Multi-Objective Incomplete Probability Information Optimization Reliability Design Based on Ant Colony Algorithm

doi:10.4236/jsea.2009.25046

Paper Menu >>

Journal Menu >>

J. Software Engineering & Applications, 2009, 2: 350-353

doi:10.4236/jsea.2009.25046 Published Online December 2009 (http://www.SciRP.org/journal/jsea)

Multi-Objective Incomplete Probability

Information Optimization Reliability

Design Based on Ant Colony Algorithm

Qiang ZHANG1,2, Shouju LI2, Ying TIAN1,3

1Liaoning Technical University, Fuxin, China; 2State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian Uni-

versity of Technology, Dalian, China; 3Fuxin Miming Company, Fuxin, China.

Email: [email protected]

Received April 19th, 2009; revised June 3rd, 2009; accepted June 15th, 2009.

ABSTRACT

In view of incomplete probability information multi-objective question, it used probabilistic perturbation method and

Edgeworth series technique to study reliability optimization design. The first four moments of basic random variables

are known under condition. It used the Ant Colony Algorithm to design cutting head roadheader, the optimized result

indicated that cutting head load fluctuation and compared energy consumption were reduced obviously at the same

time. This result enhanced roadheader operational reliability and energy effectively.

Keywords: Optimization Reliability, Multi-Objective, Probabilistic Perturbation Method, Incomplete Probability In-

formation

1. Introduction

Cutting head is the key component and important part of

roadheader which affects the roadheader efficiency and

load exceptional change. There are many published re-

ports on the cutting head’s reliability optimization re-

search overall the world, such as Zhang Xin from Shan-

dong Scientific and Technical University has studied on

cut truncation tooth arrangement and multi-objective

optimizations [1,2]; Li Xiao-huo from Liaoning Tech-

nology University has studied on cut head swinging cut-

ting and cut head design [3–5]; Ma Hong-wu from Da-

tong coal mining has studied on the cut head diameter

influence to roadheader [6]; Guo wu from IMM company

has studied on S150 cutting head [7]. The majority of

scholars use the conventional routes to research cut head

reliability optimization design, these methods are under

design variable and parameter to follow the normal dis-

tribution. Due to the complexity in real project and insuf-

ficient data message, it is prone to make errors by con-

ventional design [8–10]. This paper uses the stochastic

perturbation method and Edgeworth progression me-

thod [11–14] to discuss cutting multi-objective reliability

optimization which distributes the random parameter

obedience willfully.

2. The Reliability Design of Perturbation

Method

To calculate reliability or failure probability, it needs to

know the probability of density function or joint prob-

ability of density function. As lack of the tentative data,

it is mostly very difficult to obtain reliability or failure

probability by integral computation. Under the situation

that unable to determine the distribution generally, the

first to fourth moments (average value, variance and co-

variance, third-order moment, fourth-order moment) of

design variable are determined easily as it has enough

data, then it achieves reliable target, unknown function of

state probability distribution is transformed to the stand-

ard normal distribution expression by application fourth-

order moment technology, Edgeworth progression and

corresponding experience correlation formula [14], fi-

nally it may determine the structural element reliability.

235

34 3

11 1

()() ()()3 ()()

624 72

gg g

FyyyHyH yH y

 

 



 



 

 



 

 





Multi-Objective Incomplete Probability Information Optimization Reliability Design Based on Ant Colony Algorithm351

()

y is j Stage Hermite multinomial, its recurrence

relation is：

() ()()

() 1,()

jjj

yyHyjHy

HyHy y











The real distribution of random parameter could be

approached precisely by the Edgeworth progression. It

usually takes the progression of first to fourth items to

obtain good approximation. But it only take the progres-

sion of first to fourth items, sometimes it will cause reli-

ability to present R>1 situation because the approximate

distribution function and the real distribution function

exist deviation. The computation practice indicated that

following experience correlation formula obtained result

to approach in Monte Carlo numerical simulation under

R >1 situation; the Edgeworth progression may obtain

precise solution enough on condition of R﹤1.





() ()

1()()















As known above, this method is fit for random pa-

rameter distribution generally during the equation devel-

opment. It is more useful for the actual project.

3. Styling Ant Colony Algorithm and

Optimize Calculate

When the design requirements is , it

is , satisfies the probability

values of the restraint, R obtains by the fore-mentioned

Edgeworth progression or experience correlation formula.

