Fractal dimension-based industrial flue gas carbon monitoring and early warning method and system

Abstract

The application discloses a kind of industrial flue gas carbon monitoring early warning method and system based on fractal dimension, it is related to environmental protection field, comprising: based on continuous carbon monitoring data, first fractal dimension of t time and t-1 time is obtained using box covering algorithm respectively, second fractal dimension of t time and t-1 time is obtained using sphere covering algorithm respectively;First fractal dimension change rate is calculated based on the first fractal dimension of t time and t-1 time;Second fractal dimension change rate is calculated based on the second fractal dimension of t time and t-1 time;Determine the change rate correlation coefficient of first fractal dimension change rate and second fractal dimension change rate;Fractal dimension comprehensive change rate is calculated based on first fractal dimension change rate, second fractal dimension change rate and change rate correlation coefficient;When the absolute value of fractal dimension comprehensive change rate is greater than or equal to early warning critical value, generate industrial flue gas carbon emission abnormal alarm signal.The application realizes the effective monitoring of industrial flue gas carbon emission.

Description

Technical Field

[0001] This invention relates to the field of environmental protection technology, and in particular to a method and system for monitoring and early warning of carbon emissions from industrial flue gas based on fractal dimension. Background Technology

[0002] Carbon monitoring by industrial enterprises is fundamental to achieving coordinated pollution and carbon reduction. Accurately understanding industrial carbon emission data allows for the scientific formulation of emission reduction targets and measures, promoting the green and low-carbon transformation of industrial enterprises. Continuous monitoring of industrial flue gas carbon emissions helps industrial enterprises identify the main links and sources of carbon emissions, pinpoint potential and space for energy conservation and emission reduction, and thus optimize production processes and improve energy efficiency, achieving coordinated reduction of pollutants and greenhouse gases. However, industrial enterprises face challenges in maintaining production levels while monitoring carbon dioxide emissions to ensure they do not exceed standards. In practical engineering, excessive carbon dioxide emissions fail to meet environmental requirements, necessitating a reduction in production volume. Conversely, if existing low-carbon technologies and equipment remain unchanged, controlling carbon dioxide emissions far below environmental standards may limit production volume and negatively impact industrial enterprise revenue. Therefore, precise and continuous monitoring of industrial flue gas carbon emissions is crucial for effectively achieving carbon reduction goals for industrial enterprises.

[0003] Currently, the application of continuous monitoring of industrial flue gas carbon emissions in my country is limited. It mainly relies on manual inspection and maintenance, and carbon emissions are generally calculated based on fuel consumption and emission factor coefficients, failing to achieve truly continuous monitoring. Therefore, existing technologies cannot effectively monitor industrial flue gas carbon emissions. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for monitoring and early warning of carbon emissions from industrial flue gas based on fractal dimension, thereby achieving effective monitoring of carbon emissions from industrial flue gas.

[0005] To achieve the above objectives, the embodiments of the present invention provide the following solutions.

[0006] A method for monitoring and early warning of carbon in industrial flue gas based on fractal dimension includes: acquiring continuous carbon monitoring data at time t and time t-1 within a set time period; the carbon monitoring data includes at least carbon dioxide mass data; based on the continuous carbon monitoring data at time t, obtaining the first fractal dimension at time t using a box-covering algorithm and the second fractal dimension at time t using a sphere-covering algorithm; based on the continuous carbon monitoring data at time t-1, obtaining the first fractal dimension at time t-1 using a box-covering algorithm and the second fractal dimension at time t-1 using a sphere-covering algorithm; and based on the first fractal dimension at time t... The first fractal dimension change rate is calculated based on the first fractal dimension at time t-1; the second fractal dimension change rate is calculated based on the second fractal dimension at time t and time t-1; the correlation coefficient between the first and second fractal dimension change rates is determined; the comprehensive fractal dimension change rate is calculated based on the first, second, and correlation coefficients; and an industrial flue gas carbon emission anomaly alarm signal is generated when the absolute value of the comprehensive fractal dimension change rate is greater than or equal to the warning threshold.

