CN104729430B - A kind of tower type solar energy thermal power generation heliostat surface testing method - Google Patents

A kind of tower type solar energy thermal power generation heliostat surface testing method Download PDF

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CN104729430B
CN104729430B CN201510136376.XA CN201510136376A CN104729430B CN 104729430 B CN104729430 B CN 104729430B CN 201510136376 A CN201510136376 A CN 201510136376A CN 104729430 B CN104729430 B CN 104729430B
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mrow
heliostat
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CN104729430A (en
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朱会宾
王志峰
王华荣
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Institute of Electrical Engineering of CAS
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S80/00Details, accessories or component parts of solar heat collectors not provided for in groups F24S10/00-F24S70/00
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S23/00Arrangements for concentrating solar-rays for solar heat collectors
    • F24S23/70Arrangements for concentrating solar-rays for solar heat collectors with reflectors
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24HEATING; RANGES; VENTILATING
    • F24SSOLAR HEAT COLLECTORS; SOLAR HEAT SYSTEMS
    • F24S50/00Arrangements for controlling solar heat collectors
    • F24S50/20Arrangements for controlling solar heat collectors for tracking
    • F24S2050/25Calibration means; Methods for initial positioning of solar concentrators or solar receivers
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02EREDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E10/00Energy generation through renewable energy sources
    • Y02E10/40Solar thermal energy, e.g. solar towers

Abstract

A kind of tower type solar energy thermal power generation heliostat surface testing method, heliostat (5) to be measured is controlled by industrial computer (4), so that CCD camera (2) can gather the deformation pattern of the compound stripe pattern screen (3) of heliostat (5) reflection, the deformation bonding stripe pattern of computer (1) control CCD camera (2) collection heliostat (5) reflection, the virtual reference plane phase distribution of combined structure and mirror slope and the mapping model of phase obtain the slope distribution situation of minute surface.The face shape of heliostat to be measured (5) minute surface can be obtained based on broad sense Hermite interpolation methods.

Description

A kind of tower type solar energy thermal power generation heliostat surface testing method
Technical field
The present invention relates to a kind of heliostat surface testing method.
Background technology
Tower type solar energy thermal power generation has high light concentrating times, operating temperature height, heat transfer distance is short, thermal losses is few, system The advantages of overall efficiency is high, its output characteristics and conventional thermal power generation are closest, are the photo-thermal power generation hairs that prospect is most expected Open up one of route.Tower type solar energy thermal power generation is main by heliostat condensing system, heat absorption and thermal energy transfer systems, electricity generation system 3 Part is constituted.Sunshine is converged the heat dump reflexed on tower by heliostat condensing system by large number of heliostat, Heat energy is converted light energy into by heat dump, then generated electricity by thermodynamic cycle.During heliostat is tower type solar energy thermal power generation station Core component, account for the 40-50% of power station cost of investment, be the carrier for realizing system high efficiency photothermal deformation.Tower-type solar thermal Power station heliostat is mainly characterized in that:1) aperture area is larger, from tens square meters to square meters up to a hundred;2) heliostat in mirror Enormous amount (thousands of, or even hundreds of thousands face), and remote from a distance from heat dump, heliostat focal length is larger (from tens meters to upper Km is remote, very high to optically focused required precision);3) heliostat is spliced to form by the sub- mirror of multi-surface cell and complex-curved converged sunshine Heat dump is reflexed to, integral face shape requires high.Therefore, high-precision mirror shape is to ensure that the sunshine of heliostat convergence is accurately anti- It is mapped to the premise up to heat dump.But, on the one hand, the actual integral face shape that heliostat unit mirror in installation process is spliced to form There is certain deviation between the shape of Theoretical Design face;On the other hand, heliostat is during outdoor operation, by wind load, certainly The factors such as body gravity, temperature influence to cause surface deformation, cause heliostat minute surface can not form preferable curved surface, thereby result in Mirror shape little deviation causes the solar radiation of reflection to deviate heat dump aperture, reduction mirror light gathering efficiency.By above-mentioned mistake Poor factor causes the hot spot that convergence is reflected to shift, even deviates from out heat dump, influences the safety of tower, reduces light gathering efficiency. Therefore, quick