A method for modeling the sun shape on the Earth's surface using a B-spline mosaic model based on observational data

Abstract

The present invention discloses a method for modeling the surface solar shape of a B-spline splicing model based on observation data. The method first uses a cubic B-spline function to least square fit the CSR=5% observation data of the German Aerospace Center to construct a disc solar shape analytical model, then uses the Buie exponential model as the halo solar shape analytical model, and finally splices the disc and halo solar shapes to obtain a B-spline splicing model. Based on the principle that the composite of the inverse function and the original function is an identity function, the model is calibrated and aligned by the CSR using a cubic B-spline function. The surface solar shape analytical model established by the method has the advantages of a simple model, analytically integrated radiant energy, and high fitting accuracy. And the CSR alignment operation ensures the CSR alignment during the model use stage. The invention has a good application value in the field of photothermal solar energy simulation.

Description

Technical Field

[0001] The present invention relates to the field of solar thermal power generation, and in particular to a method for establishing an analytical surface sun shape model based on real solar intensity distribution observation data. Background Art

[0002] In the field of solar thermal power generation system simulation, the sun shape used to describe the solar intensity distribution is one of the main influencing factors of the simulation of the radiation energy density distribution, which directly affects the accuracy of the simulation. Therefore, it is crucial to construct a sun shape model that matches the actual solar intensity distribution for accurate simulation. Depending on whether the solar halo intensity distribution is considered, the sun shape is divided into two categories: extraterrestrial solar shape and surface solar shape. Compared with the extraterrestrial solar shape, the surface solar shape model established based on surface observation data is more consistent with the model of the actual solar intensity distribution. However, the common surface solar shape model is usually discontinuous in the model, and its radiation energy is difficult to integrate analytically, such as the Buie model. In addition, in this type of model, the percentage of halo energy in the total solar emission energy, that is, the halo irradiance ratio (Circumsolar Ratio, referred to as CSR) is an important parameter, but the CSR of the current surface solar model cannot be aligned, and the model input CSR is usually not equal to the CSR calculated according to the model. The above problems make the fitting accuracy of the current surface solar shape model still need to be improved. In response to these problems, this paper conducts a series of studies on the surface solar shape modeling method.

[0003] Taking into account the shortcomings of the existing model, the present invention will solve the problems of the existing model being complex, the radiation energy being unable to be analytically integrated, the fitting accuracy being low, and the CSR being unable to be aligned. Summary of the invention

[0004] The purpose of the present invention is to propose a surface solar shape modeling method based on a B-spline splicing model of observation data, in order to address the problems that the current surface solar shape model is complex, the radiation energy cannot be analytically integrated, the fitting accuracy is low, and the CSR cannot be aligned.

[0005] The object of the present invention is achieved through the following technical scheme: A method for modeling the surface sun shape of a B-spline splicing model based on observation data, comprising the following steps:

[0006] Step (1), for the optical disc part, a least squares fitting is performed on the DLR CSR 5% optical disc part data using a cubic B-spline function to obtain a solar shape analytical model of the optical disc part;

[0007] Step (2), for the halo part, using Buie exponential distribution function, to obtain the sun shape analytical model of the halo part;

[0008] Step (3), using the analytical model obtained in steps (1) and (2), based on the principle that the original function and the inverse function are combined into an identity function, a cubic B-spline function is used for CSR alignment.

[0009] Furthermore, in step (1), the B-spline function is used to perform least square fitting on the DLR CSR=5% optical disc portion data.

[0010] Furthermore, using the node vector generation method, the node vector is:

[0011] u0,u1,...,u d ,u d+1 , ..., u n ,u n+1 , ..., u n+d+1

[0012] Among them, u0=u1=...=u d =θ0,u n+1 =...=u n+d+1 =θ s ;

[0013] The nodes of other parts are generated by the following formula:

[0014] u d+j =(1-α)θ i-1 +αθ i , j = 1, ..., nd

[0015]

[0016] Here, [jp] represents the largest integer not greater than jp.

[0017] Furthermore, in step (3), a B-spline function is used to perform a CSR alignment operation.

