Blast furnace parameter backstepping method based on random forest and constrained optimization
By using a random forest model and a constrained optimization algorithm to inversely deduce blast furnace parameters, the nonlinear coupling problem in the traditional empirical model was solved, thereby improving the stability and economy of blast furnace production.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-15
- Publication Date
- 2026-03-27
AI Technical Summary
Traditional blast furnace parameter adjustments rely on manual experience, making it difficult to accurately capture nonlinear coupling relationships, leading to output fluctuations or equipment exceeding limits. Furthermore, the lack of systematic integration of multiple constraints makes it impossible to meet the actual needs of blast furnace production.
A random forest model is used to predict the daily output of blast furnaces, and the optimal operating parameters are inversely derived through a constrained optimization algorithm. A constrained optimization model is constructed, and the target daily output is optimized under multiple constraints by combining the SLSQP algorithm.
It has improved the stability and intelligence level of blast furnace production, and achieved synergistic optimization of output target, equipment safety and optimal cost.
Smart Images
Figure CN121744935A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of blast furnace ironmaking technology, and in particular to a method for back-calculating blast furnace parameters based on random forest and constraint optimization. Background Technology
[0002] The steel industry is a pillar industry of the national economy. Blast furnace ironmaking, as the core process of steel production, is responsible for converting iron ore into molten iron. Its energy consumption accounts for more than 60% of the total energy consumption of steel enterprises, and its cost accounts for more than 50%. Against the backdrop of global overcapacity and tightening environmental policies, enterprises need to achieve synergistic optimization of equipment capacity, energy consumption, and production costs while ensuring the output and quality of molten iron.
[0003] Most steel companies in China rely on the "experience of veteran workers" model to adjust blast furnace parameters. Technicians set key operating parameters such as oxygen enrichment flow rate and cold air flow rate based on historical operation records and manual judgment. They establish the correlation between operating parameters and blast furnace output through manual experience, thereby determining the parameter setting values.
[0004] Because blast furnaces are complex, multivariable, and strongly coupled reaction systems, their output is affected by nonlinear factors such as raw material composition (e.g., overall grade), equipment status (e.g., furnace top pressure), and operating parameters (e.g., oxygen enrichment flow rate). Human experience cannot fully and accurately capture the nonlinear mapping relationship between parameters and output, easily leading to over-adjustment of parameters or substandard output. Furthermore, manual operation often focuses solely on output, neglecting hard equipment constraints (e.g., exceeding the oxygen enrichment flow rate limit) and economic constraints (e.g., excessive use of high-cost raw materials). In addition, existing technologies mostly focus on positive prediction of "parameter → output" or single-dimensional parameter optimization (e.g., considering only cost minimization), lacking a systematic integration of multiple constraints related to output, equipment, and cost, thus failing to meet the actual production needs of enterprises. Summary of the Invention
[0005] In view of this, the purpose of this invention is to propose a blast furnace parameter back-calculation method based on random forest and constraint optimization, so as to solve the problems of traditional experience-driven blast furnace parameter adjustment, which is difficult to capture multi-parameter nonlinear coupling, easily leads to output fluctuations or equipment over-limits, lacks a closed-loop back-calculation mechanism from target daily output to optimal operating parameters, and does not integrate multiple constraints.
[0006] To achieve the above objectives, the technical solution adopted by this invention is: a method for back-calculating blast furnace parameters based on random forest and constraint optimization, comprising the following steps:
[0007] S1. Obtain the input parameters and target variables for blast furnace production, and based on... Criteria for handling outliers;
[0008] S2. Based on the input parameters and target variables, construct an RF (Random Forest) model to predict the daily output of the blast furnace;
[0009] S3. Based on the RF model, a constrained optimization model is constructed, and the optimal operating parameters of the blast furnace are back-derived using the SLSQP (Sequential Least Squares Programming) algorithm.
[0010] Preferably, the input parameter is the average daily oxygen-enriched flow rate. Average daily airflow Average daily furnace top pressure and daily average overall quality The target variable is daily output. Unit: tons / day.
