uncertainties”, Probabilistic Engineering

Mechanics, 23, 351-358.



Fragility Curves and Intensity Measure (IM)

It is usual that inside the vector there is some parameter describing the Intensity Measure (IM) of the

stochastic loads acting on the structure (or system);

θ

∫∞

⋅>=0

1 dIM)IMY(P)LS( iiλ

It is desirable to express the LS by means of scalar threshold values (ri*) for opportune response

parameters (ri) and to describe the structural state by using of scalar demand-to-capacity ratios (e.g. for

the limit state LSi it is Yi= ri / ri* ).

Under these assumptions, the mean rate of failure for structure exposed to hazard can be expressed as

Where P(Yi>1|IM) is the conditional probability of failure given IM, which is know as the fragility

function.

The performance can be identified with an acceptable value of the occurrence l(LS) of exceeding a

certain Limit State (LS).



Performance-Based Earthquake Engineering (PBEE)

2007 2008



State of the art

dIMIMEDPEDPPLS ∫+∞

⋅>=0

)*()(λ)( IMEDPPfunctionfragility =

EDP

IM

Aug

usti

,G

.,C

iam

pol

i,M

.,(2

008)

,“P

erfo

rmance

-Bas

edD

esig

nin

risk

asse

ssm

ent

and

reduct

ion”,

Pro

bab

ilis

tic

Engin

eeri

ng

Mec

han

ics,

23

,4

96-5

08

Jala

yer,

F.,F

ranc

hin,

P.an

dP

into

,P.E

.(20

07).

“A

scala

rdam

age

mea

sure

for

seis

mic

reli

abil

ity

analy

sis

of

RC

fram

es”,

Ear

thq

uake

Eng

ng.

and

Str

uct.

Dyn.,

36:

2059-2

079.



λ(DV) = ∫∫∫ P(DV|DM)·P(DM|EDP)·P(EDP|IM)·g(IM)·dDM·dEDP·dIM

P(x|y) conditional probability of x with respect to y

g(IM*) occurrence IM*

IM Environmental action magnitude (Intensity Measure)

EDP Engineering Demand Parameter describing the response

DM Damage Measure (components condition in terms of functionality requirements)

DV Decision Variable, it is representative of the structural performance

1. Hazard analysis g(IM)

2. Structural analysis P(EDP|IM)

3. Damage analysis P(DM|EDP)

4. Loss analysis P(DV|DM)

Risk

analysis

PEER approach for the PBEE (I)

Identifying the performance with an acceptable value of the occurrence l(DV) of exceeding a threshold

value DV.



O, D

g(IM|O,D)

g(IM)

p(EDP|IM)

P(EDP)

p(DM|EDP)

P(DM)

p(DV|DM)

P(DV)

Hazard analysis Struc’l analysis Damage analysis Loss analysis

IM: intensity

measure

EDP: engineering

demand param.DM: damage

measure

DV: decision

variable

Select

O, D

O: location

D: design

Facility

info

Decision-

making

λ(DV) = ∫∫∫ P(DV|DM)·P(DM|EDP)·P(EDP|IM)·g(IM)·dDM·dEDP·dIM

PEER approach for the PBEE (II)

Mitrani-Reiser, J. (2007). An ounce of prevention: probabilistic loss estimation for performance - based earthquake

engineering, Report EERL 2007-01, Pasadena, California, United States. Available on line at

http://peer.berkeley.edu/publications/peer_reports.html




Topological

Optimization

Design

Optimization

PBD

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START


(Option selection)

Yes



By focusing on a specific performance

requirement

Investigation on what is the best

configuration

Volume, and weight are checked but not

optimized

Probabilistic Deterministic



OPTIMIZATION OF THE SUPPORT STRUCTURE

OF OFFSHORE WIND TURBINES• System design approach for complex structural systems optimization

• Substructure typology selection

• Parametric optimization

32FB

Motivations

1. Offshore wind farms are relatively new structural facilities located in challenging

environment, the preliminary design of the structural elements is usually very

conservative. A refinement is needed.

2. An offshore wind farm is formed by a number of wind turbines (50-200 elements)

and, consequently, a small individual reduction of structural material amount can

lead to significant saving of money if regarding the whole farm.

3. A new support structure is proposed here, and the correct sizing of its structural

parts is crucial in this phase.



SYSTEM DESIGN APPROACH FOR

COMPLEX STRUCTURAL SYSTEMS

OPTIMIZATION

34

• Structural system

• Loads

• Performance-Based Design

• Substructure typology selection

• Parametric optimization

o Jacket

o Strutted innovative support

A “Complex System”

x,x’

z’

y’

Waves

Current

P

(t)v P

(t)w P

(t)u P

Turbulent

windP

Mean

wind

Vm(zP)

z

yH

h

vw(z’)

Vcur(z’)

d

Terrain



NonLinearities

Uncertainty

Interactions

A “Complex System”



A System Engineering Approach

Since the structural behavior of offshore wind turbines is influenced by nonlinearities, uncertainties

or interactions, they can be defined as complex structural system

“a set of interrelated components which interact one with another in

an organized fashion toward a common purpose” (NASA, 1995)

Structure Structural system

“a device to channeling loads”

Decomposition

Structure

Actions

Performances

Structural

System

A fundamental task concerns the Structural System and Structural Performance decomposition



Structural system

38FP

Structural decomposition

Macro - LevelDetail - Level

Structure

decomposition

Main

structure

(carrying loads)

Secondary

structure

Auxiliary

structure

Rotor-nacelle

assembly

Support structure

Energy

production

Energy transfer

Operation

Maintenance

Emergency

Substructure

Tower

Rotor

Nacelle

Blades

Foundations

Meso - Level

Junctions

Junctions

Micro - Level



Structural decomposition (II)

platform

tower

support

structure

rotor-nacelle

foundation

sea floor

water mean

level

sub-

structure

Meso - Level

Main

structure

(carrying loads)

Substructure

Tower

Rotor

Nacelle

Blades

Foundations

Rotor-nacelle

assembly

Support structure



Loads

41FP

( ) ( ) ( ) ( )( )nfexpnSnSnS jkuuuuuu kkjjkj−⋅=

( )( ) 2

t0

0

u

2

u u1.75)log(zarctan1.16(n)dnSσ ⋅+⋅−== ∫∞

5.0

0

uu2

x

u200

300(x)dxRu

1L

⋅== ∫

∞z

x

z

The mean velocity magnitude varies with the

height.

Mean c

ontr

ibution

Sto

chastic c

ontr

ibution ( )

( )[ ]5/3ju

ju2V

uu/z10,302fL1ω/2π

/zfL6,686σωS

jj +=

( )j

j

zV2π

ωzf = ( )

( )( ) ( )( )kj

2

kj

2

z

jkzVzV2π

zzCωωf

+

−=

Autospectrum

where:

α

=

hub

hubz

zUzU )(

0.14=αFor normal wind condition

( )( )

−−−

−

−=

2

5.0exp4

5

4

2

4

5exp

2

P

P

f

ff

Pf

ff

gfS

σγ

π

α

where f=2π/T is the frequency, fP=2π/TP is the peak

frequency, α is the equilibrium coefficient, g is gravity

acceleration, σ and γ parameters dependent from HS e

TP

−=

−

R

yearHTST

FHSR

11

1

1max,,,

Extreme events

analysis (Return

period TR).

