Slurry circulation control method and system based on multi-target control

Abstract

The invention provides a slurry circulation control method and system based on multi-target control, and relates to the technical field of slurry circulation control. According to the technical scheme provided by the invention, the constraint boundary and the weight coefficient of the model are modified in real time according to working condition changes. When the load of the unit fluctuates severely or the sulfur content of the coal is suddenly changed, the model structure is reconstructed, the generated multi-target fitness function accurately adapts to the optimization requirement of the suddenly changed working condition, and the Pareto leading-edge solution set obtained through iterative optimization fully reflects the optimal tradeoff relation under the current transient characteristics. After the robust optimal solution screened from the solution set is analyzed into the control instruction, the circulating pump combination and rotating speed adjustment of the slurry circulating system can accurately respond to sudden change of the working condition, control failure of a traditional fixed model under the sudden change working condition is avoided, and therefore the control effect of the desulfurization system under the complex dynamic working condition is remarkably improved.

Description

Technical Field

[0001] This application relates to the field of slurry circulation control technology, specifically to a slurry circulation control method and system based on multi-objective control. Background Technology

[0002] Currently, limestone-gypsum wet desulfurization technology is widely used in flue gas treatment in thermal power plants and chemical industries due to its high maturity. Among them, the slurry circulation system is the core subsystem, and its energy consumption accounts for the majority of the total desulfurization energy consumption.

[0003] Existing slurry circulation control methods often rely on CFD simulations to supplement operational data, constructing a transfer function for the slurry pump flow control system, and using Bode plots for time-frequency domain analysis to assess system stability. The optimal range of values ​​satisfying stable desulfurization conditions is then used as the optimization result. However, this approach is problematic in scenarios with rapid changes in operating conditions. Since the transfer function is typically obtained by linearizing a nonlinear system near a specific operating point, significant nonlinear shifts in the dynamic characteristics of the desulfurization system (such as gas-liquid mass transfer rate and pH response curve) occur when the unit load fluctuates rapidly between 50% and 100%. This leads to a decrease in the accuracy of the transfer function model constructed based on a single or limited number of operating points. In summary, the control methods in these technologies struggle to accurately control the slurry circulation system under conditions of sudden changes in operating conditions, resulting in poor control performance. Summary of the Invention

[0004] This application provides a slurry circulation control method and system based on multi-objective control, which can accurately control the slurry circulation system under sudden changes in operating conditions, thereby improving the control effect.

[0005] Firstly, this application provides a slurry circulation control method based on multi-objective control, the method comprising: Real-time operating data of the desulfurization system is collected, a state vector containing unit load, inlet sulfur content and slurry pH value is constructed, and the time derivative of each parameter in the state vector is calculated to generate a trend feature vector characterizing the severity of transient changes in the system. The current operating condition of the desulfurization system is determined based on the trend feature vector, and the set of target indicators that need to be included in the optimization under the current operating condition is selected. Based on the target indicators in the target indicator set, the constraint boundaries and weight coefficients in the preset multi-objective control model are adjusted to obtain the multi-objective fitness function; The Pareto front solution set is obtained by iteratively optimizing the population of control variables in the desulfurization system using a multi-objective fitness function. The robust optimal solution with the highest comprehensive fitness is selected from the Pareto front solution set, and the robust optimal solution is analyzed into the optimal control command for the current operating condition of the slurry circulation control system.

[0006] By employing the above technical solution, a state vector containing unit load, inlet sulfur content, and slurry pH value is constructed, and the time derivative is calculated to generate a trend feature vector, enabling real-time quantification of the severity of transient changes in the desulfurization system. The operating condition characteristics identified by the trend feature vector directly drive the dynamic selection of the target index set, ensuring that the multi-objective control model does not seek the optimal solution in a fixed structure, but rather modifies the model's constraint boundaries and weight coefficients in real time according to changes in operating conditions. When the unit load fluctuates drastically or the coal sulfur content changes abruptly, the model structure is reconstructed accordingly, and the generated multi-objective fitness function accurately adapts to the optimization requirements of the abrupt operating conditions. The Pareto front solution set obtained through iterative optimization fully reflects the optimal trade-off relationship under the current transient characteristics. After the robust optimal solution selected from the solution set is parsed into control commands, the circulation pump combination and speed regulation of the slurry circulation system can accurately respond to abrupt changes in operating conditions, avoiding the control failure of the traditional fixed model under abrupt operating conditions, thereby significantly improving the control effect of the desulfurization system under complex dynamic operating conditions.

[0007] Secondly, this application provides a slurry circulation control system based on multi-objective control, the system comprising: The data acquisition module is used to collect real-time operating data of the desulfurization system, construct a state vector containing unit load, inlet sulfur content and slurry pH value, calculate the time derivative of each parameter in the state vector, and generate a trend feature vector characterizing the intensity of transient changes in the system. The operating condition type determination module is used to determine the current operating condition type of the desulfurization system based on the trend feature vector, and to filter the set of target indicators that need to be included in the optimization under the current operating condition type. The function optimization module is used to adjust the constraint boundaries and weight coefficients in the preset multi-objective control model according to the target indicators in the target indicator set, so as to obtain the multi-objective fitness function. The function solving module is used to iteratively optimize the population of control variables in the desulfurization system using a multi-objective fitness function to obtain the Pareto front solution set. The output module is used to select the robust optimal solution with the highest comprehensive fitness from the Pareto front solution set, and to parse the robust optimal solution into the optimal control command for the current operating condition of the slurry circulation control system.

[0008] Thirdly, this application provides a computer storage medium that stores multiple instructions adapted for loading by a processor and executing any of the methods described above.

[0009] Fourthly, this application provides an electronic device including a processor, a memory, and a transceiver. The memory is used to store instructions, the transceiver is used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform any of the methods described above.

[0010] In summary, the beneficial effects of the technical solution of this application include: By employing the above technical solution, a state vector containing unit load, inlet sulfur content, and slurry pH value is constructed, and the time derivative is calculated to generate a trend feature vector, enabling real-time quantification of the severity of transient changes in the desulfurization system. The operating condition characteristics identified by the trend feature vector directly drive the dynamic selection of the target index set, ensuring that the multi-objective control model does not seek the optimal solution in a fixed structure, but rather modifies the model's constraint boundaries and weight coefficients in real time according to changes in operating conditions. When the unit load fluctuates drastically or the coal sulfur content changes abruptly, the model structure is reconstructed accordingly, and the generated multi-objective fitness function accurately adapts to the optimization requirements of the abrupt operating conditions. The Pareto front solution set obtained through iterative optimization fully reflects the optimal trade-off relationship under the current transient characteristics. After the robust optimal solution selected from the solution set is parsed into control commands, the circulation pump combination and speed regulation of the slurry circulation system can accurately respond to abrupt changes in operating conditions, avoiding the control failure of the traditional fixed model under abrupt operating conditions, thereby significantly improving the control effect of the desulfurization system under complex dynamic operating conditions. Attached Figure Description

[0011] Figure 1 This is a schematic flowchart of a slurry circulation control method based on multi-objective control according to an embodiment of this application; Figure 2 This is a schematic diagram of a slurry circulation control system based on multi-objective control according to an embodiment of this application; Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0012] Explanation of reference numerals in the attached drawings: 300, electronic device; 301, processor; 302, communication bus; 303, user interface; 304, network interface; 305, memory. Detailed Implementation

[0013] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0014] In the description of the embodiments in this application, terms such as exemplary, for example, or illustrative are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as exemplary, for example, or illustrative in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design solutions. Rather, the use of terms such as exemplary, for example, or illustrative is intended to present the relevant concepts in a specific manner.

[0015] In the description of the embodiments of this application, the term "multiple" means two or more. For example, "multiple systems" refers to two or more systems, and "multiple screen terminals" refers to two or more screen terminals. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0016] Please see Figure 1 This is a flowchart illustrating a slurry circulation control method based on multi-objective control, provided in an embodiment of this application. This method can be implemented using a computer program, a microcontroller, or run on a slurry circulation control system based on the von Neumann architecture and multi-objective control. The computer program can be integrated into the application or run as a standalone utility application. The specific steps of the slurry circulation control method based on multi-objective control are described in detail below.

[0017] S101: Collect real-time operating data of the desulfurization system, construct a state vector including unit load, inlet sulfur content and slurry pH value, calculate the time derivative of each parameter in the state vector, and generate a trend feature vector characterizing the intensity of transient changes in the system. Real-time operational data refers to physical measurements reflecting the operating status of the desulfurization system collected by a distributed sensor network at the current moment, such as process parameters like flue gas flow rate, sulfur dioxide concentration, slurry flow rate, and circulating pump current. The state vector represents a multi-dimensional array structure organized according to specific dimensions of multiple key operating parameters, used to comprehensively describe the current operating status of the system. In this embodiment, the state vector includes three core state variables: unit load, inlet sulfur content, and slurry pH value. Unit load represents the current output level of the generator unit, measured in megawatts; inlet sulfur content represents the sulfur dioxide concentration in the flue gas entering the desulfurization tower, measured in milligrams per cubic meter; and slurry pH value represents the acidity or alkalinity of the limestone slurry in the absorption tower. The time derivative refers to the instantaneous rate of change of each parameter in the state vector over time, obtained by calculating the difference between parameter values ​​at adjacent sampling times, reflecting the dynamic trend of parameter changes. The trend feature vector represents the feature vector composed of the time derivatives of each state parameter. Its magnitude quantifies the severity of transient changes in the desulfurization system; a larger magnitude indicates faster system state changes and more severe operating condition fluctuations.

[0018] Specifically, this step first involves acquiring multi-source operational data of the desulfurization system in real time using a data acquisition system with a fixed sampling period, typically one second. Three key parameters—unit load, inlet sulfur content, and slurry pH—are extracted from the acquired data and organized sequentially to construct a state vector. Then, a sliding time window method is used to calculate the time derivative of each parameter. For the current moment, the difference between the current sampled value and the previous sampled value is calculated and divided by the sampling time interval to obtain the instantaneous rate of change of each parameter. To eliminate the influence of differences in the dimensions of different parameters, a preset normalization factor is used to standardize the time derivatives of each parameter. For example, the unit load derivative is divided by the rated unit load, the inlet sulfur content derivative by the design sulfur content, and the slurry pH derivative by the normal pH range. This normalization process makes the rates of change of different physical quantities comparable, resulting in normalized components. Finally, the three normalized derivative components are combined to form a trend feature vector, which includes the unit load rate of change component, the inlet sulfur content rate of change component, and the slurry pH value rate of change component.

