A sky color modeling method based on sunny day spectral information and BP neural network method

Abstract

The application discloses a sky color modeling method based on sunny spectrum information, and solves the problems that existing sky brightness models cannot restore sky color information and color deviation exists when color is represented by correlated color temperature. The spectrum data of 145 sky surface elements of a hemisphere are measured by a spectrum sky scanner; color coordinates (x, y) of each sky surface element are solved based on the spectrum data; a zenith color model is established based on direct and scattered data; a BP neural network model framework is built; and the input layer is set as the sky surface element height angle, the sky surface element azimuth angle, the sun height angle, the sun azimuth angle and the zenith color coordinate value to obtain the final model. The method of the application establishes a model with color information to improve the application of the sky model in the field of colorimetry. The model is used to estimate the real-time sky spectrum data variation law, and provides a theoretical reference for building lighting simulation of glass with spectrum selectivity. 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 spectral information, 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 clear sky spectral information, 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 colors. The implementation scheme is as follows: Spectral data of 145 sky elements on a hemispherical surface are measured using a spectral sky scanner; the color coordinates (x, y) of each sky element are calculated based on the spectral data; a zenith color model is established based on direct and diffuse data; a BP neural network model framework is constructed; the input layer is set to the sky element elevation angle, sky element azimuth angle, solar elevation angle, solar azimuth angle, and zenith color coordinates to obtain the sky color model.

[0005] This invention is based on spectral information and proposes to use a BP neural network method to analyze and model the color of the sky. 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 clear-sky spectral information and a backpropagation (BP) neural network. The method primarily uses color coordinates calculated from measured spectra as the output layer, and parameters such as sky element positions, sun positions, and zenith color coordinates as input layers. A model representing the sky color distribution is then established using a BP neural network, comprising 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 element 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 spectral data 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]

[0012]

[0013] In the formula, K m λ is the maximum spectral optical efficiency of the human eye; λ is the radiation wavelength value, and 380-780nm is the band that can form the human eye's photometric and colorimetric perception; X, Y, and Z are the tristimulus values; P(λ) is the relative spectral power distribution of the sky test point; The color matching function is provided by CIE through experiments. x, y, z are color coordinates, x+y+z=1. Each scan yields the color coordinates of 145 sky elements.

[0014] Step 2: Establish the color coordinate model of the sky element where the zenith is located.

[0015] A model for zenith color coordinates was established using direct and diffuse radiation data.

[0016] Step 2.1: Use a radiometer to obtain the direct solar irradiance and diffuse sky irradiance at the same moment as the sky scan data;

[0017] Step 2.2: Based on direct solar irradiance and diffuse sky irradiance, a nonlinear calculation model for sky meteorological parameters is established. The least squares method is used to estimate the model parameter values, as shown in the following formula:

[0018] w = [(E d / (E d +E s )+1.041γ s 3 ] / [1+1.041γ s 3 (3)

[0019] In the formula, E d Sky diffuse irradiance (W / m2 ); E s Direct solar irradiance (W / m 2 );γ s 'w' represents the solar zenith angle; 'w' represents the sky weather index.

[0020] Step 2.3: Using the sky meteorological parameters obtained in Step 2.2, establish a calculation model for the color coordinates of the sky element containing the zenith. Estimate the parameter values ​​of this model using the least squares method, as shown in the following formula:

[0021] x = 0.33w 0.202 (4)

[0022] y = 0.33w 0.213 (5)

[0023] Step 3: Build and train the sky surface color coordinate neural network.

[0024] A neural network based on the BP algorithm is built and trained. Its inputs are the sky element elevation angle, sky element azimuth angle, solar elevation angle, solar azimuth angle and the zenith color coordinate value obtained in step 2. The outputs are the x and y color coordinate values ​​obtained in step 1.

[0025] Step 3.1: Build the BP neural network structure. The hidden layer is set to a 2-layer fully connected structure with 13 nodes in each hidden layer. The hidden layer is followed by a fully connected layer with an output of 1. The activation function in the network is set to Leaky ReLU and the loss function is set to mean squared error (MSE) Loss.

[0026] Step 3.2: Prepare training data. For the complete data used in the calculation, randomly select 90% of the data as the training set and the remaining 10% of the data as the validation set.

[0027] Step 3.3: Train the BP neural network using a loss function. The maximum number of training iterations is 500, and the learning rate is set to 0.005. Training is stopped and the model parameters are retained when the maximum number of training iterations is reached or the loss function converges.

[0028] Step 4: Predict the color coordinates of 145 sky elements and establish a sky color model.

[0029] The x and y color coordinates of 145 sky elements in real time were calculated using time and radiation data.

