Ultra-supercritical unit model parameter identification method based on improved particle swarm optimization

Abstract

The invention provides an ultra-supercritical unit model parameter identification method based on an improved particle swarm algorithm, and relates to the field of thermal power generation modeling and intelligent optimization algorithms. According to the method, a mathematical model of a boiler system, a mathematical model of a steam turbine system and a mathematical model of a water supply system are constructed, to-be-identified parameters of the ultra-supercritical unit are determined, multiple operation data of the ultra-supercritical unit in the dynamic working condition process are collected at the same time, and on the basis of an improved particle swarm optimization algorithm, the parameters of the ultra-supercritical unit are identified. By introducing an inertia weight adaptive mechanism and a local disturbance strategy, the problems that a traditional identification method is prone to falling into local optimum, sensitive to an initial value, low in convergence speed and the like are effectively solved. The method has the advantages of being high in modeling precision, high in optimizing capacity, good in adaptability and the like, efficient and accurate identification of the key parameters of the thermodynamic system can be achieved under the complex working condition, and the availability and robustness of a unit dynamic model are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of thermal power generation modeling and intelligent optimization algorithms, specifically to a method for identifying model parameters of ultra-supercritical units based on an improved particle swarm optimization algorithm. Background Technology

[0002] Ultra-supercritical units, with their advantages of high efficiency, low energy consumption, and low emissions, have become the core equipment of modern large-scale thermal power plants. Ultra-supercritical units typically operate under ultra-high temperature and high pressure steam parameters, and their thermodynamic system coupling relationships are complex, with strong nonlinear dynamic characteristics. During operation, they frequently experience large-scale load fluctuations and deep peak-shaving conditions, which places higher demands on the real-time performance and accuracy of the control system.

[0003] Establishing accurate mathematical models is a prerequisite for realizing advanced control (such as generalized predictive control (GPC), model predictive control (MPC), optimal scheduling and fault diagnosis) and digital twin modeling of ultra-supercritical units. Key thermodynamic parameters in the model (such as heat transfer coefficient, time constant, and response gain) have a decisive impact on prediction accuracy and control performance. However, due to the nonlinearity and multivariate coupling characteristics of the system, as well as the unmeasurability of field disturbances, traditional parameter identification methods (such as least squares and gradient descent) often rely on accurate prior structural information, making it difficult to obtain the global optimum. Furthermore, they are sensitive to initial conditions, have slow convergence speeds, and are ill-suited to adapting to dynamic changes under complex operating conditions.

[0004] In recent years, intelligent optimization algorithms have demonstrated strong global search capabilities and robustness in parameter identification problems, such as genetic algorithms (GA), particle swarm optimization (PSO), and differential evolution (DE). However, standard PSO suffers from problems such as being prone to getting trapped in local optima and having low convergence accuracy, which limits its application in large-scale nonlinear models. Therefore, there is an urgent need for an improved optimization algorithm that possesses both global optimization capabilities and fast convergence speed and strong stability to achieve high-precision parameter identification of mathematical models of ultra-supercritical unit thermal systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to propose a method for identifying model parameters of ultra-supercritical units based on an improved particle swarm optimization algorithm, comprising:

[0006] Step 1: Divide the ultra-supercritical unit into a boiler system, a turbine system, and a feedwater system;

[0007] The boiler system includes a combustion chamber, water-cooled walls, a superheater, a reheater, an economizer, and an air preheater; the steam turbine system includes a high-pressure cylinder, an intermediate-pressure cylinder, and a low-pressure cylinder; and the feedwater system includes a feedwater pump, a deaerator, and a heater.

[0008] Step 2: Construct mathematical models of the boiler system, steam turbine system, and feedwater system to determine the parameters to be identified for the ultra-supercritical unit.

[0009] Step 3: Collect multiple operating data of the ultra-supercritical unit under dynamic operating conditions, process all operating data, and obtain the processed data sequence;

[0010] Step 4: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, the parameters to be identified for the ultra-supercritical unit, and the processed data sequence, an improved particle swarm optimization algorithm is used to determine the initial optimal parameters.

[0011] Step 5: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, as well as the processed data sequence, the initial optimal parameters are further identified to obtain the identified parameters.

[0012] Optionally, in step 2, the mathematical model of the boiler system is constructed as follows:

[0013] ;

[0014] in, for The first derivative in time, for The first derivative in time, The pressure response time constant is The temperature response time constant, This refers to the pressure gain of the fuel input to the boiler system. The temperature gain of fuel input to the boiler system; Input of coal quantity per unit time; This is the pressure reduction coefficient of the steam turbine intake. Main steam flow rate; Main steam pressure; Main steam temperature;

[0015] Among them, the parameters to be identified in the boiler system ;

[0016] The mathematical model of the steam turbine system is expressed as follows:

[0017] ;

[0018] in, This represents the turbine output power in the time domain. for The first derivative over time; Main steam pressure, Indicates the pressure-load transfer gain. This represents the mechanical response inertia of a steam turbine;

[0019] Among them, the parameters to be identified in the steam turbine system ;

[0020] The mathematical model of the water supply system is expressed as follows:

[0021] ;

[0022] in, This refers to the boiler feedwater flow rate. for The first derivative in time, for The second derivative in time; The water supply regulation signal is the model input. It is the second-order inertial time constant; To control the delay time; For water supply system gain;

[0023] Among them, the parameters to be identified in the water supply system ;

[0024] The parameters to be identified for ultra-supercritical units include , and .

[0025] Optionally, step 3 specifically includes the following steps:

[0026] Step 3.1: Collect multiple operating data of the ultra-supercritical unit under typical dynamic operating conditions. The operating data includes various sampling data, namely, the amount of coal input per unit time. Boiler feedwater flow rate Main steam pressure Main steam temperature Steam turbine output power and water supply regulation signal ;

[0027] Step 3.2: Set up a common timeline, specifying the times on the common timeline. When any sample data in the running data is missing, linear interpolation is used to calculate the time. Sampling data Specifically, this is achieved through the following formula:

[0028] ;

[0029] in, Indicates a moment on the common timeline The first sampled data on the right, express At the corresponding time, Moments on the public timeline The first sampled data on the left, express The corresponding moment;

[0030] The sampled data corresponding to all moments on the common time axis constitute the first sampling sequence;

[0031] Step 3.3: Set a data threshold interval, remove sampled data that are not in the data threshold interval in the first sampling sequence, calculate the mean of the first data at the left time step and the first data at the right time step of the sampled data, obtain the neighbor mean, use the neighbor mean as the new sampled data, and then obtain the second sampling sequence;

[0032] The mean of the data within the sliding window is calculated by sliding a preset sliding window over the second sampling sequence. with standard deviation Specifically, this is achieved through the following formula:

[0033] ;

[0034] ;

[0035] Where L represents the length of the sliding window. Represents the time in the sliding window. Indicating the second sampling sequence Data at any given time;

[0036] exist At that time, the time in the second sampling sequence Data Replace with ,exist At that time, retain After each data point in the second sampling sequence undergoes the above processing, the third sampling sequence is obtained.

[0037] Step 3.4: For the data in the third sampling sequence, calculate the difference between the data at two adjacent time points to obtain multiple differences. Obtain the difference that is greater than or equal to a preset threshold, and obtain the corresponding data in the third sampling sequence to form the fourth sampling sequence.