heliostat minute surface surface testing is to ensure spotlight effect, improves mirror installation effectiveness, reduces cost, improves Jing Chang The key of light gathering efficiency and power station operational efficiency.At present, the detection of such mirror shape generally using three coordinate machine, laser radar, Photogrammetric and streak reflex method.Relative to first three measuring method, streak reflex method has high sensitivity, quick detection, is The advantages of uniting simple, it is adaptable to detect all kinds of minute surfaces.Document " S.Ulmer, et.al, Solar Energy, 2011,85 (4) 681-687 " detected to 39.6 square meter settled date mirror surface-shapeds in Spain PSA power stations using streak reflex method, obtain compared with Good measurement result.However, this method is distinguished using four-stepped switching policy using the projecting apparatus arranged in mirror to the white screen on tower The stripe pattern of projected horizontal, vertical both direction, at least projects 16 spoke print images, and the real-time of detection is relatively low, simultaneously Whole measurement process can only be carried out at night and easily influenceed by external light source.Therefore a kind of efficient, quick, accurate, letter is needed Easy detection method is detected to settled date mirror surface-shaped.
The content of the invention
The invention aims to overcome the shortcomings of that it is efficient, quick, accurate, easy there is provided one kind that prior art is present Tower type solar energy thermal power generation heliostat surface testing method.
Tower type solar energy thermal power generation heliostat surface testing method of the present invention comprises the following steps:
The 1st, compound stripe pattern screen is arranged on to the lower section of heat dump mouthful on heat absorption tower, heliostat to be measured and heat absorption tower is adjusted On CCD camera position so that CCD camera can observe the deformation bonding stripe pattern of heliostat to be measured reflection;Compound bar Print image screen is diffuse reflecting screen, and the fringe frequency of the compound stripe pattern presented in the horizontal direction and the vertical direction is identical;
2nd, the deformation bonding stripe pattern of a heliostat reflection to be measured is gathered using CCD camera, this picture signal is passed Transport to computer;
3rd, the deformation for asking for heliostat reflection to be measured based on window Fourier filtering and quality guiding phase developing method is answered Close the phase distribution of stripe pattern in the horizontal and vertical directions.Utilize the faces such as the acquisition of Zernike multinomials and heliostat to be measured Long-pending virtual reference plane phase distribution, according to virtual reference plane and the phase distribution of heliostat to be measured, is obtained by be determined Phase offset caused by day mirror surface-shaped;
4th, based on CCD camera, heliostat, the relative space position for being combined stripe pattern screen, foundation is drawn by heliostat minute surface The phase offset and the numerical relationship model of mirror slope risen, is obtained with reference to the phase offset as caused by heliostat minute surface in step 3 To the slope distribution of heliostat minute surface in both the horizontal and vertical directions;
5th, the 3 d shape for carrying out heliostat using broad sense Hermite interpolation algorithms is reconstructed.
Detecting system of the present invention includes CCD camera, compound stripe pattern screen, heliostat to be measured, computer etc..Compound striped Image screen is placed in below heat absorption mouth, and the heliostat to be measured in mirror is controlled to run by industrial computer, installed in tower-type solar thermal The CCD camera at electricity generation system heat absorption tower top end gathers the deformation bonding stripe pattern of heliostat reflection to be measured by computer control. Compared with existing detection method, the present invention has advantages below:
1st, the present invention is obtained using compound stripe pattern screen based on window Fourier filtering and quality guiding phase developing method Phase distribution of the heliostat in horizontal and vertical both direction is taken, only need to gather piece image can obtain heliostat minute surface Phase pushing figure, compared with the existing detection method based on four-step phase-shifting, the present invention has that real-time is higher, strong interference immunity, Affected by environment relatively low the features such as;
2nd, the present invention obtains the distribution of virtual reference plane phase using Zernike multinomials.Due to heliostat minute surface to be measured Area is larger, and the phase distribution obtained with the standard flat mirror of heliostat homalographic size to be measured is difficult to, therefore is obtained first The phase distribution of compound stripe pattern screen is taken, the virtual reference plane with heliostat homalographic is obtained with reference to Zernike multinomials Phase distribution;Compared with existing streak reflex detection method, flexibility of the invention is higher.