[0030] Step 4.1: Calculate the color coordinates of the sky element containing the zenith in real time, following the steps in Step 2.

[0031] Step 4.2: Calculate the real-time solar altitude angle and solar azimuth angle using local time and geographical location;

[0032] Step 4.3: Calculate the color coordinates of each sky element using the BP neural network trained in Step 3;

[0033] Step 4.4, as shown in the preceding analysis, the main influencing factors of the color coordinates of each sky element are the sky altitude angle and the sky direction.

[0034] The solar azimuth angle, solar altitude angle, solar azimuth angle, and zenith color coordinates are used as input layer neurons and color coordinates x, y ...

[0035]

[0036] In the formula, f(x) represents the objective function value of the output layer; σ represents the activation function, and in this study, the LeakyReLU function is used in both the input layer to the intermediate layer and the intermediate layer to the output layer; ω and b represent the weights and bias matrices corresponding to each node, respectively. The zenith color coordinates among the five variables can also be calculated using the zenith colorimetric model proposed in Section 4.3.

[0037] Step 4.5 involves performing error analysis on the five-variable model inputting the calculated zenith color coordinates. The Normalized Relative Error (NMBE) and Root Mean Square Error (CVRMSE) formulas given in the ASHRAE specification are used to analyze the model's error. These two indicators are applicable to error analysis between model calculations and measured values. The calculated specific error values ​​are: NMBEx = 0.52%; CVRMSE = 3.54%; NMBEy = 0.67%; CVRMSE = 3.55%. The model error is within the standard requirements.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (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.

[0040] (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.

[0041] (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

[0042] Figure 1 This is a flowchart illustrating a specific embodiment of the present invention. Detailed Implementation

[0043] The method will be described in detail below with reference to the accompanying drawings and embodiments.

[0044] Implementation method.

[0045] The flowchart of the implementation method is as follows Figure 1 As shown, it includes the following steps:

[0046] Step S10: Calculate the color coordinate values ​​of 145 sky surface elements based on the spectral data of the sky scanner;

[0047] Step S20: Establish a nonlinear regression model of the color coordinates of the sky element containing the zenith.

[0048] Step S30: Build and train the BP neural network;

[0049] Step S40: Predict the color coordinates of 145 sky elements and establish a sky color model;

[0050] The step S10 of the implementation method for adjusting the sky surface color coordinate values ​​based on sky scanner data further includes the following steps:

[0051] Step S100: Obtain the real-time spectral information of 145 sky elements, calculate the tristimulus values ​​of the light source for each sky element, and use the tristimulus values ​​to calculate the color coordinate values.

[0052] Step S110: Use a sky scanner to obtain spectral data of the center points of 145 sky elements;

[0053] Step S120: Calculate the spectral tristimulus values ​​of each sky element using the spectrum as the input value and the color matching function.

[0054] 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.

[0055] The adjustment step S20 of establishing the nonlinear regression model of the color coordinates of the sky element where the zenith is located in the implementation method also includes the following steps:

[0056] Step S200: Obtain direct solar irradiance and diffuse sky irradiance data using a radiation meter;

[0057] Step S210: Build a nonlinear calculation model for sky meteorological parameters and estimate the model parameter values;

[0058] Step S220: Use sky meteorological parameters to establish a calculation model for the color coordinates of the sky surface element where the zenith is located, and estimate the model parameter values.

[0059] The implementation method of building and training the BP neural network, step S30, also includes the following steps:

[0060] Step S300: Build a BP neural network structure to predict the color coordinates of the sky surface elements;

[0061] Step S310: Prepare training data by assigning labels to the sun position, sky cell position, and zenith color coordinates at each moment, with the labels being color coordinates x and y, respectively.

[0062] Step S320: Train the BP neural network. The inputs are the solar altitude angle, solar azimuth angle, altitude angle of the sky element, and azimuth angle of the sky element. The output labels are color coordinates x or y. Use MSE Loss for training. Stop training and retain the model parameters when the maximum number of training iterations is reached or the loss function converges.

[0063] The implementation method for predicting the color coordinate values ​​of 145 sky surface elements and establishing a sky color model adjustment step S40 also includes the following steps:

[0064] Step S400: Calculate the color coordinates of the sky element where the zenith is located in real time, according to step S20.

[0065] Step S410: Calculate the real-time solar altitude angle and solar azimuth angle using local time and geographical location;

[0066] Step S420: Calculate the color coordinates of each sky element using the BP neural network trained in step S30.