[0038] Step 3.5: Smooth the data in the fourth sampling sequence to obtain the filtered data, specifically achieved through the following formula:

[0039] ;

[0040] in, This represents the data in the fourth sampling sequence. Indicates time Filtered data, As a smoothing factor, Indicates time Filtered data;

[0041] The filtered data is normalized using the following formula to obtain normalized data, which is then used to form the processed data sequence.

[0042] ;

[0043] in, This represents the normalized data. This represents the minimum value of all filtered data. This represents the maximum value of all filtered data.

[0044] Optionally, step 4 specifically includes the following steps:

[0045] Step 4.1: Set multiple particles and the maximum number of iterations. Set the initial iteration count d=0; randomly generate multiple sets of identification parameters for ultra-supercritical units, and use these parameters as the initial positions of the particles. The particle velocity is initialized to obtain the initial velocity. The initial position of each particle is taken as the initial optimal position of the individual.

[0046] Step 4.2: Set the initial iteration count as the current iteration count d, and the initial position as the current position. Use the initial velocity as the current velocity. The initial optimal position of an individual is used as the current optimal position of the particle. ;

[0047] Step 4.3: For each particle, according to The processed data sequence, mathematical models of the boiler system, turbine system, and feedwater system were used to calculate the predicted main steam pressure. Predicting the main steam temperature Predicting the output power of the steam turbine And predict boiler feedwater flow ;

[0048] Step 4.4: Based on , , , Calculate the overall objective function value, including:

[0049] Calculate the mean square error Specifically, this is achieved through the following formula:

[0050] ;

[0051] Where T represents the processed data sequence ,or ,or The quantity; when m=3, and i are 1, 2, 3 respectively, They are respectively , , , They are respectively , , ;

[0052] Calculate the total objective function value Specifically, this is achieved through the following formula:

[0053] ;

[0054] in, The L1 regularization weighting factor. This is the L2 regularization weighting factor;

[0055] Step 4.5: For each particle, among the total objective function value corresponding to the current individual optimal position and the total objective function value of the particle at the current iteration number, find the one with the smallest value and take its corresponding position as the new individual optimal position. Among the total objective function values ​​of all particles, find the one with the smallest value and take its corresponding position as the global optimal position. ;

[0056] Step 4.6: At all total objective function values In the middle, get the first with the smallest value. Each particle is considered an elite particle, and all other particles are considered ordinary particles.

[0057] Current velocity of elite particles The update is performed using the following formula:

[0058] ;

[0059] in, This represents the velocity of the elite particles in the updated (d+1)th iteration. Indicates the elite velocity decay factor;

[0060] Step 4.7: Calculate the inertia weight at the current iteration number. Learning factors and learning factors ;

[0061] Calculate the inertia weight at the current iteration number. Specifically, this is achieved through the following formula:

[0062] ;

[0063] in, , Given the maximum and minimum values ​​of the inertia weights, It is a non-linear decreasing factor;

[0064] Calculate the learning factor at the current iteration number. and learning factors Specifically, this is achieved through the following formula:

[0065] ;

[0066] in, Represents learning factor initial value, Represents learning factor The final value, Represents learning factor initial value, Represents learning factor The final value;

[0067] Step 4.8: Calculate the hybrid guidance probability at the current iteration number. Specifically, this is achieved through the following formula:

[0068] ;

[0069] in, As the initial value of the probability, This is the final probability value. It is a non-linear adjustment factor;

[0070] according to Determine the mixing guidance vector of ordinary particle z. Specifically, this is achieved through the following formula:

[0071] ;

[0072] in, This represents the current optimal position of an ordinary particle z.

[0073] Step 4.9: According to , , and The current velocity of ordinary particles The initial update is performed using the following formula:

[0074] ;

[0075] in, This represents the velocity of a normal particle in the (d+1)th iteration after the initial update. and It is a random vector. This represents the current position of the ordinary particle z;

[0076] Step 4.10: Obtain the total objective function value from all elite particles. The smallest elite particle is designated as the elite optimal particle, based on the current position of the elite optimal particle. ,right After another update, the final velocity of the ordinary particle is obtained. Specifically, this is achieved through the following formula:

[0077] ;

[0078] in, For elite guidance strength, It is a random vector;

[0079] Step 4.11: Calculate the updated positions of elite particles Position updated with ordinary particles Specifically, this is achieved through the following formula:

[0080] ;

[0081] ;

[0082] Step 4.12: For any particle among elite particles and ordinary particles, if The total objective function value after dM iterations If the difference is greater than or equal to the stagnation threshold, the updated position of the particle will be taken as the final position of the particle.

[0083] like The total objective function value of the global optimal position after dM iterations If the difference is less than the stagnation threshold, the updated position of the particle is locally perturbed using the following formula to obtain the perturbed position, which is then taken as the final position of the particle.

[0084] ;

[0085] ;

[0086] in, This represents the position after the ordinary particle is disturbed. This represents the position of the elite particles after perturbation. For the disturbance amplitude, Let be a multidimensional standard normal random vector with a mean of 0 and a covariance matrix that is the identity matrix. ;

[0087] Step 4.13: In If the difference between the total objective function value of the global optimal position in the current iteration number and the total objective function value of the global optimal position in the dM iterations is less than a preset threshold, then the global optimal position is used as the initial optimal parameter, and step 5 is executed.

[0088] exist If the difference between the total objective function value of the global optimal position at the current iteration number and the total objective function value of the global optimal position at the dMth iteration number is greater than or equal to a preset threshold, then proceed to step 4.14.

[0089] Step 4.14: If the variance of the final positions of all particles is less than a preset variance threshold, and the total objective function value corresponding to the global optimal position does not decrease in R iterations, then increment the current iteration number by one, and use the final position of the elite particle as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used to randomly initialize the position and velocity of the ordinary particles, and then the process returns to step 4.3.

[0090] If the variance of the final positions of all particles is greater than or equal to a preset variance threshold, or if the total objective function value corresponding to the globally optimal position decreases in R iterations, then the current iteration number is incremented by one, and the final position of the elite particle is used as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used as the final position of the ordinary particles in the new iteration number. As the velocity of the ordinary particles in the new iteration, return to step 4.3.

[0091] Optionally, step 4.3 includes:

[0092] Based on the processed data sequence The main steam flow rate is calculated based on the regulating valve position. The processed data sequence , , as well as In Substituting into the mathematical model of the boiler system, we obtain and The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain .

[0093] Optionally, step 4.4 includes:

[0094] Calculate the mean square error Specifically, this is achieved through the following formula:

[0095] ;

[0096] Where T represents the processed data sequence ,or ,or The quantity; when m=3, and i are 1, 2, 3 respectively, They are respectively , , , They are respectively , , ;

[0097] Calculate the total objective function value Specifically, this is achieved through the following formula:

[0098] ;

[0099] in, The L1 regularization weighting factor. This is the L2 regularization weight factor.

[0100] Optionally, step 5 specifically includes the following steps:

[0101] Step 5.1: Based on the data sequence after processing the initial optimal parameters, the mathematical model of the boiler system, the mathematical model of the turbine system, and the mathematical model of the feedwater system, obtain the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate.