3rd, the present invention is filtered using window Fourier and carries out phase extraction to the deformation bonding stripe pattern of mirror-reflection, with Conventional Fourier transform method is compared, with anti-interference is stronger and obtain is phase in horizontal and vertical both direction Distribution.
4th, the present invention carries out three-dimensionalreconstruction based on broad sense Hermite interpolation algorithms to settled date mirror surface-shaped.By gradient or method Restructuring procedure to vector to 3 d shape is mainly based upon integral and calculating.In the ideal case, integration is unrelated with path, but In actual measurement process due to by detection noise, system deviation etc. influence, measured gradient be non-conservative field, path of integration and The selection of integral algorithm will result directly in different reconstructed results.Therefore, for such big data quantity, band noise, lack sampling ladder Discrete data is spent, 3 d shape reconstruction is carried out using broad sense Hermite interpolation algorithms, can ensure that the local and overall situation rebuilds essence simultaneously Degree.
Brief description of the drawings
The detecting system structural representation of Fig. 1 application solar energy thermal-power-generating of the present invention heliostat surface testing methods;
Fig. 2 solar energy thermal-power-generatings of the present invention compound stripe pattern of heliostat surface testing method.
Embodiment
The present invention is further illustrated with reference to the accompanying drawings and detailed description.
As shown in figure 1, the detecting system that solar energy thermal-power-generating of the present invention is based on heliostat surface testing method includes CCD camera 2, compound stripe pattern screen 3, industrial computer 4 and computer 1.The control of the computer 1 CCD camera 2 collection image, and Acquired image is handled;The CCD camera 2 is placed in heat absorption tower top end;The compound stripe pattern screen 3 is arranged on Absorb heat on tower;The industrial computer 4 controls the operation of heliostat 5 to be measured so that CCD camera 2 can gather answering for the reflection of heliostat 5 Close the deformation pattern of stripe pattern screen 3.
Solar energy thermal-power-generating heliostat surface testing method of the present invention comprises the following steps:
The 1st, compound stripe pattern screen 3 is arranged on to the lower section of heat dump mouthful on heat absorption tower, heliostat 5 to be measured and CCD is adjusted The position of camera 2 so that CCD camera 2 can observe the deformation bonding stripe pattern that heliostat 5 to be measured reflects;
2nd, the deformation for asking for heliostat reflection to be measured based on window Fourier filtering and quality guiding phase developing method is answered Close the phase distribution of stripe pattern in the horizontal and vertical directions.Utilize the faces such as the acquisition of Zernike multinomials and heliostat to be measured Long-pending virtual reference plane phase distribution, according to virtual reference plane and the phase distribution of heliostat to be measured, is obtained by be determined Phase offset caused by day mirror surface-shaped.
The compound stripe pattern expression formula that compound stripe pattern screen 3 is presented is:
Wherein (x, y) is the coordinate of compound stripe pattern screen 3, pxAnd pyRespectively horizontally and vertically on bar Line cycle, I0(x, y) is fringe intensity, and A (x, y) is background luminous intensity, B1(x, y) and B2(x, y) is respectively striped in level side To the amplitude with vertical direction.
The parcel phase for the compound stripe pattern that this compound stripe pattern screen 3 is presented is obtained based on window Fourier filtering method Position:
Window Fourier transform is carried out to expression formula (1) first, its conversion is as follows:
WhereinSf (u, v, ξ, η) is I0The Fourier transformation of (x, y), (u, v) is space coordinate, and (ξ, η) is frequency Domain coordinate, window function g (x, y) is Gaussian function:
σxAnd σyRespectively Gaussian function is in x and y upward standard deviation.
Secondly, formula (2) is filtered:
Wherein θ is threshold value.
