Engineering Cost Evaluation Model Based on Multi Dimension Entropy and Intelligent Algorithm
TELKOMNIKA, Vol.14, No.2A, June 2016, pp. 351~356
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v14i2A.4347
351
Engineering Cost Evaluation Model Based on Multi
Dimension Entropy and Intelligent Algorithm
1
1
2
Yanan Li* , Anders Nilsson
2
Sichuan Engineering Technical College, Sichuan, Deyang, China
Computer Department, Schlumberger, Arizona, United States of America
*Corresponding author, e-mail: [email protected]
Abstract
A complex structure has many uncertain factors and how to make a more accurate analysis on
the structure reliability by a method is the key in engineering calculation. Rough set theory is utilized to
analyze the fuzzy, random and uncertain factors and upper and lower approximation set relation is used to
calculate the value taking interval of reliability index to make reliability index analysis. The characteristic of
this analysis method is that it is not necessary to distinguish whether the uncertain parameters belong to
fuzzy scope or random scope and meanwhile, it is necessary to determine membership function of related
fuzzy variables or distribution function of random variables and reasonable value of variable is obtained via
objective rough analysis; the difference from non-probability interval reliability analysis method is that it is
not necessary to make interval standardization calculation for uncertain parameters and reliability analysis
is made in direct utilization of objective rough analysis results.
Keywords: Structure reliability index; Evaluation; Engineering cost; Rough set theory; Rough variables;
Intelligent algorithm
Copyright © 2016 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
As defined in unified standard [1] for design of structure reliability index, structure
reliability index is the capacity of the structure to complete predetermined functions in specified
time and specified condition and the corresponding probability is degree of reliability. Specified
time means the designed service life namely the time that the structure or the member can be
used for predetermined purpose without overhaul. Specified condition means “three normal”,
namely normal design, normal construction and normal predetermined function use which
means security, applicability and durability.
Traditional reliability calculation method based on probability theory and mathematical
statistics is called probability reliability calculation method and is also called conventional
reliability calculation method. Common structure reliability calculation method includes firstorder second-moment method, high-order high-moment method, optimization method, response
surface method, Monte Carlo method and random finite element method.
There are many uncertain factors in all kinds of engineering structures, such as physical
property, geometrical parameters and carried load (such as wind load, wave load and seismic
load etc.). People fail to determine the value of them in advance and influence of uncertain
factors on structure becomes more and more serious due to the limitation of conditions.
Traditional uncertain information processing method includes fuzzy set theory, evidence theory
and probability statistics theory etc.
Literature research [2, 3] indicates that, probability reliability calculation method is
sensitive to the probability model parameters and small error of probability data may lead to a
bigger error of structure reliability calculation, so probability reliability theory faces a huge
challenge. Therefore, the Thesis uses rough set theory to calculate the structure reliability index
and to simulate the uncertainty of the structure to describe the uncertain parameters of the
structure into rough variables and uses the maximum uncertainty degree allowed by the
structure to measure the reliability so as to obtain the reliability index of the structure and this
method is accurate both in the variable expression and calculation result.
Received January 16, 2016; Revised April 23, 2016; Accepted May 10, 2016
352
ISSN: 1693-6930
2. Basic Theory of Rough Set
Rough set theory [4] is a theory to process inaccurate, uncertain and incomplete data,
can effectively analyze inaccurate, inconsistent, imperfect and all kinds of incomplete
information, and is a powerful tool in relation to data inference. It was firstly put forward by
Pawlak, a Poland scientist, in 1982. It mainly has the following advantages: it only relies on
original data and does not require any external information and prior information such as
probability distribution in statistics and degree of membership in fuzzy set theory and the like, so
its description or processing for the uncertainty of the problems can be said to be relatively
objective; although other mathematical methods processing uncertain and fuzzy problems also
work out the approximate value, such as fuzzy set and evidence theory etc., the difference is
that rough set obtains approximate value via calculation with mathematical formula while fuzzy
set and other theories can only obtain approximate result relying on statistical method; it not
only applies to mass attribute analysis but also applies to quantity attribute analysis; it reduces
the attribute of redundancy and the reduction algorithm is relatively simple and the decision rule
set derived from rough set model gives minimum knowledge representation; it does not correct
the inconsistency but divides the generated inconsistent rules into certainty rules and possibility
rules; the derived result is easy to understand etc.; it can discover the abnormity in the data and
remove the noise interference in the knowledge discovery process; it is in favor of parallel
execution to improve discovery efficiency; compared to fuzzy set method or neural network
method, decision rules obtained via rough set method and the inference process are easier to
be verified and explained.
