CN105320822A - Double-objective comprehensive optimization design method for LED radiator structure parameters - Google Patents
Double-objective comprehensive optimization design method for LED radiator structure parameters Download PDFInfo
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Abstract
The invention discloses a double-objective comprehensive optimization design method for LED radiator structure parameters. According to the method, a continuous function relation between a comprehensive optimization target and the structure parameters to be optimized is accurately built through a response surface method, an orthogonal testing method and a genetic algorithm are reasonably combined to use, global optimization can be completed in a solution space of a comprehensive optimization target function of the structure parameters of a radiator in complex appearance, and a Pareto optimal solution achieving comprehensive optimization of double objectives containing improvement of LED cooling performance can be obtained, so that the optimal combination of various structure parameter design values is quickly determined according to actual requirements of the design target of the radiator, cooling efficiency of the radiator is effectively improved, the research and development period is greatly shortened, and product cost in the links of design, manufacturing, application and the like is reduced.
Description
Technical field
The invention belongs to the package cooling technical field of electronic equipment, particularly relate to a kind of orthogonal experiment and genetic algorithm are combined the structural parameters of LED radiator are optimized and reach the comprehensive optimum method for designing of two design objects simultaneously.
Background technology
Great power LED have low-power consumption, long-life, volume little, respond a series of significant performance advantages such as rapid, along with it is in the widespread use of multiple lighting field, LED lamp has become a kind of novel illumination product being expected to the conventional light source such as alternative incandescent lamp, fluorescent light and Halogen lamp LED.But because LED belongs to temperature sensitive device, if lack effective cooling measure and make thermal accumlation at chip place, to directly cause the rapid rising of junction temperature, the non-uniform Distribution of thermal stress can not only be caused, speed-up chip is aging, serious curtailment device lifetime, can also spectral shift be caused, and significantly reduce light intensity and fluorescent powder and swash and penetrate the serviceabilitys such as efficiency.Therefore, for ensureing every advantage performance of LED lamp, the heat dispersion of LED must be promoted to reduce its junction temperature of chip as much as possible.
In the measure promoting LED heat dispersion, by adopting the new techniques such as high-termal conductivity base plate for packaging, High Efficiency Thermal interface packing material, vapor chamber and heat pipe, all significantly can promote the thermal conduction capability of LED chip to heating radiator.But conducting the heat finally still needs the heat convection mode between and outside air surperficial by the fin of heating radiator to arrange the LED lamp that sheds, and the convection heat transfer' heat-transfer by convection process therefore through heating radiator is the important final link determining overall heat dissipation ability height.But for a long time, the heating radiator how designed and meet cooling requirements is often only paid close attention in engineering reality, usually to increase the external surface area of heating radiator as preferred option, but very easily cause the increase of the weight of heating radiator, volume and manufacturing cost, and too much fin also can flow by block air, not can reach the radiating effect of expection.Therefore, to reduce junction temperature of chip for while design object, the overall target the category also weight of heating radiator, volume or manufacturing cost etc. should being brought into heat dissipation design takes in, thus it is comprehensive optimum that the structural parameters through optimizing are realized in two design objects.
In order to realize the Bi-objective complex optimum comprising LED chip junction temperature, the people such as Zhang Qi and Zhuan Sixiang complete on parametric modeling and thermoanalytical basis in ANSYS finite element software, adopt the radiator structure of orthogonal experiment to high-power LED street lamp to implement optimization.Although the optimum results of two researchs all makes junction temperature of chip and heatsink weight be minimized simultaneously, between junction temperature and weight, how to realize reasonable tradeoff, concrete guiding method is not yet provided.In addition, orthogonal experiment will be chosen the parameter level with typical representative for structural parameters and carry out experiment arrangement scheme, makes the design object value corresponding to the horizontal combination of various parameter in scheme in solution space, be in discrete distribution.Due to the uncontinuity between these horizontal combination, be difficult to realize global optimizing in the solution space of complex optimum objective function, easily omit effect of optimization better but in orthogonal scheme and unlisted parameter level combination.
Genetic algorithm can complete the Bi-objective complex optimum of LED lamp equally, the people such as Su Huali have derived the heat radiator thermal resistance expression formula in forced air cooling situation, and be minimised as target with thermal resistance, genetic algorithm is adopted to complete initial optimization, then maintain design wind speed constant and reduce heat sink size, achieve reducing of heating radiator volume.But, the method does not carry out synchronous complex optimum to the thermal resistance of heating radiator and volume, the optimizing process of the volume-diminished of subsequent implementation, the result of the thermal resistance optimization before often making it departs from minimum value, therefore can not obtain the comprehensive optimum of two kinds of design objects.The people such as Li Yunze are at patent of invention (application number: disclose a kind of genetic algorithm that adopts 200910080867.1) and needle-like finned radiator spacing of fins is in the two directions implemented to the method optimized, the droop loss being intended to obtain temperature variation time constant and heating radiator reaches the minimum design object of synthesization.Although this patented method is complete feasible embodiment for Bi-objective complex optimum provides, but the prerequisite that can realize global optimizing due to genetic algorithm is: must set up comprise every design object and optimized variable continuity math equation as the complex optimum objective function of genetic algorithm, in the foundation of complex optimum objective function, this people such as patented method and Su Huali have employed identical thinking, that is: being derived by the theoretical calculation formula of thermal conduction study or Correlation farmula is obtained.But, theoretical calculation formula has the heating radiator of regular morphology under being only applicable to the situation of idealizing, the heat dispersal situations that Correlation farmula also can only be used for environment for use and scope of investigating is consistent with experiment condition, and the pattern of heating radiator also often comparison rule, and for the heating radiator with complex topography widely used in LED, its complex optimum objective function cannot select the theoretical calculation formula that is applicable to or Correlation farmula to be described.
