CN104091004B

CN104091004B - A kind of quantitative static pressure turntable Optimization Design based on modified particle swarm optiziation

Info

Publication number: CN104091004B
Application number: CN201410302534.XA
Authority: CN
Inventors: 刘志峰; 张涛; 湛承鹏; 李小燕
Original assignee: Beijing University of Technology
Current assignee: Beijing University of Technology
Priority date: 2014-06-27
Filing date: 2014-06-27
Publication date: 2017-09-22
Anticipated expiration: 2034-06-27
Also published as: CN104091004A

Abstract

The present invention relates to a kind of quantitative static pressure turntable Optimization Design based on modified particle swarm optiziation, belong to static pressure turntable design field.The parameterized model of static pressure turntable table top is set up, rigidity, damping and the general power of turntable oil film are calculated according to hydrodynamics correlation theory；Determine the number of population, the optimization range of Optimal Parameters, the speed that particle maximum is circled in the air, inertial factor parameter, setting up the speed that wherein inertial factor is circled in the air with particle in particle cluster algorithm, algorithm will in real time correct with the change of locally optimal solution and globally optimal solution；Population is write using matlab and calculates optimization program, calculates the optimal design parameters of turntable.The method have the characteristics that optimizing design to turntable using modified particle swarm optiziation, inertial factor and the speed of circling in the air of particle will at any time be corrected with locally optimal solution pbest and globally optimal solution gbest change in algorithm, can so improve convergence of algorithm speed and the accuracy of optimization.

Description

A kind of quantitative static pressure turntable Optimization Design based on modified particle swarm optiziation

Technical field

The present invention relates to a kind of Optimization Design of the quantitative static pressure turntable of double-round lubricating pad supporting, more particularly to one kind Quantitative static pressure turntable Optimization Design based on modified particle swarm optiziation, belongs to static pressure turntable design field.

Background technology

Two tables that static pressure turntable (Hydrostatic Rotary Table) makes to have relative motion with the fluid for having pressure Face separates and carried by hydrostatic pressure.Due to being separated completely by oil film between kinematic pair, so the frictional force between kinematic pair Greatly reduce, while its bearing capacity, kinematic accuracy and life-span but greatly improve.Just because of liquid static-pressure support is many excellent Point, so it is widely used in heavy machine tool and as one of its critical component.The properties of static pressure turntable are for lathe Precision and crudy have important influence, find the optimal design parameters of turntable has for the performance of General Promotion turntable Important function.

The numerous object functions for needing to optimize of design parameter of static pressure turntable are also more more complicated, carrying out the optimization of turntable If being calculated during design each possible value of each design parameter and therefrom choosing optimal solution again, then it is counted Calculation amount will be very huge, so finding a kind of optimization design of the wide optimized algorithm of the good region of search of convergence for lifting turntable Play an important role.

The content of the invention

It is an object of the invention to provide a kind of quantitative static pressure turntable optimization design side based on modified particle swarm optiziation Method, first calculate turntable static pressure oil film stiffness and damping and general power as optimization object function, afterwards using it is improved from Swarm optimization quickly and accurately finds the optimal design parameters of turntable.

To achieve the above object, the technical solution adopted by the present invention is and a kind of quantifying based on modified particle swarm optiziation Formula static pressure turntable Optimization Design, its implementation process is as follows,

S1 sets up the parameterized model of static pressure turntable table top, and the firm of turntable oil film is calculated according to hydrodynamics correlation theory Degree, damping and general power；

S2 determines the number of population, the optimization range of Optimal Parameters, the speed that particle maximum is circled in the air, inertial factor ginseng Number, set up in particle cluster algorithm, algorithm speed that wherein inertial factor is circled in the air with particle will with locally optimal solution with it is global most The change of excellent solution and correct in real time；

S3 writes population using matlab and calculates optimization program, calculates the optimal design parameters of turntable.

Compared with prior art, the present invention has the advantages that.

The method have the characteristics that optimizing inertial factor in design, algorithm to turntable using modified particle swarm optiziation And the speed of circling in the air of particle will at any time be corrected with locally optimal solution pbest and globally optimal solution gbest change, so may be used Improve convergence of algorithm speed and the accuracy of optimization.The content of the invention includes three parts, and static pressure turntable is set up in the first portion The optimization object function of optimization design, sets population number, particle maximum to circle in the air speed, inertial factor etc. in the second portion Parameter；Optimization program calculation optimization solution is write with matlab in Part III.

Brief description of the drawings

Fig. 1 static pressure turntable structure diagrams.

