2015 corso dottorato OTTIMIZZAZIONE STRUTTURALE franco bontempi
Appunti del corso di dottorato: Ottimizzazione Strutturale / Structural Optimization - parte II -...
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Ottimizzazione Strutturale [email protected] 1 Franco Bontempi Ordinario di Tecnca delle Costruzioni Facolta’ di Ingegneria Civile e Industriale Sapienza Universita’ di Roma Introduzione alla OTTIMIZZAZIONE STRUTTURALE (parte II)
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Appunti del corso di dottorato: INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE IIa parte Lezione del 28 maggio 2014 Lecture of the Ph.D. Course on STRUCTURAL OPTIMIZATION May, 28, 2014
Transcript of Appunti del corso di dottorato: Ottimizzazione Strutturale / Structural Optimization - parte II -...
Ottimizzazione Strutturale
1
Franco Bontempi
Ordinario di Tecnca delle Costruzioni
Facolta’ di Ingegneria Civile e Industriale
Sapienza Universita’ di Roma
Introduzione alla
OTTIMIZZAZIONE STRUTTURALE (parte II)
Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
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)
9
STRATEGY #1: SENSITIVITY
governance of priorities
11
STRATEGY #2: BOUNDING
behavior governance
p
(p)
p
(p)
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).
Ottimizzazione Strutturale
13
Simulation & Approximation
of the response (≈ surrogate)
Ottimizzazione Strutturale
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The nature of optimum (2)
Ottimizzazione Strutturale
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A sub-optimal solution
to a problem is one
that is less than perfect.
Slack situation: loose and not pulled tight.
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. Ottimizzazione Strutturale
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).
Ottimizzazione Strutturale
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Ottimizzazione Strutturale
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.
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.
Basic version (2)
Points for SA
• Diameter of the search graph
• Transition probabilities
• Acceptance probabilities
• Efficient candidate generation
• Barrier avoidance
• Cooling schedule
Ottimizzazione Strutturale
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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.
Remarks
;-)
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.
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.
Ottimizzazione Strutturale
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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
Cic
lo su
lle g
en
era
zio
ni
Operatori
genetici
Cic
lo su
lle p
op
ola
zio
ne
Nuova
popolazione
Fine? No
Si
Probabilità di crossover: 80%
Probabilità di mutazione: 1%
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
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Tensile crack phenomena in HCS
(splitting, bursting, spalling).
Ottimizzazione Strutturale
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Cross-section of the reference HCS
and numerical model
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Tensile deformations in the vertical
directions for the spalling effect
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The binary coding of the geometry
characteristics of the section
Ottimizzazione Strutturale
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• 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.
Ottimizzazione Strutturale
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Original values values obtained
after the optimization process
Ottimizzazione Strutturale
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1° Step
2° Step
Limit States
Service Limit States Ultimate Limit States
Prestressed Continuous Beam
Elements of nonlinear formulation
Equilibrium Equations
Nominal behavior
Level of uncertainty
Uncertainty
α - level
Random / Optimized Sampling
Cujaba River Bridge
Cujaba River Bridge
Ultimate Limit States (ULS)
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.
Ottimizzazione Strutturale
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Dissipation devices
Soil behaviorMaterial
Soil-Structure interface Contact
Support system
Pylon
Cable system
Geometrical
Soil-Structure
Response
Vehicle-StructureWind-Structure
Nonlinearities
Interactions
Action
Uncertainties
Ottimizzazione Strutturale
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Dependability attributes threats,
means and their interactions.
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Performance in relation to the
return periods of the actions.
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S N
Geometry of the long-span
suspension bridge considered.
Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
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Loading systems considered in the
genetic algorithm analysis.
Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
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Variables considered for the
definition of the loading system.
Ottimizzazione Strutturale
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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:
Ottimizzazione Strutturale
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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:
Ottimizzazione Strutturale
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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. Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
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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
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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.
Ottimizzazione Strutturale
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• 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%.
Ottimizzazione Strutturale
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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.