Definition 1[5] defines a knowledge representation system S (U,A,V, f ),PA,X U,xU,
lower approximation, upper approximation, minus zone, border zone and approximate precision
of set X about I are respectively
apr P ( X )
{x U : I ( x) X }
(1)
apr P ( X )
{x U : I ( x) X }
(2)
neg P ( X )
{x U : I ( x) X }
(3)
bnd P ( X ) apr P ( X ) apr P ( X )
P (X )
| apr P ( X ) |
(4)
(5)
| apr P ( X ) |
It can be learned from the definition of rough and fuzzy set that, for fuzzy set FX ,
apr P ( FX )
{x U :
FX
( x) 1}
(6)
apr P ( FX )
{x U :
FX
( x) 0}
(7)
It can then be learned from the definition of fuzzy set [7] that,
ker(FX ) apr P ( FX )
(8)
sup p( FX ) apr P ( FX )
(9)
It can be learned from the definition of rough membership function and rough set model
[6-8] with variable precision that, for random variable SX ,
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356
ISSN: 1693-6930
TELKOMNIKA
353
apr P ( SX )
{x U :
SX
( x) }
(10)
apr P ( SX )
{x U :
SX
( x) 1 }
(11)
In this way, membership function of fuzzy variables and probability of random variables
are not required to be considered in structure reliability analysis and all kinds of uncertain
variables are expressed as unified rough set variables, which brings great convenience to the
calculation.
3. Structure Reliability Analysis Based on Rough Set
X ( X 1 , X 2 , , X n )T ( X i =[ ai , bi ], i n ) is set to be n rough variables influencing the
structure functions and X can be geometric dimension of the structure, physical and mechanics
parameters of materials and function carried by the structure and the like. Random function'
G g ( X ) g ( X 1, X 2 ,, X n )
(12)
is called the performance function (or invalid function) of the structure. G is also a
rough variable after calculation and its mean value and dispersion are respectively G c and G r ,
assuming that
Z
Gc
Gr
(13)
It can be learned from interval reliability analysis model [9-13] that, in case of Z 1 , it
means that the structure is in reliable state, in case of Z 1 , it means that the structure is in
invalid state, and in case of 1 Z 1 , it means that the structure is in either reliable state or
invalid state namely in uncertain state and belongs to invalid state to the extent of strict
significance.
3.1. Performance Function of Double Rough Variables
Performance function
G X1 X 2 0
(14)
Where X 1 and X 2 are respectively the strength and rough variable of stress of the
structure. On the basis of the above analysis on rough variables, take
X ic X i
(15)
Xir X i
(16)
It can be learned that,
X1 X 2
Z
X1 X 2
0
X1 X 2
(17)
Otherwise
Engineering Cost Evaluation Model Based on Multi Dimension Entropy … (Yanan Li)
354
ISSN: 1693-6930
3.2. Performance Function of Multi Rough Variables
Performance function
m
G
n
b X
ai X 1i
i 1
i
2i
0
(18)
i m1
Where X 1i and X 2 i are respectively irrelevant rough variables of the structure,
It can be learned that,
Z
m
a X
i
i 1
m
| a
i
i 1
1i
| X 1i
n
bX
i m 1
n
i
2i
|b | X
i m 1
i
2i
m
a X
i 1
0
i
1i
n
bX
i m 1
i
2i
0
(19)
Otherwise
3.3. Non-linear Performance Function of Rough Variable
Aiming at general non-linear performance function, assume that
Z min(|| || ) min(max{| X 1' |, | X 2 ' |, , | X 3' |})
G g ( X ) g ( X 1, X 2 ,, X n ) 0
(20)
'
X i ' X i is rough variable on standardization and it can be learned from interval
reliability analysis model that, the greater Z , the farther the structure will be to the invalid zone
and the structure is in reliable state [14].
4. Analysis of examples
Example 1 Linear performance function G R1 R2 0.1S , where the Table 1 for
Attribute Decision Information of Performance function of rough variables is as follows:
Table 1. Attribute decision information of performance function
R2
R1
S
U
a
0.5
0.015
0.127
R1 [0.5] ,
b
c
0.265
0.017
0.136
0.375
0.0162
0.180
R1 [0.275,0.505] ,
R2 [0.016] ,
S [0.126,0.182] are unrelated rough variables.
