Artificial Neural Networks for Optimization on Large-Scale Structural Acoustics Models

119 Pages·2017·8.18 MB·English

by  Desislava Stoyanova

IT 17 073
Examensarbete 30 hp
Oktober 2017
ANN for Optimization on Large-Scale
Structural Acoustics Models
Desislava Stoyanova
Institutionen för informationsteknologi
Department of Information Technology

Abstract
ANN for Optimization on Large-Scale Structural
Acoustics Models
Desislava Stoyanova

Teknisk- naturvetenskaplig fakultet
UTH-enheten Optimization of transformer design is a challenging task which defines the dimensions
of all the transformer parts, based on a given specification in order to achieve better
Besöksadress: operating performance. The mechanical force distributions, as a result of the
Ångströmlaboratoriet
transformer operation, make the structure vibrate at twice the network frequency,
Lägerhyddsvägen 1
Hus 4, Plan 0 and ultimately lead to noise emission from the outer surface of the tank. In this paper,
an artificial intelligence technique is proposed for transformer noise data prediction as
Postadress: an optimized alternative to the finite-element method with multi-physics capabilities.
Box 536
The technique uses a feedforward artificial neural network and the backpropagation
751 21 Uppsala
of error learning rule for predicting the noisy data, along with a finite-element model

Telefon: for computing a training data set. The method considers two well-known
018 – 471 30 03 backpropagation algorithms, Levenberg–Marquardt and Bayesian Regularization, and
while both of them appear to be extremely efficient when it comes to execution time,
Telefax:
Bayesian Regularization presents considerably higher accuracy. The level of accuracy
018 – 471 30 00
as well as the fast execution time makes the application of artificial neural networks
Hemsida: for finite-element model optimization a viable and efficient approach for industrial use.

http://www.teknat.uu.se/student
Handledare: Anders Daneryd
Ämnesgranskare: Maya Neytcheva
Examinator: Mats Daniels
IT 17 073
Tryckt av: Reprocentralen ITC

Acknowledgement
I would first like to thank my thesis supervisor Anders Daneryd of the Power Devices Depart-
ment at ABB Corporate Research Center. The door of his office was always open whenever
I ran into a trouble spot or had a question about my research or writing. He consistently
allowed this paper to be my own work and inspired me to do what I am extremely passionate
about, but steered me in the right direction whenever he thought I needed it.
I would also like to acknowledge Prof. Maya Neytcheva of the Department of Information
Technology,DivisionofScientificComputingatUppsalaUniversityasthesecondreaderofthis
thesis, and I am gratefully indebted to her for her very valuable comments on this thesis.
I must also express my very profound gratitude to Camila Medina and Monika Miljanovi´c for
providing me with unfailing support and continuous encouragement throughout the process
ofresearchingandwritingthisthesis. Thankyouforthebreakfasts,coffee-breaksandadvices
– you were always there with a word of encouragement or listening ear. You should know
that your support and encouragement were worth more than I can express on paper. This
accomplishment would not have been possible without you.
Finally,Iwouldliketothankmyfamilyforsupportingmethroughoutthelastcoupleofyears,
financially, practically and with moral support, especially my grandparents. Mum, you knew
it would be a long and sometimes bumpy road, but you encouraged and supported me along
the way.
To dad who was often in my thoughts on this journey – you are missed.
Thank you!
Desislava Stoyanova
Västerås, June 2017
v

„
By far, the greatest danger of Artificial Intelligence
is that people conclude too early that they
understand it.
— Eliezer Yudkowsky
(Writer)
vii

Contents
1 Introduction 1
1.1 Motivation and Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Artificial Neural Networks 5
2.1 Components of the Neural Network . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Neuron Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Neural Network Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Feedforward Neural Networks . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Recurrent Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Completely Linked Networks . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 The bias Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.5 Number of Layers and Neurons . . . . . . . . . . . . . . . . . . . . . . 9
2.2.6 Setting Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.7 Pruning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Order in which the neuron activations are calculated . . . . . . . . . . . . . . 10
2.3.1 Synchronous Activation . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3.2 Asynchronous Activation . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Communication with the world outside the network. . . . . . . . . . . . . . . 11
2.5 Learning and training samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.1 Paradigms of Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Training patterns and teaching input . . . . . . . . . . . . . . . . . . . 13
2.5.3 Learning curve and error measurement . . . . . . . . . . . . . . . . . . 14
2.5.4 Gradient Optimization Procedures . . . . . . . . . . . . . . . . . . . . 15
2.5.5 The Hebbian Learning Rule . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 The perceptron, backpropagation and its variants . . . . . . . . . . . . . . . . 17
2.6.1 Single Layer Perceptron (SLP) . . . . . . . . . . . . . . . . . . . . . . . 18
2.6.2 Multi Layer Perceptron (MLP) . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.3 Backpropagation (BP) of error learning rule . . . . . . . . . . . . . . . 21
2.6.4 Resilient BP of error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6.5 Extensions of BP besides the Resilient BP . . . . . . . . . . . . . . . . . 26
2.7 Radial Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7.1 Components and structure of an RBF network . . . . . . . . . . . . . . 29
2.7.2 Processing of information in the RBF neurons . . . . . . . . . . . . . . 29
2.7.3 Training an RBF network. . . . . . . . . . . . . . . . . . . . . . . . . . 30
ix
2.7.4 Comparison between MLPs and RBF networks . . . . . . . . . . . . . . 30
2.8 Recurrent perceptron-like networks . . . . . . . . . . . . . . . . . . . . . . . . 31
2.8.1 Jordan networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.8.2 Elman networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.8.3 Training recurrent perceptron-like networks . . . . . . . . . . . . . . . 32
2.9 Self-organizing feature maps. . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.9.1 Structure of a SOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.9.2 Training of a self-organizing map . . . . . . . . . . . . . . . . . . . . . 35
3 Related Work 39
3.1 Top-oil temperature prediction with neural networks . . . . . . . . . . . . . . 39
3.1.1 Feedforward neural network . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.2 Elman recurrent neural network . . . . . . . . . . . . . . . . . . . . . 43
3.1.3 Performance, results and discussion . . . . . . . . . . . . . . . . . . . . 43
3.2 Neural network usage in structural crack detection . . . . . . . . . . . . . . . 45
4 3DoF Model of Vibrating System 47
4.1 Description of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Equations of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Matrix form of equations of motion . . . . . . . . . . . . . . . . . . . . 48
4.3 Train an artificial neural network . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3.1 Description of the training procedures . . . . . . . . . . . . . . . . . . 50
4.3.2 Performance of the training procedures . . . . . . . . . . . . . . . . . . 50
4.4 Further notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Multimillion DoF Model 57
5.1 Description of the data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 ANN Training Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3 Reducing the size of the data set . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.4 Stressing the data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 Further notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Conclusion 73
6.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Bibliography i
A Tables iii
B Figures vi
B.1 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
B.2 ANN training results using trainlm . . . . . . . . . . . . . . . . . . . . . . . . x
B.3 ANN training performance after stressing the data set values by 40% . . . . . xv
B.4 ANN training performance after stressing the data set values by 50% . . . . . xvii
x