第 14 卷第 9 期
2010 年 9 月
船舶力学
Journal of Ship Mechanics
Article ID: 1007一7294(2010)09-0986-12
Investigation on Synthetical Optimization of
Ship Navigation Performance
Zl/ANG Huo-ming 1•2, SUN Zhi-lin\ YANG Song-lin3, ZHANG Xiao价i2
(1 Department of Hydraulic and Ocean Engineeri吨， Zhejiang University, Hangzhou 310058, China;
2 College of Metrology Technology and Engineering, China Jiliang University, Hangzhou 310018, China;
3 School of Naval Architecture & Ocean Engineeri吨， Jiangsu University of Science andTechnology, Zhejiang
212003, China)
Abstract: Ship navigation performance optimization is a very complicated problem with many de-
sign variables, many constraints and multiple culminations. Conventional optimization algorithms often
fail to solve this problem. In this paper, a kind of conventional optimization algorithm named as com-
plex algorithm (CA), genetic algorithm (GA) and simulated annealing algorithm (SA) is used to solve
the problem of ship navigation performance optimization, output result of the three algorithm is com-
pared with each other and the best one is used as the final outcome. By this way, the real optimum
solution of the problem can be obtained with much bigger probability. It should be pointed out that
all the three algorithms were improved to some degree. The C++ language is employed on Visual C+十
to develop the computation software named as ShipPO based on OOP (the so called Object-Ori-
ented-Programming) idea. Al1出e computed results of ship navigation perfo口nance optimization listed
in this paper are carried out on the ShipPO platform and it shows that calculating one time with the
three optimization algorithms can be saved. The final result indicates 出at ShipPO has strong ab山ty to
find the global optimum solution, it can meet the engineering need very well.
Key words: ship desi伊; ship navigation perfonnance; op伽咀zation desi伊; complex algorithm;
genetic algoritlun; simulated annealing algoritlun
CLC number: Document code: A
1 Introduction
Ship navigation performance optimization is a ve巧r complicated problem with many de-
sign variables, many constraints and multiple culminations. Conventional optimization algorithm
often fails to solve the forecited problem because of that it is easily immersed in the local op-
timurn and can not jump out of it. Quite a nurnher of scholars attempted sorne intelligent algo-
rithrns such as genetic algo由hm (GA), sirnulated annealing algorithm (SA), etc , which are con-
sidered to have strong ability to find the global optimum solution, to obtain beUer results and
Received date: 2009-03-26
Foundation item: Supported by the National Natural Science Foundation of China (Grant No. 10602055) and
Nature Science Foundation of China Jiliang University (Grant )
Biography: ZHANG Huo-ming(1976-), male, post-doctor of Department of Hydraulic and Ocean Engineering,
Zhejiang University, E-mail: zhmlandi@.
第 9 期 ZHANG Huo-ming et al: Investigation on Synthetical Optimization of … 987
sometimes they realized their anticipated goal. In this paper, a kind of conventional optimiza-
tion algorithm named as complex algorithm (CA), GA and SA is used to solve the problem of
ship navigation performance optimizatÏon, output result of the three algorithm is compared with
each other and the best one is used as the final outcome. By this way, maybe we can get the
real optimum solution of the problem with much bigger probability. lt should be pointed out 由at
all the three algorithms have been improved to some degree.
The most precise methods to compute the ship navigation performance seem to be those
based on CFD[l升， but those methods need very long computing time. During the preliminary
design stage, to compute the ship navigation performance by empirical formula coming from
massive statistical analysis is proved to be a method which can save much computing time[Hl.
Generally, the previous study obtained the optimization result only by one optimization algo-
rithm[9-10] which might miss the real global optimum solution sometimes.
The C++ language is employed on Visual C++ to develop the computation software
named as ShipPOI9-111 based on OOP (the so called Object-Oriented-Programming) idea. In or-
der to test the computation ability of ShipPO, a practicallarge ship is chosen as an example. All
the computed results of the ship navigation performance optimization listed in this paper are
carried out on the ShipPO platform and it shows that calculating one time with the three opti-
mization algorithms can be saved. The final result indicates 由at ShipPO has strong ability to find
the global optimum solution, it can meet the engineering need very well.
