In-furnace three-dimensional temperature field distribution detection method based on color flame image processing

Abstract

The invention relates to the technical field of flame image processing and temperature detection, and discloses an in-furnace three-dimensional temperature field distribution detection method based on color flame image processing. The method comprises the following steps: acquiring a color flame image sequence in a furnace, after preprocessing and feature extraction, dividing the space in the furnace into a plurality of sub-regions, and calculating the initial temperature; by monitoring the dynamic characteristics of color fluctuation, brightness change and the like of each sub-region in the image sequence, the influence degree of the dynamic characteristics on the overall temperature field in the furnace is evaluated, and the weight is allocated according to the influence degree. And finally, in combination with the initial temperature value and the weight, a three-dimensional temperature field is reconstructed through a data fusion algorithm. According to the method, dynamic analysis is introduced into temperature measurement, random errors introduced by combustion pulsation are effectively restrained through reliability weighted fusion, and the accuracy and the anti-interference capacity of a temperature field distribution model are improved.

Description

A method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing Technical Field

[0001] This invention relates to the field of flame image processing and temperature detection technology, specifically a method for detecting the three-dimensional temperature field distribution inside a furnace based on color flame image processing. Background Technology

[0002] In the field of industrial combustion monitoring, accurate detection of the three-dimensional temperature field within the furnace is a core challenge for optimizing combustion efficiency and controlling pollutant emissions. Traditional contact temperature measurement methods, such as thermocouples, can only provide local point temperatures and cannot capture the temperature distribution throughout the entire furnace; they also suffer from fragility and maintenance difficulties. Non-contact temperature measurement technology based on color CCD cameras inverts temperature by analyzing the color and brightness information of flame images, providing a more comprehensive view. However, most existing technologies rely on the analysis of single or a few static images to establish static empirical models between image features and temperature. The combustion process is inherently highly turbulent and unsteady, causing the color and brightness of the flame to continuously and dramatically pulsate in the spatiotemporal dimension. This static analysis method equates transient information with time-averaged states, ignoring the dynamic characteristics of combustion, resulting in measured temperature values ​​containing significant random errors and failing to accurately reflect the average thermal state within the furnace.

[0003] In reconstructing a three-dimensional temperature field from a two-dimensional image, existing technologies generally employ interpolation algorithms based on geometric mapping. These methods implicitly assume that the data reliability of all image regions or three-dimensional spatial points is equal. In reality, the combustion stability varies significantly across different regions within a furnace. Fusing measurement data with varying reliability with equal weights leads to severe interference from noise data in high-fluctuation regions in the reconstructed three-dimensional temperature field model, reducing the overall model's accuracy and robustness. Current technologies lack a mechanism to effectively identify and quantify the reliability of measurement data from different regions, failing to assign higher weights to high-reliability data and suppress low-reliability data during reconstruction. This is a key bottleneck hindering the improvement of three-dimensional temperature field measurement accuracy. This invention aims to solve the aforementioned core problems based on dynamic characteristic analysis and data reliability weighting. Summary of the Invention

[0004] The purpose of this invention is to provide a method for detecting the three-dimensional temperature field distribution inside a furnace based on color flame image processing, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, this invention provides a method for detecting the three-dimensional temperature field distribution inside a furnace based on color flame image processing, comprising the following steps: S1: acquiring a sequence of color flame images inside the furnace through an image acquisition device, and simultaneously recording furnace structure parameters and operating parameters; S2: preprocessing the color flame image sequence, including noise reduction and color correction; extracting color features and spatial features from the preprocessed images; S3: dividing the furnace space into multiple sub-regions based on the extracted color features and spatial features, and calculating an initial temperature value for each sub-region; S4: monitoring the dynamic change characteristics of each sub-region in the image sequence, including color fluctuations and brightness changes, and calculating the degree of influence of each sub-region on the overall temperature field inside the furnace; S5: assigning a weight value to each sub-region according to the degree of influence and the initial temperature value; and constructing the three-dimensional temperature field distribution inside the furnace using the initial temperature values ​​and weight values ​​of all sub-regions through a data fusion algorithm.

[0006] Preferably, in step S1, the image acquisition device acquires a sequence of color flame images inside the furnace and simultaneously records furnace structure parameters and operating parameters, including: using a high-speed digital camera to capture the flame inside the furnace at a rate of at least 100 frames per second; and simultaneously recording the furnace geometry, fuel supply rate, air flow rate, and burner type.

[0007] Preferably, in step S2, the extraction of color and spatial features from the preprocessed image includes: preprocessing the colored flame image sequence by using Gaussian filtering to eliminate noise and using a white balance algorithm for color correction; converting the preprocessed image from RGB color space to Lab color space, extracting the L channel luminance value and the a and b channel color values, and calculating the gradient magnitude of each pixel in the image; in step S3, based on the extracted color and spatial features, dividing the furnace space into multiple sub-regions and calculating an initial temperature value for each sub-region includes: using a k-means clustering algorithm to partition the region according to the similarity of color and spatial features; and mapping the average color value of the sub-region to the temperature value by establishing a color-temperature relationship curve to obtain an initial temperature value corresponding to each sub-region.

[0008] Preferably, in step S4, monitoring the dynamic change characteristics of each sub-region in the image sequence and the degree of influence of each sub-region on the overall temperature field inside the furnace includes: calculating the standard deviation of the color value and the average brightness change rate of each sub-region in the image sequence frame. The standard deviation of the color value reflects the intensity of color fluctuation, and the average brightness change rate reflects the speed of brightness change. The calculation of the degree of influence is based on the dynamic change characteristics, using principal component analysis to extract the main change patterns, and calculating the change contribution rate of each sub-region.

