Adaptive spectrum integration narrowband k-distribution calculation method and system based on variance driving

Abstract

The present application relates to the technical field of gas radiation characteristic calculation, and specifically provides a self-adaptive spectral integral narrow-band K distribution calculation method and system based on variance driving, which obtains absorption data of each spectral point arranged in wave number order in a target narrow band; adaptively determines the number of segments according to the fluctuation degree of the absorption data along the wave number domain; sorts and segments the absorption data based on the number of segments, constructs a distribution function of the absorption coefficient with respect to the cumulative probability and obtains a discretized representation thereof; adaptively determines the number of Gaussian integral points according to the distribution complexity of the distribution function over the entire cumulative probability domain thereof; and performs Gaussian numerical integration on the target narrow band using the determined number of segments and the number of Gaussian integral points, to calculate the radiation characteristic parameters; thus, through two independent and mutually coordinated variance driving self-adaptive mechanisms, each narrow band can complete the calculation with computing resources matching the spectral complexity thereof, to achieve the balance between precision and efficiency.

Description

Technical Field

[0001] This invention belongs to the field of gas radiation characteristic calculation technology, specifically relating to an adaptive spectral integral narrowband K-distribution calculation method and system based on variance-driven approach. Background Technology

[0002] Calculating the radiation characteristics of gas molecules is a common key technology in fields such as target infrared feature analysis. Its core lies in efficiently and accurately obtaining the radiation characteristic parameters of gases under complex thermophysical conditions, especially the absorption coefficient. In the calculation of hypersonic vehicle exhaust radiation, the flow field region is usually discretized into hundreds of thousands or even millions of grid nodes. Each grid node needs to independently calculate the absorption coefficient and related radiation quantities based on its unique temperature, pressure, and component concentration conditions. Therefore, while ensuring calculation accuracy, minimizing the calculation cost of radiation characteristics of a single grid node is of great significance for realizing rapid simulation of large-scale, high-resolution exhaust radiation fields.

[0003] The most accurate computational model currently is LBL (Line-By-Line), which has the highest accuracy and is usually regarded as the benchmark solution. However, it has extremely long computation time and huge memory requirements for data loading, making it difficult to use directly in practical engineering iterative design. To balance computational cost and accuracy, the narrowband K-distribution model has been proposed in the existing technology.

[0004] In the numerical implementation of the narrowband K-distribution method, the functional relationship between the absorption coefficient and its cumulative probability needs to be discretized and sampled to construct a numerical lookup table. In traditional narrowband K-distribution methods, the number of absorption coefficient discretization segments, which describes the granularity of this lookup table, is usually fixed. If the number of segments is set too few, important details of the absorption coefficient's changes will be smoothed out, leading to errors in the interpolation of subsequent Gaussian integration points. If the number of segments is set too many, although it can improve accuracy, the computational load and storage space also increase linearly. At the same time, traditional narrowband K-distribution methods usually use a fixed Gaussian integration scheme. When using low-order integration, for narrowbands with drastic changes in absorption coefficient, it is impossible to accurately capture the abrupt changes in the absorption coefficient distribution function, resulting in insufficient computational accuracy. When using high-order integration, for narrowbands with gradual changes in absorption coefficient, it wastes computational resources.

[0005] In summary, the fixed-point scheme used in existing narrowband K-distribution methods cannot achieve the optimal balance between accuracy and efficiency across all narrowbands. Summary of the Invention

[0006] This invention aims to at least address the technical problem that the fixed-point scheme used in related narrowband K-distribution methods cannot achieve both accuracy and efficiency across all narrowbands. Therefore, the purpose of this invention is to propose a variance-driven adaptive spectral integral narrowband K-distribution calculation method, system, electronic device, and storage medium.

[0007] In a first aspect, the present invention proposes a variance-driven adaptive spectral integral narrowband K-distribution calculation method, comprising the following steps: acquiring absorption data of each spectral point arranged in wavenumber order within a target narrowband; adaptively determining the number of segments based on the fluctuation degree of the absorption data along the wavenumber domain; sorting and segmenting the absorption data based on the number of segments, constructing a distribution function of the absorption coefficient with respect to the cumulative probability and obtaining its discretized representation; adaptively determining the number of Gaussian integration points for Gaussian numerical integration of the narrowband average radiance based on the distribution complexity of the distribution function over its entire cumulative probability domain; and performing Gaussian numerical integration on the target narrowband using the determined number of segments and the number of Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband.

[0008] According to an embodiment of the present invention, the variance-driven adaptive spectral integral narrowband K-distribution calculation method first acquires the absorption data of each spectral point in the target narrowband arranged in wavenumber order; secondly, based on the fluctuation of the absorption data along the wavenumber domain, the number of segments is adaptively determined; then, based on the number of segments, the absorption data is sorted and segmented to construct the distribution function of the absorption coefficient with respect to the cumulative probability and obtain its discretized representation; next, based on the distribution complexity of the distribution function over its entire cumulative probability domain, the number of Gaussian integration points is adaptively determined; finally, using the determined number of segments and the number of Gaussian integration points, Gaussian numerical integration is performed on the target narrowband to calculate the radiation characteristic parameters. Thus, through two independent and mutually cooperating variance-driven adaptive mechanisms, each narrowband can be calculated with computational resources matching its spectral complexity, thereby effectively improving the overall computational efficiency while ensuring computational accuracy, achieving a significant balance between accuracy and efficiency. This method is particularly suitable for engineering scenarios requiring large-scale, high-resolution, and rapid simulation, such as the exhaust plume radiation field of hypersonic vehicles.

[0009] In addition, the variance-driven adaptive spectral integral narrowband K-distribution calculation method according to embodiments of the present invention may also have the following additional technical features: Further, the step of adaptively determining the number of segments based on the fluctuation of the absorption data along the wavenumber domain includes: calculating the overall dispersion of the absorption coefficients of all spectral points within the target narrowband relative to their arithmetic mean, defining it as a first variance; determining the number of segments based on the magnitude of the first variance and a preset first mapping relationship, wherein the number of segments is positively correlated with the first variance.

[0010] Further, the step of constructing the distribution function of the absorption coefficient with respect to the cumulative probability and obtaining its discretized representation includes: arranging all absorption data within the target narrowband in ascending order of numerical value; selecting multiple segment nodes between the maximum and minimum values ​​of the absorption coefficients after ascending order, based on the number of segments, to divide the absorption coefficient value range into a corresponding number of segment intervals; calculating the proportion of the spectral wavenumber width falling within each segment interval to the total wavenumber width of the target narrowband, obtaining the probability density value corresponding to each segment interval, and cumulatively calculating the cumulative probability value at each segment node; and taking the inverse function of the cumulative probability value to obtain the discrete value of the distribution function of the absorption coefficient with respect to the cumulative probability at each segment node.