[0007] Optionally, the box-covering algorithm is used to obtain the first fractal dimension at time t, specifically including: dividing the continuous carbon monitoring data at time t into multiple sub-intervals, and determining the number of non-repeating elements in each sub-interval; the number of non-repeating elements is the number of carbon monitoring data with different values ​​in the sub-interval; wherein, each sub-interval has the same interval length; calculating the average number of non-repeating elements based on the number of non-repeating elements in all sub-intervals; changing the interval length of the sub-intervals and calculating the average number of non-repeating elements under different interval lengths; establishing a first linear relationship using the least squares method based on the interval lengths of different sub-intervals and the average number of non-repeating elements under different interval lengths; the first linear relationship is the linear relationship between the average number of non-repeating elements after logarithmic operation and the interval length of the sub-interval after logarithmic operation; and obtaining the first fractal dimension at time t based on the first linear relationship.

[0008] Optionally, the first linear relationship is: In the formula, This represents the average number of unique elements. Let be the first fractal dimension at time t. Indicated by v Logarithmic operations with base 0. Let be the length of the sub-interval. It is the first constant.

[0009] Optionally, the second fractal dimension at time t is obtained using a sphere covering algorithm, specifically including: setting the sphere radius and calculating the minimum number of spheres required to cover continuous carbon monitoring data at time t; changing the value of the sphere radius to obtain the minimum number of spheres under different sphere radii; establishing a second linear relationship based on all sphere radii and the minimum number of spheres under all sphere radii using the least squares method; the second linear relationship is the linear relationship between the minimum number of spheres after logarithmic operation and the sphere radius after logarithmic operation; and obtaining the second fractal dimension at time t based on the second linear relationship.

[0010] Optionally, the second linear relationship is: In the formula, To find the minimum number of balls, Let be the second fractal dimension at time t. Indicated by v Logarithmic operations with base 0. Let the radius of the sphere be . It is the second constant.

[0011] Optionally, determining the correlation coefficient between the rate of change of the first fractal dimension and the rate of change of the second fractal dimension specifically includes: calculating the correlation coefficient using the Pearson correlation coefficient method, the Spearman correlation coefficient method, or the Kendall rank correlation coefficient method.

[0012] Optionally, calculating the comprehensive change rate of fractal dimension based on the first fractal dimension change rate, the second fractal dimension change rate, and the change rate correlation coefficient specifically includes: determining the change rate weight based on the change rate correlation coefficient and a set threshold; the set threshold includes: a first set threshold and a second set threshold; the change rate weight includes: a first weight and a second weight; and calculating the comprehensive change rate of fractal dimension based on the first weight, the first fractal dimension change rate, the second weight, and the second fractal dimension change rate.

[0013] Optionally, the change rate weight is determined based on the change rate correlation coefficient and a set threshold, specifically including: when the change rate correlation coefficient is less than the first set threshold.

[0014] .

[0015] .

[0016] .

[0017] .

[0018] In the formula, As the first weight, As the second weight, The first coefficient of variation, The second coefficient of variation, To set the length of the time period, The rate of change of the first fractal dimension. is the rate of change of the second fractal dimension.

[0019] When the correlation coefficient of the rate of change is greater than or equal to the first set threshold and less than the second set threshold.

[0020] .

[0021] .

[0022] In the formula, The correlation coefficient is the rate of change. This is for absolute value operations.

[0023] When the correlation coefficient of the rate of change is greater than or equal to the second set threshold: .

[0024] Optionally, the comprehensive rate of change of fractal dimension is calculated based on the first weight, the first rate of change of fractal dimension, the second weight, and the second rate of change of fractal dimension, specifically as follows: In the formula, The combined rate of change of fractal dimension As the first weight, As the second weight, The rate of change of the first fractal dimension. is the rate of change of the second fractal dimension.

[0025] A computer system includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the fractal dimension-based industrial flue gas carbon monitoring and early warning method.