Summary of the invention
The object of the invention is to solve above-mentioned technical matters and propose a kind of Bi-objective Synthetical Optimization method of LED radiator structural parameters, the continuity funtcional relationship between complex optimum target and structural parameters to be optimized is accurately set up by Response Surface Method, reasonably combine orthogonal experiment and genetic algorithm use, global optimizing can be completed in the solution space of complex optimum objective function for the structural parameters of complex topography heating radiator, obtain the Pareto optimum solution comprising the Bi-objective complex optimum promoting LED heat dispersion, thus according to the actual demand of fansink designs target, determine the optimum combination of each design of Structural Parameters value fast, the radiating efficiency of effective raising heating radiator, and significantly shorten the R&D cycle, save product in design, cost in the links such as manufacture and application.
For achieving the above object, the present invention adopts following technical scheme:
A Bi-objective Synthetical Optimization method for LED radiator structural parameters, comprises the following steps:
(1) the selected simple target function F implementing two the single design objects optimized
1and F
2;
(2) determine the influential heating radiator of each simple target function tool structural parameters X to be optimized
nand restriction range [X
n-min, X
n-max]; X
nnumbering N=1,2 ..., n, n are the quantity of structural parameters to be optimized;
(3) orthogonal arrage in orthogonal experiment is selected, according to the number of levels m of selected orthogonal arrage, the various structural parameters X to be optimized of mean allocation from small to large in described restriction range
nlevel value X
n(M), level value numbering M=1,2 ..., m, is wherein numbered the structural parameters X to be optimized of N
nm level value be:
According to structural parameters X to be optimized
nnumber order successively by structural parameters X to be optimized
nlevel value X
n(M) each factor row that in the orthogonal arrage be filled into, row sequence is forward, form the experimental program of described orthogonal arrage;
(4) with the structural parameters X to be optimized distributed in described orthogonal arrage
none group of horizontal combination as one group of experiment parameter of described experimental program, obtained the simple target function F of K group experiment by thermal behavior simulation calculation
1(K) numerical value, and another simple target function F obtaining the experiment of K group by presetting method
2(K) numerical value, K is experiment numbers K=1,2 ..., k;
(5) according to the experiment numbers order that described orthogonal arrage arranges, structural parameters X to be optimized is constructed respectively
nhorizontal combination matrix X, simple target function F
1numerical matrix F
1with simple target function F
2numerical matrix F
2:
(6) to the element X in horizontal combination matrix X
kN(M) at each self-corresponding structural parameters X to be optimized
nrestriction range in implement normalized, the element x in the normalization horizontal combination matrix obtained
kN(M):
According to arrangement of elements corresponding in horizontal combination matrix X, by element x
kN(M) normalization horizontal combination matrix x is formed:
Wherein, each row in normalization horizontal combination matrix x are all corresponding to a normalized structural parameters x to be optimized
nvalue, x
nfootnote N is the numbering of structural parameters to be optimized; After normalized, x
n∈ [0,1], namely [0,1] is the structural parameters x to be optimized after normalization
nrestriction range;
(7) simple target function F is obtained by Response Surface Method matching
1and F
2respectively with normalized structural parameters x to be optimized
nbetween functional relation:
Wherein, a
0, a
i, a
ijfor F
1the undetermined coefficient of functional relation, b
0, b
i, b
ijfor F
2the undetermined coefficient of functional relation; Undetermined coefficient is formed F in order respectively
1and F
2the undetermined coefficient matrix A of functional relation and B:
A＝[a
0a
1…a
na
11…a
1na
22…a
2n…a
nn]
T，
B＝[b
0b
1…b
nb
11…b
1nb
22…b
2n…b
nn]
T，
Wherein, the transposition of T representing matrix, that is: the dimension of A with B is identical, and line number is 1+n+ [n (n+1)/2], and columns is 1; In matrix A and B, the numerical value of undetermined coefficient is calculated by following formula respectively:
A＝(C
TC)
-1C
TF
1，B＝(C
TC)
-1C
TF
2，
Wherein, the element x of Matrix C in element 1 and normalization horizontal combination matrix x
kN(M) and product form composition:
Wherein, by x
kN(M) reduced representation becomes x
kN; The line number of C is k, and columns is 1+n+ [n (n+1)/2];
(8) the simple target function F of undetermined coefficient will determined in step (7)
1with x
1, x
2..., x
nbetween functional relation be programmed in a M file of MATLAB software, calculate F respectively by the GAs Toolbox real-time calling of MATLAB software
1at x
nrestriction range [0,1] in global minimum F
1-minwith global maximum F
1-max; In like manner calculate F
2at x
nrestriction range [0,1] in global minimum F
2-minwith global maximum F
2-max;
(9) the simple target function F of undetermined coefficient will determined in step (7)
1and F
2with x
1, x
2..., x
nbetween functional relation substitute into following formula respectively and be normalized,
Obtain normalized simple target function f
1and f
2with x
1, x
2..., x
nbetween functional relation;
(10) normalized simple target function f is set
1and f
2weight coefficient ω corresponding respectively in Bi-objective complex optimum objective function F
1and ω
2, by the f obtained in step (9)
1and f
