Appunti del corso di dottorato: Ottimizzazione Strutturale / Structural Optimization - parte II - Bontempi

Ottimizzazione Strutturale
franco.bontempi@uniroma1.it
1
Franco Bontempi
Ordinario di Tecnca delle Costruzioni
Facolta’ di Ingegneria Civile e Industriale
Sapienza Universita’ di Roma
Introduzione alla
OTTIMIZZAZIONE STRUTTURALE
(parte II)

2

3
Object of the course
• 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.

4
General Scheduling
• 1st Day:
Basic definitions of structure, requirements,
values, optimization, …;
• 2nd Day:
Advanced specific case of structural optimization
(service / ultimate / extreme scenarios);
• 3rd Day:
Advanced concepts (structural systems,
advanced criteria, tools of design)

5
5TECHNIQUES

6
FEW OBSERVATIONS

The function: y(x1,x2)
7

The sensibility of the function
8

9
STRATEGY #1: SENSITIVITY
governance of priorities

The boundings of the function
10

11
STRATEGY #2: BOUNDING
behavior governance
p
(p)

p
(p)


12

Design of Experiments (DOE)
• In general usage, design of experiments (DOE) or
experimental design is the design of any information-
gathering exercises where variation is present, whether under
the full control of the experimenter or not. However, in
statistics, these terms are usually used for controlled
experiments.
• Formal planned experimentation is often used in evaluating
physical objects, chemical formulations, structures,
components, and materials. Other types of study, and their
design, are discussed in the articles on computer
experiments, opinion polls and statistical surveys (which are
types of observational study), natural experiments and quasi-
experiments (for example, quasi-experimental design).
13

Sampling Points (1)
14

Sampling Points (2)
15

Simulation & Approximation
of the response (≈ surrogate)
16

17

The nature of optimum (1)
18

The nature of optimum (2)
19
A sub-optimal solution
to a problem is one
that is less than perfect.
Slack situation: loose and not pulled tight.

Example (1)
20

Example (2)
21

Bounded Rationality
Bounded rationality is the idea that in decision-making, rationality
of individuals is limited by the information they have, the
cognitive limitations of their minds, and the finite amount of time
they have to make a decision. It was proposed by Herbert A.
Simon as an alternative basis for the mathematical modeling of
decision making, as used in economics, political science and
related disciplines; it complements rationality as optimization,
which views decision-making as a fully rational process of finding
an optimal choice given the information available. Another way to
look at bounded rationality is that, because decision-makers lack
the ability and resources to arrive at the optimal solution, they
instead apply their rationality only after having greatly simplified
the choices available. Thus the decision-maker is a satisfier, one
seeking a satisfactory solution rather than the optimal one.
22

Model Extensions
• Ariel Rubinstein proposed to model bounded rationality by
explicitly specifying decision-making procedures..
• Gerd Gigerenzer opines that decision theorists have not really
adhered to Simon's original ideas and proposes and shows
that simple heuristics often lead to better decisions than
theoretically optimal procedures.
• Huw Dixon later argues that it may not be necessary to
analyze in detail the process of reasoning underlying bounded
rationality. If we believe that agents will choose an action that
gets them "close" to the optimum, then we can use the notion
of epsilon-optimization, that means you choose your actions
so that the payoff is within epsilon of the optimum. The notion
of strict rationality is then a special case (ε=0).
23

24
OPTIMIZATION METHODS
Heuristics
Nelder – Mead
Genetic Algorithm

εὑρίσκω
• Heuristic (/hjʉˈrɪstɨk/; Greek:
"Εὑρίσκω", "find" or "discover") refers
to experience-based techniques for
problem solving, learning, and
discovery that give a solution which is
not guaranteed to be optimal. Where
the exhaustive search is impractical,
heuristic methods are used to speed
up the process of finding a satisfactory
solution via mental shortcuts to ease
the cognitive load of making a
decision. Examples of this method
include using a rule of thumb, an
educated guess, an intuitive judgment,
stereotyping, or common sense.
• In more precise terms, heuristics are
strategies using readily accessible,
though loosely applicable, information
to control problem solving in human
beings and machines.
• L'euristica (dalla lingua greca εὑρίσκω,
letteralmente "scopro" o "trovo") è una
parte dell'epistemologia e del metodo
scientifico.
• Si definisce procedimento euristico, un
metodo di approccio alla soluzione dei
problemi che non segue un chiaro
percorso, ma che si affida all'intuito e
allo stato temporaneo delle
circostanze, al fine di generare nuova
conoscenza. È opposto al
procedimento algoritmico. In
particolare, l'euristica di una teoria
dovrebbe indicare le strade e le
possibilità da approfondire nel
tentativo di rendere una teoria
progressiva.

27
1

Simulated Annealing (Metropolis)
• Simulated annealing (SA) is a generic probabilistic heuristic for the
global optimization problem of locating a good approximation to the
global optimum of a given function in a large search space.
• The name and inspiration come from annealing in metallurgy, a
technique involving heating and controlled cooling of a material to
increase the size of its crystals and reduce their defects.
• This notion of slow cooling is implemented in the Simulated
Annealing algorithm as a slow decrease in the probability of
accepting worse solutions as it explores the solution space.
Accepting worse solutions is a fundamental property of heuristics
because it allows for a more extensive search for the optimum.
• The method is an adaptation of the Metropolis-Hastings algorithm, a
Monte Carlo method to generate sample states of a thermodynamic
system, invented by M.N. Rosenbluth and published in a paper by
N. Metropolis et al. in 1953.