[0026] According to the specific embodiments provided in this invention, the present invention discloses the following technical effects:

[0027] To reduce the uncertainty in judging abnormal industrial flue gas carbon emissions, this invention employs both box-covering and sphere-covering algorithms to process continuous carbon monitoring data, resulting in two different fractal dimensions: a first fractal dimension and a second fractal dimension, thus increasing the reliability of the fractal dimensions. Secondly, the rates of change of the first and second fractal dimensions are calculated separately, and the overall rate of change of the fractal dimensions is further calculated by determining the correlation coefficient between the two rates of change. This processed overall rate of change of the fractal dimensions reduces the uncertainty and redundancy of the fractal dimensions, and comparing the overall rate of change of the fractal dimensions with the warning threshold is more reliable than directly comparing the fractal dimensions with the warning threshold. Therefore, this invention, by considering continuous carbon monitoring data and comparing the overall rate of change of fractal dimensions, ensures the effectiveness of industrial flue gas carbon emission monitoring. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 A flowchart of an industrial flue gas carbon monitoring and early warning method based on fractal dimension provided in an embodiment of the present invention. Detailed Implementation

[0030] 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.

[0031] The purpose of this invention is to provide a method and system for monitoring and early warning of carbon emissions from industrial flue gas based on fractal dimension, thereby achieving effective monitoring of carbon emissions from industrial flue gas.

[0032] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0033] like Figure 1 As shown in the figure, an industrial flue gas carbon monitoring and early warning method based on fractal dimension is provided by an embodiment of the present invention, as detailed below.

[0034] Step S1: Acquire continuous carbon monitoring data at time t and time t-1 within a set time period; wherein, the carbon monitoring data includes at least one of the following: carbon dioxide mass data (in tons), carbon dioxide mass concentration data (in grams per cubic meter), and carbon dioxide volume concentration data (in volume percentage). In specific implementation, multiple gas concentration sensors can be installed at different locations on the industrial emission chimney to monitor the carbon dioxide concentration. Simultaneously, these multiple gas concentration sensors are connected to a computer platform in the main control room via signal transmission lines to collect and acquire carbon monitoring data at different time periods in real time.

[0035] Step S2: Based on continuous carbon monitoring data at time t, the first fractal dimension at time t is obtained by using the box covering algorithm, and the second fractal dimension at time t is obtained by using the sphere covering algorithm.

[0036] In this embodiment, the box covering algorithm is used to obtain the first fractal dimension at time t, as follows.

[0037] The first step is to process the continuous carbon monitoring data at time t. Divide into multiple sub-intervals of equal length and Determine the number of unique elements in each subinterval. The number of non-repeating elements is the number of carbon monitoring data points with different values ​​in the sub-interval. Among them, Let be the nth carbon monitoring data in the continuous carbon monitoring data at time t. For the carbon monitoring data at the starting position in the j-th sub-interval, For the carbon monitoring data at the end position in the j-th sub-interval, M The number of subintervals. Let be the number of non-repeating elements in the j-th subinterval.

[0038] The second step is to calculate the average number of unique elements based on the number of unique elements in all sub-intervals. That is, satisfying: .

[0039] The third step is to change the interval length of the sub-interval. h Calculate the average number of non-repeating elements for different interval lengths.

[0040] The fourth step involves establishing a first linear relationship based on the interval lengths of different sub-intervals and the average number of non-repeating elements under different interval lengths, using the least squares method. This first linear relationship is the linear relationship between the average number of non-repeating elements after logarithmic operation and the interval length of the sub-interval after logarithmic operation. The first linear relationship is as follows.

[0041] .

[0042] In the formula, Let be the first fractal dimension at time t. Indicated by v Logarithmic operations with base (for base) v There is no specific limit to the value; it can be based on a base of 10. Operations can also be performed using constants. e base In this embodiment, the operation is performed using a constant. e (Base number) It is the first constant.

[0043] Fifth step: Obtain the first fractal dimension at time t based on the first linear relationship. .

[0044] In this embodiment, the second fractal dimension at time t is obtained using the sphere covering algorithm, as detailed below.