71

,)(

+⋅=

d

zdUzU refc

x

z

d

water mean level

Wind Current and waves

JONSWAP spectrum

Design environment representation

Cross-

spectrum



Environment action model: Waves and Current

( ) ( ) ( ) ( )( ) ( ) ( ) dztztztztzDctzD

ctzd nnnndni

+++= ,,,,

2

1,

4,

2

VvVvvF ρπρ

&

Inertia term Drag term

Morison equation for slender members (wave+current) since D/L<0.2

d

|z|

z

x

d+z

dF(z,t)dz

A A Sect. A-A

D

tw

( ) ( )[ ]( )

( )

( ) ( )[ ]( )

( )tkxkh

zhkHtzxw

tkxkh

zhkHtzxu

ωω

ωω

−+

=

−+

=

sinsinh

sinh

2,,

cossinh

cosh

2,,

( ) ( )[ ]( )

( )

( ) ( )[ ]( )

( )tkxkh

zhkHtzxw

tkxkh

zhkHtzxu

ωω

ωω

−+

−=

−+

=

cossinh

sinh

2,,

sinsinh

cosh

2,,

2

2

&

&

Linear wave theory (Airy)H



Wind force on moving member

( )

( ) RctUCtF

RctUCtF

arelariaDD

arelariaLL

)(2

1),(

)(2

1),(

2

2

ραα

ραα

=

=

2

2

1UACF airaeroD ρ=

Wind force on the tower

φφ cossin LDx FFF +=

ac

R

Picture from:

Hau Erich, Wind Turbines: Fundamentals, technologies, Application,

Economics, 2nd edition. Springer-Verlag Berlin Heidelberg 2006.

xF

αc

Vortex Shedding displacements (across wind)

( )[ ]ct

across

SSD

r

⋅⋅⋅+=

2

max 243.01

29.1

π

2

4

D

mSc

⋅

⋅⋅=

ρ

υπ

Wind actions



Physics (I): Mean wind rotational sampling

( ) ( ) ( )12 ddd zFzFF iii S

X

S

X

S

X −=∆

z1

Ω

z2

Ω

Time t2Time t1

Vm(z1)

Vm(z2)

Tributary

area

S

Ω

dFXS

Angular

rotational

velocity

hub

( ) ( ) ( )tFFtF ii

hub

i SX

SX

SX ⋅⋅∆+= Ωcosd

2

1d

Additional peak in the wind force spectra

1.E-15

1.E-11

1.E-07

1.E-03

1.E+01

1.E+05

0.00001 0.001 0.1 10

Frequency [Hz]

Forc

e S

pec

tra

SF

XF

X

1Ω



Processo stocastico

m-dimensionale (mD)

n-variato (nV)

Il processo dipende da m parametri

deterministici

Il processo è costituito da un vettore di n

componenti (processi stocastici

monovariati) tra i quali è possibile definire

densità di probabilità congiunte

Stazionarietà: di ordine j, se le statistiche

sugli insiemi fino all’ordine j-esimo sono

costanti nel tempo

Ergodicittà: se i momenti stocastici del

processo coincidono con quelli della singola

realizzazione

Gaussianità: si i momenti stocastici di ordine

superiore al secondo sono nulli

1D – 1V

[ ] ∫ ∫ ∫+∞

∞−

+∞

∞−

+∞

∞−

=ssXss

dxdxdxxpxxxXXXEs

...)(.......... 212121

ρβαρβα

Momento stocastico di ordine j

ρβα +++= ...j

Wind turbulent component characteristics (I)



1D – 2V

=

),t(tRS

),t(tR),t(tR

),t(tR),t(tR),t(tR

),t(tR),t(tR),t(tR),t(tR

),t(tR

YY

XYXX

YYYXYY

XYXXXYXX

X)(

15

1555

515111

51511111

51

2

ijijijtttt >−= con τ

i(τR)(τR),t(tR),t(tR XXXjiX ogniper )1551 ===

Se il processo è stazionario

⋅+

=⋅= ∫

+∞

∞

−

0)(Im

)(Im0

)()(Re

)(Re)( )

2

1)(

-ω

ω

ωω

ωω

πω ωτ

YX

XY

YYYX

XYXXi

XYXYS

Si

SS

SSdτe(τRS

Matrice densità spettrale di potenza

Wind turbulent component characteristics (II)



Physics (II): Turbulent wind rotational sampling

Variation of the turbulent force spectra with the blade position during its rotational

motion

Halfpenny A. (1988). Dynamic Analysis of Both On and Offshore Wind Turbines in the Frequency Domain. Ph.D. thesis.

University College London..

Connell J.R. (1988). “A PRIMER OF TURBULENCE AT THE WIND TURBINE ROTOR”, Solar Energy, 41 (3), 281-293

The wind forces acing on the Beam Element (BE) implies two different contributions:

i) the fluctuating component due to the variation of mean wind experimented by the BE at different height

during its rotational motion, and

ii) the so called “rotational sampled turbulent wind”, that is the stochastic contribution due to the incoming

wind turbulence experimented by the rotating BE



R

ΩΩΩΩ

Vm(r)r

Vm(zhub)

u(r,t)

XY

Z

Aerodynamic actions by the BEM theory

Wind velocities and reference systems

- Evaluate the relative angle of attack and the relative speed of the wind with respect to specific blade portions (BEs) at different locations

Ω·r·(1+a’)

α

Y

X

DL

β

φφφφ

VmR(r)=

Vm(r)·(1-a)W

Rotor

plane

u(r,t)

v(r,t)

α’

FX= ½*ρ*Vm2 (cL·cosϕ+ cD·sinϕ)

aerodynamic force

reference system axis

wind velocity



ENVIRONMENT

Structure

Non

environmental

solicitations

STRUCTURE

Structural (non-environmental)

system

Site-specific environment

Wind site

basic

parameters

Other

environmental

agents

Waves site

basic

parameters

Wind, wave and current actions

Aerodynamic and Aeroelastic

phenomena

Hydrodynamic phenomena

1. Aleatoric

2. Epistemic

3. Model

Types of uncertainties

1. Aleatoric

2. Epistemic

3. Model

1. Aleatoric

2. Epistemic

3. Model

Propagation Propagation

Interaction

parametersStructural parametersIntensity

Measure

( )IM ( )IP ( )SP

EXCHANGE ZONE

Interaction phenomena in the environmentWind-wave-current interaction

Aeolian-hydrodynamic interactions

)10(01.0 1 mzVVcurr hourwind =⋅=

Wind speed- wave

height correlation

Wind generated

currents

)164.00291.0221.0(2

110

2

10 +⋅−⋅= VVH s

Correlation data by Zaaijer, 2006, taking into account the

Italy Waves Atlas.



