A clinker firing parameter feasibility analysis method based on kernel density estimation

Abstract

The application provides a clinker firing parameter feasibility analysis method based on kernel density estimation, and belongs to the technical field of cement production control. An industrial computer collects control parameter data in a historical operation process of a cement production line, and establishes a historical sample data set; the collected control parameter data is cleaned and preprocessed, outliers are removed, and standardization processing is performed; a one-dimensional kernel density estimation model is established for each control parameter data; before being output to an actuator, the control parameter data is input into the above one-dimensional kernel density estimation model, a probability density value is calculated, a plurality of probability density values are weighted and superimposed, and a joint probability density value is obtained; the obtained joint probability density value is compared with a feasibility threshold value, and when the joint probability density value is greater than or equal to the feasibility threshold value, it is judged that the control parameter data can be used for actual operation. The application evaluates the feasibility of the control parameter recommended by the model, and guarantees the safety of cement production.

Description

Technical Field

[0001] This invention belongs to the field of cement production control technology. Specifically, this invention relates to a feasibility analysis method for clinker calcination parameters based on kernel density estimation. Background Technology

[0002] In cement production, clinker calcination is a crucial step determining cement performance and energy consumption levels, and its quality directly impacts product stability and economic efficiency. The clinker calcination process typically involves several key control parameters, including kiln feed rate, high-temperature blower speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and preheater coal feed rate. The proper configuration of these parameters is essential for ensuring stable clinker calcination temperature, improving thermal efficiency, and reducing energy consumption. Currently, in industrial production, the setting of clinker calcination parameters mainly relies on the experience and judgment of operators. Experienced operators can usually manually adjust parameters based on production conditions and historical trends to ensure clinker quality. However, this method suffers from significant subjectivity and instability; different operators may make different adjustment decisions for the same production conditions, leading to inconsistent parameter settings. Furthermore, in recent years, some companies have attempted to use machine learning models to model historical data and recommend parameter combinations through algorithms to achieve intelligent control. However, the parameter combinations recommended by such methods sometimes exceed the feasible operating conditions and are difficult to apply directly in actual production.

[0003] Chinese Patent 116294660A discloses a method for optimizing and controlling the head coal pressure of a cement kiln, including: 1) determining limiting conditions, including kiln condition index limits, kiln current limits, secondary air temperature limits, and ammonia flow trend limits; 2) calculating recommended values, calculating the recommended values ​​of the relevant parameters on the kiln output based on the limiting conditions of each parameter initially determined in the previous step; 3) selecting recommended values, selecting recommended values ​​from the order of priority: recommended kiln condition comprehensive index, recommended kiln current magnitude, recommended secondary air temperature, head coal to tail coal ratio, recommended ambient temperature, and recommended NOx in the kiln tail flue, to obtain the recommended value selection result; 4) calculating the head coal recommended value and adjusting the cement kiln head coal pressure. This step adjusts the head coal feed rate based on the head coal recommended value. The formula for the head coal recommended value is: Head coal recommended value = current set value + recommended value selection result.

[0004] The existing technology does not assess the feasibility of the recommended control parameters, which may result in recommended parameter combinations sometimes exceeding the range of feasible operating conditions, causing production failures. Summary of the Invention

[0005] The present invention aims to provide a feasibility analysis method for clinker calcination parameters based on kernel density estimation, so as to evaluate the feasibility of recommended control parameters and ensure the safety of cement production.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] This invention provides a method for feasibility analysis of clinker calcination parameters based on kernel density estimation, comprising the following steps:

[0008] Step 1: The industrial control computer collects control parameter data from the historical operation of the cement production line and establishes a historical sample dataset;

[0009] Step 2: Clean and preprocess the collected control parameter data, remove outliers and standardize them;

[0010] Step 3: Establish a one-dimensional kernel density estimation model for each control parameter data;

[0011] Step 4: Before the control parameter data is output to the actuator, it is first input into the above one-dimensional kernel density estimation model to calculate the probability density value. Then, multiple probability density values ​​are weighted and superimposed to obtain the joint probability density value.