[0102] Step 5.2: Based on the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate, as well as the processed data sequence... , , and Calculate the root mean square error (RMSE) and the goodness of fit (FIT).

[0103] Step 5.3: When RMS is greater than the preset error threshold or FIT is less than the preset fitting threshold, take the initial optimal parameter as the center and generate multiple new sets of ultra-supercritical unit parameters to be identified according to the preset disturbance range, and return to step 4; when RMS is less than or equal to the preset error threshold and FIT is greater than or equal to the preset fitting threshold, take the initial optimal parameter as the parameter identification completed, and complete the parameter identification.

[0104] The beneficial effects of adopting the above technical solution are as follows:

[0105] This invention constructs mathematical models of the boiler system, turbine system, and feedwater system, and determines the parameters to be identified for ultra-supercritical units. Simultaneously, it collects multiple operational data points of the ultra-supercritical unit under dynamic operating conditions. Based on an improved particle swarm optimization (IPSO) algorithm, by introducing an adaptive inertial weight mechanism and a local perturbation strategy, it effectively overcomes the problems of traditional identification methods, such as being prone to getting trapped in local optima, sensitivity to initial conditions, and slow convergence speed. This method has advantages such as high modeling accuracy, strong optimization capability, and good adaptability. It can achieve efficient and accurate identification of key parameters of the thermal system under complex operating conditions, significantly improving the usability and robustness of the unit's dynamic model. This invention provides a solid modeling foundation for the design of advanced control strategies, the construction of digital simulation platforms, and operational optimization of ultra-supercritical units, and has broad engineering application value and promising prospects. Attached Figure Description

[0106] Figure 1 This is a schematic diagram of the process for identifying model parameters of ultra-supercritical units based on an improved particle swarm optimization algorithm in an embodiment of the present invention.

[0107] Figure 2 This is a fitting curve of the main steam pressure output in an embodiment of the present invention;

[0108] Figure 3 This is a fitting curve of the main steam temperature output in an embodiment of the present invention;

[0109] Figure 4 This is a graph showing the power output fitting curve in an embodiment of the present invention;

[0110] Figure 5 This is a histogram showing the main steam pressure output error distribution in an embodiment of the present invention.

[0111] Figure 6 This is a histogram showing the main steam temperature output error distribution in an embodiment of the present invention.

[0112] Figure 7 This is a histogram showing the output error distribution of the steam turbine output power (i.e., generator power) in an embodiment of the present invention.

[0113] Figure 8 The graphs show the convergence curves of different algorithms in the embodiments of the present invention. Detailed Implementation

[0114] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0115] To address the problems existing in current technologies, this invention provides a parameter identification method for ultra-supercritical unit models based on an improved particle swarm optimization algorithm. This method enhances the fitting accuracy and dynamic response consistency of thermal system models, overcoming the shortcomings of existing methods in terms of modeling accuracy and optimization stability. The method has a clear overall structure, high identification efficiency, and is suitable for modeling complex nonlinear multivariable systems. Figure 1 This may include the following steps:

[0116] Step 1: Divide the ultra-supercritical unit into a boiler system, a turbine system, and a feedwater system;

[0117] The boiler system includes a combustion chamber, water-cooled walls, superheater, reheater, economizer, and air preheater. The turbine system includes a high-pressure cylinder, an intermediate-pressure cylinder, and a low-pressure cylinder. The feedwater system includes a feedwater pump, a deaerator, and a heater. During the modeling process, each system adheres to the fundamental physical laws of thermodynamic systems and incorporates engineering operational characteristics to ensure the model possesses good dynamic expressiveness, adaptability, and structural combinability. All system inputs and outputs are observable physical quantities of a distributed control system (DCS), facilitating subsequent identification and deployment.

[0118] Step 2: Construct mathematical models of the boiler system, steam turbine system, and feedwater system, and connect them using a unified data interface to achieve modular and hierarchical modeling; then determine the parameters to be identified for the ultra-supercritical unit.

[0119] As the core heat source of ultra-supercritical units, the boiler system's main function is to effectively transfer the heat energy released from pulverized coal combustion to the water and steam in the boiler tube system, completing the efficient conversion of chemical energy into thermal energy. This system typically exhibits characteristics such as strong coupling, strong nonlinearity, significant dynamic hysteresis, and substantial thermal inertia. In engineering operation, the main steam pressure and main steam temperature, as key output parameters of the boiler, not only directly reflect the boiler's thermal stability but are also core control indicators for load regulation and ensuring operational safety. Both are standard monitoring quantities that can be acquired in real-time by the on-site DCS system. From a physical modeling perspective, the boiler's input variables are the pulverized coal feed rate and feedwater flow rate. Through the law of conservation of heat and the principle of fluid inertia, a dynamic differential relationship can be established with the output parameters, providing a theoretical basis for the mathematical modeling and parameter identification of the boiler system.

[0120] Based on this, the boiler system adopts a nonlinear state-space structure of first-order lag + integral form, and the mathematical model of the boiler system is expressed as follows:

[0121] ;

[0122] in, for The first derivative in time, for The first derivative in time, The pressure response time constant is The temperature response time constant, This refers to the pressure gain of the fuel input to the boiler system. The temperature gain of fuel input to the boiler system; Coal input per unit time (MW thermal power); This is the pressure reduction coefficient of the steam turbine intake. The main steam flow rate (kg / s) can usually be obtained indirectly through valve position and turbine load. Main steam pressure (MPa) (from boiler output); Main steam temperature (°C);

[0123] Among them, the parameters to be identified in the boiler system These parameters reflect the boiler's thermal response characteristics and pressure regulation capabilities, and are the core content of this system's identification.

[0124] As the core of power conversion in ultra-supercritical units, the steam turbine's main function is to convert the thermal energy of high-temperature, high-pressure steam into mechanical energy to drive the generator and output electrical power. Due to the influence of the large-inertia rotor system, the turbine's speed-load dynamic response can typically be approximated as a first-order lag system, exhibiting good linearity. In the modeling process, the main steam pressure serves as the turbine's primary driving input, while the generated active power is the typical output response; the dynamic relationship between the two is stable and observable. Considering the relatively small dynamic impact of control valves and regulating systems on the entire energy path, they can be simplified and incorporated into the transfer gain parameters for unified modeling in engineering practice. The unit load, as a real-time acquired variable of the DCS system, provides a reliable data foundation for the turbine system's model output, giving the system good identifiability and engineering adaptability.

[0125] Based on this, the present invention employs a first-order inertial linear transfer function:

[0126] ;

[0127] in, This represents the turbine output power in the complex frequency domain. The main steam pressure (MPa) is in the complex frequency domain. For the Laplace operator;

[0128] Converting the above formula into a time-domain representation yields the mathematical model of the steam turbine system, which is expressed as:

[0129] ;

[0130] in, The turbine output power in the time domain can usually be calculated from a power meter or load command. for The first derivative over time; Main steam pressure (MPa). Indicates the pressure-load transfer gain. This represents the mechanical response inertia of a steam turbine;

[0131] Among them, the parameters to be identified in the steam turbine system ;

[0132] In ultra-supercritical units, the feedwater system plays a crucial role in maintaining the dynamic balance between the boiler's water-cooled walls and the steam drum water level. Its stable operation is essential for ensuring the safety and responsiveness of the boiler's thermal system. At the control level, the feedwater system's response to control commands (such as feedwater valve opening or pump frequency) typically exhibits second-order dynamic characteristics with significant inertia and time delay. Its core variables, such as feedwater flow rate, boiler inlet feedwater pressure, and regulating valve positions, can be frequently acquired and monitored through a DCS system, providing observable data support for model inputs and outputs. As the direct material input to the boiler, changes in feedwater flow rate directly affect the boiler's thermal balance and steam generation rate, making it an indispensable and important input variable in boiler system modeling.