2 Optimization algorithm
Complex algorithm (CA)
In engineering design, the complex algorithm (CA) is a direct way for solving constrained
nonlinear programming problemsI12-131• 1t is simple in calculation, wide in application, and com-
mon in engineering technology. Generally 1 the CA is mainly used in optimum design problems
with continuous variables. 1n this paper, the CA computation procedure and termination crite-
rion are improved. The detailed discreption of CA and its improvement are in Refs.[12] and [13].
The main improvement of the CA used in this paper when comparing with the ordinarγone is
presented as follows.
Speedup technologyl131
When adjusting the complex form,we need frequently to ca町 out the comparison of the
goal function value of the complex apexes with each other in order to realize sorting them so
as to find the most poor point, while in a cyclic process, the majority of the apexes are un;'
changed. Under certain sítuations, the objectíve function computation is possíble quite time-
consuming. If all the goal function value is recomputed at each time of comparison, it will con-
sume massive time. In order to avoid time wasting, we can establish a tempora可 array to save
the goal function value of the complex form apexes at the time of building them. Only the
changed apex target value will be adjusted at each time of circulation. This can accelerate the
988 船舶力学
computation speed of the complex algorithm in this paper to a certain extent.
Genetic algorithm (GA)
第 14 卷第 9 期
The genetic algorithm (GA)[14斗勾 is a kind of widely-used, high efficient, randomly search-
ing and optimizing method which is developed based on the evolutionism principle. Comparing
w1由也e traditional optimization algorithms, it has the characteristics such as easily using, inde-
pendent on the mathematical character of the problem, and has a strong ability to find the global
optImum, etc.
It can be said that the genetic algorithm is a kind of idea which simulates the evolution
in biology and human being world, sometimes it is called the evolvement algorithm. Its imple-
ment method is not exclusive. The algorithm varies with the change of chromosome coding, se-
lection, crossover, variation strategy and termination criterion. The genetic algorithm mentioned
in this paper is detailedly described in Ref.[14]. Its characteristic can be summarized as float-
ing data coding, comparatively common roulette method for detection to ca口Y out evolution,
is selected as the crossover probability p c' is selected as the mutation probability p m' to
decide the original population by randomly assigning between the feasible area, and to comprise
the constraint conditions and the objective function value as the fitness of the chromosome, by
assigning a large number as the maximum permissible evaluation generations as the termÏna-
tlOn cntenon.
Simulated annealing algorithm (SA)
In 1982, Kirkpatrick proposed one kind of approximate effective algorithm for solving the
NP completeness combination optimization question, namely the simulated annealing algorithm
(σSA)[阳16←创ω-→lη叫7
Metropoli白s accepting criterion is used and the group of parameters of the so -called cooling
progre臼ss chm眈t are employed to c∞on仕01 由e alg伊orithm course, which enables the algorithm to give
an approximate optimal solution in the multinomial time. 咀lis approximate optimal solution can
satisfy the practical project need under the ovelWhelming majority situation. 咀le SA is detailedly
descripted in Refs.[16] and [17].
Generally speaking, the effective running of SA mainly depends on the following three 臼
pects: (1) A group of suitable cooling progress chart parameter; (勾 Suitable neighborhood struc-
ture, namely 出e new solution generating rule; (3) Reasonable termination criterion, namely when
to stop the optimization.
In order to enable this algorithmωobtain satisfaction results, it is essential to choose differ-
ent cooling progress chart parameters according to different questions, and sometimes the neigh-
borhood structure also needs to be greatly modified aiming at the special questions. Under this
situation, the author proposed some principle for choosing the cooling progress chart controlling
parameters and the neighborhood structure, and made some improvements[l7] to the ordinary SA.
The practice has proved that if the cooling progress chart parameters and the neighborhood
structure selection are appropriate, the SA can find the global optimal solution effectively.
第 9 期 ZHANG Huo-ming et al: Investigation on Synthetical Optimization of … 989
3 Mathematical model of ship navigation performance optimization
Design variables
Ship navigation performance mainly includes speediness, manoeuvrability and seakeeping.