[0009] Preferably, in step S5, the method for calculating the weight value includes: normalizing the degree of influence and combining it with the dispersion of the initial temperature value, and using the entropy weight method to calculate the weight value; wherein, the normalized degree of influence is positively correlated with the weight value.

[0010] Preferably, in step S5, the method for constructing the three-dimensional temperature field distribution inside the furnace includes: using an inverse distance weighted interpolation method, taking the weight value of each sub-region as the interpolation weight, spatially interpolating the initial temperature value, and then using a radial basis function network for smoothing to generate a continuous three-dimensional temperature field.

[0011] Preferably, in the inverse distance weighted interpolation method, the interpolation weight of each sub-region is calculated based on the spatial distance between the sub-region and its neighboring sub-regions, with the weight increasing as the distance increases; the radial basis function network uses a Gaussian kernel function as the basis function and learns the distribution of the interpolated temperature data through training.

[0012] Preferably, after the continuous three-dimensional temperature field is generated, step S5 further includes verifying the accuracy of the temperature field. The specific steps include: measuring the actual temperature point inside the furnace through a thermocouple array, comparing the measured value with the predicted value of the three-dimensional temperature field at the corresponding location, and calculating the average absolute error as an accuracy index.

[0013] Preferably, in the step of verifying the accuracy of the temperature field, the thermocouple array is arranged in key positions inside the furnace, including near the burner and in the central area of ​​the furnace; the average absolute error calculation is based on all measurement points, and if the average absolute error exceeds a preset threshold, the color-temperature relationship curve and weight value calculation method are adjusted.

[0014] Preferably, the steps of adjusting the color-temperature relationship curve and weight value calculation method include: using an iterative optimization algorithm, including gradient descent, to minimize the mean absolute error, updating the color-temperature mapping parameters and weight calculation parameters, and then re-executing steps S1 to S5 until the mean absolute error is lower than a preset threshold.

[0015] Compared with existing technologies, the beneficial effects of this invention are: by analyzing the dynamic characteristics such as color fluctuations and brightness changes in each sub-region of an image sequence, the influence of that region on the overall temperature field inside the furnace can be quantified. The dynamic characteristics of the combustion flame directly reflect its combustion stability. A region with drastic and irregular fluctuations in color and brightness has lower reliability in transient temperature measurement, and its corresponding contribution rate is also smaller. Conversely, regions with stable dynamic changes have more reliable data and a higher contribution rate. Introducing the dynamic characteristics of combustion into the temperature measurement model breaks through the limitation of traditional static image analysis methods that equate transient information with time-averaged information. This allows the judgment of the reliability of temperature data in each sub-region to be deepened from the level of simple brightness or color intensity to the level of statistical stability in the time domain.

[0016] Based on the degree of influence of dynamic changes, differentiated weight values ​​can be assigned to each sub-region, and these weight values ​​are used to fuse data with the initial temperature values ​​to construct the final three-dimensional temperature field. This process realizes the transformation from "equal-weight reconstruction" to "reliability-weighted reconstruction." In the data fusion algorithm, data from sub-regions with high reliability are given greater weight and dominate the reconstruction model; while data from sub-regions with low reliability and drastic fluctuations are given smaller weights, effectively suppressing the random noise and errors they contain. This adaptive weighting mechanism enables the reconstructed three-dimensional temperature field model to more accurately reflect the real, time-averaged heat release distribution within the furnace, reducing random errors caused by combustion pulsations and improving the anti-interference capability and measurement accuracy of the entire temperature field distribution model. Attached Figure Description

[0017] Figure 1 is a schematic diagram of the working principle of the furnace three-dimensional temperature field distribution detection method based on color flame image processing provided by the present invention; Figure 2 is a flowchart of image acquisition and preprocessing provided by the present invention; Figure 3 is a flowchart of thermocouple arrangement and error judgment provided by the present invention; Figure 4 is an analysis diagram of the temperature field accuracy verification results provided by the present invention; Figure 5 is an analysis diagram of the parameter optimization process provided by the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Please refer to Figure 1 for an example. This invention provides a method for detecting the three-dimensional temperature field distribution inside a furnace based on color flame image processing. The method includes: S1: acquiring a sequence of color flame images inside the furnace through an image acquisition device, and simultaneously recording furnace structural parameters and operating parameters, which provide basic data for subsequent processing; S2: preprocessing the color flame image sequence, including noise reduction and color correction, to improve image quality; extracting color features and spatial features from the preprocessed images, which are used to characterize the visual attributes of the flame; S3: based on the extracted color features and spatial features, dividing the furnace space into multiple sub-regions, and... An initial temperature value is calculated for each sub-region, based on the color-temperature mapping relationship. S4: The dynamic changes of each sub-region in the image sequence are monitored, including color fluctuations and brightness changes, and the influence of each sub-region on the overall temperature field inside the furnace is calculated. These dynamic changes reflect the stability of the combustion process. S5: Based on the degree of influence and the initial temperature value, a weight value is assigned to each sub-region. This weight value quantifies the importance of different sub-regions. Using the initial temperature values ​​and weight values ​​of all sub-regions, a three-dimensional temperature field distribution inside the furnace is constructed through a data fusion algorithm, ultimately generating a continuous three-dimensional temperature field model. This method, by integrating image processing, feature analysis, and data fusion techniques, achieves non-contact temperature field detection and is suitable for various industrial furnace environments.

[0020] Referring to Figure 2, in step S1, the image acquisition device employs a high-speed digital camera. This camera captures the flame inside the furnace at a rate of at least 100 frames per second. This high frame rate effectively captures rapid dynamic changes and transient characteristics during combustion. The high-speed digital camera is equipped with appropriate filters and optical lenses to adapt to the high-temperature, high-brightness environment inside the furnace. Simultaneously, furnace structural parameters and operating parameters are recorded. These parameters include the furnace's geometric dimensions, and operating parameters include fuel supply rate, airflow, and burner type. These parameters are recorded in real-time and stored in a correlated database, and are timestamped and synchronized with the acquired color flame image sequence to provide accurate contextual information for subsequent analysis.

