Non-Gaussian random process prediction optimization control method based on Wasserstein fuzzy set

Abstract

The invention discloses a non-Gaussian random process prediction optimization control method based on a Wasserstein fuzzy set, and belongs to the technical field of blast furnace ironmaking system control. Aiming at the problems of modeling uncertainty and insufficient robustness under external disturbance and non-Gaussian disturbance existing in a traditional method, the method comprises the following steps: setting a coal injection amount, an oxygen-enriched flow, a cold air flow, a molten iron temperature and a Si content by collecting a pressure difference of a blast furnace ironmaking system; a blast furnace iron-making system is used for building a blast furnace neural network prediction model, output in a period of time in the future is predicted based on the current blast furnace state and the neural network model, a predicted output error is regarded as a random variable, and a Wasserstein fuzzy set with empirical distribution as the center is built to describe distribution uncertainty of the Wasserstein fuzzy set; in an MPC rolling optimization process, Wasserstein distance constraint is introduced, a distribution robust optimization problem is converted into a solvable optimization problem, and a group of optimal control sequences are obtained, so that a system does not depend on a specific random distribution hypothesis, and modeling errors and non-Gaussian external disturbance can be effectively processed.

Description

Technical Field

[0001] This invention belongs to the field of blast furnace ironmaking system control technology, specifically involving a non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets. Background Technology

[0002] Steel is an indispensable basic material in modern industrial society, and the stable and efficient operation of blast furnace ironmaking, as the core link in steel manufacturing, is crucial. Blast furnace ironmaking is an extremely complex physicochemical process carried out under high temperature and high pressure, involving the interaction and coupled reactions of gas, liquid, and solid multiphase flows. However, the strong nonlinearity, large hysteresis, and multiple coupling characteristics of this process pose enormous challenges to its accurate modeling and optimized control. The fundamental difficulties lie in the uncertainty of modeling the intrinsic mechanism and the frequent unknown external disturbances.

[0003] In terms of modeling, hundreds of interconnected chemical reactions occur simultaneously inside the blast furnace, including the core iron oxide reduction reaction and pulverized coal gasification combustion. The high complexity of these reactions, the huge differences between different reaction rates, and their extreme sensitivity to temperature, pressure, and gas phase composition mean that any mathematical model based on deterministic mechanisms suffers from significant mechanistic uncertainties. Furthermore, the material movement within the furnace encompasses the countercurrent movement of the downward-flowing charge (solids and melts) and the upward-flowing gas, constituting a typical complex fluid dynamics system. The heat, mass, and momentum transfer processes of the solid, liquid, and gas phases are intertwined, making their precise mathematical description extremely difficult and introducing a large number of model errors and unmodeled dynamics.

[0004] In addition to inherent uncertainties, blast furnace systems are constantly subjected to various strong external disturbances. Fluctuations in the composition of upstream raw materials and fuels (such as ore grade and coke quality) are the most common and difficult-to-predict sources of disturbance. Furthermore, changes in equipment condition (such as furnace lining erosion and cooling wall efficiency) and fluctuations in operating conditions (such as slight changes in blast humidity and oxygen enrichment) together constitute a continuous, time-varying disturbance environment with unknown statistical characteristics (usually non-Gaussian distribution).

[0005] In traditional predictive optimization control of blast furnace ironmaking, the design of control strategies typically relies heavily on precise mathematical models of the process. The core of these methods is the assumption that the probability distributions of modeling errors and external disturbances follow a Gaussian distribution, and on this basis, an index based on the second moment of the error is used as the optimization objective. This paradigm implicitly simplifies system uncertainty into symmetric, light-tailed random variables, assuming that their statistical properties can be fully characterized by the mean and variance. However, actual blast furnace operation is a dynamic process with large time delays, strong coupling, and complex nonlinear characteristics. Its inherent modeling uncertainties and external disturbances (such as fluctuations in raw material composition, measurement noise, and changes in operating conditions) often exhibit significant non-Gaussian characteristics statistically, such as heavy-tailed, skewed, or multimodal distributions. This complex and uncertain probability distribution characteristic makes the blast furnace control problem essentially a bibrushed optimization problem. The extreme outliers and structural biases present in such distributions far exceed the expressive power of the traditional Gaussian modeling framework.