To caηy out optimization on it generally refers to select appropriate ship parameters under
given restriction conditions and make the designed ship have the optimum navigation perfor-
mance. This problem is a complicated one. It is related to many ship parameters. Based on
theoretical analysis (FENG Youzhang, 1995), we select ship length-L, ship breadth-B, ship
draft-T, ship cube coefficient-CB, ship middle transverse section coefficient-CM, ship design
waterline surface coefficient-C",p' position of ship longitudinal floating center-LCB' diameter of
screw propeller-Dp' the ratio of tr町 area to the surface area of the propeller-A E/A 0' ratio of
propeller pitch to its diameter 一PI鸟， rotation speed of p严ro叩p严eιlle
t如otally twelve parameters as the design variables. In order to describe this problen> simply, we
T
use a vector X to represent the design variables as follows, X' = {L , B, T, CB, CM, C",p, LCB' Dp'
AE/A o' 凹'Dp ' n, V, I.
Objective function
Because ship navigation performance includes three aspects, we should select three in-
dexes to represent 出ese 出ree performances respectively[5. 叼. In order to judge whether 由e ship
speediness performance is good, we can select ship speediness judging factor-Csp as 出e objec-
tivehnCHon-csp is similar to 也e navy coefficient and it can judge whether ship speediness per-
formance, ship linetype and propeller open water performance are good. It is an integrated
judgement factor and is comparatively useful for ship design work. Referring to the naηr factor,
出e speediness object function can be defined as follows.
PIi'/(η。ηHηR)=)=ιJ 飞 κ
.ð. -- V-
、
..
,,
···A ，，
E电、
where .ð. is ship displacement，几 is the effective power, TJo is the propeller open water efficien-
cy, TJH is the ship hull efficiency, TJR is the relative rotation efficiency.
咀le judgement of ship manoeuvrabi1ity is related to many aspects. 1n order not to make
the problem so complicated, we select the linear additional power average sum of beeline sta-
bility coefficient-VarL' turning coefficient-VarT, direction changing coefficient-V arC' as formula
(2) shows.
Mv=PL 几L+PTVarT+PCVarC (勾
where PL' PT' Pc represents the weight coefficient of the three kinds of manoeuvrability perfor-
mance respectively. The weight coefficient can be selected as , and 0 .27 respectively.
Just like 气，风 is also the function of the design vector X. It can be marked as Mv =Mv (X) .
For seakeeping performance,we can select the linear weighted average sum of ship' s pitch-
990 船舶力学 第 14 卷第 9 期
ing angle and surging extent as the objective value and before adding the two we should com-
press them into the sector between 0 and 1. This objective value is expressed by Sv. 1t is the
直mction of the design variable vector X and wind, current, wave and other environment p町ame-
ters. Here, it is supposed that the sea condition has been specified, then we can get Sv=S. (X).
F or the three indexes mentioned above, we can take their linear weighted average sum be-
fore compressing them into the sector between 0 and 1 as the ship navigation performance ob-
jective function. Under this situation, the objective function is as folIows.
!(X)=α1Csp01 +α2 1吨。1+αßv01 . (3)
where the suffix (01) means the standard value by compressing into the sector of (0-1). And
0::::;吼叫工α产1.
More detailed description of the objective function is in the master' s degree paper of
Ref.[14].
Constraint conditions
.1 1nequation restriction conditions
(功 Iρwer and upp凹 limits of the design variables are such as L, B, T, CB, Cwp ' CM, LCB'
必凶必
Df A JA 。， P/Dy n, vs·It can be marked as xi4Xigx&-Where xt represents the lower
uh
limit of no. i variable, X; represents 出e upper limit of no. i variable.
(b) Stability condition which is mainly about GM. GM=GM(X)>, while GM(X) Ìs as
folIows.
100 .....2 GM(X) ~~ !~~ " B- (4)
M ,--, 80000+D臼
where D.. represents the ship displacement (t) , the unit of GM and B is feet which needs to be
transformed to meter, lft= 8m.
如) Comfortable condition which i岱s ma啤句叩i杠n均1
T飞伊(啤X) i扫s a部S f，岛'ollo呐.
2 2
,, 1 B +4Z 乙 (X)= V 二万二L
-M
(5)
where Zg represents the height of the center of gravity of the ship, GM represent8 由e original 8ta-
bility height of the ship.
(d) Seakeeping demand which is mainly about the rolling extent. φfφa (X) ::::; 100 , while
φ。 (X) is as follows.