[0021] In step S2, the preprocessing of the colored flame image sequence uses Gaussian filtering to eliminate noise. Gaussian filtering is a linear smoothing filter that uses a convolution kernel generated by a Gaussian function to weight the average pixel value of the image through convolution operations, effectively suppressing high-frequency noise components in the image.

[0022] In practice, the kernel size and standard deviation parameters of the Gaussian filter need to be set according to the image resolution and noise level; for example, using 3... 3 or 5 The convolution kernel is 5, and a white balance algorithm is used for color correction. The white balance algorithm adjusts the gain of the red, green and blue channels by identifying neutral color areas in the image or using preset reference white points to compensate for color distortion caused by changes in lighting conditions, making the flame color representation more realistic and reliable.

[0023] Color and spatial features are extracted from the preprocessed image. The image is converted from the RGB color space to the Lab color space, a color space based on human visual perception. In Lab, the L channel represents brightness information, the a channel represents the green-red color components, and the b channel represents the blue-yellow color components. The conversion process involves non-linear transformations, which better distinguish between color and brightness information. The L channel brightness value and the a and b channel color values ​​are extracted as color features, which characterize the brightness and color distribution of the flame. Simultaneously, the gradient magnitude of each pixel in the image is calculated as a spatial feature. The gradient magnitude is obtained by applying edge detection algorithms such as the Sobel operator, reflecting the texture details and boundary information of the flame area in the image.

[0024] In step S3, the k-means clustering algorithm is used to group image pixels into multiple clusters based on the similarity of color and spatial features. In practice, k-means clustering is an unsupervised machine learning method. The input data for k-means clustering includes the L-channel, a-channel, and b-channel values ​​of each pixel, as well as the gradient magnitude. These feature values ​​need to be normalized to eliminate the influence of dimensions. The k-means clustering algorithm iteratively updates the cluster centers until the sum of squared errors within each cluster is minimized, ultimately dividing the image space into a predetermined number of sub-regions, each with high feature consistency.

[0025] By establishing a color-temperature relationship curve—a mapping model based on blackbody radiation principles or pre-calibrated experimental data—the average color value of a sub-region is mapped to a corresponding temperature value, thus calculating an initial temperature value for each sub-region. In practice, for each sub-region generated by the k-means clustering algorithm, the average values ​​of the a and b channels of all pixels within it in the Lab color space are calculated. These average values ​​are then input into the color-temperature relationship curve for lookup or calculation to obtain the initial temperature value for that sub-region. The color-temperature relationship curve can be implemented using multinomial fitting, lookup tables, or neural network models to ensure accurate conversion from color space to temperature space.

[0026] It should be noted that the sampling rate setting of a high-speed digital camera needs to balance the amount of data and the processing burden. An excessively high frame rate may lead to data redundancy, while an excessively low frame rate may result in the loss of important dynamic information. In practical implementation, a rate of 100 frames per second is a baseline value, which can be adjusted according to the specific furnace size and combustion characteristics in actual applications. The high-speed digital camera should have high dynamic range imaging capabilities to handle the strong contrast between light and dark areas inside the furnace and avoid overexposure or underexposure of images. Among the synchronously recorded furnace structural and operational parameters, the furnace's geometric dimensions include length, width, and height; the fuel supply rate is recorded in units of mass flow rate or volumetric flow rate; air flow includes primary and secondary air flow rates; and the burner type involves specifications such as structural form and fuel type.

[0027] In Gaussian filtering, the choice of convolution kernel parameters directly affects the denoising effect and the degree of image detail preservation. Larger kernel sizes and standard deviations produce stronger smoothing effects but may blur image details. White balance algorithms can employ the gray-world assumption, the perfect reflector method, or machine learning-based methods; the specific choice depends on the application scenario and accuracy requirements. Color space conversion from RGB to Lab requires precise mathematical transformation formulas, and the converted Lab values ​​should be range-adjusted to suit subsequent processing. The mathematical transformation formulas follow international standard conversion procedures, first converting RGB color space values ​​to XYZ color space, and then from XYZ color space to Lab color space. The RGB to XYZ conversion is based on the primary color matrix and gamma correction parameters of the image acquisition device used, ensuring that the conversion process conforms to the device's color response characteristics. The XYZ to Lab conversion uses the XYZ tristimulus values ​​under standard light sources as a reference, mapping XYZ values ​​to Lab values ​​that conform to the human eye's color perception rules through nonlinear transformation. The entire conversion process strictly follows the CIE 1976 Lab color space definition specification.

[0028] During feature extraction, gradient magnitude calculation can employ various operators; for example, the Sobel operator is computationally efficient, while the Prewitt operator is more sensitive to noise. A trade-off between accuracy and computational cost is necessary when choosing one. The implementation of the k-means clustering algorithm requires careful consideration of the initial cluster center selection. The k-means++ algorithm can be used to optimize the initialization process and avoid getting trapped in local optima. The number of clusters can be optimized using evaluation methods such as the elbow rule or the silhouette coefficient method, ensuring that the sub-region division is neither too coarse nor too fine.

[0029] When using the elbow method for optimization, a series of consecutive candidate cluster numbers are first set. For each candidate number, k-means clustering is performed, and the sum of squared intra-cluster errors corresponding to each cluster result is calculated. Then, a curve is plotted with the number of candidate clusters as the horizontal axis and the sum of squared intra-cluster errors as the vertical axis. When the slope of the curve gradually decreases to form an "elbow," the number of clusters at that position is the optimal choice. This approach ensures the consistency of features among sub-regions while avoiding coarse region division due to too few clusters or over-subdivision of sub-regions due to too many clusters.

