A sky color modeling method based on brightness and color coordinate relationship

Abstract

The application discloses a sky color modeling method based on the relationship between brightness and color coordinates, which combines the solar elevation angle and the azimuth angle to solve parameters by fitting and analyzing the measured sky surface unit brightness and the corresponding color coordinates calculated based on spectral information, and finally establishes a model capable of representing the sky color distribution, so that the model with color information is established to improve the application of the sky model in the field of colorimetry. The model provided by the application estimates the real-time sky spectral data variation rule, provides a theoretical reference for building lighting simulation with spectral selective glass, and the color coordinates are more scientific and accurate than the correlated color temperature.

Description

Technical Field

[0001] This invention relates to a sky color modeling method based on the relationship between brightness and color coordinates, belonging to the field of natural lighting simulation technology for buildings. Background Technology

[0002] Natural light not only provides brightness and visual appeal but also improves work efficiency and health. Furthermore, as a crucial component of green building, it possesses significant energy-saving potential. The quantification of natural lighting typically utilizes static parameters (illuminance and daylight factor) and dynamic parameters (percentage of natural daylight hours, effective daylight intensity, etc.). The calculation of these parameters relies on numerical simulation, which presupposes the establishment of a sky brightness distribution model. Commonly used models include cloudy sky models, clear sky models, and all-weather sky models.

[0003] However, natural light possesses not only brightness characteristics but also color information, which has a significant impact on human visual, non-visual, and perceptual abilities. Color research often relies on colorimetric indicators such as color rendering index, correlated color temperature, and color coordinates. The color of the sky changes with time and weather conditions, which has a significant impact on color research, such as evaluating the performance of spectrally selective windows; increasing the realism of outdoor scene rendering; assisting in the development of dimmable and color-tunable lighting control systems; and constructing more realistic artificial sky dome experimental systems. Therefore, establishing a sky color model (a mathematical model that reflects the laws governing sky color changes) is essential.

[0004] This invention discloses a sky color modeling method based on the relationship between brightness and chromaticity coordinates, mainly addressing the problems of existing sky brightness models failing to reproduce sky color information and color deviation existing when using correlated color temperature to represent color. The implementation scheme is as follows: Brightness and spectral data of 145 sky elements are measured using a spectral sky scanning luminance meter; the chromaticity coordinates (x, y) of each sky element are calculated based on the spectral data; the brightness and chromaticity coordinate data of sky elements at the same time and location are correlated, and nonlinear regression analysis is performed with brightness as the independent variable and chromaticity coordinates as the dependent variable; further nonlinear regression analysis is performed with the obtained correlation coefficient as the dependent variable and the solar altitude angle and azimuth angle as independent variables; the two formulas are combined to obtain the final sky color model; and the accuracy of the model is verified using new data.

[0005] This invention proposes to use the relationship between brightness and color coordinates for nonlinear fitting analysis to model the sky color. Summary of the Invention

[0006] To address the issues of existing sky models failing to represent sky color and exhibiting color deviation, this invention proposes a sky color modeling method based on the relationship between brightness and color coordinates. This method primarily involves fitting and analyzing the measured brightness of sky elements with their corresponding color coordinates calculated based on spectral information. Combined with solar altitude and azimuth angles, parameters are solved to ultimately establish a model that can represent the distribution of sky color. The method includes the following steps:

[0007] Step 1: Calculate the color coordinates of 145 sky elements based on the measured spectral data.

[0008] For a single sky scan, the color coordinates of each sky surface source need to be obtained through spectral measurement, calculation of the tristimulus values ​​of the light source, and calculation of the color coordinates.

[0009] Step 1.1: Use the SP400 sky scanner to obtain the brightness values ​​and spectrum of 145 sky elements;

[0010] Step 1.2: Calculate the color coordinates of each sky element using the spectrum as input, and calculate the color coordinates according to the following formula:

[0011] The calculation formula is as follows:

[0012]

[0013]

[0014] In the formula, K m It has the highest spectral light efficiency for the human eye. λ is the wavelength; X, Y, Z are the tristimulus values; P(λ) is the relative spectral power distribution of the sky test point; The color matching function is given by CIE through experiments, where x, y, and z are color coordinates, and x + y + z = 1.

[0015] Step 2: Using the logarithm of the brightness value as the independent variable and the color coordinates obtained in Step 1 as the dependent variable, establish a linear regression calculation model for color coordinates x and y.

[0016] Step 2.1 shows a clear logarithmic relationship between the sky element color coordinates and brightness at a single moment. Therefore, a logarithmic relationship is used for fitting, resulting in the calculation model shown below:

[0017]

[0018] In the formula, a and c are slope constants, b and d are intercept constants, and L is luminance.

[0019] Step 3: Calculate the parameters a, b, c, and d in the calculation model obtained in Step 2.1 (taking y = ax + b as an example):

[0020] Step 3.1: Calculate the average x and y coordinates of the sky element color coordinates from 1 to 145 at each time point obtained in Step 1. and

[0021] Step 3.2, subtract xi from each sky element (1-145). Get Δxi, subtract yi We obtain Δyi.