29

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Basic version (1)

33

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Points for SA
• Diameter of the search graph
• Transition probabilities
• Acceptance probabilities
• Efficient candidate generation
• Barrier avoidance
• Cooling schedule
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2

Nelder-Mead Method (Amoeba)
• The Nelder–Mead method or downhill simplex
method or amoeba method is a commonly used
nonlinear optimization technique, which is a
well-defined numerical method for problems for
which derivatives may not be known.
• The Nelder–Mead technique is a heuristic
search method that was proposed by John
Nelder & Roger Mead (1965) for minimizing an
objective function in a many-dimensional space.

43

Genetic Algorithm (GA)
• The original motivation for the GA approach was a biological
analogy. In the selective breeding of plants or animals, for example,
offspring are sought that have certain desirable characteristics,
characteristics that are determined at the genetic level by the way
the parents’ chromosomes combine. In the case of GAs, a
population of strings is used, i.e. chromosomes.
• The recombination of strings is carried out using analogies of
genetic crossover and mutation, and the search is guided by the
results of evaluating the objective function f for each string in the
population.
• Based on this evaluation, strings that have higher fitness (i.e.,
represent better solutions) can be identified, and these are given
more opportunity to breed.

45

Coding
• One of the distinctive features of the GA approach is to
allow the separation of the representation of the problem
from the actual variables in which it was originally
formulated. In line with biological usage of the terms, it
has become customary to distinguish the ‘genotype’—
the encoded representation of the variables, from the
‘phenotype’—the set of variables themselves.
47

Genotype space = {0,1}L
(mappa)
Phenotype space
(territorio)
Encoding
(representation)
Decoding
(inverse representation)
01101001
01001001
10010010
10010001
Translation

Costruzione della
popolazione iniziale
Valutazione della
funzione di fitness
di tutti gli individui
Selezione
Riproduzione
Crossover
Mutazione
M/2 cicli
Ciclosullegenerazioni
Operatori
genetici
Ciclosullepopolazione
Nuova
popolazione
Fine?
No
Si
Probabilità di crossover: 80%
Probabilità di mutazione: 1%

Mating, Mutation, Selection
51

EXCEL
52

6USES
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OPTIMIZATION OF HCS

55

Precast hollow core slabs (HCS)
56

Tensile crack phenomena in HCS
(splitting, bursting, spalling).
• splitting cracks: caused by stresses resulting from
the development of prestressing in the anchorage
zone, that may generate traction stresses in the
concrete.
• bursting cracks: a local effect, generated by the
strand slippage into the slab end while the former
widens slightly on being cut.
• spalling cracks: occurring above the axis of the
strands in the HCS end zone, caused also by the
development of prestressing in the concrete at the
slab ends where only the lower part holding the
strands begins to be prestressed.Ottimizzazione Strutturale
57

Tensile crack phenomena in HCS
(splitting, bursting, spalling).
58

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Cross-section of the reference HCS
and numerical model
60

Tensile deformations in the vertical
directions for the spalling effect
61

The binary coding of the geometry
characteristics of the section
62

• The fitness function F includes terms to represent
the weight of the slab.
• First, functions gi(x), represents the geometry
constraints, implicitly satisfied during the definition of
the variable space.
• Functions hi(x) represent the structural safety
constraints. In this study, two checks are carried out:
1. the first one on the bending stress, carried out after the
initial structural analyses on the meso-scale model.
2. the second one, on the spalling stress, carried out on the
micro-scale model.
• If both checks are positive, the individual is fitting the
constrain conditions, otherwise, it is discarded and a
different element is introduced in the population.
63

64

65

Original values values obtained
after the optimization process
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OPTIMIZATION OF S&T

89
OPTIMIZATION AS A TOOL
FOR EXPLORATION

a
90

Limit States
Service Limit States Ultimate Limit States

Elements of nonlinear formulation

b
122

Uses of genetic algorithm
• To perform the stochastic exploration of
the load space;
• To handle the uncertainties related to the
definition of the loads;
• To investigate the global behavior of the
structure by means of the definition of the
envelope diagram of the performances;
• To define the worst load combination;
• To scrutinize the exact value of a specific
performance.
123

124

Dissipation devices
Soil behavior
Material
Soil-Structure interface Contact
Support system
Pylon
Cable system
Geometrical
Soil-Structure
Response
Vehicle-StructureWind-Structure
Nonlinearities
Interactions
Action
Uncertainties
125

126

Dependability attributes threats,
means and their interactions.
127

Performance in relation to the
return periods of the actions.
128

S N
Geometry of the long-span
suspension bridge considered.
129

The design variables and
the performance levels
130

A genetic algorithm approach for
performance assessment
• The performance of a long-span suspension bridge is
investigated by means of a GA approach.
• Focus is given to three aspects of the structural behavior of
the bridge:
1) maximum vertical displacement;
2) maximum longitudinal and transversal slope;
3) maximum tension in main cable and in the tower legs.
• The load scenarios that lead to the most severe performance
metrics are explored in the space of the load variables by an
optimization process based on GA’s.
• The implementation of a GA based optimization is essential
since the traditional optimization techniques are rather
ineffective, due to the high number of dimensions of the load
variables space and the presence of numerous local optimum
points.
131

Loading systems considered in the
genetic algorithm analysis.
132

Remarks on loading system
• Traffic and train loads are directed vertically but the
possibility to have a longitudinal component due to the
acceleration (A) or the deceleration (D) is also taken into
account.
• In addition, a torque is present if the traffic loads are not
positioned on the axis of the respective box girder
section.
• The wind action, assumed always present and flowing
transversally to the longitudinal axis of the bridge,
produces lift, drag and torque.
• In order to represent analytically the entire loading
system, 16 variables are needed.
• Since each of the girders is formed by 123 finite
elements, the position of the loads will be defined by
integer variables, ranging, in general, from 0 to 123.
133

