CN106682292A - Blade root structure optimization method of dimensionality reduction simulated annealing algorithm - Google Patents
Blade root structure optimization method of dimensionality reduction simulated annealing algorithm Download PDFInfo
- Publication number
- CN106682292A CN106682292A CN201611154821.6A CN201611154821A CN106682292A CN 106682292 A CN106682292 A CN 106682292A CN 201611154821 A CN201611154821 A CN 201611154821A CN 106682292 A CN106682292 A CN 106682292A
- Authority
- CN
- China
- Prior art keywords
- value
- design variable
- maximum stress
- blade root
- dimensional
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Abstract
The invention discloses a blade root structure optimization method of a dimensionality reduction simulated annealing algorithm. The method includes the steps that firstly, a design variable in the optimization process is determined, and two-dimensional parameterization modeling and three-dimensional parameterization modeling of a target blade are completed; secondly, an N0 set of design variables is randomly generated, an initial average value mu0 and an initial standard deviation delta0 of maximum stress value relative errors of a two-dimensional model and a three-dimensional model under the N0 set of design variables are calculated through a finite element method; thirdly, according to a computation result of the three-dimensional finite element model, the blade root is optimized through the simulated annealing algorithm, a dimensionality reduction rule is introduced according to the initial average value mu0 and the initial standard deviation delta0 of the relative errors in the Metropolis sampling process, the finite element computation amount is reduced, and the average value and the standard deviation of the relative errors is updated after three-dimensional model computation is conducted; when the annealing temperature is lower than a set value or a target function value is stable, the computation process is converged if the result is verified to be within a permissible error range, and optimization is completed. The method has the advantages of being high in convergence speed, capable of saving computation resources and time and the like.
Description
Technical field
The present invention relates to turbine blade field, more particularly to a kind of leaf and root structure optimization method.
Background technology
As China's fired power generating unit constantly develops to Large Copacity, high parameter direction, the safety and reliability of steam turbine is asked
Topic is also increasingly taken seriously.Be constantly in the steam turbine blade of HTHP adverse circumstances during for work, blade root be by
It is fixed on the connection parts in impeller or rotating shaft, and carries the huge centrifugal force of blade and other load.Work as leaf
It is huge so as to cause when stress suffered by root somewhere exceedes material limits, it is possible to leaf destruction can be caused and make steam turbine failure
Economic loss, it is therefore necessary to improve leaf and root structure to reduce its stress level, improve unit operation reliability,.
It is the blade root optimization method for mainly using at present that FInite Element and optimized algorithm are combined.By finite element software
The calculating of complete blade pair three dimensional non-linear contact model simultaneously extracts stress result, then using optimized algorithm by " dividing
The mode of analysis --- assessment --- amendment " completes the search to optimal leaf and root structure, and the purpose of stress level is reduced to reach.This
Planting optimization method has the advantages that optimum results high precision, but because the finite element grid quantity of three dimensional non-linear contact model is huge
Greatly, and calculating process convergence it is relatively difficult, so this optimization method generally requires to take considerable time and computer resource.Cause
This, it is necessary to set up a kind of result high precision, calculating process Fast Convergent and time-consuming short blade root optimization method.
The content of the invention
It is an object of the invention to provide a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing, by introducing dimensionality reduction
Criterion, using two dimension and three-dimensional finite element model cross validation during simulated annealing optimization, has with certain probability with two dimension
Limit unit calculates and replaces dimensional Finite Element, can solve the problem that in current blade root optimization method that convergence is slow, the problem that time-consuming.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of leaf and root structure optimization method of dimensionality reduction simulated annealing, comprises the following steps：
The first step, determines the design variable in optimization process, and complete to the two-dimensional parameterization modeling of target blade and three
Dimension parametric modeling；
Second step, generates N at random0Group design variable, this N is gone out by FEM calculation0Group design variable under two dimensional model and
The initial average output value μ of threedimensional model maximum stress value relative error0δ poor with primary standard0；
3rd step, begins through simulated annealing and blade root is optimized with the result of calculation of three-dimensional finite element model,
Initial average output value μ in Metropolis sampling processes according to relative error0δ poor with primary standard0Dimensionality reduction criterion is introduced,
Reduce FEM calculation amount, and the average value and standard deviation of relative error are updated after threedimensional model calculating is carried out；
When annealing temperature is less than arranges value or object function value stabilization, calculated if product test is in allowable error
Process is restrained, and completes the structure optimization to blade root；Otherwise, gained minimum target functional value σ is calculated with the last timeoptInstitute
Corresponding design variable xoptFor initial designs variable and initialize parameter-embedded in remaining optimization process, repeat step again
Three optimize, until meeting the condition of convergence, complete the structure optimization to blade root.