[0030] When using the silhouette coefficient method for optimization, the silhouette coefficient of all data points is calculated for each candidate cluster number. The higher the silhouette coefficient, the stronger the closeness between the data point and its cluster and the better the separation from other clusters. The candidate number with the largest average silhouette coefficient is selected as the optimal number of clusters to ensure that each sub-region after division can accurately reflect the similarity difference of color and spatial features, and achieve reasonable partitioning of the furnace space.

[0031] Establishing the color-temperature relationship curve is the core of temperature estimation, requiring a large amount of calibration data. The calibration process should be conducted under controlled experimental conditions using standard temperature measurement equipment, such as thermocouples or radiation thermometers, to simultaneously acquire temperature values ​​and image data, establishing a reliable mapping relationship. Understandably, the accuracy of the initial temperature calculation directly affects the accuracy of the final three-dimensional temperature field; therefore, the color-temperature relationship curve needs to be periodically calibrated and updated to adapt to different fuel types and combustion conditions.

[0032] In practical implementation, the image acquisition stage also needs to consider the camera installation position and viewing angle. Multiple cameras can capture images from different angles to obtain more comprehensive information about the furnace interior. In this case, camera calibration and image registration are required first. The preprocessing stage may also include other steps such as image distortion correction and contrast enhancement, but the core remains Gaussian filtering and white balance. During feature extraction, in addition to Lab color space and gradient magnitude, other features such as texture features and shape features can be considered, but this embodiment is limited to color features and spatial features. The feature weight allocation of the k-means clustering algorithm needs to be set reasonably. The importance of color features and spatial features may be different, and the optimal weight ratio needs to be determined experimentally.

[0033] The rationality of feature weight allocation is reflected in the following: the allocated weights enable the clustering results to accurately distinguish regions with different combustion states within the furnace, ensuring strong consistency in color and spatial features within the same sub-region, significant feature differences between different sub-regions, and precise matching of the subsequent color-temperature mapping requirements after partitioning. The optimal weight ratio needs to be obtained through multiple sets of comparative experiments. The experiments will set multiple different combinations of color and spatial feature weights for different furnace structures, fuel types, and combustion conditions, perform k-means clustering operations respectively, and evaluate the effect of each weight based on the intra-cluster consistency and inter-cluster separation of the clustering results. Finally, the optimal ratio suitable for the current operating conditions will be selected. This ratio is not a fixed value and will be dynamically adjusted according to changes in furnace operating parameters and flame combustion state to ensure that the sub-regions generated by clustering always conform to the spatial distribution law of actual combustion within the furnace. The color-temperature relationship curve may vary due to factors such as fuel composition and pressure conditions; therefore, multiple curve models need to be established to adapt to different operating conditions.

[0034] Optionally, the image acquisition device is not limited to a high-speed digital camera; other types of color imaging devices, such as CCD or CMOS cameras, can also be used, but the frame rate requirement must be met. In preprocessing algorithms, for noise reduction, in addition to Gaussian filtering, median filtering or bilateral filtering can be considered; color correction can also employ methods based on color temperature estimation. During feature extraction, color space conversion is not limited to Lab space; HSV or YUV spaces can also be used, but Lab space has advantages in color perception uniformity. Clustering algorithms, besides k-means, can also use DBSCAN or mean shift algorithms, but k-means performs well in terms of computational efficiency and stability. In calculating the initial temperature value, the color-temperature relationship curve can be based on a theoretical model (such as Planck's radiation law) or fitted with empirical data, while ensuring mapping accuracy.

[0035] In step S4, the dynamic change characteristics of each sub-region in the image sequence are monitored by calculating the standard deviation of color values ​​and the average rate of change of brightness for each sub-region in the image sequence frames. The standard deviation of color values ​​is calculated for each sub-region generated by the k-means clustering algorithm. The calculation process covers the a-channel and b-channel color value sequences of all frames in the image sequence. For each sub-region, the standard deviation of a-channel values ​​and the standard deviation of b-channel values ​​of all pixels in the entire image sequence time span are calculated. These two standard deviations quantify the severity of the color component fluctuation of the sub-region over time. The average rate of change of brightness is calculated based on the L-channel brightness value sequence. The difference of the average L-channel values ​​of sub-regions between adjacent image frames is calculated, and then divided by the time interval to obtain the rate of change. Finally, the absolute values ​​of the rates of change are averaged across all consecutive frames to obtain an index reflecting the speed of brightness change.

[0036] The calculation of the impact of each sub-region on the overall temperature field within the furnace is based on the aforementioned dynamic change characteristics. Principal component analysis (PCA) is used to extract the main change patterns, transforming multiple correlated variables into a set of linearly uncorrelated variables, i.e., principal components. In practice, PCA is a statistical method. The input data is a matrix, where rows represent different sub-regions and columns represent dynamic characteristic indicators, including the standard deviation of color values ​​in channel a, the standard deviation of color values ​​in channel b, and the average brightness change rate. Each characteristic indicator needs to be standardized to eliminate dimensional differences. The calculation process of PCA includes calculating the covariance matrix, solving for eigenvalues ​​and eigenvectors, and then sorting the eigenvalues ​​from largest to smallest and selecting the top k principal components. These principal components can explain most of the variance in the original data. The contribution rate of each sub-region is calculated by weighted combination of its loadings on different principal components and eigenvalues. A larger contribution rate indicates a more significant impact of the dynamic changes in that sub-region on the fluctuations of the overall temperature field within the furnace.