[0011] Further, the step of adaptively determining the number of Gaussian integration points for the narrowband average radiance Gaussian numerical integration based on the distribution complexity of the distribution function over its entire cumulative probability domain includes: calculating the numerical dispersion of the distribution function over its entire cumulative probability domain based on the discretized representation of the distribution function, defining it as the second variance; and adaptively selecting a Gaussian integration scheme of the corresponding order according to the magnitude of the second variance and a preset second mapping relationship to determine the number of Gaussian integration points, wherein the number of Gaussian integration points is positively correlated with the second variance.

[0012] Further, the calculation of the second variance includes: dividing the cumulative probability domain of the distribution function into multiple continuous sub-intervals according to the number of segments; taking the distribution function value at the midpoint of each sub-interval as the representative value of the sub-interval, and taking the length of the sub-interval as the probability width; calculating the mean of the distribution function over the entire cumulative probability domain by weighted averaging based on the representative values ​​and probability widths of all the sub-intervals; calculating the second statistical moment of the distribution function over the entire cumulative probability domain based on the mean, the representative values ​​of each sub-interval, and the probability widths of each sub-interval; and calculating the second variance based on the difference between the second statistical moment and the square of the mean.

[0013] Furthermore, the second mapping relationship is a threshold judgment rule, which includes: when the second variance is less than the first threshold, the distribution function is determined to change smoothly, and a four-point Gaussian integration scheme is selected; when the second variance is not less than the first threshold and less than the second threshold, the distribution function is determined to change moderately, and a seven-point Gaussian integration scheme is selected; when the second variance is not less than the second threshold, the distribution function is determined to change drastically, and a twelve-point Gaussian integration scheme is selected; wherein, the first threshold and the second threshold are preset according to the spectral band and the gas type.

[0014] Furthermore, before calculating the second variance, the variance-driven adaptive spectral integral narrowband K-distribution calculation method further includes: performing preprocessing on the discretized representation of the distribution function, including monotonicity verification and outlier removal, to ensure that the calculation result of the second variance is not affected by data noise or numerical error.

[0015] Further, the step of performing Gaussian numerical integration on the target narrowband using the determined number of segments and the number of Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband includes: selecting a determined number of Gaussian integration points and corresponding weight coefficients for each integration point on the cumulative probability interval, wherein the sum of all the weight coefficients is normalized to one; obtaining the absorption coefficient value corresponding to each Gaussian integration point by interpolation according to the discretized representation of the distribution function; substituting each absorption coefficient value into the radiation calculation function to obtain the radiation value at each Gaussian integration point; summing the products of the radiation values ​​at all Gaussian integration points and their corresponding weight coefficients, and using the summed result as the average radiation of the target narrowband, thereby obtaining the average absorption coefficient and average transmittance of the target narrowband.

[0016] Furthermore, the target narrowband is the spectral narrowband corresponding to any one of the multiple grid nodes formed after spatial discretization in the radiation calculation domain of the hypersonic vehicle's exhaust plume flow field; for different grid nodes, the number of segments and the number of Gaussian integration points corresponding to each are independently and adaptively determined according to the characteristics of the absorption data at the grid node, so that the computational complexity of each narrowband matches its spectral complexity.

[0017] Secondly, based on the same inventive concept, this invention also proposes a variance-driven adaptive spectral integral narrowband K-distribution calculation system, comprising: a data acquisition module for acquiring absorption data of each spectral point arranged in wavenumber order within a target narrowband; a first adaptive module for adaptively determining the number of segments based on the fluctuation of the absorption data along the wavenumber domain; a distribution function construction module for sorting and segmenting the absorption data based on the number of segments, constructing a distribution function of the absorption coefficient with respect to the cumulative probability, and obtaining its discretized representation; a second adaptive module for adaptively determining the number of Gaussian integration points for Gaussian numerical integration of the narrowband average radiance based on the distribution complexity of the distribution function over its entire cumulative probability domain; and a radiation characteristic calculation module for performing Gaussian numerical integration on the target narrowband using the determined number of segments and the number of Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband.

[0018] The variance-driven adaptive spectral integral narrowband K-distribution calculation system provided in the second aspect has the same technical features as the variance-driven adaptive spectral integral narrowband K-distribution calculation method provided in the first aspect. Therefore, it also has similar technical effects as the first aspect, which will not be described in detail here.

[0019] Thirdly, based on the same inventive concept, the present invention also proposes an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; the memory is used to store computer programs; and the processor, when executing the computer program stored in the memory, implements the steps of the variance-driven adaptive spectral integral narrowband K-distribution calculation method as described in the above embodiments of the present invention.

[0020] The electronic device provided in the third aspect has the same technical features as the variance-driven adaptive spectral integral narrowband K-distribution calculation method provided in the first aspect. Therefore, it also has similar technical effects as the first aspect, which will not be described in detail here.

[0021] Fourthly, based on the same inventive concept, the present invention also proposes a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the variance-driven adaptive spectral integral narrowband K-distribution calculation method as described in the above embodiments of the present invention.

[0022] The computer-readable storage medium provided in the fourth aspect has the same technical features as the variance-driven adaptive spectral integral narrowband K-distribution calculation method provided in the first aspect, and therefore also has similar technical effects as the first aspect, which will not be described in detail here.

[0023] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0024] The above and additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of a variance-driven adaptive spectral integral narrowband K-distribution calculation method according to an embodiment of the present invention; Figure 2 This is a schematic diagram comparing two fixed integration points according to a specific embodiment of the present invention; Figure 3 This is a schematic diagram comparing the errors of two integration schemes according to a specific embodiment of the present invention; Figure 4This is a schematic diagram comparing the root mean square errors of two integration schemes according to a specific embodiment of the present invention. Figure 5 This is a schematic diagram of the exhaust flow field temperature of a BEM-II engine according to a specific embodiment of the present invention; Figure 6 This is a schematic diagram comparing the results of different integration formats and LBL under Case 1 of a specific embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the relative error between different integration point schemes and the narrowband numerical averaging result of LBL under Case 1 of a specific embodiment of the present invention; Figure 8 This is a schematic diagram comparing the results of different numbers of integration points and LBL under Case 2 of a specific embodiment of the present invention; Figure 9 This is a schematic diagram comparing the results of LBL with different numbers of integration points under Case 3 of a specific embodiment of the present invention; Figure 10 This is a schematic diagram of the root mean square error of different schemes under three working conditions according to a specific embodiment of the present invention. Figure 11 This is a schematic diagram illustrating the calculation time of different schemes under three working conditions according to a specific embodiment of the present invention; Figure 12 This is a structural block diagram of a variance-driven adaptive spectral integral narrowband K-distribution calculation system according to an embodiment of the present invention; Figure 13 This is a structural block diagram of an electronic device according to an embodiment of the present invention.