The probability optimization design model may be

solved by model transformation as follows.



() 0PgX R



() 0RPgXR

min



()() ()

X EfXfX

St.

() 0,(1,,)

() 0,(1,,

qX il

hX jm





 



 



1) Initialize the population. Produce N to answer at

random in the independent variable defined area to build

the population, calculate adaptation degree of the indi-

vidual, arrange order according to the size, and to give

the same pheromone initial value to them. Produce M

ants, including G overall ants, L some ants.

2) Overall Search. Seek overall ants to operate explor-

ing. Through crossed and variable operating, produce

new G ants to replace the present population G ants.

3) Some Search. Seek some ant to operate excavating

one by one, calculate N individuals to choose probability

Pi (x), choose L individual as the goal, optimize and

search for the goal individual, and lead individuals to

better position.

4) Pheromone is evaporated. Carry out pheromone to

volatilize after changing and taking.

5) Check the condition of stopping. Finish one search,

population is checked to be satisfied with disappearing

terms. If it is satisfied, export and solve optimally at pre-

sent. Otherwise, it transfers to the step 2). The next is to

be searched, until disappearing or meeting the request of

schedule.

4. Multi-Objective Optimization Reliability

Design for Cutting Head of Roadheader

Model

4.1 Design Variable Choose

Transversal spacing top, circumferential distribution an-

gle δ, way speed v, rotational speed n are design vari-

ables:

X=[x1, x2, x3, x4] T= [top, δ, v, n] T

4.2 Objective Function Establish

In the design of cutting head according to the load fluc-

tuation and compared to the energy consumption com-

putational method, it makes the smallest cut angle of Ra,

sway resistance Rb, longitudinal force Rc, the load tor-

que coefficient of variation Mc, energy consumption Hw.

It takes objective function of cutting head multi-objective

optimization reliability design.

This article uses the linear weighted sum law to trans-

form the multi-objective optimizations for the simple tar-

get optimization. Considered various simple targets have

the equal status. It realizes the multi-objective standardi-

zations. The transformed objective function expression

is:

() ()()()()

() abcc w

abc c

RRRMH

xfxfxfxfx

Fx ffff f



The formulas: ()

x, ()

()

xare respectively simple goal optimization func-

tions. The denominator is the simple goal optimum

value.

4.3 Constraints Determine

Considering the actual situation, it establishes fuzzy re-

liability constraints.

1) Bolt between cutting head and the cutting head axis

is intensity fuzzy reliable restraint:

4P / (md)







(1)

Use the stochastic perturbation method and Edgeworth

progression method, then the max shear stress reliability

design restraint is:

Multi-Objective Incomplete Probability Information Optimization Reliability Design Based on Ant Colony Algorithm

352

Table 1. Optimal solution and goal function value

top δ v n

3.601 42.021 2.937 38.265

routine calculation Ra routine calculation Rbroutine calculation Rcroutine calculation Mcroutine calculation Hw

54.734 28.611 27.327 23.136 4.861

the optimize Ra the optimize Rb the optimize Rc the optimize Mc the optimize Hw

51.101 25.457 26.65 22.726 3.685

g(X)=R 0R





(2)

2) Truncation tooth fatigue fuzzy reliable restraint:

When the load changes function of number N＞106, by

reliability design request 1



, it obtains reliability re-

strain:

g(X)=R0





 (3)

3) Transversal spacing nominal optimum value scope:

g(X)=x2



＞0 (4)

g(X)=6 x1

＞0 (5)

4) Circumferential angular interval scope:

g(X)=15 x



＞0 (6)

g(X)=x 60



＞0 (7)

5) Sway speed scope:

g(X)=x 1



＞0 (8)

g(X)=6x3

＞0 (9)

6) Rotational speed scope:

g(X)=15 x



＞0 (10)

10 4

g(X)=x 80



＞0 (11)

7) Truncation tooth distributed limit:

11 m

g(X)= 85





＞0 (12)

8) Cutting power limit:

12e j

g(X)=P P



＞0 (13)

9) The installs truncation tooth spacing limit:

13 k

g(X) =L80



＞0 (14)

4.4 Optimizations Resolvent

According to the algorithm described above, it optimized

and asked for resolving. The parameter is established

based on the most different long λ corresponding half

step by step, the overall situation searches for step count

k =40, Utilize Mab7.0 software to establish calculating

algorithm procedure. The experiment indicated that the

spiral drill weight reduced 16.77% and transported the

efficiency enhanced 7.05% through the optimization de-

sign.