[0019] In some embodiments, the construction of state vectors and the generation of trend feature vectors can be achieved in various ways. Optionally, a state estimation method based on Kalman filtering is adopted. First, a state-space model of the desulfurization system is established, with unit load, inlet sulfur content, and slurry pH value as state variables. State equations and observation equations are established to describe the dynamic characteristics of the system. Then, the Kalman filter is used to optimally estimate the noisy sensor measurements. Through recursive calculations in two steps—prediction and update—a high-precision filtered state vector is obtained. Next, the state prediction step of the Kalman filter directly outputs the first-order derivative estimates of the state variables. The derivative is calculated using the state transition matrix inside the filter. Finally, the derivative estimates are adaptively normalized. The normalization factor is dynamically adjusted based on historical statistical data so that the normalization factor can adapt to seasonal changes and long-term trends in operating conditions, generating a trend feature vector that accurately reflects the dynamics of the system. It is understood that other methods can also be used to calculate the time derivative, which is not limited here.

[0020] S102: Determine the current operating condition type of the desulfurization system based on the trend feature vector, and select the set of target indicators that need to be included in the optimization under the current operating condition type; Among them, operating condition type refers to the different operating modes of the desulfurization system classified according to its operating state characteristics. Different operating condition types correspond to different control requirements and optimization focuses. This embodiment includes four typical types: steady-state maintenance condition, load ramp-up condition, load decline condition, and chemical oscillation condition. The target index set refers to the combination of performance indicators that need to be included in the multi-objective optimization calculation based on the current operating condition type. These include environmental targets such as outlet sulfur dioxide concentration and desulfurization efficiency, economic targets such as circulating pump power consumption, limestone consumption, and operating costs, and quality targets such as slurry density, gypsum crystallization quality, and slurry activity.

[0021] Specifically, this step determines the current operating condition of the desulfurization system and selects corresponding optimization targets through hierarchical judgment logic. First, the Euclidean modulus of the trend feature vector is calculated and compared with a preset steady-state threshold. The steady-state threshold is usually determined based on historical system operating data and represents the upper limit of normal steady-state fluctuations. If the modulus is less than the steady-state threshold, it indicates that all state parameters change very smoothly, and the system is in quasi-static operation, which is judged as a steady-state maintenance condition. At this time, economic and quality targets are selected as the focus of optimization because the system is already in a stable and compliant state with relatively low environmental pressure. The focus can be on reducing operating costs and improving gypsum quality to create value for subsequent sales. If the modulus is greater than or equal to the steady-state threshold, it indicates that the system has significant fluctuations, and the second-level judgment is entered. The first component of the trend feature vector represents the unit load change rate, and the second component represents the inlet sulfur content change rate. If either component is positive, it indicates that the desulfurization load is increasing, and the system is facing greater desulfurization pressure, which is judged as a load ramp-up condition. Environmental and economic targets are then selected, prioritizing ensuring that outlet emissions do not exceed standards during load increases, while also considering economic efficiency to avoid excessive adjustments and energy waste. If both the first and second components are negative, it indicates that the load and sulfur content are decreasing simultaneously, and the desulfurization pressure is reduced. This is identified as a load reduction condition. Economic and quality objectives are then selected, and economic optimization is performed during the period of reduced desulfurization pressure. The circulation volume and limestone supply are appropriately reduced, while the slurry quality is optimized to prepare for the next load increase. If the absolute values ​​of both the first and second components are less than the preset explicit threshold, it indicates that the load and sulfur content changes are not significant. However, if the absolute value of the third component in the trend feature vector, which represents the pH change of the slurry, is greater than the preset fluctuation threshold, it indicates that the chemical state of the slurry is fluctuating abnormally. This is identified as a chemical oscillation condition. In this case, it is necessary to comprehensively balance the environmental, economic, and quality objectives simultaneously to prevent abnormal pH fluctuations from causing a decrease in desulfurization efficiency or a deterioration in slurry quality. The chemical state of the system is stabilized through multi-objective synergistic control.

[0022] S103: Based on the target indicators in the target indicator set, adjust the constraint boundaries and weight coefficients in the preset multi-objective control model to obtain the multi-objective fitness function; In this context, constraint boundaries refer to the restrictions on the range of values ​​for control variables in a multi-objective control model. Control variables include adjustable operating parameters such as slurry circulation pump speed, slurry flow rate, oxidation air volume, and makeup water flow rate. Constraint boundaries include two categories: equipment physical limits and process safety constraints. Equipment physical limits, such as maximum circulation pump speed and maximum valve opening, are provided by the equipment manufacturer. Process safety constraints, such as minimum circulation volume and maximum liquid level, are determined by process design specifications. Weighting coefficients represent the relative importance allocation scheme of each optimization objective in the multi-objective control model. They quantify the priority of different objectives in comprehensive optimization. Weighting coefficients are usually normalized to sum to one; a larger weighting coefficient indicates a higher importance of the corresponding objective in optimization. The multi-objective fitness function is a mathematical function that comprehensively evaluates the quality of a control scheme. It combines multiple optimization objectives into a single evaluation index through weighted summation or other aggregation methods, and also includes a constraint violation penalty term. It guides subsequent evolutionary optimization algorithms in searching for optimal control parameters; a smaller or larger fitness function value indicates a better control scheme.

[0023] Specifically, this step involves parametrically adjusting the multi-objective control model based on the selected set of target indicators. First, the constraint boundaries are adjusted by identifying the first unselected indicator from the target indicator set. These indicators have low priority under the current operating conditions, and their corresponding constraint ranges are set to the physical limits of the equipment, allowing the control variables to vary within the maximum feasible region. For the second selected indicator included in the optimization, stricter constraint protection is introduced. The calculation method involves calculating the boundary contraction coefficient corresponding to the magnitude of the trend feature vector based on a preset monotonically increasing contraction function. This coefficient ranges from 0 to 1; the larger the magnitude, the larger the contraction coefficient, indicating a stronger constraint contraction is needed. Then, the physical limits of the equipment are contracted. For example, the upper limit of the circulating pump speed is contracted by a ratio of one minus the contraction coefficient, and the lower limit is expanded by a ratio of one plus the contraction coefficient, resulting in a narrower allowable control domain as a dynamic defensive boundary. This makes the control action more conservative when the system fluctuates drastically, avoiding over-adjustment that exacerbates system oscillations. For adjusting the weighting coefficients, firstly, the fixed maintenance proportion of unselected indicators outside the target indicator set is determined, and the remaining weights are used as the total dynamic allocation amount. Then, a response mapping relationship is established based on the real-time changes in the trend feature vector. For example, when the first component representing load change is positive and large, the demand intensity of environmental protection targets increases, and the real-time demand intensity value of each selected target is calculated. Next, the demand intensity is normalized, and the total dynamic allocation amount is distributed proportionally to each selected target to obtain the weighting coefficient of each target. Finally, a fitness function is constructed. The predicted values ​​of each target are weighted and summed using the weighting coefficients to obtain a weighted evaluation term. At the same time, it is detected whether the control variables exceed the dynamic defensive boundary. For individuals that exceed the boundary, a penalty term is calculated based on the degree of deviation. The weighted evaluation term and the penalty term are combined to generate the final multi-objective fitness function.

[0024] S104: Use a multi-objective fitness function to iteratively optimize the population of control variables in the desulfurization system to obtain the Pareto front solution set; In evolutionary optimization algorithms, the control variable population refers to a group of individuals, each representing a set of control variable values. For example, it could be a vector containing multiple control parameters such as slurry circulation pump speed, limestone slurry feed rate, and oxidation air volume. Iterative optimization represents an optimization search process that improves the population quality generation by generation, simulating natural evolution. Each iteration retains individuals with high fitness and eliminates inferior individuals, causing the population to evolve towards the optimal solution. The Pareto front represents the set of all non-dominated solutions in a multi-objective optimization problem. These solutions form a front in the objective space, where any solution on the front, while improving one objective, inevitably leads to the deterioration of other objectives, representing the optimal compromise in multi-objective optimization. The Pareto front solution set refers to the set of approximate Pareto optimal solutions obtained after iterative optimization, containing multiple control schemes that perform well under different objective trade-offs. A non-dominated solution is a solution in multi-objective optimization that is not strictly dominated by other solutions; that is, there is no other solution that is no worse than this solution in all objectives and is strictly better than this solution in at least one objective.

[0025] Specifically, this step employs a multi-objective evolutionary algorithm to optimize the search for control variables. First, the control variable population is initialized by randomly generating several individuals within the allowable control domain of a dynamically defensive boundary constraint. Each individual represents a feasible solution for a set of slurry circulation control parameters. Then, an iterative loop is entered. For each individual in the population, multiple performance indicators of the desulfurization system are predicted based on the current control parameters. For example, the outlet sulfur dioxide concentration, total power consumption of the circulating pump, and slurry gypsum quality are predicted using a mechanistic model or a data-driven model. The predicted indicator values ​​are substituted into the constructed multi-objective fitness function to calculate the comprehensive fitness score for each individual. Based on the fitness values, individuals are non-dominated and sorted, dividing the population into multiple non-dominated levels. The first level contains the non-dominated solutions of the current population, i.e., the current Pareto front. Genetic operations are performed to generate offspring. Parent individuals are selected using tournament selection or roulette wheel selection methods. Simulated binary crossover or differential evolution crossover is performed on the parents to generate offspring. Then, polynomial mutation or Gaussian mutation is performed on the offspring to introduce random perturbations, ensuring that the offspring inherit the excellent characteristics of their parents while also possessing the ability to explore new solution spaces. The parent and offspring generations are merged to form a mixed population. Non-dominated sorting and crowding calculations are then performed again. A specified number of individuals are selected from the mixed population to form the next generation, prioritizing the retention of individuals with higher non-dominated levels and, within the same level, prioritizing the retention of individuals with higher crowding to maintain solution diversity. This iterative process is repeated until the termination condition is met. The final output is the current set of non-dominated solutions as the Pareto front solution set, which contains multiple control strategies that perform well under different objective trade-offs.

[0026] S105: Select the robust optimal solution with the highest comprehensive fitness from the Pareto front solution set, and parse the robust optimal solution into the optimal control command for the current operating condition of the slurry circulation control system.

[0027] Among them, comprehensive fitness refers to the overall evaluation index of an individual in multi-objective optimization after considering the performance of all objectives simultaneously. It includes not only the weighted performance of each optimization objective, but also comprehensive characteristics such as robustness and stability of the solution. Robust optimal solution represents the control scheme with the strongest disturbance resistance and stability in the Pareto front solution set. This scheme can maintain good performance under parameter uncertainty or external disturbances, and has higher practical application value compared to other front solutions. Analysis is used to represent the mapping process of converting the abstract numerical solution output by the optimization algorithm into specific executable control commands, including restoring normalized decision variables to actual physical quantities and generating setpoints for each actuator. Optimal control commands refer to the specific operating commands sent to each actuator of the slurry circulation control system. These commands directly drive the actions of field equipment to achieve the optimized control effect.