Further, in step one：
For certain certain type of blade root, its specific geometry, i.e. x is determined by n parameterall=(x1,
x2,…,xn) be the blade root geometric shape parameterses；
In optimization process, a parameter to stress value sensitive is chosen as design variable, now take xdes=
(x1,x2,…,xa) as the design variable in blade root shape optimization problem, wherein xdes∈xall；xall=(x1,x2,…,xn) in
The form parameter for not being selected as design variable is design constant.
Further, step 2 is specifically included：
Random generation N0Group design variable, completes this N by way of step one0The two dimension of group design variable correspondence blade root
Parametric modeling and 3 D Parametric Modeling；By finite element software, completed to two dimensional model after boundary condition is set
Solved with threedimensional model stress analysis, and extract maximum stress value each time respectively, remember two dimensional model maximum stress result
ForThreedimensional model maximum stress result is
With threedimensional model maximum stress value as actual value, two dimensional model maximum stress value is calculated value, then maximum stress phase
To the average value of errorStandard deviation
Further, step 3 is specifically included：
Parameter-embedded, initial annealing initial temperature T first in initialization simulated annealing0, final temperature Tend、
Final iterations S under rate of temperature fall q and Current Temperatures；
Initialization design variable and target function value；Set the initial designs variable x of blade rootdes0, and by finite element
Method completes the 3 D Parametric Modeling to blade root, calculates the target function value for obtaining now, i.e. initial maximum stress σmax0；
1) iterative parameter under initialization Current Temperatures；Make the iterations count=1 under Current Temperatures；
2) the inner iteration flow of optimization is entered, in current annealing temperature T1With blade root design variable xdes1Under, it is random raw first
Into one group of new design variable x for meeting blade root geometric relationshipdes2, and complete the two-dimensional parameterization modeling to blade root, meter
Calculate target function value now, i.e., two dimensional model maximum stress σ now2Dtemp；For first time inner iteration, T is taken1=T0,
xdes1=xdes0；
3) introduce dimensionality reduction criterion and judged：
Introduce the following inequality group being made up of two formula：
Formula 1：σtempmax≤σmax1
Formula 2：σtempmin≥σmax1
Wherein, a is uniform random number of the value in (0,1), T1It is current annealing temperature；
σtempave=σ2Dtemp+T1ln(a)-μ1σmax1, it is statistical average stress；
σtempmax=σtempave+κδ1σmax1, it is statistics maximum stress；
σtempmin=σtempave-κδ1σmax1, it is statistics minimum stress；
κ is convergence rate coefficient, and value is between [1,3]；μ1、δ1And σmax1For when the last time calculates in iterative process
The average value of the maximum stress relative error for being generated, standard deviation and maximum stress value；For first time inner iteration, μ1=μ0,
δ1=δ0, σmax1=σmax0, μ0It is the initial average output value of maximum stress value relative error, δ0For primary standard is poor, σmax0For initial
Maximum stress value；
If there is any one formula to set up in formula 1,2, receive dimensionality reduction criterion, no longer carry out the calculating of threedimensional model；
If formula 1 is set up, new value, this stylish target function value σ are directly received in optimization processmax=σ2Dtemp, new design
Variable xdes=xdes2；If formula 2 is set up, new value is directly refused in optimization process, target function value and design now become
Value keeps constant, i.e. σmax=σmax1, xdes=xdes1；
If 4) formula 1 and formula 2 are invalid, refuse dimensionality reduction criterion, three-dimensional is proceeded by according to new design variable
Parametric modeling, and finite Element Intensity Analysis are completed, extract maximum stress value σ now3Dtemp, then utilize
Metropolis criterions judge whether to receive the new value of three-dimensional finite element model, firstly generate a value in the random of (0,1)
Number b, if σ3Dtemp＜ σmax1OrThen receive the new value obtained by threedimensional model calculating, this is stylish
Target function value σmax=σ3Dtemp, new design variable xdes=xdes2；If two inequality are unsatisfactory for, refusal is three-dimensional
New value obtained by model calculating, target function value and design variable value now keep constant, i.e. σmax=σmax1, xdes=
xdes1；
5) the new value of each parameter after this inner iteration is updated as the initial value of inner iteration next time；After completing to judge,
Object function maximum stress value σmax1=σmax, design variable xdes1=xdes, the iterations count=count+ under Current Temperatures
1；If dimensionality reduction criterion is rejected, the mean error of current maximum stress valueWhen
The standard deviation of preceding maximum stress valueWherein N is upper
The quantity of contrasting data in an iteration；
6) then repeat step 2) -5), until under the inner iteration number of times count=S under Current Temperatures, S are Current Temperatures
Final iterations；
7) minimum value and corresponding design for recording the object function during S inner iteration is calculated under Current Temperatures become
Amount, is designated as σ respectivelyT1And xT1, now this outer iteration flow terminate；
8) annealing temperature and design variable value are updated to start outer iteration flow next time；This stylish annealing temperature T2=
qT1, q is rate of temperature fall, T1It is the annealing temperature in last outer iteration；New outer iteration initial target functional value σmax1=σT1,
Initial designs variate-value xdes1=xT1；
9) weight step 1) -8), when annealing temperature is less than arranges value or object function value stabilization, complete to blade root
Structure optimization.