[0018] Furthermore, the sampling method of the sampling points is as follows: the interval [0, 1] is evenly divided into one hundred micro-intervals of equal length, the midpoints of the micro-intervals are taken as CSR sampling points, and the CSR is set to zero and the sampling points are added, for a total of 101 sampling points.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: the surface solar shape analytical model established by the present invention based on the real solar intensity distribution observation data using the cubic B-spline function and the Buie exponential distribution model has the advantages of simple model, analytical integration of radiant energy, and high fitting accuracy. The CSR calibration and alignment operation is performed on the model based on the principle that the composite of the inverse function and the original function is an identity function, which ensures the CSR alignment during the model use phase. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1This is the cubic B-spline function fitting result graph;

[0021] Figure 2 is the CSR calibration alignment diagram;

[0022] Figure 3 This is a partial result diagram of the B-spline splicing model in the semi-logarithmic coordinate system;

[0023] Figure 4 It is a comparison diagram of model errors, where (a) is the maximum absolute value error diagram and (b) is the root mean square error diagram. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described below in conjunction with embodiments and accompanying drawings.

[0025] Example

[0026] Assume that the analytical model of the sun shape is:

[0027]

[0028] Where θ represents the angle offset, θ disk Indicates the maximum angular displacement of the central disk of the sun, which is 4.65 mrad, θ aureole Indicates the maximum angular deviation of the peripheral halo, which is 43.6 mrad. Here, the unit of θ is mrad.

[0029] The total radiant energy of the disc and halo can be derived as follows:

[0030]

[0031] Among them, Φ disk Here, the unit of θ is rad. When θ is sufficiently small, sin(θ)≈θ, cos(θ≈1, so

[0032]

[0033] Similarly,

[0034]

[0035] Among them, Φ aureole represents the total radiant energy of the halo part. CSR(χ) is defined as the total radiant energy of the halo part Φ aureole and total radiation energy Φ all The ratio of total radiation energy Φ all Refers to the radiant energy including the disc and halo.

[0036]

[0037] The construction of the B-spline splicing model in this paper includes the following steps:

[0038] S1, construct the disc sun shape analytical model. Assume that the disc sun shape analytical model is:

[0039]

[0040] Among them, N i，d (θ) represents the B-spline basis function, P i Represents the B-spline function control coefficient.

[0041] See also Figure 1 The circle in the figure represents the DLR (German Aerospace Center) CSR = 5% observation data, and the angle offset θ of the data ranges from 0mrad to 4.7mrad, with a total of 17 data points. The cubic B-spline function with the first and last point interpolation is used for least squares fitting, and the parameter is the angle offset:

[0042] θ0=0, θ1=0.4, θ2=0.8,..., θ s-2 =4.4,θ s-1 =4.6,θ s =4.7

[0043] Among them, s=16.

[0044] For a given ordered set of two-dimensional data points The node vector is generated as follows:

[0045] Assume the node vector is:

[0046] u0, u1, ..., u d,u d+1 , ..., u n ,u n+1 , ..., u n+d+1

[0047] Among them, u0=u1=...=u d =θ0,u n+1 =...=u n+d+1 =θ s This node vector generation method ensures that the fitting function interpolates the beginning and end points of the data sequence.

[0048] The remaining node vectors are generated by the following formula:

[0049] u d+j =(1-α)θ i-1 +αθ i , j = 1, ..., nd

[0050]

[0051] Here, [jp] represents the largest integer not greater than jp. This node generation method can ensure that there is at least one parameter value between any two adjacent node vectors. According to the Schoenberg-Whitney theorem, it can ensure that the final least squares problem has a unique solution.

[0052] B-spline least squares fitting using interpolation of the first and last points,

[0053] Q0=φ disk (θ0)=P0,Q s =φ disk (θ s )=P n

[0054] therefore,

[0055]

[0056] The objective function is:

[0057]

[0058] because

[0059]

[0060] make

[0061] D k =Q k -N 0，d (θ k )Q0-N n，d (θ k )Q s

[0062] So the objective function is

[0063]

[0064] Without confusion, the above formula

[0065] D=(D1,D2,...,D m-1 ) T , P=(P1,P2,...,P n-1 ) T

[0066]

[0067] To minimize the objective function, we only need

[0068]

[0069] Right now

[0070] N T NP=N T D

[0071] After a lot of experiments, this paper uses cubic B-spline function and selects 7 control coefficients for fitting. The fitting results are as follows Figure 1 The control coefficients are shown in Table 1.

[0072] Table 1: Control coefficients of B-spline splicing model

[0073]

[0074] S2, build the analytical model of the halo sun shape. The halo part directly uses the Buie exponential distribution model, and the analytical model is:

[0075]

[0076] The halo sun shape is a CSR-related analytical model, where

[0077] κ=0.9ln(13.5χ)χ -0.3 ,γ=2.2ln(0.52χ)χ 0.43 -0.1

[0078] S4, splicing the disc and the halo sun shape. Splicing the disc and the halo sun shape obtained in the above two steps can get the B-spline splicing model:

[0079]

[0080] The model results are as follows Figure 3 shown.

