CN105372807B - A kind of H β composite optimization methods of the collateral support of astronomical optics telescope primary mirror - Google Patents

A kind of H β composite optimization methods of the collateral support of astronomical optics telescope primary mirror Download PDF

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CN105372807B
CN105372807B CN201510601606.5A CN201510601606A CN105372807B CN 105372807 B CN105372807 B CN 105372807B CN 201510601606 A CN201510601606 A CN 201510601606A CN 105372807 B CN105372807 B CN 105372807B
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primary mirror
optimization
collateral support
point
telescope primary
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CN105372807A (en
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王海仁
娄铮
程景全
郑宪忠
左营喜
杨戟
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Purple Mountain Observatory of CAS
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Abstract

The present invention relates to a kind of H β composite optimization methods of the collateral support optimization of astronomical optics telescope primary mirror, more particularly to the collateral support of astronomical optics telescope primary mirror.The technical problem to be solved in the present invention only has a parametric variable when being the collateral support optimization optimization of existing astronomical optics telescope primary mirror, and obtained strong point design is bad, and computational methods are not low precisions, is exactly that speed is slow and be not global optimum.In order to solve the above technical problems, the technical solution adopted by the present invention is：A kind of H β composite optimization methods of the collateral support of astronomical optics telescope primary mirror.A kind of H β composite optimization methods of the collateral support of astronomical optics telescope primary mirror are described in detail the present invention, and H β composite optimization methods are a kind of high-precision optimization methods.