[0022] Step 3.3: Solve for ∑Δxi·Δyi and ∑(Δxi). 2 .

[0023] Step 3.4, further calculate a = ∑Δxi·Δyi / ∑(Δxi) 2 ;

[0024] Step 4: Establish a multiple linear regression model with parameters a, b, c, d obtained in Step 3 as dependent variables and solar altitude angle γ and azimuth angle θ as dependent variables.

[0025] Step 4.1, through the fitting results at different times, reveals that the model coefficients a and b change continuously over time. Considering that the time variation depends on the change in the sun's position, the solar altitude angle γ and azimuth angle θ are added to the model:

[0026]

[0027] Step 4.2: By calculating all the linear fitting relationships for every half hour throughout the year, the parameters a, b, c, and d for all times are calculated using the linear regression formula. At the same time, the solar altitude angle γ and azimuth angle θ for the corresponding times are calculated. Using these two angles as independent variables and the four parameters in the model as dependent variables, a multiple linear regression analysis is performed.

[0028] Step 4.3: By comparing the fitting results of four data sizes—an entire year, 6 months, 3 months, and 1 month—it was found that the 1-month data had the best fitting effect. Therefore, the fitting was performed on a monthly basis. The model parameters for that month can be calculated using the above method, thus obtaining a multiple linear regression model with the logarithm of brightness as the independent variable, as shown below.

[0029]

[0030]

[0031] Step 4.4: Select data on a monthly basis and perform error analysis on the obtained sky chromaticity model. Use the Normalized Relative Error (NMBE) and Root Mean Square Error (CVRMSE) formulas given in the ASHRAE standard to analyze the model's error. These two indicators are applicable to error analysis between model calculations and measured values. The calculated NMBE value for the x-coordinate model is 3.34%, and the CVRMSE value is 9.26%. The NMBE value for the y-coordinate model is 2.91%, and the CVRMSE value is 7.89%. The model error is within the standard requirements.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] (1) Existing sky models are widely used only in photometry, and their application in colorimetry is lacking. When simulating and rendering outdoor scenes, they cannot accurately represent the sky's color as it changes over time. Therefore, the method of this invention establishes a model with color information to improve the application of sky models in the field of colorimetry.

[0034] (2) With technological advancements, various spectrally selective windows have been widely adopted. When simulating indoor daylighting in buildings with spectrally selective windows, real-time sky spectral data is required to match the glass's transmission spectrum for more accurate simulation calculations. However, existing sky brightness models lack sky spectral information, making such spectral-based calculations impossible. Therefore, the model proposed in this invention can be used to estimate the real-time changes in sky spectral data, providing a theoretical reference for daylighting simulation in buildings with spectrally selective windows.

[0035] (3) Research on sky spectral models, both domestically and internationally, is still in its early stages, with most studies focusing on establishing a relationship model between sky brightness and correlated color temperature. However, mathematical models based on correlated color temperature cannot accurately correspond to sky colors due to color deviation issues (the same color temperature corresponds to different colors). Therefore, when studying the variation patterns of the sky spectrum, the color coordinates proposed in this invention are more scientific and accurate than correlated color temperature. Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating a specific embodiment of the present invention. Detailed Implementation

[0037] The method will be described in detail below with reference to the accompanying drawings and embodiments.

[0038] The flowchart of the implementation method is as follows Figure 1 As shown,

[0039] Includes the following steps:

[0040] Step S10: Calculate the color coordinate values ​​of 145 sky elements based on the sky scanner data;

[0041] Step S20: Using the logarithm of luminance as the independent variable and chromaticity coordinates as the dependent variable, establish a linear regression model for chromaticity coordinates x and y.

[0042] Step S30: Calculate the parameters a, b, c, and d in the model;

[0043] Step S40: Establish a multiple linear regression model with parameters a, b, c, d and solar altitude angle γ and azimuth angle θ as dependent variables;

[0044] Step S10 of the implementation method for calculating the sky surface color coordinates based on sky scanner data further includes the following steps:

[0045] Step S100: Obtain the spectral information of 145 sky elements, calculate the tristimulus values ​​of the light source for each sky element, and calculate the color coordinate values ​​from the tristimulus values.

[0046] Step S110: Use a sky scanner to obtain spectral data of the center points of 145 sky elements;

[0047] Step S120: Calculate the spectral tristimulus values ​​of each sky element using the spectrum as the input value and the color matching function.

[0048] Step S130: Calculate the color coordinates of each sky element. Using the tristimulus values ​​of each sky element as the standard, calculate the color coordinates x and y.

[0049] The parameters a, b, c, and d in the calculation model of the implementation method, step S30 further includes the following steps:

[0050] Step S300: Calculate the average x and y coordinates of the sky element colors from 1 to 145 at each time point obtained in Step 1. and

[0051] Step S310: Subtract xi from each sky element (1-145) Get Δxi, subtract yi We obtain Δyi;

[0052] Step S320: Solve for ∑Δxi·Δyi and ∑(Δxi). 2 ;

[0053] Step S330, further calculate a = ∑Δxi·Δyi / ∑(Δxi) 2 ;

[0054] The implementation method for establishing a multiple linear regression model S40 also includes the following steps:

[0055] Step S400: By analyzing the fitting results at different times, it was found that the model coefficients a and b change continuously over time. Considering that the time variation depends on the change in the sun's position, the solar altitude angle γ and azimuth angle θ were added to the model.