2functional relation be updated to following formula, obtain Bi-objective complex optimum objective function F and x
1, x
2..., x
nbetween functional relation:
F＝ω
1f
1+ω
2f
2，
Wherein ω
1∈ [0,1], ω
2∈ [0,1], and ω
1+ ω
2=1;
(11) functional relation of Bi-objective complex optimum objective function F step (10) determined is programmed in a M file of MATLAB software, adopts the GAs Toolbox optimization identical with step (8) optimum configurations to obtain F at normalized structural parameters x to be optimized
nrestriction range [0,1] in one or more groups Pareto optimum solution, all containing multiple Pareto optimum solution in each group;
(12) the structural parameters x normalized to be optimized corresponding to each Pareto optimum solution step (11) obtained
none group optimize value be updated to the simple target function F obtained in step (7)
1and F
2respectively with normalized structural parameters x to be optimized
nbetween functional relation, calculate the simple target function F that each Pareto optimum solution is corresponding
1and F
2optimum results; By structural parameters x normalized to be optimized corresponding for each Pareto optimum solution
none group optimize value be updated to following formula:
X
N＝x
N(X
N-max-X
N-min)+X
N-min，
Calculate heating radiator structural parameters X to be optimized
none group optimize value;
(13) by all simple target function F
1and F
2optimum results carry out map data, form optimum results data plot; In this optimum results data plot, each data point is with one group of simple target function F
1and F
2one of them optimum results be horizontal ordinate, with another optimum results for ordinate is determined;
(14) in described optimum results data plot, draw and optimize F corresponding to pre-structure parameter
1and F
2result, select to be on Pareto forward position and transverse and longitudinal coordinate figure is all less than the data point optimizing pre-structure realizes comprehensive optimum in restriction range alternative design result as two single design objects;
(15) set the optimization higher limit of a single design object function, then from described alternative design result, find out data point below this optimization higher limit and nearest, the structural parameters X to be optimized corresponding to this data point
none group optimize value and be the values of the structural parameters after heating radiator Bi-objective complex optimum.
In step (1), a design object of two single design objects is make one in LED chip junction temperature, key node temperature or heat radiator thermal resistance corresponding simple target function F
1numerical value reduces, and another design object is make in the weight of heating radiator, volume or manufacturing cost corresponding simple target function F
2numerical value reduces.
In step (2), described structural parameters X to be optimized
ncomprise continuity parameter and discreteness parameter, described structural parameters X to be optimized
nin be less than or equal to 1 containing the number of discreteness parameter.
Described continuity parameter comprises the processing dimension in heating radiator, and described discreteness parameter comprises fin quantity, material coefficient of heat conductivity.
In step (3), according to structural parameters X to be optimized
nnumber order when filling forward each factor row of row sequence in orthogonal arrage successively, the factor row being greater than the quantity of structural parameters to be optimized are set to blank column, and when the orthogonal arrage identical because of prime number has multiple, and the more orthogonal arrage of selection level number is filled.
In step (4), described presetting method is: when often organizing another simple target function F corresponding to experiment
2during for heatsink weight, F in the experiment of this group
2(K) numerical value adopts the analog computation of three-dimensional machinery design software to obtain; When simple target function F
2during for heating radiator volume, F in the experiment of this group
2(K) numerical value is obtained by the product of three maximum outer profile sizes of heating radiator in three-dimensional system of coordinate; If simple target function F
2during manufacturing cost for heating radiator, F in the experiment of this group
2(K) numerical value need carry out accounting by consumptive material and processing cost and obtain.
In step (8), the optimum configurations of described GAs Toolbox is: Population Size controls between 20 ~ 100, selection opertor adopts and is uniformly distributed algorithm at random, mutation operator selects TSP question algorithm, crossover operator selects two-point crossover algorithm, crossover probability is set to 0.8, and heredity stops for being more than or equal to for 100 generations.
In step (11), when only containing continuity parameter in the structural parameters to be optimized selected, by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by described GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain Bi-objective complex optimum objective function F at normalized structural parameters x to be optimized
nrestriction range [0,1] in one group of Pareto optimum solution; When containing a discreteness parameter in the structural parameters to be optimized selected, first multiple normalized level value is defined as in the restriction range of correspondence respectively to this discreteness parameter, then for the level value that each limits, respectively by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by described GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain the restriction range [0 of Bi-objective complex optimum objective function F in other normalization continuity parameters, 1] one group of Pareto optimum solution in, the group number of Pareto optimum solution is identical with the number of the limited level value of discreteness parameter.