Description

A kind of H- β composite optimization methods of the collateral support of astronomical optics telescope primary mirror
Technical field
The present invention relates to the collateral support optimization of astronomical optics telescope primary mirror, more particularly to astronomical optics telescope primary mirror side A kind of H- β composite optimization methods of support.
Background technology
Astronomical telescope (Astronomical Telescope) is the important tool for observing celestial body, can not turgidly Say, without the birth and development of telescope, just there is no modern astronomy.As telescope the improvement of performance and carries in every respect Height, astronomy are also just experiencing huge leap, promote understanding of the mankind to universe rapidly.Due to the light collecting light ability of telescope Strengthen with the increase of bore, the light collecting light ability of telescope is stronger, it becomes possible to see darker farther celestial body, therefore, celestial body The more bigbore telescope of development need of physics.
But as the increase for aperture of mirror of looking in the distance, a series of technical problem are comed one after another.On the one hand, telescope from Crossing conference again makes len distortion quite obvious, and on the other hand, mirror body temperature inequality also makes minute surface produce distortion, and then influences imaging Quality.
The collateral support of giant optical telescope primary mirror uses push-pull-shear sides supported design more, when optimization design Only β (at collateral support point both shear force and shear force and footpath power and ratio) parametric variable, and strong point z-axis direction is high Degree H only simple sets mirror thickness centre position.However, H adjustment offside mirror surface-shaped influences are very big, H is simply placed in Mirror thickness centre position is not optimal design, does not have but correlation technique to solve this problem in the prior art.
In addition, in existing computational methods, zeroth order optimization is not used typically, because while zeroth order optimization can be Global optimum, but have result precision low, the needs of supported design can not be met；Existing algorithm is typically inclined to excellent using single order Change method, because the precision of its measuring and calculating is high, however, its shortcoming is also apparent from, it is impossible to which it is local optimum to avoid obtaining, and computing speed Degree is too slow, and by existing method, under conditions of using high-performance computer, each side supported design obtained in one month One preferred plan belongs to faster, and the general all more than one of the design of the collateral support of primary mirror.
The content of the invention
The technical problem to be solved in the present invention, which is that existing astronomical optics telescope primary mirror is collateral, to be supportted when optimization optimizes only There is a parametric variable, obtained strong point design is bad, and computational methods are not low precisions, is exactly speed slowly and is not Global optimum.
In order to solve the above technical problems, the technical solution adopted by the present invention is：The collateral support of astronomical optics telescope primary mirror A kind of H- β composite optimization methods, using H and β as optimized variable, offside minute surface establishes object function：
[γ1,γ2,L,γm]=[H, β] (1)
It is somebody's turn to do and takes and scans dividing mode side mirror face is divided into finite element grid；2) zeroth order optimization is carried out to supporting surface, A low precision global value is obtained, the tolerance of the zeroth order optimization is n times of the mesh spacing to be obtained in step 1, n >=1, N is integer；3) based on the low precision global value that step 2 obtains, the region for optimizing to obtain to zeroth order uses First-Order Optimization Method Local optimum is carried out, obtains high accuracy support point value, the tolerance of the First-Order Optimization Method is to be walked with the grid obtained in step 1 It is long.
Object function is set by optimized variable of H and β, overcomes and ignores H effects in existing method, cause the branch calculated The problem of support point position is bad, being optimized using zeroth order optimization, its advantage is that speed is very fast, however, shortcoming becomes apparent from, Its precision is even below the desired value for the object function tried to achieve by algorithm merely, therefore, will not be adopted in existing optimization Work is optimized with zeroth order optimization, however, in the methods of the invention, first passing through zeroth order optimization and quickly obtaining global optimum Value, then on this basis, local optimum is calculated with First-Order Optimization Method, to overcome asking for zeroth order optimization computational accuracy difference Topic, while it also avoid the shortcomings that First-Order Optimization Method calculating speed is slow.The realization of all of above step is all based on large-scale limited Meta software ANSYS platforms and APDL LISP program LISP programming realizations.
It is an advantage of the invention that：Object function is set by optimized variable of H and β simultaneously, improves the branch that function calculates The accuracy of support point position；Global optimum is quickly drawn by zeroth order optimization, then used on the basis of global optimum First-Order Optimization Method carries out local optimum, obtains high-precision supporting point position, in this manner, in medium-performance PC (individual's meters Calculation machine) under, each design of primary mirror support obtains a preferred plan within a hour.
Brief description of the drawings
Fig. 1 is WFST primary mirror diagrammatic cross-sections.
Fig. 2 is WFST primary mirror side stay schematic diagrams.
Fig. 3 is WFST primary mirror parameterized models.
Fig. 4 is one of WFST primary mirrors 1/72 mesh generation figure.
Fig. 5 is the whole primary mirror mesh generation figures of WFST.
Fig. 6 is that WFST primary mirrors side support loads apply schematic diagram.
Fig. 7 is object function RMSe and design variable H and relation four-dimensional figure when the strong point is N=6.