Variables considered for the
definition of the loading system.
134

Description of loading system
135

Binary coding
• The position variables are implemented in binary
code with a dimension of eight bits (the minimum
dimension able to represent the position of the
loads on the bridge deck):
• In this row vector, x1 defines the position of the
train on the bridge deck, in binary code: for
example, if the train load starts from the fifteenth
element on the deck, the variable x1 is:
136

Population
• The GA starts by considering an initial population of N
row vector x created assigning random values to the
unknown variables; each row of the matrix X represents
the chromosome of one solution:
137

Target functions
• In order to evaluate the performance of the bridge, the
following six target functions are considered:
1. the vertical displacement (negative) for the bridge deck;
2. the horizontal displacement (positive) for the bridge
deck;
3. the longitudinal slope for the bridge deck;
4. the transversal slope for the bridge deck;
5. the axial tension for the main cables;
6. the stress state induced by the axial action and the two
bending moments for the bridge tower legs.
• Each performance is measured by the peak value over
all nodes of the bridge deck.
138

Evolution of population
• For each target function, the genetic algorithm
creates new populations of N row vector x in order
to find the worse configurations of the considered
loads.
• The genetic algorithm works by evaluating the target
function in correspondence with each assumed
vector x.
• If the population contains a N number of x vectors,
the best N/2 vectors are saved in a new population
while the other vectors are erased.
• To complete the new population, additional N/2
vectors are formed from the saved vectors using the
genetic operator of mutation and crossover.
139

Mutation
• The mutation on the generic vector i of the
population n changes a single bit of a
randomly selected chromosome; for example
provides the change from 1 to 0:
• As a result a new vector k is obtained for the
population n+1.
140

Crossover
• The crossover on the generic vectors i and j of
population n is provided in this example:
• where a group of cells of chromosomes i and j is
selected and the respective states changed.
• As a result there are two new vectors k and l for the
population n+1. Ottimizzazione Strutturale
141

Remarks
• When N/2 new vectors are created, the genetic algorithm
restarts with the evaluation of the target function for each
vector xn+1.
• It should be observed that a genetic algorithm is a
stochastic evolutionary procedure because the operators
of mutation and crossover are not deterministic but there
is a probability of occurrence for each operator.
• Usually the probability of occurrence of the mutation
operator is low (0 – 5%) while the probability of
occurrence of the crossover operator is high (70 – 90%).
• What makes this procedure attractive is the fact that
usually there is a large interdependence between the
quality of results and of the choice of these parameters.
142

143

• The FE model consists of 1614 elements (beams, no
compression cable elements and gaps) and 1140 nodes.
• For each of the six previously chosen performance
metrics (target functions), GA analysis is performed with
an initial randomly chosen population of 100
chromosomes. For each chromosome the structural
analysis, accounting for geometrical and material
nonlinearities, is developed using ADINA, starting each
time from the reference configurations under permanent
loads and adding the traffic and wind loads.
• The custom software reads the output evaluation and
performs the genetic recombination of the chromosomes
to get a new generation of chromosomes: 100 cycles of
regeneration are considered for a total of 10000 different
load scenarios, each of them leading to a nonlinear
structural analysis.
• The probability of occurrence of the crossover operator
is of 80% while the probability of occurrence of the
mutation operator is of 2%.
144

145

Remarks
• It is clear that the convergence of the variables that
define the train position (A) is better than the one that
defines the position of the light traffic load (B).
• From a design point of view, it means that the influence
of the railway load in defining the vertical displacement is
much higher than the traffic load.
• In addition, it can be observed that the railway loads
converge towards two different edges (North and South).
This is due to the fact that the geometry of the bridge is
almost symmetrical.
146

Vertical displacement envelope
147

Transversal slope envelope
148

Longitudinal slope envelope
149

150

Comparative importance
of the loads.
151

7THEORETICAL ASPECTS OF DESIGN
152

INDEX
• Knowledge
• People
• Design process as a decision process
• Limits
• Scale effects
• Ergonomy
153

154
KNOWLEDGE

CONOSCENZA
RICHIESTA
DA UN PROGETTO
EVOLUTIVO
CONOSCENZA
RICHESTA
DA UN PROGETTO
INNOVATIVO
BASE DI
CONOSCENZA
ATTUALE
La crescita di conoscenze
155

Evolutive vs Innovative Design
156Ottimizzazione Strutturale

Knowledge Growth Process
KNOWLEDGE
REQUIRED
BY AN EVOLUTIVE
DESIGN
NEW KNOWLEDGE
REQUIRED BY
AN INNOVATIVE
DESIGN
ACTUAL
KNOWLEDGE BASIS

158

159

160

161
STRUTTURECON
COMPORTAMENTOPERFORMA

162
STRUTTURECON
COMPORTAMENTOVETTORIALE

163
STRUTTURECON
COMPORTAMENTOSEZIONALE

164
STRUTTURECON
COMPORTAMENTODISUPERFICIE

Evolutive Jump
165

166

Horizons
168

Failure due to errors
169

Failure due to errors
170

Ships
171

Failure due to unexpected facts
172

NASA System Complexity
173

Causes of system failure
100%
Time
%offailure
Unknown phenomena
Known phenomena
Research
level
Design code
level
past present future
A
BB B
C
Humanerrors
174

HPLC vs LPHC EVENTS
HPLC
HIGH PROBABILITY
LOW CONSEQUENCES
LPHC
LOW PROBABILITY
HIGH CONSEQUENCES
COMPLEXITY:
Nonlinear Behavior and
Structural Organization
PROBLEM
FRAMEWORK
Deterministic
Stochastic
QUALITATIVE /
DETERMINISTIC
ANALYSIS
QUANTITATIVE
PROBABILISTIC
ANALYSIS
PRAGMATIC
SCENARIOS
ANALYSIS
175