[0028] Specifically, this step involves selecting the most robust optimal solution for the current operating conditions from the Pareto front solution set and converting it into executable control instructions. First, robustness is evaluated for each candidate solution in the Pareto front solution set. Using Monte Carlo simulation, each candidate solution undergoes multiple performance evaluations under parameter uncertainty conditions, calculating the mean and variance of performance indicators. A smaller variance indicates better robustness. Alternatively, sensitivity analysis is used to calculate the sensitivity of the candidate solution to key uncertain parameters; lower sensitivity indicates less sensitivity to parameter fluctuations. Then, the overall fitness is calculated. Multiple dimensions of the candidate solutions, such as multi-objective performance, robustness indicators, and engineering feasibility indicators, are normalized and weighted to obtain a fitness score reflecting the overall quality of the solution. Alternatively, a multi-attribute decision model is established, and methods such as the ideal point method are used to evaluate the closeness of each candidate solution to the ideal solution. The solution with the highest closeness is the one with the highest overall fitness. The candidate solution with the highest overall fitness score is selected as the robust optimal solution. This solution not only performs excellently in multi-objective optimization but also possesses good stability and practical operability. Finally, the robust optimal solution is analyzed and transformed to restore the optimization variables from the normalized interval to the actual physical dimensions. For example, the normalized speed value is restored to the actual speed. According to the communication protocol format of the control system, a standardized control command data packet is generated, which includes information such as device address, parameter type, and set value. The control commands are then sent to each actuator of the slurry circulation system through the industrial fieldbus to drive the equipment to operate according to the optimal scheme.

[0029] Based on the above embodiments, as an optional implementation method, the method of collecting real-time operating data of the desulfurization system in S101, constructing a state vector including unit load, inlet sulfur content and slurry pH value, and calculating the time derivative of each parameter in the state vector to generate a trend feature vector characterizing the intensity of transient changes in the system can be specifically achieved through the following steps S201-S203.

[0030] S201: Sliding window sampling is performed on the unit load, inlet sulfur content and slurry pH value in the state vector. The difference ratio between the current sampling time and the previous sampling time is calculated to obtain the time derivative of each parameter, and the time derivative is used as the real-time physical change rate. The difference ratio is the quotient obtained by dividing the difference between the parameter value at the current time and the parameter value at the previous time by the time interval, and is used to quantify the rate of change of the parameter.

[0031] Specifically, real-time measurements of unit load, inlet sulfur content, and slurry pH are continuously read at a fixed sampling period and stored in a time-series data cache. The first-order difference can be calculated using a sliding window method, with the following formula: ;in, This represents the i-th parameter in the state vector. The time derivative of the parameter. Indicates the sampling period.

[0032] When calculating the time derivative, the parameter values ​​at the current sampling time and the previous sampling time are extracted from the buffer. Differential operations are then performed on the three parameters—unit load, inlet sulfur content, and slurry pH—by subtracting the previous parameter value from the current value to obtain the change in the parameter over one sampling period. This change is then divided by the sampling time interval to obtain the change in the parameter per unit time, i.e., the time derivative of each parameter. A positive time derivative indicates an upward trend, while a negative time derivative indicates a downward trend. The absolute value reflects the rate of change of the parameter.

[0033] S202: Normalize the real-time physical change rate using a preset benchmark normalization factor to obtain multiple vector components corresponding to each parameter. The benchmark normalization factor refers to a pre-defined standardization parameter used to eliminate differences in the dimensions of different physical quantities. A corresponding normalization coefficient is set for each state variable. Normalization processing represents the mathematical operation of mapping physical quantities with different dimensions and numerical ranges to a unified dimensionless numerical range through a linear transformation. Vector components are used to represent the scalar elements of the trend characteristic vector in each dimension, with each component corresponding to the normalized time derivative of a state parameter.

[0034] Specifically, since unit load, inlet sulfur content, and slurry pH value have different physical units and numerical ranges, directly using time derivatives for comparison and combination results in dimensional inconsistencies. Therefore, benchmark normalization factors are set for each of the three parameters: the normalization factor for unit load is set to the rated load value, the normalization factor for inlet sulfur content is set to the design coal sulfur content value, and the normalization factor for slurry pH value is set to the allowable pH variation range. The time derivative of each parameter is divided by its corresponding benchmark normalization factor to obtain dimensionless standardized values. The normalized values ​​eliminate the differences in physical units, making the rates of change of different parameters comparable. Each normalized time derivative value serves as a component of a trend feature vector, with the three parameters corresponding to three vector components, forming elements in a three-dimensional vector space.

[0035] S203: Combine the vector components to obtain the trend feature vector that characterizes the severity of transient changes in the system.

[0036] Specifically, following the order of unit load, inlet sulfur content, and slurry pH, three normalized vector components are arranged sequentially to form a three-dimensional vector. This vector corresponds to a point in three-dimensional space, and the position of the point reflects the current transient change characteristics of the system. The magnitude of this vector is calculated by squaring each of the three components, summing the squared values, and then taking the square root of the sum to obtain the vector length. The vector magnitude comprehensively reflects the intensity of system changes in various dimensions; a larger magnitude indicates a faster overall system state change and more severe operational fluctuations. This vectorized representation compresses the change information of multiple parameters into a single feature vector, preserving both the direction and magnitude of each parameter's change and providing a quantitative indicator of the overall system fluctuation.

[0037] Based on the above embodiments, as an optional implementation method, the method of determining the current operating condition type of the desulfurization system according to the trend feature vector in S103 and screening the set of target indicators to be included in the optimization under the current operating condition type can be implemented through the following steps S301-S305.

[0038] S301: Calculate the magnitude of the trend feature vector. If the magnitude is less than the preset steady-state threshold, determine that the current working condition is a steady-state condition and select economic and quality targets as the target indicator set. The modulus of the trend feature vector refers to the scalar value obtained by calculating the Euclidean norm of the trend feature vector, used to quantify the severity of the transient changes in the overall desulfurization system. Specifically, if the trend feature vector contains three components—the rate of change of unit load, the rate of change of inlet sulfur content, and the rate of change of slurry pH—then the modulus is calculated as the square root of the sum of the squares of these three components. For example, when the three components are 0.02, 0.01, and 0.015, the calculated modulus is approximately 0.0265. The steady-state threshold represents a pre-set critical value used to distinguish between steady-state operation and dynamic changes in the system. This threshold is determined based on statistical analysis of historical operating data of the desulfurization system and is typically set between 0.05 and 0.1. When the modulus is below this threshold, it indicates that the system parameters change slowly and are in a relatively stable state. The steady-state maintenance condition refers to the operating state in which the desulfurization system maintains relatively stable and small-amplitude changes in key parameters such as unit load, inlet flue gas sulfur content, and slurry chemical properties. Under this condition, the system does not require frequent adjustments to the control strategy. Economic objectives are used to represent optimization indicators aimed at reducing operating costs, reducing energy consumption, and optimizing reagent usage efficiency, such as minimizing the power consumption of the slurry circulation pump and reducing the consumption of limestone slurry. Quality objectives refer to optimization indicators that ensure the quality of desulfurization product gypsum meets the requirements for subsequent utilization or disposal, including control targets for parameters such as gypsum moisture content, purity, and crystal morphology.

[0039] Specifically, the three components of the trend feature vector are squared respectively, the three squared values ​​are summed, and the square root of the sum is taken to obtain the vector magnitude. The calculated magnitude is compared with a preset steady-state threshold. If the magnitude is less than the steady-state threshold, it indicates that the rate of change of the three parameters—unit load, inlet sulfur content, and slurry pH—is at a low level, and the overall system fluctuation is small, thus determining the current operating state as a steady-state condition. Under steady-state conditions, the desulfurization system has been operating stably and meets the standards, with relatively low environmental pressure. The optimization focus shifts to reducing operating costs and improving product quality. Therefore, economic and quality objectives are selected from a preset target library, and these two types of objectives are combined to form the target index set for the current operating condition.

[0040] S302: If the modulus is greater than or equal to the steady-state threshold, then extract the first component representing the change in unit load and the second component representing the change in inlet sulfur content from the trend feature vector; The modulus greater than or equal to the steady-state threshold indicates that the Euclidean norm of the trend feature vector reaches or exceeds a preset critical value, suggesting that the desulfurization system is in a significant dynamic change process rather than a steady-state operation. In this case, further analysis of the specific change pattern is needed to accurately identify the operating condition type. The first component refers to the vector element in the trend feature vector specifically used to characterize the time-varying rate of change of the unit load parameters. A positive value indicates that the unit load is increasing, and a negative value indicates that the load is decreasing. The absolute value reflects the rate of change of the load; for example, a first component of 0.15 indicates that the load is increasing at a relatively fast rate, and -0.20 indicates that the load is decreasing rapidly. The second component represents the time-varying rate of change of the sulfur dioxide concentration or sulfur content in the inlet flue gas. The numerical characteristics of this component directly reflect the trend of pollutant load changes entering the desulfurization system. A positive value indicates that an increase in inlet sulfur content leads to a heavier desulfurization burden, while a negative value indicates that a decrease in inlet sulfur content reduces desulfurization pressure. Unit load variation refers to the increase or decrease in the generating power or steam output of a generator unit as required by grid dispatch or fuel supply. Unit load variation directly affects the flue gas volume and the absolute emission of pollutants in the flue gas. Inlet sulfur content variation refers to the change in the sulfur dioxide concentration in the flue gas entering the desulfurization system as a result of changes in the sulfur content of the coal, adjustments to combustion conditions, or fluctuations in flue gas composition. Increased inlet sulfur content significantly increases the treatment difficulty and reagent consumption of the desulfurization system.

[0041] When the magnitude of the trend feature vector exceeds the steady-state threshold, it indicates that the desulfurization system has moved out of steady-state operation and entered a dynamic operating condition. However, the magnitude value alone cannot distinguish the specific type of dynamic operating condition; therefore, further analysis of the internal structural features of the trend feature vector is required. Specifically, the system extracts the values ​​of the first and second components from the trend feature vector according to predetermined component index positions. These two components correspond to the unit load change rate and the inlet sulfur content change rate, respectively, and are the two most important external disturbance factors affecting the operating state of the desulfurization system. By extracting the values ​​of these two key components and their positive and negative signs, the system can further subdivide the operating condition type in subsequent steps based on the specific numerical characteristics of these components. For example, it can determine whether the disturbance is caused by a rapid load increase, a fluctuation caused by a rapid load decrease, or a situation where the load and sulfur content are relatively stable but the chemical reaction process is oscillating.