[0006] This traditional predictive control framework, based on the Gaussian assumption and mean performance index, has significant limitations when dealing with real non-Gaussian uncertainties. First, it fails to adequately capture and describe extreme events and anomalous fluctuations in the modeling error and disturbance distribution, leading to insufficient uncertainty estimation by the controller. Second, the optimization objective focuses solely on minimizing the mean or variance of the error, neglecting differences in distribution shape. This results in a significant decrease in control performance, or even instability, when faced with disturbances exhibiting non-Gaussian statistical characteristics in reality. Therefore, traditional methods often perform poorly in addressing the complex uncertainties and non-Gaussian disturbances prevalent in blast furnace ironmaking processes, failing to achieve stable and accurate control. Summary of the Invention

[0007] To address the problems of insufficient robustness under modeling uncertainties and external disturbances, as well as non-Gaussian disturbances, in traditional methods, this invention provides a predictive optimization control method for non-Gaussian stochastic processes based on Wasserstein fuzzy sets.

[0008] To achieve the above objectives, the present invention employs the following technical solutions:

[0009] A non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets, the method comprising the following steps:

[0010] Step 1: Collect the pressure difference of the blast furnace ironmaking system 1. Set the pulverized coal injection rate Oxygen-enriched flow rate Cold air flow molten iron temperature and Si content A neural network prediction model for blast furnaces was established using data from the blast furnace ironmaking system.

[0011] The specific operation of step 1 is as follows:

[0012] A neural network prediction model for blast furnace ironmaking is established using a multi-layer perceptron (MLP) neural network to capture the nonlinear dynamic relationship between input and output variables, and to predict the temperature of molten iron. and Si content Set the pressure difference as the model output variable. Oxygen-enriched flow rate 1. Set the pulverized coal injection rate Cold air flow The data is set as the input variables of the model; compared with other neural networks, MLP has a strong nonlinear fitting ability, simple model, stable training, high computational efficiency, and seamless integration with the MPC framework. Therefore, MLP is used to build the neural network in this invention.

[0013] Suppose a Multi-Layer Percceptron (MLP) neural network model has L hidden layers, then the overall calculation formula is:

[0014]

[0015] in, The activation function for the hidden layer. For input variables, For the first The weight matrix of the layer, For the first The layer's bias matrix;

[0016] Constructing a dynamic mapping relationship between control inputs and outputs using a multilayer perceptron neural network:

[0017]

[0018] in, and These represent the actual input and actual output of the system control, respectively. This represents the predicted output of the neural network prediction model for blast furnace ironmaking. A neural network prediction model for blast furnace ironmaking; and These are the time delay parameters for the output and input, respectively;

[0019] Particle Swarm Optimization (PSO) is used to optimize the parameters of a multilayer perceptron neural network, improving the convergence speed and global search capability of the neural network prediction model for blast furnace ironmaking. The process of PSO is as follows:

[0020]

[0021]

[0022] in, , The maximum number of iterations, For inertial weights, and These are individual learning factors and group learning factors, respectively. and These are random numbers that follow a uniform distribution. In the first After the next iteration, the particles The optimal solution has been found. In the first The optimal solution in the entire particle swarm after the next iteration; and Distributed as particles In the After the nth iteration A velocity vector and a position vector of dimension, where , For population size, and , represents the dimension of the particle to be searched.

[0023] Step 2: Based on the current blast furnace status and the blast furnace neural network prediction model, predict the future using Model Predictive Control (MPC). Output variable values ​​for each sampling period;

[0024] The specific operation of step 2 is as follows:

[0025] Read the current blast furnace system output The optimized MLP neural network model trained in step 1 is used to predict the future through Model Predictive Control (MPC). The output variable value for each sampling period To predict the time domain length; assume a future control time domain The internal control input remains unchanged, that is The predicted output is:

[0026]

[0027] in, Indicates at time step Time Predicted output at time step It is a model function. At time step Control input.

[0028] Step 3: Treat the error between the output of the blast furnace ironmaking system and the output of the neural network model as a random variable, and construct a Wasserstein fuzzy set centered on the empirical distribution of historical error samples to describe the distributional uncertainty of the random variable;

[0029] The specific operation of step 3 is as follows:

[0030] Predictions from historical data collected by the neural network prediction model for blast furnace ironmaking Compared with actual measured value Error between An error sample set is formed, and based on the error sample set, an empirical distribution is constructed. Wasserstein fuzzy set centered It is used to describe the uncertainty of the distribution of random variables;

[0031] The constructed experience distribution It is a discrete uniform distribution, and the formula is:

[0032]

[0033] in, Indicates the number of samples. It is a sample The Dirac measure at a point represents the measure of concentration at that point;

[0034] The Wasserstein fuzzy set quantifies and constrains the uncertainty of probability distributions through Wasserstein distance. Its core component is a "sphere" centered on the empirical distribution and with Wasserstein distance as its radius. This sphere contains all probability distributions that may be similar to the true distribution, thus forming a set that describes the uncertainty of the distribution.