[0056] Step S410: By calculating all the linear fitting relationships for every half hour throughout the year, the parameters a, b, c, and d for all times are calculated using the linear regression formula. At the same time, the solar altitude angle γ and azimuth angle θ for the corresponding times are calculated. Using these two angles as independent variables and the four parameters in the model as dependent variables, a multiple linear regression analysis is performed.

[0057] Step S420: By comparing the fitting results of four data sizes—an entire year, 6 months, 3 months, and 1 month—it was found that the data for 1 month had the best fitting effect. Therefore, the fitting was performed on a monthly basis. The model parameters for that month could be calculated using the above method, thus obtaining a multiple linear regression model with the logarithm of brightness as the independent variable.

[0058] Step S430: Select data in monthly units and perform error analysis on the sky color model obtained above. Use the Normalized Relative Error (NMBE) and Root Mean Square Error (CVRMSE) formulas given in the ASHRAE specification to perform error analysis on the obtained model. These two indicators are applicable to the error analysis between model calculation and measured values.

Claims

1. A sky color modeling method based on the relationship between brightness and chromaticity coordinates, which involves fitting and analyzing the measured brightness of sky elements with the corresponding chromaticity coordinates calculated based on spectral information, solving for parameters by combining solar altitude angle and azimuth angle, and finally establishing a model representing the sky color distribution, characterized in that: Step S10: Calculate the color coordinate values ​​of 145 sky surface elements based on the spectral data collected by measurement; Step S20: Using the logarithm of luminance as the independent variable and chromaticity coordinates as the dependent variable, establish a linear regression model for chromaticity coordinates x and y. Step S30: Calculate the parameters a, b, c, and d in the model; Step S40: Establish parameters a, b, c, d and the solar altitude angle. and azimuth A multiple linear regression model with the dependent variable as the dependent variable; For a single sky scan, the color coordinates of each sky surface source need to be obtained through spectral measurement, calculation of the tristimulus values ​​of the light source, and color coordinate calculation, including the following steps: Step 1: Calculate the color coordinates of 145 sky elements based on the measured spectral data; Step 1.1: Use a sky scanner to obtain the brightness values ​​and spectrum of 145 sky elements; Step 1.2: Calculate the color coordinates of each sky element using the spectrum as the input value, and calculate the color coordinates according to the following formula: The calculation formula is as follows: （1）； （2）； In the formula, K m For maximum spectral light efficiency K m =100 / ( )P( ); Wavelength; X, Y, Z are tristimulus values; P( The relative spectral power distribution of the sky test points; ( ), ( ), ( (x, y, z) is the color matching function given by CIE through experiments, where x, y, z are color coordinates, and x+y+z=1; Step 2: Using the logarithm of the brightness value as the independent variable and the color coordinates obtained in Step 1 as the dependent variable, establish a linear regression calculation model for color coordinates x and y. Step 2.1 shows a clear logarithmic relationship between the sky element color coordinates and brightness at a single moment. Therefore, a logarithmic relationship is used for fitting, resulting in the calculation model shown below: （3）； In the formula, a and c are slope constants, b and d are intercept constants, and L is luminance; Step 3: Calculate the parameters a, b, c, and d in the calculation model obtained in Step 2.1: Step 3.1: Calculate the average x and y coordinates of the sky element color coordinates from 1 to 145 at each time point obtained in Step 1. and ; Step 3.2, using the corresponding sky element minus get , minus get ; Step 3.3, Solve and ; Step 3.4, obtain ; ; Step 4: Establish the relationship between the parameters a, b, c, d obtained in Step 3 and the solar altitude angle. and azimuth A multiple linear regression model with the dependent variable as the dependent variable; Step 4.1: By examining the fitting results at different times, it was found that the model coefficients a and b change continuously over time. Considering that the time variation depends on the change in the sun's position, the solar altitude angle was added to the model. and azimuth : （4）； Step 4.2: By calculating all linear fitting relationships for every half hour throughout the year, the parameters a, b, c, and d for all times are calculated using the linear regression formula. Simultaneously, the solar altitude angle for the corresponding time is calculated. and azimuth Using these two perspectives as independent variables and the four parameters in the model as dependent variables, we conducted a multiple linear regression analysis. Step 4.3: Fit the model on a monthly basis and calculate the model parameters for each month. This will give you the multiple linear regression model with the logarithm of brightness as the independent variable, as shown below. （5）； （6）； Step 4.4: The normalized relative error (NMBE) and root mean square error (CVRMSE) formulas given in the ASHRAE specification are used to perform error analysis on the obtained model. These two indicators are applicable to the error analysis between the model calculation and the measured values. Data on a monthly basis are selected to perform error analysis on the sky color model obtained above. The calculated NMBE value of the color coordinate x model is 3.34%, and the CVRMSE value is 9.26%. The NMBE value of the color coordinate y model is 2.91%, and the CVRMSE value is 7.89%.

Images