Compared with prior art, the invention has the beneficial effects as follows:
(1) the parameter level combination with typical representative can be selected by orthogonal experiment in solution space, make between the experiment of the often group of arrangement dispersed, neat comparable, ensure the rationality of experimental program, be conducive to obtaining by less experiment number the demand data meeting later use Response Surface Method fitting function relational expression;
(2) data orthogonal experiment obtained obtain the functional relation between objective function and structural parameters to be optimized by Response Surface Method matching, higher fitting precision can be ensured, and the continuity math equation that can obtain after normalized for genetic algorithm optimization, realize the global optimizing in solution space;
(3) by the process of fitting treatment of Response Surface Method, reasonably combine orthogonal experiment and genetic algorithm use, can for the heat spreader structures parameter with complex topography widely used in LED, in the solution space of its complex optimum objective function, complete global optimizing, and the complex situations of continuity parameter and the mixing of discreteness parameter can be processed;
(4) Pareto forward position can realize in the comprehensive optimum alternative design result of Bi-objective being in, can according to the actual demand of fansink designs target, determine the optimum combination of each design of Structural Parameters value fast, the radiating efficiency of effective raising heating radiator, and significantly shorten the R&D cycle, save the cost of product in the links such as design, manufacture and application.
Accompanying drawing explanation
Fig. 1 is the process flow diagram of the Bi-objective Synthetical Optimization method of LED radiator structural parameters;
Fig. 2 A-2B is respectively vertical view and the front elevation of the heronsbill shape LED radiator optimization pre-structure of the embodiment of the present invention;
Fig. 3 is the result data figure of heronsbill shape LED radiator after completing weight and junction temperature of chip biobjective scheduling of the embodiment of the present invention.
Embodiment
Below, in conjunction with example, substantive distinguishing features of the present invention and advantage are further described, but the present invention is not limited to listed embodiment.
Shown in Fig. 1 ~ 3, the Bi-objective Synthetical Optimization method of LED radiator structural parameters, comprises the following steps:
(1) selected two the simple target function F implementing complex optimum
1and F
2
Before optimal design, first will select two the single design objects implementing complex optimum, one of them design object is heat radiation performance, generally shows as the simple target function F such as LED chip junction temperature, key node temperature or heat radiator thermal resistance
1the reduction of numerical value, another design object is generally weight, the simple target function F such as volume or manufacturing cost of heating radiator
2the reduction of numerical value, finally realizes the comprehensive optimum of two single design objects in restriction range;
The present embodiment mainly with the heronsbill shape LED radiator shown in Fig. 2 for optimization object, the selected simple target function F implementing complex optimum
1for LED chip junction temperature, another simple target function F
2for heatsink weight.Before optimization is implemented to heating radiator, F
1=89.05 DEG C, F
2=2.12kg, the target of biobjective scheduling realizes comprehensively minimum in restriction range of two single design objects.
(2) determine the influential heating radiator of simple target function tool structural parameters X to be optimized
nand restriction range [X
n-min, X
n-max], wherein, the numbering N=1 of structural parameters to be optimized, 2 ..., n, n are the quantity of structural parameters to be optimized;
Heating radiator structural parameters to be optimized relate to the processing dimension, fin quantity, material coefficient of heat conductivity etc. of primary structure in heating radiator; The processing dimension of heating radiator is generally continuity parameter, and the fin quantity of heating radiator and material coefficient of heat conductivity are generally discreteness parameter, and the number containing discreteness parameter in the structural parameters to be optimized of selection mostly is 1 most; The design upper limit X of the structural parameters value to be optimized that the specific demand etc. that the restriction range of structural parameters to be optimized is generally choice of material, manufacturing technology, application conditions and product is determined
n-maxwith design lower limit X
n-min, that is: X
n∈ [X
n-min, X
n-max];
In the present embodiment, determine the structural parameters X to be optimized of heronsbill shape LED radiator
nand the numerical value before optimizing is followed successively by: fin thickness X
1fin quantity X in=2.4mm, 1/4th regions
2=8, fin length X
3=150mm, fin height X
4=40mm and central cylinder diameter X
5=56mm.Wherein, the fin quantity X in 1/4th regions
2for discreteness parameter, X
2numerical value be positive integer, other parameters are continuity parameter.
Structural parameters X to be optimized
nrestriction range [X
n-min, X
n-max] be shown in Table 1.
Table 1 structural parameters X to be optimized
nrestriction range
(3) select the orthogonal arrage in orthogonal experiment and determine X
nlevel value
Select the orthogonal arrage Lk (m in orthogonal experiment
c), wherein L is the code name of orthogonal arrage, and k is experiment number, and m is number of levels, and c is because of prime number; Compared with the quantity n of the structural parameters to be optimized determined with step (2), in orthogonal arrage, should c=n or c-n=1 be met because of prime number c, when the orthogonal arrage identical because of prime number c has multiple, the orthogonal arrage that selection level number m is more; According to structural parameters X to be optimized
nnumbering will determine X by orthogonal arrage
nlevel value order fill each factor row that row sequence is forward in orthogonal arrage successively, the factor row being greater than the quantity n of structural parameters to be optimized are set to blank column;
In the present embodiment, select the orthogonal arrage L in orthogonal experiment
25(5
6), wherein experiment number k=25, number of levels m=5, because of prime number c=6.According to the number of levels m of selected orthogonal arrage, the level value X of various structural parameters to be optimized of mean allocation from small to large in restriction range
n(M), the numbering M=1 of level value, 2 ..., m.M the level value being numbered the structural parameters to be optimized of N can be expressed as:
The all X obtained
nthe level value distributed in restriction range is shown in Table 2.