8 e 9 luglio 2010
EXPLOSIONS - ESPLOSIONI
http://www.francobontempi.org/handling.php
13 e 14 novembre 2008
FIRE - INCENDIO
http://www.francobontempi.org/handling_08.php
176

177
PEOPLE

VALUES

179

Nonaka-Takeuchi Concept
180

Nonaka & Takeuchi:
conoscenza esplicite e implicite
181

182

The spiral of Knowledge
183

184

185

186

187

188

189

190

191

192

193
DESIGN PROCESS AS
DECISION PROCESS

194

195

196
LIMITS

197

LIMITS
198

LIMITS
199

LIMITS
200

LIMITS
201

202

203

Reaching limits
204

S Curve
205

Dalian, June 2008 207
0
500
1000
1500
2000
2500
3000
3500
SPAN 1100 1298 1385 1410 1624 1991 3300
BISA
N-
VER
RAZZ
JIAN
GYN
HUM
BER
GRE
AT
AKA
SHI
MES
SINA

Lorenz
210

Mental Heritage
211

Bias
212

Hybrid Solution
213

214

215

216

217
SCALE EFFECTS

218

SCALEEFFECTS
219

Quebec Bridge
220

Quebec Bridge Failure
221

Chord Members
222

2nd Quebec Bridge
223

Dalian, June 2008 224
GLOBAL LEVEL
3300 m
Local level
200 m
Example: Size Effect

225
ERGONOMY

226

227

228

Interactions
229

230

231

232

Ciclodivita
233

8OPERATIVE ASPECTS OF DESIGN
234

INDEX
• The structure of design
• The organization of the design process
• Complexity
• System decomposition
• Analysis models vs. design models
235

236
THE STRUCTURE
OF DESIGN

237

238

239

Meccanica Strutturale
240

Ingegneria Strutturale
241

Processo di analisi
e processo di sintesi (1)
DATI
CALCOLO
RISULTATI
START
END
START
END
MODIFICA
K=K+1
K=0
DATI
K
CALCOLO
RISULTATI
K
TEST
SI’ NO
Pre-processing
Post-processing
242

Processo di analisi
e processo di sintesi (2)
START
END
MODIFICA
K=K+1
K=0
DATI
K
CALCOLO
RISULTATI
K
TEST
SI’ NO
ANALISI
SINTESI
243

244

245

246

247

248

249

250

Sviluppo top-down
copertura omogenea
approfondimento
251

Sviluppo bottom-up
copertura omogenea
sviluppo di
un filone
252

Sviluppo mixed
253

Direct and Inverse problems in
Structural Engineering

• A direct problem is an analysis problem: it consists in
the evaluation of the response of a structure
immersed in its design environment, i.e. under
assigned external actions and other boundary
conditions as constrains, in agreement with the
fulfilment of all the design constrains, by using a
suitable model.
• Inverse problems are, on the other hand, those for
which the structural response constitutes available
known data. the inverse problems can be so
classified:
1. Synthesis problems: given the actions and the
constraints, the structure is designed to obtain a
specific structural response;
2. Control problems: given a description for the
structure and the mandatory structural response, an
appropriate action to generate that response is
searched;
3. Identification problems: given both the actions and
the structural response, the model is looked for.

Data related to different
structural problems

Top-Down and Bottom-Up
approach for problem solving

aESEMPIO DI PROGETTO DI STRUTTURE
PRECOMPRESSE
258

Strutture precompresse
Problema diretto (analisi)
• Dato il tiro del cavo di
precompressione
• date le eccentricità
del cavo
trovare
• il diagramma del
momento dovuto alla
precompressione.
Problema inverso
(progetto)
• Dato il diagramma
del momento (dovuto
ai carichi esterni)
trovare
• il tiro del cavo di
precompressione
• e le eccentricità del
cavo nelle varie
sezioni.

ANALISI:
dato il tiro del cavo
e le sue eccentricità
si ricava il diagramma del
momento

PROGETTO:
dato il diagramma del
momento (esterno)
trovare il tiro del cavo
e le sue eccentricità
in modo da annullarlo
momento

Reti neurali (2)
DIAGRAMMA
DEL MOMENTO
TIRO DEL CAVO
ECCENTRICITA’

bESEMPIO DI IDENTIFICAZIONE STRUTTURALE
267

Tiro cavi all'ancoraggio
115000
120000
125000
130000
135000
140000
600 1100 1600 2100 2600 3100
Tempo (s)
Tiro(Ton)
Sponda siciliana, lato nord Sponda calabrese, lato nord
Sponda siciliana, lato sud Sponda calabrese, lato sud
AXIAL FORCE IN THE MAIN CABLES (1)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
FB 268

Tiro cavi all'ancoraggio
115000
120000
125000
130000
135000
140000
600 1100 1600 2100 2600 3100
Tempo (s)
Tiro(Ton)
Sponda siciliana, lato nord Sponda calabrese, lato nord
Sponda siciliana, lato sud Sponda calabrese, lato sud
AXIAL FORCE IN THE MAIN CABLES (2)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
Vento = f(s,t)
FB 269

Hierarchical damage identification strategy
0,0
0,5
1,0
1,5
2,0
0 20 40 60 80
Damage detection
Identification of the
portion of the deck
element
STEP 1:
DAMAGE DETECTION
IDENTIFICATION OF
THE AREA
STEP 2:
IDENTIFICATION OF
THE ELEMENT
QUANTIFICATION OF
THE DAMAGE

Step 1a: approximation of the response
time-history using neural networks
Initial architecture
of the network
4 inputs + 4 hidden units
Measure of network
performance
 
N
wE
ERMS
*
2

Response time
history in sensor
#m
ktf  2tf tf1tf 1tf
Structural system
Ambient excitation
...
...