[0042] S303: If the first component or the second component is greater than the preset change explicit threshold, determine that the current working condition is a load ramp-up working condition, and select environmental protection targets and economic targets as the target indicator set. Among them, either the first or second component exceeding the explicit change threshold means that at least one of the parameters, either the unit load change rate or the inlet sulfur content change rate, exceeds a pre-set significant change threshold, indicating that the parameter is undergoing a significant increase. This threshold is typically set between 0.08 and 0.15, determined based on the specific desulfurization system's response characteristics. The explicit change threshold represents the critical value used to determine whether a parameter change is significant enough to cause a change in operating condition. Changes below this threshold are considered normal fluctuations insufficient to alter the operating condition judgment, while changes above this threshold are considered significant disturbances requiring adjustment of the control strategy. Load ramp-up operating condition refers to a dynamic operating state where the unit's power generation load is continuously increasing or the inlet flue gas sulfur content is rising significantly. Under this condition, the pollutant treatment load faced by the desulfurization system increases rapidly, and failure to strengthen control in a timely manner may lead to the risk of exceeding emission standards at the outlet. Environmental targets refer to optimization indicators centered on ensuring that the concentration of pollutants such as sulfur dioxide in the flue gas outlet of the desulfurization system continuously and stably meets environmental emission standards. These include specific objectives such as minimizing the outlet SO2 concentration, maximizing desulfurization efficiency, and maintaining emission compliance rates. For example, ensuring that the outlet SO2 concentration is always below the emission limit of 35 mg / Nm³. Economic targets here specifically refer to optimization directions that minimize operating costs while ensuring environmental compliance. This includes controlling the number of slurry circulation pumps in operation, optimizing the supply flow rate of limestone slurry to avoid excessive consumption, and rationally adjusting the operating parameters of the oxidation blowers, striving to achieve economical operation while meeting desulfurization requirements.

[0043] When the numerical judgment results of the first or second component extracted from the trend feature vector show that at least one component exceeds the explicit change threshold, it indicates that the desulfurization system is facing a challenging operating condition of rapid load growth. Specifically, if the first component, i.e., the unit load change rate, is greater than the explicit change threshold, it means that the generator unit is performing load increase operations, resulting in a rapid increase in flue gas flow. Even if the inlet sulfur concentration remains unchanged, the absolute amount of sulfur dioxide entering the desulfurization system will increase significantly. If the second component, i.e., the inlet sulfur change rate, is greater than the explicit change threshold, it indicates that changes in coal sulfur content or combustion conditions are causing a rapid increase in the pollutant concentration per unit of flue gas. Even if the flue gas flow remains unchanged, it will significantly increase the desulfurization burden. If both components exceed the threshold simultaneously, it means that the system is facing a dual rapid increase in flue gas volume and pollutant concentration, and the desulfurization difficulty increases dramatically. Under this load ramping condition, the system's primary task is to ensure that the outlet emissions continue to meet the standards and avoid environmental risks. Therefore, environmental targets must be included in the optimization target set as hard constraints. At the same time, considering that load ramping is usually a transient process rather than a long-term state, economic targets also need to be taken into account to avoid overly aggressive control that would lead to unnecessary cost waste. For example, by accurately calculating, only the necessary number of circulation pumps can be added instead of starting all of them. Therefore, the system selects environmental and economic targets as the target indicator set for this condition and temporarily excludes quality targets from the optimization scope in order to concentrate computing resources on addressing the current main contradiction.

[0044] S304: If both the first component and the second component are negative and their absolute values ​​are greater than the change explicit threshold, the current operating condition is determined to be a load reduction operating condition, and economic and quality targets are selected as the target indicator set. Negative values ​​for both the first and second components indicate that the rates of change in unit load and inlet sulfur content are simultaneously less than zero, meaning both parameters are decreasing. The presence of negative values ​​signifies a continuous reduction in the pollutant treatment pressure faced by the desulfurization system. An absolute value greater than the explicit change threshold means that after taking the absolute values ​​of both the first and second components, their values ​​exceed the preset significant change threshold. This indicates that the rate of decrease in load and sulfur content is sufficiently rapid rather than a slow decline. This rapid decrease can cause the desulfurization system to quickly shift from a high-load to a low-load state. If control parameters are not adjusted in time, it may lead to over-desulfurization or wasted equipment idling. The load reduction condition refers to a dynamic operating state where the unit's power generation load is rapidly decreasing and the inlet flue gas sulfur content is simultaneously and significantly decreasing. Under this condition, the treatment demand of the desulfurization system decreases sharply, and the original high-intensity control strategies, such as parallel operation of multiple circulating pumps and high-flow slurry supply, are no longer necessary. At this time, the system should adjust its control strategy in a timely manner to reduce operating intensity. Economic objectives are particularly important under reduced load conditions, as the lower processing load provides a good opportunity for energy conservation and consumption reduction. Priority should be given to measures such as reducing the number of circulating pumps in operation, reducing the circulating slurry flow rate, and optimizing the oxidation air volume to minimize power consumption and reagent consumption. Quality objectives refer to, on the basis of controlling operating costs, making full use of the surplus processing capacity after the load reduction, and improving the quality characteristics of the desulfurization by-product gypsum by optimizing slurry pH control, extending the residence time of slurry in the absorption tower, and improving oxidation reaction conditions. This will improve the gypsum's moisture content, purity, whiteness, and other indicators, creating better conditions for the comprehensive utilization of gypsum.

[0045] When both the first and second components are negative and their absolute values ​​exceed the explicit threshold for change, the control system can clearly identify that the desulfurization unit is currently operating under a condition of rapid load reduction. Specifically, a negative first component indicates that the unit is performing a load reduction operation, with the flue gas flow rate showing a rapid downward trend, and the amount of flue gas entering the desulfurization system per unit time significantly reduced. A negative second component indicates that the sulfur dioxide concentration in the inlet flue gas is also decreasing synchronously, possibly due to the switching of coal to low-sulfur coal or optimization of combustion conditions leading to a reduction in pollutant generation. The simultaneous rapid decrease of both components means that the total amount of pollutants (the product of concentration and flow rate) that the desulfurization system needs to treat is decreasing significantly, and the control parameters originally configured to cope with high loads, such as full operation of the circulating pump and high flow rate of slurry supply, are clearly excessive. Under this reduced load condition, the urgency of environmental protection goals is greatly reduced. Even with a more conservative control strategy, emission compliance can be easily achieved after the load is reduced. Therefore, there is no need to prioritize environmental protection goals. The system should shift its focus to economic goals, maximizing economic benefits by reducing equipment operating intensity, minimizing energy consumption, and avoiding excessive chemical dosage. Meanwhile, since the system's processing capacity is relatively ample, quality goals can be appropriately considered. Fine-tuning can improve gypsum quality without affecting environmental compliance. Therefore, the system selects economic and quality goals as the target indicator set for this condition, providing a clear direction for subsequent multi-objective optimization.

[0046] S305: If the absolute values ​​of the first and second components are both less than the preset explicit change threshold, and the absolute value of the third component in the trend feature vector representing the change in slurry pH is greater than the preset fluctuation threshold, the current working condition is determined to be a chemical oscillation working condition, and environmental protection goals, economic goals, and quality goals are selected as the target indicator set.

[0047] The absolute values ​​of the first and second components being less than the explicit threshold mean that the absolute values ​​of the unit load change rate and the inlet sulfur content change rate are both lower than the preset significant change threshold. This indicates that these two main external disturbance parameters are currently in a relatively stable state, and their changes are insufficient to cause a change in the operating condition type on their own. For example, the absolute value of the first component is 0.03, which is less than the threshold of 0.08, and the absolute value of the second component is 0.04, which is also less than the threshold. The third component represents the time change rate of the slurry pH value. This component reflects the dynamic change trend of the chemical characteristics of the desulfurization slurry. Rapid fluctuations in pH value usually indicate instability in the chemical reaction process within the absorber, which may be due to chemical equilibrium instability caused by internal factors such as fluctuations in slurry circulation flow, uneven limestone supply, and improper distribution of oxidizing air. The fluctuation threshold is a critical value specifically used to determine whether pH value changes constitute abnormal oscillations in the chemical reaction. This threshold is usually set between 0.10 and 0.20. When the absolute value of the pH value change rate exceeds this threshold, it indicates that the chemical characteristics of the slurry are undergoing drastic fluctuations, requiring stabilization control measures. Chemical oscillation operation refers to the periodic or non-periodic drastic fluctuations in the internal chemical reaction process of a desulfurization system under relatively stable external loads. This manifests as rapid rises and falls in slurry pH, fluctuations in desulfurization efficiency, and unstable gypsum crystal growth. This condition is typically caused by inherent instability due to inappropriate control strategies, slurry component imbalances, or abnormal equipment operation. Environmental objectives need to be incorporated into optimization under chemical oscillation conditions because drastic pH fluctuations can lead to decreased desulfurization efficiency, affecting the stability of emission compliance. Optimized control is essential to quickly restore chemical reaction stability and ensure continuous emission compliance. Economic objectives are equally important under this condition because chemical oscillation often involves uneven reagent consumption and unstable energy consumption. Optimized control is needed to reduce resource waste caused by fluctuations and achieve stable economic operation. Quality objectives are particularly critical under chemical oscillation conditions because frequent pH fluctuations directly affect the gypsum crystal growth process, leading to quality problems such as uneven gypsum particle size, decreased purity, and increased moisture content. Incorporating quality objectives into optimization can improve gypsum quality while stabilizing the chemical reaction.

[0048] When the system detects that the absolute values ​​of the first and second components are both less than the explicit threshold, but the absolute value of the third component is greater than the fluctuation threshold, it indicates that the desulfurization system is facing a special operating condition: relatively small external load disturbances but unstable internal chemical processes. Specifically, the relative stability of the unit load and inlet sulfur content indicates that the amount of pollutants treated by the desulfurization system remains basically constant. In theory, maintaining unchanged control parameters should achieve stable operation. However, the absolute value of the third component, i.e., the pH change rate of the slurry, exceeds the fluctuation threshold, indicating that the pH of the slurry in the absorption tower is undergoing an abnormally rapid change. This change is not caused by external load fluctuations but by an imbalance in the internal chemical reaction or a coupling effect of the control loop. For example, a small adjustment in the flow rate of the slurry circulation pump may cause a change in the residence time of the slurry in the tower, which in turn affects the absorption rate of sulfur dioxide and the dissolution rate of limestone, ultimately leading to pH fluctuations. Alternatively, fluctuations in the airflow of the oxidation blower may cause instability in the rate of calcium sulfite oxidation to calcium sulfate, affecting the concentration balance of various components in the slurry and causing pH fluctuations. Chemical oscillation is one of the most complex operating conditions for desulfurization systems because it involves the interaction and nonlinear coupling of multiple physicochemical processes. Under this condition, the system needs to focus on three optimization objectives simultaneously: first, environmental objectives must be included to prevent pH fluctuations from causing a decrease in desulfurization efficiency and affecting emission standards; second, economic objectives need to be considered to avoid excessive consumption of reagents or increased energy consumption due to chemical imbalance; and finally, quality objectives must be emphasized because pH instability directly damages the quality of gypsum crystals. Therefore, the system selects the complete set of environmental, economic, and quality objectives as the target indicator set for this operating condition.