Fig. 2 supports oil pad structure sketch.

Fig. 3 precompressed oil pad structure sketches.

Fig. 4 Optimizing Flow figures.

Fig. 5 rigidity and the parato of damping scheme.

Embodiment

The present invention is described in further detail below with reference to drawings and examples.

The present invention implements a kind of Optimization Design of the static pressure turntable of double-round lubricating pad supporting, below in conjunction with the accompanying drawings, to this The implementation of invention is specifically described.

Fig. 1 is the static pressure turntable mesa structure sketch that double-round is supported, and turntable supports lubricating pad, precompressed by turntable table top, pedestal Lubricating pad is constituted, and the deadweight of turntable is G, and the fuel delivery that each lubricating pad wherein supports lubricating pad by quantitative oil pump feed is Q₀, precompressed lubricating pad Fuel delivery be Q₁。

Fig. 2 Fig. 3 is the structure diagram of supporting lubricating pad and precompressed lubricating pad, and it is round that precompressed lubricating pad, which is annular lubricating pad and supports lubricating pad, Shape lubricating pad.

Step (1), the foundation of object function

According to dimensional analysis by continuity equation and N-S equation simplifications and solve to one-dimensional Reynolds equation and outflow oil sealing The flow of the fluid on side is：

R is radius in above formula, and η is the viscosity of fluid, and p is the pressure of oil film, and h is oil film thickness, t be the time so It is the extrusion speed of upper rail face squeeze film, Q (r) is flow.

1.1st, lubricating pad bearing capacity calculation is supported

Support lubricating pad structure diagram as shown in Figure 2 it be circular shape structure key dimension indicated in figure, R₁For Lubricating pad internal diameter R₂For the external diameter h of lubricating pad_iFor the oil film thickness of lubricating pad, then there is boundary condition for the lubricating pad of circular quantitative compensation：

H in above formula_iFor the oil film thickness of i-th of lubricating pad, p_iFor the oil film pressure distribution of i-th of lubricating pad, p_0iFor i-th of oil The oil pocket pressure of pad, Q₀For fuel delivery.The oil pocket of each supporting lubricating pad can be solved by bringing boundary condition (3) into equation (1) and (2) Pressure p_0iWith pressure distribution p_i(r)

And then the bearing capacity F of each supporting lubricating pad can be obtained_iFor：

Then the stiffness and damping of supporting lubricating pad is respectively with pump power：

Wherein K_SiTo support the rigidity of lubricating pad, C_SiTo support the damping of lubricating pad, N_TiTo support the general power of lubricating pad, R_kFor The radius of support ring R when lubricating pad is first lap_k=R_L, it is R when lubricating pad is located at the second circle_k=R_S。

1.2nd, the calculating of precompressed lubricating pad bearing capacity

Precompressed lubricating pad as shown in Figure 3 is annular lubricating pad, has the boundary condition to be for annular lubricating pad：

h_yFor the oil film thickness of precompressed lubricating pad, p_yFor precompressed lubricating pad oil film pressure distribution, p_0yFor precompressed lubricating pad oil pocket pressure, Q₁For precompressed lubricating pad fuel delivery.(8) formula generation such as (1), (2) formula be can obtain into the oil pocket pressure p of precompressed lubricating pad_0ySealing oil edge pressure point Cloth p_1y(r)、p_2y(r) it is：

And then the bearing capacity F of precompressed lubricating pad can be calculated_yFor：

So the stiffness K of precompressed lubricating pad_yDamp C_yWith general power N_TyFor：

The integral rigidity damping and the calculating of pump power of 1.3 turntables

The supporting system of turntable by each supporting lubricating pad and precompressed lubricating pad be formed in parallel so the integral rigidity of turntable, damping with Pump power is：

K in above formula_ZFor the axial rigidity of turntable, K_tFor rigidity of toppling, C_ZFor axial damping, C_tFor the damping, N of toppling_TTo be total Pump power, n1 is the number that first lap supports lubricating pad, and n2 is that the number of the second circle supporting lubricating pad rule of thumb typically has n2= 2n1.The object function of turntable optimization design can be written as:

F=min [K_Z,K_t,C_Z,C_t,-N_T]^T (15)

Need optimization parameter be：P=[R_S,R_L,R₁,R₂,R_C1,R_C2,R_C3,R_C4,h_s,h_y,Q₀,η,n1]