It carried on multi-objective optimization design to cut-

ting head of roadheader by compilation optimization de-

sign procedure, obtained optimal solution and the opti-

mized goal function value in Table1.

5. Conclusions

This article proposed a practical efficacious device to

design cutting head which obeyed the willfully distribut-

ing random parameter reliability optimization. The cut-

ting head reliability optimization multi-objective reliabil-

ity optimization design method can reduce design cycles

and save experimental funds, raise design level, and en-

hance forecast accuracy. The practice indicated that cut-

ting head load fluctuation and compared energy con-

sumption were obviously reduced at the same time. This

result enhanced roadheader operational reliability and

energy effectively.

6. Acknowledgments

The study is partially financial supported by the program

Ministry of Education Doctor Fundation of China

(20060147001); Chinese coal machine equipment com-

pany scientific research foundation; Outstanding youth

scientific research fund in Liaoning technology univer-

sity; Scientific research plan of outstanding young tea-

cher in Liaoning technology university mechanical engi-

neering institute; Graduate student scientific research

fund in Liaoning technology university; Dalian Science

and Technology University of structure state key labora-

tory open fund (G0818); Liaoning Province safety pro-

duction development plan 2009.

REFERENCES

[1] X. Zhang, J. W. Zhang and M. Yang, “Optimal design for

pick arrangement parameters on cutting head of

roadheader based on minimum load fluctuation [J],”

Machine Design and Research, Vol. 21, No. 1, pp. 64–68,

2005.

[2] X. Zhang and Q. L. Zeng, “The study of multi-objective

optimization design for cutting head of roadheader [J],”

Coal Mine Machinery, Vol. 6, No. 1, pp. 1–3, 2005.

Multi-Objective Incomplete Probability Information Optimization Reliability Design Based on Ant Colony Algorithm353

[3] X. H. Li, J. Tian and Y. Huang, “Kinematics simulation

of a horizontal cutting head in cutting process [J],”

Journal of Heilongjiang Institute of Science, Vol. 11, No.

1, pp. 17–20, 2001.

[4] X. H. Li, “Simulation study of random loads on a cutting

head of roadhead [J],” Journal of China Coal Society, Vol.

25, No. 5, pp. 525–529, 2000.

[5] X. H. Li, “Design and research on cutting head of

roadheader [M],” Chinese Overseas Chinese Publishing

house, Beijing, 1997.

[6] H. W. Ma, “Significant effect of taper cutting head to

tunnelling machine [J],” Coal Technology, Vol. 25, No. 5,

pp. 9–11, 2006.

[7] W. Guo, F. L. Wang and C. C. Pei, “The improvement to

design of S150 roadheader cutting [J],” Coal Mine

Machinery, Vol. 27, No. 8, pp. 122–123, 2006.

[8] X. L. Li and Z. X. Han, “Fuzzy reliability optimal design

of cylindrical spiral compression spring based on genetic

algorithm [J],” Journal of Machine Design, Vol. 21, No. 1,

pp. 34–35, 2004.

[9] H. Z. Huang, “The machine design fuzzy optimization

principle and applies [M],” Beijing Scientific Publishing, 1997.

[10] X. J. Fu, “Spring fuzzy reliability optimization design

[J],” Machine Design & Manufacture, Vol. 37, No. 1, pp.

4–6, 2000.

[11] X. D. He and Y. M. Zhang, B. C. Wen, “Reliability-

robust design of compressive bar under incomplete

probability information [J],” Journal of Aerospace Power,

Vol. 22, No. 9, pp. 1532–1536, 2007.

[12] Y. M. Zhang, Q. L. Liu and B. C. Wen, “Reliability

sensitivity design of vehicle familiar spring [J],”

Engineering Science, Vol. 6, No. 1, pp. 74–78, 2004.

[13] Y. M. Zhang, X. D. He and Q. L. Liu, “Reliability-based

robust design of coil tube-spring under incomplete

probability information [J],” Structure & Environment

Engineering, Vol. 31, No. 4, pp. 35–40, 2004.

[14] Y. M. Zhang, X. D. He, Q. L. Liu and B. C. Wen,

“Reliability-based optimization of coil-tube springs based

on incomplete probability information [J],” Journal of

Applied Sciences, Vol. 22, No. 3, pp. 347–350, 2004.