Further, step 9) in, when current annealing temperature is less than final temperature, i.e. T ＜ TendWhen, or continuous 50
When the minimum value of object function does not change in secondary outer iteration, to minimum target functional value σ nowoptCorresponding sets
Meter variable xopt3 D Parametric Modeling is carried out, and carries out stress analysis to extract maximum stress result by finite element method
σ3Dopt；
If meetingThen calculating process is restrained, and the structure optimization of blade root is finished, now outer to change
The corresponding design variable of minimum target functional value is the optimum shape parameter obtained by the optimization of this blade root during generation；
IfThen with design variable xoptFor initial designs variable and initialize remaining optimization process
It is parameter-embedded, repeat step three is optimized again, until meeting the condition of convergence.
Relative to prior art, the invention has the advantages that：
In the blade root optimization method that the present invention is set up, in simulated annealing, using the meter of two-dimensional finite element model
Calculate result to be predicted the stress result of three-dimensional finite element model, by introducing dimensionality reduction criterion, in simulated annealing optimization process
It is middle to utilize two dimension and three-dimensional finite element model cross validation, calculated with two dimensional finite element in terms of instead of three-dimensional finite element by certain probability
Calculate, the computing resource needed for reducing large-scale finite element analysis, and the time for making optimization calculating required greatly shortens, and saves a large amount of
Computer resource.
Brief description of the drawings
Fig. 1 is the general flow chart of the inventive method；
Fig. 2 is certain tooth fir tree blade root of example four；Wherein Fig. 2 (a) is front view；Fig. 2 (b) is top view；
Fig. 3 is the flow chart of dimensionality reduction simulated annealing；
Fig. 4 is that dimensionality reduction criterion receives the interval schematic diagram interval with refusal；Wherein Fig. 4 (a) is that dimensionality reduction criterion receives interval
Schematic diagram；Fig. 4 (b) dimensionality reductions criterion refuses interval diagram.
Specific embodiment
Embodiments of the present invention are described in detail below in conjunction with accompanying drawing.
Refer to shown in Fig. 1, a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing of the invention, including following four
Individual step：
First, complete to the two-dimensional parameter modeling of target blade and 3 D Parametric Modeling
For certain certain type of blade root, generally require n parameter to determine its specific geometry, i.e. xall=
(x1,x2,…,xn) be the blade root geometric shape parameterses；And in optimization process, often only need to choose a to stress value change
Change sensitive parameter as design variable, now take xdes=(x1,x2,…,xa) as the design in blade root shape optimization problem
Variable, wherein xdes∈xall；xall=(x1,x2,…,xn) in be not selected as the form parameter as design constant of design variable.
It is determined that, it is necessary to carry out parametric modeling to the blade root after design variable in optimization problem.According to engineering reality
The experience trampled, chooses design constant, and be the geometric shape parameterses x that variable form can determine that blade root with design variableall
=(x1,x2,…,xn).Then further according to the centrifugal force under actual condition, the blade profile model of suitable size is chosen, you can set up leaf
The two-dimensional model and three-dimensional entity model of piece, choose flat unit and solid element respectively in finite element software afterwards,
Complete two-dimensional parameter modeling and the 3 D Parametric Modeling of blade.