Step (2), modified particle swarm optiziation

Because Optimal Parameters are more and the object function of optimization is also relatively more so being carried out using particle cluster algorithm to it excellent Change.The selection of parameter optimization scope will be in each initial parameter values P₀On the basis of change a fixed percentage up and down, then it is each It is limited to above and below parameter：

b_aIt is exactly that the parameter that adjusts optimization range may be configured as 0.2 for border regulatory factor.Particle number np is set afterwards Be set to 2 times of optimised number of parameters also can suitably increase certainly, then define maximum speed of circling in the air and be：Max_v=P*b_aIt is used Sex factor is set to w_i,j=w₀+(pbest_i-gbest_j), w in formula₀5, i, which is can use, for the initial inertia factor represents i-th of particle, j Represent iteration j calculating.The circle in the air calculating formula of speed of particle is in modified particle swarm optiziation：

C in formula₁,c₂,c₃For regulatory factor, pbestx is the optimal location that single particle undergoes, and gbestx is global optimum I.e. the optimal location of the whole colony's experience in position, x is the position of particle, vx is the speed that particle circles in the air, and Rand is -1 to 1 Random number.Then the calculating formula of particle new position is：

x_i,j=x_i,j-1+vx_i,j (18)

Fitness function during optimization is exactly that object function is：

Adp=[K_Z,K_t,C_Z,C_t,-N_T]^T (19)

Step (3), the implementation of improved particle group optimizing program

Modified particle swarm optiziation calculation procedure is write with matlab, and its calculation process is illustrated in figure 4：(1) presses 2.1 Step sets initial parameter P₀, b_a, w₀, P_{max_bund}, P_{min_bund}, c₁, c₂, c₃, pbest₀, gbest₀；(2) presses formula w_i,j=w₀+ (pbest_i-gbest_j) calculate the speed vx that circles in the air that inertial parameter w is calculated particle by formula (17) again, back-pushed-type (18) each The new position x of each particle_new；(3) judges whether the position of each particle then needs to recalculate particle speed within the limits prescribed Degree and particle position are untill meeting boundary condition then with new position x_newCalculate new fitness value adp_new；(4) is pressed Globally optimal solution and locally optimal solution are updated according to following formula

(5) whether determining program meets end condition and is so terminated and result of calculation is defeated if program if met after Go out, as being unsatisfactory for, return to second step and proceed to calculate until program determination.

The validity of this method is illustrated in order to provide an example under clearer explanation this method.Select P= (R₁,R₂,R_C1,R_C2,R_C3,R_C4,Q₀) it is that the initial value of each parameter of optimised parameter is P₀=(0.15,0.165,0.19,0.22, ), 0.24,0.27,1.4e-4 border regulatory factor b_aJust take 0.2.Particle number np takes 14, w₀5 are taken, maximum iteration is 100 steps.Then running optimizatin program can be obtained by optimum results.Fig. 5 is the parato figures of rigidity and overall rate, as seen from the figure In reduction, rigidity is increasing the pump power of optimization process intermediate station, and the result of optimization is as shown in table 1：

The stiffness and damping for being not difficult to find out turntable from result has been lifted and pump power is reduced significantly, this Show that this method can carry out the optimization design of turntable.

Table1 optimum results

Claims

1. a kind of quantitative static pressure turntable Optimization Design based on modified particle swarm optiziation, S1 sets up static pressure turntable table top Parameterized model, according to hydrodynamics correlation theory calculate turntable oil film rigidity, damping and general power；

S2 determines the number of population, and the optimization range of Optimal Parameters, the speed that particle maximum is circled in the air, inertial factor parameter is built The speed that wherein inertial factor is circled in the air with particle in vertical particle cluster algorithm, algorithm is by with locally optimal solution and globally optimal solution Change and correct in real time；

S3 writes particle cluster algorithm optimization program using matlab, calculates the optimal design parameters of turntable；

Turntable supports lubricating pad, precompressed lubricating pad composition by turntable table top, pedestal；The deadweight of turntable is G, and each lubricating pad has constant displacement pump Fuel feeding, wherein the fuel delivery of supporting lubricating pad is Q₀, the fuel delivery of precompressed lubricating pad is Q₁；Precompressed lubricating pad is annular lubricating pad and supports oil Pad is circular lubricating pad；

It is characterized in that：This method to implement process as follows,

Step 1, the foundation of object function,

According to dimensional analysis is by continuity equation and N-S equation simplifications and solution obtains one-dimensional Reynolds equation and outflow sealing oil edge The flow of fluid is：

R is radius in above formula, and η is the viscosity of fluid, and p is the pressure of oil film, and h is oil film thickness, and t is the time, soIt is The extrusion speed of upper rail face squeeze film, Q (r) is flow；