[0081] S4, CSR calibration alignment.

[0082] like Figure 2 As shown in Figure 2, the modeling process of the B-spline splicing model theoretically determines that the CSRs are no longer aligned. For any given CSR Given , the corresponding CSR can be calculated by the B-spline splicing model Generated , the two are one-to-one corresponding. Therefore, we can get a one-to-one mapping relationship, set as y = f(χ). According to the one-to-one mapping relationship, we know that there is a CSR Given To CSR Generated The inverse function f of the mapping -1 (χ). If we want to find its inverse function, then for any given CSR = χ, we first substitute the inverse function to find χ cali =f-1 (χ), and then use this χ cali As an independent variable, it is introduced into the B-spline splicing model, thereby obtaining the analytical expression of the sun shape with the initial given CSR = χ. According to the principle that the composite of the inverse function and the original function is the same function, that is, χ = f(f -1 (χ)), it can be seen that the CSR calculated by the solar shape analytical model is equal to χ.

[0083] Because the above inverse function cannot be expressed explicitly, the function approximation method is used to approximate its inverse function. The specific process can be divided into the following steps:

[0084] Step (1), divide the interval [0, 1] evenly into 100 micro-intervals of equal length, take the midpoint of the micro-interval as the CSR sampling point, and set the CSR to zero and add the sampling point, for a total of 101 sampling points;

[0085] Step (2), bring the CSR sampling points into the B-spline splicing model expression, and calculate the corresponding CSR value according to the model formula, and a total of 101 groups of [sampling points, CSR values ​​calculated by the model] can be obtained;

[0086] Step (3), for the 101 sets of data obtained in the above steps, the CSR value calculated by the model is used as the independent variable, the sampling point is used as the dependent variable, and the least squares fitting approximation is performed using the first and last point interpolation of the cubic B-spline function. The fitting result is used as the approximation of the above inverse function.

[0087] like Figure 2 As shown, the B-spline splicing model calibration alignment legend represents the composite function curve of the above inverse function and the original function. The function curve and the y=x curve basically coincide with each other, which indicates that the alignment operation basically guarantees the CSR alignment of the model.

[0088] like Figure 4 As shown in Figure 2, as a surface solar shape model, like the Buie model, the B-spline splicing model obtained by fitting based on the same observation data has a smaller maximum absolute error and root mean square error than the corresponding fitting error of the Buie model.

Claims

1. A method for modeling the surface sun shape of a B-spline splicing model based on observation data, characterized in that: The following steps are involved: Step (1), for the optical disc part, using a cubic B-spline function to perform a least squares fit on the DLR CSR 5% optical disc part data to obtain a solar shape analytical model of the optical disc part; wherein, using a cubic B-spline function to perform a least squares fit on the DLR CSR 5% optical disc part data specifically includes: using a node vector generation method, the node vector is: u0, u1,...,u d ,in d+1 ,...,in n ,in n+1 ,...,in n+d+1 Among them, u0=u1=...=u d =θ0,u n+1 =...=u n+d+1 =θ s ; θ0 represents the angle offset of the first endpoint, θ s Indicates the angular offset of the end point; The nodes of other parts are generated by the following formula: you d+j =(1-α)θ i-1 +ath i ,j=1,...,nd Here, [jp] represents the largest integer not greater than jp, θ i represents the angle offset of the i-th node; Step (2), for the halo part, use the Buie exponential distribution function to obtain the sun shape analytical model of the halo part; wherein the expression of the Buie exponential distribution function is: Where, κ = 0.9ln(13.5χ)χ -0.3 ,γ=2.2ln(0.52χ)χ 0.43 -0.1, χ represents a given CSR value, φ aureole (θ) represents the Buie exponential distribution function, θ represents the angle offset, θ disk Indicates the maximum angular displacement of the central disk of the sun, θ aureole Indicates the maximum angle offset of the peripheral halo; Step (3), using the analytical model obtained in steps (1) and (2), based on the principle that the original function and the inverse function are combined into an identity function, use the cubic B-spline function to perform CSR alignment; wherein, the CSR alignment method specifically includes: the sampling method of sampling points: uniformly divide the interval [0, 1] into one hundred equal-length micro-intervals, take the midpoint of the micro-interval as the CSR sampling point, and set the CSR to zero, add the sampling point, and a total of 101 sampling points.

Images