[0045] The first step is to set the sphere radius r and calculate the minimum number of spheres required to cover continuous carbon monitoring data at time t, i.e., to satisfy... and ;in, To find the minimum number of balls, For the i-th carbon monitoring data, Indicated by Centered on, with r A sphere with radius , Let L be the union of L balls. Includes All elements.

[0046] The second step is to change the sphere radius. r The value of is used to obtain the minimum number of balls for different ball radii.

[0047] The third step involves establishing a second linear relationship based on all sphere radii and the minimum number of spheres under all sphere radii, using the least squares method. This second linear relationship is the linear relationship between the minimum number of spheres after logarithmic operations and the sphere radii after logarithmic operations. The second linear relationship is as follows.

[0048] .

[0049] In the formula, Let be the second fractal dimension at time t. It is the second constant.

[0050] The fourth step is to obtain the second fractal dimension at time t based on the second linear relationship. .

[0051] Step S3: Based on the continuous carbon monitoring data at time t-1, the first fractal dimension at time t-1 is obtained using the box covering algorithm. The second fractal dimension at time t-1 is obtained using the sphere covering algorithm. ;in, and The determination process and step 2 and The determination process is the same, the difference is that the carbon monitoring data involved in steps 2 and 3 are different.

[0052] Step S4: First fractal dimension based on time t and the first fractal dimension at time t-1 Calculate the rate of change of the first fractal dimension That is, satisfying: .

[0053] Step S5: Second fractal dimension based on time t and the second fractal dimension at time t-1 Calculate the rate of change of the second fractal dimension That is, satisfying: .

[0054] Step S6: Determine the rate of change of the first fractal dimension Second fractal dimension change rate rate of change correlation coefficient In this embodiment, the Pearson correlation coefficient method, Spearman correlation coefficient method, or Kendall rank correlation coefficient method can be used to calculate the rate of change correlation coefficient. If multiple algorithms are used to calculate the correlation coefficient of rate of change, then the average of all the obtained correlation coefficients of rate of change needs to be calculated, and this average value is used as the final correlation coefficient of rate of change. .

[0055] Step S7: Based on the rate of change of the first fractal dimension Rate of change of the second fractal dimension Correlation coefficient with rate of change Calculate the overall rate of change of fractal dimension .

[0056] In this embodiment, step S7 is as follows.

[0057] Step S71: Based on the correlation coefficient of the rate of change The change rate weights are determined by setting thresholds; the thresholds include a first threshold and a second threshold; the change rate weights include a first weight and a second weight. The first weight... Second weight The process of determining is as follows.

[0058] When the rate of change correlation coefficient When the value is less than a first preset threshold (in this embodiment, the first preset threshold is 0.5), the first weight... Second weight The following relationship is satisfied.

[0059] .

[0060] .

[0061] .

[0062] .

[0063] In the formula, The first coefficient of variation, The second coefficient of variation, Set the length of the time period.

[0064] When the rate of change correlation coefficient When the first weight is greater than or equal to the first set threshold and less than the second set threshold (the second set threshold is 0.8 in this embodiment), the first weight... Second weight The following relationship is satisfied.

[0065] .

[0066] .

[0067] In the formula, This is for absolute value operations.

[0068] When the rate of change correlation coefficient When the threshold is greater than or equal to the second set threshold: .

[0069] Step S72: Based on the first weight Rate of change of the first fractal dimension Second weight Second fractal dimension change rate Calculate the overall rate of change of fractal dimension The details are as follows.

[0070] .

[0071] Step S8: When the absolute value of the combined rate of change of the fractal dimension is greater than or equal to the warning threshold. When an industrial flue gas carbon emission anomaly alarm signal is generated, it is necessary to effectively control the industrial flue gas carbon monitoring system (including at least the gas concentration sensors, signal transmission lines, and computer platform mentioned in step 1) and check whether the industrial flue gas carbon monitoring system is functioning properly. If the industrial flue gas carbon monitoring system is malfunctioning, it is necessary to troubleshoot the faulty parts one by one and repair or replace them in a timely manner, such as replacing the gas concentration sensor in the faulty part; if the industrial flue gas carbon monitoring system is functioning properly, it is necessary to adjust the production workload of the emission source and recalculate the comprehensive change rate of the fractal dimension after the production workload adjustment to ensure that it meets the requirements. And control it at the optimal production volume.