1.1st, lubricating pad bearing capacity calculation is supported

The structure for supporting lubricating pad is circular shape structure, R₁For lubricating pad internal diameter, R₂For the external diameter of lubricating pad, h_iIt is thick for the oil film of lubricating pad Degree, then have boundary condition for the lubricating pad of circular quantitative compensation：

H in above formula_iFor the oil film thickness of i-th of lubricating pad, p_iFor the oil film pressure distribution of i-th of lubricating pad, p_0iFor i-th lubricating pad Oil pocket pressure, Q₀For fuel delivery；Bring boundary condition (3) into equation (1) and (2) solve the oil pocket pressure p of each supporting lubricating pad_0iWith Pressure distribution p_i(r)

<mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>&eta;</mi> </mrow> <mrow> <msubsup> <mi>&pi;h</mi> <mi>i</mi> <mn>3</mn> </msubsup> </mrow> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mrow> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mn>2</mn> </msub> </mfrac> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <mi>&eta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mn>1</mn> </msub> </mfrac> <mo>)</mo> <mo>-</mo> <msubsup> <mi>R</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mn>2</mn> </msub> </mfrac> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <msubsup> <mi>h</mi> <mi>i</mi> <mn>3</mn> </msubsup> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>h</mi> <mi>i</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>R</mi> <mn>2</mn> </msub> <msub> <mi>R</mi> <mn>1</mn> </msub> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> 1

And then obtain the bearing capacity F of each supporting lubricating pad_iFor：

<mrow> <msub> <mi>F</mi> <mi>i</mi> </msub> <mo>=</mo> <msubsup> <mi>&pi;R</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>p</mi> <mrow> <mn>0</mn> <mi>i</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mi>&pi;</mi> <munderover> <mo>&Integral;</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> <msub> <mi>R</mi> <mn>2</mn> </msub> </munderover> <msub> <mi>rp</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>r</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

Wherein K_SiTo support the rigidity of lubricating pad, C_SiTo support the damping of lubricating pad, N_TiTo support the general power of lubricating pad, R_kFor support ring Radius, when lubricating pad be first lap when R_k=R_L, it is R when lubricating pad is located at the second circle_k=R_S；

1.2nd, the calculating of precompressed lubricating pad bearing capacity

Precompressed lubricating pad is annular lubricating pad, has the boundary condition to be for annular lubricating pad：

h_yFor the oil film thickness of precompressed lubricating pad, p_yFor precompressed lubricating pad oil film pressure distribution, p_0yFor precompressed lubricating pad oil pocket pressure, Q₁For Precompressed lubricating pad fuel delivery；(8) formula generation such as (1), (2) formula is obtained into the oil pocket pressure p of precompressed lubricating pad_0y, sealing oil edge pressure distribution p_1y (r)、p_2y(r) it is：

<mrow> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mi>r</mi> <mn>2</mn> </msup> <mn>3</mn> <mi>&eta;</mi> </mrow> <mrow> <msubsup> <mi>&pi;h</mi> <mi>y</mi> <mn>3</mn> </msubsup> </mrow> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>h</mi> <mi>y</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>-</mo> <mfrac> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mrow> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mn>4</mn> </mrow> </msub> </mfrac> <mo>)</mo> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> <mi>&eta;</mi> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mrow> <mi>C</mi> <mn>4</mn> </mrow> <mn>2</mn> </msubsup> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mn>3</mn> </mrow> </msub> </mfrac> <mo>)</mo> <mo>-</mo> <msubsup> <mi>R</mi> <mrow> <mi>C</mi> <mn>3</mn> </mrow> <mn>2</mn> </msubsup> <mi>l</mi> <mi>n</mi> <mo>(</mo> <mfrac> <mi>r</mi> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mn>4</mn> </mrow> </msub> </mfrac> <mo>)</mo> <mo>)</mo> </mrow> </mrow> <msubsup> <mi>h</mi> <mi>y</mi> <mn>3</mn> </msubsup> </mfrac> <mfrac> <mrow> <mo>&part;</mo> <msub> <mi>h</mi> <mi>y</mi> </msub> </mrow> <mrow> <mo>&part;</mo> <mi>t</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mi>l</mi> <mi>n</mi> <mrow> <mo>(</mo> <mfrac> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mn>4</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>C</mi> <mn>3</mn> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow> 2