[0011] Preferably, the above is based on The specific steps for handling outliers according to the criteria are as follows: For each input parameter, calculate the mean. and standard deviation Eliminate those that meet the requirements The sample, of which, For daily output Similarly, calculate its mean. and standard deviation Remove fluctuations exceeding Outliers.
[0012] Preferably, the specific steps for constructing the RF model to predict the daily output of the blast furnace are as follows: First, random sampling is performed, and from the preprocessed valid samples, sampling with replacement is used to generate... A training subset, The first step is to determine the number of trees; the second step is to randomly select features and construct the decision tree. For each decision tree, when splitting a node, features are randomly selected from only four input parameters. One characteristic, For hyperparameters and The optimal splitting threshold is selected using the MSE criterion; then, the ensemble output is performed, and after the decision tree training is complete, any combination of input parameters is considered. ,Will Predicted daily yield of trees Taking the average, we obtain the final predicted value: .
[0013] Preferably, the specific mathematical expression of the constrained optimization model is:
[0014]
[0015] in, Decision variable vector; , , and Let be the decision variables, where This is the average daily oxygen-enriched flow rate. The average daily airflow rate This represents the average daily furnace top pressure. The average daily quality; The objective function is... Given a target daily output; Daily output predicted by the RF model; These are the weight coefficients of the objective function; The total cost function is a parameter. , , and The transformation cost for each decision variable; This is a lower bound constraint; Upper limit constraint; For the first The minimum allowed value for each operating parameter; For the first The maximum allowed value for each operating parameter; .
[0016] Preferably, the specific steps for back-deriving the optimal operating parameters of the blast furnace using the SLSQP algorithm are as follows:
[0017] a. Parameter initialization: Use the midpoint of the upper and lower limits of each parameter as the initial point to ensure that the search starting point is located in the center of the feasible region;
[0018] b. Iterative optimization: The algorithm iteratively executes the process of "parameter standardization → RF model prediction of daily output → calculation of objective function and constraint satisfaction → parameter update", and achieves gradient descent by solving the quadratic programming subproblem;
[0019] c. Convergence criterion: When the change in the objective function is less than... Parameter adjustment range is less than Alternatively, the iteration can stop after 1000 iterations, and the optimal parameter combination will be output.
[0020] The beneficial effects of this invention are as follows: By constructing an RF model to predict the daily output of a blast furnace, the nonlinear coupling relationship between the four input parameters and the daily output is characterized; by constructing a constrained optimization model and using the SLSQP algorithm to reverse the calculation from the target daily output to the optimal operating parameters under multiple constraints, the shortcomings of the traditional experience model are effectively solved, the stability and intelligence level of blast furnace production are improved, and the synergistic optimization of output target, equipment safety and cost optimization is achieved. Attached Figure Description
[0021] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0022] Figure 1 This is a schematic diagram of the process of the present invention;
[0023] Figure 2 This is a scatter plot comparing the predicted and actual daily output of blast furnaces using the RF model of this invention.
[0024] Figure 3 This is the histogram of the error distribution of the RF model of this invention. Detailed Implementation
[0025] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains.
[0026] like Figure 1 As shown, a method for back-calculating blast furnace parameters based on random forest and constrained optimization includes the following steps:
[0027] S1. Obtain the input parameters and target variables for blast furnace production, and based on... The criteria handle outliers.
[0028] First, the input parameters and target variables for blast furnace production were obtained. Experimental data came from three 1080m³ blast furnaces and one 700m³ blast furnace in a steel company. 3 The daily production records of the blast furnace from June 2024 to September 2025 contain more than 1,900 valid samples. Each sample includes four input parameters and one target variable. The definitions and physical ranges of the four input parameters are shown in Table 1; the target variable is the daily output, in tons per day.