[0012] Step 5: Compare the obtained joint probability density value with the feasibility threshold. When the joint probability density value is greater than or equal to the feasibility threshold, it is determined that the control parameter data can be used for actual operation.

[0013] In step one, the collected control parameter data includes the kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and decomposer coal feed rate.

[0014] In step three, the formula for the one-dimensional kernel density estimation function of the one-dimensional kernel density estimation model is:

[0015] ;

[0016] Where x represents the control parameter data to be verified, x i Let be the i-th sampled value in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, and K(·) be the kernel function.

[0017] In step three, under the scenario of multi-parameter joint analysis, a multi-dimensional joint kernel density estimation model is established for multiple control parameter data. The multi-dimensional kernel density estimation function formula of the multi-dimensional joint kernel density estimation model is as follows:

[0018] ;

[0019] Where x j For the control parameter data to be verified, x ij Let be the j-th component of the i-th sample in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, K(·) be the kernel function, and d be the dimension of the data.

[0020] When a Gaussian kernel is used as the kernel function, the kernel function formula is:

[0021] .

[0022] Alternatively, the Epanechnikov kernel can be used as the kernel function. The kernel function formula is as follows:

[0023] .

[0024] The bandwidth parameter of the one-dimensional kernel density estimation function is determined using the Silverman rule, and the calculation formula is as follows:

[0025] ;

[0026] in denoted as , where is the standard deviation of the historical sample data in the historical sample dataset, and n is the number of historical sample data.

[0027] The bandwidth parameter of the multidimensional joint kernel density estimation model is determined by cross-validation.

[0028] The historical sample dataset is updated regularly, and the one-dimensional kernel density estimation model is also updated.

[0029] The technical effects of this invention are as follows:

[0030] (1) By introducing a kernel density estimation model, this invention provides a feasibility verification mechanism for the control parameters recommended by machine learning, which can effectively avoid the recommended parameters from exceeding the reasonable range of history, thereby significantly improving the accuracy and safety of parameter settings.

[0031] (2) This invention reduces subjective interference from human experience by using quantitative judgment of probability density, thereby improving the stability and consistency of the clinker firing process. Furthermore,

[0032] (3) This invention takes data-driven approach as its core, making full use of historical production information and avoiding the limitations of relying on manual adjustment. Since kernel density estimation does not depend on any distribution assumptions, the model has strong universality and adaptability, and can be widely applied to production scenarios with different kiln types, different raw material ratios and different operating conditions.

[0033] (4) The present invention continuously learns new data through a dynamic update mechanism to ensure the timeliness and accuracy of the analysis results.

[0034] (5) The present invention has strong adaptability to different working conditions. It can adapt to key control scenarios with single parameters, as well as complex working conditions with multiple parameters coupled, taking into account both local parameter characteristics and overall combination effect.

[0035] (6) The present invention effectively improves the level of intelligent control of the clinker calcination process, reduces energy consumption, and improves production efficiency. Attached Figure Description

[0036] This manual includes the following figures, which illustrate the following:

[0037] Figure 1 This is a flowchart of a feasibility analysis method for clinker calcination parameters based on kernel density estimation according to the present invention. Detailed Implementation

[0038] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings, in order to help those skilled in the art to have a more complete, accurate and in-depth understanding of the inventive concept and technical solution of the present invention, and to facilitate its implementation.

[0039] This invention provides a method for feasibility analysis of clinker calcination parameters based on kernel density estimation, comprising the following steps:

[0040] Step 1: The industrial control computer collects control parameter data from the historical operation of the cement production line and establishes a historical sample dataset;

[0041] Step 2: Clean and preprocess the collected control parameter data, remove outliers and standardize them;

[0042] Step 3: Establish a one-dimensional kernel density estimation model for each control parameter data;

[0043] Step 4: Before the control parameter data is output to the actuator, it is first input into the above one-dimensional kernel density estimation model to calculate the probability density value. Then, multiple probability density values ​​are weighted and superimposed to obtain the joint probability density value.

[0044] Step 5: Compare the obtained joint probability density value with the feasibility threshold. When the joint probability density value is greater than or equal to the feasibility threshold, it is determined that the control parameter data can be used for actual operation.