By taking the blade root in Fig. 2 as an example, from the front view and top view of the blade root, the blade root is come by n=37 parameter
Determine its geometry：b1,b2,…,b8Totally 8 circumferential shape parameters, h1,h2,…,h21Totally 21 radial shape parameters, R1,
R2,…,R5Totally 5 radius parameters, θ1,θ2Totally 2 angle parameters and blade root axial length L.
So for the blade root xall=(b1,b2,…,h1,h2…,R1,R2,…,θ1,θ2, L), choose to blade root stress shadow
The larger form parameter of sound is x as design variable, such as G- Design variabledes=(θ1,θ2,b5,b8,h12,h14,h16,R1,R5)。
On the basis of front view, selection axle center is the origin of coordinates, and the coordinate of all key points of gain of parameter according to blade root sets
All key points, afterwards according to the level in " point --- line --- face ", that is, generate the two-dimensional model of blade；It is flat in two dimension
On the basis of surface model, along the distance of the normal extension blade root axial length in the face, that is, the 3D solid mould of blade is generated
Type.
The mesh generation that finite element flat unit has carried out blade pair two-dimensional model is chosen afterwards, that is, complete blade
Two-dimensional parameterization is modeled；Choose finite element solid unit to complete the mesh generation to leaf three-dimensional model, that is, complete blade
3 D Parametric Modeling.
The two-dimensional parameter modeling of wheel rim and 3 D Parametric Modeling mode are identical with blade root.
2nd, N is generated at random0Group design variable, calculates the initial average output value μ of maximum stress value relative error0And primary standard
Difference δ0。
Random generation N0Group design variable, completes this N by way of step one0The two dimension of group design variable correspondence blade root
Parametric modeling and 3 D Parametric Modeling.By finite element software, completed to two dimensional model after boundary condition is set
Solved with threedimensional model stress analysis, and extract maximum stress value each time respectively, remember two dimensional model maximum stress result
ForThreedimensional model maximum stress result is
With threedimensional model maximum stress value as actual value, two dimensional model maximum stress value is calculated value, then maximum stress phase
To the average value of errorStandard deviation
For the blade root shown in Fig. 2, the quantity N of initial control data is can use0=20.
3rd, dimensionality reduction criterion is introduced in simulated annealing
As shown in Figure 3.
Parameter-embedded, initial annealing initial temperature T first in initialization simulated annealing0, final temperature Tend、
Final iterations S under rate of temperature fall q and Current Temperatures.T can be made0=1000, Tend=1 × 10-5, q=0.9, S=100.
Initialization design variable and target function value.Set the initial designs variable x of blade rootdes0, and by finite element
Method completes the 3 D Parametric Modeling to blade root, calculates the target function value for obtaining now, i.e. initial maximum stress σmax0。
1) iterative parameter under initialization Current Temperatures.Make the iterations count=1 under Current Temperatures.
2) the inner iteration flow of optimization is entered.In current annealing temperature T1With blade root design variable xdes1(in first time
Iteration, takes T1=T0, xdes1=xdes0) under, it is first randomly generated one group of new design variable for meeting blade root geometric relationship
xdes2, and the two-dimensional parameterization modeling to blade root is completed, and calculating target function value now, i.e., two dimensional model maximum now should
Power σ2Dtemp。
3) introduce dimensionality reduction criterion and judged.
Carry out dimensionality reduction judgement as shown in Figure 4.
Introduce the following inequality group being made up of two formula：
Formula 1：σtempmax≤σmax1
Formula 2：σtempmin≥σmax1
Wherein, a is uniform random number of the value in (0,1), T1It is current annealing temperature；
σtempave=σ2Dtemp+T1ln(a)-μ1σmax1, it is statistical average stress；
σtempmax=σtempave+κδ1σmax1, it is statistics maximum stress；
σtempmin=σtempave-κδ1σmax1, it is statistics minimum stress；
κ is convergence rate coefficient, and value is generally between [1,3]；μ1、δ1And σmax1It is last meter in iterative process
The average value of the maximum stress relative error generated during calculation, standard deviation and maximum stress value are (for first time inner iteration, μ1
=μ0, δ1=δ0, σmax1=σmax0, μ0It is the initial average output value of maximum stress value relative error, δ0For primary standard is poor, σmax0For
Initial maximum stress value).