[0133] Based on this, considering the inertia and delay characteristics, the following structure is adopted:

[0134] ;

[0135] in, The boiler feedwater flow rate in the complex frequency domain;

[0136] Converting the above formula into a time-domain representation yields the mathematical model of the water supply system, which is expressed as:

[0137] ;

[0138] in, This represents the boiler feedwater flow rate (kg / s). for The first derivative in time, for The second derivative in time; For water supply regulation signals (such as valve position and frequency commands), the model input is used. It is the second-order inertial time constant; To control the delay time; For water supply system gain;

[0139] Among them, the parameters to be identified in the water supply system These parameters reflect the response speed and control lag of the water supply system.

[0140] The parameters to be identified for ultra-supercritical units include , and ;

[0141] This invention also provides system coupling and interface design, which will be described in detail below:

[0142] (1) Explanation of coupling relationship:

[0143] Boiler system output → As input to the steam turbine system;

[0144] Steam turbine system output → Provided to the control system for load coordination;

[0145] Water supply system output → Feedback is sent to the boiler system as input;

[0146] Boiler output steam flow can be It is obtained indirectly from the estimation of the control valve position.

[0147] (2) The following is an overview table of input and output variables;

[0148] Table 1. Overview of Input and Output Variables

[0149] (3) Summary of advantages of modeling:

[0150] The mathematical model constructed in this step exhibits good engineering feasibility and scalability. The inputs and outputs of each system are selected from physical quantities that can be directly measured by the DCS system, facilitating data acquisition and model deployment in actual units. The model structure is built upon the physical mechanisms of the thermodynamic system, possessing clear physical meanings for its parameters and good identifiability, making it suitable for both offline analysis and online adaptive identification. Each system has a high degree of structural independence and interface consistency, supporting on-demand interchangeability or expansion, and can adapt to ultra-supercritical units of different capacity levels and system structures.

[0151] Step 3: Collect multiple operating data of the ultra-supercritical unit under dynamic operating conditions, process all operating data, and obtain the processed data sequence;

[0152] To ensure the accuracy and engineering deployability of the model identification results, this invention requires the construction of a high-quality sample set based on actual unit operating data before parameter identification. The data preprocessing process includes data acquisition, time alignment, anomaly removal, noise reduction, and normalization transformation, aiming to improve the temporal consistency, physical rationality, and numerical stability of the data.

[0153] Step 3.1: Collect multiple operating data of the ultra-supercritical unit under typical dynamic operating conditions. The operating data includes various sampling data, namely, the amount of coal input per unit time. Boiler feedwater flow rate Main steam pressure Main steam temperature Steam turbine output power and water supply regulation signal ;according to The main steam flow rate is calculated based on the regulating valve position. ;

[0154] Specifically, operational data should be exported from the unit's DCS system or historical data platform (such as HIS), and the sampling period is recommended to be set to [period missing]. Ensure that the input and output variables have sufficient dynamic resolution. The data acquisition period should cover multiple typical dynamic operating conditions, including load increase, load decrease, steady-state operation, and short-term disturbance response, to facilitate model generalization. Each acquired variable corresponds to the system's input and output physical quantities to ensure that the data required for subsequent identification is complete and valid.

[0155] Step 3.2: Set up a common timeline, specifying the times on the common timeline. When any sample data in the running data is missing, linear interpolation is used to calculate the time. Sampling data Specifically, this is achieved through the following formula:

[0156] ;

[0157] in, Indicates a moment on the common timeline The first sampled data on the right, express At the corresponding time, Moments on the public timeline The first sampled data on the left, express The corresponding moment;

[0158] The sampled data corresponding to all moments on the common time axis constitute the first sampling sequence;

[0159] Step 3.3: To eliminate outliers introduced by acquisition errors, instrument failures or external shocks, set a data threshold range, remove the sampled data in the first sampling sequence that is not in the data threshold range, calculate the mean of the first data at the left time and the first data at the right time of the sampled data to obtain the neighbor mean, use the neighbor mean as the new sampled data, and then obtain the second sampling sequence.

[0160] The mean of the data within the sliding window is calculated by sliding a preset sliding window over the second sampling sequence. with standard deviation Specifically, this is achieved through the following formula:

[0161] ;

[0162] ;

[0163] Where L represents the length of the sliding window. Represents the time in the sliding window. Indicating the second sampling sequence Data at any given time;

[0164] exist At that time, the time in the second sampling sequence Data Replace with ,exist At that time, retain After each data point in the second sampling sequence undergoes the above processing, the third sampling sequence is obtained.

[0165] Step 3.4: For the data in the third sampling sequence, calculate the difference between the data at two adjacent time points to obtain multiple differences. Obtain the difference that is greater than or equal to a preset threshold. This segment is the dynamic segment. Obtain the corresponding data in the third sampling sequence to form the fourth sampling sequence.

[0166] Among them, the preset threshold If M consecutive differences are less than the threshold This is the steady-state segment. M=30~60. Only time periods with significant dynamic changes are retained for model training to enhance the timeliness of identification and response capture capabilities.

[0167] Identify the most valuable dynamic response segments for model recognition from long-term series data, and remove steady-state segments with little information to improve training efficiency and the model's ability to capture dynamic characteristics.

[0168] Step 3.5: Smooth the data in the fourth sampling sequence to obtain the filtered data, specifically achieved through the following formula:

[0169] ;

[0170] in, This represents the data in the fourth sampling sequence. Indicates time Filtered data, As a smoothing factor, a value of 0.1 to 0.2 is recommended; Indicates time Filtered data; filtering can effectively preserve the dynamic characteristics of variables and improve the model's ability to fit the real system response in subsequent identification.

[0171] To eliminate the influence of differences in variable dimensions on the weights of the objective function, the filtered data is normalized using the following formula to obtain normalized data, which is then used to form the processed data sequence.

[0172] ;

[0173] in, This represents the normalized data. This represents the minimum value of all filtered data. This represents the maximum value of all filtered data; normalization improves the numerical stability during the identification process, which helps to improve the convergence speed and parameter estimation accuracy of the optimization algorithm.

[0174] This invention proposes an improved particle swarm optimization algorithm (IPSO) that integrates multiple strategies. Based on the classic particle swarm optimization algorithm, it introduces a hybrid guidance strategy, an elite preservation mechanism, nonlinear convergence control, and diversity maintenance methods, thereby improving global optimization capability and convergence speed, and effectively avoiding getting trapped in local optima. Building upon the standard particle swarm optimization algorithm, an adaptive adjustment mechanism for inertial weights is introduced to enhance the global search capability of particles, and a local optimum perturbation strategy is used to enhance the algorithm's ability to escape local optima, thus improving overall optimization convergence and stability.