[0049] Based on the above embodiments, as an optional implementation method, in S103, the constraint boundary and weight coefficient in the preset multi-objective control model are adjusted according to the target indicators in the target indicator set to obtain the multi-objective fitness function. This can be specifically achieved through the following steps S401-S403.

[0050] S401: Based on the selection status of each target indicator in the target indicator set and the severity of the working condition represented by the magnitude of the trend feature vector, the constraint boundary in the multi-objective control model is adjusted to a dynamic defensive boundary that limits the allowable control domain at the current moment. The selection status of the target indicators refers to the activation status of each optimized target indicator (environmental protection target, economic target, and quality target) after the aforementioned operating condition identification process is completed. This activation status can be represented by Boolean values ​​or numerical indicators. For example, a selection status of 1 for the environmental protection target indicates activation, while 0 indicates inactivation. The combination of selection statuses differs under different operating conditions. Under steady-state operating conditions, only the economic and quality targets are selected. The severity of the operating condition represents the dynamic change intensity of the current operating state of the desulfurization system, quantified by the magnitude of the trend feature vector. A larger magnitude indicates more drastic changes in system parameters and a more unstable operating condition. For example, a magnitude of 0.03 indicates a stable operating condition, while a magnitude of 0.25 indicates drastic changes. This indicator directly reflects the severity of the disturbances faced by the system and the urgency of control adjustments. Constraint boundaries refer to the restrictions on the value range of each control variable (such as circulating pump flow rate, slurry pH setpoint, oxidation air volume, etc.) in a multi-objective control model. Traditional static constraint boundaries remain fixed throughout the entire operation, for example, the circulating pump flow rate is always constrained between 50 m³ / h and 300 m³ / h, which cannot be dynamically adjusted according to actual operating conditions. The allowable control domain refers to the actual feasible range of values ​​for each control variable that is allowed to be adjusted under the current operating conditions. This range should not only meet the basic requirements for the safe and stable operation of the system, but also provide sufficient degrees of freedom for the optimization algorithm to achieve multi-objective optimization. Dynamic defensive boundaries refer to constraint boundaries that are dynamically adjusted based on the current operating condition type, severity, and selected target indicators. When operating conditions change drastically, the boundary shrinks to improve the conservatism and safety of control. When operating conditions are stable, the boundary is moderately widened to allow for more aggressive optimization strategies. For example, under load ramp-up conditions and with a large modulus, the lower limit of the circulating pump flow rate is increased from 50 m³ / h to 100 m³ / h to ensure sufficient desulfurization capacity, and the pH setting range is narrowed from 5.0-6.0 to 5.3-5.7 to avoid excessive fluctuations. This dynamic adjustment mechanism can adaptively balance optimization performance and operational safety under different operating conditions.

[0051] After determining the operating condition type and selecting the target index set, the system needs to intelligently adjust the constraints of the control model before executing multi-objective optimization control to adapt to the control requirements and risk characteristics under different operating conditions. Specifically, the system first reads the selection status information of each target in the current target index set, identifies which targets are activated and included in the optimization, and which targets are temporarily excluded. Different combinations of targets have significantly different requirements for the constraint boundaries. For example, when the environmental protection target is selected, it means that the system is facing emission compliance pressure. At this time, the constraint boundaries should be conservative to ensure sufficient desulfurization margin. Specifically, this means raising the lower limit of the circulating slurry flow rate and the lower limit of the slurry pH value to prevent a decrease in desulfurization efficiency due to insufficient control. When only the economic and quality targets are selected, it means that the environmental pressure is relatively small, and the constraint boundaries can be appropriately relaxed to allow for more flexible optimization space, such as allowing the circulating pump flow rate to drop to a lower value to save energy. Simultaneously, the system extracts the magnitude of the trend feature vector as a quantitative indicator of the severity of the operating condition. This magnitude value is mapped to the contraction or expansion coefficient of the constraint boundary, typically using a piecewise linear function or an exponential function. For example, when the magnitude is less than 0.05, the boundary expansion coefficient is 1.2, meaning the boundary range expands by 20%. When the magnitude is between 0.05 and 0.15, the coefficient linearly decreases to 1.0. When the magnitude is greater than 0.15, the coefficient drops to 0.8, meaning the boundary range contracts by 20%. The system comprehensively considers both the target selection state and the severity of the operating condition, dynamically adjusting the upper and lower limits of the constraints for each control variable in the multi-objective control model to generate a dynamic defensive boundary that adapts to the allowable control domain at the current moment.

[0052] Based on the above embodiments, as an optional implementation method, in S401, according to the selection status of each target indicator in the target indicator set and the severity of the working condition represented by the magnitude of the trend feature vector, the constraint boundary in the multi-objective control model is adjusted to a dynamic defensive boundary that limits the allowable control domain at the current moment. Specifically, this can be achieved through the following steps S4011-S4013.

[0053] S4011: Identify the first unselected indicator in the target indicator set and set the constraint range corresponding to the first indicator to the preset physical limit value of the equipment. The identification process for the first indicator involves traversing the three dimensions of environmental protection, economic, and quality objectives, checking the activation status flags of each objective, and classifying objectives with a status flag of 0 or false as the first indicator. For example, when the objective selection state vector is [1, 1, 0], it indicates that environmental protection and economic objectives are selected, while the quality objective is the first indicator. The constraint range refers to the range of values ​​that the control variables are allowed to take during the optimization process. This range is limited by upper and lower boundaries to ensure that the control parameters do not exceed a reasonable range, leading to system malfunctions or equipment damage. The setting of the constraint range directly affects the search space and the feasibility of the solution in the optimization algorithm. The physical limits of equipment refer to the maximum or minimum operating parameter values ​​that each actuator and piece of equipment in a desulfurization system can achieve under the conditions permitted by design specifications and safety standards. These limits are provided by the equipment manufacturer or determined according to the parameters on the equipment nameplate, and represent the physical boundaries by which the equipment can operate safely and reliably. For example, the physical limit flow range of a circulating pump is 20 to 350 m³ / h, the physical measurable range of slurry pH value is 3.0 to 8.0, and the physical limit of oxidation blower air volume is 500 to 5000 Nm³ / h.

[0054] Setting the constraint range to the equipment's physical limits means that for the unselected first indicator, the system does not impose additional constraints on its corresponding control variables, allowing these control variables to be freely adjusted within the entire safe operating range of the equipment. The purpose of this strategy is to provide maximum flexibility and adjustment space for the optimization of the selected second indicator, avoiding excessive constraints that limit optimization performance. For example, when the quality target is not selected, the constraint range for the pH control variable, which is closely related to gypsum quality, can be set to the physical limit of 3.0 to 8.0, instead of shrinking to the conventional optimization range of 5.0 to 6.0. This gives the system greater leeway in pH adjustment to better achieve the selected environmental and economic goals.

[0055] After completing the determination of the operating condition type and the screening of the target indicator set, in the first step of constructing the dynamic defensive boundary, the system needs to adopt a relaxed constraint strategy for the unselected target indicators to maximize the degree of optimization freedom. Specifically, the system first reads the selection status information of each target from the target indicator set, identifies which targets' activation flags are in an unselected state through logical judgment, classifies these unselected targets as first indicators, and establishes a first indicator list. For example, if the environmental protection target is not selected under the load reduction condition, the system adds the environmental protection target to the first indicator list. The system then queries the mapping table between the first indicator and the control variables to determine which control variables mainly affect the performance of the first indicator. For the control variables associated with the first indicator, the system reads the corresponding physical limit values ​​of the equipment from the pre-configured equipment parameter database. These limit values ​​are usually stored in the form of a range of [minimum value, maximum value]. For example, the physical limit of the circulating pump flow rate is [20, 350] m³ / h, the physical limit of the pH value setting is [3.0, 8.0], the physical limit of the oxidation air volume is [500, 5000] Nm³ / h, and the physical limit of the limestone slurry supply flow rate is [5, 80] m³ / h. The system directly assigns the read physical limit values ​​of the equipment to the constraint boundary parameters of the corresponding control variables in the multi-objective control model without any shrinkage or adjustment. For example, the flow rate constraint of the circulating pump is set to Q_pump∈[20, 350] m³ / h, and the pH value constraint is set to pH_set∈[3.0, 8.0]. This setting method ensures that the optimization algorithm has the most relaxed adjustment range for the control variables related to the first index, and can search for the optimal solution within the entire safe operating range of the equipment.

[0056] S4012: Identify the second selected indicator in the target indicator set, and calculate the boundary contraction coefficient corresponding to the modulus of the trend feature vector according to the preset contraction function. The boundary contraction coefficient is positively correlated with the modulus. The second indicator refers to the performance indicator selected from the target indicator set and required to be included in the current operating condition optimization calculation. The shrinkage function is a mathematical function that establishes the mapping relationship between the trend feature vector magnitude and the boundary shrinkage coefficient. This function takes the magnitude value as input and outputs the corresponding shrinkage coefficient. The boundary shrinkage coefficient represents the degree of shrinkage of the constraint boundary relative to the physical limit value of the equipment. Its value ranges from zero to one; a larger value indicates a higher degree of shrinkage.

[0057] Specifically, the system first identifies selected targets from the target indicator set. By traversing the target state structure or vector, it extracts target items with a state flag of true or 1, categorizes these targets as secondary indicators, and establishes a secondary indicator list. For example, under load ramp-up conditions, both environmental and economic targets have activation flags of true, so the system adds these two targets to the secondary indicator list as objects that currently require focused optimization and careful constraint. Then, the system queries the mapping relationship between the secondary indicators and control variables to determine which control variables primarily affect the performance of the secondary indicators. For example, environmental targets are mainly affected by circulating pump flow rate, pH setting, and oxidation air volume, while economic targets are affected by the number of circulating pumps in operation, slurry supply flow rate, and oxidation air volume. These control variables are marked as the set of variables requiring dynamic constraint contraction. The system reads the trend feature vector magnitude value calculated in the aforementioned operating condition determination step. This magnitude quantifies the dynamic intensity of the current operating condition; for example, a magnitude value of 0.18 indicates that the system is in a relatively drastic dynamic change process. The system calls a preset shrinkage function to map the modulus value. If a piecewise linear shrinkage function is used, the shrinkage coefficient is set to linearly increase from 0.40 to 0.60 when the modulus is in the range of 0 to 0.10, linearly increase from 0.60 to 0.85 when the modulus is in the range of 0.10 to 0.20, and remain at 0.90 when the modulus is greater than 0.20. Then, for a modulus of 0.18, the shrinkage coefficient k is calculated by linear interpolation as k = 0.60 + (0.18 - 0.10) / (0.20 - 0.10) × (0.85 - 0.60) = 0.80. Alternatively, if the exponential contraction function k = 0.35 + 0.60 × (1 - exp(-4 × L)) is used, substituting the modulus L = 0.18 into the calculation yields k = 0.35 + 0.60 × (1 - exp(-0.72)) ≈ 0.35 + 0.60 × 0.513 ≈ 0.658. The system stores the calculated boundary contraction coefficient in variables, ready to be used in the next step to perform contraction calculations on the physical limits of the equipment, generating the dynamic defensive boundary of the control variable corresponding to the second index. This mechanism of dynamically adjusting the constraint boundary based on the severity of the operating conditions can achieve moderate contraction of constraints to improve control accuracy and safety margin when the operating conditions are stable, and moderate relaxation of constraints to provide sufficient control adjustment capability to cope with the adaptive effect of large disturbances when the operating conditions are severe.