[0037] In step S5, the step of assigning a weight value to each sub-region based on the degree of influence and the initial temperature value includes: normalizing the degree of influence by subtracting the minimum value of the change contribution rate of all sub-regions from the change contribution rate of each sub-region, and then dividing by the difference between the maximum and minimum values ​​of the change contribution rate of all sub-regions, achieving a linear transformation to a closed interval of 0 to 1, making the change contribution rates of all sub-regions comparable. Then, combining the dispersion of the initial temperature value, the weight value is calculated using the entropy weight method, an objective weighting method based on the concept of information entropy. In specific implementation, an evaluation matrix is ​​first constructed, with rows corresponding to each sub-region and columns corresponding to two evaluation indicators (i.e., the normalized degree of influence and the initial temperature value). The initial temperature value also needs to be normalized. For each evaluation indicator, its information entropy is calculated. Information entropy reflects the dispersion of the indicator's numerical distribution. The smaller the information entropy, the greater the role of the indicator in distinguishing different sub-regions, and therefore, a higher weight should be assigned. The indicator weight is calculated using the following formula:

[0038] in: The weight representing the j-th evaluation indicator. The information entropy represents the j-th evaluation index. The information entropy represents the k-th evaluation index. It is the total number of evaluation indicators (in this embodiment) ), This represents the sum of the inadequacy of the information entropy of all evaluation indicators.

[0039] The final weight value of each sub-region is the normalized value of its two evaluation indicators and the corresponding indicator weights. The weighted sum is calculated using the following formula:

[0040] in: Indicates the first The final weight value of each sub-region Indicates the first The value of the "normalized degree of influence" index for each sub-region. Indicates the first The value of the "normalized initial temperature value" index for each sub-region. The weight of the indicator representing the "normalized degree of influence" is... This indicates the weight of the index "normalized initial temperature value". This indicates the total number of sub-regions.

[0041] Furthermore, the weight value is positively correlated with the degree of influence, meaning that the sub-region with a higher degree of influence will ultimately receive a larger weight value.

[0042] Understandably, the calculation of dynamic change features relies on high-quality image sequence data. The image frame rate must be high enough to capture meaningful dynamic information; a rate of at least 100 frames per second can meet the monitoring needs of most industrial combustion processes. The calculation of the standard deviation of color values ​​requires a sufficiently long time series to ensure statistical significance, typically requiring the analysis of image sequences containing hundreds of frames. In the calculation of the average brightness change rate, the time interval is determined by the image acquisition frame rate, and differencing operations can effectively capture the instantaneous trend of brightness change. The application of principal component analysis can extract the core change patterns from multiple dynamic features, avoiding analytical biases caused by feature collinearity. The number of principal components selected for retention is usually based on a cumulative variance contribution rate reaching a certain threshold (e.g., 85%).

[0043] In implementing the entropy weight method, constructing the evaluation matrix is ​​crucial. The normalized degree of influence and the initial temperature value must accurately reflect the relative importance of the sub-regions. The formula for calculating information entropy is:

[0044] in: Represents information entropy. It is the number of sub-regions. This represents the proportion of the normalized value of the i-th sub-region under the j-th evaluation index. It is understandable that the entropy weight method can objectively allocate weights based on the dispersion of the data itself, avoiding the arbitrariness of subjective judgment and making the weight allocation more scientific and reasonable. The final weight value integrates dynamic change characteristics and initial temperature information, considering both the stability factors of the combustion process and the absolute level of the temperature itself.

[0045] In some embodiments, the monitoring of dynamic change characteristics can be extended to more indicators; for example, the mean change rate of color values, higher-order moment statistics, etc., but this embodiment is limited to the two core indicators of color value standard deviation and average brightness change rate. Principal component analysis can also be replaced by other dimensionality reduction techniques, such as factor analysis or independent component analysis, but principal component analysis has advantages in computational efficiency and interpretability. In entropy weight calculation, if the information entropy of an indicator is close to 1, it indicates that the indicator has low discrimination, and its weight will approach 0. In this case, adjusting the indicator or introducing other features can be considered. The results of weight allocation need to be consistent to ensure that the weight distribution conforms to physical expectations; for example, high-temperature regions or regions with drastic fluctuations should generally receive higher weights. Optionally, the calculation of dynamic characteristics can consider analysis at different time scales, such as separating short-term fluctuations from long-term trends, by designing high-pass and low-pass filters to process time series data. Data standardization before principal component analysis can use different methods such as min-max standardization or Z-score standardization; the specific choice depends on the characteristics of the data distribution. The weight calculation in the entropy weight method can also introduce subjective weights for combination to form a comprehensive subjective and objective weighting method. After the weights are allocated, the weight values ​​can be smoothed or outliers corrected to ensure the rationality of the weight distribution and avoid the weights of individual sub-regions being too high or too low, which would affect the overall temperature field reconstruction quality inside the furnace.

[0046] In specific implementation, the method for constructing the three-dimensional temperature field distribution inside the furnace includes: using the inverse distance weighted interpolation method: using the weight value of each sub-region as the interpolation weight to perform spatial interpolation on the initial temperature value.

[0047] First, a three-dimensional regular grid covering the entire furnace space needs to be constructed. The density of the grid points determines the spatial resolution of the final three-dimensional temperature field distribution. The temperature value of each grid point is calculated by weighted averaging of the initial temperature values ​​of all sub-regions within a certain neighborhood. The weight used for weighted averaging consists of two parts: one part is the weight value of each sub-region itself calculated in step S5, and the other part is the weight calculated based on the spatial distance from the grid point to the geometric center of each sub-region. The closer the distance, the greater the weight. The spatial distance weight is usually calculated using a power function of the reciprocal of the spatial distance. The power parameter is a real number greater than zero, used to control the rate at which the weight decays with distance. For any grid point, the interpolated temperature value of that grid point is the weighted sum of the initial temperature values ​​of all sub-regions affecting that grid point and the comprehensive weight; where the comprehensive weight refers to the combination of the weight value of the sub-region itself and the weight calculated based on the spatial distance from the grid point to the geometric center of the sub-region.