[0025] Figure label: 100 - Variance-driven adaptive spectral integral narrowband K-distribution calculation system; 110 - Data acquisition module; 120 - First adaptive module; 130 - Distribution function construction module; 140 - Second adaptive module; 150 - Radiation characteristic calculation module. Detailed Implementation

[0026] The embodiments of the present invention are described in detail below, and the embodiments described with reference to the accompanying drawings are exemplary.

[0027] To address the issue that fixed-point schemes used in narrowband K-distribution methods in related technologies cannot achieve both accuracy and efficiency across all narrowbands, this invention provides a variance-driven adaptive spectral integral narrowband K-distribution calculation method, system, electronic device, and storage medium. The following references... Figures 1-13 This invention describes a variance-driven adaptive spectral integral narrowband K-distribution calculation method, system, electronic device, and storage medium based on embodiments of the present invention.

[0028] Figure 1 This is a flowchart of a variance-driven adaptive spectral integral narrowband K-distribution calculation method according to an embodiment of the present invention. Figure 1 As shown, a variance-driven adaptive spectral integral narrowband K-distribution calculation method according to an embodiment of the present invention includes the following steps: Step S1: Obtain the absorption data of each spectral point within the target narrow band, arranged in wavenumber order.

[0029] In a specific embodiment, let a certain narrow band Δ η shared within m Spectral points (with fixed wavenumber intervals, typically calculated line-by-line at high resolution), spectral points j The absorption coefficient is k j , j =1,2,…, m Absorption coefficient k j Arranged in order of wavenumber, this reflects the variation of the absorption coefficient with wavenumber. Specifically, narrowband Δ η Internal spectral points j The absorption coefficient is k j The calculation formula is as follows: In the formula, S i For a single spectral line i line strength, For spectral line type function, N i This represents the molecular number density.

[0030] Specifically, the embodiments of the present invention first acquire the absorption data of each spectral point arranged in wavenumber order within the target narrow band; thus providing the most basic and realistic data source for all subsequent adaptive judgments and numerical calculations, ensuring that the entire method can make decisions directly based on the original physical characteristics of the spectrum, and avoiding information loss caused by data preprocessing or model simplification.

[0031] Step S2: Adaptively determine the number of segments based on the degree of fluctuation of the absorbed data along the wavenumber domain.

[0032] In a specific embodiment, the variance of the absorption data of all spectral points within the target narrowband can be calculated first, denoted as the first variance. The first variance directly measures the fluctuation range of the absorption coefficient in the wavenumber domain within the narrowband. Then, based on the magnitude of the first variance, the number of segments for discretizing the absorption coefficient is adaptively determined according to a preset empirical mapping relationship or threshold judgment rule. The number of segments is positively correlated with the first variance: the smaller the variance, the fewer segments are required; the larger the variance, the more segments are required.

[0033] Specifically, in this embodiment of the invention, the number of segments is adaptively determined based on the degree of fluctuation of the absorbed data along the wavenumber domain. This eliminates the drawback of the fixed number of segments in traditional methods, allowing for the use of fewer segments in narrow bands with gentle spectral changes to save computational resources and storage space, and the use of more segments in narrow bands with drastic spectral changes to ensure the accuracy of the subsequent distribution function construction. This achieves a balance between accuracy and efficiency during the database construction stage.

[0034] Step S3: Based on the number of segments, sort and segment the absorbed data, construct the distribution function of the absorption coefficient with respect to the cumulative probability, and obtain its discretized representation.

[0035] In a specific embodiment, the absorption data within the narrow band can be arranged from smallest to largest, and the maximum and minimum values ​​can be selected. Then, according to the adaptive number of segments determined in step S2, the entire value range of the absorption coefficient can be divided into a corresponding number of segment intervals. Next, the proportion of the spectral wavenumber width falling within each segment interval to the total wavenumber width can be calculated to obtain the probability density value corresponding to that segment interval. Then, the cumulative probability value at each segment node can be obtained through cumulative calculation. Finally, the cumulative probability distribution function can be inverted to obtain the discretized representation of the distribution function of the absorption coefficient with respect to the cumulative probability (i.e., a series of discrete data points).

[0036] Specifically, the embodiments of the present invention then sort and segment the absorption data based on the number of segments, construct the distribution function of the absorption coefficient with respect to the cumulative probability, and obtain its discretized representation; thereby transforming the complex, oscillating wavenumber domain spectral information into a monotonic, smooth cumulative probability domain distribution function, completing the core transformation of the narrowband K-distribution method, providing direct input for subsequent efficient and accurate Gaussian numerical integration, and serving as a key bridge connecting spectral physical properties and numerical calculation.

[0037] Step S4: Based on the complexity of the distribution function over its entire cumulative probability domain, adaptively determine the number of Gaussian integration points for the Gaussian numerical integration of the narrowband average radiance.

[0038] In a specific embodiment, the variance of the distribution function over its entire cumulative probability domain can be calculated based on the discretized representation of the distribution function obtained in step S3, denoted as the second variance. The second variance measures the abrupt change characteristics of the distribution function curve and the required number of Gaussian integration points: when the variance is large, it means that there are absorption coefficients with significantly different orders of magnitude within the narrow band, and these large values ​​are often concentrated in a narrow interval close to 1 in the cumulative probability domain, causing the distribution function to undergo a drastic change in this interval, requiring higher-order integration to capture details; conversely, if the variance is small, the distribution function curve changes smoothly, and lower-order integration can meet the accuracy requirements; then, based on the magnitude of the second variance and according to a preset mapping relationship, the corresponding order of Gaussian integration scheme can be adaptively selected to determine the number of Gaussian integration points, and the number of Gaussian integration points is positively correlated with the second variance.

[0039] Specifically, the embodiments of the present invention then adaptively determine the number of Gaussian integration points based on the distribution complexity of the distribution function over its entire cumulative probability domain; thereby breaking through the limitation of the traditional method of uniformly using a fixed number of integration points for all narrow bands, so that low-order integrals are used in narrow bands where the absorption coefficient distribution function changes gently to avoid redundant calculations, and high-order integrals are used in narrow bands where the distribution function changes drastically to ensure calculation accuracy, thereby achieving an adaptive balance between overall calculation accuracy and efficiency in the calculation and solution stage.

[0040] Step S5: Using the determined number of segments and Gaussian integration points, perform Gaussian numerical integration on the target narrowband to calculate the radiation characteristic parameters of the target narrowband.

[0041] In a specific embodiment, the number of Gaussian integration points determined in step S4 and the corresponding weight coefficients of each integration point can be selected first in the cumulative probability interval [0,1]. Then, the absorption coefficient value corresponding to each Gaussian integration point can be obtained by interpolation based on the discretized representation of the distribution function obtained in step S3. Next, each absorption coefficient value can be substituted into the radiation calculation function to obtain the radiation value at each Gaussian integration point. Finally, the products of the radiation values ​​at all Gaussian integration points and their corresponding weight coefficients can be accumulated and summed to obtain the average radiation of the target narrowband, and thus obtain the radiation characteristic parameters such as the average absorption coefficient and average transmittance of the target narrowband.