Modeling strategy

51FP

Structural

system

modeling

Structure

Actions

Interactions

Modeling

levels

Systemic

Macro

Meso

Micro

Model level

Scale Detail level Type of Finite Elements

Systemic level

wind farmapproximate shape of the structural

componentsBEAM elements

Macro level

single turbine

approximate shape of the structural

components, correct geometrical

ratios between the components

BEAM elements

Meso level

single turbinedetailed shape of the structural

componentsSHELL, BRICK elements

micro level

individual componentsdetailed shape of the connecting

partsSHELL, BRICK elements

Differentiation of the modeling levels

Bontempi F., Li H., Petrini F., Manenti S., (2008). Numerical modeling for the analysis and design of offshore wind turbines, Proceedings of

ASEM'08, Jeju, Korea, 26-28 May 2008



1°1°

Macro

Global response

Meso Micro

Levels of modeling and results detail level

Jacket - Tower

connection

Detailed global response and medium-detailed local response

Detailed local response and analysis of connections



Substructure typology selection

54FP


Topological

Optimization

Design

Optimization

PBD

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START

Shape optimization





(Option selection)

Yes





Classical and innovative support structure

Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore wind turbines.

Report for MTC OTC Project

Water depth (m) Foundation type

0-10 Gravity based

0-30 Mono-pile

>20 Tripod/Jacket

>50 FloatingBontempi, F. (2010). Advanced topics

for offshore wind turbines. Earth&Space

2010 Conference

Strutted Quadruped

Others: Gravity-

based, Tension

leg



Monopile [m] Tripod [m] Jacket [m]

h a.s.l.=100

d=35

l found=40

D =5

tw=0,05

D found=6

h a.s.l. =100

d =35

l found =40

D =5

tw =0,05

D tripod =2,5

tw tripod =0,05

D found =2,5

h a.s.l. =100

d =35

l found =40

D =5

tw =0,05

Comparison of support structure typologies (Macro-Level models)

z

y x

Wind

Fluid-dynamic

Geotechnical

Foundation

Immersed

Emergent

d

l found

h a.s.l.

z

y x

z

y x

Wind

Fluid-dynamic

Geotechnical

Foundation

Immersed

Emergent

d

l found

h a.s.l.

D = tower diameter

D found =foundation piles diameters

tw= tower tubular thickness

h a.s.l.=100m

d=35m



Modal analysis

1° 3°5°1° 3°5°

3° 5°1° 3° 5°1°

0

0,5

1

1,5

2

2,5

1 3 5

Modes

Fre

q. [H

z] monopile tripod jacket

3P

1P

Stiff-Stiff

Soft-Stiff

Soft-Soft



Static extreme analysis

Wind on the

towerWind on the rotor-

nacelle assemblyCurrent and

wave

Design

Situation

D.L.C.

(GL, 2005)

Wind

Condition

(steady)

Marine

Condition

(regular)

Type of

Analysis

Load Factors γF

Environ. Grav. Inert.

Parked

(standstill or

idling)

6.1b Uhub=Ue100 H=Hred100

Ultimate

strength1.35 1.1 1.25

6.1c Uhub=Ured100 H=Hmax100

Ultimate

strength1.35 1.1 1.25

6.3b Uhub=Ue1 H=Hred100

Ultimate

strength1.35 1.1 1.25

Vento su torre-Monopila

0

20

40

60

80

100

120

0 2000 4000 6000 8000

Azione [N/m]

qu

ota

s.l

.m.

[m]

Comb 6.1b Comb 6.1cLoad Case 6.1b

Load Case 6.1c

Heig

ht

ab

ov

e m

ea

n s

ea

lev

el [m

]

Wind induced drag per unit length [N/m]

Vento su torre-Monopila

0

20

40

60

80

100

120

0 2000 4000 6000 8000

Azione [N/m]

qu

ota

s.l

.m.

[m]

Comb 6.1b Comb 6.1cLoad Case 6.1b

Load Case 6.1c

Heig

ht

ab

ov

e m

ea

n s

ea

lev

el [m

]

Wind induced drag per unit length [N/m]

Drag e Inerzia (corrente+onde)-

Monopila

0

5

10

15

20

25

30

0 20000 40000 60000 80000

Azione [N/m]

qu

ota

su

l fo

nd

ale

[m

]

Comb 6.1b Comb 6.1cLoad Case 6.1c

Heig

ht

ab

ov

e b

ott

om

[m

]

Wave-current induced force per unit length [N/m]

Drag e Inerzia (corrente+onde)-

Monopila

0

5

10

15

20

25

30

0 20000 40000 60000 80000

Azione [N/m]

qu

ota

su

l fo

nd

ale

[m

]

Comb 6.1b Comb 6.1cLoad Case 6.1c

Heig

ht

ab

ov

e b

ott

om

[m

]

Wave-current induced force per unit length [N/m]



Static extreme analysis – Performances comparison

Reazione totale taglio a terra [ton]

0

100

200

300

400

500

600

700

Monopila Tripode Jacket

6.1b 6.1c 6.3b

Resultant shear stress at the bottom [N]104

104 Momento ribaltante [ton*m]

0

5000

10000

15000

20000

25000

30000

35000

40000


6.1b 6.1c 6.3bSpostamento navicella [m]

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5


6.1b 6.1c 6.3b

Resultant overturning moment at the bottom [N*m]

Horizontal hub displacement [m]

104

Monopile Tripod Jacket

Reazione totale taglio a terra [ton]

0

100

200

300

400

500

600

700


6.1b 6.1c 6.3b

Resultant shear stress at the bottom [N]104

104 Momento ribaltante [ton*m]

0

5000

10000

15000

20000

25000

30000

35000

40000


6.1b 6.1c 6.3bSpostamento navicella [m]

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5


6.1b 6.1c 6.3b

Resultant overturning moment at the bottom [N*m]

Horizontal hub displacement [m]

104

Monopile Tripod Jacket

Combination 6.1b (GL 2005) Monopile Tripod Jacket

Action

Wind on rotor [ton] 166,3

166,3 166,3

Wind on tower [ton] 74

74 42,8

Wave and current [ton] 337,2

337,2 350

Overturning moment [ton*m] 35045,6

35045,6 33708,7

Reactions at mud

line

Shear reaction at mud line [ton] 577,5

577,5 559,1

Vertical reaction at mud line (no piles) [ton]

1071,41035,63

(max/pile=1501,8)

1376,8

(max/pile =992,9)

Structural checks

Maximum stress in the tower [N/mm2]

286230 151

Nacelle displacement [m] 4,66

3,72 1,82



Comparison between classical support structures

Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore wind turbines.