[0035] The Wasserstein fuzzy set Based on empirical distribution Centered on, with Let be the set of probability distributions with radius , representing all empirical distributions. Wasserstein distance between No more than the radius probability distribution The formula for Wasserstein fuzzy sets is:

[0036]

[0037] The formula for Wasserstein distance is:

[0038]

[0039] radius The formula is:

[0040]

[0041] in, It is the probability distribution space; For the output dimension, This is a sample of the prediction error for the Wasserstein sphere center distribution, i.e., the empirical distribution of the Wasserstein sphere center. random variables, To output the predicted probability distribution Random error; The distance between random variables ; for and The joint distribution; For coefficients, For a given confidence level.

[0042] Step 4: In the rolling optimization process of model predictive control, feedback correction and the Wasserstein fuzzy set constraint are introduced to construct a split-Bruker constraint problem. The performance index function is minimized under the worst probability distribution while satisfying the output and input constraints.

[0043] The specific operation of step 4 is as follows:

[0044] Step 4.1: Through the feedback adjustment mechanism in model predictive control, the predicted output at future times is corrected in real time to overcome the effects of model mismatch and disturbances. The formula is:

[0045]

[0046] in, The correction matrix has a range of (0,1). The output predicted by the current model. This represents the actual output at the current moment. Indicates the future number Step-by-step correction prediction output; Indicates the future number The model predicts the output of each step;

[0047] Step 4.2: After in The first moment The output constraints for each prediction step are expressed as follows:

[0048]

[0049] in, and To output the maximum and minimum values, Let be a random variable, following a predicted probability distribution. , For auxiliary probability distribution, The expected value of the distribution;

[0050] because It is a constant, and the constraint is written as:

[0051]

[0052] Based on the constructed empirical distribution formula:

[0053]

[0054] Will Transform into:

[0055]

[0056] make Based on strong duality theory and the maximum-minimum inequality, the above equation can be transformed into a solvable deterministic problem:

[0057]

[0058]

[0059]

[0060]

[0061] in, This represents the first [number] element in the training dataset. The first data point One sample, It represents the infinite norm; Indicates transpose; and As dual variables, Representing auxiliary decision variables, using matrices sum vector Define a polyhedral set of uncertainties (a common type of closed convex set);

[0062] Step 4.3: Construct the objective function based on the above formulas. The objective function Aimed at minimizing the expected setpoint for future output tracking Errors, while penalizing excessively large control increments. At the same time, it ensures that the blast furnace ironmaking system can still meet the operating constraints under the worst disturbance, and the operating constraints include output constraints, input constraints, slack variable constraints, dual norm constraints, and dual variable constraints.

[0063] objective function The formula is:

[0064]

[0065] in, and These are the lengths of the prediction time domain and the control time domain, respectively. and It is a positive definite weight matrix used to balance the tracking and control increments. The punishment To optimize the expected cost in the worst-case scenario, Indicating the future Expected output value; Indicates the future number The rate of change of the control input for each step;

[0066] The output constraints are:

[0067]

[0068] The input constraints are:

[0069]

[0070] The slack variable constraint is:

[0071]

[0072] The dual norm constraint is:

[0073]

[0074] The dual variable constraint is:

[0075]

[0076] These constraints ensure the robustness of the system under uncertainty.

[0077] Step 5: Solve the optimization problem to obtain the optimal control sequence at the current moment, and add the first control variable in the optimal control sequence to the blast furnace ironmaking system to generate a new output for iteration.

[0078] The specific operation of step 5 is as follows:

[0079] Step 5.1: Use a genetic algorithm to optimize and solve for the optimal control sequence. Only the first control variable in the sequence Apply to the blast furnace system;

[0080] Step 5.2: Obtain the next sampling time The system outputs new measurement values. ; Controller Starting from a new point, repeat steps 2 through 5 to form a closed-loop feedback, rolling forward optimized control process.