[0175] Step 4: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, the parameters to be identified for the ultra-supercritical unit, and the processed data sequence, an improved particle swarm optimization algorithm is used to determine the initial optimal parameters.

[0176] Step 4.1: Set multiple particles and the maximum number of iterations. Set the initial iteration count d=0; randomly generate multiple sets of identification parameters for ultra-supercritical units, and use these parameters as the initial positions of the particles. The particle velocity is initialized to obtain the initial velocity. The initial position of each particle is taken as the initial optimal position of the individual.

[0177] The parameters to be identified for ultra-supercritical units are expressed as follows:

[0178] ;

[0179] in, .

[0180] Thus, the position of each particle ,in The number of algorithm iterations reflects the time dimension of the optimization process. Represents the particle index, where This represents the total number of particles in the particle swarm. Its dimension matches the total number of parameters to be identified in the unit model, encompassing all key parameters from the three major subsystems: boiler, turbine, and feedwater system. Each particle... Representative at the In the next iteration, a candidate solution in the parameter space is a set of possible parameter combinations.

[0181] Step 4.2: Set the initial iteration count as the current iteration count d, and the initial position as the current position. Use the initial velocity as the current velocity. The initial optimal position of an individual is used as the current optimal position of the particle. ;

[0182] Step 4.3: For each particle, according to The processed data sequence, mathematical models of the boiler system, turbine system, and feedwater system were used to calculate the predicted main steam pressure. Predicting the main steam temperature Predicting the output power of the steam turbine And predict boiler feedwater flow ;

[0183] Specifically, based on the processed data sequence The main steam flow rate is calculated based on the regulating valve position. The processed data sequence , , as well as In Substituting into the mathematical model of the boiler system, we obtain and The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain ;

[0184] Step 4.4: Based on , , , Calculate the overall objective function value, including:

[0185] After completing the model structure construction and data preprocessing, a reasonable objective function needs to be designed as an evaluation criterion in subsequent optimization algorithms. The objective function should accurately measure the output error of the model while avoiding overfitting or underfitting of parameters, thereby improving the stability and universality of the identification results under different working conditions.

[0186] The objective is to minimize the error between the model output and the actual measurement data. A multivariate error function is constructed as the objective function and used for fitness evaluation of the subsequent optimization algorithm.

[0187] Calculate the mean square error This item serves as the primary evaluation criterion for model fitting performance and is the core basis for parameter optimization. It is specifically implemented through the following formula:

[0188] ;

[0189] Where T represents the processed data sequence ,or ,or The quantity; when m=3, and i are 1, 2, 3 respectively, They are respectively , , , They are respectively , , ;

[0190] To prevent overfitting of the model with limited samples (i.e., identifying the minimum error point caused by the parameters infinitely approaching the noise), an L2 regularization term is introduced to limit the parameters from being too large, thereby improving the stability of the model.

[0191] If the model contains a large number of redundant parameters or input features, in order to avoid underfitting or insufficient sparse expression, an L1 regularization term is introduced to make some unimportant parameters tend to 0, thereby achieving structure selection and compression.

[0192] Calculate the total objective function value Specifically, this is achieved through the following formula:

[0193] ;

[0194] in, >0 represents the L1 regularization weight factor. The L1 term has the function of controlling parameter sparsity and can be used to control the number of parameters and improve the interpretability of the model. It is especially effective in scenarios with redundant variables or excessively high model complexity. >0 represents the L2 regularization weight factor; the larger the value, the stronger the suppression of large parameter changes. This helps to improve the smoothness of parameter distribution and the model's generalization ability on non-training data.

[0195] λ1 and λ2 are typically selected through cross-validation or empirical methods. The overall objective function balances identification accuracy, structural simplicity, and parameter stability. In actual identification, λ1 and λ2 are set through empirical adjustment or cross-validation. For example, for small to medium-sized models, λ1 can be initially set to 0.01 and λ2 to 0.001; for systems with high-dimensional inputs or overly complex models, λ1 can be appropriately increased (e.g., 0.05~0.1) to enhance sparsity.

[0196] Step 4.5: For each particle, among the total objective function value corresponding to the current individual optimal position and the total objective function value of the particle at the current iteration number, find the one with the smallest value and take its corresponding position as the new individual optimal position. Among the total objective function values ​​of all particles, find the one with the smallest value and take its corresponding position as the global optimal position. Among them, in boiler parameters , In the optimization, the lower This means a more accurate dynamic fit of the main steam pressure.

[0197] Step 4.6: At all total objective function values In the middle, get the first with the smallest value. Each particle is considered an elite particle, and all other particles are considered ordinary particles.

[0198] Current velocity of elite particles The update is performed using the following formula:

[0199] ;

[0200] in, This represents the velocity of the elite particles in the updated (d+1)th iteration. Indicates the elite velocity decay factor;

[0201] Step 4.7: Calculate the inertia weight at the current iteration number. Learning factors and learning factors ;

[0202] To accelerate the initial search speed and improve the convergence accuracy in later stages, the inertia weight decreases non-linearly. The inertia weight at the current iteration number is calculated. Specifically, this is achieved through the following formula:

[0203] ;

[0204] in, , Given the maximum and minimum values ​​of the inertia weights, is the nonlinear decreasing factor, and is a hyperparameter that needs to be designed in advance;

[0205] Calculate the learning factor at the current iteration number. and learning factors Specifically, this is achieved through the following formula:

[0206] ;

[0207] in, Represents learning factor The initial value, i.e., the value when the algorithm starts at iteration number d=0. Values, Represents learning factor The final value, i.e., the algorithm's maximum number of iterations. hour The target value. Represents learning factor initial value, Represents learning factor The final value; , Similarly, this design allows the algorithm to gradually transition from "exploration-driven" to "convergence-driven," improving recognition accuracy. Among these, , , , , , These are all preset hyperparameters and need to be designed in advance.

[0208] In complex optimization problems (such as strongly nonlinear models of ultra-supercritical units), all particles prematurely converge to the same global optimum, easily leading to a rapid loss of population diversity and getting trapped in local optima. Search behavior is relatively fixed, and the balance between exploration and exploitation capabilities depends on… and The fixed settings are as follows. To avoid the population getting trapped in local optima, a hybrid guiding vector is introduced, and the specific calculation method is described in detail in step 4.8.

[0209] Step 4.8: Calculate the hybrid guidance probability at the current iteration number. Specifically, this is achieved through the following formula:

[0210] ;

[0211] in, As the initial value of the probability, This is the final probability value. It is a non-linear adjustment factor;

[0212] according to Determine the mixing guidance vector of ordinary particle z. Specifically, this is achieved through the following formula:

[0213] ;

[0214] in, This represents the current optimal position of an ordinary particle z.

[0215] in, It is an improved hybrid guidance probability in the particle swarm optimization algorithm, used to control the switching strategy between "individual historical optimum" and "global optimum" during particle updates. For each particle in each generation, its third term (social cognition term) is the attraction target. It is no longer a fixed global optimum, but rather a time-varying probability. The optimal solution is randomly selected between the individual optimal solution and the global optimal solution. The low probability in the early stages leads to a higher probability in the early stages. Choosing the global optimum as a guide encourages the population to quickly converge towards the currently discovered potential optimum region, enabling a robust global exploration and avoiding excessive dispersion and low search efficiency in the initial stages. This process continues with the number of iterations. As the concentration increases, the particles have a higher probability. Selecting the optimal individual as the guide.