[0058] S4013: Use the boundary contraction coefficient to perform contraction calculation on the physical limit value of the equipment to obtain the upper and lower limit ranges of the allowable change of the control variable at the current moment, and use the upper and lower limit ranges as the dynamic defensive boundary of the allowable control domain at the current moment.

[0059] The upper and lower limits refer to the range of values ​​that the control variable is allowed to take at the current moment, which are determined by the contracted upper and lower limits.

[0060] After the boundary contraction coefficient is calculated, the system enters the final crucial step of constructing the dynamic defensive boundary, which is to perform constraint boundary contraction calculations on the control variables related to the second index and generate the final allowable control domain. Specifically, the system first reads the physical limit value of each control variable that needs boundary contraction from the equipment parameter database. The physical limit is expressed in the form of upper and lower limits paired with [V_min_phy, V_max_phy]. For example, the physical limit of the circulating pump flow rate is [20, 350] m³ / h, i.e., V_min_phy=20 and V_max_phy=350. The system calculates the center value and radius of the physical limit of the control variable. The center value V_center = (V_min_phy + V_max_phy) / 2 represents the midpoint of the physical limit interval, and the radius V_radius = (V_max_phy - V_min_phy) / 2 represents the distance from the center to the boundary. For the circulating pump flow rate, the calculated center value V_center = (20 + 350) / 2 = 185 m³ / h, and the radius V_radius = (350 - 20) / 2 = 165 m³ / h. The system uses the boundary contraction coefficient k calculated in the previous steps to perform a contraction operation on the radius, calculating the contracted radius V_radius_new = k × V_radius. For example, when the contraction coefficient k = 0.70, the contracted radius V_radius_new = 0.70 × 165 = 115.5 m³ / h. This contracted radius represents the maximum distance the control variable is allowed to deviate from the center value under the current operating conditions. The system calculates the upper and lower limits of the dynamic defensive boundary based on the contracted radius and center value. The lower limit is calculated as V_min_dyn = V_center - V_radius_new, and the upper limit is calculated as V_max_dyn = V_center + V_radius_new. For the circulating pump flow rate, the calculated lower limit V_min_dyn = 185 - 115.5 = 69.5 m³ / h and the upper limit V_max_dyn = 185 + 115.5 = 300.5 m³ / h. Therefore, the allowable control domain of this control variable at the current moment is [69.5, 300.5] m³ / h. The system performs the above contraction calculation process on all control variables related to the second index to generate their respective dynamic defensive boundaries. For example, if the physical limit of the pH value variable is [3.0, 8.0] and the contraction coefficient is 0.70, then the calculated center value is 5.5, the physical radius is 2.5, the contracted radius is 1.75, and the dynamic boundary is [3.75, 7.25]. Each candidate control scheme generated by the optimization algorithm during the iterative search process must satisfy the constraints of these dynamic defensive boundaries.

[0061] S402: Determine the target weight coefficients of each target indicator in the multi-objective control model based on the real-time change characteristics of the trend feature vector. Among them, the target index refers to the performance index that needs to be optimized simultaneously in multi-objective optimization control, including environmental objectives (such as minimizing the SO2 concentration at the outlet and maximizing the desulfurization efficiency), economic objectives (such as minimizing the power consumption of the circulating pump and minimizing the limestone consumption), and quality objectives (such as maximizing the purity of gypsum and minimizing the moisture content). Different objectives often have conflicting relationships. For example, improving the desulfurization efficiency usually requires increasing the power consumption of the circulating pump, which conflicts with the economic objective.

[0062] After the dynamic defensive boundary adjustment is completed, the system needs to further determine the relative importance of each objective indicator in multi-objective optimization to guide the optimization algorithm in making reasonable trade-offs and decisions among multiple potentially conflicting objectives. Specifically, the system continuously monitors the real-time numerical changes of the trend feature vector, extracts the operating condition evolution information and disturbance characteristics contained therein, and intelligently determines which objectives should be given higher priority at the current moment based on the current value, trend of change, and interrelationship of each component. The system first analyzes the value and sign of the first component, namely the load change rate. If the component is positive and the value is large, it indicates that the load is rapidly increasing. At this time, the desulfurization system is facing the pressure of a rapid increase in pollutant treatment volume, and the importance of environmental protection objectives is significantly increased. The system should set the weight coefficient of environmental protection objectives to a higher value to ensure the priority of emission compliance, while appropriately reducing the weight of economic and quality objectives. If the first component is negative and the absolute value is large, it indicates that the load is rapidly decreasing and the environmental pressure is reduced. At this time, the weight of economic objectives should be increased to make full use of energy saving and consumption reduction during low-load periods, and the weight of quality objectives can also be appropriately increased to optimize gypsum quality. The system further analyzes the second component, namely the inlet sulfur content change rate. If this component rises rapidly, it indicates that the concentration of pollutants entering the desulfurization system is increasing, which will further strengthen the weight of environmental protection targets. If this component declines, the weight of environmental protection targets can be appropriately reduced.

[0063] Based on the above embodiments, as an optional implementation method, the method of determining the target weight coefficients of each target indicator in the multi-objective control model according to the real-time change characteristics of the trend feature vector in S402 can be specifically implemented through the following steps S4021-S4023.

[0064] S4021: Calculate the total dynamic allocation of the target indicator set based on the fixed maintenance percentage of indicators outside the target indicator set. The fixed maintenance percentage refers to the fixed share reserved in the weight allocation for indicators not selected from the target indicator set, used to ensure that the basic performance of these non-key indicators is not ignored. The dynamic allocation total represents the remaining weight share after deducting the fixed maintenance percentage from the total weight, which can be flexibly allocated among the selected target indicators.

[0065] Specifically, all unselected indicators outside the target indicator set are identified. The preset weight allocation strategy is queried to obtain a fixed maintenance percentage reserved for these non-optimization priority indicators. This fixed percentage ensures that even if some targets are not optimization priorities under the current conditions, their performance still accounts for a certain proportion in the fitness function, preventing complete neglect that could lead to severe deterioration of these indicators. The total weight value is set to one, and the fixed maintenance percentage is subtracted to obtain the remaining weight share. This remaining share is the dynamic allocation total, specifically used for distribution among the selected priority targets in the target indicator set. The size of the dynamic allocation total depends on the number of unselected indicators and their respective fixed percentage settings. Typically, the selected priority targets occupy a larger weight share, reflecting the optimization focus under the current conditions.

[0066] S4022: Based on the real-time change characteristics of the trend feature vector, establish the response mapping relationship between each target indicator in the target indicator set and the fluctuating state of the desulfurization system, and calculate the real-time demand intensity of each target indicator. The response mapping relationship refers to the corresponding association rule between the optimization requirements of target indicators and the changing characteristics of trend feature vectors, describing the changing patterns of the importance of each target under different fluctuation modes. Real-time demand intensity is used to represent the urgency and necessity of optimizing a specific target indicator under the current operating conditions; a larger value indicates that the target needs to be prioritized.

[0067] Specifically, the three components of the trend feature vector are extracted, and the magnitude, sign, and relative relationship of each component are analyzed to identify the main fluctuation characteristics of the current system. Based on a pre-defined response mapping rule base, a correlation is established between fluctuation characteristics and target demands. When the absolute value of the first component is significant, the demand intensity for environmental protection targets related to load adaptation increases; when the absolute value of the second component is significant, the demand intensity for environmental protection targets related to pollutant control increases; and when the absolute value of the third component is significant, the demand intensity for quality targets related to chemical stability increases. For economic targets, the demand intensity is negatively correlated with the overall volatility; the more stable the system, the greater the space for economic optimization.

[0068] S4023: Normalize the real-time demand intensity of each target indicator, allocate the total dynamic allocation amount proportionally to each target indicator in the target indicator set, and obtain the target weight coefficient of each target indicator.

[0069] Specifically, the real-time demand intensity values ​​of all selected targets in the target indicator set are obtained, and these values ​​are summed to obtain the total demand intensity. A normalization operation is performed on the demand intensity of each target, dividing its demand intensity by the total demand intensity to obtain its normalized demand ratio. This normalization process ensures that the sum of the demand ratios of all selected targets equals one, forming a standardized allocation weight coefficient. The normalized demand ratio of each target is multiplied by the total dynamically allocated amount to obtain the actual weight value allocated to that target; this value is the target weight coefficient. The allocation result of the weight coefficient reflects both the relative importance of each target under the current operating conditions and ensures that the total weight conforms to the preset allocation framework. Targets with higher demand intensity receive larger weight coefficients, occupying a higher evaluation weight in the fitness function, guiding the optimization algorithm to prioritize improving the performance of these key targets.

[0070] S403: Construct a multi-objective fitness function based on dynamic defensive boundaries and target weight coefficients.

[0071] The dynamic defensive boundary refers to the constraints on each control variable dynamically adjusted according to the type and severity of the operating conditions in the preceding steps. This boundary limits the feasible solution space of the multi-objective optimization algorithm when searching for optimal control parameters, ensuring that the control scheme generated during the optimization process is always within a safe and reliable range. The multi-objective fitness function is a comprehensive evaluation function used in multi-objective optimization algorithms (such as genetic algorithms and particle swarm optimization) to evaluate the quality of candidate solutions. This function transforms multiple potentially conflicting objective indicators into a single fitness value through weighted summation or other aggregation methods. A larger fitness value (or a smaller value, depending on the definition) indicates better overall performance of the candidate solution. The construction of the fitness function requires embedding the dynamic defensive boundary as a constraint or penalty term into the function structure. This ensures that solutions violating the boundary constraints are assigned a poor fitness value or are directly judged as infeasible solutions. Simultaneously, the objective weight coefficients need to be incorporated as coefficients of each sub-objective term into the weighted summation formula, so that objectives with higher weights contribute more to the overall fitness. A typical form of the fitness function is shown below.