[0081] Compared with the prior art, the present invention has the following advantages:

[0082] 1. Strong robustness and excellent dynamic performance: Compared with traditional MPC, the method proposed in this invention significantly reduces output response overshoot and achieves faster stabilization. This indicates that the method can effectively cope with the worst-case distribution caused by model mismatch and unknown disturbances, ensuring that the system remains stable under uncertain environments and achieving accurate setpoint tracking, while also helping to reduce process energy consumption;

[0083] 2. Smooth control input: Compared with the aggressive control commands that traditional MPC may generate in pursuit of instantaneous optimality, this invention naturally generates smoother and physically easier-to-execute control signals through the sub-Brow bar optimization framework. This helps to reduce wear on actuators and mechanical stress on equipment, extend equipment life, and ensure stable production.

[0084] 3. Adjustable robustness-performance trade-off mechanism: Based on a comparison of control effects under different Wasserstein sphere radii, adjusting the radius parameter r allows for a flexible and quantitative trade-off between the system's speed (performance) and conservatism (robustness). This provides a convenient and effective adjustment method for addressing control requirements under different operating conditions (such as prioritizing tracking accuracy or interference resistance). Attached Figure Description

[0085] Figure 1 This is a schematic diagram of a blast furnace ironmaking system, which mainly includes five modules: a feeding system, a blast furnace gas treatment system, a pulverized coal injection system, a hot blast system, and an iron tapping system.

[0086] Figure 2 This is a specific implementation of the non-Gaussian stochastic process prediction optimization control method strategy based on Wasserstein fuzzy sets in the present invention.

[0087] Figure 3 The Wasserstein ball is the main method in the specific implementation scheme of this invention;

[0088] Figure 4The Wasserstein sphere radius in a specific embodiment of the present invention Compared with the control effect of ordinary MPC;

[0089] Figure 5 The Wasserstein sphere radius in a specific embodiment of the present invention A comparison chart of inputs from a standard MPC;

[0090] Figure 6 This is a comparison of the control output under different Wasserstein sphere radii in a specific embodiment of the present invention;

[0091] Figure 7 This is a comparison of control inputs under different Wasserstein sphere radii in a specific embodiment of the present invention;

[0092] Figure 8 This is a flowchart of the non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets in a specific embodiment of the present invention.

[0093] Figure 9 This is a flowchart of the Wasserstein fuzzy set construction process in a specific embodiment of the present invention;

[0094] Figure 10 This is a flowchart of the control method proposed in a specific embodiment of the present invention. Detailed Implementation

[0095] To gain a deeper understanding of this invention, we will provide a comprehensive and detailed description. However, this invention has various implementations and is not limited to the specific examples listed herein. These examples are presented to enhance a full understanding of the disclosure of this invention.

[0096] The process flow of the blast furnace ironmaking system is as follows: Figure 1As shown, the blast furnace mainly comprises several key components: the blast furnace body, the feeding system, the hot blast system, the pulverized coal injection system, the gas dust removal system, the slag and iron handling system, and the tapping system. The blast furnace body is further subdivided into the throat, shaft, waist, belly, and hearth. During ironmaking, flux, coke, and ore are charged from the top of the furnace in a specific ratio. However, fluctuations in the chemical composition and physical properties of the raw materials are major sources of disturbance. Changes in ore grade and coke ash content directly affect the chemical reactions and thermal state within the furnace, thus disrupting operational stability. Simultaneously, hot blast preheated to 1000-1300°C by the hot blast system, along with fuel, is blown into the furnace through tuyeres, promoting a gasification reaction between the coke and the injected carbon-based materials to produce high-temperature reducing gas. However, fluctuations in hot blast temperature and pressure, as well as uneven pulverized coal injection, can cause additional operational disturbances, affecting the stability of the reducing atmosphere within the furnace. As the gas rises, it undergoes a complex physicochemical reaction with the descending furnace charge, ultimately producing molten iron and slag. These accumulate in the hearth and are discharged through the taphole. This process can be strongly disturbed by internal factors such as uneven distribution of the furnace charge and changes in coke porosity, leading to significant uncertainties in the reaction process. Consequently, the composition and temperature of the resulting molten iron and slag fluctuate. It is particularly important to note that measurement noise and errors in the detection system are also significant sources of interference. For example, the lag in molten iron temperature detection and errors in silicon content analysis can introduce inaccurate information into the closed-loop control.

[0097] The input variable for a blast furnace ironmaking system is pressure difference. 1. Set the pulverized coal injection rate Oxygen-enriched flow rate Cold air flow The output variable is the temperature of the molten iron. and Si content This implementation method collects data in real time from the blast furnace ironmaking system production line, obtaining 330 sets of input and output data to model the blast furnace ironmaking system, and 110 sets of input and output data to predict the blast furnace ironmaking system.

