optimization design for screw wash-sand machine …...optimization design for screw wash-sand...

Optimization Design for Screw Wash-Sand Machine

Based on Fruit Fly Optimization Algorithm

Yun-Fei Fu, Jie Gong, Zheng Peng, Ji-Hua Li, Si-Dong Li,

Pu-Wang Li* and Zi-Ming Yang**

Agricultural Product Processing Research Institute at Chinese Academy of Tropical Agricultural Sciences,

Chinese Agricultural Ministry Key Laboratory of Tropical Crop Products Processing,

Zhanjiang 524001, P.R. China

Abstract

The aim of this study is to minimize the specific energy consumption of the screw wash-sand

machine. Let the diameter of the screw structure, pitch, diameter of the screw axis, blade thickness,

installation angle, and the speed of the screw axis be the design variables, and take the minimum

specific energy consumption as the optimization objective. According to the complexity of the

optimization problem in this study, the fruit fly optimization algorithm (FOA) is used to execute the

optimization design of the screw wash-sand machine. The non-stationary multi-stage assignment

penalty function is adopted to cope with the constrained optimization problem. To judge the stability

and reliability of the optimal solution and find the sensitive factors of the optimization design, the

sensitivity analyses of the objective function and constraint conditions to the design variables are

carried out. By simulation, the optimized structure parameters of the screw wash-sand machine and the

data of the objective sensitivity and constraint sensitivity are obtained. The simulation results show

that the specific energy consumption decreases by 4.59%; the diameters of the screw structure and

screw axis are sensitive factors of the optimization design.

Key Words: Fruit Fly Optimization Algorithm, Non-stationary Multi-stage Assignment Penalty

Function, Wash-sand Machine, Sensitivity Analysis, Specific Energy Consumption

1. Introduction

With the rapid development of the economy in the

world, the consumption of the sand used as the concrete

fine aggregate becomes increasingly pronounced [1�4].

Particularly, with the accelerating development of the

urbanization in the southeast coastal area in China, many

coastal cities are faced with a dilemma that the river sand

resource will be exhausted. Therefore, replacing river

sand with sea sand will be a tendency [1]. In fact, it has

been a long time since sea sand was used in the Japan’s

construction industry. In Japan, above 90% of the sand

for building is sea sand. In China, many coastal areas store

plenty of sea sand resources. However, various kinds of

salts and hazardous materials will have detrimental ef-

fects on the concrete, which causes that the application

and popularization of the sea sand in the construction

industry are constrained to some extent. Also, research

shows that Cl ion in sea sand will corrode the steel bar,

which can weaken the durability of concrete, so Cl ion is

a main factor causing the failure of the architectural struc-

ture [2�4]. If the sea sand without desalting is used in the

construction engineering, then some serious engineering

accidents will occur. Therefore, the research on the re-

lated technology of desalting sea sand has some social

and economic benefits.

In the domestic and overseas, there are three main

Journal of Applied Science and Engineering, Vol. 19, No. 2, pp. 149�161 (2016) DOI: 10.6180/jase.2016.19.2.05

*Corresponding author. E-mail: [email protected]

**Corresponding author. E-mail: [email protected]

sorts of sea sand desalination technologies: the natural

cleaning method with fresh water, natural placement

method, and mechanical method [5]. Currently, the me-

chanical method is widely used in China. Although the

cost of the mechanical method is the largest, its produc-

tion efficiency is also the highest. The wash-sand ma-

chine is a major component of the sea sand desalination

mechanical system. There are two main types of wash-

sand machines: the screw wash-sand machine and rotat-

ing wheel sand washing machine. As the sand washing

capacity of the screw wash-sand machine performs bet-

ter than that of the rotating wheel sand washing machine,

the screw wash-sand machine is taken as the research

object [6]. Because of its some advantages (i.e., the long

screw, seal design, simple structure, strong processing

ability, easy maintenance, etc.), the screw wash-sand ma-

chine is widely used in the sea sand desalination field.

One of the most commonly used mechanical wash-sand

systems in China is shown in Figure 1 [7,8]. Figure 1

shows that this machine is an important part of the me-

chanical wash-sand system. In fact, the screw wash-sand

machine is a core part in various kinds of mechanical

wash-sand systems, and its operation performance will

affect the output and quality of desalted sea sand greatly.