[0029]
[0030] Secondly, to eliminate noise interference in the raw data, the input parameters and daily output need to be preprocessed, i.e., based on... The criteria for handling outliers are as follows: For each input parameter, calculate the mean. and standard deviation Eliminate those that meet the requirements For the sample, if the daily average oxygen-enriched flow rate suddenly changes to 0 cubic meters per hour, among which, For daily output Similarly, calculate its mean. and standard deviation Remove fluctuations exceeding Outliers were identified; ultimately, 1328 valid samples were retained.
[0031] S2. Based on the input parameters and target variables, construct an RF model to predict the daily output of the blast furnace.
[0032] The mapping relationship between blast furnace daily output and input parameters exhibits three main characteristics: strong nonlinearity, multivariate coupling, and local dynamics. The gain in daily output from increasing the average daily oxygen-enriched flow rate is affected by the adjustment of the average daily top pressure; fluctuations in the average daily comprehensive grade alter the correlation between the average daily cold blast flow rate and daily output. Traditional linear models struggle to accurately characterize these complex relationships. RF, as an ensemble learning algorithm, reduces the risk of overfitting through a voting mechanism of multiple decision trees, while also possessing the ability to handle high-dimensional features and capture nonlinear interaction effects, thus meeting the technical requirements of blast furnace output prediction.
[0033] (1) Constructing the RF model
[0034] The core of Randomization (RF) is randomness and ensemble. By randomly sampling both samples and features, multiple independent decision trees are generated. The RF model is then used to output results in classification tasks via voting or in regression tasks via averaging. For the regression problem of blast furnace production prediction, the construction of an RF model can be broken down into three steps: random sample sampling, random feature selection and decision tree construction, and ensemble output.
[0035] First, random sampling was performed. From the 1328 preprocessed valid samples, samples were generated using sampling with replacement. A training subset, To determine the number of trees, for each subset, approximately 63.2% of the original samples are selected, and the unselected samples constitute "out-of-bag samples" used for unbiased evaluation of the model's generalization ability. This sampling method reduces the impact of single-sample noise on the model and lays the foundation for the diversity of subsequent trees.
[0036] Secondly, there is the random selection of features and the construction of decision trees. For each decision tree, when splitting a node, features are randomly selected from only four input parameters. One characteristic, For hyperparameters and The optimal splitting threshold is selected by minimizing the mean squared error (MSE) criterion. Taking the daily average oxygen-enriched flow rate as an example, the splitting process is as follows: iterate through all possible values of the parameter and divide the sample into... and Two groups, of which The critical threshold is used to calculate the average error of daily output. ,in, This represents the average daily output. The number of values for daily output; select the value that minimizes the mean square error. Minimum critical threshold Using the current node as the splitting criterion, this splitting process is repeated until the number of samples contained in the node is less than the preset minimum sample size threshold, or the depth of the tree reaches the preset maximum depth limit.
[0037] Next is the ensemble output. To effectively counteract the overfitting tendency of a single decision tree—which may suffer from prediction bias due to local sample noise—the average result of multiple trees is used to reduce this bias and improve the model's generalization ability. All algorithms perform this ensemble on any combination of input parameters after the decision trees are trained. ,Will Predicted daily yield of trees Taking the average, we obtain the final predicted value: .
[0038] (2) Predictive model analysis
[0039] To comprehensively verify the performance of the RF model, a test set was used for evaluation, and it was compared with the BP (back propagation) neural network model. Evaluation metrics included Mean Absolute Error (MAE), Mean Squared Error (MSE), and Coefficient of Determination. Table 2 shows a comparative analysis of the evaluation indicators for the two models.
[0040]
[0041] Wherein, MAE is the average of the absolute errors between the predicted and actual values; the smaller the value, the smaller the error in the model's prediction. MSE is the average of the squared errors between the predicted and actual values; the smaller the value, the higher the overall accuracy. The value closest to 1 reflects the model's ability to fit data patterns; the better. RF models perform well in terms of MAE, MSE, and... The RF model outperformed the BP neural network model in all three metrics. The reasons for this are: the BP neural network model requires a large sample size, and the insufficient sample size in this paper led to its insufficient generalization ability; the RF model's ensemble mechanism and Bootstrap sampling made it perform better in small and medium sample scenarios, which is in line with the characteristics of the research data.