[0045] In step one, the collected control parameter data includes the kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and decomposer coal feed rate.

[0046] In step three, the formula for the one-dimensional kernel density estimation function of the one-dimensional kernel density estimation model is:

[0047] ;

[0048] Where x represents the control parameter data to be verified, x iLet be the i-th sampled value in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, and K(·) be the kernel function.

[0049] In step three, under the scenario of multi-parameter joint analysis, a multi-dimensional joint kernel density estimation model is established for multiple control parameter data. The multi-dimensional kernel density estimation function formula of the multi-dimensional joint kernel density estimation model is as follows:

[0050] ;

[0051] Where x j For the control parameter data to be verified, x ij Let be the j-th component of the i-th sample in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, K(·) be the kernel function, and d be the dimension of the data.

[0052] When a Gaussian kernel is used as the kernel function, the kernel function formula is:

[0053] .

[0054] Alternatively, the Epanechnikov kernel can be used as the kernel function. The kernel function formula is as follows:

[0055] .

[0056] The bandwidth parameter of the one-dimensional kernel density estimation function is determined using the Silverman rule, and the calculation formula is as follows:

[0057] ;

[0058] in denoted as , where is the standard deviation of the historical sample data in the historical sample dataset, and n is the number of historical sample data.

[0059] The bandwidth parameter of the multidimensional joint kernel density estimation model is determined by cross-validation.

[0060] The historical sample dataset is updated regularly, and the one-dimensional kernel density estimation model is also updated.

[0061] The following is a detailed description of the feasibility analysis method for clinker calcination parameters based on kernel density estimation according to the present invention.

[0062] An industrial control computer collects key control parameter data from the historical operation of a cement production line. In this embodiment, the collected control parameter data includes seven parameters: kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and preheater coal feed rate. The collected data is then cleaned and preprocessed, outliers are removed, and the data is standardized to ensure its usability. This invention specifically collects core control parameters for cement production, comprehensively covering key processes in clinker calcination. The established historical sample dataset accurately reflects the actual production operation status, providing complete data support for subsequent feasibility analysis.

[0063] Next, a one-dimensional kernel density estimation model is established for each control parameter, or a multi-dimensional joint kernel density estimation model is used, wherein the formula for the one-dimensional kernel density estimation function is:

[0064]

[0065] Where x represents the control parameter data to be verified, x i Let be the i-th sampled value in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, and K(·) be the kernel function.

[0066] In the context of multi-parameter joint analysis, the mathematical expression of the multidimensional joint kernel density estimation model is:

[0067]

[0068] Where x j For the control parameter data to be verified, x ij Let be the j-th component of the i-th sample in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, K(·) be the kernel function, and d be the dimension of the data. The above formula can characterize the joint distribution features of multiple control parameters under historical operating conditions within the same probability space.

[0069] The kernel function in the above formula is used to measure the influence weight of the sample points on the probability density of the target parameter value. It can be selected according to the distribution characteristics of historical data. In this invention, the kernel function can be the Gaussian kernel function or the Epanechnikov kernel function.

[0070] The mathematical expression for the Gaussian kernel function is:

[0071]

[0072] Where exp(x) = e x .

[0073] The Gaussian kernel function is characterized by its continuity, smoothness, and infinite support domain. It is suitable for working conditions where the control parameters of clinker calcination change continuously over time, the historical sample distribution is relatively smooth, or there are long-tailed characteristics.

[0074] The mathematical expression for the Epanechnikov kernel function is:

[0075] The value is valid when |u|≤1 and zero when |u|>1. This kernel function has a finite support domain characteristic, which can highlight the distribution characteristics of the parameter within the local historical operating conditions range, thereby reducing the influence of remote samples on the probability density estimation results.

[0076] The bandwidth parameter (h) in the kernel density estimation model described above controls the smoothness of the probability density curve. Its value directly affects the accuracy of the model in depicting historical operating conditions. When the sample size is large and the distribution is relatively stable, the Silverman rule can be used to automatically determine the bandwidth parameter. The calculation formula is as follows:

[0077]

[0078] in denoted as , where is the standard deviation of the historical sample data in the historical sample dataset, and n is the number of historical sample data.