[0042] Specifically, in the final embodiment of the present invention, the determined number of segments and Gaussian integration points are used to perform Gaussian numerical integration on the target narrowband to calculate the radiation characteristic parameters. Thus, with the optimal computing resources matching the complexity of each narrowband, the efficient and accurate conversion from spectral data to the radiation characteristic parameters required for engineering is completed, providing reliable data support for subsequent large-scale flow field radiation calculations.

[0043] Therefore, the variance-driven adaptive spectral integral narrowband K-distribution calculation method according to embodiments of the present invention first acquires the absorption data of each spectral point in the target narrowband arranged in wavenumber order; secondly, based on the fluctuation of the absorption data along the wavenumber domain, the number of segments is adaptively determined; then, based on the number of segments, the absorption data is sorted and segmented to construct the distribution function of the absorption coefficient with respect to the cumulative probability and obtain its discretized representation; next, based on the distribution complexity of the distribution function over its entire cumulative probability domain, the number of Gaussian integration points is adaptively determined; finally, using the determined number of segments and the number of Gaussian integration points, Gaussian numerical integration is performed on the target narrowband to calculate the radiation characteristic parameters; thus, through two independent and mutually cooperating variance-driven adaptive mechanisms, each narrowband can be calculated with computational resources matching its spectral complexity, thereby effectively improving the overall computational efficiency while ensuring computational accuracy, achieving a significant balance between accuracy and efficiency, and is particularly suitable for engineering scenarios requiring large-scale, high-resolution, and rapid simulation, such as the exhaust plume radiation field of hypersonic vehicles.

[0044] In one embodiment of the present invention, the number of segments is adaptively determined based on the degree of fluctuation of the absorption data along the wavenumber domain, including: calculating the overall dispersion of the absorption coefficients of all spectral points within the target narrowband relative to their arithmetic mean, defining it as a first variance; and determining the number of segments according to the magnitude of the first variance and a preset first mapping relationship, wherein the number of segments is positively correlated with the first variance.

[0045] In a specific embodiment, the mean of the absorption data within the narrow band is first calculated. : The variance of the absorption coefficient within the narrowband (That is, the first variance) is: , It directly measures the fluctuation of the absorption coefficient in the wavenumber domain within a narrowband: for narrowbands with small variance, only a few discrete segments are needed to describe it; for narrowbands with large variance, more segments are required; empirical mapping relationships can be used to determine the number of discrete segments. : Therefore, the number of segments in the narrow band can be adaptively adjusted based on the fluctuation of the absorption data within the narrow band with wavenumber. In practical applications, the threshold can be adjusted according to the resolution of the spectrum and the type of gas.

[0046] Specifically, the embodiments of the present invention calculate the variance of the absorption data as the first variance and determine the number of segments based on a preset positive correlation mapping relationship; thereby providing a quantitative index with extremely low computational cost (almost no additional cost) and clear physical meaning. This index can accurately capture the density and intensity changes of spectral lines within a narrow band, providing a robust and reliable numerical criterion for adaptive segmentation, making the selection of the number of segments based on evidence, and avoiding the efficiency loss or accuracy reduction caused by manual trial and error or conservative settings.

[0047] In one embodiment of the present invention, constructing the distribution function of the absorption coefficient with respect to the cumulative probability and obtaining its discretized representation includes: arranging all absorption data within the target narrowband in ascending order of numerical value; selecting multiple segment nodes between the maximum and minimum values ​​of the absorption coefficients after ascending order, based on the number of segments, dividing the absorption coefficient value range into a corresponding number of segment intervals; calculating the proportion of the spectral wavenumber width falling within each segment interval to the total wavenumber width of the target narrowband, obtaining the probability density value corresponding to each segment interval, and cumulatively calculating the cumulative probability value at each segment node; and taking the inverse function of the cumulative probability value to obtain the discrete value of the distribution function of the absorption coefficient with respect to the cumulative probability at each segment node.

[0048] In a specific embodiment, the narrowband absorption data are arranged from smallest to largest to form a monotonically increasing sequence, and then the sequence is determined based on the number of segments. N Determined between the maximum and minimum values N +1 segmentation nodes divide the absorption coefficient range into N 1 interval; then obtain the probability density function for each interval. f(k) Cumulative probability density function g(k) and distribution function k(g) : , , In the formula, , , For spectral line overlap parameters, k The absorption coefficient is... The average absorption coefficient, x mole fraction p For pressure, B and S This is an intermediate value that has no actual physical meaning. , , erf ( ) represents the error function; thus, a series of discrete points are obtained, which leads to the discretized representation of the distribution function, i.e., a series of interpolation nodes.

[0049] Specifically, in this embodiment of the invention, the absorption coefficients are sorted, segmented, and statistically analyzed for probability density and cumulative probability. Finally, the inverse function is taken to obtain a discrete representation of the distribution function. This process strictly follows the theoretical basis of the narrowband K-distribution, converting physical spectral data into a lookup table format usable for numerical calculation. The generated distribution function is the core of all subsequent calculations, and its accuracy is directly guaranteed by the number of segments determined adaptively in the preceding steps. The rationality of the number of segments ensures that the lookup table can accurately reflect the transition details of the original spectrum in the most concise manner.

[0050] In one embodiment of the present invention, the number of Gaussian integration points for the Gaussian numerical integration of narrowband average radiance is adaptively determined based on the distribution complexity of the distribution function over its entire cumulative probability domain. This includes: calculating the numerical dispersion of the distribution function over its entire cumulative probability domain based on the discretized representation of the distribution function, defining it as the second variance; and adaptively selecting a Gaussian integration scheme of the corresponding order according to the magnitude of the second variance and a preset second mapping relationship to determine the number of Gaussian integration points, wherein the number of Gaussian integration points is positively correlated with the second variance.

[0051] In a specific embodiment, the variance (i.e., the second variance) of the distribution function in the cumulative probability domain can be calculated first based on the discrete points of the distribution function. The specific calculation method for the second variance can be obtained by numerical integration of the piecewise linear function. The magnitude of the second variance is directly related to the abrupt change characteristics of the distribution function curve. Then, based on the value of the second variance, a threshold can be used to select the integration scheme: for example, when the variance is less than 10... -8 When the variance is between 10, choose 4-point integration; when the variance is between 10, choose 4-point integration -8 With 10 -6 When the variance is greater than 10, choose 7 points for integration; -6 When choosing, select 12 points.

[0052] Specifically, in this embodiment of the invention, the variance of the distribution function is calculated as the second variance, and the number of Gaussian integration points are determined based on a preset positive correlation mapping relationship. This criterion directly measures the degree of change of the integrand in the integration domain. The upper bound of the error of the Gaussian integral is related to the higher-order derivative of the integrand; the more drastic the change of the function, the more integration points are required. The second variance provides a rigorous mathematical basis for the selection of the number of integration points, making the adaptive selection not only physically intuitive but also mathematically reasonable, thus ensuring the integration accuracy.