As shown in Fig. 4 (a), if there is any one formula to set up in formula 1,2, receive dimensionality reduction criterion, i.e., need not be again
Carry out the calculating of threedimensional model.If formula 1 is set up, new value, this stylish target function value are directly received in optimization process
σmax=σ2Dtemp, new design variable xdes=xdes2；If formula 2 is set up, new value is directly refused in optimization process, now
Target function value and design variable value keep constant, i.e. σmax=σmax1, xdes=xdes1。
4) as shown in Fig. 4 (b), if above formula 1 and formula 2 are invalid, dimensionality reduction criterion is refused, according to new design
Variable proceeds by 3 D Parametric Modeling, and completes finite Element Intensity Analysis, extracts maximum stress value σ now3Dtemp,
Then judge whether to receive the new value of three-dimensional finite element model using Metropolis criterions, firstly generate a value (0,
1) random number b, if σ3Dtemp＜ σmax1Or σ3Dtemp-σmax1≤-T1Ln (b), then receive new obtained by threedimensional model calculating
Value, this stylish target function value σmax=σ3Dtemp, new design variable xdes=xdes2；If two inequality are unsatisfactory for,
New value obtained by refusal threedimensional model calculating, target function value and design variable value now keep constant, i.e. σmax=
σmax1, xdes=xdes1。
5) the new value of each parameter after this inner iteration is updated as the initial value of inner iteration next time.After completing to judge,
Object function maximum stress value σmax1=σmax, design variable xdes1=xdes, the iterations count=count under Current Temperatures
+1；If dimensionality reduction criterion is rejected, the mean error of current maximum stress valueWhen
The standard deviation of preceding maximum stress valueWherein N is upper
The quantity of contrasting data in an iteration.
6) then repeat step 2) -5), until under the inner iteration number of times count=S under Current Temperatures, S are Current Temperatures
Final iterations.
7) minimum value and corresponding design for recording the object function during S inner iteration is calculated under Current Temperatures become
Amount, is designated as σ respectivelyT1And xT1, now this outer iteration flow terminate.
8) annealing temperature and design variable value are updated to start outer iteration flow next time.This stylish annealing temperature T2=
qT1, q is rate of temperature fall, T1It is the annealing temperature in last outer iteration；New outer iteration initial target functional value σmax1=σT1,
Initial designs variate-value xdes1=xT1。
9) weight step 1) -8), when annealing temperature is less than arranges value or object function value stabilization, complete to blade root
Structure optimization：
When current annealing temperature is less than final temperature, i.e. T ＜ TendWhen, or the object function in continuous 50 outer iterations
When the minimum value of (blade root maximum stress value) does not change, to minimum target functional value σ nowoptCorresponding design
Variable xopt3 D Parametric Modeling is carried out, and carries out stress analysis by finite element method to extract maximum stress result σ3Dopt。
If meetingThen calculating process is restrained, and the structure optimization of blade root is finished.Now during outer iteration
The corresponding design variable of minimum target functional value is the optimum shape parameter obtained by the optimization of this blade root.
IfThen with design variable xoptFor initial designs variable and initialize remaining optimization process
It is parameter-embedded, repeat step three is optimized again, until meeting the condition of convergence.
Claims (5)
1. a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing, it is characterised in that comprise the following steps：
The first step, determines the design variable in optimization process, and complete the two-dimensional parameterization modeling to target blade and three-dimensional ginseng
Numberization is modeled；
Second step, generates N at random0Group design variable, this N is gone out by FEM calculation0Two dimensional model and three-dimensional under group design variable
The initial average output value μ of model maximum stress value relative error0δ poor with primary standard0；
3rd step, begins through simulated annealing and blade root is optimized with the result of calculation of three-dimensional finite element model,
Initial average output value μ in Metropolis sampling processes according to relative error0δ poor with primary standard0Dimensionality reduction criterion is introduced, is subtracted
Small FEM calculation amount, and the average value and standard deviation of relative error are updated after threedimensional model calculating is carried out；
When annealing temperature is less than arranges value or object function value stabilization, the calculating process if product test is in allowable error
Restrained, completed the structure optimization to blade root.
2. a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing according to claim 1, it is characterised in that step
In rapid one：
For certain certain type of blade root, its specific geometry, i.e. x is determined by n parameterall=(x1,
x2,...,xn) be the blade root geometric shape parameterses；
In optimization process, a parameter is chosen as design variable, now take xdes=(x1,x2,...,xa) as blade root shape
Design variable in optimization problem, wherein xdes∈xall；xall=(x1,x2,...,xn) in be not selected as the shape of design variable
Parameter is design constant.