[0079] In cases where historical data distribution is complex, exhibits multi-peak distribution, or production conditions change frequently, this embodiment employs cross-validation to determine the bandwidth parameter of the kernel density estimation model. The industrial control computer uses historical stable operating data of a specific clinker calcination control parameter (e.g., kiln feed rate) as a sample set. Based on the dispersion of the sample data, multiple candidate bandwidth parameter values ​​are selected. Each candidate bandwidth parameter is evaluated using leave-one-out cross-validation, which involves sequentially removing individual samples from the sample set and constructing a kernel density estimation model using the remaining sample data. The probability density estimate of the removed samples under this model is calculated. By summarizing the probability density estimates for all samples, the overall probability density estimation error corresponding to the candidate bandwidth parameter is obtained. By comparing the estimation errors under different candidate bandwidth parameters, the bandwidth parameter that minimizes the probability density estimation error is selected as the final bandwidth value of the kernel density estimation model. This allows for a more accurate characterization of the distribution characteristics of clinker calcination control parameters under historical conditions, even under multi-peak distribution or frequently changing operating conditions, thus improving the reliability of the control parameter feasibility analysis results.

[0080] In this invention, the control parameters are recommended by an intelligent control system or a machine learning model. Before controlling the actuator through the control parameters, the industrial control computer represents the combination of recommended control parameters as a parameter composed of multiple control parameters, and sends it as input to a pre-built kernel density estimation model. By weighted superposition of the kernel function response of the parameter in the historical sample probability space, the corresponding joint probability density value is obtained. When the probability density values ​​of kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and decomposer coal feed rate are all calculated using a one-dimensional kernel density estimation model, weights need to be assigned to the probability density values ​​of kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and decomposer coal feed rate respectively. When a multi-dimensional joint kernel density estimation model is used, weights need to be assigned to the probability density values ​​calculated by different multi-dimensional joint kernel density estimation models respectively. For example, the first multi-dimensional joint kernel density estimation model involves the calculation of probability density values ​​of kiln feed rate, kiln speed, kiln head coal feed rate, and kiln head exhaust fan speed, while the second multi-dimensional joint kernel density estimation model involves the calculation of probability density values ​​of high-temperature fan speed, grate cooler speed, and decomposer coal feed rate. Weights need to be assigned to the probability density values ​​calculated by the first and second multi-dimensional joint kernel density estimation models respectively. When the multi-dimensional joint kernel density estimation model involves all of the above control parameters, no weights need to be assigned. This invention calculates the joint probability density value by weighted superposition and designs differentiated weighting strategies for different modeling scenarios. It is suitable for scenarios with independent analysis of one-dimensional multi-parameters as well as scenarios with multiple multi-dimensional models. It can highlight the influence weight of key parameters or core models, so that the joint probability density value accurately reflects the degree of fit between the parameter combination and historical stable operating conditions, avoiding the limitations of single parameter evaluation.

[0081] The joint probability density value is used to characterize the probability level of the recommended combination of control parameters in the historical stable operating condition distribution of clinker calcination and its closeness to historical operating conditions. This invention sets a feasibility threshold, such as a boundary determined by the lower 5% quantile of the density distribution. When the density value of the recommended parameter combination is lower than this threshold, the combination is considered to be in a low-probability region of the historical distribution, meaning it may exceed the feasible range of the production process and requires further adjustment or verification. When the density value is higher than or equal to the threshold, the parameter combination is considered to have a high probability of occurrence historically, belonging to the feasible region and can be used for actual control operations. This invention effectively avoids production risks caused by exceeding the process range by setting a feasibility threshold, applies high-probability combinations in production, and ensures production stability. To ensure the long-term adaptability of the model, this invention also proposes a dynamic update mechanism based on a time window, that is, by periodically adding the latest production data, updating the historical sample dataset, and redetermining the kernel density function, the model can reflect changes in the production environment and equipment status. This invention can also be combined with the visualization module of the industrial control computer to display the position and distribution relationship of the recommended parameters in the form of probability distribution curves, density contour plots, etc., providing operators with intuitive judgment basis.