Report for MTC OTC Project

Water depth (m) Foundation type

0-10 Gravity based

0-30 Mono-pile

>20 Tripod/Jacket

>50 Floating

peso monotubo 205.78 t

peso tripode 635.58 t

peso jacket 473.38 t

PESI SUPPORTO "E"

1057.8 t

735.58 t



Parametric optimization

62FP


Topological

Optimization

Design

Optimization

PBD

No

Structural check

Best design

config?

Refine

STOP

Pre sizing

Performance

requirements

Advanced

Model

Basic

Models

Conceptual

design

START




in economical way

Shape optimization





(Option selection)

Yes



Jacket support

64

GEOMETRIADimensioni in elevazione

Dimensioni in pianta

• Altezza totale: 180 m

• Altezza fuori terra: 140 m

• Altezza sopra il pelo libero: 105 m



MODELLAZIONE

2835 nodi

2910 elementi linearidi 11 tipologie

44 elementi piani



Vincoli

Traslazione impedita

alla base dei pali

nelle tre direzioni

Traslazione

impedita nel

piano

orizzontale

a 10 m al di

sotto del fondale

marino

Azioni esterne

Totale carichi

orizzontali:

725,25 [t]

Peso proprio

della struttura:

1.165 [t] (navicella

inclusa)

Totale carichi

verticali:

1.515 [t]

Configurazioni

di carico

I CONFIGURAZIONE

II CONFIGURAZIONE

Configurazioni



105 Parametri

42 Potenziali variabili di progetto

8 relative alla “forma” della struttura

34 relative alle sezioni degli elementi

DESIGN OPTIMIZATION (D. O.)



• Variabili di progetto (Design variables DV’s): sono grandezze indipendenti e cambiando il loro valore si persegue l’ottimizzazione del problema;

• Variabili di stato (State variables SV’s): sono “grandezze dipendenti” in quantofunzioni delle variabili di progetto;

Elementi del problema

• Funzione obiettivo (Objective function OBJ) che si intende minimizzare. È unica e anch’essa è una grandezza dipendente;

Funzione obiettivo (OBJ): minimizzare il peso

MINIMIZZARE IL VOLUME (VO)



MOLTIPLICATORE CARICO CRITICO (BLF) ≥ 2,5

Variabili di stato (SV):



MASSIMA TENSIONEDI TRAZIONE(LTS) ≥FYS = 355*106/1,15 N/m2

MASSIMA TENSIONE DICOMPRESSIONE (LTC) ≥ FYC = 355*106/1,7 N/m2

Variabili di stato (SV):



JORIZOD1

TW1]]]]

SOSTEGNO[[[[OD2

TW2

ORIZZ]]]]OD3

TW3

TUBO-02]]]]OD7

TW7

JVERT[[[[ OD5

TW5

JDIAG]]]]OD6

TW6

DIAG]]]]OD4

TW4

TUBO-1]]]]OD10

TW10

TUBO-2]]]]OD9

TW9

TUBO-0]]]]OD8

TW8

Design variables



Un

de

tect

ed

bu

ckli

ng

Ass

em

bla

ge

co

nst

rain

sAcceptable Unacceptable

Special checks on unconsidered aspects



In sintesi si ha:

• la necessariamente unica funzione obiettivo (OBJ ) MINIMIZZARE IL VOLUME (VO)

• le 3 variabili di stato (SV ), vincoli dell’ottimizzazione:[[[[[[[[

MASSIMA TENSIONEDI TRAZIONE(LTS)

MASSIMA TENSIONE DICOMPRESSIONE (LTC)

MOLTIPLICATORE CARICO CRITICO (BLF)

• le 20 variabili di progetto (DV ), grandezze su cui si opera:

DIAMETRI DEGLI ELEMENTI (OD)

[[[[ SPESSORI DEGLI ELEMENTI (TW)



Generazione casuale di configurazioni(OPTYPE,RAND)

INDAGINI DEL DOMINIO

Scansione globale dello spazio di progetto(OPTYPE,SWEEP)

Ad ogni ciclo genera valori casuali delle

variabili di progetto

Genera valori delle variabili di progetto

cambiando il valore di una variabile di

progetto per volta e mantenendo per le altre

il valore di riferimento scelto dall’utente



ANALISITIPOLOGIE DI ANALISI SAM FOOM SAMFOOM SAMEU FOOMEU SAMFOOMEU

GENERAZIONE CASUALE

SCANSIONE GLOBALE SPAZIO DI PROGETTO

SELEZIONE SOLUZIONI AMMISSIBILI

METODO DEL PROBLEMA APPROSSIMATO

SELEZIONE DELLA SOLUZIONE MIGLIORE

OTTIMIZZAZIONE AL PRIMO ORDINE

0,8 * FYC

0,8 * FYC

1,2 * BLF

SAM= sub-problem approximation method

FOOM= First-order optimization method

SAMFOOM=SAM+FOOM

----EU= --- + Heuristic assumptions

0.8*LTCmax

0.8*LTSmax

1.2*BLF



Andamento normalizzato degli elementi del problema

CARICO ORIZZONTALE ORTOGONALE ALLE BASI DEL JACKET

SAMEU SAMFOOMFOOMEU SAMFOOMEU SAMFOOM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

START

LTC/LTC*

BLF/BLF*

LTS/LTS*

VO/VO*



CARICO ORIZZONTALE IN DIREZIONE DELLA DIAGONALE DELLA BASE DEL JACKET

SAMEU45 SAM45 FOOM45 FOOMEU45 SAMFOOMEU45SAMFOOM45

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

START

LTC/LTC*

BLF/BLF*

LTS/LTS*

VO/VO*

Andamento normalizzato degli elementi del problema



SAMFOOM 45 OD1 0,59 TW1 0,014

OD2 0,99 TW2 0,016

OD3 0,80 TW3 0,014

OD4 0,60 TW4 0,014

OD5 1,30 TW5 0,016

OD6 0,50 TW6 0,014

OD7 4,16 TW7 0,050

OD8 4,64 TW8 0,055

OD9 3,86 TW9 0,046

OD10 3,40 TW10 0,041

LTC [N/m2] -3,470E+08 VO [m3] 129,03

BLF 8,21 LTCE 1162

LTS [N/m2] 2,809E+08 LTSE 950

Risultati per l’analisi SAMFOOM45

0

10

20

30

40

50

60

70

80

90

100

RA

PP

OR

TO

[%

]

JORIZZ SOSTEGNO ORIZZ DIAG JVERT JDIAG TUBO 2 TUBO 0 TUBO 1 TUBO 2

SEZIONI

ODn/ODn*TWn/TWn*

0.00

0.01

0.02

0.03

0.04

0.05

0.06

TW

[m

]


SEZIONI

STARTSAMFOOM 45

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

OD

[m

]


SEZIONI

STARTSAMFOOM 45



16% DI RIDUZIONEDEL VOLUMETOTALE (VO)

24% DI RIDUZIONE DEL VOLUME DELLA TORRE

1% DI RIDUZIONEDEL VOLUMEDEL JACKET

Results



Controllo della frequenza naturale della strutturain relazione all’azione dinamica della turbina (movimento del rotore): eventuale accoppiamentodella frequenza della struttura con quella del vento e del moto ondoso.