[0067] Step S430: As the aforementioned analysis shows, the main influencing factors for the color coordinates of each sky element are the sky altitude angle, sky azimuth angle, solar altitude angle, solar azimuth angle, and zenith color coordinates. This invention uses these five variables as input layer neurons and the color coordinates x as output layer neurons to establish a neural network model.

[0068] Step S440: Perform error analysis on the obtained model using the Normalized Relative Error (NMBE) and Root Mean Square Error (CVRMSE) formulas given in the ASHRAE specification. These two indicators are applicable to error analysis between model calculations and measured values.

Claims

1. A sky color modeling method based on clear sky spectral information, characterized in that, Includes the following steps: Step S10: Calculate the color coordinate values ​​of 145 sky surface elements based on the measured spectral data; Step S20: Establish a nonlinear regression model of the color coordinates of the sky element containing the zenith. Step S30: Build and train the BP neural network; Step S40: Predict the color coordinates of 145 sky elements; Specifically, it includes: Step 1: Calculate the color coordinates of 145 sky elements based on the measured spectral data; 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. Step 1.1: Obtain spectral data of 145 sky elements using a sky scanner; 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: （1）； （2）； In the formula, K m The maximum spectral luminous efficacy for the human eye; λ is the radiation wavelength value, with 380~780nm being the band that enables the human eye to perceive luminance and colorimetry; X, Y, Z are the tristimulus values; P( The relative spectral power distribution of the sky test points; ( ), ( ), ( () is the color matching function given by CIE through experiments, x, y, z are color coordinates, x+y+z=1, and each scan obtains the color coordinates of 145 sky elements; Step 2: Establish the color coordinate model of the sky element containing the zenith; A model for zenith color coordinates was established using direct and diffuse radiation data. Step 2.1: Use a radiometer to obtain the direct solar irradiance and diffuse sky irradiance at the same moment as the sky scan data; Step 2.2: Based on direct solar irradiance and diffuse sky irradiance, a nonlinear calculation model for sky meteorological parameters is established. The least squares method is used to estimate the model parameter values, as shown in the following formula: （3）； In the formula, E d E represents sky diffuse irradiance. s Direct solar irradiance; γ s 'w' represents the solar zenith angle; 'w' represents the sky weather index. Step 2.3: Using the sky meteorological parameters obtained in Step 2.2, establish a calculation model for the color coordinates of the sky element containing the zenith. Estimate the parameter values ​​of this model using the least squares method, as shown in the following formula: （4）； （5）； Step 3: Build and train the sky surface element color coordinate neural network; Build and train a neural network based on the BP algorithm. Its inputs are the sky element elevation angle, sky element azimuth angle, solar elevation angle, solar azimuth angle and the zenith color coordinate value obtained in step 2. The outputs are the x and y color coordinate values ​​obtained in step 1. Step 3.1: Build the BP neural network structure. The hidden layer is set to a 2-layer fully connected structure with 13 nodes in each hidden layer. The hidden layer is followed by a fully connected layer with an output of 1. The activation function in the network is set to Leaky ReLU and the loss function is set to mean squared error (MSE) Loss. Step 3.2: Prepare training data. For the complete data used in the calculation, randomly select 90% of the data as the training set and the remaining 10% of the data as the validation set. Step 3.3: Train the BP neural network using a loss function. The maximum number of training iterations is 500, and the learning rate is set to 0.

005. Training is stopped and the model parameters are retained when the maximum number of training iterations is reached or the loss function converges. Step 4: Predict the color coordinates of 145 sky elements and establish a sky color model; The x and y color coordinates of 145 sky cells in real time were calculated using time and radiation data; Step 4.1: Calculate the color coordinates of the sky element containing the zenith in real time, following the steps in Step 2. Step 4.2: Calculate the real-time solar altitude angle and solar azimuth angle using local time and geographical location; Step 4.3: Calculate the color coordinates of each sky element using the BP neural network trained in Step 3; Step 4.3: Calculate the color coordinates of each sky element using the BP neural network trained in Step 3; Step 4.4, as shown in the preceding analysis, the main influencing factors of the color coordinates of each sky element are the sky altitude angle and the sky direction. The solar altitude angle, solar azimuth angle, and zenith color coordinates are used as input layer neurons, and the color coordinates x are used as output layer neurons to build a neural network model. Step 4.5: Perform error analysis on the five-variable model inputting the calculated zenith color coordinates. Analyze the model using the Normalized Relative Error (NMBE) and Root Mean Square Error (CVRMSE) formulas given in the ASHRAE specification. These two indicators are applicable to error analysis between model calculations and measured values. The calculated error values ​​are: NMBEx = 0.52%; CVRMSE = 3.54%; NMBEy = 0.67%; CVRMSE = 3.55%.

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