0
0,2
0,4
0,6
0,8
1
600 1100 1600 2100 2600time
Uz
Training Test A Test B Test C
Step 1a: example – vertical displacement

testA
0,2
0,4
0,6
0,8
1
0 25 50 75 100time
Uz
testA
NN
testB
0,2
0,4
0,6
0,8
1
0 25 50 75 100time
Uz
testB
NN
testC
0,2
0,4
0,6
0,8
1
0 25 50 75 100time
Uz
testC
NN
0
0,01
0,02
0,03
0,04
0,05
0,06
0 100 200 300 400time
err
Training TestA TestB TestC
LEARNEDBEHAVIOR

testD
0,4
0,6
0,8
1
0 25 50 75 100time
Uz
testD
NN
0
0,1
0,2
0,3
0,4
0 100 200 300 400 500time
err
Training TestA TestB TestC TestD
ANOMALOUSBEHAVIOR

Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
0,0
0,5
1,0
1,5
2,0
0 20 40 60 80
Damaged section
Error in function approximation in the undamaged sections
Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
DETAIL
Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
Training Undamaged
0,0
0,5
1,0
1,5
0 20 40 60 80
Step 1b: damage detection - identification of the area
Damage is intended as reduction
of stiffness in hangers, cables,
transverse beams.
- hangers: reduction from 5% to 80%
- cable: reduction from 1% to 10%
- transverse: reduction from 5% to 30%

...
...
Response time history
in sensor #n
 iMDp
1dtf 3tf 1tf2tf tf kntf  1ntf2ntf ntf 
ntnt fye  e 0
e > 0
undamaged
Anomalies in section #n
M i optimal model
Network model M i
i = i +1
Network model M i+1
yes no
   ?1 ii MDpMDp 
 1iMDp
stop
Damage in section #n
Structural
system
Ambient excitation
e > 0 in all
sections?
Restart training from f(t+dt)
yes
Go to
phase 2
training test
no
Anomaly in section
#m
Damage in section
#m
Go to
Phas
e 2
Continu
e in time
Response time history
in sensor #m
BASICBAYES

Damage in the transverse (wind excitation)
0,00
0,02
0,04
0,06
30% 10% 5%
Damage in the transverse (train excitation)
0,00
0,02
0,04
0,06
0,3 0,1 0,05
Damage in the cable (train excitation)
0,0
0,3
0,6
0,9
30% 1% 0,50%
Damage in the cable (wind excitation)
0,0
0,3
0,6
0,9
10% 1% 0,50%
Damage in the hanger (wind excitation)
0,00
0,02
0,04
80% 50% 10% 5%
Damage inthe hanger (trainexcitation)
0,00
0,02
0,04
50% 20% 10% 5%
Damage detection
using wind actions and traffic loads
hangers cables transverse
Mean values of the increment of the error with respect to the undamaged situation

1° finestra temporale
Vertical displacement
-0.006
-0.004
-0.002
0.000
0.002
0.004
0.006
400 450 500 550 600 650 700 750 800 850 900
t(s)
x(m)
Step 2: identification of the damaged element &
quantification of the damage
Response for train excitation
A
B
C
1
2
3
4
5
err A
err B
err C
D1
D2
D3
D4
D5
Error in function
approximation Location and
level of the
damage
400 examples are created for the training set considering
different scenarios

In order to give a global and intuitive representation of the results, two quantities have
been defined as follows:
 Location: it gives a measure of the error in the positioning of the damage
yt
yt
iloc


)(
where t is the vector of the target values and y is the vector coming from the network
model. If this quantity is equal to one the damage is well localized.
 Intensity: it gives a measure of the error in quantifying the level of damage
y
t
i )int(
If it is equal to one, the level of damage is correctly estimated.
Step 2: measures of identification of the element &
quantification of the damage

Intensity (optimized model)
0
1
2
3
0 10 20 30
Intensity (model 20 units)
0
1
2
3
0 10 20 30
Location (optimized model)
0,0
0,4
0,8
1,2
0 10 20 30
Location (model 20 units)
0,0
0,4
0,8
1,2
0 10 20 30
Test: comparison of location and intensity
70% 90%
50% 68%
LOCATION 20 UNITS
INTENSITY 11 UNITS
LOCATION 11 UNITS
INTENSITY 20 UNITS

POSTERIOR FOR , 
TRAINING: OPTIMIZATION
w = wMAP?
?   DMEVDMEV ii 1
INFERENCE OF NEW DATA
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
,  = MP, MP
DATA PRE- PROCESSING
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
DATA POST PROCESSING
PROBABILISTIC MODEL
no
INPUT
CHOOSE INITIAL , 
INITIALIZE WEIGHTS w
RE-ESTIMATION OF , 
yes
n
o
Wγ 
yes
no
i= i+1
is 1,…,k
‘very large’?
k= k-1
yes
no
0,0
0,5
1,0
1,5
2,0
0 20 40 60 80
Damage detection
portion of the deck
element