[0082] The beneficial effects of the present invention are described in detail below.

[0083] This invention introduces a kernel density estimation model to provide a feasibility verification mechanism for control parameters recommended by machine learning, which can effectively avoid recommended parameters from exceeding the reasonable range of history, thereby significantly improving the accuracy and safety of parameter settings.

[0084] This invention reduces subjective interference from human experience by quantifying probability density, thereby improving the stability and consistency of the clinker firing process. Furthermore,

[0085] This invention is data-driven at its core, making full use of historical production information and avoiding the limitations of relying on manual adjustments. Since kernel density estimation does not depend on any distribution assumptions, the model has strong universality and adaptability, and can be widely applied to production scenarios with different kiln types, different raw material ratios, and different operating conditions.

[0086] This invention continuously learns new data through a dynamic update mechanism, ensuring the timeliness and accuracy of the analysis results.

[0087] This invention is highly adaptable to different working conditions. It can be adapted to key control scenarios with a single parameter as well as complex working conditions with multiple parameters coupled, taking into account both local parameter characteristics and overall combined effect.

[0088] This invention effectively improves the level of intelligent control in the clinker calcination process, reduces energy consumption, and increases production efficiency.

[0089] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution; or the direct application of the inventive concept and technical solution to other situations without modification, are all within the protection scope of the present invention.

Claims

1. A feasibility analysis method for clinker calcination parameters based on kernel density estimation, characterized in that, Includes the following steps: Step 1: The industrial control computer collects control parameter data from the historical operation of the cement production line and establishes a historical sample dataset; Step 2: Clean and preprocess the collected control parameter data, remove outliers and standardize them; Step 3: Establish a one-dimensional kernel density estimation model for each control parameter data; Step 4: Before the control parameter data is output to the actuator, it is first input into the above one-dimensional kernel density estimation model to calculate the probability density value. Then, multiple probability density values ​​are weighted and superimposed to obtain the joint probability density value. Step 5: Compare the obtained joint probability density value with the feasibility threshold. When the joint probability density value is greater than or equal to the feasibility threshold, it is determined that the control parameter data can be used for actual operation.

2. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 1, characterized in that: In step one, the collected control parameter data includes the kiln feed rate, high-temperature fan speed, kiln speed, kiln head coal feed rate, grate cooler speed, kiln head exhaust fan speed, and decomposer coal feed rate.

3. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 1, characterized in that: In step three, the formula for the one-dimensional kernel density estimation function of the one-dimensional kernel density estimation model is: ； Where x represents the control parameter data to be verified, x i Let be the i-th sampled value in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, and K(·) be the kernel function.

4. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 1, characterized in that: In step three, under the scenario of multi-parameter joint analysis, a multi-dimensional joint kernel density estimation model is established for multiple control parameter data. The multi-dimensional kernel density estimation function formula of the multi-dimensional joint kernel density estimation model is as follows: ； Where x j For the control parameter data to be verified, x ij Let be the j-th component of the i-th sample in the historical sample dataset, n be the total number of historical sample data, h be the bandwidth parameter, K(·) be the kernel function, and d be the dimension of the data.

5. A feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 3 or 4, characterized in that: When a Gaussian kernel is used as the kernel function, the kernel function formula is: 。 6. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 5, characterized in that: Alternatively, the Epanechnikov kernel can be used as the kernel function. The kernel function formula is as follows: 。 7. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 3, characterized in that: The bandwidth parameter of the one-dimensional kernel density estimation function is determined using the Silverman rule, and the calculation formula is as follows: ; in denoted as , where is the standard deviation of the historical sample data in the historical sample dataset, and n is the number of historical sample data.

8. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 4, characterized in that: The bandwidth parameter of the multidimensional joint kernel density estimation model is determined by cross-validation.

9. The feasibility analysis method for clinker calcination parameters based on kernel density estimation as described in claim 1, characterized in that: The historical sample dataset is updated regularly, and the one-dimensional kernel density estimation model is also updated.

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