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356
R2 [0.015,0.018] ,
S [0.1]
and
ISSN: 1693-6930
TELKOMNIKA
355
0.5 0.016 0.1 0.1
[0.275,0.505] [0.015,0.018] 0.1 [0.126,0.182]
[1,1.433]
Z
Example 2 Consider some non-linear limit performance function G
where
R [0.627] ,
R [0.582,0.672] ,
S [2.18] ,
567 RS 0.5 H 2 ,
S [2.071,2.289] ,
H [32.8]
and
H [31.16,34.44] are unrelated rough variables.
Z min(|| || ) min(max{| R ' |, | S ' |, , | H ' |})
567 RS 0.5 H 2 0
R 0.627 0.09 R '
S 2.18 0.109 S '
H 32.8 1.64 H '
Substituting it into the conditional equation, there is
567(0.627 0.09 R ' )(2.18 0.109S ' ) 0.5(32.8 1.64H ' )(32.8 1.64H ' ) 0
The solution is
Z 1.56
5. Conclusion
There are all kinds of uncertain variables in engineering structure analysis and rough
set theory can make it convenient to simulate the uncertainty of the structure and describe the
uncertain parameters of the structure into rough interval variables. A new calculation method for
structure reliability index is put forward in accordance with structure non-probability reliability
analysis method and in utilization of interval reliability analysis theory. This method more fully
considers the influence of uncertainty of variables on the structure, improves the accuracy of
structure reliability calculation and provides analysis of examples.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Wei R, Shen X, Yang Y. Urban Real-Time Traffic Monitoring Method Based on the Simplified
Network Model. International Journal of Multimedia & Ubiquitous Engineering. 2016; 11(3): 199-208.
Oklilas AF, Irawan B. Implementasi FTP Server dengan Metode Transfer Layer Security untuk
Keamanan Transfer Data Menggunakan CentOS 5.8. Jurnal Generic. 2014; 9(2): 348-355.
Gu W, Lv Z, Hao M. Change detection method for remote sensing images based on an improved
Markov random field. Multimedia Tools and Applications. 2015; 1-16.
Chen Z, Huang W, Lv Z. Towards a face recognition method based on uncorrelated discriminant
sparse preserving projection. Multimedia Tools and Applications. 2015; 1-15.
Cotilla-Sanchez E, Hines PDH, Barrows C, et al. Comparing the Topological and Electrical Structure
of the North American Electric Power Infrastructure. Systems Journal IEEE. 2011; 6(4): 616-626.
Su T, Wang W, Lv Z. Rapid Delaunay triangulation for randomly distributed point cloud data using
adaptive Hilbert curve. Computers & Graphics. 2016; 54: 65-74.
De NS, Leoncini X. Critical behavior of the XY-rotor model on regular and small-world networks.
Physical Review E Statistical Nonlinear & Soft Matter Physics. 2013; 88(1-1): 2252-2279.
Liu M, Zhang G, Song X, et al. Design of the Monolithic Integrated Array MEMS Hydrophone. IEEE
Sensors Journal. 2016; 16(4): 989-995.
Engineering Cost Evaluation Model Based on Multi Dimension Entropy … (Yanan Li)
356
[9]
[10]
[11]
[12]
[13]
[14]
ISSN: 1693-6930
T Sutikno, D Stiawan, I.M.I Subroto. Fortifying Big Data infrastructures to Face Security and Privacy
Issues. TELKOMNIKA Telecommunication Computing Electronics and Control. 2014; 12(4): 751-752.
Ontrup J, Wersing H, Ritter H. A computational feature binding model of human texture perception.
Cognitive Processing. 2004; 5(1): 31-44.
Sekhar A, Raghavendrarajan V, Kumar RH, et al. An Interconnected Wind Driven SEIG System
Using SVPWM Controlled TL Z-Source Inverter Strategy for Off-Shore WECS. Indonesian Journal of
Electrical Engineering and Informatics (IJEEI). 2013; 1(3): 89-98.
Pennestrì E, Belfiore NP. On Crossley's contribution to the development of graph based algorithms
for the analysis of mechanisms and gear trains. Mechanism & Machine Theory. 2015; 89: 92-106.
Radha K, Rao BT, Babu SM, Rao KT, Reddy VK, Saikiran P. Service Level Agreements in Cloud
Computing and Big Data. International Journal of Electrical and Computer Engineering (IJECE).
2015; 5(21): 158-165.
Jiang D, Xu Z, Lv Z. A multicast delivery approach with minimum energy consumption for wireless
multi-hop networks. Telecommunication Systems. 2015: 1-12.