[0053] In one embodiment of the present invention, the calculation of the second variance includes: dividing the cumulative probability domain of the distribution function into multiple continuous sub-intervals according to the number of segments; taking the distribution function value at the midpoint of each sub-interval as the representative value of the sub-interval, and taking the length of the sub-interval as the probability width; calculating the mean of the distribution function over the entire cumulative probability domain by weighted averaging based on the representative values ​​and probability widths of all sub-intervals; calculating the second statistical moment of the distribution function over the entire cumulative probability domain based on the mean, the representative values ​​of each sub-interval, and the probability widths of each sub-interval; and calculating the second variance based on the difference between the second statistical moment and the square of the mean.

[0054] In a specific embodiment, the cumulative distribution function is obtained after spectral rearrangement and segmentation. g discrete sequence { g 0 , g 1 ,…,g N} and the corresponding distribution function k ( g ) value sequence { k 0 ,k 1 ,…k N},in g 0=0, g N =1, these discrete points constitute the distribution function. k(g) Piecewise linear approximation; in each cell [ g i-1 ,g i ]( i =1,2,…, N On, k(g) Approximately a constant, taking the value at the midpoint of the interval as representative, the value at the midpoint of the interval k value for: This interval lies on the probability axis g Width on for: Then the mean μ and second-order statistical moments They can be approximated as: , At this point, the second variance That is: .

[0055] Specifically, this invention provides a second variance calculation method based on piecewise linear approximation. This second variance calculation method makes full use of the discretized data generated in step S3. The calculation process is simple and efficient, without the need for additional function evaluation or high-cost integration operations. Its essence is to approximate the variance integral with high precision on the discrete grid. It can accurately quantify the overall dispersion of the distribution function in the entire domain while ensuring computational efficiency, providing a quantitative and reliable basis for the selection of the number of integration points.

[0056] In one embodiment of the present invention, the second mapping relationship is a threshold judgment rule, which includes: when the second variance is less than the first threshold, the distribution function is determined to change smoothly, and a four-point Gaussian integral scheme is selected; when the second variance is not less than the first threshold and less than the second threshold, the distribution function is determined to change moderately, and a seven-point Gaussian integral scheme is selected; when the second variance is not less than the second threshold, the distribution function is determined to change drastically, and a twelve-point Gaussian integral scheme is selected; wherein, the first threshold and the second threshold are preset according to the spectral band and the type of gas.

[0057] In a specific embodiment, after statistical analysis of a large number of different gases (such as CO2 and H2O) under different wavelengths and operating conditions, a first threshold of 10 can be set. -8 Second threshold = 10 -6 ; when the variance Less than about 10 -8 When the variance is constant, the distribution function is almost constant throughout the narrow band; when the variance is constant... Between 10 -8 With 10 -6 When the variance changes moderately, the distribution function exhibits a moderate change. Greater than approximately 10 -6 At this time, the distribution function often spans three or more orders of magnitude; therefore, different integration schemes can be adaptively selected, such as adaptive 4-point, 7-point, and 12-point integration schemes, i.e.: In the formula, This represents the number of Gaussian integration points. Specifically, the first and second thresholds can be fine-tuned based on the specific spectral database and engineering accuracy requirements.

[0058] Specifically, this embodiment of the invention introduces explicit threshold judgment rules to map continuously changing variance values ​​to discrete, engineering-mature integration schemes (4 points, 7 points, 12 points). This design not only makes the algorithm logic clear and easy to program, but also makes full use of the integration templates that have been widely verified in existing narrowband K-distribution methods. By pre-calibrating the threshold, the robustness and universality of the adaptive strategy are ensured, and it can be flexibly applied to different gas types and spectral bands.

[0059] In one embodiment of the present invention, before calculating the second variance, the variance-driven adaptive spectral integral narrowband K-distribution calculation method further includes: performing preprocessing on the discretized representation of the distribution function, including monotonicity verification and outlier removal, to ensure that the calculation result of the second variance is not affected by data noise or numerical error.

[0060] In a specific embodiment, the discrete point sequence of the distribution function generated in step S3 can be verified to ensure that it is strictly monotonically increasing; if non-monotonic points are found, they can be corrected by local smoothing or interpolation; at the same time, outlier points that deviate significantly from the nearby trend can be removed. These outliers may originate from minor flaws in the spectral database or rounding errors in numerical calculations.

[0061] Specifically, the embodiments of the present invention introduce a data preprocessing step before calculating the second variance; thereby effectively eliminating minor noise and outliers that may come from spectral databases or numerical calculation processes, significantly enhancing the robustness and reliability of the second variance criterion; thus avoiding distortion of variance calculation due to contamination of individual data points, and consequently misjudging the number of integration points, ensuring the reliability of the adaptive algorithm in engineering applications.

[0062] In one embodiment of the present invention, a Gaussian numerical integration is performed on the target narrowband using a determined number of segments and Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband. This includes: selecting a determined number of Gaussian integration points and weighting coefficients corresponding to each integration point on the cumulative probability interval, wherein the sum of all weighting coefficients is normalized to one; obtaining the absorption coefficient value corresponding to each Gaussian integration point by interpolation based on the discretized representation of the distribution function; substituting each absorption coefficient value into the radiation calculation function to obtain the radiation value at each Gaussian integration point; summing the products of the radiation values ​​at all Gaussian integration points and their corresponding weighting coefficients, and using the summed result as the average radiation of the target narrowband, thereby obtaining the average absorption coefficient and average transmittance of the target narrowband.

[0063] In a specific embodiment, g Select a set of Gaussian integration points on the space [0,1] g i and the corresponding weights w i , satisfying Σ w i =1; Δ for the entire narrowband spectral range η The average radiation within the narrow band, through the narrow band n q The Gaussian weighted summation at each integration point yields the average radiation intensity within the narrow band. The calculation can be transformed into a set of g Integrals from 0 to 1 In the formula,g i The point is the Gaussian integral point. w i for g i The corresponding weight value, I This represents the radiation intensity.

[0064] Average absorption coefficient within narrow band and average transmittance The calculation is as follows: , .

[0065] Specifically, the weighting coefficients of the Gaussian integral points can be found in Tables 1-3 below.

[0066] Table 1. Weighting coefficients for the 4-point integral.

[0067] Table 2. Weighting coefficients for the 7-point integral.

[0068] Table 3. Weighting coefficients for 12-point integrals

[0069] Specifically, this embodiment of the invention transforms complex integral operations into a weighted summation over a finite number of points using a standard quadrature formula. This step is the final execution stage of the narrowband K-distribution method, and its computational efficiency is directly determined by the number of Gaussian integration points selected adaptively in the preceding steps, while the computational accuracy is guaranteed by both the number of segments and the number of integration points. The normalized weighting coefficients and the precise evaluation based on interpolation ensure that this step can complete the solution of radiation characteristic parameters with the optimal computational load while ensuring accuracy.