Hz209636,0foptnat

====−−−−

Hz249565,0fnat ====

Controllo delle caratteristiche dinamiche

f1Pmin f1PMAX f3Pmin f3PMAX

Soft-

Soft

Soft-

Stiff

Stiff-

Stiff

Hz1150,060

9,6f

minP1========

Hz2017,060

1,12f

PMAX1========

Hz3450,0f3f minP1minP3 ====⋅⋅⋅⋅====

Hz6050,0f3fPMAX1PMAX3

====⋅⋅⋅⋅====



Strutted innovative support

82

Summary

x1

x2

• Structure and piles 180 m

• Structure height: 140 m

• Immersed: 35 m

• Over water level: 105 m

Local constraints:

• maximum Von Mises ideal stress equals to

300MPa (strength criterion);

• maximum compression stress equals to

200MPa (local instability criterion);

• maximum ratio diameter/thickness equals to

100 (local instability criterion);

Global constraints:

• Eulerian buckling multiplier greater that 5;

• maximum horizontal displacement permitted

4 m.

• Objective Function: TOTAL VOLUME



Optimization problem algorithm



Macro-level model: Design variables trend

Diameters Thicknesses



Macro-level model: State variables trend

Compression stresses Von Mises stresses



Macro-level model: Configuration evolution



Macro-level model: Objective function



Meso-level model



Meso-level model: Effective buckling modes detection

Macro-level model Meso-level model

1° buckling mode load multipler = 9,08

1° buckling mode load

multipler = 10,12



Optimal configuration

•VOLUME=116 [m3]

Diamet ers[m] Thicknesses[m] d/t

D1 2.25 T1 3.1E-02 72.5

D2 3.14 T2 4.2E-02 75.5

D3 4.03 T3 4.2E-02 96.9

D4 4.56 T4 4.2E-02 109.5

D5 5.09 T5 5.2E-02 97.5

D6 2.37 T6 3.3E-02 71.8

D7 5.09 T7 5.2E-02 97.5

D8 5.30 T8 5.4E-02 98.3

D9 5.05 T9 5.4E-02 93.7

D10 4.80 T10 5.4E-02 89.1

D11 4.55 T11 5.4E-02 84.5

D12 4.31 T12 4.4E-02 97.9

D13 3.84 T13 4.4E-02 87.3

D14 3.37 T14 4.4E-02 76.7

D15 2.91 T15 4.4E-02 66.0

D16 2.44 T16 3.8E-02 64.8

D17 1.52 T17 1.6E-02 95.9

D18 2.32 T18 2.3E-02 99.4



Monopile-Quadruped comparison

Quadruped:• VOLUME = 116 [m3]• Weight = 904 [t]• D max = 5 [m]

Monopile:• VOLUME = 234 [m3]• Weight = 1057 [t]• D max = 9 [m]

peso monotubo 205.78 t

peso tripode 635.58 t

peso jacket 473.38 t

PESI SUPPORTO "E"

1057.8 t

735.58 t



Considerations on OWTs optimization

1. The Design Optimization of Owts is a fundamental step in the design of Offshore

Wind Farms.

2. The Design Optimization of such a complex structural systems has been carried out by

assuming simplified models for the actions.

3. Multi level detail models are needed in order to capture the main physical aspects.

4. A new support structure is proposed here, the optimization produced good results in

terms of weight if compared with another feasible solution (a monopile support

structure).



PERFORMANCE-BASED OPTIMIZATION

OF AN HIGH-RISE BUILDING FOR WIND• Performance-Based Wind Engineering (PBWE) procedure

• Models for tall buildings and Occupant Comfort assessment

• Probabilistic Performance-Based analysis

• Probabilistic Performance-Based optimization by a TMD

94FB

Performance-Based Wind Engineering (PBWE) procedure

95

The problem of risk assessment is disaggregated into the following elements:

- site and structure-specific hazard analyses, that is, the assessment of the probability density

functions f(IM), f(SP) and f(IP|IM, SP);

- structural analysis, aimed at assessing the probability density function of the structural response

f(EDP|IM,IP,SP) conditional on the parameters characterizing the environmental actions, the

wind-fluid-structure interaction and the structural properties;

- damage analysis, that gives the damage probability density function f(DM|EDP) conditional on

EDP;

- finally, loss analysis, that is the assessment of G(DV|DM), where G(·|·) is a conditional

complementary cumulative distribution function.

G(DV) = ∫…∫ G(DV|DM) · f(DM|EDP) · f(EDP|IM, IP, SP) · f(IP|IM,SP) ·

· f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP

PBWE procedure

Interaction

Parameters

Structural

Parameters

Intensity

measureIM IP SP

Engineering

Demand

Parameters

EDPDamage

MeasureDM

Decision

VariableDV



O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Aerodynamic

analysisStruc’l analysis Damage analysis Loss analysis

IM: intensity measure

IP: interaction

parameters

EDP: engineering

demand parameters

DM: damage measures DV: decision variables

Select

O, DO: location

D: design

Environment

info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural system

parameters

Structural

system info

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Aerodynamic

analysisStruc’l analysis Damage analysis Loss analysis

IM: intensity measure

IP: interaction

parameters

EDP: engineering

demand parameters

DM: damage measures DV: decision variables

Select

O, DO: location

D: design

Environment

info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural system

parameters

Structural

system info

O, D

g(IM|O,D)

g(IM)

p(EDP|IM)

P(EDP)

p(DM|EDP)

P(DM)

p(DV|DM)

P(DV)


IM: intensity

measure

EDP: engineering


measure

DV: decision

variable

Select

O, D

O: location

D: design

Facility

info

Decision-

making

O, D

g(IM|O,D)

g(IM)

p(EDP|IM)

P(EDP)

p(DM|EDP)

P(DM)

p(DV|DM)

P(DV)


IM: intensity

measure

EDP: engineering


measure

DV: decision

variable

Select

O, D

O: location

D: design

Facility

info

Decision-

making

PB

WE

PB

EE



Models for tall buildings and Occupant

Comfort assessment

98

Loss of serviceability

Loss

of

inte

gri

ty o

f

no

n-s

tru

ctu

ral

ele

me

nts

Mo

tio

n p

erc

ep

tio

n

by b

uild

ing

occ

up

an

ts

Bas

hor,

R.

and

Kar

eem

,A

.(2

007)

."P

rob

abil

isti

cP

erfo

rman

ceE

val

uat

ion

of

Bu

ildin

gs:

An

Occ

up

ant

Co

mfo

rtP

ersp

ecti

ve"

,P

roc.

12

thIn

tern

atio

nal

Co

nfe

ren

ceon

Win

d

En

gin

eeri

ng,

1-6

July

,C

airn

s,A

ust

rali

a.A

vai

lable

on

line

athtt

p:/

/ww

w.n

d.e

du/~

nat

haz

/

[Acc

esse

d1

5Ju

ne

20

10

].