3. a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing according to claim 1, it is characterised in that step
Rapid two specifically include：
Random generation N0Group design variable, completes this N by way of step one0The two-dimensional parameter of group design variable correspondence blade root
Change modeling and 3 D Parametric Modeling；By finite element software, completed after boundary condition is set to two dimensional model and three
Dimension module stress analysis is solved, and extracts maximum stress value each time respectively, and note two dimensional model maximum stress result isThreedimensional model maximum stress result is
With threedimensional model maximum stress value as actual value, two dimensional model maximum stress value is calculated value, then maximum stress is relative by mistake
Poor average valueStandard deviation
4. a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing according to claim 1, it is characterised in that step
Rapid three specifically include：
Parameter-embedded, initial annealing initial temperature T first in initialization simulated annealing0, final temperature Tend, cooling speed
Final iterations S under rate q and Current Temperatures；
Initialization design variable and target function value；Set the initial designs variable x of blade rootdes0, and it is complete by finite element method
The 3 D Parametric Modeling of paired blade root, calculates the target function value for obtaining now, i.e. initial maximum stress σmax0；
1) iterative parameter under initialization Current Temperatures；Make the iterations count=1 under Current Temperatures；
2) the inner iteration flow of optimization is entered, in current annealing temperature T1With blade root design variable xdes1Under, it is first randomly generated one
The new design variable x for meeting blade root geometric relationship of groupdes2, and the two-dimensional parameterization modeling to blade root is completed, calculate this
When target function value, i.e., two dimensional model maximum stress σ now2Dtemp；For first time inner iteration, T is taken1=T0, xdes1=
xdes0；
3) introduce dimensionality reduction criterion and judged：
Introduce the following inequality group being made up of two formula：
Formula 1：σtempmax≤σmax1
Formula 2：σtempmin≥σmax1
Wherein, a is uniform random number of the value in (0,1), T1It is current annealing temperature；
σtempave=σ2Dtemp+T1ln(a)-μ1σmax1, it is statistical average stress；
σtempmax=σtempave+κδ1σmax1, it is statistics maximum stress；
σtempmin=σtempave-κδ1σmax1, it is statistics minimum stress；
κ is convergence rate coefficient, and value is between [1,3]；μ1、δ1And σmax1By being given birth to during last calculating in iterative process
Into the average value of maximum stress relative error, standard deviation and maximum stress value；For first time inner iteration, μ1=μ0, δ1=
δ0, σmax1=σmax0, μ0It is the initial average output value of maximum stress value relative error, δ0For primary standard is poor, σmax0It is initial maximum
Stress value；
If there is any one formula to set up in formula 1,2, receive dimensionality reduction criterion, no longer carry out the calculating of threedimensional model；If public
Formula 1 is set up, then directly receive new value, this stylish target function value σ in optimization processmax=σ2Dtemp, new design variable
xdes=xdes2；If formula 2 is set up, new value, target function value now and design variable value are directly refused in optimization process
Keep constant, i.e. σmax=σmax1, xdes=xdes1；
If 4) formula 1 and formula 2 are invalid, refuse dimensionality reduction criterion, three-dimensional parameter is proceeded by according to new design variable
Change modeling, and complete finite Element Intensity Analysis, extract maximum stress value σ now3Dtemp, it is then accurate using Metropolis
Then judge whether to receive the new value of three-dimensional finite element model, random number b of the value in (0,1) is firstly generated, if σ3Dtemp＜
σmax1Or σ3Dtemp-σmax1≤-Tl1N (b), then receive the new value obtained by threedimensional model calculating, this stylish target function value
σmax=σ3Dtemp, new design variable xdes=xdes2；If two inequality are unsatisfactory for, refusal threedimensional model calculates gained
New value, target function value and design variable value now keep constant, i.e. σmax=σmax1, xdes=xdes1；
5) the new value of each parameter after this inner iteration is updated as the initial value of inner iteration next time；After completing to judge, mesh
Scalar functions maximum stress value σmax1=σmax, design variable xdes1=xdes, the iterations count=count+ under Current Temperatures
1；If dimensionality reduction criterion is rejected, the mean error of current maximum stress valueWhen
The standard deviation of preceding maximum stress valueWherein N is upper
The quantity of contrasting data in an iteration；
6) then repeat step 2) -5), until the inner iteration number of times count=S under Current Temperatures, S are final under Current Temperatures
Iterations；
7) minimum value and corresponding design variable of object function during S inner iteration is calculated are recorded under Current Temperatures,
It is designated as respectivelyAnd xT1, now this outer iteration flow terminate；
8) annealing temperature and design variable value are updated to start outer iteration flow next time；This stylish annealing temperature T2=qT1, q
It is rate of temperature fall, T1It is the annealing temperature in last outer iteration；New outer iteration initial target functional valueInitially
Design variable value xdes1=xT1；
9) weight step 1) -8), when annealing temperature is less than arranges value or object function value stabilization, complete the structure to blade root
Optimization.