[0070] In one embodiment of the present invention, the target narrowband is the spectral narrowband corresponding to any one of the multiple grid nodes formed after spatial discretization in the radiation calculation domain of the hypersonic vehicle exhaust plume flow field; for different grid nodes, the number of segments and the number of Gaussian integration points corresponding to each are independently and adaptively determined according to the characteristics of the absorption data at the grid node, so that the computational complexity of each narrowband matches its spectral complexity.

[0071] In a specific embodiment, in the simulation of the hypersonic vehicle exhaust flow field, the entire flow field is divided into hundreds of thousands or even millions of grids. Each grid cell has different temperatures, pressures, and component concentrations, and therefore its absorption spectral characteristics are also different. This method is applied to each independent grid node, and adaptive calculations of steps S1 to S5 are performed independently for the specific spectral data of that node. For example, in the shock layer grid with a large temperature gradient and dense spectral lines, this method will automatically select a high number of segments and a high-order integral; while in the wake region grid with uniform temperature and weak absorption, a low number of segments and a low-order integral will be automatically selected.

[0072] Specifically, this embodiment of the invention applies an adaptive method to each independent grid node of a large-scale flow field, thereby achieving on-demand allocation of computing resources. Each grid node achieves the required accuracy with the minimum computational cost determined by its own spectral characteristics, which brings a huge cumulative efficiency improvement globally. Compared with the traditional global unified scheme, this method can significantly reduce the total computation time of large-scale engineering simulation without sacrificing overall accuracy, providing a feasible technical path for the rapid and high-fidelity prediction of the exhaust plume radiation field of hypersonic vehicles.

[0073] The advantages and benefits of the variance-driven adaptive spectral integral narrowband K-distribution calculation method of the above embodiments of the present invention are verified and explained below with a specific embodiment. In this specific embodiment, a comparative experiment between the present method and LBL (Line-By-Line) is provided.

[0074] Figure 2 This is a schematic diagram comparing two fixed integration point counts according to a specific embodiment of the present invention. For example... Figure 2 As shown in this specific embodiment, to ensure that the error of the selected 12-point fixed integral is within a reasonable range in terms of calculation accuracy and efficiency, the results of 18-point integration, 16-point fixed integration, 12-point fixed integration, and line-by-line calculation method were first verified. Simultaneously, the errors between the three integration point schemes were calculated. The 4.3μm band of CO2 was selected for verification, and the calculation conditions were: temperature T = 1200K, pressure P = 1 atm, and mole fraction... x CO2 =0.38, the calculation result is for example Figure 2 As shown.

[0075] Figure 3 This is a schematic diagram comparing the errors of two integration schemes according to a specific embodiment of the present invention. Figure 3 As shown in this specific embodiment, the relative errors between the three models and LBL were verified simultaneously, such as... Figure 3 As shown, its relative error for: In the formula, These are the radiation characteristic parameter values ​​calculated by this method. These are the radiation characteristic parameter values ​​calculated using the LBL method.

[0076] Figure 4 This is a schematic diagram comparing the root mean square errors of two integration schemes according to a specific embodiment of the present invention. Figure 4 As shown in this specific embodiment, to more intuitively demonstrate the differences between different integration schemes, the root mean square error (RMSE) was calculated between the three fixed integration point schemes and the LBL in the narrowband numerical averaging results, as follows: Figure 4 Root mean square error for: In the formula, for The mean, This represents the total number of narrowbands used for validation and evaluation.

[0077] Depend on Figure 3 The relative error results shown indicate that the overall relative errors of the three schemes—18-point fixed integration, 16-point fixed integration, and 12-point fixed integration—are all controlled within ±0.08. Further observation... Figure 4 The root mean square error in the 18-point fixed integral. The accuracy is 0.047235 for the 16-point fixed integral and 0.046583 for the 12-point fixed integral. The accuracy does not increase monotonically with the number of nodes, but fluctuates. The root mean square error (RMSE) plot shows that the RMSE values ​​of the three are very close, indicating that the 18-point and 16-point fixed integral schemes do not offer a significant improvement in accuracy compared to the 12-point scheme. However, using 18-point and 16-point fixed integrals increases the number of integration points in each narrow band by 6 and 4 points respectively compared to the 12-point scheme, resulting in a corresponding increase in computational load of approximately 50% and 33.3%, while the error is not significantly improved. Therefore, considering both computational accuracy and efficiency, the 12-point fixed integral can be considered sufficient to meet the accuracy requirements of this specific embodiment. Based on this, the 18-point and 16-point fixed integrals will not be used in the following calculations; the 12-point fixed integral will be the highest acceptable choice.

[0078] Figure 5 This is a schematic diagram of the exhaust flow field temperature of a BEM-II engine according to a specific embodiment of the present invention. Figure 5 As shown in this specific embodiment, to verify the accuracy of this method, this embodiment is based on a high-temperature molecular spectral database, targeting the CO2 absorption band at 4.3 μm (wavenumber range 2000~2500 cm⁻¹). -1Numerical calculations were performed on the radiation characteristic parameters of the BEM-II engine; flow field simulations were conducted on the exhaust plume of the BEM-II engine, such as... Figure 5 Three typical and different calculation conditions were selected. Table 4 shows the calculation conditions of CO2 gas under different temperatures, pressures and other conditions.

[0079] Table 4 Calculation conditions for isothermal, homogeneous CO2 gas

[0080] Figure 6 This is a schematic diagram comparing the results of different integration schemes and LBL under Case 1 of a specific embodiment of the present invention. Figure 7 This is a schematic diagram illustrating the relative error between different integration point schemes and the LBL numerical averaging result in the narrowband under Case 1 of a specific embodiment of the present invention. Figure 6 and Figure 7 As shown, in this specific embodiment, the fixed integration point method and the adaptive spectral integration method under the calculation condition of Case 1 are first verified. The calculation condition is a temperature of T = 927.91 K and a mole fraction of x CO2 =0.12, pressure P=0.93atm; the calculation results are compared and verified with LBL; Figure 3 and Figure 4 The calculation results for LBL with different integration point schemes are presented; to ensure the consistency of the comparison results, the line-by-line calculation method uses 0.01cm. -1 To achieve high spectral resolution and facilitate comparison with the output of this method at the same spectral scale, the calculation results of the line-by-line calculation model are displayed at a spectral width Δ. η =5cm -1 The values ​​were averaged within the range; the comparison results are as follows: Figure 6 and Figure 7 As shown.

[0081] from Figure 6 and Figure 7 The calculation results show that when the integration scheme is a 12-point Gaussian integral with an adaptive number of integration points, the relative error of the calculation results is basically around ±0.05, with a maximum relative error of 0.081. This error is also affected by the numerical averaging in the narrow band using the line-by-line calculation method. When the integration scheme is a 7-point Gaussian integral, the maximum relative error reaches 0.15. And when the integration scheme is a 4-point Gaussian integral, the maximum relative error is as high as 0.245.