[0098] The strategy of the non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets in this embodiment is as follows: Figure 2 As shown, it includes:

[0099] A non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets, the method comprising the following steps:

[0100] Step 1: Collect the pressure difference of the blast furnace ironmaking system 1. Set the pulverized coal injection rate Oxygen-enriched flow rate Cold air flow molten iron temperature and Si content A neural network prediction model for blast furnaces was established using data from the blast furnace ironmaking system; pressure difference. 1. Set the pulverized coal injection rate Oxygen-enriched flow rate Cold air flow The data can be directly extracted from various sensors in the blast furnace ironmaking system, including the temperature of molten iron. and Si content The Si content can be detected using temperature sensors and a Si content analyzer in the tapping system. A neural network prediction model for the blast furnace is established based on data from the blast furnace ironmaking system.

[0101] The specific operation of step 1 is as follows:

[0102] A neural network prediction model for blast furnace ironmaking is established using a multi-layer perceptron (MLP) neural network to capture the nonlinear dynamic relationship between input and output variables, and to predict the temperature of molten iron. and Si content Set the pressure difference as the model output variable. Oxygen-enriched flow rate 1. Set the pulverized coal injection rate Cold air flow The data is set as the input variables of the model; compared with other neural networks, MLP has a strong nonlinear fitting ability, simple model, stable training, high computational efficiency, and seamless integration with the MPC framework. Therefore, MLP is used to build the neural network in this invention.

[0103] Suppose a Multi-Layer Percceptron (MLP) neural network has L hidden layers, then the overall calculation formula is:

[0104]

[0105] in, The activation function for the hidden layer. For input variables, For the first The weight matrix of the layer, For the first The layer's bias matrix;

[0106] Constructing a dynamic mapping relationship between control inputs and outputs using a multilayer perceptron neural network:

[0107]

[0108] in, and These represent the actual input and actual output of the system control, respectively. This represents the predicted output of the neural network prediction model for blast furnace ironmaking. A neural network prediction model for blast furnace ironmaking; and These are the time delay parameters for the output and input, respectively;

[0109] Particle Swarm Optimization (PSO) is used to optimize the parameters of a multilayer perceptron neural network, improving the convergence speed and global search capability of the neural network prediction model for blast furnace ironmaking. The process of PSO is as follows:

[0110]

[0111]

[0112] in, , The maximum number of iterations, For inertial weights, and These are individual learning factors and group learning factors, respectively. and These are random numbers that follow a uniform distribution. In the first After the next iteration, the particles The optimal solution has been found. In the first The optimal solution in the entire particle swarm after the next iteration; and Distributed as particles In the After the nth iteration A velocity vector and a position vector of dimension, where , For population size, and , represents the dimension of the particle to be searched.

[0113] Step 2: Based on the current blast furnace status and the blast furnace neural network prediction model, predict the future using Model Predictive Control (MPC). Output variable values ​​for each sampling period;

[0114] The specific operation of step 2 is as follows:

[0115] Read the current blast furnace system output The optimized multilayer perceptron neural network model trained in step 1 is used to predict the future through model predictive control (MPC). The output variable value for each sampling period To predict the time domain length; assume a future control time domain The internal control input remains unchanged, that is The predicted output is:

[0116]

[0117] in, Indicates at time step Time Predicted output at time step It is a model function. In time step Control input.

[0118] Step 3: Treat the error between the blast furnace ironmaking system output and the neural network model output as a random variable, and construct a Wasserstein fuzzy set centered on the empirical distribution of historical error samples to describe the distributional uncertainty of the random variable; the flowchart for constructing the Wasserstein fuzzy set is shown below. Figure 9 As shown;

[0119] The specific operation of step 3 is as follows:

[0120] Predictions from historical data collected by the neural network prediction model for blast furnace ironmaking Compared with actual measured value Error between An error sample set is formed, and based on the error sample set, an empirical distribution is constructed. Wasserstein fuzzy set centered It is used to describe the uncertainty of the distribution of random variables;

[0121] The constructed experience distribution It is a discrete uniform distribution, and the formula is:

[0122]

[0123] in, Indicates the number of samples. It is a sample The Dirac measure at a point represents the measure of concentration at that point;

[0124] The Wasserstein fuzzy set quantifies and constrains the uncertainty of the probability distribution through Wasserstein distance, such as Figure 3As shown, its core component is a "sphere" centered on the empirical distribution and with the Wasserstein distance as its radius. This sphere contains all probability distributions that may be similar to the true distribution, thus forming a set that describes the uncertainty of the distribution.