Table 2 structural parameters X to be optimized
nlevel value
According to structural parameters X to be optimized
nnumber order fill forward each factor row of row sequence in orthogonal arrage as shown in table 3 successively, remaining last factor row are set to blank column.
Table 3 orthogonal arrage L
25(5
6) experimental program
(4) F in often group experiment is also obtained by orthogonal arrage experiment arrangement scheme
1and F
2numerical value
With orthogonal arrage L
25(5
6) in one group of horizontal combination of structural parameters to be optimized of distributing as one group of experiment parameter of experimental program, the experiment numbers K=1 in scheme, 2 ..., k.For the experiment of K group, calculate junction temperature of chip F by ICEPAK thermal behavior simulation software
1(K) numerical value, and adopt the analog computation of SOLIDWORKS three-dimensional machinery design software to obtain heatsink weight F
2(K) numerical value, all experimental results finally obtained are shown in Table 4.
Table 4 orthogonal experiments
It should be noted that, when often organizing another simple target function F corresponding to experiment
2during for heating radiator volume, K group experiment F
2(K) numerical value can be obtained by the product of heating radiator in three-dimensional system of coordinate three maximum outer profile sizes; If F
2during manufacturing cost for heating radiator, K group experiment F
2(K) numerical value need carry out accounting by consumptive material and processing cost and obtain.
(5) horizontal combination matrix X and F is built
1and F
2numerical matrix F
1and F
2
The experiment numbers order arranged according to orthogonal arrage, constructs horizontal combination matrix X, the simple target function F of structural parameters to be optimized as follows respectively
1numerical matrix F
1with simple target function F
2numerical matrix F
2:
Wherein, the arbitrary element X in horizontal combination matrix X
kN(M) footnote K represents experiment numbers, and footnote N represents the numbering of the structural parameters to be optimized being filled in each factor row in orthogonal arrage, and the numbering M of level value is determined by the distribution of selected orthogonal arrage; Numerical matrix F
1and F
2in arbitrary element F
1and F (K)
2(K) K also all represents experiment numbers.
(6) horizontal combination matrix X is processed into normalization horizontal combination matrix x
In the restriction range of each self-corresponding structural parameters to be optimized, normalized is implemented to all elements in horizontal combination matrix X, in the experiment of K group, is numbered M level value X of the structural parameters to be optimized of N
kN(M) after normalized, the element x in the normalization horizontal combination matrix obtained
kN(M) be shown below:
According to arrangement of elements corresponding in horizontal combination matrix X, by element x
kN(M) normalization horizontal combination matrix x is formed:
Wherein, each row in normalization horizontal combination matrix x are all corresponding to a normalized structural parameters x to be optimized
nvalue, its footnote N is similarly the numbering of structural parameters to be optimized; After normalized, x
n∈ [0,1], namely [0,1] is the structural parameters x to be optimized after normalized
nrestriction range.
(7) F is obtained by Response Surface Method matching
1and F
2respectively with x
nfunctional relation
Simple target function F is obtained by Response Surface Method matching
1and F
2respectively with normalized structural parameters x to be optimized
ni.e. x
1, x
2..., x
nbetween functional relation, functional relation all can be expressed as second order polynomial form:
Wherein, a
0, a
i, a
ijfor F
1the undetermined coefficient of functional relation, b
0, b
i, b
ijfor F
2the undetermined coefficient of functional relation.Undetermined coefficient is formed F in order respectively
1and F
2the undetermined coefficient matrix A of functional relation and B:
A＝[a
0a
1…a
na
11…a
1na
22…a
2n…a
nn]
T，
B＝[b
0b
1…b
nb
11…b
1nb
22…b
2n…b
nn]
T，
Wherein, the transposition of T representing matrix, that is: the dimension of A with B is identical, and line number is 1+n+ [n (n+1)/2], and columns is 1.In matrix A and B, the exact numerical values recited of undetermined coefficient is calculated by following formula respectively:
A＝(C
TC)
-1C
TF
1，B＝(C
TC)
-1C
TF
2，
Wherein, the element x of Matrix C in element 1 and normalization horizontal combination matrix x
kN(M) and product form composition:
Wherein, by x
kN(M) reduced representation becomes x
kN; The line number of C is k, and columns is 1+n+ [n (n+1)/2].
By above-mentioned calculating, determine the simple target function F of undetermined coefficient
1and F
2respectively with x
1, x
2..., x
nbetween functional relation be:
(8) genetic algorithm optimization obtains F
1and F
2respective global minimum and maximal value
The simple target function F of undetermined coefficient will be determined in step (7)
1with x
1, x
2..., x
nbetween functional relation be programmed in a M file of MATLAB software, and the GAs Toolbox real-time calling carried by MATLAB software calculate F respectively
1at x
nrestriction range [0,1] in global minimum F
1-min=72.80 DEG C and global maximum F
1-max=96.36 DEG C.Being set to of each major parameter of GAs Toolbox: Population Size (Populationsize) controls between 50, selection opertor (Selectionfunction) adopts and is uniformly distributed algorithm (Stochasticuniform) at random, mutation operator (Mutationfunction) selects TSP question algorithm (Adaptivefeasible), crossover operator (Crossoverfunction) selects two-point crossover algorithm (Twopoints), crossover probability (Crossoverfraction) is set to 0.8, it was 100 generations that heredity stops algebraically (Stallgenerations).