282
THE ORGANIZATION
OF DESIGN PROCESS

Sicurezza in caso d’incendio
1
2
3
4
5
6
7
8
9
Strategie per
la gestione
dell'incendio
1
Prevenzione
2
Gestione
dell'evento
3
Gestione
dell'incendio
4
Gestione delle
persone e
dei beni
15
Difesa sul posto
16
Spostamento
17
Disposibilità
delle vie
di fuga
18
Far avvenire
il deflusso
19
Controllo
della quantità
di
combustibile
5
Soppressione
dell'incendio
10
Controllo
dell'incendio
attraverso il
progetto
13
Automatica
11
Manuale
12
Controllo dei
materiali
presenti
6
Controllo
del movimento
dell'incendio
7
Resistenza e
stabilità
strutturale
14
Contenimento
9
Ventilazione
8
1
2
3
4
5
6
7
8
9
Strategie per
la gestione
dell'incendio
1
Prevenzione
2
Gestione
dell'evento
3
Gestione
dell'incendio
4
Gestione delle
persone e
dei beni
15
Difesa sul posto
16
Spostamento
17
Disposibilità
delle vie
di fuga
18
Far avvenire
il deflusso
19
Controllo
della quantità
di
combustibile
5
Soppressione
dell'incendio
10
Controllo
dell'incendio
attraverso il
progetto
13
Automatica
11
Manuale
12
Controllo dei
materiali
presenti
6
Controllo
del movimento
dell'incendio
7
Resistenza e
stabilità
strutturale
14
Contenimento
9
Ventilazione
8
283

Stile della rappresentazione
grafica dei processi
AVANTI
AVANTI
PADRE
FIGLIO FIGLIO
LINEE
ENTRANTI
LINEE
USCENTI“NO”
“SI’”
284

285

286

287

288

289

290

291

292

293

294

295

296

297

Forward vs. Reverse
Engineering
298

299

Qualita’ documenti (1)
300

Qualita’ documenti (2)
301

Simboli base
302

Altri simboli
303

Decisioni e connessioni
304

305

306

307

308

309
COMPLEXITY

310

311

312

313

314

315

Geometric Complexity
316

317

318

319
COMPLEXITY DEFINITION
linear interactions nonlinear
loosecouplingstight
mechanical behavior
structuralorganization
319

320
FACTORS INFLUENCING
STRUCTURAL COMPLEXITY
NON LINEAR
BEHAVIOR
LINEAR

321
3300183 183777 627
960 3300 m 810
+77.00 m
+383.00 +383.00
+54.00
+118.00
+52.00 +63.00
3300183 183777 627
960 3300 m 810
+77.00 m
+383.00 +383.00
+54.00
+118.00
+52.00 +63.00
Dispositivi di Dissipazione
Comportamento del Suolo
Non Linearità di Materiale
Interfaccia Suolo-Struttura Non Linearità di Contatto
Pendini
Torri
Cavi Principali
Non Linearità Geometrica
NON LINEARITA’

322
FACTORS INFLUENCING
LOW
AMBIGUITY
UNCERTAINTY
HIGH
NON LINEAR
BEHAVIOR
LINEAR

323
3300183 183777 627
960 3300 m 810
+77.00 m
+383.00 +383.00
+54.00
+118.00
+52.00 +63.00
3300183 183777 627
960 3300 m 810
+77.00 m
+383.00 +383.00
+54.00
+118.00
+52.00 +63.00
Incertezze legate al modello strutturale
Incertezze legate alla modellazione dei carichi
Incertezze legate alla geometria ed ai materiali
INCERTEZZE

324
FACTORS INFLUENCING
LOW
AMBIGUITY
UNCERTAINTY
HIGH
TIGHT
COUPLING
INTERACTIONS
CONNECTIONS
LOOSE
NON LINEAR
BEHAVIOR
LINEAR

325
Interazione Struttura - Traffico
Interazione Struttura - Vento
Interazione Struttura - Terreno
INTERAZIONI

326
LIVELLO GLOBALE
3300 m
livello locale
200 m
N.B. 1 - EFFETTO SCALA

327
HUMANWARESOFTWARE
HARDWARE
PROGETTO
COSTRUZIONE
(MATERIALI – COMPONENTI)
COMPORTAMENTO
UMANO
N.B. 2

Fire, Heat Transfer, Structural and
Human Behavior Models.
328

329
SYSTEM DECOMPOSITION

330FB nov 05 330
ELEMENTI E COMPONENTI
STRUTTURALI
ORGANIZZAZIONE
Le relazioni stabili di funzione, funzionalità
e topologia che danno significato agli
elementi indipendentemente dalla loro specificità.
STRUTTURA
Elementi specifici che tramite le relazioni
strutturali formano una configurazione persistente nel
tempo
SISTEMA
Struttura durevole di elementi organizzati, che
viene osservata come unità che presenta
caratteristiche emergenti.

StructuralSystems
331

332

333

System Definitions
• ANSI/EIA-632-1999: "An aggregation of end products and enabling products to
achieve a given purpose."
• IEEE Std 1220-1998: "A set or arrangement of elements and processes that are
related and whose behavior satisfies customer/operational needs and provides for life
cycle sustainment of the products."
• ISO/IEC 15288:2008: "A combination of interacting elements organized to achieve
one or more stated purposes."
• NASA Systems Engineering Handbook: "(1) The combination of elements that
function together to produce the capability to meet a need. The elements include all
hardware, software, equipment, facilities, personnel, processes, and procedures
needed for this purpose. (2) The end product (which performs operational functions)
and enabling products (which provide life-cycle support services to the operational
end products) that make up a system."
• INCOSE Systems Engineering Handbook: “Homogeneous entity that exhibits
predefined behavior in the real world and is composed of heterogeneous parts that
do not individually exhibit that behavior and an integrated configuration of
components and/or subsystems."
• INCOSE: "A system is a construct or collection of different elements that together
produce results not obtainable by the elements alone. The elements, or parts, can
include people, hardware, software, facilities, policies, and documents; that is, all
things required to produce systems-level results. The results include system level
qualities, properties, characteristics, functions, behavior and performance. The value
added by the system as a whole, beyond that contributed independently by the parts,
is primarily created by the relationship among the parts; that is, how they are
interconnected."
334