[0125] The constructed experience distribution It is a discrete uniform distribution, and the formula is:

[0126]

[0127] in, Indicates the number of samples. It is a sample The Dirac measure at a point represents the measure of concentration at that point;

[0128] The Wasserstein fuzzy set Based on empirical distribution Centered on, with Let be the set of probability distributions with radius , representing all empirical distributions. Wasserstein distance between No more than the radius probability distribution The formula for Wasserstein fuzzy sets is:

[0129]

[0130] The formula for Wasserstein distance is:

[0131]

[0132] radius The formula is:

[0133]

[0134] in, It is the probability distribution space; For the output dimension, This is a sample of the prediction error for the Wasserstein sphere center distribution, i.e., the empirical distribution of the Wasserstein sphere center. random variables, To output the predicted probability distribution Random error; For coefficients, For a given confidence level.

[0135] Step 4: In the rolling optimization process of model predictive control, feedback correction and the Wasserstein fuzzy set constraint are introduced to construct a split-Bruker constraint problem. The performance index function is minimized under the worst probability distribution while satisfying the output and input constraints.

[0136] The specific operation of step 4 is as follows:

[0137] Step 4.1: Through the feedback adjustment mechanism in model predictive control, the predicted output at future times is corrected in real time to overcome the effects of model mismatch and disturbances. The formula is:

[0138]

[0139] in, The correction matrix has a range of (0,1). The output predicted by the current model. This represents the actual output at the current moment. Indicates the future number Step-by-step correction prediction output; Indicates the future number The model predicts the output of each step;

[0140] Step 4.2: After in The first moment The output constraints for each prediction step are expressed as follows:

[0141]

[0142] in, and To output the maximum and minimum values, Let be a random variable, following a predicted probability distribution. , For auxiliary probability distribution, The expected value of the distribution;

[0143] because It is a constant, and the constraint is written as:

[0144]

[0145] Based on the constructed empirical distribution formula:

[0146]

[0147] Will Transform into:

[0148]

[0149] make Based on strong duality theory and the maximum-minimum inequality, the above equation can be transformed into a solvable deterministic problem:

[0150]

[0151]

[0152]

[0153]

[0154] in, This represents the first [number] element in the training dataset. The first data point One sample, It represents the infinite norm; Indicates transpose; and As dual variables, Representing auxiliary decision variables, using matrices sum vector Define a set of uncertainties in the form of a polyhedron;

[0155] Step 4.3: Construct the objective function based on the above formulas. The objective function Aimed at minimizing the expected setpoint for future output tracking Errors, while penalizing excessively large control increments. At the same time, it ensures that the blast furnace ironmaking system can still meet the operating constraints under the worst disturbance, and the operating constraints include output constraints, input constraints, slack variable constraints, dual norm constraints, and dual variable constraints.

[0156] objective function The formula is:

[0157]

[0158] in, and These are the lengths of the prediction time domain and the control time domain, respectively. and It is a positive definite weight matrix used to balance the tracking and control increments. The punishment To optimize the expected cost in the worst-case scenario, Indicating the future Expected output value; Indicates the future number The rate of change of the control input for each step;

[0159] The output constraints are:

[0160]

[0161] The input constraints are:

[0162]

[0163] The slack variable constraint is:

[0164]

[0165] The dual norm constraint is:

[0166]

[0167] The dual variable constraint is:

[0168]

[0169] These constraints ensure the robustness of the system under uncertainty.

[0170] Step 5: Solve the optimization problem to obtain the optimal control sequence at the current moment, and add the first control variable in the optimal control sequence to the blast furnace ironmaking system to generate a new output for iteration.

[0171] The specific operation of step 5 is as follows:

[0172] Step 5.1: Use a genetic algorithm to optimize and solve for the optimal control sequence. Only the first control variable in the sequence Applied to the blast furnace system; genetic algorithms such as Figure 10 As shown.

[0173] Step 5.2: Obtain the next sampling time The system outputs new measurement values. ; Controller Starting from a new point, repeat steps 2 through 5 to form a closed-loop feedback, rolling forward optimized control process.