Adopt M file edit method same as described above and the optimum configurations of GAs Toolbox, calculate F
2at x
nrestriction range [0,1] in global minimum F
2-min=1.02kg and global maximum F
2-max=3.38kg.
(9) by F
1and F
2be processed into normalized simple target function f
1and f
2
The simple target function F of undetermined coefficient will be determined in step (7)
1and F
2with x
1, x
2..., x
nbetween functional relation substitute into following formula respectively and be normalized, obtain normalized simple target function f
1and f
2with x
1, x
2..., x
nbetween functional relation:
(10) by f
1and f
2and weight coefficient expresses Bi-objective complex optimum objective function F
Normalized simple target function f is set
1and f
2weight coefficient ω corresponding respectively in Bi-objective complex optimum objective function F
1and ω
2, and the f will obtained in step (9)
1and f
2functional relation be updated to following formula, obtain Bi-objective complex optimum objective function F and x
1, x
2..., x
nbetween functional relation:
F＝ω
1f
1+ω
2f
2，
Wherein ω
1∈ [0,1], ω
2∈ [0,1], and ω
1+ ω
2=1.The value size of the weight coefficient that normalized simple target function is corresponding, reflects the significance level that this objective function is considered in Bi-objective complex optimum.
(11) genetic algorithm optimization obtains the Pareto optimum solution of F in each weight coefficient value
The functional relation of Bi-objective complex optimum objective function F step (10) determined is programmed in a M file of MATLAB software, adopts the method identical with step (8) to arrange each major parameter of GAs Toolbox.When only containing continuity parameter in the structural parameters to be optimized selected, by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain F at x
nrestriction range [0,1] in one group of Pareto optimum solution; When containing a discreteness parameter in the structural parameters to be optimized selected, first need in its restriction range, to be defined as multiple normalized level value respectively to this discreteness parameter, then for the level value situation that each limits, respectively by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain the restriction range [0 of F in other normalization continuity parameters, 1] one group of Pareto optimum solution in, the level value of each discreteness parameter limited all can obtain one group of Pareto optimum solution, and the group number of Pareto optimum solution is identical with the number of the limited level value of discreteness parameter.All containing multiple Pareto optimum solution in each group Pareto optimum solution.
Owing to containing a discreteness parameter in the structural parameters to be optimized that the present embodiment is selected, i.e. fin quantity, first need in its restriction range, to be defined as 5 normalized level values respectively to this discreteness parameter, then for the level value situation that each limits, respectively by adjustment weight coefficient, by ω
1with value between being interposed between 0 ~ 1 between 0.05, the minimum value of the Bi-objective complex optimum objective function F by GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain the one group Pareto optimum solution of F in the restriction range [0,1] of other normalization continuity parameters.The level value of each discreteness parameter limited all can obtain one group of Pareto optimum solution, and the present embodiment has divided 5 levels to fin quantity, therefore obtains 5 groups of Pareto optimum solutions altogether.All containing multiple Pareto optimum solution in each group Pareto optimum solution.
(12) F corresponding to each Pareto optimum solution is calculated
1, F
2and X
noptimization value
The all corresponding normalized structural parameters x to be optimized of each Pareto optimum solution in step (11)
none group optimize value, by x
none group optimize value be updated to the simple target function F obtained in step (7)
1and F
2respectively with normalized structural parameters x to be optimized
nbetween functional relation, thus calculate simple target function F corresponding to each Pareto optimum solution
1and F
2optimum results; And by x corresponding for each Pareto optimum solution
none group optimize value be updated to following formula:
X
N＝x
N(X
N-max-X
N-min)+X
N-min，
Heating radiator structural parameters X to be optimized can be calculated
none group optimize value.Therefore, heating radiator structural parameters X to be optimized
neach group optimize value all correspond to one group of simple target function F
1and F
2optimum results.
(13) to F
1and F
2optimum results carry out map data and mark Pareto forward position
By all simple target function F
1and F
2optimum results carry out map data, as shown in Figure 3.Each data point in figure is with one group of simple target function F
1and F
2one of them optimum results be horizontal ordinate and another is determined for ordinate.When only containing continuity parameter in the structural parameters to be optimized selected, all data points in figure are all on Pareto forward position, and when containing a discreteness parameter in the structural parameters to be optimized selected, then only have coordinate position to be on Pareto forward position near the data point of true origin.Owing to containing a discreteness parameter, i.e. fin quantity in the structural parameters to be optimized that the present embodiment is selected, then coordinate position is only had to be on Pareto forward position near the data point of true origin.
(14) draw and optimize F under pre-structure parameter
1and F
2result and determine alternative optimal design
At F
1and F
2optimum results data plot (Fig. 3) in, draw and optimize F corresponding to pre-structure parameter
1and F
2result, to be only on Pareto forward position and transverse and longitudinal coordinate figure is all less than the data point optimizing pre-structure, could to realize the alternative design result of comprehensive optimum as two single design objects in restriction range.
