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Exemplary application of Artifficial Neural
Networks (ANNs) for load capacity
assessment of steel girders with defects
Mieszko KUŻAWA January 5th 2016
Faculty of Civil Engineering
Plate girder parameters:
• Geometry parameters:
• h
• a/h,
• t
• Defect parameters:
• Type – material loses of web
• Location – P1-P9
• Extent – 1/9 area of panel
• Intensity – 100%
a a
L
tfh
tf
ts
ts
ts
tw
Side view
bf
Cross-section
A-A
Lt
P1 P2 P3
P4P5
holeP6
P7 P8 P9
P1P2P3
P4P5
hole
P7P8P9
P5
A
A
D
• Using FEM evaluate the impact of the specified type of defect on the critical load-bearing capacity of given structure taking into account the variability of defects parameters as well as its basic geometrical parameters.
• Perform representation of knowledge related to imapct of defects on the critical load-bearing capacity of given structure by means of ANNs
Scope of the exercise
Artificial Neural Networks (ANNs)
ANNs are a family of statistical (pattern) learning models inspired by biological neural
networks (the central nervous systems of animals, in particular the brain).
ANNs are used to estimate or approximate functions that can depend on a large number
of inputs and are generally unknown.
ANNs are generally presented as systems of interconnected "neurons" which exchange
messages between each other.
The connections have numeric weights that can be tuned based on experience, making
neural nets adaptive to inputs and capable of learning.
The example of very simple ANN
• Let 𝒙𝟏, 𝒙𝟐, 𝒙𝒊, … 𝒙𝒏 be the ANN’s inputs and 𝒚𝟏, 𝒚𝟐, 𝒚𝒊, … 𝒚𝒏 be the desired outputs of the network .
• A set of weights 𝒘𝟏, 𝒘,𝒘𝒊, …𝒘𝒏 can be selected to help relate the inputs to the outputs.
• The linear combination of inputs and weights is called net:
𝑛𝑒𝑡 = 𝑤𝑖 ∙
𝑛
𝑘=0
𝑥𝑖
• The network output is then defined by means of activation function:
𝑓 𝑛𝑒𝑡 =
𝑦1𝑦2𝑦𝑖𝑦𝑚
Activation functions f(net)
Defining
procedure
of ANN
Basic parameters of applied NN:
• Type: multilayer perceptron,
• No of layers: 3,
• Activation function: sigmiodal / sigmoidal symmetric,
• Training algorithm: incremental supervised back-propagation
method.
hw
tf
Vult
tw
bf
warstwa wejściowa
warstwy pośrednie
warstwa wyjściowa
Oznaczenia:
klasa
obciążeń
Lt
V(x/Lt)
M(x/Lt)
schemat
statyczny Input layer
Hidden layer
Output layer
Architecture of design ANN
ANNs input
• Geometry parameters:
• α = a/h
• λ = h/t,
• Defects parameters:
• P1 (defect intensity in P1),
• P2,
• ….
• P9,
Output to be represented by ANNs:
• Damage indicator ηw specyfing the
percentage reduction of plate
girder’s buckling load capacity due
to occured defect.
%100
cr
d
crcr
P
PP
where:
Pcr – minimum critical (buckling)
load calculated for intact
structure.
Pcrd – minimum critical (buckling)
load calculated for damaged
structure.
Values of damage indicators, calculated using buckling analysis for single defect localized in
consecutive web areas Pi, to be represented by ANNs
Applied software for ANN design
Cross platform Visual GUI Tool for the Fast Artificial Neural
Network Library
Fast Artificial Neural
Network Library is a free
open source neural
network library, which
implements multilayer
artificial neural networks in
C with support for both
fully connected and
sparsely connected
networks.
URL:
http://code.google.com/p
/fanntool/
Comparison of desired (obtained using FEM) and calculated by means of different ANNs damaged indicators
FEM analysis
Thank you for your
attention!