[0174] Figure 4 The comparison between the control performance of the proposed method and the conventional MPC method shows that the proposed method has superior control performance and a tracking effect closer to the expected value. The proposed method significantly reduces output response overshoot and achieves faster stabilization. This indicates that the proposed method can effectively handle the worst-case scenario caused by model mismatch and unknown disturbances, ensuring system stability under uncertain conditions and achieving accurate setpoint tracking, while also helping to reduce process energy consumption.

[0175] Figure 5The Wasserstein sphere radius in a specific embodiment of the present invention Compared with the input of ordinary MPC, it can be seen that the input of the method of the present invention is smoother. Compared with the aggressive control instructions that may be generated by traditional MPC in pursuit of instantaneous optimality, the present invention naturally generates a smoother and physically easier-to-execute control signal through the decomposed bar optimization framework, which helps to reduce the wear of actuators and mechanical stress of equipment, extend equipment life, and ensure production stability.

[0176] Figure 6 and Figure 7 This paper compares the control output and control input under different Wasserstein sphere radii in specific embodiments of the present invention. As the Wasserstein sphere radius increases, the control performance of the blast furnace ironmaking process changes significantly. When the Wasserstein sphere radius is 0.1731 and 0.2234, the silicon content and molten iron temperature can achieve good tracking effect, and the control input does not saturate. When the Wasserstein sphere radius is further increased to 0.3870 and 0.5473, although the control output remains stable, the control input reaches the constraint boundary at some times. Nevertheless, even if the control input reaches the boundary value, the stochastic process can still remain within the boundary without exceeding the boundary. This shows that the proposed control method has high robustness and effectiveness when considering non-Gaussian modeling errors and disturbances.

[0177] Table 1 Different Wasserstein radius parameters

[0178]

[0179] Table 1 shows the different Wasserstein radius parameters in the specific embodiments of the present invention. Through reasonable parameter design, even with a large sphere radius, the stochastic process still maintains the stability of input and output, verifying the applicability and reliability of the method in the face of complex uncertainty conditions.

[0180] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A predictive optimization control method for non-Gaussian stochastic processes based on Wasserstein fuzzy sets, characterized in that, The method includes the following steps: Step 1: Collect the pressure difference of the blast furnace ironmaking system 1. Set the pulverized coal injection rate Oxygen-enriched flow rate Cold air flow molten iron temperature and Si content A neural network prediction model for blast furnaces was established using data from the blast furnace ironmaking system. Step 2: Based on the current blast furnace status and the blast furnace neural network prediction model, predict the future through model predictive control. Output variable values ​​for each sampling period; Step 3: Treat the error between the output of the blast furnace ironmaking system and the output of the neural network model as a random variable, and construct a Wasserstein fuzzy set centered on the empirical distribution of historical error samples to describe the distributional uncertainty of the random variable; Step 4: In the rolling optimization process of model predictive control, feedback correction and the Wasserstein fuzzy set constraint are introduced to construct a split-Bruker constraint problem. The performance index function is minimized under the worst probability distribution while satisfying the output and input constraints. Step 5: Solve the optimization problem to obtain the optimal control sequence at the current moment, and add the first control variable in the optimal control sequence to the blast furnace ironmaking system to generate a new output for iteration.

2. The non-Gaussian stochastic process predictive optimization control method based on Wasserstein fuzzy sets according to claim 1, characterized in that, The specific operation of step 1 is as follows: A neural network prediction model for blast furnace ironmaking is established using a multilayer perceptron neural network model to capture the nonlinear dynamic relationship between input and output variables, and to predict the temperature of molten iron. and Si content Set the pressure difference as the model output variable. Oxygen-enriched flow rate 1. Set the pulverized coal injection rate Cold air flow Set the data as model input variables; Suppose a multilayer perceptron neural network model has L hidden layers, then the overall calculation formula is: ； in, The activation function for the hidden layer. For input variables, For the first The weight matrix of the layer, For the first The layer's bias matrix; Constructing a dynamic mapping relationship between control inputs and outputs using a multilayer perceptron neural network model: ； in, and These represent the actual input and actual output of the system control, respectively. This represents the predicted output of the neural network prediction model for blast furnace ironmaking. A neural network prediction model for blast furnace ironmaking; and These are the time delay parameters for the output and input, respectively; The particle swarm optimization algorithm is used to optimize the parameters of a multilayer perceptron neural network model, thereby improving the convergence speed and global search capability of the blast furnace ironmaking neural network prediction model. The process of the particle swarm optimization algorithm is as follows: , ,in, , The maximum number of iterations, For inertial weights, and These are individual learning factors and group learning factors, respectively. and These are random numbers that follow a uniform distribution. In the first After the next iteration, the particles The optimal solution has been found. In the first The optimal solution in the entire particle swarm after the next iteration; and Distributed as particles In the After the nth iteration A velocity vector and a position vector of dimension, where , For population size, and , represents the dimension of the particle to be searched.