[0072] The fitness value is calculated as: w1 × f1(x) + w2 × f2(x) + w3 × f3(x) - penalty term, where w1, w2, and w3 are the objective weight coefficients, f1, f2, and f3 are the normalized environmental, economic, and quality objective functions, respectively, x is the control variable vector, and the penalty term is used to handle constraint violations. The quality of the function construction directly affects whether the optimization algorithm can quickly converge to the optimal solution that meets the actual requirements. Therefore, careful design of key parameters such as the mathematical expressions of each sub-objective, the normalization method, and the penalty term coefficients is necessary.

[0073] Once the dynamic defensive boundary and target weight coefficients are determined, the system needs to integrate this information to construct a fitness function that can be directly used by multi-objective optimization algorithms. This function is the key bridge connecting operational analysis and optimization solutions. Specifically, the system first defines the basic framework of the fitness function, determining whether to use a weighted summation method, an ideal point method, or other multi-objective aggregation methods. The most commonly used method is the weighted summation method, which involves linearly weighting the objective functions. For environmental objectives, the system constructs a sub-function f1(x) representing the degree to which the outlet SO2 concentration deviates from the target value, for example, f1(x) = (C_SO2_out - C_target)², where C_SO2_out is the predicted outlet SO2 concentration calculated based on the control variable x, and C_target is the target concentration limit, such as 35 mg / Nm³. The smaller the value of this sub-function, the better the environmental performance. For economic objectives, the system constructs a sub-function f2(x) representing operating costs, for example, f2(x) = α × P_ The formula is: pump + β × Q_limestone, where P_pump is the power consumption of the circulating pump, Q_limestone is the limestone consumption, and α and β are cost coefficients. A smaller value for this sub-function indicates better economic efficiency. For quality targets, the system constructs a sub-function f3(x) characterizing the deviation of gypsum quality from the ideal value. For example, f3(x) = (purity_ideal - purity_actual)² + (moisture content_actual - moisture content_ideal)². A smaller value for this sub-function indicates that the quality is closer to the ideal state. Since the dimensions and numerical ranges of the three sub-functions may differ significantly, the system needs to normalize each sub-function, mapping them to the same numerical interval such as [0, 1]. Common methods include maximum / minimum value normalization or Z-score standardization. After normalization, the system multiplies the previously determined target weight coefficients w1, w2, and w3 by their corresponding normalized sub-functions to construct a weighted summation term.

[0074] The weighted sum is calculated as: w1 × norm_f1(x) + w2 × norm_f2(x) + w3 × norm_f3(x). Next, the system needs to incorporate the dynamic defensive boundary into the fitness function using a constraint handling mechanism. This can be achieved using either a penalty function method or a constraint domination method. If a penalty function method is used, a penalty term can be constructed.

[0075] The penalty value is calculated as Σ_imax(0, g_i(x))² + Σ_jmax(0, h_j(x))², where g_i(x) and h_j(x) represent the degree of violation of inequality and equality constraints, respectively. The max function ensures that penalties are only imposed on cases that violate constraints, and the penalty term significantly reduces the fitness of solutions that violate constraints. Finally, the system combines the weighted sum with the penalty term to construct a complete multi-objective fitness function.

[0076] Fitness(x) = -(w1×norm_f1(x) + w2×norm_f2(x) + w3×norm_f3(x)) - λ×penalty value, where the negative sign indicates that the optimization objective is to minimize the fitness value, and λ is the penalty coefficient used to balance the relative importance of objective optimization and constraint satisfaction. This fitness function will serve as the criterion for evaluating the merits of each candidate control scheme during the iterative search of subsequent optimization algorithms.

[0077] Based on the above embodiments, as an optional implementation method, the method of constructing a multi-objective fitness function based on the dynamic defensive boundary and target weight coefficient in step S403 specifically includes steps S4031-S4033.

[0078] S4031: Use the target weight coefficient to perform a weighted summation of the predicted values ​​of each target indicator to obtain a weighted evaluation term that represents the optimization requirements of the current working condition; The predicted values ​​of the target indicators refer to the expected performance values ​​of environmental, economic, and quality indicators calculated by the desulfurization system prediction model for a specific individual in the control variable population. The predicted values ​​can be represented as a vector form f = [f_env, f_econ, f_qual], where f_env represents the predicted environmental target value (e.g., SO2 emission concentration), f_econ represents the predicted economic target value (e.g., comprehensive energy consumption), and f_qual represents the predicted quality indicator value (e.g., gypsum purity). The calculation of the predicted values ​​relies on the aforementioned established mathematical model or data-driven model of the desulfurization system. The model input is the control variable parameters, and the output is the predicted values ​​of each target indicator. The prediction process considers the dynamic characteristics, coupling relationships, and time delay effects of the system. The general formula for weighted summation can be expressed as F_weighted = ∑(w_i × f_i), where i traverses all target dimensions. For a three-objective optimization problem, this can be expanded to F_weighted = w_env × f_env + w_econ × f_econ + w_qual × f_qual. The weighted evaluation term is a comprehensive evaluation index obtained through weighted summation. The magnitude of this index reflects the overall performance of the control scheme under the current operating conditions. The specific optimization direction depends on the definition of the objective function. If a minimization objective is adopted, a smaller weighted evaluation term value indicates a better scheme; if a maximization objective is adopted, a larger value indicates a better scheme. The weighted evaluation term represents the optimization requirements under the current operating conditions, meaning that this index comprehensively reflects the system's focus and optimization pursuit across different performance dimensions under the current operating conditions. Dynamic adjustment of the weights allows the weighted evaluation term to adaptively reflect the control priorities under different operating conditions.

[0079] Specifically, for each candidate individual in the control variable population, its control parameters are input into the desulfurization system prediction model, which outputs predicted values ​​for environmental indicators (such as SO2 emission concentration), economic indicators (such as comprehensive energy consumption), and quality indicators (such as gypsum purity). After normalizing each target prediction value, the target weight coefficient vector determined in step S402 is used. The weighted summation is calculated using the following formula:

[0080] In the formula, These are the normalized predicted values ​​for environmental protection, economic, and quality targets, respectively. (Calculated...) This refers to the weighted evaluation item that represents the current operating condition optimization requirements.

[0081] S4032: Detect whether individuals in the control variable population satisfy the dynamic defensive boundary, and calculate the constraint penalty term for the deviating individuals based on the degree of deviation from the dynamic defensive boundary; The degree of deviation refers to the magnitude by which one or more control variables of an individual exceed the dynamic defensive boundary. The degree of deviation can be defined as `violation_j = max(0, x_j - x_j_max_dyn) + max(0, x_j_min_dyn - x_j)`. In this formula, the first term calculates the deviation exceeding the upper limit, and the second term calculates the deviation below the lower limit. The `max` function ensures that a positive value is only generated for constraint violations. The magnitude of the deviation reflects the severity of the constraint violation, and the total degree of deviation can be defined as `Total_violation = ∑_jviolation_j`. The constraint penalty term is a penalty value added to the fitness function of an individual that violates the dynamic defensive boundary constraints. This penalty term is usually designed to be positive and increases with the degree of deviation, so that individuals with more severe constraint violations receive worse fitness scores and are gradually eliminated during the optimization process. The constraint penalty term can be calculated in different forms, such as linear penalty, quadratic penalty, and exponential penalty. A common linear penalty formula is P_constraint=λ×∑_jviolation_j, where λ is the penalty coefficient. The quadratic penalty formula is P_constraint=λ×∑_j(violation_j)², which imposes a more severe penalty on individuals with large-scale constraint violations. The penalty term can also be normalized to P_constraint=λ×∑_j[violation_j / (x_j_max_dyn-x_j_min_dyn)]² to eliminate the influence of differences in the dimensions of different variables. The constraint penalty term plays a role in guiding the optimization algorithm to converge to the feasible region in the fitness function. Through the penalty mechanism, the algorithm tends to retain and reproduce feasible solutions that satisfy the constraints.

[0082] Specifically, the values ​​of each control variable for each candidate individual are extracted and compared one by one with the dynamic defensive boundary generated in step S401. If the j-th variable If the value exceeds this boundary, calculate its normalized deviation. If the deviation is not exceeded, the deviation is 0. Based on the deviations of all variables, a quadratic penalty strategy is used to calculate the constraint penalty term: ; In the formula, Here, is the preset global penalty coefficient, and n is the total number of control variables. If all variables for an individual satisfy the dynamic boundary conditions, then... This penalty mechanism forces the optimization algorithm to converge to the shrunken allowable control domain when operating conditions change abruptly, thus avoiding the output of dangerous control commands.

[0083] S4033: Combine the weighted evaluation term with the boundary penalty term to generate a multi-objective fitness function.

[0084] Specifically, the system first clarifies the optimization direction of the fitness function. In the multi-objective control of desulfurization systems, the minimization objective design is usually adopted, that is, the smaller the fitness function value, the better the individual. This design allows the weighted evaluation term and the constraint penalty term to be naturally combined by addition. The system defines the general form of the fitness function as Fitness(x^(i))=F_weighted(x^(i))+P_constraint(x^(i)), which expands to Fitness(x^(i))=∑_{k=1}^{N_obj}w_k×f_k_norm(x^(i))+λ×∑_{j=1}^n[violation_norm_j(x^(i))]². For each individual x^(i) in the population, the system reads the pre-calculated weighted evaluation term value F_weighted^(i) and constraint penalty term value P_constraint^(i), and performs the addition operation Fitness^(i) = F_weighted^(i) + P_constraint^(i). This value is the final fitness function value of that individual. For feasible individuals that satisfy all constraints, their constraint penalty term P_constraint^(i) = 0, and their fitness function value is entirely determined by the weighted evaluation term Fitness^(i) = F_weighted^(i). In this case, the fitness reflects the individual's performance in multi-objective optimization. The system organizes the fitness function values ​​of all individuals into a fitness vector: Fitness_pop=[Fitness^(1), Fitness^(2), ..., Fitness^(N_pop)]^T∈R^(N_pop×1). In this vector, smaller values ​​correspond to better individuals, while larger values ​​correspond to individuals with poor performance or who violate constraints. The system sorts and ranks the individuals in the population based on the fitness vector and calculates the selection probability of each individual. In the fitness-based selection mechanism, the selection probability of individual i can be calculated as p_select^(i)=(Fitness_max-Fitness^(i)) / ∑_j(Fitness_max-Fitness^(j)), where Fitness_max=max_i*Fitness^(i) is the worst fitness value in the population. This formula transforms the minimization problem into a probability allocation that gives individuals with low fitness a high selection probability, or, in the ranking selection mechanism, the selection probability of an individual depends only on its fitness ranking rather than its specific value. The system can also implement an elite retention strategy, defining an elite set Elite={x^(i)|Fitness^(i)≤Fitness_threshold}, where Fitness_threshold is the elite threshold. Elite individuals are directly copied into the next generation of the population to ensure that the optimal solution discovered during the optimization process is not lost.The generated multi-objective fitness function serves as the core evaluation tool of the optimization algorithm and is repeatedly called in the subsequent iterative evolution process. The algorithm dynamically adjusts the search strategy according to the size and distribution of the fitness value. After T generations of evolution, the population will gradually converge to the region with a small fitness function value. The final output of the optimal individual x*=argmin_{x∈Population(T)}Fitness(x) is the optimal control parameter configuration of the desulfurization system under the current operating conditions.