Fig. 8 be when the strong point is N=6 and object function RMSe optimum value 34.63nm primary mirror reflecting surface relative to former coordinate It is deformation map.
Fig. 9 is minimum half light path error map when the strong point is N=6 and object function RMSe optimum value 34.63nm.
Figure 10 is object function RMSe and design variable H and relation graphics when the strong point is N=12.
Figure 11 is that primary mirror reflecting surface is sat relative to original when the strong point is N=12 and object function RMSe optimum value 26.69nm Mark system deformation map.
Figure 12 is minimum half light path error map when the strong point is N=12 and object function RMSe optimum value 26.99nm.
Figure 13 is object function RMSe and design variable H and relation four-dimensional figure when the strong point is N=18.
Figure 14 is that primary mirror reflecting surface is sat relative to original when the strong point is N=18 and object function RMSe optimum value 23.71nm Mark system deformation map.
Figure 15 is minimum half light path error map when the strong point is N=18 and object function RMSe optimum value 23.71nm.
Embodiment
The present invention comprises the following steps：
1) using H and β as optimized variable, offside minute surface establishes object function：
[γ1,γ2,L,γm]=[H, β] (2)
And take and scan dividing mode side mirror face is divided into finite element grid；
2) zeroth order optimization is carried out to supporting surface, obtains a low precision global value, the tolerance of the zeroth order optimization be with N times of the mesh spacing obtained in step 1, n >=1, n are integer；
3) based on the low precision global value that step 2 obtains, the region for optimizing to obtain to zeroth order uses First-Order Optimization Method Local optimum is carried out, obtains high accuracy support point value, the tolerance of the First-Order Optimization Method is to be walked with the grid obtained in step 1 It is long.
The following general structure optimization problem mathematical formulae of optimization mathematical principle of step 1
It is described as follows：
s.t. γi≤γi≤γi(i=1,2,3, L, m)
gj≤gj(γ)≤g (j=1,2,3, L, n1)
hj≤hj(γ)≤hj(j=1,2,3, L, n2) (3)
wj≤wj(γ)≤w (j=1,2,3, L, n3)
Object function (Π):To every kind of possible design, (Π) all returns to a desired value, typically passes through various optimizations Seek (Π) minimum value.Design variable (γ):One function or vector array, object function become as design variable changes Change.State variable (g, h, w):To giving structure, the corresponding one group of state variable of each group of design variable.Zero be related in step 2 Rank optimization mathematical principle is as follows：
Using least square fitting, object function can be write as following form:
By penalty function, design variable and state variable restricted problem are changed into unconstrained problem, can be obtained：
Here γiIt is design variable, gi,hi,wiIt is state variable, Υ, G, H, W are their penalty function respectively.Π0It is mesh Mark reference value, pkRepresent response surface parameter.When the binding occurrence of design variation or state variable close to them, penalty value It increased dramatically.
The First-Order Optimization Method mathematical principle being related in step 3 is as follows：First-Order Optimization Method
Unconstrained problem equation is as follows：
Here Q (γ, q) is dimensionless without constrained objective function；Pγ,Pg,Ph,PwRespectively design variable and state variable Penalty function.Π0Be object function Π reference values in whole design space, object function and state variable penalty function are carried out Differential.To each iteration (j), Optimizing Search direction d is introduced(i).. then in next step (j+1) design variable as shown in formula (7) The S in the equationjFor line search parameter, corresponding to direction of search d(j)Upper minimum Q values.
γ(j+1)=γ(j)+Sjd(j) (7)
When jth walk iterative target function and j+1 step iteration and optimum value (b) meet some step equations (8), then restrain. Here τ is object function tolerance.
|Π(j)-Π(j-1)|≤τand|Π(j)-Π(b)≤τ (8)
Primary mirror half light path margin of error of minimum description is for small deformation elastomer, and each components of strain and displacement constitutive relation are such as Under：
Here so that reflecting surface is parabola primary mirror as an example, if primary mirror, when not having gravity, reflecting surface has preferable parabolic Face shape：
X2+Y2=4f (Z+c) (10)
Here f is focal length, and c is summit.Primary mirror structure will deform under gravity, and mirror surface node will Deviate the position of original parabolic surface.Assuming that the most preferably identical parabola of reflecting surface at this moment be present, if this is optimal Parabola is expressed as on new coordinate system：
Consider any point i on paraboloid surface, then pass through the direction cosines of the point and the normal perpendicular to parabolic surface For：
Assuming that the displacement in this under external force is (ui,vi,wi), the point after deformation is with optimal paraboloidal distance Δi, then have
X-(Xi+ui)=± Δicosα1
Y-(Yi+vi)=± Δicosα2
Z-(Zi+wi)=± Δicosα3
For N number of node, textured surface is for preferable paraboloidal root-mean-square distance deviation
Gained root-mean-square error can not represent the effective deviation in surface above, and real surface Root Mean Square error should be passed through Minimum half light path of optimization obtains.Root mean square half path-length error of minimum is as follows：
ei=Δicosβi
Here β is surface normal and the angle of parabolic axis.
Embodiment 1
Specific item scalar functions, design variable and state by taking 2.5 meters of collateral supports of big visual field Survey telescope (WFST) primary mirror as an example The setting of variable
As shown in figure 1, the wave-length coverage of WFST observations is 320nm to 1000nm, so being set in the support of gravitational load lower axle Minimum half path-length error of root mean square is counted no more than 10nm.Primary mirror is crescent, and upper and lower surface is all focal length f=2.13 Parabola, primary mirror thickness h=120.00mm, internal diameter φ1=1000.00mm, external diameter φ2=2500.00mm.