According to the number of the screw axis, there are

two categories of screw wash-sand machines: the single

screw wash-sand machine and double screw wash-sand

machine. For the convenience of the research, the single

screw wash-sand machine is taken as the research object.

The structural diagram of the screw wash-sand machine

is shown in Figure 2 [9]. From Figure 2, it can be seen

that the screw wash-sand machine consists of the lower

bearing assembly, flume, screw axis, outrigger, upper

bearing assembly, coupling, motor, and reducer. The mo-

tor is the power source of the screw wash-sand machine.

With the help of the motor and reducer, the screw struc-

ture can be driven at a uniform speed. The screw struc-

ture plays a role of agitating the sea sand and water in the

flume. With the stirring action of the screw structure, the

impurities in sea sand are washed away. Impurities are

discharged from the drainage pipe under the effect of wa-

ter flow. The washed sea sand is discharged from the dis-

charge opening with the running of the screw blade, and

then the objective of desalinating sea sand is achieved.

Actually, it has been shown in many papers reporting

the researches regarding the screw machine. Uematu and

Nakamura (1960) revealed how the power requirement

and the efficiencies of the screw conveyer are affected

by the ratio of pitch to the diameter of the screw struc-

ture and the tip clearance [10]. Qian, Gu, and Zhang

(1996) formulated the semi-empirical equation of the out-

put of the twin screw conveyer and studied the factors

affecting the output [11]. Yu and Arnold (1997) deter-

mined an analytical solution calculating the torque of the

screw feeders, which can be used to predict torque char-

acteristics [12]. Roberts (1999) investigated the volume-

150 Yun-Fei Fu et al.

Figure 1. Mechanical wash-sand system.

Figure 2. Screw wash-sand machine.

tric performance of enclosed screw conveyors with par-

ticular reference to the influence of vortex motion and

presented an analysis of the vortex motion in vertical or

steeply inclined screw or auger conveyors [13]. Shimizu

and Cundall (2001) used the 3D distinct element (DEM)

to examine the performance of screw conveyors [14].

Zhang, Mao, and Ding (2008) adopted the ant colony

algorithm to minimize the weight and maximize the ef-

ficiency of the screw coal miner [15]. Owen and Cleary

(2009) displayed how operating factors affect the per-

formance of the screw conveyor by utilizing the discrete

element method (DEM) to simulate a single-pitch screw

conveyor with periodic boundary conditions [16]. Ren,

Xia, and Ye (2012) used the theoretical calculation to

determine the corresponding structure sizes and mo-

tion parameters of the screw structure without shaft for

high-temperature mechanized charging and discharg-

ing in magnesium reduction process and applied the fi-

nite element method to analyze the bending and torsion

stress of the screw structure without shaft [17]. Zhang,

Fu, Han, and Yuan (2012) applied SPEA (strength pa-

reto evolutionary algorithm) to execute the multi-objec-

tive fuzzy reliability optimization of the screw coal miner,

aiming at maximizing the productivity and minimizing

the energy consumption and weight [18]. Zhang, Rui,

Zhou, and Tong (2014) adopted PSO (particle swarm

optimization algorithm) to minimize the deformation of

the shaft-less screw structure used for conveying the high

viscosity and large specific gravity materials [19]. How-

ever, the studies on the screw wash-sand machine are

seldom discussed. Gawande, Navale, and Keste (2013)

reported a novel sand washing machine, which consists

of the screen, chassis, screw conveyor, rotary bucket ele-

vator, and transmission [20]. In particular, the screw

structure is also used as the key component for washing

the sand in this novel sand washing machine, showing

that the screw structure has strong ability of washing sand.

To reduce the specific energy consumption, the fruit

fly optimization algorithm is used for optimizing the struc-

ture parameters of the screw wash-sand machine. Firstly,

the optimization mathematical model of the screw wash-

sand machine is established. Then, the optimization is

carried out with the fruit fly optimization algorithm. Fi-

nally, the sensitivities of the objective function and con-

straint conditions to the design variables are analyzed.

The research on the optimization design of the screw

wash-sand machine can improve not only the compre-

hensive performance of the screw wash-sand machine

but also the overall performance of the mechanical wash-

sand system. With the improvement of the wash-sand te-

chnical level, the competitive power of desalted sea sand

will become stronger, and the degrees of approval will

become higher, which will promote the application and

promotion of desalted sea sand. As the screw wash-sand

machine is a key part in the sea sand desalination me-

chanical system, the continuous study on the screw wash-

sand will promote the development of the sea sand desa-

lination industry.