[0216] Particles rely more on their own search experience, conducting detailed deep searches within their respective local regions. This effectively prevents the entire population from becoming homogenized prematurely, maintains population diversity, and thus makes it more likely that they will escape local optima and discover globally better solutions.

[0217] Step 4.9: According to , , and The current velocity of ordinary particles The initial update is performed using the following formula:

[0218] ;

[0219] in, This represents the velocity of a normal particle in the (d+1)th iteration after the initial update. and For random vectors (express and These are two independent random variables that follow a uniform distribution, and their values ​​range in the interval (0,1). This represents the current position of the ordinary particle z;

[0220] Step 4.10: Obtain the total objective function value from all elite particles. The smallest elite particle is designated as the elite optimal particle, based on the current position of the elite optimal particle. ,right After another update, the final velocity of the ordinary particle is obtained. Specifically, this is achieved through the following formula:

[0221] ;

[0222] in, For elite guidance strength, It is a random vector;

[0223] Step 4.11: Calculate the updated positions of elite particles Position updated with ordinary particles Specifically, this is achieved through the following formula:

[0224] ;

[0225] ;

[0226] Step 4.12: For any particle among elite particles and ordinary particles, if The total objective function value after dM iterations If the difference is greater than or equal to the stagnation threshold, the updated position of the particle will be taken as the final position of the particle.

[0227] like The total objective function value of the global optimal position after dM iterations If the difference is less than the stagnation threshold (the stagnation threshold is a very small positive number (e.g., ε=0.001), which represents the tolerance for fitness changes), then the updated position of the particle is locally perturbed using the following formula to obtain the perturbed position, and the perturbed position is taken as the final position of the particle.

[0228] ;

[0229] ;

[0230] in, This represents the position after the ordinary particle is disturbed. This represents the position of the elite particles after perturbation. The amplitude of the perturbation decreases with each algebraic step to ensure that the perturbation weakens in later stages and avoids disrupting convergence. Let be a multidimensional standard normal random vector with a mean of 0 and a covariance matrix that is the identity matrix. It is used to generate random perturbation directions in the parameter space.

[0231] Step 4.13: In If the difference between the total objective function value of the global optimal position in the current iteration number and the total objective function value of the global optimal position in the dM iterations is less than a preset threshold, then the global optimal position is used as the initial optimal parameter, and step 5 is executed.

[0232] exist If the difference between the total objective function value of the global optimal position at the current iteration number and the total objective function value of the global optimal position at the dMth iteration number is greater than or equal to a preset threshold, then proceed to step 4.14.

[0233] Step 4.14: If the variance of the final positions of all particles is less than a preset variance threshold (a very small positive number, such as 0.01; if the variance is lower than this value, it indicates that the particle positions are highly clustered and diversity is lost), and the total objective function value corresponding to the global optimal position has not decreased in R iterations, then increment the current iteration number by one, and use the final position of the elite particle as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used to randomly initialize the position and velocity of the ordinary particles, and then the process returns to step 4.3.

[0234] If the variance of the final positions of all particles is greater than or equal to a preset variance threshold, or if the total objective function value corresponding to the globally optimal position decreases in R iterations, then the current iteration number is incremented by one, and the final position of the elite particle is used as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used as the final position of the ordinary particles in the new iteration number. As the velocity of the ordinary particles in the new iteration number, return to step 4.3;

[0235] Step 5: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, as well as the processed data sequence, the initial optimal parameters are further identified to obtain the identified parameters.

[0236] Step 5.1: Based on the data sequence after processing the initial optimal parameters, the mathematical model of the boiler system, the mathematical model of the turbine system, and the mathematical model of the feedwater system, obtain the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate.

[0237] Step 5.2: Based on the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate, as well as the processed data sequence... , , and Calculate the root mean square error (RMSE) and the goodness of fit (FIT).

[0238] Step 5.3: When RMS is greater than the preset error threshold or FIT is less than the preset fitting threshold, take the initial optimal parameters as the center and generate multiple new sets of ultra-supercritical unit parameters to be identified according to the preset disturbance range (±5%), and return to step 4, specifically step 4.2; when RMS is less than or equal to the preset error threshold and FIT is greater than or equal to the preset fitting threshold, take the initial optimal parameters as the parameters to be identified, and complete the parameter identification.

[0239] The preset error threshold can be 0.03, and the preset fitting threshold can be 95%.

[0240] Furthermore, the error is obtained by subtracting the actual values ​​from the predicted values ​​output by the three mathematical models in the processed data sequence. This leads to the generation of the basic generation correction amount. It is used to adjust the coal powder feed, water supply valve opening and steam valve control to achieve model-based load tracking and pressure stabilization control.

[0241] Furthermore, this invention encapsulates the mathematical models of the boiler system, steam turbine system, and feedwater system into DLL (Dynamic Link Library) or FMU (Functional Mock-up Unit, a cross-platform model encapsulation format based on the FMI standard) interface modules, and integrates them into the plant simulation platform or DCS control host. This supports automatic retraining of the models every hour, forming a closed-loop mechanism of "data-driven + model feedback," and realizing the unification of online modeling, dynamic updates, and real-time control.

[0242] Based on the above technical solution, the present invention conducted the following experiments:

[0243] Example 1: Mathematical models of the boiler system, steam turbine system, and feedwater system are constructed in MATLAB / Simulink. The boiler system's mathematical model uses a first-order lag + integral nonlinear state equation to describe its main steam pressure dynamics; the steam turbine system's mathematical model is simplified to a first-order inertial transfer function representing the load power response; the feedwater system's mathematical model uses a second-order inertial transfer function with a pure delay element to simulate hydrodynamic and thermal inertia. Interface signals for each subsystem include main steam pressure, main steam temperature, and boiler feedwater flow rate, which can be measured and used for data transfer between systems. All subsystems are initialized with default engineering calibration parameters (e.g., the boiler's time constant is approximately...). The time constant of the steam turbine is approximately 30 s. The time constants of the two inertial links in the water supply system are approximately 5 s and approximately 100 s respectively. For 10 s and It is 30 seconds, pure delay. The gain coefficient of fuel input to the main steam pressure is approximately 5 s. The gain coefficient of fuel input to the main steam temperature is 1.2. The transfer gain from main steam pressure to power generation is 1.0. The system gain from the water supply valve position to the flow rate is 1.1. The pressure drop coefficient of steam intake in a steam turbine The values ​​are set to 0.05, and then they are cascaded to form a simulation model of the entire machine. The simulation solver selected is the rigid ODE solver ode15s, and the maximum step size is set to 0.05. The time interval is set to 0.5 s to ensure the stability and accuracy of the numerical solution over a longer time span. The total simulation time in this embodiment is set to 3 hours to cover multiple operating condition variations. The boiler output steam flow rate can be indirectly obtained by estimating the control valve position.

[0244] Three typical operating conditions were designed to test the model's dynamic response and generate "true value" data:

[0245] Linear load increase condition (50%→100%): Starting from 50% of the unit's rated load, the load command is linearly increased to 100% over a period of time. This process simulates the unit's smooth load increase process.