As shown in Fig. 2 lateral support described in WFST primary mirrors designs, under minute surface vertical case, in primary mirror external diameter r2Circumference The selection of height H (away from primary mirror bottom parabola vertex distance) place is on the symmetrical N points (by taking N=6 as an example) in XZ faces and YZ faces, the N on face Point is with r2Circumference is on circumscribed circle n-shaped summit, gives this six points to apply sinusoidal or cosine form shear force N respectivelyτ, footpath Power Nr and axle power Fz, balance the gravity and gravity torque of primary mirror.Referring to formula (16) (21).β is shear force at collateral support point with cutting The ratio of the sum of both power and footpath power, in (21) formula, it is free variable that we, which add H,.
Nr=Frcosθ,Nτ=Fτsinθ,Fz=v0cosθ. (16)
∑Nrcosθ+∑NτSin θ=G. (18)
∑Frcos2θ+∑Fτsin2θ=G. (19)
∑FZR cos θ=GL=G (H-H0). (20)
∑v0R cos 2θ=G (H-H0). (21)
From formula (3)~formula (6) and formula (14)~(21), it is recognised that WFST primary mirrors are collateral to support the object function optimized, Design variable and state variable, it can be set to
[γ1,γ2,L,γm]=[H, β] (22)
Here primary mirror material is using devitrified glass for the foundation of FEM model, as shown in table 1.
The microcrystal glass material performance of table 1
As shown in figure 3, primary mirror parameterized model is built by APDL programmings, model, which is taken, scans division.
As illustrated in figures 4-5, it is finite element grid.
As shown in fig. 6, position load applying mode, illustrates by taking N=18 as an example here, wherein there is three points to constrain it respectively θ and z directions (under cylindrical coordinates) free degree, these three points just differ 120 °, form equilateral triangle summit, such primary mirror is quiet Fixed support, will not produce and cause calculation error by constraint；Other each points apply sinusoidal or cosine form shear force Nτ, footpath power Nr and axle power Fz；Whole primary mirror applies acceleration g in vertical direction.
During optimization, first to be optimized using zeroth order optimization method to primary mirror support, what is obtained is one The relatively low global value of precision.Secondly, optimized on the basis of zeroth order optimization using first order optimization method.So, we obtain Be global high-precision optimum value.
Finite element result
WFST primary mirror supports have following three kinds of N schemes.The first is total strong point N=6；Second is total strong point N= 12；The third is total strong point N=18.
As shown in Fig. 7, Figure 10 and Figure 13, object function RMS during N=6,12 and 18 is represented respectivelyeWith design variable H and β The graphics for changing and changing, and the iterative process of First-Order Optimization Method.N=in N=12 in N=6 in Fig. 7, Figure 10, Figure 13 18.The object function corresponding optimum value that three kinds of strong point designs have been marked in figure is respectively 34.63nm, 26.99nm and 23.71nm.It can also be seen that object function RMS from figureeIt is very sensitive to design variable H changes, so H is design variable It is very necessary.
As shown in Fig. 8, Figure 11 and Figure 14, primary mirror reflecting surface phase during three kinds of strong point design optimums is represented respectively To former coordinate Aberration nephogram [referring to equation (10)] as can be seen from Fig., their deformation cloud atlas are symmetrical.
As shown in Fig. 9, Figure 12 and Figure 15, represent to sit relative to new during these three strong point design optimums respectively Mark the light path error map of minimum half [referring to formula (11)~(15)] of system.
The optimum optimization the results list of table 2
Table 2 lists object function RMSeOptimum value and now respective design variable H and β and peak-to-peak value PV.From table 2 As can be seen that the strong point increases at 12 points from 6 points, RMSeThere is larger reduction with PV.Increase at 18 points from the strong point 12, RMSeIt is less to reduce amplitude with PV.This explanation, when the strong point is 18, RMSeLimiting value is begun to PV.
According to WFST design requirements, half path-length error of supported design root mean square minimum must be less than on the downside of gravitational load 30nm.It can be seen that, work as N from Fig.7~Fig.15 and Table 2P=12 and 18 minimum half light paths of their optimal root mean square miss Difference is respectively that 26.99nm and 23.71nm meets WFST to the collateral support design requirement of primary mirror.Although RMS during N=12e=0.084 λmin(λmin=320nm) RMS when being more than N=18e=0.074 λmin, but support structure designs are more simple during N=18.So It is identical meet design requirement on the premise of, structure design simplifies closer to structure during N=18 limiting value.
It is a kind of high-precision optimization method that result more than, which can be seen that H- β composite optimization methods,.

Claims (1)

  1. A kind of 1. H- β composite optimization methods of the collateral support of astronomical optics telescope primary mirror, it is characterized in that comprising the following steps：
    1) using H and β as optimized variable, offside minute surface establishes object function：
    And take and scan dividing mode side mirror face is divided into finite element grid；
    Wherein, β be at collateral support point both shear force and shear force and footpath power and ratio, H is strong point z-axis direction height；△i It is displacement (us of any point i on paraboloid surface under external forcei,vi,wi), the point and optimal paraboloidal distance after deformation；N For node number；
    ei=△icosβi, βiIt is surface normal and the angle of parabolic axis；
    [γ1,γ2,L,γm] it is the design variable that general structure optimization problem mathematical formulae describes；
    2) zeroth order optimization is carried out to supporting surface, obtains a low precision global value, the tolerance of the zeroth order optimization is with step 1) n times of the mesh spacing obtained in, n >=1, n are integer；
    3) based on the low precision global value that step 2) obtains, the region for optimizing to obtain to zeroth order is carried out using First-Order Optimization Method Local optimum, high accuracy support point value is obtained, the tolerance of the First-Order Optimization Method is with step 1）In obtained mesh spacing.
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