AI__._ Z 轧(X)=乌+于(白
where C1 represents the inf1uence of the wave on the damp, C2 represents 出e inf1uence of the
ship s可le on the damp, C3 represents inf1uence of the relative size of hilge keel and the BfT val-
第 9 期 ZHANG Huo-ming et al: Investigation on Synthetical Optimization of … 991
ue on the damp, Zg represents the height of the center of gravity of the ship.
(e) Manoeuvrability demand which is mainly about the size of the relative turning diame-
,_D,(X)
ter of the ship. For the single propeller ship, D.' =一一一一<， while Ds (X) is as follows. L
D.(X) ...,.\ ",^"Ch ... ,..,.. Tri= .,., B . 194 ，.，~ n S
s' -一=-203 ':b + 4 ~ -13一+一-← -:ll... Cι (Sr- 1 ) δ.. L -~ L δ LT-h\-l
(7)
AD ~_(T 1\( δi
+ ~!'r. C.(Sr-2 )+:!.+ ,;, -1 I1 ~ 1 (Sr-1 ) LTUh\~r - ",.," LT'v. , \ TL 川 lδ I ) \~T
where Ch represents the chord length of the rudder， δrepresents the rudder angle, direction of
left is positive, A B rep陀sents 出e waterishlogged 缸ea of the bow，乓 represents the length of the
spread out of the rudder, T represents the draft of the trial voyage, TL represents the design draft,
Sr represents the offal style. H the offal style is open water, then Sr =1 , else if it is closed, Sr
=2.
(f) The designed propeller should satisfy the vacuole demand. According to the Keller for-
mula, we can set up the inequation restriction formula as follows.
+ rn. TT A"
7<" T_+K- -~J> 乓O
(1飞-1飞 )DL Ao
(8)
where p. represents the static pressure of the propeller shaft center, p. represents the boiloff pres-
sure of the weather at 15 centigrade, T
o
represents the propeller thrust, Z represents the pro-
peller leaf number, K is a constant number, for the fast two propeller ship its value is 0, for
the other type of ships with two propellers its value is , and for the single propeller ship
K=.
Equation restriction conditions
(a) The buoyancy demand namely that the displacement should be kept unchangeable.
Dis=PLBTCB (到
where D is represents the assigned displacement.
(b) Torque moment balance. 咀lÎs means that under the design status the torsion moment
that the main engine provides to the propeller must equal to the one 由at the propeller ab-
sorbs. It can be expressed as follows.
'YJR'YJ.~P~ '" TT 2 ..,.5 号在二-ALKQPnDp=0 (10)
where Np represents the propeller shaft number，乓 represents 出e main engine power, n mp阳re
sent怡s the rotation speed of the propeller, p represents the density of the water.
(c) Thrust balance. It demands that the effective thrust 出at the propeller provides must
equal to the ship hull resistance under the corresponding speed.
2 4
NpK,pn Dp (l-t )-R=O 、‘•• ,, 4··A 4EEA ,, .. ‘、
where t represents the thrust decrease fraction, K , represents the propeller thrust coefficient, R
represents the ship hull resistance.
992 船舶力学 第 14 卷第 9 期
4 Ship performance optimization example
According to the former described mathematical model, the C++ language is employed
on Visual C++ to develop the computation software named as ShipPO (abbreviation of ship
navigation performance optimization) based on OOP which is the so called Object-Oriented-Pro-
gramming idea. 1t should be pointed out that for GA, the larger objective function value rep-
resents better result while in CA and SA, the smaller is better. So during coding, the above
mentioned ship performance numerical model should be modified so as to match the corre-
sponding optimization algorithm. A simple solution method is to make 0. , which is expressed
by f(X) in formula (22) act as the objective function value for CA while for CA and SA.
And 由e e甲lation as well as the inequation constraints are processed according to the preceding
text so 由刨出ey will be absorbed into the objective function value. 1n order to test 出e computa-
tion ability of ShipPO, a large ship is chosen as an example. All the computed results of the
ship navigation performance optimization listed in this paper are computed by ShipPO.
The algorithm performance of the improved CA, GA and SA have been verified in Refs.
[12-17] respectively. More detailed description of ShipPO is in Ref.[lO].
Now to optimize the certain ship type which adopts AU-4 propeller, single shaft, and its
fully loaded displacement is 50 0∞t.咀le other design variable range of it is listed in the follow-
ing Tab. 1.