[0085] The following are system embodiments of this application, which can be used to execute the method embodiments of this application. For details not disclosed in the system embodiments of this application, please refer to the method embodiments of the application.

[0086] Please see Figure 2 This illustration shows a schematic diagram of a slurry circulation control system based on multi-objective control, provided in an exemplary embodiment of this application. The system can be implemented entirely or partially through software, hardware, or a combination of both. The slurry circulation control system based on multi-objective control includes: The data acquisition module is used to collect real-time operating data of the desulfurization system, construct a state vector containing unit load, inlet sulfur content and slurry pH value, calculate the time derivative of each parameter in the state vector, and generate a trend feature vector characterizing the intensity of transient changes in the system. The operating condition type determination module is used to determine the current operating condition type of the desulfurization system based on the trend feature vector, and to filter the set of target indicators that need to be included in the optimization under the current operating condition type. The function optimization module is used to adjust the constraint boundaries and weight coefficients in the preset multi-objective control model according to the target indicators in the target indicator set, so as to obtain the multi-objective fitness function. The function solving module is used to iteratively optimize the population of control variables in the desulfurization system using a multi-objective fitness function to obtain the Pareto front solution set. The output module is used to select the robust optimal solution with the highest comprehensive fitness from the Pareto front solution set, and to parse the robust optimal solution into the optimal control command for the current operating condition of the slurry circulation control system.

[0087] This application also provides a computer storage medium that can store multiple instructions. The instructions are adapted to be loaded and executed by a processor as described in the above embodiments of the slurry circulation control method based on multi-objective control. For the specific execution process, please refer to the detailed description of the embodiments, which will not be repeated here.

[0088] Please see Figure 3 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 3As shown, the electronic device 300 may include: at least one processor 301, at least one network interface 304, user interface 303, memory 305, and at least one communication bus 302.

[0089] The communication bus 302 is used to enable communication between these components.

[0090] The user interface 303 may include a display screen and a camera.

[0091] The network interface 304 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0092] The processor 301 may include one or more processing cores. The processor 301 connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in the memory 305, and by calling data stored in the memory 305. Optionally, the processor 301 may be implemented using at least one hardware form of digital signal processing, field-programmable gate array, or programmable logic array. The processor 301 may integrate one or more of the following: a central processing unit (CPU), a graphics processing unit (GPU), and a modem. The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content required for display; and the modem handles wireless communication. It is understood that the modem may also not be integrated into the processor 301 and may be implemented as a separate chip.

[0093] The memory 305 may include random access memory (RAM) or read-only memory (ROM). Optionally, the memory 305 may include a non-transitory computer-readable medium. The memory 305 may be used to store instructions, programs, code, code sets, or instruction sets. The memory 305 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system, instructions for at least one function (such as touch functionality, sound playback functionality, image playback functionality, etc.), instructions for implementing the various method embodiments described above, etc.; the data storage area may store data involved in the various method embodiments described above, etc. Optionally, the memory 305 may also be at least one storage device located remotely from the aforementioned processor 301. Figure 3 As shown, the memory 305, which serves as a computer storage medium, may include an operating system, a network communication module, a user interface module, and an application program for a slurry circulation control method based on multi-objective control.

[0094] exist Figure 3In the electronic device 300 shown, the user interface 303 is mainly used to provide an input interface for the user and to obtain the user input data; while the processor 301 can be used to call an application program stored in the memory 305 for a slurry circulation control method based on multi-objective control. When executed by one or more processors, the electronic device executes one or more methods as described in the above embodiments.

[0095] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0096] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of other embodiments of this disclosure upon considering the specification and practical application disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure.

Claims

1. A slurry circulation control method based on multi-objective control, characterized in that, The method includes: Real-time operating data of the desulfurization system is collected, a state vector containing unit load, inlet sulfur content and slurry pH value is constructed, and the time derivative of each parameter in the state vector is calculated to generate a trend feature vector characterizing the severity of transient changes in the system. The current operating condition type of the desulfurization system is determined based on the trend feature vector, and the set of target indicators to be included in the optimization under the current operating condition type is selected. Based on the target indicators in the target indicator set, the constraint boundaries and weight coefficients in the preset multi-objective control model are adjusted to obtain the multi-objective fitness function; The Pareto front solution set is obtained by iteratively optimizing the population of control variables in the desulfurization system using a multi-objective fitness function. The robust optimal solution with the highest comprehensive fitness is selected from the Pareto front solution set, and the robust optimal solution is parsed into the optimal control command for the current operating condition of the slurry circulation control system.

2. The method according to claim 1, characterized in that, The calculation of the time derivatives of each parameter in the state vector to generate a trend feature vector characterizing the severity of transient changes in the system includes: The unit load, inlet sulfur content, and slurry pH value in the state vector are sampled using a sliding window. The difference ratio between the current sampling time and the previous sampling time is calculated to obtain the time derivative of each parameter, and the time derivative is used as the real-time physical change rate. The real-time physical change rate is normalized using a preset benchmark normalization factor to obtain multiple vector components corresponding to each parameter. By combining the vector components, a trend feature vector representing the severity of transient changes in the system is obtained.

3. The method according to claim 1, characterized in that, The step of determining the current operating condition type of the desulfurization system based on the trend feature vector and filtering the set of target indicators to be included in the optimization under the current operating condition type includes: Calculate the magnitude of the trend feature vector. If the magnitude is less than the preset steady-state threshold, determine that the current working condition is a steady-state condition, and select economic and quality targets as the target indicator set. If the modulus is greater than or equal to the steady-state threshold, then extract the first component representing the change in unit load and the second component representing the change in inlet sulfur content from the trend feature vector; If the first component or the second component is greater than the preset change explicit threshold, the current working condition is determined to be a load ramp-up working condition, and environmental protection targets and economic targets are selected as the target indicator set. If both the first component and the second component are negative and their absolute values ​​are greater than the change explicit threshold, the current operating condition is determined to be a load reduction operating condition, and economic and quality targets are selected as the target indicator set. If the absolute values ​​of the first component and the second component are both less than the preset explicit change threshold, and the absolute value of the third component in the trend feature vector that represents the change in slurry pH value is greater than the preset fluctuation threshold, the current working condition is determined to be a chemical oscillation working condition, and environmental protection goals, economic goals and quality goals are selected as the target indicator set.

4. The method according to claim 1, characterized in that, The step of adjusting the constraint boundaries and weight coefficients in the preset multi-objective control model based on the target indicators in the target indicator set to obtain the multi-objective fitness function includes: Based on the selection status of each target indicator in the target indicator set and the severity of the working condition represented by the magnitude of the trend feature vector, the constraint boundary in the multi-objective control model is adjusted to a dynamic defensive boundary that limits the allowable control domain at the current moment. Based on the real-time change characteristics of the trend feature vector, the target weight coefficients of each target indicator in the multi-objective control model are determined; Based on the dynamic defensive boundary and the target weight coefficient, a multi-target fitness function is constructed.

5. The method according to claim 4, characterized in that, The step of adjusting the constraint boundary in the multi-objective control model to a dynamic defensive boundary that limits the allowable control domain at the current moment, based on the selection status of each indicator in the target indicator set and the magnitude of the trend feature vector, includes: Identify the first unselected indicator in the target indicator set, and set the constraint range corresponding to the first indicator to a preset physical limit value of the device. Identify the second indicator selected in the target indicator set, and calculate the boundary contraction coefficient corresponding to the modulus of the trend feature vector according to the preset contraction function. The boundary contraction coefficient is positively correlated with the modulus. The physical limit value of the device is calculated by using the boundary contraction coefficient to obtain the upper and lower limit ranges of the allowable change of the control variable at the current moment, and the upper and lower limit ranges are used as the dynamic defensive boundary of the allowable control domain at the current moment.

6. The method according to claim 4, characterized in that, The step of determining the target weight coefficients of each target indicator in the multi-objective control model based on the real-time change characteristics of the trend feature vector includes: Calculate the total dynamic allocation of the target indicator set based on the fixed maintenance percentage of indicators outside the target indicator set. Based on the real-time change characteristics of the trend feature vector, establish the response mapping relationship between each target indicator in the target indicator set and the fluctuation state of the desulfurization system, and calculate the real-time demand intensity of each target indicator. The real-time demand intensity of each target indicator is normalized and calculated, and the total amount of dynamic allocation is distributed proportionally to each target indicator in the target indicator set to obtain the target weight coefficient of each target indicator.

7. The method according to claim 4, characterized in that, The construction of a multi-objective fitness function based on the dynamic defensive boundary and the target weight coefficients includes: The predicted values ​​of each target indicator are weighted and summed using the target weight coefficients to obtain a weighted evaluation term that represents the optimization needs of the current working condition. Detect whether individuals in the control variable population satisfy the dynamic defensive boundary, and calculate the constraint penalty term for the deviating individuals based on the degree of deviation from the dynamic defensive boundary; The weighted evaluation term is combined with the boundary penalty term to generate a multi-objective fitness function.

8. A slurry circulation control system based on multi-objective control, characterized in that, The system includes: The data acquisition module is used to collect real-time operating data of the desulfurization system, construct a state vector containing unit load, inlet sulfur content and slurry pH value, calculate the time derivative of each parameter in the state vector, and generate a trend feature vector characterizing the intensity of transient changes in the system. The operating condition type determination module is used to determine the current operating condition type of the desulfurization system based on the trend feature vector, and to filter the set of target indicators that need to be included in the optimization under the current operating condition type. The function optimization module is used to adjust the constraint boundaries and weight coefficients in the preset multi-objective control model according to the target indicators in the target indicator set, so as to obtain the multi-objective fitness function. The function solving module is used to iteratively optimize the population of control variables in the desulfurization system using a multi-objective fitness function to obtain the Pareto front solution set. The output module is used to select the robust optimal solution with the highest comprehensive fitness from the Pareto front solution set, and parse the robust optimal solution into the optimal control command for the current operating condition of the slurry circulation control system.

9. A computer storage medium, characterized in that, The computer storage medium stores a plurality of instructions, which are adapted to be loaded by a processor and executed as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, The device includes a processor, a memory, and a transceiver, wherein the memory is used to store instructions, the transceiver is used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 7.

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