The fundamental component of frequency spectrum in the horizontal and vertical directions choose after filtering respectively simultaneously after.Therefore, it is described The wrapped phase of compound stripe pattern in the horizontal and vertical directionsRespectively:
Wherein,WithWrapped phase upward respectively x and y, (x, y) is space coordinate,WithRespectivelyIn the upward fundamental component of x and y,With RespectivelyWithInverse Fourier transform, g (x, y) be formula (2) in Gaussian function.
Finally, wrapped phase is obtained based on quality guiding phase-unwrapping algorithmWithPhase distribution φ0x(x, y) and φ0y(x,y)。
By above-mentioned continuous phase distribution phi0x(x, y) and φ0y(x, y) is expressed as the polynomial linear combination tables of Zernike Up to formula:
Wherein znFor n-th Zernike multinomial,For n-th Zernike multinomial coefficient.
Coefficient is solved based on least-squares algorithmUtilize the phase distribution φ of this coefficients to construct virtual plane0'x (x, y) and φ0'y(x,y)。
3rd, based on CCD camera, heliostat, the relative space position for being combined stripe pattern screen, foundation is drawn by heliostat minute surface The phase offset and the numerical relationship model of mirror slope risen, is obtained with reference to the phase offset as caused by heliostat minute surface in step 3 To the slope distribution of heliostat minute surface in both the horizontal and vertical directions.
Industrial computer 4 controls heliostat 5 to be measured so that CCD camera, and 2 can gather the compound stripe pattern of the reflection of heliostat 5 The deformation pattern of screen 3.The deformation bonding stripe pattern that the control CCD camera collection heliostat 5 of computer 1 reflects, deformation bonding bar The expression formula of print image is as follows:
I1(x, y)=a (x, y)+b1(x,y)cos[φx(x,y)]+b2(x,y)cos[φy(x,y)] (7)
Wherein I1(x, y) is the light distribution of stripe pattern, and a (x, y) is background light intensity, b1(x, y) and b2(x, y) difference Represent the modulation degree on horizontally and vertically, φx(x, y) and φy(x, y) is represented horizontally and vertically respectively On by the mirror shape of heliostat 5 to be measured modulate phase.
Formula (7) is respectively obtained into heliostat using calculating process and quality the guiding phase-unwrapping algorithm of formula (2) to formula (5) The phase of minute surface in the horizontal direction and the vertical direction1x(x, y) and φ1y(x,y)。
Detecting system as shown in Figure 1 understands that the relation of heliostat mirror slope and phase is:
Wherein α is the acquisition angles of CCD camera, SlopexFor the slope distribution of minute surface in the horizontal direction, SlopeyFor mirror The slope distribution of face in vertical direction.
Minute surface phase based on acquisition1x(x, y) and φ1yThe phase of (x, y) and virtual plane0'x(x, y) and φ0'y (x, y), convolution (8) can obtain the slope distribution Slope of minute surface in the horizontal direction and the vertical directionxAnd Slopey
4th, the 3 d shape of heliostat is reconstructed using broad sense Hermite interpolation algorithms.
The heliostat mirror slope to be measured of acquisition is carried out using the broad sense Hermite interpolation algorithms based on RBF Three-dimensionalreconstruction.Define interpolation method as follows:
Wherein X=(x, y)T, αiAnd βi(1≤i≤N) is unknowm coefficient, ψ:R2→ R is RBF, ψxAnd ψyRespectively Be RBF ψ in x and y upward partial derivative, s (X) is heliostat face to be measured shape function.The parsing of this interpolation method is set up to lead Number is with surveying slope data SlopexAnd SlopeyMatching relationship:
Wherein j is j-th of sampled point, that is, solves following linear equation:
Wherein, ψxx, ψxy, ψyyFor ψ second-order partial differential coefficients respectively to x, to x, y second-order mixed partial derivative and the second order to y Partial derivative;The factor alpha asked for based on formula (11)iAnd βi, reconstruct face shape in formula (9) interpolation is applied it to, heliostat to be measured is obtained The 3 d shape s (X) of minute surface.