2. Mathematical Model

2.1 Design Variables

The structure diagram of the screw structure in the

screw wash-sand machine is shown in Figure 3. In Fig-

ure 3, L is the transportation distance in meters; D is the

diameter of the screw structure in meters; S is the pitch

in meters; d is the diameter of the screw axis in meters;

� is the installation angle in degrees. For simplifying the

structure diagram of the screw structure, the blade thick-

ness w is not shown in Figure 3. Actually, the working

principle of the screw structure in the screw wash-sand

machine is similar to that of the Archimedes screw [21,

22]. With the help of the rotation of the screw structure,

the screw blade is able to transport sea sand from the

flume to the discharge opening. Due to the deadweight of

sea sand and the friction between sea sand and the trough,

sea sand will not rotate with the rotation of the screw

Optimization Design for Screw Wash-Sand Machine Based on Fruit Fly Optimization Algorithm 151

Figure 3. Screw structure in the screw wash-sand machine.

blade. However, sea sand can be conveyed in the axial

direction under the axial force caused by the screw blade.

The design variables of the screw wash-sand machine

are mainly the combination of the geometrical size and

physical properties of components. In actual engineer-

ing, the transportation distance of the screw wash-sand

machine can be determined based on the concrete me-

chanical wash-sand system. According to the structural

characteristics and operation characteristics of the screw

wash-sand machine, let the diameter of the screw struc-

ture D, pitch S, diameter of the screw axis d, blade thick-

ness w, installation angle �, and the speed of the screw

axis n be design variables. That is,

2.2 Objective Function

In a mechanical design problem, there are many fea-

sible design schemes. The task of the optimum design is

to find the optimum scheme from them. To find the opti-

mum scheme, the objective of the optimization problem

should be determined first. The objective function re-

flects the relationship among different design variables,

and it is used to measure certain performance index re-

quired by the design. The construction and selection of

the objective function are related to the practicality of

the optimization result, so the correct selection of the ob-

jective function is intensely crucial. The specific energy

consumption, which is the ratio of the driving power of

the motor to the production capacity, is a main technical

and economic index of machinery equipments [23�25].

The specific energy consumption can reflect the com-

prehensive properties of the machinery equipment well.

Therefore, let the specific energy consumption be the op-

timization objective. The specific energy consumption of

the screw wash-sand machine is

(1)

where H is the specific energy consumption in kilo-

watt-hours per ton, N is the driving power of the motor

in kilowatts, and Q is the production capacity in tons

per hour.

At present, the screw wash-sand machine has no for-

mula for calculating the production capacity. Since the

working principle of the screw wash-sand machine is si-

milar to that of the screw conveyor, the formula of the

production capacity of the screw conveyor is used to cal-

culate the production capacity of the screw wash-sand

machine, as given by [26,27]

(2)

where Ag is the section area of sand in square meters, �

is the conveying velocity of sand in meters per second, �

is the material accumulation density in tons per meter

cubed, n is the rotational speed of the screw axis in ra-

dians per minute, � is the material filling factor, and C

is the inclination factor.

The driving power of the screw wash-sand machine is

used to overcome various resistance caused in the course

of washing sea sand. Particularly, when washing sea

sand, the screw wash-sand machine doesn’t require extra

energy to eliminate Cl ion. The reason is that in the me-

chanical sand washing system, the ozone water is poured

into the screw wash-sand machine to remove Cl ion [7,

8]. In other words, the chemical approach is adopted to

get rid of Cl ion. Therefore, the total power of the screw

wash-sand machine mainly contains three parts: the

power used for washing sand, power used for no-load

running, and additional power caused by the incline. The

driving power of the screw wash-sand machine is

(3)

where P is the driving power of the screw wash-sand

machine in kilowatts and � is the running resistance fac-

tor.

The driving power of the motor is

(4)

where N is the driving power of the motor in kilowatts,

K is the power reserve coefficient of the motor, and � is

the machinery driving efficiency. In general, the ma-


chinery driving efficiency of the screw wash-sand ma-

chine is in the range 0.9 � 0.94.