Ottimizzazione Strutturale
146
INDEX
• Knowledge
• People
• Design process as a decision process
• Limits
• Scale effects
• Ergonomy
Ottimizzazione Strutturale
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CONOSCENZA
RICHIESTA
DA UN PROGETTO
EVOLUTIVO
CONOSCENZA
RICHESTA
DA UN PROGETTO
INNOVATIVO
BASE DI
CONOSCENZA
ATTUALE
La crescita di conoscenze
Ottimizzazione Strutturale
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Knowledge Growth Process
KNOWLEDGE
REQUIRED
BY AN EVOLUTIVE
DESIGN
NEW KNOWLEDGE
REQUIRED BY
AN INNOVATIVE
DESIGN
ACTUAL
KNOWLEDGE BASIS
157Ottimizzazione Strutturale
Ottimizzazione Strutturale
161
ST
RU
TT
UR
E C
ON
CO
MP
OR
TA
ME
NT
O P
ER
FO
RM
A
Ottimizzazione Strutturale
162
ST
RU
TT
UR
E C
ON
CO
MP
OR
TA
ME
NT
O V
ET
TO
RIA
LE
Ottimizzazione Strutturale
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ST
RU
TT
UR
E C
ON
CO
MP
OR
TA
ME
NT
O S
EZ
ION
ALE
Ottimizzazione Strutturale
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ST
RU
TT
UR
E C
ON
CO
MP
OR
TA
ME
NT
O D
I S
UP
ER
FIC
IE
Dalian, June 2008 167
Causes of system failure
100%
Time
% o
f fa
ilure
Unknown phenomena
Known phenomena
Research
level
Design code
level
past present future
A
BB B
C
Hu
man
err
ors
Ottimizzazione Strutturale
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HPLC vs LPHC EVENTS
HPLCHIGH PROBABILITY
LOW CONSEQUENCES
LPHCLOW PROBABILITY
HIGH CONSEQUENCES
COMPLEXITY:Nonlinear Behavior andStructural Organization
PROBLEMFRAMEWORK
Deterministic
Stochastic
QUALITATIVE /DETERMINISTIC
ANALYSIS
QUANTITATIVEPROBABILISTIC
ANALYSIS
PRAGMATICSCENARIOS
ANALYSIS
Ottimizzazione Strutturale
175
8 e 9 luglio 2010
EXPLOSIONS - ESPLOSIONIhttp://www.francobontempi.org/handling.php
13 e 14 novembre 2008
FIRE - INCENDIOhttp://www.francobontempi.org/handling_08.php
176
Nonaka & Takeuchi:
conoscenza esplicite e implicite
Ottimizzazione Strutturale
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Dalian, June 2008 206
Dalian, June 2008 207
0
500
1000
1500
2000
2500
3000
3500
SPAN
SPAN 1100 1298 1385 1410 1624 1991 3300
BISA
N-
VER
RAZZ
JIAN
GYN
HUM
BER
GRE
AT
AKA
SHI
MES
SINA
Dalian, June 2008 208
Dalian, June 2008 209
Dalian, June 2008 224
GLOBAL LEVEL
3300 mLocal level
200 m
Example: Size Effect
INDEX
• The structure of design
• The organization of the design process
• Complexity
• System decomposition
• Analysis models vs. design models
Ottimizzazione Strutturale
235
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
TESTSI’ NO
Pre-processing
Post-processing
Ottimizzazione Strutturale
242
Processo di analisi
e processo di sintesi (2)
START
END
MODIFICA
K=K+1
K=0
DATI
K
CALCOLO
RISULTATI
K
TESTSI’ NO
AN
AL
ISI
SIN
TE
SI
Ottimizzazione Strutturale
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Sviluppo top-down
copertura omogenea
approfondimento
Ottimizzazione Strutturale
251
Sviluppo bottom-up
copertura omogenea
sviluppo di
un filone
Ottimizzazione Strutturale
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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
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 cavoe le sue eccentricità
si ricava il diagramma del momento
PROGETTO:dato il diagramma del momento (esterno)
trovare il tiro del cavoe le sue eccentricità
in modo da annullarlo momento
Reti neurali (1)
Reti neurali (2)
DIAGRAMMA DEL MOMENTO
TIRO DEL CAVOECCENTRICITA’
Discretizzazione
Tiro cavi all'ancoraggio
115000
120000
125000
130000
135000
140000
600 1100 1600 2100 2600 3100
Tempo (s)
Tir
o (
To
n)
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)
Tir
o (
To
n)
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
Identification of the
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
wEERMS
*2
Response time
history in sensor
#m
ktf 2tf tf1tf 1tf
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
LE
AR
NE
D B
EH
AV
IOR
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
AN
OM
ALO
US
BE
HA
VIO
R
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
1dtf 3tf 1tf2tf tf kntf 1ntf2ntf 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
1iMDp
stop
Damage in section #n
Structural
system
Ambient excitation
e > 0 in all
sections? Restart training from f(t+dt)
yes
Go to
phase 2training 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