[0048] Then, a radial basis function (RBF) network is used for smoothing to generate a continuous three-dimensional temperature field. The RBF network is a neural network model used for function approximation and interpolation. In the specific implementation, the discrete grid point temperature values ​​obtained by the inverse distance weighted interpolation method are used as training samples for the RBF network. The input of the samples is the three-dimensional spatial coordinates of the grid points, and the output is the corresponding interpolated temperature value. Specifically, a three-dimensional regular grid covering the furnace space is first constructed. For each grid point, all sub-regions within its surrounding neighborhood are selected. A comprehensive weight is calculated by combining the weight value of each sub-region with the spatial distance from the grid point to the geometric center of the sub-region. The closer the distance, the greater the weight. Then, the discrete temperature value of the grid point is obtained by weighted averaging the initial temperature value of each sub-region with the corresponding comprehensive weight. The RBF network uses the Gaussian kernel function as the basis function. The mathematical form of the Gaussian kernel function is defined by the following formula:

[0049] in: It is the r-th radial basis function at point in space. The output value at that location, It is a three-dimensional coordinate vector. These are the coordinates of the center point of the r-th radial basis function. It is the width parameter of the r-th radial basis function, which controls the extent of the function's expansion around the center point. Representing a spatial point To the center point The Euclidean distance. The training process of a radial basis function network involves determining a set of center points. Width parameters The connection weights of the output layer are used to minimize the fitting error of the network to the training samples. The connection weights are usually solved using the least squares method. The trained radial basis function network can take the three-dimensional coordinates of any point in the furnace space as input and output a smooth and continuous temperature prediction value, thus forming the final three-dimensional temperature field distribution.

[0050] It is understandable that the choice of neighborhood range is crucial in the inverse distance weighted interpolation method. A neighborhood radius that is too small may result in holes in the interpolation result, while a neighborhood radius that is too large may blur local features. The neighborhood range is typically set based on the average size and distribution density of the sub-regions. The choice of the power parameter affects the smoothness of the interpolation result; a higher power value makes the contribution of neighboring points more prominent, resulting in a less smooth interpolation surface; a lower power value makes the weight distribution more uniform, resulting in a smoother interpolation surface. Configuration parameters for the radial basis function network include the number of hidden layer nodes (i.e., the number of radial basis functions), the center point selection strategy, and the width parameter. Center points can be randomly selected from the training samples or determined using clustering methods such as k-means clustering to ensure that the center points represent the data distribution. Width parameter... It can be set as a certain percentage of the average distance between all center points, or it can be set individually for each center point.

[0051] In some embodiments, the inverse distance weighted interpolation method can introduce obstacle constraints. When there are physical partitions or other structures inside the furnace, the interpolation process should avoid crossing these obstacles, which requires defining a spatial connectivity matrix. The basis functions of radial basis function networks are not limited to Gaussian kernel functions; multiple quadratic functions or inverse multiple quadratic functions can also be used, but Gaussian kernel functions have good locality and smoothness. In addition to the standard least squares method, training algorithms for radial basis function networks can also employ iterative algorithms, such as gradient descent, for large-scale problems, or use regularization techniques to prevent overfitting.

[0052] Optionally, the data fusion process can be performed in stages. For example, two-dimensional slices can be interpolated first and then stacked into a three-dimensional volume, or three-dimensional volume interpolation can be performed directly. The initial three-dimensional mesh calculated by the inverse distance weighted interpolation method can have non-uniform resolution, using a denser mesh in regions with large temperature gradients and a sparser mesh in regions with uniform temperature to improve computational efficiency. The smoothing effect of the radial basis function network can be improved by adjusting the width parameter. To control, larger Smaller values ​​produce smoother output but may lose detail; While this approach preserves more detail, it may introduce noise. Understandably, the combination of inverse distance weighted interpolation and radial basis function networks effectively transforms discrete, weighted sub-region temperature observations into a physically plausible, spatially continuous three-dimensional temperature field model. This model reflects the spatial distribution of the original data and eliminates non-physical fluctuations that may be caused by interpolation through smoothing.

[0053] Referring to Figure 3, after generating the continuous three-dimensional temperature field, step S5 further includes verifying the accuracy of the temperature field. Specifically, this involves measuring the actual temperature points inside the furnace using a thermocouple array. The thermocouple array is positioned at key locations within the furnace, including the vicinity of the burner and the central region of the furnace. These locations are typically areas with significant or representative temperature gradient changes. The thermocouple array consists of multiple standard K-type or S-type thermocouples installed according to predetermined spatial coordinates. The measuring ends of the thermocouples are inserted into the furnace through special sleeves on the furnace wall. The installation positions of the thermocouples need to be precisely calibrated and aligned with the spatial coordinate system of the three-dimensional temperature field distribution model to ensure spatial consistency. The measured values ​​of the thermocouple array are compared with the predicted values ​​of the three-dimensional temperature field at the corresponding locations. The corresponding location refers to the coordinate point where the three-dimensional coordinates of the thermocouple measurement point are projected onto the three-dimensional temperature field distribution model. The predicted temperature value at this coordinate point is extracted from the three-dimensional temperature field distribution model and compared one-to-one with the measured values ​​recorded by the thermocouples at the same time.

[0054] The mean absolute error (MAO) is calculated as an accuracy indicator. The MAO is calculated based on all measurement points and is the arithmetic mean of the absolute values ​​of the differences between the measured temperature values ​​and the predicted values ​​of the three-dimensional temperature field at all thermocouple measurement points. The formula for calculating the MAO is shown below:

[0055] in: Represents the mean absolute error. This represents the total number of valid measurement points in the thermocouple array. This represents the actual temperature value measured by the thermocouple at the i-th measurement point. This represents the predicted temperature value at the i-th measurement point extracted from the three-dimensional temperature field distribution model. The mean absolute error (MAE) is calculated based on all measurement points. If the MAE exceeds a preset threshold, the color-temperature relationship curve and weight calculation method are adjusted. The preset threshold is a value pre-set according to measurement accuracy requirements and application scenarios; for example, it can be set to 50 degrees Celsius or a certain percentage of the relative error.