Substituting Eqs. (2) and (4) into Eq. (1) gives

(5)

Since the objective is to minimize the specific energy

consumption of the screw wash-sand machine, the value

of Eq. (5) should be as low as possible. Therefore, the

objective function can be expressed as

2.3 Constraint Functions

2.3.1 Constraint Condition of Diameters

To improve the loading space of the screw structure,

the diameter of the screw axis should be as small as pos-

sible. But if the diameter of the screw axis is too small,

the manufacturing difficulty will increase. Through syn-

thetical consideration, the ranges of main parameters are

0.5 D 1.5, 0.3D d 0.4D

Thus, constraint conditions are

g1(x) = x1 � 0.5 0, g2(x) = 1.5 � x1 0,

g3(x) = x3 � 0.3x1 0, g4(x) = 0.4x1 � x3 0

2.3.2 Constraint Condition of Pitch

The selection of the pitch S should be based on the

layout of the screw wash-sand machine, characteristics

of sand, and diameter of the screw structure. The general

equation of the pitch S is

S = cD (6)

where c is the proportional coefficient of the pitch S and

diameter D.

Generally, the proportional coefficient c is in the

range 0.8 c 1. Therefore, the range of the pitch S is

0.8D S 1.0D


g5(x) = x2 � 0.8x1 0, g6(x) = x1 � x2 0

2.3.3 Constraint Conditions of Blade Thickness and

Installation Angle

Since most of the design parameters of the screw

wash-sand machine are the design variables in the opti-

mization design, the load on the blade can’t be determined

accurately. The selection of the blade thickness should

meet strength requirements. According to the strength

design principle, the range of the blade thickness can be

determined. That is,

0.01 w 0.05

According to the structure size of other mechanical

equipments in the mechanical wash-sand system, the in-

stallation angle of the screw wash-sand machine should

be in the range

15� � 20�


g7(x) = x4 � 0.01 0, g8(x) = 0.05 � x4 0,

g9(x) = x5 � 15 0, g10(x) = 20 � x5 0

2.3.4 Constraint Condition of Speed

The speed of the screw axis has great influence on

the production capacity. In general, the faster the screw

axis runs, the stronger the transmission capacity will

be. However, if the speed exceeds a critical value, sand

will be drawn out due to excessive friction centrifugal

force, causing that the axial motion of sand can’t be ex-

ecuted [19]. Thus, the speed of the screw axis should be

restricted. The limiting condition of the speed is

(7)

and


(8)

To simplify, let

(9)

So

(10)

where K� is the comprehensive coefficient of material,

nmax is the maximum critical speed in radians per minute,

g is the acceleration due to the earth’s gravity in meters

per second squared, and A� is the synthetic characteris-

tic coefficient of material.

Normally, the speed of the screw axis is in the range

of 8 to 12 rad/min. Thus, constraint conditions are

2.3.5 Constraint Condition of Stiffness

The screw axis of the screw wash-sand machine is

an axis with a large span, and it only has one section. The

simplified mechanical model of the screw axis is shown

in Figure 4. Due to the effect of the load, the screw axis

will produce bending deformation. If the deformation

amount of the screw axis exceeds the allowable limit,

then the screw axis will be unable to work normally and

even may lose its working performance [28]. Therefore,

the constraint condition of the stiffness of the screw axis

is overwhelmingly necessary.

Based on mechanics of material, the maximum de-

flection of the screw axis is given by the equation [28]

(11)

where fmax is the maximum deflection in meters, E is

elastic modulus in tons per second squared, q is uniform

load in newtons per meter, G is the mass of the screw

structure in tons, and I is the inertia moment of the screw

axis in meters4.

The mass of the screw structure is given by the equa-

tion

(12)

but

(13)

(14)

Substituting Eqs. (13) and (14) into Eq. (12) gives

(15)

where V1 is the volume of the screw axis in cubic me-

ters, V2 is the volume of the blade in cubic meter, is

the material density of the screw structure in tons per

meter cubed, and w is blade thickness in meters.

Substituting (15) into Eq. (11) gets

(16)

The constraint condition of stiffness is that the maxi-

mum deflection should not be larger than the allowable

deflection; that is,

fmax [f] (17)


Figure 4. Mechanical model of the screw axis.

where [f] is the allowable deflection in meters. For

general utility shafts, the allowable deflection is in the

range of 0.0001L to 0.0005L [29].

Thus, the constraint condition is

2.3.6 Constraint Condition of Reliability

Reliability is a vital quality index of products be-

cause it expresses the normal service ability of products.