[0246] Trapezoidal load reduction condition (100%→40%): The load command is reduced from 100% of the rated value to 40%, with a trapezoidal change in between (first rapidly decreasing to a lower value, holding for a period of time, and then continuing to decrease to 40%). This condition simulates a more drastic load reduction process and possible steady-state pauses.

[0247] Random Disturbance Condition (±2% Random Fluctuation): Near a constant load (e.g., 50% of rated load), a random power command disturbance signal of ±2% is superimposed. This part lasts for several minutes and is used to simulate the impact of random load fluctuations on the system.

[0248] The aforementioned load commands are converted into corresponding model input sequences such as fuel supply rate and feedwater valve opening through a pre-set mapping strategy, driving the overall machine simulation model to run. Simulation yields "real" response data of the output quantities of the three main mathematical models under various operating conditions over time. The simulation output is recorded with a sampling period of 1 second, resulting in high-resolution time-series data. Simultaneously, to simulate measurement noise, Gaussian white noise with an amplitude of approximately 5% of the true signal value is superimposed on the output data as a measurement error. Through this process, a simulation dataset covering three operating conditions is finally obtained, including thousands of time points (approximately 10,800 points over 3 hours, with approximately 4,500 valid input / output samples after filtering out incomplete data), providing benchmark "true value" data for subsequent parameter identification.

[0249] The simulation sampling data was cleaned and filtered to improve data quality. This resulted in a high-quality dataset of approximately 4500 model identification samples (including normalized input-output pairs). The cleaned data sequences were continuous, smooth, and had a high signal-to-noise ratio, laying a solid foundation for the construction of the objective function and the parameter identification of the improved PSO algorithm in subsequent steps 3–4 of the invention.

[0250] After data preparation, an improved particle swarm optimization algorithm (IPSO) was used to identify the parameters to be identified for the ultra-supercritical unit. The experimental design included the following aspects:

[0251] IPSO Algorithm Parameter Settings: This section sets the main parameters of the particle swarm optimization algorithm, including the particle swarm size (number of particles) and the maximum number of iterations. Considering the dimensionality of the model parameters and the complexity of the problem, this embodiment selects a particle number of N=30 and a maximum number of iterations of [missing value]. =100. Inertia weight Initial value (also the maximum value of inertia weight) The weight is set to 0.9, and the minimum weight is set to 0.4 to balance global search and local development capabilities; ensuring... Non-linear decreasing factor The initial value of the individual learning factor is 2.0. All are set to 2.5, the final value of the individual learning factor The initial value for the social learning factor is 0.5 to provide a moderate convergence acceleration. The final value of the social learning factor is 0.5. The value is 2.5. In the hybrid guidance strategy, the initial local guidance probability is set to 0.3, and the final probability value is 0.8. The size of the elite subgroup in the elite subgroup preservation and sharing mechanism... Set to 5, Elite Guidance Strength The elite velocity decay factor is 0.3. The value is 0.2. The stagnation judgment window in the local stagnation perturbation criterion of the diversity preservation and restart mechanism. The value is 10, the stagnation threshold is 0.001, and the disturbance amplitude is... The initial value is set to 0.1, and the final value of the perturbation amplitude is 0.01; in the restart mechanism, the variance threshold is 0.01, and the globally optimal stagnation algebra is... It is 15.

[0252] Parameter value boundaries: Determine a reasonable initial range for the parameters to be identified. Since the physical meaning of each subsystem parameter is clear, based on experience, the time constant parameters of each dynamic element are limited to between 0.5 s and 50 s (covering the response speed range of typical thermodynamic systems), the gain coefficient is limited to between 0.1 and 5 times the calibration value, and the delay time constant is limited to between 0 and 10 s. These boundary conditions ensure that the particle swarm optimization algorithm searches within a reasonable physical range, avoiding non-physical interpretations.

[0253] Objective function construction: The objective function for parameter identification is defined as a measure of the error between the model output and the true data. In this embodiment, the objective function is the weighted mean square error (WMSE) of multiple outputs: the sum of squares of the time-series errors of the main steam pressure, main steam temperature, and turbine output power are calculated and then weighted to obtain the overall error T = 4500 (sampling points), where m is 3. It is 0.01. The value is 0.001. The particle swarm optimization algorithm aims to minimize the overall error.

[0254] Identification process recording and termination criteria: Initiate the IPSO algorithm to iteratively optimize model parameters. Initially, assign a set of parameters to be identified to each particle randomly. (Sampling is performed uniformly within the aforementioned boundary range), and the fitness (i.e., the overall objective function value) is calculated. During iteration, particles update their velocity and position based on their individual optimal position and the global optimal position. The algorithm records the global optimal fitness value and the corresponding parameter combination for each generation to plot the convergence trajectory for post-analysis. The algorithm terminates when the maximum number of iterations (e.g., 100 generations) is reached or the fitness decrease is less than a preset threshold (e.g., improvement of less than 0.001 for several consecutive generations). The final output of the optimal parameters is the identified set of model parameters.

[0255] Through the experimental design described above, the improved PSO algorithm can fully utilize the preprocessed data for parameter optimization search. Compared with the standard PSO, IPSO improves on parameter selection and inertia weight strategy, and can be expected to achieve faster convergence speed and more accurate parameter identification results.

[0256] After parameter identification is completed, the obtained optimal parameters are injected into the mathematical models of the boiler system, steam turbine system, and feedwater system to form the identification model. Then, the identification model is driven to run using the same input sequence (load command sequence) as in the data generation stage, generating the model's output results under various operating conditions. Comparing the output of the identification model with the original simulation "true value" data allows for the evaluation of the accuracy of parameter identification.

[0257] Output the fitting results: Figure 2 , Figure 3 , Figure 4 Comparison curves (fitting curves) between the simulated true values ​​and the output of the IPSO identification model are presented for the three output variables—main steam pressure, main steam temperature, and turbine output power—under the three operating conditions described above. As can be seen from the figures, the model output curves can effectively track the changing trends of the actual data. During the 50%→100% load increase phase, the identification model accurately reproduces the dynamic increase in main steam pressure and temperature, and the power generation ramp-up curve almost coincides with the actual value. During the 100%→40% load decrease phase, the model output also closely follows the actual changes, showing good agreement in both the rapid decline phase and the intermediate plateau phase. In the random disturbance phase, the model's response to small fluctuations of ±2% is also highly consistent with the true value. Overall, the improved PSO identification model has a high degree of fit to the dynamic changes in output under the three typical operating conditions, without significant lag or deviation.

[0258] Error distribution analysis: In order to further quantify the accuracy of the identification model, statistical analysis was performed on the residuals between the model output and the true value. Figure 5 , Figure 6 , Figure 7 Histograms of error distributions for the three outputs—main steam pressure, main steam temperature, and power generation—were plotted. The error distributions show that the residuals of all three outputs exhibit a symmetrical distribution close to zero mean, with most errors falling within a narrow range near zero. Specifically, the errors in pressure and power are mainly within ±2% of the rated value, while the temperature error is even smaller, almost entirely within ±1%. This indicates that the identification model does not exhibit systematic bias and can accurately predict both the average level and dynamic changes of each output simultaneously. In contrast, the error distribution of the unmodified standard PSO identification model is more dispersed, with the standard deviations of the pressure and power residuals increasing by approximately 0.5%–1% of the rated value compared to the IPSO model, suggesting that the outputs of the standard PSO identification model occasionally deviate more significantly from the true value. Overall, the residuals of the IPSO algorithm identification model are more concentrated and smaller, reflecting its higher identification accuracy.