BA
SIC
BA
YE
S
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 in the hanger (train excitation)
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
ytiloc
)(
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
ti )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
oWγ
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
Identification of the
portion of the deck
Identification of the
element
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
4Gestione 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
10Controllo
dell'incendio
attraverso il
progetto
13
Automatica
11
Manuale
12
Controllo dei
materiali
presenti
6Controllo
del movimento
dell'incendio
7Resistenza 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
4Gestione 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
10Controllo
dell'incendio
attraverso il
progetto
13
Automatica
11
Manuale
12
Controllo dei
materiali
presenti
6Controllo
del movimento
dell'incendio
7Resistenza e
stabilità
strutturale
14
Contenimento
9
Ventilazione
8Ottimizzazione Strutturale
283
Stile della rappresentazione
grafica dei processi
AVANTI
AV
AN
TI
PADRE
FIGLIO FIGLIO
LINEE
ENTRANTI
LINEE
USCENTI“NO”
“SI’”
Ottimizzazione Strutturale
284
319
COMPLEXITY DEFINITION
linear interactions nonlinear
loose
c
ou
pli
ng
stight
mechanical behavior
str
uctu
ral o
rgan
izati
on
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 SuoloNon Linearità di Materiale
Interfaccia Suolo-Struttura Non Linearità di Contatto
Pendini
Torri
Cavi Principali
Non Linearità Geometrica
NON LINEARITA’
322
FACTORS INFLUENCING
STRUCTURAL COMPLEXITY
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
STRUCTURAL COMPLEXITY
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 mlivello locale
200 m
N.B. 1 - EFFETTO SCALA
327
HUMANWARESOFTWARE
HARDWARE
PROGETTO
COSTRUZIONE
(MATERIALI – COMPONENTI)
CO
MP
OR
TA
ME
NT
O
UM
AN
ON.B. 2
Fire, Heat Transfer, Structural and
Human Behavior Models.
328
Ottimizzazione Strutturale
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.
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."
Ottimizzazione Strutturale
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”.
Ottimizzazione Strutturale
335
336
337
MIC
RO
LIV
EL
LO
variabili
MA
CR
OL
IVE
LL
OM
ES
OL
IVE
LL
O
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
341
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
ANCHORAGESSUPPORTING
CONDITION
HIGHWAY BOX-GIRDER
CROSS BOX-GIRDER
RAILWAY BOX-GIRDER
INNER
OUTER
BRIDGE
SUPERSTRUCTURE
MACRO-LEVELS
MESO-LEVELS
MAIN CABLES
HANGERS
SUSPENSION
SYSTEM
SADDLES
FRANCO BONTEMPI 343
344
Criterio meccanico: B-D regions
(c)
345
346
347
348
349
350
351
352
353
• 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
ma
gn
itu
de
of a
ctio
ns
Ottimizzazione Strutturale
359
RESILIENCE
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 dependability of a system
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
the dependability of a system
An understanding of the things
that can affect the dependability
of a system
A way to assess
the dependability of a system
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
Ottimizzazione Strutturale
361
362
HAZARD
IN-D
EPTH
DEFE
NCE
HOLES DUE TO
ACTIVE ERRORS
HOLES DUE TO
HIDDEN ERRORS
362
Failure Path
Structural Design
Ottimizzazione Strutturale
363
WIND & TEMPERATURE
SOIL & EARTHQUAKE
AN
TH
RO
PIC
US
E
(hig
hw
ay
& r
ail
wa
y)
ST
RU
CT
UR
AL
BE
HA
VIO
R
&
EX
PE
CT
ED
PE
RF
OR
MA
NC
E
JUDGEMENT
&
DECISIONS
NEGOTIATION &
REFRAMINGNo
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.
Traditional design procedure
• 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
Performance-Based Design
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.
Ottimizzazione Strutturale
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
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
CO
NV
EN
TIO
NA
L M
OD
ELIN
G:
QU
AS
I ST
AT
IC R
EP
RE
SE
NT
AT
ION
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
12 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 / [email protected] 373
374
375
STRATEGY #1: SENSITIVITY
376
STRATEGY #2: BOUNDING
377
Super
ControlloreProblema 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 modelingcommercial
codes