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356
ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013
DOI: 10.12928/TELKOMNIKA.v14i2A.4347
351
Engineering Cost Evaluation Model Based on Multi
Dimension Entropy and Intelligent Algorithm
1
1
2
Yanan Li* , Anders Nilsson
2
Sichuan Engineering Technical College, Sichuan, Deyang, China
Computer Department, Schlumberger, Arizona, United States of America
*Corresponding author, e-mail: [email protected]
Abstract
A complex structure has many uncertain factors and how to make a more accurate analysis on
the structure reliability by a method is the key in engineering calculation. Rough set theory is utilized to
analyze the fuzzy, random and uncertain factors and upper and lower approximation set relation is used to
calculate the value taking interval of reliability index to make reliability index analysis. The characteristic of
this analysis method is that it is not necessary to distinguish whether the uncertain parameters belong to
fuzzy scope or random scope and meanwhile, it is necessary to determine membership function of related
fuzzy variables or distribution function of random variables and reasonable value of variable is obtained via
objective rough analysis; the difference from non-probability interval reliability analysis method is that it is
not necessary to make interval standardization calculation for uncertain parameters and reliability analysis
is made in direct utilization of objective rough analysis results.
Keywords: Structure reliability index; Evaluation; Engineering cost; Rough set theory; Rough variables;
Intelligent algorithm
Copyright © 2016 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
As defined in unified standard [1] for design of structure reliability index, structure
reliability index is the capacity of the structure to complete predetermined functions in specified
time and specified condition and the corresponding probability is degree of reliability. Specified
time means the designed service life namely the time that the structure or the member can be
used for predetermined purpose without overhaul. Specified condition means “three normal”,
namely normal design, normal construction and normal predetermined function use which
means security, applicability and durability.
Traditional reliability calculation method based on probability theory and mathematical
statistics is called probability reliability calculation method and is also called conventional
reliability calculation method. Common structure reliability calculation method includes firstorder second-moment method, high-order high-moment method, optimization method, response
surface method, Monte Carlo method and random finite element method.
There are many uncertain factors in all kinds of engineering structures, such as physical
property, geometrical parameters and carried load (such as wind load, wave load and seismic
load etc.). People fail to determine the value of them in advance and influence of uncertain
factors on structure becomes more and more serious due to the limitation of conditions.
Traditional uncertain information processing method includes fuzzy set theory, evidence theory
and probability statistics theory etc.
Literature research [2, 3] indicates that, probability reliability calculation method is
sensitive to the probability model parameters and small error of probability data may lead to a
bigger error of structure reliability calculation, so probability reliability theory faces a huge
challenge. Therefore, the Thesis uses rough set theory to calculate the structure reliability index
and to simulate the uncertainty of the structure to describe the uncertain parameters of the
structure into rough variables and uses the maximum uncertainty degree allowed by the
structure to measure the reliability so as to obtain the reliability index of the structure and this
method is accurate both in the variable expression and calculation result.
Received January 16, 2016; Revised April 23, 2016; Accepted May 10, 2016
352
ISSN: 1693-6930
2. Basic Theory of Rough Set
Rough set theory [4] is a theory to process inaccurate, uncertain and incomplete data,
can effectively analyze inaccurate, inconsistent, imperfect and all kinds of incomplete
information, and is a powerful tool in relation to data inference. It was firstly put forward by
Pawlak, a Poland scientist, in 1982. It mainly has the following advantages: it only relies on
original data and does not require any external information and prior information such as
probability distribution in statistics and degree of membership in fuzzy set theory and the like, so
its description or processing for the uncertainty of the problems can be said to be relatively
objective; although other mathematical methods processing uncertain and fuzzy problems also
work out the approximate value, such as fuzzy set and evidence theory etc., the difference is
that rough set obtains approximate value via calculation with mathematical formula while fuzzy
set and other theories can only obtain approximate result relying on statistical method; it not
only applies to mass attribute analysis but also applies to quantity attribute analysis; it reduces
the attribute of redundancy and the reduction algorithm is relatively simple and the decision rule
set derived from rough set model gives minimum knowledge representation; it does not correct
the inconsistency but divides the generated inconsistent rules into certainty rules and possibility
rules; the derived result is easy to understand etc.; it can discover the abnormity in the data and
remove the noise interference in the knowledge discovery process; it is in favor of parallel
execution to improve discovery efficiency; compared to fuzzy set method or neural network
method, decision rules obtained via rough set method and the inference process are easier to
be verified and explained.