In the reliability design, the load, strength, and other de-

sign parameters can be taken as random variables, so

load properties, material properties, and the properties of

other design parameters can be described in a more ob-

jective and scientific way. Meanwhile, the objective of

the reliability design is to ensure the probability of the

strength greater than the load. The reliability design can

quantitatively describe the safety degree of the design.

The main acting force of the screw axis is torque, and

when the screw wash-sand machine washes sea sand, the

torque of the screw axis is almost invariable. Assume that

both the stress and strength of the screw axis follow the

Gauss distribution. According to the relationship between

the stress and strength in the reliability design, the reli-

ability coefficient is given by [30,31]

(18)

where Z is the reliability coefficient, � is the mean value

of the allowable shear stress in pascals, �� is the stan-

dard deviation of the allowable shear stress in pascals, �

is the mean value of the shear stress in pascals, �� is the

standard deviation of the shear stress in pascals, and T

is the mean value of torque in newton-meters.

According to statistical results, the standard devia-

tion of the strength is about 10 percent of the mathemati-

cal expectation [31]. Therefore, the approximate formula

of the standard deviation of the allowable shear stress ��

and the mean value of the allowable shear stress � can be

expressed by

(19)

According to the method of moments in the reli-

ability design, the distributed parameters of the random

variable function y = f (x) are as follows [30,31]:

(20)

(21)

where y is the random variable, E(y) is the mathematical

expectation of the random variable y, D(y) is the vari-

ance of the random variable y, X1, X2,…, Xi are mutually

independent random variables, and �1, �2,…, �i are the

mean value of above mutually independent random

variables, respectively.

Based on Eq. (21), the standard deviation of the shear

stress �� can be calculated as

(22)

where �T is the standard deviation of torque in newton-

meters and �d is the diameter deviation of the screw

axis in meters.

Due to the limitation of the precision of manufactur-

ing equipments, the precision of measuring tools, the op-

eration level of workers, conditions, environments, etc.,

the dimensions of the parts after machine work have

some randomness. Normally, the dimensional deviation

of parts always follows the Gauss distribution. Based on

the triple standard difference method, the diameter devi-

ation of the screw axis can be expressed by [30,31]

(23)

where � is the deviation factor of the diameter.

According to the triple standard difference method,

the standard deviation of torque can be expressed by

(24)

where � is the deviation factor of the load.


Substituting Eqs. (3), (19), (22), (23), and (24) into

Eq. (18) yields

(25)

Based on the application requirements of the screw

axis, let the reliability R be 0.95. The reliability coeffi-

cient Z can be determined as

Z [Z] (26)

where [Z] is the reliability coefficient. When the reli-

ability of the screw axis is 0.95, the value of the reli-

ability coefficient [Z] is 1.64 [31].

Thus, the constraint condition is

3. Determination of Optimization Algorithm

The existing optimization methods can be classified

into two major types: traditional deterministic optimi-

zation methods and intelligent optimization algorithms.

Traditional deterministic optimization methods, such as

the steepest descent algorithm, newton algorithm, conju-

gate gradient algorithm, simplex algorithm, variable me-

tric method, sequential quadratic programming algorithm,

and penalty function method, generally have perfect ma-

thematical basis and strict mathematical definition [32].

However, traditional deterministic optimization methods

have following restrictions [32]: (a) traditional determi-

nistic optimization methods do not fare well over a broad

spectrum of problem domains; (b) traditional determi-

nistic optimization methods are not suitable for solving

multi-modal problems as they tend to obtain a local op-

timal solution; (c) traditional deterministic optimization

methods are not ideal for solving multi-objective optimi-

zation problems; (d) traditional deterministic optimiza-

tion methods are not suitable for solving problems in-

volving large number of constraints.