(15) by optimization upper limit determination optimal result and the values of the structural parameters of a design object
The specific requirement that further refinement radiator performance is optimized, namely sets the optimization higher limit of a single design object function, then from F
1and F
2optimum results data plot alternative design result in, find out data point below this optimization higher limit and nearest, this data point can meet be less than or equal to the prerequisite of the optimization higher limit of the single design object function of setting under, ensure that another single design object obtains overall minimum, the X corresponding to this data point
none group optimize value be heating radiator realize Bi-objective complex optimum after values of the structural parameters.
In the present embodiment, setting heatsink weight F
2optimization higher limit be 1.6kg, then in the alternative design result of Fig. 3, find out below 1.6kg and nearest data point, the heatsink weight F of this data point
2=1.56kg, junction temperature of chip is overall minimum, F
1=81.83 DEG C, the X corresponding to this data point
none group optimize value be heating radiator realize Bi-objective complex optimum after values of the structural parameters, be followed successively by: fin thickness X
1fin quantity X in=1.5mm, 1/4th regions
2=6, fin length X
3=130mm, fin height X
4=60mm and central cylinder diameter X
5=44mm.Compared with the optimization pre-structure of heating radiator, the junction temperature of chip after heating radiator realizes Bi-objective complex optimum reduces 8.11%, and heatsink weight reduces 26.42%.
The above is only the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.
Claims (8)
1. a Bi-objective Synthetical Optimization method for LED radiator structural parameters, is characterized in that, comprise the following steps:
(1) the selected simple target function F implementing two the single design objects optimized
1and F
2;
(2) determine the influential heating radiator of each simple target function tool structural parameters X to be optimized
nand restriction range [X
n-min, X
n-max]; X
nnumbering N=1,2 ..., n, n are the quantity of structural parameters to be optimized;
(3) orthogonal arrage in orthogonal experiment is selected, according to the number of levels m of selected orthogonal arrage, the various structural parameters X to be optimized of mean allocation from small to large in described restriction range
nlevel value X
n(M), level value numbering M=1,2 ..., m, is wherein numbered the structural parameters X to be optimized of N
nm level value be:
According to structural parameters X to be optimized
nnumber order successively by structural parameters X to be optimized
nlevel value X
n(M) each factor row that in the orthogonal arrage be filled into, row sequence is forward, form the experimental program of described orthogonal arrage;
(4) with the structural parameters X to be optimized distributed in described orthogonal arrage
none group of horizontal combination as one group of experiment parameter of described experimental program, obtained the simple target function F of K group experiment by thermal behavior simulation calculation
1(K) numerical value, and another simple target function F obtaining the experiment of K group by presetting method
2(K) numerical value, K is experiment numbers K=1,2 ..., k;
(5) according to the experiment numbers order that described orthogonal arrage arranges, structural parameters X to be optimized is constructed respectively
nhorizontal combination matrix X, simple target function F
1numerical matrix F
1with simple target function F
2numerical matrix F
2:
(6) to the element X in horizontal combination matrix X
kN(M) at each self-corresponding structural parameters X to be optimized
nrestriction range in implement normalized, the element x in the normalization horizontal combination matrix obtained
kN(M):
According to arrangement of elements corresponding in horizontal combination matrix X, by element x
kN(M) normalization horizontal combination matrix x is formed:
Wherein, each row in normalization horizontal combination matrix x are all corresponding to a normalized structural parameters x to be optimized
nvalue, x
nfootnote N is the numbering of structural parameters to be optimized; After normalized, x
n∈ [0,1], namely [0,1] is the structural parameters x to be optimized after normalization
nrestriction range;
(7) simple target function F is obtained by Response Surface Method matching
1and F
2respectively with normalized structural parameters x to be optimized
nbetween functional relation:
Wherein, a
0, a
i, a
ijfor F
1the undetermined coefficient of functional relation, b
0, b
i, b
ijfor F
2the undetermined coefficient of functional relation; Undetermined coefficient is formed F in order respectively
1and F
2the undetermined coefficient matrix A of functional relation and B:
A＝[a
0a
1…a
na
11…a
1na
22…a
2n…a
nn]
T，
B＝[b
0b
1…b
nb
11…b
1nb
22…b
2n…b
nn]
T，
Wherein, the transposition of T representing matrix, that is: the dimension of A with B is identical, and line number is 1+n+ [n (n+1)/2], and columns is 1; In matrix A and B, the numerical value of undetermined coefficient is calculated by following formula respectively:
A＝(C
TC)
-1C
TF
1，B＝(C
TC)
-1C
TF
2，
Wherein, the element x of Matrix C in element 1 and normalization horizontal combination matrix x
kN(M) and product form composition:
Wherein, by x
kN(M) reduced representation becomes x
kN; The line number of C is k, and columns is 1+n+ [n (n+1)/2];
(8) the simple target function F of undetermined coefficient will determined in step (7)
1with x
1, x
2..., x
nbetween functional relation be programmed in a M file of MATLAB software, calculate F respectively by the GAs Toolbox real-time calling of MATLAB software
1at x
nrestriction range [0,1] in global minimum F
1-minwith global maximum F
1-max; In like manner calculate F
2at x
nrestriction range [0,1] in global minimum F
2-minwith global maximum F
2-max;
(9) the simple target function F of undetermined coefficient will determined in step (7)
1and F
2with x
1, x
2..., x
nbetween functional relation substitute into following formula respectively and be normalized,
Obtain normalized simple target function f
1and f
2with x
1, x
2..., x
nbetween functional relation;
(10) normalized simple target function f is set
1and f
2weight coefficient ω corresponding respectively in Bi-objective complex optimum objective function F
1and ω
2, by the f obtained in step (9)
1and f
2functional relation be updated to following formula, obtain Bi-objective complex optimum objective function F and x
1, x
2..., x