[0056] Refer to Table 1, which shows typical data collected during the verification process, illustrating the coordinates, measured temperatures, and model-predicted temperatures of some thermocouple measurement points at a specific moment.

[0057] Table 1: Temperature Verification Data for Thermocouple Measurement Points

[0058] Understandably, the arrangement of the thermocouple array requires careful design to ensure that the measurement points cover representative temperature distribution areas within the furnace, especially high-temperature zones, low-temperature zones, and areas with drastic temperature changes. The installation of the thermocouples must consider high-temperature resistance, corrosion resistance, and signal transmission stability. Measurement data needs to be recorded in real-time by the data acquisition system and synchronized with the timestamps of the image acquisition system. The calculated mean absolute error objectively quantifies the overall prediction bias of the three-dimensional temperature field distribution model. If the mean absolute error exceeds a preset threshold, it indicates that the current model has significant systematic errors, and the model parameters must be corrected.

[0059] In some embodiments, the preset threshold can be set to different levels according to different operating conditions or furnace regions. For example, a stricter threshold can be set in the high-temperature zone near the burner, while a relatively lenient threshold can be set in the furnace outlet region. Measurement data from the thermocouple array can be used to calculate other error indices, such as root mean square error or maximum absolute error, as supplementary information to the mean absolute error. Adjusting the color-temperature relationship curve and weighting method is a systematic process involving a re-examination of parameter settings across multiple stages, from feature extraction to data fusion.

[0060] Optionally, the verification process can be repeated under multiple different operating loads to evaluate the robustness of the three-dimensional temperature field distribution model under different operating conditions. If the mean absolute error continues to exceed a preset threshold, it may be necessary to check the calibration status of the image acquisition equipment, the effectiveness of the preprocessing algorithm, or the measurement accuracy of the thermocouple itself. It is understood that the verification step is a crucial step in ensuring the reliability of the method in practical applications. By comparing non-contact measurement results with contact standard measurement results, it provides an objective basis for model calibration and optimization.

[0061] Referring to Figure 4, the temperature field verification results based on thermocouple array measurements are shown. The figure compares the actual measured temperatures with the model's predicted temperatures at multiple measurement points, visually presenting the differences through bar charts. Each measurement point includes the actual thermocouple reading, the model's predicted temperature value, and the calculated absolute error. Figure 4 uses a grouped bar chart format, with blue bars representing the actual thermocouple measured temperatures and red bars representing the model's predicted temperatures. Specific temperature values ​​are labeled above each bar for accurate comparison. Error values ​​are displayed in red above each group of bars, highlighting the prediction accuracy at the measurement point. By calculating the average absolute error across all measurement points, the overall prediction accuracy of the three-dimensional temperature field distribution model can be quantitatively evaluated. This metric reflects the model's reliability in practical applications and provides a benchmark for subsequent parameter optimization. Figure 4 also includes auxiliary elements such as grid lines and legends to enhance the readability and professionalism of the data.

[0062] The adjustment of the color-temperature relationship curve and the calculation of weight values ​​employ an iterative optimization algorithm, including gradient descent. This algorithm aims to minimize the mean absolute error (MAO) by updating the color-temperature mapping parameters and weight calculation parameters. The color-temperature mapping parameters are a set of coefficients defining the functional relationship between color and temperature values; for example, in a polynomial fitting model, they might include constant, linear, and quadratic coefficients, which are dimensional combinations to ensure the function output is in temperature dimensions. The weight calculation parameters are those that influence the final weight allocation during the entropy weighting method; for example, the scale factor involved in feature matrix normalization. These parameters are typically dimensionless. Gradient descent updates these parameters iteratively. The core of each iteration is calculating the gradient of the objective function (i.e., the MAO) with respect to the parameter vector to be optimized and adjusting the parameter values ​​along the negative gradient direction.

[0063] The parameter updates in gradient descent follow the formula:

[0064] in: This represents the vector consisting of all parameters to be optimized at the k-th iteration. This represents the parameter vector after the (k+1)th iteration update. The mean absolute error function represents the range of parameter values. For parameter vectors The gradient of the gradient vector is such that each component of the gradient vector has the dimension of the mean absolute error divided by the dimension of the corresponding parameter. This represents the learning rate matrix, which is a diagonal matrix where each element on the diagonal... It is the learning rate for the i-th component in the parameter vector.

[0065] Understandably, the learning rate matrix The introduction of the learning rate matrix is ​​crucial for ensuring dimensional consistency. It is not a single dimensionless scalar, but rather a matrix capable of coordinating the synchronous updating of parameters with different physical dimensions. Diagonal elements The specific value needs to be set based on the empirical range and sensitivity of the corresponding parameter. Initial values ​​are typically determined through trial and error or empirical formulas, and adaptive strategies can be used for adjustment during iteration. Gradient The calculation of is usually achieved through numerical methods, such as using the finite difference method to approximate the partial derivatives, which requires multiple calls to the complete calculation process from parameters to mean absolute error.

[0066] In some embodiments, the learning rate matrix This can be simplified to a scalar learning rate multiplied by a diagonal matrix, where the elements of the diagonal matrix are determined by the reference dimensions of the parameters, thus simplifying implementation complexity. Gradient descent can employ more advanced variants, such as momentum-based gradient descent or the Adam algorithm. These algorithms introduce momentum terms or adaptive learning rate adjustments into the update rule, but their core update steps still require maintaining dimensional consistency. Parameter vector The initial value should be as close as possible to the physical expected value to accelerate convergence and avoid getting trapped in local minima.