To improve the performance of optimization algo-

rithms and overcome the limitations of traditional opti-

mization algorithms, a plenty of novel optimization al-

gorithms (i.e., intelligent algorithms), such as the evolu-

tionary programming, genetic algorithm, immune algo-

rithm, plant growth simulation algorithm, simulated an-

nealing, ant colony algorithm, particle swarm optimiza-

tion, differential evolution, harmony elements algorithm,

shuffled frog leaping algorithm, grenade explosion algo-

rithm, artificial fish school algorithm, and artificial bee

colony algorithm, are proposed by many scholars from

different countries [33�36]. The development of these

optimization algorithms is based on simulating or reveal-

ing some natural phenomena or process. The thought

and content of intelligent algorithms involve the mathe-

matics, biological evolution, social behavior, artificial

intelligence, statistical mechanics, and so on. Although

the manifestation and principle of these optimization al-

gorithms are different, they have some common charac-

teristics: the population search, random search, paral-

lelism, and global superiority. However, these optimiza-

tion algorithms also have common defects: the compli-

cated computational process and difficulty of understand-

ing for beginners [37]. Therefore, Pan, W. T., a scholar

from Taiwan, proposes the fruit fly optimization algo-

rithm (FOA) in 2011 [38]. The calculation process of

FOA is very simple, and it is very easy for ordinary engi-

neers and technicians to understand FOA. For the above

reasons and the complexity of the optimization problem

in this study, FOA is adopted to execute the optimization

design of the screw wash-sand machine.

The foraging behavior of the fruit fly is superior to

other species, especially in osphresis and vision, which

is as shown in Figure 5 [37]. The olfactory organs of the

fruit fly can collect various kinds of the odors that float in

air, and can even smell the food source outside 40 km.

When approaching the position of food, the fruit fly can

use keen vision to find food and the gathering place of

companions, and then flies to that direction.

The main steps of FOA are summarized as follows

[37]:

Step 1. Initialize the position of the fruit fly group

randomly.

Init X_axis; Init Y_axis


Step 2. Set the random direction and distance of the

individual fruit fly using smell to find food.

Xi = X_axis + RandomValue

Yi = Y_axis + RandomValue

Step 3. With the position of food unknown, estimate

the distance to the origin first (Dist), and then calculate

the smell concentration judgment value (S), which is the

reciprocal of the distance.

Disti = X Yi i

2 2�

Si = 1/ Disti

Step 4. Substitute smell concentration judgment

value (S) into smell concentration judgment function (or

called Fitness function) so as to find the smell concentra-

tion (Smelli) of the individual location of the fruit fly.

Smelli = Function(Si)

Step 5. Find the fruit fly whose smell concentration

is the maximum in the fruit fly group; namely, solve for

the maximal value.

[bestSmellbestIndex] = max(Smell)

Step 6. Retain the optimal value of the smell concen-

tration and X- and Y-coordinates. Then, the fruit fly group

flies to that position by using vision and forms a new ga-

thering place.

Smellbest = bestSmell

X_axis = X(bestIndex)

Y_axis = Y(bestIndex)

Step 7. In the course of iterative optimization, exe-

cute steps 2 through 5 repeatedly, and determine whether

the smell concentration is superior to that of the previous

iteration. If so, execute step 6.

4. Optimization Example

4.1 Optimal Calculation Based on FOA

Take a kind of screw wash-sand machine as the re-

search object. Related parameters, which are provided

by a manufacturing enterprise, are listed as follows:

The optimization design for the screw wash-sand ma-

chine is a nonlinear programming problem with six un-

known variables and fifteen constraint conditions. There

are many methods used to solve constrained minimiza-

tion problems, such as the feasible direction, gradient

projection method, active set method, penalty function

method, and so forth. The most common approach for

solving constrained optimization problems is the use of a

penalty function. Penalty functions are distinguished into

two main categories: stationary and non-stationary, and

results obtained using non-stationary penalty functions

are superior to those obtained using stationary functions

[39�41]. Therefore, this study adopts the non-stationary

multi-stage assignment penalty function to solve the con-

strained optimization problem. The optimization is exe-

cuted with FOA, and the algorithm program is compiled

by using MATLAB. Research shows that if the size of

the fruit fly population is small, then the search path will

be unstable, the convergence rate will be slow, and the

execution speed of the program will be fast; if the size of

the fruit fly population is large, then the search path will

be stable, the convergence rate will be fast, and the exe-

cution speed of the program will be slow [42]. By con-

sidering the complexity of the optimization problem in

this study, let iteration times be 30000 and population


Figure 5. Illustration of the body look of the fruit fly andgroup iterative food searching of fruit fly.

sizes be 75 in FOA. FOA is executed four times, and si-

mulation results are exactly the same, showing that the

stability of FOA is very excellent. The obtained optimi-

zation process of FOA is shown in Figure 6. In Figure 6,

it is manifest that after approximately 10000 iterations,

the specific energy consumption of the screw wash-sand

machine reaches the minimum, which provides the va-

lidity of the selection of iteration times and population

sizes. The comparison between the results of the optimi-

zation design and that of the original design is shown in

Table 1.