The lower and upper limits of the design variables
Co C~f C，ψ LC8 Dp AE1Ao PlDp
n
Items L (m) B (m) T(m) (r/min) 飞往n)(%L)
Lower-limit 250 35 135
Upper-limit 270 36 180 24
For the ship example mentioned above, the optimization algorithms of CA, SA and GA are
employed to compute the optimum solution in turn. For CA, GA and SA, the algorithm control-
ling parameters are selected just as -4 show respectively. The meaning of all the param-
eters listed in the following tables is described in the former paper.
Controlling parameter of CA Controlling parameter of GA
ltems Value ltems Value
POPSlZE (population size) 2∞
& (the iteration precision) -6 MAXGENS (the larges evolution generations) 300
MST (the largest iteration times permitted) 5000 PXOVER (crossover proportion)
PMUTATION (mutation proportion)
For the three optimization algorithms，也e computer time is listed in the following and
由e optimization process curve is showed in -3 respectively. 币le optimization results of the
three algorithms are listed in . From , it can be seen that the consuming computer time
order is CA<GA<SA, while the computation speed order of the three algorithms 缸e CA>GA>
SA. As those curves shown in -3, we can see that both CA and SA searcher the solution
993 ZHANG Huo-ming et al: Investigation on Synthetical Optimization of … 第 9 期
from low to high of the objective function values while GA is from the opposite order, namely
from high to low. It should be pointed out 出at for GA, the larger objective function value rep-
resents better result while in CA and SA, the smaller is better. But, as those shown in ,
由e objective function value is all Ov' which is expressed by f( X) in formula (22), and not
伐， it shows 由at Ov presented by SA is the largest.
Controlling parameter of SA The time consumed for
the optimization
Va1ue Items
10 Computing time
CA 18 < 2s
278 < 288
4548 < 455s SA 5
RTfαιsnR
Algorithm
1000 GA
100
The optimization resuIts
Optimization AIgorithm
GA SA
∞ 4
19
22
77
15
11
11
51
81
CA
2
261
261
L (m)
B (m)
T(m)
CB
C
C 叩
LCB
Dp (m)
AE1AO
PlDp
n (r/min)
V, (1m)
一Csp01
M,
S,
O
D;, (t)
Propeller efFective 出rust (kN)
Ship hull resistance R (k问
Propeller t01可ue 你)
Propeller torque supplied by main engine (kN. m)
GM(m)
兀 (s)
D
伊 n
Item8
19
ω
(AE1AO)min
994
Items
船舶力学 第 14 卷第 9 期
Continue 6
Optimization AIgorithm
CA GA SA
43 44
32
+09 +09 +09
Effective power P. (k W)
Main engine power p, (k W)
η。
ηH
ηR
Ship hull wet surface area S (m ")
Friction drag coefficient 乌
Residual resistance coefficient C
Froude 's number F
Reynold 's number R,
P时natic coeEidentq
tre
(问
)hh
F副斗
450
400
350
300
食 250
ζ200
150
100 I…
FLLLl
300
250
200
击"
100
50 。.1
o t 0 ....
50 100 150 200 250 300 350 400 0 100 200 300 0 100 200 300 400 500 600
T垃1届 Tim岱 Tim田
Optimization process of CA Optimization process of GA Optimization process of SA
So, for this ship navigation performance optimization example, the final result should be
selected 部由at from SA. In , not only the design variable but also the other corresponding
p缸ameters are listed out. By doing so, it is ve可 easy for us to see whether the equation and in-
equation constraints are satisfied.
As shown in , the D;., computed by SA is 49 which is ve可 close to the assigned
value 50 000 and the error is only %. Simil盯 situation appears between the propeller ef-
fective thrust and the ship hull resistance as well as the propeller torque and the propeller
torque supplied by the main engine. 咀le propeller effective thrust is 2 and the ship
hull resistance is 2 , the error between the two is %. The propeller torque is
2 kN • m and propeller tor，年le supplied by the main engine is 2 kN. m, the er-
ror between the two is %. Overall speaking, the error for the equation constraints is so
tiny that it can be omitted. So it is obvious that the equation conditions are very well satisfied.
The original stability height GM(m) is 31 (>), the rolling period ~伊 (s) is 65
(>), the rolling angle 旷 is (<1 0 0 ) , the relative turning diameter D. is 73
(<), the needed (AE/Ao)mm is 050253(<).It is obvious that the inequation conditions
are also very well satisfied. The other corresponding parameters are listed in while their
meaning has been explained in the former paper.