[0067] Referring to Figure 5, the complete process of optimizing the temperature field model parameters using the gradient descent algorithm is illustrated. The main curve in the figure shows the trend of the mean absolute error as the number of iterations changes, clearly demonstrating the effectiveness of the optimization algorithm in minimizing prediction error. The two auxiliary curves represent the dynamic adjustment process of the color mapping parameters and weight calculation parameters, respectively. The convergence characteristics of the optimization process can be observed from the error curves; the error decreases rapidly in the initial stage and then gradually stabilizes. This change pattern is consistent with the typical behavior of the gradient descent algorithm, indicating that parameter adjustment effectively improves the model's prediction performance. The fluctuations in the parameter curves reflect the algorithm's process of finding the optimal solution in the parameter space. Figure 5 also marks the key nodes in the optimization process, including the initial error, the final error, and the location of the optimal solution. These markings help to understand the effectiveness and convergence of the optimization algorithm. The dual Y-axis design allows for the simultaneous display of error changes and parameter adjustments in Figure 5, facilitating the analysis of the correlation between the two.

[0068] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art 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 appended claims and their equivalents.

Claims

1. A method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing, characterized in that, The process includes the following steps: S1: Acquire a sequence of colored flame images inside the furnace using an image acquisition device, and simultaneously record furnace structure parameters and operating parameters; S2: Preprocess the colored flame image sequence, including noise reduction and color correction; extract color features and spatial features from the preprocessed images; S3: Based on the extracted color and spatial features, the furnace space is divided into multiple sub-regions, and an initial temperature value is calculated for each sub-region; S4 Monitor the dynamic change characteristics of each sub-region in the image sequence, including color fluctuations and brightness changes, and calculate the degree of influence of each sub-region on the overall temperature field inside the furnace; S5: Assign a weight value to each sub-region based on the degree of influence and the initial temperature value; use the initial temperature value and weight value of all sub-regions to construct the three-dimensional temperature field distribution inside the furnace through a data fusion algorithm.

2. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 1, characterized in that, In step S1, the image acquisition device acquires a sequence of color flame images inside the furnace and simultaneously records the furnace structure parameters and operating parameters, including: using a high-speed digital camera to capture the flame inside the furnace at a rate of at least 100 frames per second; and simultaneously recording the furnace geometry, fuel supply rate, air flow rate, and burner type.

3. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 2, characterized in that, In step S2, the extraction of color and spatial features from the preprocessed image includes: preprocessing the colored flame image sequence by using Gaussian filtering to eliminate noise and using a white balance algorithm for color correction; converting the preprocessed image from RGB color space to Lab color space, extracting the L channel luminance value and the a and b channel color values, and calculating the gradient magnitude of each pixel in the image; in step S3, based on the extracted color and spatial features, the furnace space is divided into multiple sub-regions, and an initial temperature value is calculated for each sub-region, including: using a k-means clustering algorithm to partition the region according to the similarity of color and spatial features; and mapping the average color value of the sub-region to the temperature value by establishing a color-temperature relationship curve to obtain an initial temperature value corresponding to each sub-region.

4. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 3, characterized in that, In step S4, the dynamic change characteristics of each sub-region in the image sequence and the degree of influence of each sub-region on the overall temperature field inside the furnace are monitored. This includes: calculating the standard deviation of the color value and the average rate of change of brightness of each sub-region in the image sequence frame. The standard deviation of the color value reflects the intensity of color fluctuation, and the average rate of change of brightness reflects the speed of brightness change. The calculation of the degree of influence is based on the dynamic change characteristics. The main change patterns are extracted using the principal component analysis method, and the change contribution rate of each sub-region is calculated.

5. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 4, characterized in that, In step S5, the method for calculating the weight value includes: normalizing the degree of influence and combining it with the dispersion of the initial temperature value, and using the entropy weight method to calculate the weight value; wherein, the normalized degree of influence is positively correlated with the weight value.

6. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 5, characterized in that, In step S5, the method for constructing the three-dimensional temperature field distribution inside the furnace includes: using an inverse distance weighted interpolation method, taking the weight value of each sub-region as the interpolation weight, spatially interpolating the initial temperature value, and then using a radial basis function network for smoothing to generate a continuous three-dimensional temperature field.

7. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 6, characterized in that, In the inverse distance weighted interpolation method, the interpolation weight of each sub-region is calculated based on the spatial distance between the sub-region and its neighboring sub-regions, with the weight increasing as the distance increases. The radial basis function network uses a Gaussian kernel function as the basis function and learns the distribution of the interpolated temperature data through training.

8. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 6, characterized in that, After the continuous three-dimensional temperature field is generated, step S5 further includes verifying the accuracy of the temperature field. The specific steps include: measuring the actual temperature point inside the furnace through a thermocouple array, comparing the measured value with the predicted value of the three-dimensional temperature field at the corresponding location, and calculating the average absolute error as an accuracy index.

9. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 8, characterized in that, In the step of verifying the accuracy of the temperature field, the thermocouple array is arranged in key positions inside the furnace, including near the burner and in the central area of ​​the furnace; the calculation of the mean absolute error is based on all measurement points, and if the mean absolute error exceeds a preset threshold, the color-temperature relationship curve and the weight value calculation method are adjusted.

10. The method for detecting three-dimensional temperature field distribution inside a furnace based on color flame image processing according to claim 9, characterized in that, The steps of adjusting the color-temperature relationship curve and weight value calculation method include: using an iterative optimization algorithm, including gradient descent, to minimize the mean absolute error, updating the color-temperature mapping parameters and weight calculation parameters, and then re-executing steps S1 to S5 until the mean absolute error is lower than a preset threshold.

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