5. a kind of leaf and root structure optimization method of dimensionality reduction simulated annealing according to claim 4, it is characterised in that step
It is rapid 9) in, when current annealing temperature be less than final temperature, i.e. T ＜ TendWhen, or the object function in continuous 50 outer iterations
When minimum value does not change, to minimum target functional value σ nowoptCorresponding design variable xoptCarry out three-dimensional parameter
Change modeling, and carry out stress analysis by finite element method to extract maximum stress result σ3Dopt；
If meetingThen calculating process is restrained, and the structure optimization of blade root is finished, now outer iteration
The corresponding design variable of minimum target functional value is the optimum shape parameter obtained by the optimization of this blade root in journey；
IfThen with design variable xoptFor initial designs variable and initialize in remaining optimization process
Parameter is put, repeat step three is optimized again, until meeting the condition of convergence.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611154821.6A CN106682292B (en) | 2016-12-14 | 2016-12-14 | A kind of leaf and root structure optimization method of dimensionality reduction simulated annealing |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611154821.6A CN106682292B (en) | 2016-12-14 | 2016-12-14 | A kind of leaf and root structure optimization method of dimensionality reduction simulated annealing |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106682292A true CN106682292A (en) | 2017-05-17 |
| CN106682292B CN106682292B (en) | 2019-10-11 |
Family
ID=58869303
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611154821.6A Active CN106682292B (en) | 2016-12-14 | 2016-12-14 | A kind of leaf and root structure optimization method of dimensionality reduction simulated annealing |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106682292B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110705079A (en) * | 2019-09-25 | 2020-01-17 | 哈尔滨工程大学 | Centrifugal compressor structure optimization method based on simulated annealing algorithm |
| CN110717223A (en) * | 2019-09-19 | 2020-01-21 | 合肥通用机械研究院有限公司 | Optimization method of reed valve plate |
| CN111929338A (en) * | 2020-07-29 | 2020-11-13 | 同济大学 | Fuel cell catalyst layer analysis method based on simulated annealing algorithm three-dimensional reconstruction |
| CN112052542A (en) * | 2020-10-15 | 2020-12-08 | 华东理工大学 | Intelligent design method and system of ultrasonic rolling amplitude transformer for blade surface strengthening |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000145402A (en) * | 1998-11-12 | 2000-05-26 | Mitsubishi Heavy Ind Ltd | Axial turbine cascade |
| CN101418813A (en) * | 2008-12-10 | 2009-04-29 | 北京航空航天大学 | Optimum design method for wall whorl of compressor |
| CN102096736A (en) * | 2011-01-28 | 2011-06-15 | 重庆大学 | Asymptotic variational method-based method for simulating and optimizing composite material laminated plate |
| CN104102834A (en) * | 2014-07-10 | 2014-10-15 | 南京工程学院 | Method for identifying sound recording locations |
| CN105808867A (en) * | 2016-03-16 | 2016-07-27 | 徐州工程学院 | Building height optimization design method based on simulated annealing algorithm |
-
2016
- 2016-12-14 CN CN201611154821.6A patent/CN106682292B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2000145402A (en) * | 1998-11-12 | 2000-05-26 | Mitsubishi Heavy Ind Ltd | Axial turbine cascade |
| CN101418813A (en) * | 2008-12-10 | 2009-04-29 | 北京航空航天大学 | Optimum design method for wall whorl of compressor |
| CN102096736A (en) * | 2011-01-28 | 2011-06-15 | 重庆大学 | Asymptotic variational method-based method for simulating and optimizing composite material laminated plate |
| CN104102834A (en) * | 2014-07-10 | 2014-10-15 | 南京工程学院 | Method for identifying sound recording locations |
| CN105808867A (en) * | 2016-03-16 | 2016-07-27 | 徐州工程学院 | Building height optimization design method based on simulated annealing algorithm |
Non-Patent Citations (3)
| Title |
|---|
| 周书敬等: "《改进的粒子群-模拟退火算法在桁架结构优化设计中的应用》", 《钢结构》 * |
| 孙伟等: "《基于模拟退火算法的布局优化技术研究》", 《第七届中日机械技术史及机械设计国际学术会议》 * |