Structure vs. Structural System
• This requires evolving from a simplistic
idealization of the structure as
“device for channeling loads”
to the idea of the structural system,
intended as
“a set of interrelated components working
together toward a common purpose”.
335

337
MICROLIVELLO
variabili
MACROLIVELLOMESOLIVELLO
ELEMENTO
COMPONENTE
SOTTO
STRUTTURA
STRUTTURA
SISTEMA
STRUTTURALE
PONTE
Il MACROLIVELLO, che comprende il Ponte nella
sua globalità e i sistemi strutturali;
Il MESOLIVELLO, che include le diverse strutture
e sottostrutture che compongono il sistema
strutturale;
Il MICROLIVELLO, nel quale vengono descritti i
componenti delle sottostrutture e i rispettivi
elementi costituenti.
Per ciascun livello devono essere poi identificate e
definite le variabili di progetto.
Il complesso sistema strutturale deve essere scomposto,
ovvero sottostrutturato, in livelli crescenti di dettaglio:
Scomposizione Strutturale

338
SISTEMA
STRUTTURALE
PRINCIPALE
ZONE SPECIALI DI
IMPALCATO
SISTEMA DI
RITEGNO/SOSTEGNO
SISTEMA
STRUTTURALE
SECONDARIO
SISTEMA DI
SOSPENSIONE
IMPALCATO
CORRENTE
FONDAZIONI DELLE TORRI
ANCORAGGI
TORRI
SELLE
CAVI PRINCIPALI
PENDINI
CASSONI STRADALI
CASSONE FERROVIARIO
TRAVERSO
INTERNE
TERMINALI
SISTEMA STRUTTURALE
AUSILIARIO
STRADALE
FERROVIARIO
FUNZIONAMENTO
MANUTENZIONE
EMERGENZA
PONTE
MACROLIVELLO
MESOLIVELLO

339
Individuazione delle
VARIABILI di progetto
per ciascun elemento
Individuazione degli
ELEMENTI
per ciascun componente
Individuazione dei
COMPONENTI
di ciascuna sottostruttura
SOTTOSTRUTTURAZIONE
del sistema globale
per lo studio di dettaglio
delle singole prestazioni
SISTEMA DI
RITEGNO/SOSTEGNO
FONDAZIONI DELLE TORRI
ANCORAGGI
TORRI

340
Rappresentazione ipertestuale:
modellazione ad oggetti e rappresentazione
ad albero del problema strutturale

342
MAIN
STRUCTURAL
SYSTEM
AUXILIARY
STRUCTURAL
SYSTEM
SECONDARY
STRUCTURAL
SYSTEM
SPECIAL
DECK ZONES
BRIDGE
DECK
HIGHWAY SYSTEM
RAILWAY SYSTEM
OPERATION
MAINTENANCE
EMERGENCY
FOUNDATION OF TOWERS
TOWERS
ANCHORAGES
SUPPORTING
CONDITION
HIGHWAY BOX-GIRDER
CROSS BOX-GIRDER
RAILWAY BOX-GIRDER
INNER
OUTER
BRIDGE
SUPERSTRUCTURE
MACRO-LEVELS
MESO-LEVELS
MAIN CABLES
HANGERS
SUSPENSION
SYSTEM
SADDLES

344
Criterio meccanico: B-D regions
(c)

354

355
PERFORMANCE

• STRUTTURA – situazione puntuale:
definita nello spazio e nel tempo.
• SISTEMA STRUTTURALE – estensione:
– spaziale:
ambiente / contesto
sostenibilita’ / compatibilita’
– temporale:
ciclo di vita (life-cycle) - robustezza
Struttura / Sistema Strutturale
356

Structural System
357October 2012 www.francobontempi.org

• SISTEMA STRUTTURALE:
1. complessita’ del quadro prestazionale
(affidabilita’, sicurezza /security,
dependability)
2. CONCEZIONE STRUTTURALE
3. ANALISI STRUTTURALE:
motore del processo decisionale
strumenti generali e efficaci
Structural Analysis and Design
358

Macro-level Meso-level Micro-level
magnitudeofactions
359

DEPENDABILITY
ATTRIBUTES
THREATS
MEANS
RELIABILITY
FAILURE
ERROR
FAULT
FAULT TOLERANT
DESIGN
FAULT DETECTION
FAULT DIAGNOSIS
FAULT MANAGING
DEPENDABILITY
of
STRUCTURAL
SYSTEMS
AVAILABILITY
SAFETY
MAINTAINABILITY
permanent interruption of a system ability
to perform a required function
under specified operating conditions
the system is in an incorrect state:
it may or may not cause failure
it is a defect and represents a
potential cause of error, active or dormant
INTEGRITY
ways to increase
the dependability of a system
An understanding of the things
that can affect the dependability
of a system
A way to assess
the trustworthiness
of a system which allows
reliance to be justifiably placed
on the service it delivers
SECURITY
High level / active
performance
Low level / passive
performance
ATTRIBUTES
THREATS
MEANSMEANS
RELIABILITYRELIABILITY
FAILURE
ERROR
FAULT
FAULT TOLERANT
DESIGN
FAULT TOLERANT
DESIGN
FAULT DETECTIONFAULT DETECTION
FAULT DIAGNOSISFAULT DIAGNOSIS
FAULT MANAGINGFAULT MANAGING
DEPENDABILITY
of
STRUCTURAL
SYSTEMS
AVAILABILITY
SAFETY
MAINTAINABILITY
permanent interruption of a system ability
to perform a required function
under specified operating conditions
the system is in an incorrect state:
it may or may not cause failure
it is a defect and represents a
potential cause of error, active or dormant
INTEGRITY
ways to increase
An understanding of the things
that can affect the dependability
of a system
A way to assess
the trustworthiness
of a system which allows
reliance to be justifiably placed
on the service it delivers
SECURITY
High level / active
performance
Low level / passive
performance
361