[0042] from Figure 2Looking at the scatter plot, the blue dots are generally distributed around the red dashed line, which represents the ideal reference line where the predicted and actual values are equal. This is especially true when the actual daily output is in the mid-to-high range, such as around 2000-3800 tons; the dots are dense and close to the dashed line, indicating that the RF model performs well in this output range, and the predicted values accurately reflect the actual values. Although there are some deviations at certain low output points and a few mid-to-high output points, such as when the actual daily output is below 1000 tons, the overall trend is in line with expectations, demonstrating the RF model's good fitting ability.
[0043] Let's look again. Figure 3 and combined Figure 2 Further analysis shows that the errors in the RF model are mainly concentrated within a narrow range, indicating that most prediction errors are small. In industrial production, keeping the error in blast furnace daily output prediction within a reasonable range is crucial for subsequent parameter back-calculation and production planning. This concentrated error distribution means that the model can provide relatively reliable prediction results in most cases and offers a reliable output assessment tool for subsequent optimization.
[0044] S3. Based on the RF model, a constrained optimization model is constructed, and the optimal operating parameters of the blast furnace are back-derived using the SLSQP algorithm.
[0045] The core of blast furnace parameter back-calculation is to solve for the optimal combination of operating parameters from the target output, under the premise of meeting production targets and industrial constraints. Step S3 transforms this problem into a constrained optimization model. By constructing the objective function, setting constraints, and designing an efficient solution algorithm, it achieves coordinated optimization of output target achievement, equipment safety, and cost optimization. The constrained optimization model design is based on the RF model and is closely related to the RF model in all aspects, from objective function construction and constraint setting to optimization solution. The specific implementation method is as follows.
[0046] (1) Constructing the objective function and setting constraints
[0047] In constrained optimization models, the objective function and constraints are constructed to achieve the two key objectives of balancing target output and cost optimization. The parameter back-calculation problem can be formally defined as: given a target daily output... The optimal combination of operating parameters needs to be found within the feasible region of the parameters. The objective function is minimized while satisfying all constraints. The mathematical expressions for the objective function and constraints are shown below:
[0048]
[0049] in, Decision variable vector; , , and Let be the decision variables, where This is the average daily oxygen-enriched flow rate. The average daily airflow rate This represents the average daily furnace top pressure. The average daily quality; The objective function is... Daily output predicted by the RF model; These are the weight coefficients of the objective function; The total cost function is a parameter. , , and The transformation cost for each decision variable; This is a lower bound constraint; Upper limit constraint; For the first The minimum allowed value for each operating parameter; For the first The maximum allowed value for each operating parameter.
[0050] (2) Design an efficient solution algorithm
[0051] For the above-mentioned constrained optimization model, considering the high real-time requirements of production and the small problem size, the SLSQP algorithm is selected as the solver. Its advantages are that it supports nonlinear constraint processing, has a fast convergence speed (converging in 100-500 iterations), and has excellent efficiency in solving small and medium-sized problems.
[0052] The solution process is implemented based on Python's scipy.optimize.minimize module, and the core steps are as follows:
[0053] a. Parameter initialization: Take the midpoint of the upper and lower limits of each parameter as the initial point. For example, the initial value of the daily average oxygen enrichment flow rate is 11500 m³ / h. Ensure that the search starting point is located in the center of the feasible region.
[0054] b. Iterative optimization: The algorithm iteratively executes the process of "parameter standardization → RF model prediction of output → calculation of objective function and constraint satisfaction → parameter update", and achieves gradient descent by solving the quadratic programming subproblem;
[0055] c. Convergence criterion: When the change in the objective function is less than... Parameter adjustment range is less than Alternatively, the iteration can stop after 1000 iterations, and the optimal parameter combination will be output.