[0082] Figure 8 This is a schematic diagram comparing the results of different integration points and LBL under Case 2 conditions according to a specific embodiment of the present invention. Figure 9This is a schematic diagram comparing the results of different integration points and LBL under Case 3 of a specific embodiment of the present invention. Figure 8 and Figure 9 As shown, in this specific embodiment, both Case 2 and Case 3 were calculated simultaneously, and the two calculation cases were compared with the line-by-line calculation method. In order to more intuitively show the differences between different integration schemes, the root mean square error between the different integration schemes for the three cases and the line-by-line calculation method was calculated between the narrowband numerical average results.

[0083] Figure 10 This is a schematic diagram of the root mean square error under three different schemes in a specific embodiment of the present invention. Figure 11 This is a schematic diagram illustrating the calculation time for different schemes under three working conditions according to a specific embodiment of the present invention. For example... Figure 10 and Figure 11 As shown in this specific embodiment, it can be seen that the root mean square error (RMSE) of the adaptive integral is not much different from that of the fixed 12-point integral, and is smaller than that of the 7-point and 4-point fixed integrals. The 4-point fixed integral has a larger RMSE in all three operating conditions. This is because the fixed 7-point and fixed 4-point integral schemes have insufficient sampling points in narrow bands where the absorption coefficient changes drastically (such as near strong spectral lines), making it impossible to accurately capture the abrupt changes, resulting in larger errors. The adaptive method can dynamically select higher-order integrals (such as 12 points) on complex spectral bands according to the variance of the absorption coefficient distribution within the narrow band, thereby effectively controlling such errors. The overall error is significantly smaller than that of the fixed 7-point and 4-point integral schemes. Compared to the fixed 12-point integration scheme, the adaptive spectral integration method has almost the same relative error and root mean square error. However, in the weak absorption spectral band region where the absorption coefficient changes gradually, the adaptive spectral integration method can automatically identify and switch to a lower order integration (such as 4-point or 7-point), thus effectively avoiding redundant calculations. Statistical results show that, while maintaining almost the same computational accuracy and error as the fixed 12-point integration scheme, the overall computational cost of the adaptive spectral integration method is about 3 / 5 of that of the fixed 12-point integration scheme. When dealing with transmission problems of the same scale, the adaptive integration scheme saves a lot of computation time while avoiding redundant calculations. Compared with the traditional fixed-point integration, it achieves a balance between computational accuracy and efficiency. Figure 11 The calculation times required for the line-by-line calculation method, the fixed 12-point integration method, and the adaptive integration point method are given for the above three working conditions.

[0084] In summary, the variance-driven adaptive spectral integral narrowband K-distribution calculation method provided by this invention introduces the variance of the absorbed data and the variance of the absorption coefficient distribution function as quantitative criteria. This allows for automatic identification of the complexity of the K-distribution within each narrowband: switching to a low number of discrete segments or a low-order integral (e.g., 4 points) in narrowbands with smaller variance to avoid redundant calculations; and switching to a high number of discrete segments or a high-order integral (e.g., 12 points) in narrowbands with larger variance to ensure sampling accuracy. Comparative tests show that, while maintaining almost the same computational accuracy as the fixed 12-point integral scheme, the overall computational efficiency of this method is approximately 1.5 times that of the fixed 12-point integral scheme. This adaptive mechanism enables each narrowband to complete the calculation with computational resources matching its complexity, thus achieving a balance between accuracy and efficiency.

[0085] A further embodiment of the present invention discloses a variance-driven adaptive spectral integral narrowband K-distribution calculation system. Figure 12 This is a block diagram of a variance-driven adaptive spectral integral narrowband K-distribution calculation system according to an embodiment of the present invention. Figure 12 As shown, in one embodiment of the present invention, the variance-driven adaptive spectral integral narrowband K-distribution calculation system 100 includes: a data acquisition module 110, a first adaptive module 120, a distribution function construction module 130, a second adaptive module 140, and a radiation characteristic calculation module 150.

[0086] Specifically, the data acquisition module 110 is used to acquire the absorption data of each spectral point arranged in wavenumber order within the target narrow band.

[0087] The first adaptive module 120 is used to adaptively determine the number of segments based on the degree of fluctuation of the absorbed data along the wavenumber domain.

[0088] The distribution function construction module 130 is used to sort and segment the absorbed data based on the number of segments, construct the distribution function of the absorption coefficient with respect to the cumulative probability, and obtain its discretized representation.

[0089] The second adaptive module 140 is used to adaptively determine the number of Gaussian integration points for the Gaussian numerical integration of the narrowband average radiation based on the distribution complexity of the distribution function over its entire cumulative probability domain.

[0090] The radiation characteristic calculation module 150 is used to perform Gaussian numerical integration on the target narrowband using the determined number of segments and Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband.

[0091] It should be noted that the specific implementation of the variance-driven adaptive spectral integral narrowband K-distribution calculation system 100 in this embodiment of the invention is similar to the specific implementation described in the variance-driven adaptive spectral integral narrowband K-distribution calculation method in the above embodiments of the invention, and therefore has similar technical effects. For details, please refer to the description in the section on variance-driven adaptive spectral integral narrowband K-distribution calculation method. To reduce redundancy, it will not be repeated here.

[0092] Further embodiments of the present invention also disclose an electronic device, Figure 13 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Figure 13 As shown, in one embodiment of the present invention, the electronic device includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; the memory is used to store computer programs; when the processor executes the computer programs stored in the memory, it implements the variance-driven adaptive spectral integral narrowband K-distribution calculation method as described in any of the above embodiments of the present invention.

[0093] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0094] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0095] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0096] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0097] The method provided in this invention can be applied to electronic devices. Specifically, the electronic device can be a desktop computer, a portable computer, a smart mobile terminal, a server, etc. No limitation is made herein; any electronic device that can implement this invention falls within the protection scope of this invention.

[0098] It should be noted that the specific implementation of the electronic device in the embodiments of the present invention is similar to the specific implementation described in the above embodiments of the present invention based on the variance-driven adaptive spectral integral narrowband K-distribution calculation method, and therefore has similar technical effects. For details, please refer to the description in the section on the variance-driven adaptive spectral integral narrowband K-distribution calculation method. To reduce redundancy, it will not be repeated here.

[0099] A further embodiment of the present invention discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the variance-driven adaptive spectral integral narrowband K-distribution calculation method as described in any of the above embodiments of the present invention.

[0100] It should be noted that the specific implementation of the computer-readable storage medium in the embodiments of the present invention is similar to the specific implementation described in the above embodiments of the present invention regarding the variance-driven adaptive spectral integral narrowband K-distribution calculation method, and therefore has similar technical effects. For details, please refer to the description in the section on the variance-driven adaptive spectral integral narrowband K-distribution calculation method. To reduce redundancy, it will not be repeated here.