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1

B2

H

Dis

pla

cem

en

ts

Acc

ele

rati

on

s

Discomfort level in terms of

perception thresholds

Usually Across wind vibration is

critical for comfort

The reference period for comfort

evaluation is 1 year

1

2

3 1st natural frequency is dominant4

1

10

100

0,1 1

a [

cm/s

2]

f [Hz]

Office Apartment

Italian Guidelines

f1

Sca

lar

thre

sho

ld

Serviceability under Wind (II)

Case study structure

Structure and FE model

Structure

Height H= 305 m

Lengths B1=B2= 50 m (square)

No of floors = 74

3d f

ram

e o

n t

he

exte

rnal

per

imet

er

centr

al c

ore

bracing system

A steel structure

Finite Element model

B1

B2

H

FE Model

About 10,000 Elements

About 4,000 Nodes

About 24,000 DOFs



Experimental model of Actions

Spen

ceS.

M.J

.,G

ioff

rèM

.,G

usel

laV

.(20

08a)

.In

flu

ence

of

hig

her

mo

des

on

the

dy

nam

ic

re-s

po

nse

of

irre

gula

rand

regula

rta

llb

uil

din

gs,

Pro

c.6

thIn

tern

atio

nal

Co

lloq

uiu

mo

nB

luff

Bod

ies

Aer

od

ynam

ics

and

Ap

pli

cati

ons

(BB

AA

VI)

,M

ilan

o,

Ital

y,Ju

ly20-2

4,

2008.

Boundary Layer Wind Tunnel of

the CRIACIV in Prato, Italy

-60

-40

-20

0

20

40

60

80

100

120

140

3000 3200 3400 3600 3800

F [KN]

t [s]

Along Across

1:5

00

S

cale

mo

de

l

Response time

history

Time domain structural analyses

(Experimental actions)

Time domain

analyses

Experimental

forces

Time domain analyses

-30

-20

-10

0

10

20

30

3500 3600 3700 3800 3900 4000

aL, aD

[cm/s2]

t [s]Along Across

( )

( )

( ) )(),(

),,(exp1

),(),(

22

212

2

ωχωρ

ωξξ

ωρω

⋅⋅⋅⋅=

=⋅⋅−⋅

⋅⋅⋅⋅=

∫ ∫

hSVc

dAdAfA

hSVchS

uumxD

A A

uumxDDD tt

( )

)(),h(S

)(HVc

),h(S)(H),h(S

2

uu

22

mxD

DD

2

rr tttt

ωχω

ωρ

ωωω

⋅⋅

⋅⋅⋅⋅

=⋅=

⋅+

−

⋅

⋅⋅

=

2

0

2

2

2

0

2

2

0

2

2

41

1

1)(

ω

ων

ω

ω

ωω

mH

rrm

pgrr σ⋅+= rg

Wind action spectra

(analytical)

Response spectra

Peak response

Frequency domain response

Frequency domain analyses

Response Peak Factor

Analytical model of the buffeting forces

( ) ( ) ( ) ( )( )ωfexpωSωSωS jkuuuuuu kkjjkj−=

( )( )

( ) ( )( )kj

2

kj

2

z

jkzVzV2π

zzCωωf

+

−=

Cross-spectrum

5.0

0

uu2

x

u200

300(x)dxRu

1L

⋅== ∫

∞z

were:

( )( ) [ ]5/3

ju

jux2

u

uu/zLf10.3021ω/2π

/zLfσ6.686ωS

jj ⋅⋅+⋅

⋅⋅⋅=

( )( ) 2

fri0

0

u

2

u

u1.75)log(zarctan1.16

(n)dnSσ

⋅+⋅−=

== ∫∞

)z(V2π

zωf

jm

j

⋅

⋅=

Autospectrum

( )3ew(t)2ev(t)1eu(t))

j(zmV)

jz(t;

jV

rrrr⋅+⋅+⋅+=

α

10m

10

zV(z)V

⋅=

Sola

ri,G

.Pic

card

o,G

.(20

01).

Pro

bab

ilis

tic

3-D

turb

ule

nce

mo

deli

ng

for

gust

bu

ffet

ing

of

stru

cture

s,P

robab

ilis

tic

Engin

eeri

ng

Mec

han

ics,

(16),

73

–8

6.

Turb

ule

nt w

ind

velo

city sp

ectra

(an

aly

tical)

Model of the Vortex shedding forces

(Varying with the angle of attack)

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

0.000 0.001 0.010 0.100 1.000

PS

D

n [Hz]

Total Force spectrum

Turbulence force spectrum

Vortex shedding force spectrum

Exp

erim

en

tal w

ind

force

spe

ctra

Extra

po

latio

n o

f an

an

aly

tical

Vo

rtex sh

ed

din

g fo

rce sp

ectra

Model of the Vortex shedding forces

n

Co

mp

atib

ility o

f an

aly

tical

an

d e

xpe

rime

nta

l spe

ctra

1.E+01

1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

0.000 0.001 0.010 0.100 1.000

PS

D

n [Hz]

Total Force spectrum

Turbulent component

Vortex shedding component

Global force spectrum

Analytical wind spectra

n



1

10

100

0.1 1

aL

,Dp

[cm

/s2]

n [Hz]

Office Apartment aLp aD

p

f1

aL

,Dp

[cm

/s2]

n [Hz]

-30

-20

-10

0

10

20

30

3500 3600 3700 3800 3900 4000

aL, aD

[cm/s2]

t [s]Along Across

Structural response- max accelerations

Time domain: resultsStructural response – accelerations

Comfort evaluation

Across

Along

Reference mean

wind velocity:

Vm(H) = 35 m/s

(annual mean

recurrence)

Alongw(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1

B2

H

Across

0

5

10

15

20

25

30

-20 0 20 40 60

aLp

[cm/s2]

θ [deg]

aLp

aDp

Due to

vortex

shedding

effect



Probabilistic Performance-Based analysis

105

Hazard analysis

Aeolian risk assessment

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interaction

analysisStructural analysis Damage analysis Loss analysis

IM: intensity

measure

IP: interaction

parameters

EDP: engineering


measure

DV: decision

variable

Select

O, DO: location

D: design

Environme

nt info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural

system parameters

Structural

system

info

( ) ( )

θ−⋅

θ⋅

θ

θ=θ

θ−θ

θ

)(10

1)(10

10, exp)(

)(),(f

10

kk

Vc

V

c

V

c

kV

The roughness length z0 is characterized by a lognormal

PDF. The mean value μz0 and the standard deviation σz0

of z0 are expressed as function of θ (assuming a slight

difference between four sectors, i.e. a mean value of z0

varying between 0.08 m and 0.12 m and a COVz0 equal

to 0.30).

V10 and θ are described by their joint probability

distribution function

IM =

θ

V10

z0

Parameters c(θ) and k(θ) are derived from NIST® wind

speed database.