3. The non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets according to claim 2, characterized in that, The specific operation of step 2 is as follows: Read the current blast furnace system output The optimized and trained multilayer perceptron neural network model from step 1 is used to predict the future through model-based predictive control. The output variable value for each sampling period To predict the time domain length; assume a future control time domain The internal control input remains unchanged, that is The predicted output is: ,in, Indicates at time step Time Predicted output at time step It is a model function. In time step Control input.

4. The non-Gaussian stochastic process predictive optimization control method based on Wasserstein fuzzy sets according to claim 3, characterized in that, The specific operation of step 3 is as follows: Predictions from historical data collected by neural network prediction models for blast furnace ironmaking Compared with actual measured value Error between An error sample set is formed, and based on the error sample set, an empirical distribution is constructed. Wasserstein fuzzy set centered It is used to describe the uncertainty of the distribution of random variables; The constructed experience distribution It is a discrete uniform distribution, and the formula is: ,in, Indicates the number of samples. It is a sample The Dirac measure at a point represents the measure of concentration at that point; The Wasserstein fuzzy set Based on empirical distribution Centered on, with Let be the set of probability distributions with radius , representing all empirical distributions. Wasserstein distance between No more than the radius probability distribution The formula for Wasserstein fuzzy sets is: ； The formula for Wasserstein distance is: ； radius The formula is: ； in, It is the probability distribution space; For the output dimension, This is a sample of the prediction error for the Wasserstein sphere center distribution, i.e., the empirical distribution of the Wasserstein sphere center. random variables, To output the predicted probability distribution Random error; The distance between random variables ; for and The joint distribution; For coefficients, For a given confidence level.

5. The non-Gaussian stochastic process predictive optimization control method based on Wasserstein fuzzy sets according to claim 4, characterized in that, The specific operation of step 4 is as follows: Step 4.1: Through the feedback correction mechanism in model predictive control, the predicted output at future times is corrected in real time to overcome the effects of model mismatch and disturbances. The formula is: ， in, The correction matrix has a range of (0,1). The output predicted by the current model. This represents the actual output at the current moment. Indicates the future number Step-by-step correction prediction output; Indicates the future number The model predicts the output of each step; Step 4.2: After in The first moment The output constraints for each prediction step are expressed as follows: ,in, and To output the maximum and minimum values, Let be a random variable, following a predicted probability distribution. , For auxiliary probability distribution, The expected value of the distribution; because It is a constant, and the constraint is written as: According to the constructed empirical distribution formula: ,Will Transform into: ， make Based on strong duality theory and the maximum-minimum inequality, the above equation can be transformed into a solvable deterministic problem: ， ， , ,in, This represents the first [number] element in the training dataset. The first data point One sample, It represents the infinite norm; Indicates transpose; and As dual variables, Representing auxiliary decision variables, using matrices sum vector Define a set of uncertainties in the form of a polyhedron; Step 4.3: Construct the objective function based on the above formulas. The objective function Minimize future output tracking expected setpoint Errors, while penalizing excessively large control increments. At the same time, it ensures that the blast furnace ironmaking system can still meet the operating constraints under the worst disturbance, and the operating constraints include output constraints, input constraints, slack variable constraints, dual norm constraints, and dual variable constraints. objective function The formula is: ， in, and These are the lengths of the prediction time domain and the control time domain, respectively. and It is a positive definite weight matrix used to balance the tracking and control increments. The punishment To optimize the expected cost in the worst-case scenario, Indicating the future Expected output value; Indicates the future number The rate of change of the control input for each step; The output constraints are: ； The input constraints are: ； The slack variable constraint is: ； The dual norm constraint is: ； The dual variable constraint is:

6. The non-Gaussian stochastic process prediction optimization control method based on Wasserstein fuzzy sets according to claim 5, characterized in that, The specific operation of step 5 is as follows: Step 5.1: Use a genetic algorithm to optimize and solve for the optimal control sequence. Only the first control variable in the sequence Apply to the blast furnace system; Step 5.2: Obtain the next sampling time The system outputs new measurement values. ; Controller Starting from a new point, repeat steps 2 through 5 to form a closed-loop feedback, rolling forward optimized control process.

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