Definition 1[5] defines a knowledge representation system S (U,A,V, f ),PA,X U,xU,
lower approximation, upper approximation, minus zone, border zone and approximate precision
of set X about I are respectively
apr P ( X )
{x U : I ( x) X }
(1)
apr P ( X )
{x U : I ( x) X }
(2)
neg P ( X )
{x U : I ( x) X }
(3)
bnd P ( X ) apr P ( X ) apr P ( X )
P (X )
| apr P ( X ) |
(4)
(5)
| apr P ( X ) |
It can be learned from the definition of rough and fuzzy set that, for fuzzy set FX ,
apr P ( FX )
{x U :
FX
( x) 1}
(6)
apr P ( FX )
{x U :
FX
( x) 0}
(7)
It can then be learned from the definition of fuzzy set [7] that,
ker(FX ) apr P ( FX )
(8)
sup p( FX ) apr P ( FX )
(9)
It can be learned from the definition of rough membership function and rough set model
[6-8] with variable precision that, for random variable SX ,
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356
ISSN: 1693-6930
TELKOMNIKA
353
apr P ( SX )
{x U :
SX
( x) }
(10)
apr P ( SX )
{x U :
SX
( x) 1 }
(11)
In this way, membership function of fuzzy variables and probability of random variables
are not required to be considered in structure reliability analysis and all kinds of uncertain
variables are expressed as unified rough set variables, which brings great convenience to the
calculation.
3. Structure Reliability Analysis Based on Rough Set
X ( X 1 , X 2 , , X n )T ( X i =[ ai , bi ], i n ) is set to be n rough variables influencing the
structure functions and X can be geometric dimension of the structure, physical and mechanics
parameters of materials and function carried by the structure and the like. Random function'
G g ( X ) g ( X 1, X 2 ,, X n )
(12)
is called the performance function (or invalid function) of the structure. G is also a
rough variable after calculation and its mean value and dispersion are respectively G c and G r ,
assuming that
Z
Gc
Gr
(13)
It can be learned from interval reliability analysis model [9-13] that, in case of Z 1 , it
means that the structure is in reliable state, in case of Z 1 , it means that the structure is in
invalid state, and in case of 1 Z 1 , it means that the structure is in either reliable state or
invalid state namely in uncertain state and belongs to invalid state to the extent of strict
significance.
3.1. Performance Function of Double Rough Variables
Performance function
G X1 X 2 0
(14)
Where X 1 and X 2 are respectively the strength and rough variable of stress of the
structure. On the basis of the above analysis on rough variables, take
X ic X i
(15)
Xir X i
(16)
It can be learned that,
X1 X 2
Z
X1 X 2
0
X1 X 2
(17)
Otherwise
Engineering Cost Evaluation Model Based on Multi Dimension Entropy … (Yanan Li)
354
ISSN: 1693-6930
3.2. Performance Function of Multi Rough Variables
Performance function
m
G
n
b X
ai X 1i
i 1
i
2i
0
(18)
i m1
Where X 1i and X 2 i are respectively irrelevant rough variables of the structure,
It can be learned that,
Z
m
a X
i
i 1
m
| a
i
i 1
1i
| X 1i
n
bX
i m 1
n
i
2i
|b | X
i m 1
i
2i
m
a X
i 1
0
i
1i
n
bX
i m 1
i
2i
0
(19)
Otherwise
3.3. Non-linear Performance Function of Rough Variable
Aiming at general non-linear performance function, assume that
Z min(|| || ) min(max{| X 1' |, | X 2 ' |, , | X 3' |})
G g ( X ) g ( X 1, X 2 ,, X n ) 0
(20)
'
X i ' X i is rough variable on standardization and it can be learned from interval
reliability analysis model that, the greater Z , the farther the structure will be to the invalid zone
and the structure is in reliable state [14].
4. Analysis of examples
Example 1 Linear performance function G R1 R2 0.1S , where the Table 1 for
Attribute Decision Information of Performance function of rough variables is as follows:
Table 1. Attribute decision information of performance function
R2
R1
S
U
a
0.5
0.015
0.127
R1 [0.5] ,
b
c
0.265
0.017
0.136
0.375
0.0162
0.180
R1 [0.275,0.505] ,
R2 [0.016] ,
S [0.126,0.182] are unrelated rough variables.