[0101] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example.

[0102] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A variance-driven adaptive spectral integral narrowband K-distribution calculation method, characterized in that, Includes the following steps: Acquire absorption data of each spectral point within the target narrow band, arranged in wavenumber order; The number of segments is adaptively determined based on the degree of fluctuation of the absorbed data along the wavenumber domain; Based on the number of segments, the absorbed data is sorted and segmented to construct the distribution function of the absorption coefficient with respect to the cumulative probability and obtain its discretized representation. Based on the complexity of the distribution function over its entire cumulative probability domain, the number of Gaussian integration points for the Gaussian numerical integration of narrowband average radiance is adaptively determined. Using the determined number of segments and the number of Gaussian integration points, Gaussian numerical integration is performed on the target narrowband to calculate the radiation characteristic parameters of the target narrowband.

2. The method for calculating the narrowband K-distribution based on variance-driven adaptive spectral integral as described in claim 1, characterized in that, The adaptive determination of the number of segments based on the degree of fluctuation of the absorbed data along the wavenumber domain includes: The overall dispersion of the absorption coefficients of all spectral points within the target narrowband relative to their arithmetic mean is calculated and defined as the first variance; The number of segments is determined based on the magnitude of the first variance and a preset first mapping relationship, wherein the number of segments is positively correlated with the first variance.

3. The method for calculating the narrowband K-distribution of spectral integral based on variance-driven approach according to claim 1, characterized in that, The construction of the distribution function of the absorption coefficient with respect to the cumulative probability and the acquisition of its discretized representation include: All absorption data within the target narrowband are sorted in ascending order of numerical value; Based on the number of segments, multiple segment nodes are selected between the maximum and minimum values ​​of the absorption coefficient after ascending order, and the absorption coefficient value range is divided into a corresponding number of segment intervals. The proportion of the spectral wavenumber width falling within each segment interval to the total wavenumber width of the target narrowband is statistically analyzed to obtain the probability density value corresponding to each segment interval, and the cumulative probability value at each segment node is calculated cumulatively. By inverting the cumulative probability value, discrete values ​​of the distribution function of the absorption coefficient with respect to the cumulative probability at each segment node are obtained.

4. The method for calculating the narrowband K-distribution of spectral integral based on variance-driven method according to claim 1, characterized in that, The step of adaptively determining the number of Gaussian integration points for the narrowband average radiance numerical integration based on the distribution complexity of the distribution function over its entire cumulative probability domain includes: Based on the discretized representation of the distribution function, the numerical dispersion of the distribution function over its entire cumulative probability domain is calculated and defined as the second variance; Based on the magnitude of the second variance, and according to a preset second mapping relationship, a Gaussian integration scheme of the corresponding order is adaptively selected to determine the number of Gaussian integration points, wherein the number of Gaussian integration points is positively correlated with the second variance.

5. The method for calculating the narrowband K-distribution of spectral integral based on variance-driven method according to claim 4, characterized in that, The calculation of the second variance includes: The cumulative probability domain of the distribution function is divided into multiple continuous sub-intervals according to the number of segments; For each sub-interval, the distribution function value at the midpoint of the sub-interval is taken as the representative value of the sub-interval, and the length of the sub-interval is taken as the probability width; The mean of the distribution function over the entire cumulative probability domain is calculated by weighted averaging based on the representative values ​​and probability widths of all the sub-intervals. The second statistical moment of the distribution function over the entire cumulative probability domain is calculated based on the mean, the representative value of each sub-interval, and the probability width of each sub-interval. The second variance is calculated based on the difference between the second-order statistical moments and the square of the mean.

6. The method for calculating the narrowband K-distribution of spectral integral based on variance-driven method according to claim 4, characterized in that, The second mapping relationship is a threshold judgment rule, which includes: When the second variance is less than the first threshold, it is determined that the distribution function changes smoothly, and the four-point Gaussian integral scheme is selected. When the second variance is not less than the first threshold and less than the second threshold, it is determined that the degree of change of the distribution function is moderate, and the seven-point Gaussian integral scheme is selected. When the second variance is not less than the second threshold, it is determined that the distribution function changes drastically, and the twelve-point Gaussian integral scheme is selected; The first threshold and the second threshold are preset according to the spectral band and the type of gas.

7. The method for calculating the narrowband K-distribution based on variance-driven adaptive spectral integral as described in claim 4, characterized in that, Before calculating the second variance, the variance-driven adaptive spectral integral narrowband K-distribution calculation method further includes: The discretized representation of the distribution function is preprocessed, including monotonicity verification and outlier removal, to ensure that the calculation result of the second variance is not affected by data noise or numerical error.

8. The method for calculating the narrowband K-distribution based on variance-driven adaptive spectral integral as described in claim 1, characterized in that, The step of performing Gaussian numerical integration on the target narrowband using the determined number of segments and the number of Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband includes: A certain number of Gaussian integration points and corresponding weight coefficients are selected on the cumulative probability interval, wherein the sum of all the weight coefficients is normalized to one. Based on the discretized representation of the distribution function, the absorption coefficient value corresponding to each Gaussian integration point is obtained by interpolation; Substitute each absorption coefficient value into the radiation calculation function to obtain the radiation value at each Gaussian integration point. The product of the radiation value at all Gaussian integration points and its corresponding weighting coefficient is summed, and the summation result is used as the average radiation of the target narrowband, thereby obtaining the average absorption coefficient and average transmittance of the target narrowband.

9. The method for calculating the narrowband K-distribution based on variance-driven adaptive spectral integral according to any one of claims 1 to 8, characterized in that, The target narrowband is the spectral narrowband corresponding to any one of the multiple grid nodes formed after spatial discretization in the radiation calculation domain of the hypersonic vehicle's exhaust plume flow field. For different grid nodes, the number of segments and the number of Gaussian integration points are independently and adaptively determined based on the characteristics of the absorption data at the grid node, so that the computational complexity of each narrowband matches its spectral complexity.

10. A variance-driven adaptive spectral integral narrowband K-distribution calculation system, characterized in that, include: The data acquisition module is used to acquire the absorption data of each spectral point within the target narrowband, arranged in wavenumber order. The first adaptive module is used to adaptively determine the number of segments based on the degree of fluctuation of the absorbed data along the wavenumber domain. The distribution function construction module is used to sort and segment the absorbed data based on the number of segments, construct the distribution function of the absorption coefficient with respect to the cumulative probability, and obtain its discretized representation. The second adaptive module is used to adaptively determine the number of Gaussian integration points for the Gaussian numerical integration of the narrowband average radiation based on the distribution complexity of the distribution function over its entire cumulative probability domain. The radiation characteristic calculation module is used to perform Gaussian numerical integration on the target narrowband using the determined number of segments and the number of Gaussian integration points to calculate the radiation characteristic parameters of the target narrowband.

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