(Annual occurrence)



Interaction analysis IP =

gr

CD

CL

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interaction


IM: intensity

measure

IP: interaction

parametersEDP: engineering


measure

DV: decision

variable

Select

O, DO: location

D: design

Environme

nt info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural

system parameters

Structural

system

info




Interaction analysis

The aerodynamic coefficients CD ,CL are described by Gaussian

distributions. Mean values are expressed as a function of θ, varying from

those corresponding to a square shape (for θ = 0°) to those corresponding

to a rhomboidal shape (for θ = 45°); the coefficient of variations of CL and

CD are taken equal to 0.07 and 0.05.

IP =

gr

CD

CL

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interaction


IM: intensity

measure

IP: interaction



measure

DV: decision

variable

Select

O, DO: location

D: design

Environme

nt info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural

system parameters

Structural

system

info

0

0.2

0.4

0.6

0.8

1

1.2

-90 -60 -30 0 30 60 90M

ean

aer

od

ynam

ic c

oef

fici

ents

µ µ

DCµ

60 90

θ [deg]

LCµ

462.2507.1265.02 +ξ+ξ−=µ

rg

( )

≤⋅η

>⋅η

⋅η+

−⋅η

=σ

+

+

+

+

122if650

122if46

213

45

2

21

.T.

.T.

)Tln(

.

)Tln(

.

windr,e

windr,e

windr,e

windr,e

gr

( )

<≤

η

<≤

η−

=η +

+

+

1690if

690100if

380631 450

r

r

r

r

.

r

r,e

q.

.q.

.q.

r

rr σ

σ=+η & Vanmarcke

(1975)

(Obtained from time-domain analyses)

The peak response factor gr is described by a Gaussian distribution function

g*r = -0.256ξ2 + 1.507ξ + 2.462

3.00

3.40

3.80

4.20

4.60

0.5 1 1.5 2 2.5

g*r

ξ [%]

rgµ

rgµ


Structural analysis EDP = aLp

O

f(IM|O)

f(IM)f(IP|IM,SP)

f(IP)

f(EDP|IM,IP,SP)

G(EDP)

f(DM|EDP)

G(DM)

f(DV|DM)

G(DV)

Hazard analysis

Interaction


IM: intensity

measure

IP: interaction



measure

DV: decision

variable

Select

O, DO: location

D: design

Environme

nt info

Decision-

making

D

f(SP|D)

f(SP)

Structural

characterization

SP: structural

system parameters

Structural

system

info

G(EDP) = ∫…∫ G(EDP|IM, IP, SP) · f(IP|IM,SP) · f(IM) · f(SP) · dIP · dIM · dSPMonte Carlo sim

(5000 runs)

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1

B2

H

aLp

Reduced

formulation




Risk Curve. EDP= aLp = peak acceleration in across wind direction

The annual probabilities of exceeding the human perception thresholds for

apartment and office building vibrations are 0.0576 and 0.0148 respectively.

w(t;z2)Vm(z2)

Vm (z1)

Vm (z3)

V(t;z2)

v(t;z2)u(t;z2)

X

Z

Y

θ

B1

B2

H

aLp

Ciampoli M, Petrini F. (2011). “Performance-Based Aeolian Risk assessment and reduction for tall buildings”,

Probabilistic Engineering Mechanics, accepted for publication.




Probabilistic Performance-Based optimization by a TMD

111

TUNED MASS DAMPER (TMD)

C1

K1 CTMD

KTMD

M1

MTMD



C1

K1 CTMD

KTMD

M1

MTMD

Sistema Principale(struttura)1 = massa 1 = 12 ∙ 1 = rigidezza 1 = 2 ∙ 1 ∙ 1 ∙ 1 =

= smorzamento




C1

K1 CTMD

KTMD

M1

MTMD

Sistema Principale(struttura)

Sistema Secondario(TMD) = 1 = rapporto tra le masse

= 1 = rapporto tra le pulsazioni

= 2 ∙ ∙ ∙ =

= smorzamento TMD

T M D T L D

1 = massa 1 = 12 ∙ 1 = rigidezza 1 = 2 ∙ 1 ∙ 1 ∙ 1 =

= smorzamento




C1

K1 CTMD

KTMD

M1

MTMD

Sistema Principale(struttura) = 1 = rapporto tra le masse

= 1 = rapporto tra le pulsazioni

= 2 ∙ ∙ ∙ =

= smorzamento TMD

In cui:

= = pulsazione naturale

= = 2∙ ∙ = smorzamento percentuale

con i = 1, TMD T M D T L D

1 = massa 1 = 12 ∙ 1 = rigidezza 1 = 2 ∙ 1 ∙ 1 ∙ 1 =

= smorzamento

Sistema Secondario(TMD)




= 000.56 0 < 10 1 ≤ 0 ≤ 20.5 ∙ 0 ∙ 0 0 ≥ 2"

0 = 6 #/%2 = per i piani adibiti ad uffici; (a) 0 = 4 #/%2 = per i piani adibiti ad abitazioni; (b) 0 = frequenza fondamentale dell’edificio.

Uffici

Abitazioni

EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE



= 000.56 0 < 10 1 ≤ 0 ≤ 20.5 ∙ 0 ∙ 0 0 ≥ 2"


Uffici

Abitazioni

1.E-04

1.E-03

1.E-02

1.E-01

1.00E-01

RP

SD

Frequenza (Hz)

Non controllata




= 000.56 0 < 10 1 ≤ 0 ≤ 20.5 ∙ 0 ∙ 0 0 ≥ 2"


Uffici

Abitazioni

1.E-04

1.E-03

1.E-02

1.E-01

1.00E-01

RP

SD

Frequenza (Hz)

Controllata

Non controllata






- Undamped primary system

- Sinusoidal external force

Closed-form solution and optimization

Den Hartog problem



Modal superposition resolution method (I)

[ ]∑=

⋅≈

p

ii

iiTMD

i

TMD

tytyt

t

1 2

11

1)()(

)(

)(

φ

φ

ξ

ξ

Strømmen E., Hansen E.H. (2001). On the use of tuned mass dampers to suppress vortex shedding induced vibrations. Wind and Structures, 4(1), 19-30.

Each mode shape a 2 DoF modal

problem is solved

Physical response parameter (e.g. displacement) of the primary structure

Solution response parameter (e.g. displacement) of the primary structure

for modal problem i

Modal shape displacement value of the primary structure

)(1 tξ

)(1 tyi

i1φ



Modal superposition resolution method (II)

Strømmen E., Hansen E.H. (2001). On the use of tuned mass dampers to suppress vortex shedding induced vibrations. Wind and Structures, 4(1), 19-30.