Claims (1)

1. a kind of tower type solar energy thermal power generation heliostat surface testing method, described detection method comprises the following steps:
(1) the deformation bonding stripe pattern of heliostat reflection to be measured is gathered using CCD camera, and is stored in a computer, then is tied Close window Fourier filtering method and quality guiding phase developing method obtains the deformation bonding bar graph of heliostat reflection to be measured As phase distribution in the horizontal and vertical directions;
(2) phase distribution with the virtual reference plane of heliostat homalographic to be measured is obtained using Zernike multinomials, according to void Intend reference planes and the phase distribution of heliostat to be measured, obtain the phase offset as caused by the shape of heliostat face to be measured;
(3) relative space position of CCD camera in detecting system, heliostat to be measured and compound stripe pattern screen, sets up Phase offset caused by heliostat minute surface to be measured and mirror slope numerical relationship model, with reference to the phase in step (1) and step (2) Bit distribution, obtains the slope distribution of heliostat minute surface in the horizontal direction and the vertical direction;
(4) based on heliostat slope distribution in broad sense Hermite interpolation methods and step (3), heliostat minute surface face to be measured is obtained Shape is reconstructed;
In the step (2), the phase with the virtual reference plane of heliostat homalographic to be measured is obtained using Zernike multinomials The method of distribution is as follows:
The parcel phase for the compound stripe pattern that the compound stripe pattern screen (3) is presented is obtained based on window Fourier filtering method Bit distribution φ0x(x, y) and φ0y(x, y), the polynomial linear combination expression formulas of Zernike are expressed as by this phase distribution:
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mn>0</mn> <mi>x</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <msubsup> <mi>k</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>k</mi> <mn>0</mn> <mn>1</mn> </msubsup> <mo>+</mo> <msubsup> <mi>k</mi> <mn>1</mn> <mn>1</mn> </msubsup> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mi>n</mi> <mn>1</mn> </msubsup> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;phi;</mi> <mrow> <mn>0</mn> <mi>y</mi> </mrow> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>&amp;infin;</mi> </munderover> <msubsup> <mi>k</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>k</mi> <mn>0</mn> <mn>2</mn> </msubsup> <mo>+</mo> <msubsup> <mi>k</mi> <mn>1</mn> <mn>2</mn> </msubsup> <msub> <mi>z</mi> <mn>1</mn> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> <mo>+</mo> <mn>...</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mi>n</mi> <mn>2</mn> </msubsup> <msub> <mi>z</mi> <mi>n</mi> </msub> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced>
Wherein znFor n-th Zernike multinomial,For n-th Zernike multinomial coefficient;(x, y) is compound bar The coordinate of print image screen;
Coefficient is solved based on least-squares algorithmUtilize the phase distribution φ ' of this coefficients to construct virtual plane0x(x, Y) with φ '0y(x,y);
The step (4) is based on broad sense Hermite interpolation and heliostat slope distribution reconstructs heliostat minute surface 3 d shape to be measured Method it is as follows:
It is respectively Slope to obtain the slope of heliostat minute surface to be measured in the horizontal direction and the vertical direction by described step (3)x And Slopey, defining Hermite interpolating functions is:
<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&amp;alpha;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;psi;</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
Wherein X=(x, y)T, αiAnd βi(1≤i≤N) is unknowm coefficient, ψ:R2→ R is RBF,
ψxAnd ψyRespectively RBF ψ in x and y upward partial derivative,
S (X) is heliostat face to be measured shape function;(x, y) is the coordinate of compound stripe pattern screen;
Set up this interpolation method parsing derivative and survey slope data SlopexAnd SlopeyMatching relationship:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>s</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>Slope</mi> <mi>x</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>s</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>Slope</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mn>1</mn> <mo>&amp;le;</mo> <mi>j</mi> <mo>&amp;le;</mo> <mi>N</mi> </mrow>
Wherein j is j-th of sampled point;
Solve following linear equation:
Wherein, ψxx, ψxy, ψyyFor ψ second-order partial differential coefficients respectively to x, to x, y second-order mixed partial derivative and the second order local derviation to y Number;
Based on the factor alpha asked foriAnd βi, that is, obtain the 3 d shape s (X) of heliostat minute surface to be measured.
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