第 9 期 . ZHANG Huo-• ning et al: Investigation on Synt由he创ti沁cal Optimization of ..… .川 995
Based on the above analysis, the final optimization solution of this example is as follows:
x:={2505928, 3509532, 902615, 061122, 095064, OM, , , 06,
77, , 19 ), j(X.)= 01.
5 Conclusions
Ship navigation performance optimization is a verγcomplicated problem wi由 12 design
variables, 30 constraints and multiple culminations. Conventional optimization algorithms of-
ten fail to solve this problem because it is easily immersed in the local optimum and can not
jump out of it. In this paper, the improved CA, GA and SA are employed to solve the question.
In order to simplify this question, the ship navigation performance optimization mathematical
model is set up based on the empirical formula. Based on the former described mathematical
model, the C++ language is employed on Visual C++ to develop the computation software
named as ShipPO with help of the OOP idea.
An example of practical ship navigation performance optimization is computed on Ship-
PO, the results indicate that ShipPO has strong ability to find the global optimum solution
quickly, whose computer time is no more than 1+28+454=482s (臼 6min)， it can meet the en-
gineering need ve可 welL The idea presented in this paper that to obtain the final optimization
solution by the above mentioned three optimization algorithms including CA, GA and SA can get
the real global optimum solution of the problem with much bigger probability than 由at only
from one kind of optimization algorithm.
The CA, GA and SA can be used in multi-dimension complicated function optimization
computation. It has no special demand for the mathematic character of the function. Moreover
its computing speed is relatively rapid and it can perfectly find the optimum or 由e approxi-
mately optimum solution. For the above computation example, if different optimization algorithm
controlling parameters are selected or the variable range is changed, the result may vary only a
little bit. But generally speakíng, the three optímízatíon algorithms have 甲lÎte good stability,
which has been verified in [12-17] respectively. Based on the above reasons, we think 由at those
algorithms have quite strong practicability and significance of been promoted. It is feasible to
adopt them to the engineering problem which is similar to ship navigation optimization.
Maybe the more reasonable mathematical model of ship navigation performance optimiza-
tion should be set up by CFD, but unfortunately, which will demand for very powerful com-
puter with much higher speed and floppy disk with larger capacity. With the development of
the computer technology, perhaps in the near future, we can comput
996 船舶力学 第 14 卷第 9 期
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第 9 期 ZHANG Huo-ming et al: Investigation on Synthetical Optimization of …
船舶航行性能综合优化研究
张火明口，孙志林杨松林 3 张晓菲 2
(1浙江大学水利与海洋工程系，杭州 31∞Q8; 2 中国计量学院计量测试工程学院，杭州 31∞18;
3 江苏科技大学船舶与海洋工程学院，江苏镇江 212003)
997
摘要:船舶航行性能优化是一个非常复杂的问题，它具有多个设计变量，多个约束和多个极点。传统的优化方法通常无
法解决该问题。文中采用了一种传统的优化方法一复合形法(CA)和遗传算法(GA) ，模拟退火算法 (SA)来计算船舶航行
性能优化问题，比较了三种优化方法的输出结果并选取最好的那个解作为最终的优化结果。通过这种方法，可以以更高
的概率获得真实的最优解。应该指出的是，这三种算法都作了某种程度上的改进。作者采用 C++语言基于面向对象思想
开发了计算软件-ShipPO。文中列出的所有船舶航行性能优化计算结果都是在 ShipPO 平台上计算出来的，结果表明采用
三种优化方法计算一次船舶航行性能优化问题耗时并不太多。最终的结果表明 ShipPO 具有很强的寻找全局最优解的
能力，它能够很好地满足工程需要。
关键词:船舶设计:船舶航行性能;优化设计;复合形法:遗传算法;模拟退火算法
中国分类号: 文献标识码:A
作者简介:张火明(1976-) ，男，浙江大学水利与海洋工程系博士后，中国计量学院计最测试工程学院副教授，
硕士生导师:
孙志林(1958-) ，男，浙江大学水利与海洋工程系教授，博士生导师;
杨松林(1956-) ，男，江苏科技大学船舶与海洋工程学院教授，博士生导师;
张晓菲(1985-) ，女，中国计量学院计量测试工程学院硕士研究生。