And then calculate the bearing capacity F of precompressed lubricating pad_yFor：

<mrow> <msub> <mi>F</mi> <mi>y</mi> </msub> <mo>=</mo> <mi>&pi;</mi> <mrow> <mo>(</mo> <msubsup> <mi>R</mi> <mrow> <mi>C</mi> <mn>3</mn> </mrow> <mn>2</mn> </msubsup> <mo>-</mo> <msubsup> <mi>R</mi> <mrow> <mi>C</mi> <mn>2</mn> </mrow> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mrow> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mi>&pi;</mi> <munderover> <mo>&Integral;</mo> <msub> <mi>R</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> </munderover> <msub> <mi>rp</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>r</mi> <mo>+</mo> <mn>2</mn> <mi>&pi;</mi> <munderover> <mo>&Integral;</mo> <msub> <mi>R</mi> <mrow> <mi>c</mi> <mn>3</mn> </mrow> </msub> <msub> <mi>R</mi> <mrow> <mi>c</mi> <mn>3</mn> </mrow> </msub> </munderover> <msub> <mi>rp</mi> <mrow> <mn>2</mn> <mi>y</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mi>d</mi> <mi>r</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

The supporting system of turntable is formed in parallel by each supporting lubricating pad with precompressed lubricating pad, then integral rigidity, damping and the pump of turntable Power is：

K in above formula_ZFor the axial rigidity of turntable, K_tFor rigidity of toppling, C_ZFor axial damping, C_tFor the damping, N of toppling_TFor total pump work Rate, n1 is the number that first lap supports lubricating pad, and n2 is the number of the second circle supporting lubricating pad, rule of thumb there is n2=2n1；Turntable is excellent The object function for changing design is written as:

F=min [K_Z,K_t,C_Z,C_t,-N_T]^T (15)

Step 2, modified particle swarm optiziation

Because Optimal Parameters are more and the object function of optimization also compares many, so being optimized using particle cluster algorithm to it； The selection of parameter optimization scope will be in each initial parameter values P₀On the basis of up and down change a fixed ratio, then each parameter it is upper Lower limit is：

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>max</mi> <mo>_</mo> <mi>b</mi> <mi>u</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>b</mi> <mi>a</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>P</mi> <mrow> <mi>min</mi> <mo>_</mo> <mi>b</mi> <mi>u</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>P</mi> <mn>0</mn> </msub> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>b</mi> <mi>a</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow> 3

b_aFor border regulatory factor, the parameter of optimization range is exactly adjusted, 0.2 is set to；Particle number np is set afterwards, is set to 2 times of optimised number of parameters, then defining maximum speed of circling in the air is：Max_v=P*b_a, inertial factor is set to w_i,j=w₀+ (pbest_i-gbest_j), w in formula₀5, i is taken to represent i-th of particle for the initial inertia factor, j represents iteration j calculating；Improve Particle cluster algorithm in the circle in the air calculating formula of speed of particle be：

<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>vx</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>w</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>*</mo> <msub> <mi>vx</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>*</mo> <mi>R</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>pbestx</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo>*</mo> <mi>R</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>gbestx</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>3</mn> </msub> <mo>*</mo> <mi>R</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mo>*</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>pbestx</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>gbestx</mi> <mrow> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

C in formula₁,c₂,c₃For regulatory factor, pbestx is the optimal location that single particle undergoes, and gbestx is global optimum position Put, that is, whole colony experience optimal location, x is the position of particle, and vx is the speed circled in the air of particle, and Rand is yes and -1 arrived The number randomly generated between 1；Then the calculating formula of particle new position is：

x_i,j=x_i,j-1+vx_i,j (18)

Fitness function during optimization is exactly that object function is：

Adp=[K_Z,K_t,C_Z,C_t,-N_T]^T (19)

The implementation of the improved particle group optimizing program of step 3

Modified particle swarm optiziation calculation procedure is write with matlab, and its calculation process is：(1) sets initial ginseng by 2.1 steps Number P₀, b_a, w₀, P_{max_bund}, P_{min_bund}, c₁, c₂, c₃, pbest₀, gbest₀；(2) presses formula w_i,j=w₀+(pbest_i-gbest_j) Calculate inertial parameter w, then calculate by formula (17) the speed vx that circles in the air of particle, back-pushed-type (18) calculate the new position of each particle Put x_new；(3) judges that whether within the limits prescribed, otherwise the position of each particle needs to recalculate particle rapidity and particle position Put, untill meeting boundary condition；Then with new position x_newCalculate new fitness value adp_new；(4) is according to the following formula more New globally optimal solution and locally optimal solution

(5) whether determining program meets end condition after, is terminated if meeting so program and exports result of calculation, As being unsatisfactory for, return to second step and proceed to calculate until program determination.