Table 1 shows that the diameter of the screw struc-

ture increases by 8.4%; the pitch increases by 9.23%; the

diameter of the screw axis decreases by 11.79%; the

blade thickness decreases by 26.67%; the installation

angle decreases by 25%; the rotational speed decreases

by 5.56%; the mass of the screw structure decreases by

21.26%; the production capacity increases by 21.22%;

the driving power of the motor increases by 15.68%; the

specific energy consumption decreases by 4.59%, which

shows that optimization results achieve the objective of

reducing the specific energy consumption. Although this

study only takes the specific energy consumption of the

screw wash-sand machine as the research object, the spe-

cific energy consumption can reflect various indexes of

the screw wash-sand machine comprehensively. Thus,

the selection of the objective function is correct.

4.2 Sensitivity Analysis

The minor changes of the design variables may cause

a great fluctuation of the performance indexes of the me-

chanical structure. The sensitivity analysis is a crucial

step in the optimization design [43�45]. The aim of the

sensitivity analysis is to analyze the effect of the small

changes of the design variables on the optimal solution.

In general, the lower the sensitivity is, the smaller the dif-

ference between the actual situation and theoretical cal-

culation are. Therefore, the sensitivity analysis is ex-

tremely important for some practical engineering prob-

lems.

The derivative of the objective function with respect

to the design variables is defined as the objective sensi-

tivity [43]:

(27)

where X* is the optimal solution vector.

The obtained objective sensitivities are as follows:

From the above data, it is evident that the objective

function is not sensitive to the design variables, showing

that the optimal solution obtained in this study has high

stability and reliability.

The derivative of constraint conditions with respect

to the design variables is defined as the constraint sensi-

tivity:

(28)

The obtained constraint sensitivities are as follows:


Figure 6. The curve of optimization process.

Table 1. Comparison between original design and optimization design

Parameters D S d w � n G Q N H

Original design 0.750 0.65 0.280 0.015 20 9 4.190 43.552 3.036 0.0697

Optimization design 0.813 0.71 0.247 0.011 15 8.5 3.299 52.795 3.512 0.0665

Change rate % +8.4 +9.23 -11.79 -26.67 -25 -5.56 -21.26 +21.22 +15.68 -4.59

From the above data, it is notable that the constraint

condition of the speed g11 is sensitive to the diameter of

the screw structure D and the constraint condition of reli-

ability g15 is sensitive to the diameter of the screw axis d.

Thus, the diameter of the screw structure D and the dia-

meter of the screw axis d are sensitive factors. To avoid

changing the original intention of the optimization de-

sign in this study, the dimensions of the diameters of the

screw axis and screw structure should be strictly limited

within manufacturing processes, especially the diameter

of the screw axis.

5. Conclusions

By analyzing the sand washing technology of the

screw wash-sand machine, the objective function, design

variables, and constraint conditions are determined, and

then the optimization mathematical model is established.

The case-based design of the screw wash-sand machine

is executed with FOA, the program of which is compiled

by using MATLAB. The obtained conclusions are as fol-

lows:

(1) Compared with the original design, the specific energy

consumption of the optimized screw wash-sand ma-

chine decreases by 4.59%, proving the validity of the

optimization mathematical model.

(2) The optimal solution obtained using the fruit fly opti-

mization algorithm has high stability and reliability.

(3) The diameters of the screw structure and screw axis

are sensitive factors in the optimization design, which

should be strictly limited within manufacturing pro-

cesses.

(4) The fruit fly optimization algorithm can solve the op-

timization problem of structure parameters well. This

new intelligent algorithm will provide a new idea for

the mechanical optimization design field.

(5) In our future work, the screw wash-sand machine

will be manufactured to carry out the experimental

verification on the basis of the optimized structure

parameters.

Acknowledgements

The authors gratefully acknowledged the Financial

Support by the Foundation of Science and Technology

Competitive Allocation of Zhanjiang (No. 2014A02010),

the Funds for Innovation Introduced and Integration

Project of Hainan Province (No. KJHZ2014-10), and the

Fundamental Research Funds for Rubber Research Insti-

tute, CATAS (No. 1630022013019).

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Manuscript Received: Jul. 31, 2015

Accepted: Nov. 22, 2015


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