362
HAZARD
IN-DEPTH
DEFENCE
HOLES DUE TO
ACTIVE ERRORS
HOLES DUE TO
HIDDEN ERRORS
362
Failure Path

Structural Design
363
WIND & TEMPERATURE
SOIL & EARTHQUAKE
ANTHROPICUSE
(highway&railway)
STRUCTURALBEHAVIOR
&
EXPECTEDPERFORMANCE
JUDGEMENT
&
DECISIONS
NEGOTIATION &
REFRAMING
No
STRUCTURAL
MODELING

Traditional design procedure
• The traditional design procedure that lead
to the “as built” construction are:
1) Formulation of the problem;
2) Synthesis of the solution;
3) Analysis of the proposed solution;
4) Evaluation of the solution performances;
5) Construction.

• Difficulties associated with this kind of approach
are evident. The “As Built” structure could be
different from the “As Designed” one, due to
different factors like fabrication mistakes or
unexpected conditions during the construction
phase, or also due to non appropriate design
assumptions. These last could create doubts about
the accuracy of the analysis results leading to a
predicted behavior which does not correspond to
the real one.
• One then can add:
6) Monitoring of the real construction;
7) Comparison between results from monitoring
and expected behaviour results;
8) Increase in the accuracy of expectation of the
future structural behaviour.

Further steps added considering
a monitoring system

9) Reformulation: development of advanced methods for
a more accurate description of the required behavior
and of the required performance;
10)Weak Evaluation: this methodology assumes that the
analysis is exact and that all the actions are known
exactly, from the probabilistic viewpoint;
11)Model improvement: the necessity connected with
the models improvement comes from experiences
based on monitoring, where expected and measured
behaviors on “as built” structures are compared;
12)Strong Evaluation: a third kind of evaluation becomes
possible when the improvement aims at assigning
more accurate values to the used parameters and to
define more accurate modelling hypothesis.

370
Functional Analysis/
Resources Allocation
- Decomposition to lower-level function
- Allocate performance
- Define functional interfaces
- Define functional architecture
Requirement
loop
Design loop
PROCESS
INPUT
Historic Analyses
Evolutive / Innovative
Design
Risk Management
PROCESS
OUTPUT
Synthesis
- Transform architecture
- Define alternative product concepts
- Define physical interfaces
- Define alternative product
and process solutions
Requirements Analysis
- Analyze missions and enviroments
- Identify functional requirements
- Define performance and design
constraint requirement
System
Modeling
And
Analysis

371
ANALYSIS MODELS vs.
DESIGN MODELS

372
STRATEGY #0:
DECOMPOSITION

373
STRUCTURAL
QUALITY
- design life
- railway
runability
- highway
runability
- free channel
- robustness
- durability
- management
GLOBAL
GEOMETRY
AND
TOPOLOGY
TOPOLOGY
- suspension system
- towers
- towers foundation
- anchor system
- main deck
- deck landing
- ...
GLOBAL GEOMETRY
- main span
- sx span
- dx span
SECTIONAL GEOMETRY
- continuous girder sections
- transverse section
- main cables
- hangers
- towers
- secondary elements
MATERIALS
CHARACTERISTICS
- girders
- cables
SYNTHESIS OF
STRUCTURAL
SOLUTION
AND
DOCUMENTATION
BOUNDARY
CONDITIONS
CONSTRAINTS:
rigid and elastic
constraints,
imposed
displacements
NATURAL
ACTIONS
- temperature
- wind
- earthquake
ANTROPIC
ACTIONS
a) permanent
loading
system
b) variable
- railway
- highway
c) accidental
CONVENTIONALMODELING:
QUASISTATICREPRESENTATION
BASIC STRUCTURAL
CONFIGURATION
PARAMETERS
- individuation
- definition
- uncertainty
- description
- bounding
GLOBAL
MODELING
- 2D
- 3D
MODELING WITH
DYNAMIC INTERACTION
ALTERNATIVE STRUCTURAL
CONFIGURATIONS
GLOBAL
OPTIMIZATION
- topology
- morphology
- parametric
LOCAL
OPTIMIZATION
- girders section
- transverse
section
- restraint zone
EXPERT AND
FIXED CHOICES
MEASURES
a) qualitative
b) materials volumes
c) serviceability
- modal characteristics
- deflections
- deformations
- reversibility
d) collapse scenarios
- collapse characteristics
- robustness
e) accidental scenarios
- configurations
- risks
DETAILED
MODELING
EXTENDED
MODELING
1
2 3
4
5
6
7
Numerical Modeling for the
Structural Analysis and Design of
MESSINA STRAIT BRIDGE:
subdivision and development of activities.
FB - june 6, 2005 / franco.bontempi@uniroma1.it
373

377
Super
Controllore
Problema Risultato
Solutore #1
Solutore #2
Voting System
STRATEGY #3: REDUNDANCY

378
STRUCTURAL
MODELING
CODE
Global Frame Models Local Models
Frame
Work
Substruct-
ured Models
STRUCTURAL
MODELING
CODE
Global Frame Models Local Models
Frame
Work
Substruct-
ured Models
structural configurations
specificity of the modeling
commercial
codes

379
Str
o N
GER
www.stronger2012.com

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