[0056] This process balances solution accuracy with industrial real-time performance, and can quickly output optimal parameters that satisfy all constraints.
[0057] (3) Experimental analysis
[0058] Using the target daily output of 3200-3500 tons / day as the variable range, 20 independent solution results were generated using the SLSQP algorithm. The distribution characteristics of the solution set within the industrial feasible domain were analyzed from two dimensions: equipment constraint satisfaction rate and output constraint compliance rate.
[0059] Of the 20 solutions, 18 solutions met the upper and lower limits of the daily average oxygen enrichment flow, daily average cold air flow, daily average furnace top pressure, and daily average comprehensive grade, achieving a constraint satisfaction rate of 90%. The two solutions that did not meet the constraints were mainly due to the daily average oxygen enrichment flow approaching the equipment's upper limit, requiring re-solution with corrected constraints.
[0060] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity.
[0061] This invention aims to cover all such substitutions, modifications, and variations that fall within the scope of protection. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.
Claims
1. A method for back-calculating blast furnace parameters based on random forest and constrained optimization, characterized in that, Includes the following steps: S1. Obtain the input parameters and target variables for blast furnace production, and based on... Criteria for handling outliers; S2. Based on the input parameters and target variables, construct an RF model to predict the daily output of the blast furnace; S3. Based on the RF model, a constrained optimization model is constructed, and the optimal operating parameters of the blast furnace are back-derived using the SLSQP algorithm.
2. The method according to claim 1, characterized in that, The input parameter is the average daily oxygen-enriched flow rate. Average daily airflow Average daily furnace top pressure and daily average overall quality ; The target variable is daily output. Unit: tons / day.
3. The method according to claim 1, characterized in that, The and based on The specific steps for handling outliers according to the criteria are as follows: For each input parameter, calculate the mean. and standard deviation Eliminate those that meet the requirements The sample, of which, For daily output Similarly, calculate its mean. and standard deviation Remove fluctuations exceeding Outliers.
4. The method according to claim 1, characterized in that, The specific steps for constructing the RF model to predict the daily output of the blast furnace are as follows: First, random sampling is performed. From the preprocessed valid samples, sampling with replacement is used to generate... A training subset, The first step is to determine the number of trees; the second step is to randomly select features and construct decision trees. For each decision tree, when splitting a node, features are randomly selected from only four input parameters. One characteristic, For hyperparameters and The optimal splitting threshold is selected using the MSE criterion; then, the ensemble output is performed, and after the decision tree training is complete, any combination of input parameters is considered. ,Will Predicted daily yield of trees Taking the average, we obtain the final predicted value: .
5. The method according to claim 1, characterized in that, The specific mathematical expression of the constrained optimization model is as follows: in, Decision variable vector; , , and Let be the decision variables, where This is the average daily oxygen-enriched flow rate. The average daily airflow rate This represents the average daily furnace top pressure. The average daily quality; The objective function is... Given a target daily output; Daily output predicted by the RF model; These are the weight coefficients of the objective function; The total cost function is a parameter. , , and The transformation cost for each decision variable; This is a lower bound constraint; Upper limit constraint; For the first The minimum allowed value for each operating parameter; For the first The maximum allowed value for each operating parameter; .
6. The method according to claim 1, characterized in that, The specific steps for back-deriving the optimal operating parameters of the blast furnace using the SLSQP algorithm are as follows: a. Parameter initialization: Use the midpoint of the upper and lower limits of each parameter as the initial point to ensure that the search starting point is located in the center of the feasible region; b. Iterative optimization: The algorithm iteratively executes the process of "parameter standardization → RF model prediction of daily output → calculation of objective function and constraint satisfaction → parameter update", and achieves gradient descent by solving the quadratic programming subproblem; c. Convergence criterion: When the change in the objective function is less than... Parameter adjustment range is less than Alternatively, the iteration can stop after 1000 iterations, and the optimal parameter combination will be output.