[ ]∑=

⋅≈

p

ii

iiTMD

i

TMD

tytyt

t

1 2

11

1)()(

)(

)(

φ

φ

ξ

ξ

Each mode shape a 2 DoF modal

problem is solved

Physical response parameter (e.g. displacement) of the primary structure

Solution response parameter (e.g. displacement) of the primary structure

for modal problem i

Modal shape displacement value of the primary structure

)(1 tξ

)(1 tyi

i1φ

Where

For evaluating the VS spectra see next slide

Optimization parameters

Design Parameters

γ = mTMD/mtot

β = ωTMD/ ω1

ξ* = damping of TMD



C1

K1 CTMD

KTMD

M1

MTMD


305 m



ANALISI PARAMETRICA CON TMD

= ##1 ; = 1 ; = smorzamento;



TMD

Design Parameters

γ = mTMD/mtot

β = ωTMD/ ω1

ξ* = damping of TMD

Aeolian Risk reduction by TMD

90

0.125 0.145 0.165 0.185

β = 0.70 ; ξ* = 1% - 10% β = 0.80 ; ξ* = 1% - 10%

β = 0.90 ; ξ* = 1% - 10% β = 1.02 ; ξ* = 1% - 10%

β = 1.10 ; ξ* = 1% - 10% β = 1.20 ; ξ* = 1% - 10%

β = 1.30 ; ξ* = 1% - 10% Uncontrolled

Apartment Office

aL

p[m

m/s

2]

n [Hz]

β = ξ* =

β = ξ* =

β = ξ* =

β = ξ* =

β = ξ* =

β = ξ* =

β = ξ* =

Parametric analysis Effects on risk

γ = 1/150



CONFIGURAZIONE OTTIMALE DEL TMD

= # # 1 = 1150 ⇒ # ≅ 568 *+

Realizzata con una sfera di acciaio

di raggio pari a circa 2.60 m

= 8%, per limitare gli spostamenti

sulla massa del TMD

= 1 =1, il che consente di

ottenere un risultato migliore



INTRODUZIONE DI UN SECONDO TMD

Accelerazione di picco

Non controllata 15.6 cm/s2

TMD 1 10.6 cm/s2

TMD 2 9.63 cm/s2

γ β ξ Piano

TMD 1 1/300 1 0.05 74

TMD 2 1/300 1 0.05 38

305 m

160 m3

30

0.1 1

a (m/s2)

n0 (Hz)

Uffici

Residenze

Non controllata

1 TMD

2 TMD



PERFORMANCE-BASED OPTIMIZATION OF AN HIGH-RISE BUILDING

STRUCTURAL SYSTEM FOR RELIABILITY

AGAINST PROGRESSIVE COLLAPSE

• Robustness of high-rise buildings in case of fire

• The role of the outrigger and of the lateral bracing

• Multi-hazard considerations

• Structural system optimization

128FB

Robustness of high-rise buildings

in case of fire

time

Tem

pera

ture

PREVENTION PROTECTION

Passive Measures

Ignition

Flashover

Active Measures

ROBUSTNESS

Ineffectiveness

of measures

Robustness role in case of fire

Joelma Building,

Sao Paulo (1974)

Mandarin Oriental

Hotel, Beijing (2009)

Windsor Tower,

Madrid (2005)



Case study40 floors, 160 m heigth, 35 m x 35 m floor, office building

RENDERING STRUCTURAL SYSTEM FEM MODEL



Case study

Outrigger

Bracing

System

Frame BFrame A

Frame B

Frame A



The role of the outrigger and of

the lateral bracing

Frame A Assumptions

- Collapse for displacement of 1 meter on the top

- Exposure to 180 minutes of ISO Curve

- 30 cases of fire changing initial fire location and number of

involved columns

Frame B

FIRE LOCATION 6th floor

t

T

Nominal

ISO 8344

0

200

400

600

800

1000

0 10 20 30 40 50 60

ISO 834

θ ipe 270

θ ipe 300

θ hem 260

θ hea 240

θ hem280

Progressive collapse assessment



Progressive collapse assessment

Frame A Assumptions

- Collapse for displacement of 1 meter on the top

- Exposure to 180 minutes of ISO Curve

- 30 cases of fire changing initial fire location and number of

involved columns

Frame B



1 Heated Column

2 Heated Columns

3 Heated Columns

4 Heated Columns

5 Heated Columns

30 min - 696°C 30 min - 696°C 30 min - 696°C 30 min - 696°C 30 min - 696°C

Frame B - Worst case scenarios



Progressive Collapse

1 Heated Column

2 Heated Columns

3 Heated Columns

4 Heated Columns

5 Heated Columns

After 180 min After 107 min After 93 min After 102 min After 87 min



Frame A - Worst case scenarios

1 Heated Column

2 Heated Columns

3 Heated Columns

4 Heated Columns

5 Heated Columns

26 min - 640°C 28 min - 680°C 29 min - 690°C 30 min - 696°C 31 min - 705°C



1 Heated Column

2 Heated Columns

3 Heated Columns

4 Heated Columns

5 Heated Columns

After 180 min After 180 min After 126 min After 144 min After 100 min




Outrigger role

VMises Deformation

Without Fire

1 Heated

Column

2 Heated

Columns

3 Heated

Columns

4 Heated

Columns

5 Heated

Columns

195235 156 117 78 39 0 plastic elastic



Frame BFrame A

SWAY COLLAPSE NO-SWAY COLLAPSE




Multi-hazard considerations

Lateral Force: Dir. +Z

SCENARIO

Without Wind Wind Γ=0.5 Wind Γ=1.0 Wind Γ=1.5



SCENARIO


Lateral Force: Dir. -Z



Lateral Force: Dir. +Z

DEFORMED SHAPE


After 180 min After 140 min After 152 min After 82 min

88 minVertical

69 minOutwards

16 minOutwards

<10 minOutwards



Structural system optimization

Configurations: position of the outrigger

CONFIGURATIONS

G A B C

STEEL MASS [TON]

877 857 877 877



Configurations: vertical brace system

CONFIGURATIONS

G D E F

STEEL MASS [TON]

877 817 994 939



Multi-hazard analyses – 3 heated columns




Initial



153

CONCLUSIONS

1. Due to their nature complex, real structures requires advanced models, both for

actions and structural parts.

2. A suitable way to deal with the above is the adoption of a systemic approach, that is

the switching from the vision of a structure as an isolated entity to the vision of a

structure as “a set of interrelated components which interact one with another in an

organized fashion toward a common purpose”.

3. The systemic vision is particularly useful in presence of non-linear interactions (i.e.

between the structure and the environment), cascading effects, high level of

uncertainty.

4. Classical optimization algorithms are, in general, not exhaustive for conducting the

optimization of such a structural systems, if not coupled with rational, heuristic

considerations from the designer.

5. One of the most rational way to deal with the design of complex structures is the

Performance-Based Design approach, that can be conducted both in deterministic

or in probabilistic terms.

6. The Performance-Based Optimization is an appropriate way to optimize complex

structural systems.



optimization course rome 05_05_2015_fp

Engineering

aspects of structural

franco bontempi

design consulting

wind service

real structural systemstools

research topics

introduction of basic

advanced ideas