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!