| 黄庆华等: "《汔轮机调节级叶片三维接触有限元强度可靠性分析》", 《热力透平》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110717223A (en) * | 2019-09-19 | 2020-01-21 | 合肥通用机械研究院有限公司 | Optimization method of reed valve plate |
| CN110717223B (en) * | 2019-09-19 | 2023-08-04 | 合肥通用机械研究院有限公司 | Optimization method of reed valve plate |
| CN110705079A (en) * | 2019-09-25 | 2020-01-17 | 哈尔滨工程大学 | Centrifugal compressor structure optimization method based on simulated annealing algorithm |
| CN110705079B (en) * | 2019-09-25 | 2023-01-03 | 哈尔滨工程大学 | Centrifugal compressor structure optimization method based on simulated annealing algorithm |
| CN111929338A (en) * | 2020-07-29 | 2020-11-13 | 同济大学 | Fuel cell catalyst layer analysis method based on simulated annealing algorithm three-dimensional reconstruction |
| CN112052542A (en) * | 2020-10-15 | 2020-12-08 | 华东理工大学 | Intelligent design method and system of ultrasonic rolling amplitude transformer for blade surface strengthening |
| CN112052542B (en) * | 2020-10-15 | 2023-10-13 | 华东理工大学 | Intelligent design method and system for ultrasonic rolling amplitude transformer for blade surface strengthening |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106682292B (en) | 2019-10-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106682292A (en) | Blade root structure optimization method of dimensionality reduction simulated annealing algorithm | |
| CN105893694A (en) | Complex system designing method based on resampling particle swarm optimization algorithm | |
| CN106991212B (en) | Root strength prediction method based on GA _ PSO (genetic Algorithm-particle swarm optimization) GRNN (generalized regression neural network) algorithm | |
| CN106354920B (en) | Base bearing axle sleeve strength analysis method and interference analysis method in Wind turbines | |
| CN109992889B (en) | Wind power plant model building method and system and wake value calculating method and system | |
| CN105678015B (en) | A kind of Multidisciplinary systems pneumatic structure coupling optimum design method of hypersonic three-dimensional wing | |
| CN106126860A (en) | A kind of hypersonic wing Robust Optimal Design considering mismachining tolerance | |
| CN114444215A (en) | Motion simulation method, device and equipment based on Cartesian grid | |
| CN112949217B (en) | Wind turbine generator wake flow regional modeling and rapid analysis method | |
| CN114676522B (en) | Pneumatic shape optimization design method, system and equipment integrating GAN and migration learning | |
| CN116244988B (en) | High-quality quadrilateral grid conformal construction method for plate spinning multi-grid method simulation | |
| CN104239625A (en) | Corrective fluid motion equation linear iteration-based steady state solution method | |
| CN104750948A (en) | Optimization method for processing multiple extreme values and multiple restricted problems in flight vehicle design | |
| CN111898212A (en) | Impeller mechanical profile design optimization method based on BezierGAN and Bayesian optimization | |
| CN108509718B (en) | Far-field wake two-dimensional analytic model based on mass conservation | |
| CN107038308A (en) | A kind of regular grid terrain modeling method based on linear interpolation | |
| CN114091377A (en) | Method for calculating wake flow wind speed of dynamic double-Gaussian wind turbine based on space change | |
| CN112733455A (en) | Correction method, system, device and storage medium of water turbine modeling data | |
| CN115062563A (en) | Wind turbine three-dimensional wake flow wind speed calculation method based on space change | |
| CN105956318B (en) | Based on the wind power plant group of planes division methods for improving division H-K clustering method | |
| CN107545600A (en) | A kind of Virtual Terrain modeling method based on linear interpolation | |
| Waibel et al. | Physics meets machine learning: Coupling FFD with regression models for wind pressure prediction on high-rise facades | |
| Safari et al. | A novel combination of adaptive tools for turbomachinery airfoil shape optimization using a real-coded genetic algorithm | |
| CN115310388B (en) | Method for calculating three-dimensional asymmetric double-Gaussian wake flow wind speed of wind turbine with space variation | |
| Gurbuz et al. | Offsetting operations via closed ball approximation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |