A General Neural Network Model for Estimating
Telecommunications Network Reliability
Journal: IEEE Transactions on Reliability, Vol. 58, No. 1, March 2009.
Authors: Fulya Altiparmak, Berna Dengiz, and Alice E. Smith, Senior Member of IEEE.
Instructor : Frank Yeong-Sung Lin, Ph.D.
Students: D96725001 陳君銘, D97725002 黃健誠
2009-06-08
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Author
Home page for Professor Smith:
http://www.eng.auburn.edu/~aesmith/
Alice E. Smith is Professor and Chair of the Industrial and
Systems Engineering Department at Auburn University.
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References
D. W. Coit and A. E. Smith, “Solving the redundancy allocation problem using a
combined neural network/genetic algorithm approach,” Computers and Operations
Research, vol. 23, no. 6, pp.515–526, 1996.
B. Dengiz, F. Altiparmak, and A. E. Smith, “Efficient optimization of all-terminal
reliable networks, using an evolutionary approach,” IEEE Trans. on Reliability, vol.
46, pp.18–26, 1997.
C. Srivaree-ratana, and A. E. Smith, “Estimating All-Terminal Network Reliability
Using a Neural Network,” Proceedings of the 1998 IEEE International Conference
on Systems, Man, and Cerbernetics, San Diego, CA, 1998, vol. 5, pp.4734-4740.
C. Srivaree-ratana, A. Konak, and A. E. Smith, “Estimation of All-terminal network
reliability using an artificial neural network,” Computers and Operations Research,
vol. 29, pp. 849–868, 2002.
F. Altiparmak, B. Dengiz, and A. E. Smith, “Reliability estimation of computer
communication networks: ANN models,” Proceedings Eighth IEEE International
Symposium on Computers and Communication (IEEE ISCC’03), Antalya-Kemer,
Turkey, 2003, vol. 2, pp.1353–1358.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Reliability(可靠度)
The Advisory Group on Reliability of Electronic Equipment
(AGREE), established on August 21, 1952.
AGREE, “Reliability of Military Electronic Equipment,”
Advisory Group on the Reliability of Electronic Equipment
(AGREE), U.S. Government Printing Office, Washington, DC.
Foundation work on reliability theory, June 4, 1957.
Reliability is defined as the ability of a system or component to
perform its required functions under stated conditions for a
specified period of time.
「產品於既定的時間內，在特定的使用環境條件下，執行
特定的功能，成功完成工作目標的機率」。
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Abstract
This paper proposes a new encoding method for using neural
network models to estimate the reliability of
telecommunications networks with identical link reliabilities.
Drawback of previous approaches:
Long vector length of the inputs required to represent the
network link architecture.
The specificity of the neural network model to a certain
system size.
This study demonstrates both the precision of the neural
network estimate of reliability, and the ability of the neural
network model to generalize to a variety of network sizes
(small to large scale communications networks).
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Introduction
The exact calculation of all-terminal network reliability is an
NP-hard problem, with computational effort growing
exponentially with the number of nodes and links in the
network.
There exists no algorithm with a polynomial time to compute
all-terminal network reliability.
Because of the impracticality of calculating all-terminal
network reliability for networks of moderate to large size,
Monte Carlo simulation methods to estimate network
reliability and upper and lower bounds to bound reliability
have been used as alternatives.
Valiant, L.G., “The Complexity of Enumeration and Reliability Problems,” SIAM Journal on
Computing, Vol. 8, Issue 3, pp.410-421, 1979.
Provan, J. S. and M. O. Ball, “The complexity of counting cuts and of computing the probability that a
graph is connected,” SIAM Journals on Computing, Vol. 12, Issue 4, pp. 777–788, 1983.
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Introduction (cont’d)
In this study, a generalized artificial neural network (General
ANN) is proposed to estimate all-terminal network reliability
for networks.
This study use an input encoding that, unlike previous
approaches, does NOT rely on a vector of all possible links
between nodes.
Advantages:
The first is that a single ANN model can be used for
multiple network sizes and topologies.
The second advantage is that the input information to the
ANN is compact, which makes the method tractable, even
for large sized networks.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Artificial Neural Network
An ANN has the ability to learn relationships between given
sets of input and output data by changing the weights.
This process is called: training the ANN (Back Propagation).
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Artificial Neural Network (cont’d)
The performance of the ANN model is a function of several
design parameters such as the number of hidden layers, the
number of hidden neurons in each hidden layer, the size of the
training set, and the training parameters.
The technique of k-fold cross validation is particularly useful
because it makes the most of a limited size data set.
The data set is divided (randomly) into multiple sets (cross
validation would include sets, where is the data set size, while
grouped cross validation would include sets).
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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The General ANN Method
This study identified compact, easily calculated measures of
network connectivity and reliability as the candidate set of
inputs:
ND: of each node, 0 if the node is not present
NDmin: minimum node degree of the network
NDmed: median node degree of the network
NDmax: maximum node degree of the network
LR: link reliability
NL: number of links
C: link connectivity
UB: network reliability upper bound
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The General ANN Method
5 input configurations were studied:
1) ND, LR, UB
2) ND, NL, LR, UB
3) ND, C, LR, UB
4) ND, NL, C, LR, UB
5) NDmin, NDmed, NDmax, NL, C, LR, UB.
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The General ANN Method (cont’d)
5 input configurations:
Input
neurons
22
23
23
24
7
1
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8
9
10
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0
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1
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0
0
0
1
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0
0
0
0
0
1
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1
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1
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1
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0
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0
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0
0
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1
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1
0
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The General ANN Method (cont’d)
The output of the ANN is the estimation of all-terminal
network reliability (one real valued neuron).
The target network reliability of each network is estimated
using a Monte Carlo simulation method.
This study used randomly generated data sets for training and
validation considering five different link reliabilities (0.80,
0.85, 0.90, 0.95, and 0.99), and five different link connectivity
values (1 to 5), so that there are 25 design points.
RMSE: root mean squared error.
MAD: mean absolute deviation
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The General ANN Method (cont’d)
A preliminary experimental study, the number of hidden
neurons, and training data size were set to 15, and 2400,
respectively.
The model was validated using 5-fold cross validation, where
each validation network was trained and tested using 2400, and
600 observations, respectively.
A final application network was trained using all members of
the data set, i.e. 3000 observations, and its validation was
inferred using the average of the prediction error of the five
validation networks.
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Comparison of Input Data Groupings
This study give the results of 5-fold cross validation for the
neural networks considering the 5 different configurations.
The ERROR used to calculate RMSE is the difference between
the Monte Carlo simulation, and the Neural Network
estimation of the all-terminal network reliability.
RMSE: root mean squared error
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Comparison of the General ANN (GNN),
and Specific ANN (SNN) Models
All RMSE values of the General ANN are smaller than the
specific ANN, and the UB.
RMSE: root mean squared error
MAD: mean absolute deviation
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The Performance of the General Model
on New Network Sizes
This table shows no systematic error patterns in terms of
network size.
It appears that the General ANN can be used to estimate allterminal network reliability for any network size from 10 to 20
nodes with similar estimation error.
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Scaling Up to Large Networks
This table gives 5-fold cross validation results for large
networks (30, 35, 40 nodes).
While the average RMSE value is 0.04325 for the General
ANN, it is 0.08504 for the upper bound.
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Scaling Up to Large Networks (cont’d)
This table gives the RMSE, and MAD values. See that there
are no systematic error patterns in terms of network size.
These results show that the scale up of the General ANN
approach is good, and that this approach is viable for networks
of realistic size.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Application to Real Communications Systems
This study considered three real networks to better investigate
the effectiveness of the General ANN approach.
These are Authorized licensed Arpanet, the European Optical
Network, and the communications network of Gazi University.
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Application to Real Communications Systems (cont’d)
The General ANN estimates of system reliability were
compared with the actual system reliability (using Monte Carlo
simulation), the upper bound of system reliability, and the
estimate of system reliability using a specific ANN developed
for that network architecture.
The General ANN developed expressly for performed very
well, better than both the UB, and the Specific ANN.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Conclusions
This study presented a novel method of encoding
communications networks for ANN that accommodates
networks of varying node and link sizes.
Single ANN model can be used for multiple network sizes and
topologies.
In design optimization, one might use the General ANN for
screening many designs to gauge the trade off between system
reliability and cost.
An exact method or computationally laborious Monte Carlo
simulation should be used on the final few candidate network
designs to ascertain the precise system reliability.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Appendix
This study must note that there are different network
topologies which yield the same values of the inputs to the
General ANN.
Authors studied this aspect by generating some differing
networks with the same number of nodes, links, node degrees,
link reliabilities, etc.; but which have different all terminal
network reliability.
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Appendix
The General ANN approach CANNOT discriminate among
networks with the same topological inputs.
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Appendix
The reliabilities estimated by the UB, Monte Carlo simulation
(MC), the General ANN (GNN) approach, and a specific ANN
(SNN) trained for that topology.
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Demo ANN – Using Qnet
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Qnet
Training Mode
Network Design：決定隱藏層
數及輸入、輸出層單元數，且
可決定轉換函數。
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Qnet (cont’d)
Training Data：「Input Data
File」選取文字檔案位置，
並選取輸入層起始欄位，
如果資料非經過正規化處
理，則不勾選「Normalize
Input」。
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Qnet (cont’d)
Input Data File
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Qnet (cont’d)
Training Parameters
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Qnet (cont’d)
Training
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Qnet (cont’d)
Result：
前為目標值；後為預測值
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Qnet (cont’d)
Recall Mode
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Outline
Abstract
Introduction
Artificial Neural Networks
The General ANN Method
Application to Real Communications Systems
Conclusions
Appendix
Demo
Comments
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Comments
This paper presented a novel method of encoding
communications networks for ANN.
Experimental results shows that the General ANN is equivalent
or superior in estimation accuracy to ANN models developed
for a specific sized network.
The study elaborated more detail about the experimental
results of the proposed method and the compared methods.
The experiment is fair to use k-fold cross validation.
The authors considered three real networks to better investigate
the effectiveness of the General ANN approach.
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Thank you !
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