nbetween functional relation:
F＝ω
1f
1+ω
2f
2，
Wherein ω
1∈ [0,1], ω
2∈ [0,1], and ω
1+ ω
2=1;
(11) functional relation of Bi-objective complex optimum objective function F step (10) determined is programmed in a M file of MATLAB software, adopts the GAs Toolbox optimization identical with step (8) optimum configurations to obtain F at normalized structural parameters x to be optimized
nrestriction range [0,1] in one or more groups Pareto optimum solution, all containing multiple Pareto optimum solution in each group;
(12) the structural parameters x normalized to be optimized corresponding to each Pareto optimum solution step (11) obtained
none group optimize value be updated to the simple target function F obtained in step (7)
1and F
2respectively with normalized structural parameters x to be optimized
nbetween functional relation, calculate the simple target function F that each Pareto optimum solution is corresponding
1and F
2optimum results; By structural parameters x normalized to be optimized corresponding for each Pareto optimum solution
none group optimize value be updated to following formula:
X
N＝x
N(X
N-max-X
N-min)+X
N-min，
Calculate heating radiator structural parameters X to be optimized
none group optimize value;
(13) by all simple target function F
1and F
2optimum results carry out map data, form optimum results data plot; In this optimum results data plot, each data point is with one group of simple target function F
1and F
2one of them optimum results be horizontal ordinate, with another optimum results for ordinate is determined;
(14) in described optimum results data plot, draw and optimize F corresponding to pre-structure parameter
1and F
2result, select to be on Pareto forward position and transverse and longitudinal coordinate figure is all less than the data point optimizing pre-structure realizes comprehensive optimum in restriction range alternative design result as two single design objects;
(15) set the optimization higher limit of a single design object function, then from described alternative design result, find out data point below this optimization higher limit and nearest, the structural parameters X to be optimized corresponding to this data point
none group optimize value and be the values of the structural parameters after heating radiator Bi-objective complex optimum.
2. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, it is characterized in that, in step (1), a design object of two single design objects is make one in LED chip junction temperature, key node temperature or heat radiator thermal resistance corresponding simple target function F
1numerical value reduces, and another design object is make in the weight of heating radiator, volume or manufacturing cost corresponding simple target function F
2numerical value reduces.
3. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, is characterized in that, in step (2), and described structural parameters X to be optimized
ncomprise continuity parameter and discreteness parameter, described structural parameters X to be optimized
nin be less than or equal to 1 containing the number of discreteness parameter.
4. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 3, it is characterized in that, described continuity parameter comprises the processing dimension in heating radiator, and described discreteness parameter comprises fin quantity, material coefficient of heat conductivity.
5. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, is characterized in that, in step (3), according to structural parameters X to be optimized
nnumber order when filling forward each factor row of row sequence in orthogonal arrage successively, the factor row being greater than the quantity of structural parameters to be optimized are set to blank column, and when the orthogonal arrage identical because of prime number has multiple, and the more orthogonal arrage of selection level number is filled.
6. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, it is characterized in that, in step (4), described presetting method is: when often organizing another simple target function F corresponding to experiment
2during for heatsink weight, F in the experiment of this group
2(K) numerical value adopts the analog computation of three-dimensional machinery design software to obtain; When simple target function F
2during for heating radiator volume, F in the experiment of this group
2(K) numerical value is obtained by the product of three maximum outer profile sizes of heating radiator in three-dimensional system of coordinate; If simple target function F
2during manufacturing cost for heating radiator, F in the experiment of this group
2(K) numerical value need carry out accounting by consumptive material and processing cost and obtain.
7. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, it is characterized in that, in step (8), the optimum configurations of described GAs Toolbox is: Population Size controls between 20 ~ 100, selection opertor adopts and is uniformly distributed algorithm at random, and mutation operator selects TSP question algorithm, and crossover operator selects two-point crossover algorithm, crossover probability is set to 0.8, and heredity stops for being more than or equal to for 100 generations.
8. the Bi-objective Synthetical Optimization method of LED radiator structural parameters according to claim 1, is characterized in that, in step (11), when in the structural parameters to be optimized selected only containing continuity parameter time, by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by described GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain Bi-objective complex optimum objective function F at normalized structural parameters x to be optimized
nrestriction range [0,1] in one group of Pareto optimum solution; When containing a discreteness parameter in the structural parameters to be optimized selected, first multiple normalized level value is defined as in the restriction range of correspondence respectively to this discreteness parameter, then for the level value that each limits, respectively by adjustment weight coefficient ω
1and ω
2value, the minimum value of the Bi-objective complex optimum objective function F by described GAs Toolbox real-time calling and under calculating each weight coefficient value, thus obtain the restriction range [0 of Bi-objective complex optimum objective function F in other normalization continuity parameters, 1] one group of Pareto optimum solution in, the group number of Pareto optimum solution is identical with the number of the limited level value of discreteness parameter.
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