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356
R2 [0.015,0.018] ,
S [0.1]
and
ISSN: 1693-6930
TELKOMNIKA
355
0.5 0.016 0.1 0.1
[0.275,0.505] [0.015,0.018] 0.1 [0.126,0.182]
[1,1.433]
Z
Example 2 Consider some non-linear limit performance function G
where
R [0.627] ,
R [0.582,0.672] ,
S [2.18] ,
567 RS 0.5 H 2 ,
S [2.071,2.289] ,
H [32.8]
and
H [31.16,34.44] are unrelated rough variables.
Z min(|| || ) min(max{| R ' |, | S ' |, , | H ' |})
567 RS 0.5 H 2 0
R 0.627 0.09 R '
S 2.18 0.109 S '
H 32.8 1.64 H '
Substituting it into the conditional equation, there is
567(0.627 0.09 R ' )(2.18 0.109S ' ) 0.5(32.8 1.64H ' )(32.8 1.64H ' ) 0
The solution is
Z 1.56
5. Conclusion
There are all kinds of uncertain variables in engineering structure analysis and rough
set theory can make it convenient to simulate the uncertainty of the structure and describe the
uncertain parameters of the structure into rough interval variables. A new calculation method for
structure reliability index is put forward in accordance with structure non-probability reliability
analysis method and in utilization of interval reliability analysis theory. This method more fully
considers the influence of uncertainty of variables on the structure, improves the accuracy of
structure reliability calculation and provides analysis of examples.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Wei R, Shen X, Yang Y. Urban Real-Time Traffic Monitoring Method Based on the Simplified
Network Model. International Journal of Multimedia & Ubiquitous Engineering. 2016; 11(3): 199-208.
Oklilas AF, Irawan B. Implementasi FTP Server dengan Metode Transfer Layer Security untuk
Keamanan Transfer Data Menggunakan CentOS 5.8. Jurnal Generic. 2014; 9(2): 348-355.
Gu W, Lv Z, Hao M. Change detection method for remote sensing images based on an improved
Markov random field. Multimedia Tools and Applications. 2015; 1-16.
Chen Z, Huang W, Lv Z. Towards a face recognition method based on uncorrelated discriminant
sparse preserving projection. Multimedia Tools and Applications. 2015; 1-15.
Cotilla-Sanchez E, Hines PDH, Barrows C, et al. Comparing the Topological and Electrical Structure
of the North American Electric Power Infrastructure. Systems Journal IEEE. 2011; 6(4): 616-626.
Su T, Wang W, Lv Z. Rapid Delaunay triangulation for randomly distributed point cloud data using
adaptive Hilbert curve. Computers & Graphics. 2016; 54: 65-74.
De NS, Leoncini X. Critical behavior of the XY-rotor model on regular and small-world networks.
Physical Review E Statistical Nonlinear & Soft Matter Physics. 2013; 88(1-1): 2252-2279.
Liu M, Zhang G, Song X, et al. Design of the Monolithic Integrated Array MEMS Hydrophone. IEEE
Sensors Journal. 2016; 16(4): 989-995.
Engineering Cost Evaluation Model Based on Multi Dimension Entropy … (Yanan Li)
356
[9]
[10]
[11]
[12]
[13]
[14]
ISSN: 1693-6930
T Sutikno, D Stiawan, I.M.I Subroto. Fortifying Big Data infrastructures to Face Security and Privacy
Issues. TELKOMNIKA Telecommunication Computing Electronics and Control. 2014; 12(4): 751-752.
Ontrup J, Wersing H, Ritter H. A computational feature binding model of human texture perception.
Cognitive Processing. 2004; 5(1): 31-44.
Sekhar A, Raghavendrarajan V, Kumar RH, et al. An Interconnected Wind Driven SEIG System
Using SVPWM Controlled TL Z-Source Inverter Strategy for Off-Shore WECS. Indonesian Journal of
Electrical Engineering and Informatics (IJEEI). 2013; 1(3): 89-98.
Pennestrì E, Belfiore NP. On Crossley's contribution to the development of graph based algorithms
for the analysis of mechanisms and gear trains. Mechanism & Machine Theory. 2015; 89: 92-106.
Radha K, Rao BT, Babu SM, Rao KT, Reddy VK, Saikiran P. Service Level Agreements in Cloud
Computing and Big Data. International Journal of Electrical and Computer Engineering (IJECE).
2015; 5(21): 158-165.
Jiang D, Xu Z, Lv Z. A multicast delivery approach with minimum energy consumption for wireless
multi-hop networks. Telecommunication Systems. 2015: 1-12.
TELKOMNIKA Vol. 14, No. 2A, June 2016 : 351 – 356