[0072] To better verify the effectiveness of the aforementioned industrial flue gas carbon monitoring and early warning method based on fractal dimension, this embodiment of the invention uses hourly data, acquiring 2000 continuous carbon monitoring data points over 24 hours and treating them as a sequence. Based on this sequence, the first fractal dimension at different times is obtained using the calculation methods in steps S2 to S5. Second fractal dimension Rate of change of the first fractal dimension Second fractal dimension change rate For specific data, please refer to Table 1.

[0073] Table 1. Results of fractal dimension and rate of change of fractal dimension

[0074]

[0075] Secondly, the Pearson correlation coefficient method is used to calculate... and The correlation coefficient of the rate of change was obtained Then, based on the judgment method in step S71, determine the first coefficient of variation. Second coefficient of variation And thus obtain , Based on the above data, the overall rate of change of fractal dimension at different times is calculated using step S72. For specific data, please refer to Table 2.

[0076] Table 2 Results of Fractal Dimension Change Rate and Overall Change Rate

[0077]

[0078] When the absolute value of the combined rate of change of the fractal dimension (Warning threshold) Take 3%, or adjust according to the actual project requirements. When the value is specified, an abnormal industrial flue gas carbon emission alarm signal is issued, and the industrial flue gas carbon monitoring system is checked for normal operation. If the industrial flue gas carbon monitoring system is abnormal, it is repaired or replaced in a timely manner; if the industrial flue gas carbon monitoring system is normal, the production operation volume of the emission source is adjusted to ensure that... And control it at the optimal production volume.

[0079] Furthermore, embodiments of the present invention also provide a computer system, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described industrial flue gas carbon monitoring and early warning method based on fractal dimension.

[0080] In summary, the present invention also has the following technical effects.

[0081] 1) Effectively reduces human workload and improves objectivity. This invention, through fractal analysis of carbon monitoring data of industrial flue gas, can automatically identify abnormal carbon emissions and issue early warning signals, greatly reducing the workload of existing manual inspection methods and effectively avoiding the subjective influence of manual inspection methods.

[0082] 2) Improve the efficiency of system equipment maintenance and upkeep. This invention uses the rate of change of fractal dimension to predict abnormal carbon emissions in industrial flue gas, effectively achieving predictive maintenance. It provides a long lead time, reduces the frequency of regular manual inspections, and improves overall operation and maintenance efficiency.

[0083] 3) High accuracy, high reliability, and high degree of automation. The process of acquiring continuous carbon monitoring data, constructing fractal dimension, and calculating correlation coefficients in this invention includes redundant design and considerations, ensuring the accuracy and reliability of the calculation results.

[0084] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0085] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for monitoring and early warning of carbon in industrial flue gas based on fractal dimension, characterized in that, include: Acquire continuous carbon monitoring data at time t and time t-1 within a set time period; The carbon monitoring data includes at least carbon dioxide mass data; Based on continuous carbon monitoring data at time t, the first fractal dimension at time t is obtained by using the box covering algorithm, and the second fractal dimension at time t is obtained by using the sphere covering algorithm. Based on continuous carbon monitoring data at time t-1, the first fractal dimension at time t-1 is obtained by using the box covering algorithm, and the second fractal dimension at time t-1 is obtained by using the sphere covering algorithm. Calculate the rate of change of the first fractal dimension based on the first fractal dimension at time t and time t-1; Calculate the rate of change of the second fractal dimension based on the second fractal dimension at time t and time t-1; Determine the correlation coefficient between the rate of change of the first fractal dimension and the rate of change of the second fractal dimension; The comprehensive change rate of fractal dimension is calculated based on the first fractal dimension change rate, the second fractal dimension change rate, and the correlation coefficient of the change rate. When the absolute value of the comprehensive rate of change of the fractal dimension is greater than or equal to the warning threshold, an alarm signal for abnormal carbon emissions of industrial flue gas is generated.

2. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 1, characterized in that, The first fractal dimension at time t is obtained using the box covering algorithm, specifically including: The continuous carbon monitoring data at time t is divided into multiple sub-intervals, and the number of non-repeating elements in each sub-interval is determined; the number of non-repeating elements is the number of carbon monitoring data with different values ​​in the sub-interval; wherein, each sub-interval has the same length. Calculate the average number of non-repeating elements based on the number of non-repeating elements in all sub-intervals; Change the interval length of the sub-interval and calculate the average number of non-repeating elements under different interval lengths; Based on the interval lengths of different sub-intervals and the average number of non-repeating elements under different interval lengths, the least squares method is used to establish the first linear relationship; the first linear relationship is the linear relationship between the average number of non-repeating elements after logarithmic operation and the interval length of the sub-interval after logarithmic operation. The first fractal dimension at time t is obtained based on the first linear relationship.

3. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 2, characterized in that, The first linear relationship is: ； In the formula, This represents the average number of unique elements. Let be the first fractal dimension at time t. Indicated by v Logarithmic operations with base 0. Let be the length of the sub-interval. It is the first constant.

4. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 1, characterized in that, The second fractal dimension at time t is obtained using the sphere covering algorithm, specifically including: Set the sphere radius and calculate the minimum number of spheres required to cover continuous carbon monitoring data at time t; By changing the value of the ball radius, the minimum number of balls can be obtained for different ball radii; Based on all sphere radii and the minimum number of spheres under all sphere radii, a second linear relationship is established using the least squares method; the second linear relationship is the linear relationship between the minimum number of spheres after logarithmic operation and the sphere radius after logarithmic operation. The second fractal dimension at time t is obtained based on the second linear relationship.

5. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 4, characterized in that, The second linear relationship is: ； In the formula, To find the minimum number of balls, Let be the second fractal dimension at time t. Indicated by v Logarithmic operations with base 0. Let the radius of the sphere be . It is the second constant.

6. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 1, characterized in that, Determining the correlation coefficient between the rate of change of the first fractal dimension and the rate of change of the second fractal dimension specifically includes: The correlation coefficient of the rate of change is calculated using the Pearson correlation coefficient method, the Spearman correlation coefficient method, or the Kendall rank correlation coefficient method.

7. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 1, characterized in that, The comprehensive rate of change of fractal dimension is calculated based on the first rate of change of fractal dimension, the second rate of change of fractal dimension, and the correlation coefficient of the rate of change. Specifically, this includes: The weight of the rate of change is determined based on the correlation coefficient of the rate of change and a set threshold; the set threshold includes: a first set threshold and a second set threshold; the weight of the rate of change includes: a first weight and a second weight. The comprehensive rate of change of fractal dimension is calculated based on the first weight, the first rate of change of fractal dimension, the second weight, and the second rate of change of fractal dimension.

8. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 7, characterized in that, The weight of the rate of change is determined based on the correlation coefficient of the rate of change and a set threshold, specifically including: When the rate of change correlation coefficient is less than the first preset threshold: ； ； ； ； In the formula, As the first weight, As the second weight, The first coefficient of variation, The second coefficient of variation, To set the length of the time period, The rate of change of the first fractal dimension. The rate of change of the second fractal dimension; When the correlation coefficient of the rate of change is greater than or equal to the first preset threshold and less than the second preset threshold: ； ； In the formula, The correlation coefficient is the rate of change. This is for absolute value operations; When the correlation coefficient of the rate of change is greater than or equal to the second set threshold: .

9. The industrial flue gas carbon monitoring and early warning method based on fractal dimension according to claim 7, characterized in that, The comprehensive rate of change of fractal dimension is calculated based on the first weight, the first rate of change of fractal dimension, the second weight, and the second rate of change of fractal dimension, specifically as follows: ； In the formula, The combined rate of change of fractal dimension As the first weight, As the second weight, The rate of change of the first fractal dimension. is the rate of change of the second fractal dimension.

10. A computer system, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the industrial flue gas carbon monitoring and early warning method based on fractal dimension as described in any one of claims 1-9.

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