[0259] Quantitative performance metrics: To objectively compare the accuracy of the identification results of the improved PSO and the standard PSO, Table 2 lists the key error metrics for each output of the two algorithms, including root mean square error (RMSE), mean absolute percentage error (MAPE), and goodness of fit (expressed as a percentage, with higher values ​​indicating better fit). These metrics are all calculated based on unnormalized actual physical quantities.

[0260] Table 2 Comparison of error indices between standard PSO and improved PSO identification models Output variables RMSE (Standard PSO) RMSE (Improved PSO) MAPE (Standard PSO) MAPE (Improved PSO) Goodness of fit (Standard PSO) Goodness of fit (improved PSO) Main steam pressure 0.03 0.02 2.8% 1.9% 90% 95% Main steam temperature 0.02 0.015 1.5% 1.0% 92% 96% Power generation 0.025 0.018 2.0% 1.4% 89% 94% Overall Average 0.025 0.018 2.1% 1.4% 90% 95%

[0261] As shown in Table 2, the improved PSO algorithm outperforms the standard PSO algorithm in all output error metrics. Taking main steam pressure as an example, the improved PSO model has an RMSE of 0.02 (normalized units), which is about 33% lower than the standard PSO's 0.03; the pressure MAPE decreases from 2.8% to 1.9%, and the goodness of fit improves from 90% to 95%. The identification results for main steam temperature and power generation also show similar improvement trends, with MAPE decreasing by about 0.5 percentage points and the goodness of fit improving by more than 4%. Overall, on average, the improved PSO algorithm reduces the overall root mean square error of the model output by about 28%, the mean absolute error by about 0.7 percentage points, and the overall goodness of fit by 5 percentage points, reaching a level of about 95%.

[0262] Table 3. Comparison of Iterative Convergence Characteristics (Standard PSO vs. Improved PSO) index Standard PSO Improve PSO Comparison and explanation Initial objective function value (iteration 0) 0.25 0.25 The two algorithms start from the same point. Number of iterations to reach a stable platform ≈ 50s ≈ 30s IPSO converges approximately 20 generations earlier than PSO. Platform interval objective function value ≈ 0.050 ≈ 0.040 The IPSO platform has an error rate approximately 20% lower. The optimal objective function value after 100 iterations ≈ 0.030 ≈ 0.021 IPSO's final error is approximately 30% lower than PSO's. The globally optimal decrease within 100 generations (relative to the starting point) 88 % 92 % IPSO saw a larger overall decline. Convergence rate Slow—Fast—Flat Fast and flat IPSO experienced a sharp drop in the early stages, followed by a more pronounced leveling off later. Final parameter fluctuation amplitude (maximum drift within 10 generations) ≈ 8 % ≈ 3 % IPSO particle swarm optimization converges more compactly.

[0263] The improved PSO algorithm not only enhances identification accuracy but also exhibits significantly better convergence behavior. Table 3 summarizes the iterative characteristics of the two algorithms in this embodiment: the improved PSO reaches a stable plateau after approximately 30 generations, while the standard PSO requires approximately 50 generations to stabilize; the plateau error of the improved PSO is approximately 0.040, about 20% lower than that of the standard PSO; and at 100 generations, its optimal objective function value is about 30% lower than that of the standard PSO. Furthermore, the parameter fluctuation of the improved PSO in the last 10 generations is only about 3%, while the standard PSO still has about 8% drift, further demonstrating that the improved algorithm converges more compactly and stably.

[0264] The simulation results show that the improved PSO algorithm not only controls the overall mean square error and percentage error to a very small range, but also significantly improves the convergence speed and final accuracy (see Table 3). Compared with the standard PSO, the improved PSO achieves a lower objective function value and maintains smaller final parameter fluctuations under the same number of iterations, verifying the performance improvement effect of adaptive inertia weights and local perturbation strategies.

[0265] It should be noted that this embodiment is based on simulation data, and the data quality and operating condition coverage are still limited: the random disturbances and noise levels are relatively simple and cannot fully reflect the complex disturbances in actual units; the simulation model has the same structure as the model to be identified and is idealized, without considering unmodeled dynamics and time-varying parameters. Therefore, although the simulation results verify the effectiveness and reliability of the improved PSO identification method, its disturbance rejection capability and robustness still need to be further tested in a real-world environment. Embodiment 2 will use an actual operating ultra-supercritical unit as the object to conduct engineering verification of the method to evaluate its application effect under real operating conditions.

[0266] Example 2: Engineering deployment and rolling identification application of actual ultra-supercritical units;

[0267] This example selects a real 1000MW ultra-supercritical coal-fired unit as the research object. This unit adopts single-reheat ultra-supercritical parameters, with main steam parameters of approximately 25MPa / 570℃, reheat steam temperature of approximately 600℃, and rated steam flow rate... The flow rate is close to 480 kg / s. The main equipment includes an ultra-supercritical boiler, steam turbine, and generator set. A distributed control system (DCS) is used for coordinated control on-site. The DCS data acquisition cycle is typically on the order of 1 second, and operational data is stored long-term through a plant-level historical information system. However, due to the significant nonlinearity and time-varying characteristics of ultra-supercritical units, traditional modeling and parameter setting methods struggle to accurately obtain the model form and parameters, resulting in insufficient model identification accuracy of the current control system and hindering the full realization of control optimization potential. This manifests as large control deviations and frequent adjustments under heavy load variations, necessitating improved parameter identification methods to enhance model accuracy and meet engineering control requirements.

[0268] During normal unit operation, key variable data are collected using the DCS and historical databases to construct the sample set required for identification. The collected input and output variables include... (Pulverizer output) wait, , The data collected included steam parameters such as reheat steam temperature, the opening of major regulating valves (e.g., feedwater regulating valve, main steam valve position), and unit power generation. To ensure sufficient dynamic range coverage, the data collection period was selected during a time of significant load fluctuation (March 15, 2025, 12:00–18:00), encompassing the load change from base load to peak load. The data sampling period was set to 1 second to obtain sufficient temporal resolution. Data integrity was strictly monitored during the collection process, and missing values ​​due to sensor malfunctions or communication interruptions were removed; if a small number of missing values ​​existed, interpolation was used to fill them in. The obtained raw data ensured to include both steady-state and dynamic operating conditions, including load increases, decreases, and disturbances, to provide comprehensive identification information. After preliminary checks to confirm data quality, the data for this period was exported for later use.

[0269] To improve the accuracy of the identification model, the collected raw data undergoes standardized preprocessing. First, all variable data is cleaned: a sliding window method is applied to detect and remove outliers (such as instantaneous jump points), and outliers exceeding reasonable ranges are replaced with the mean of nearest neighbors or directly deleted, ensuring smooth and reliable input-output curves. Second, denoising and smoothing are performed: mean filtering and wavelet filtering are used to reduce high-frequency noise in 1-second sampled data sequences, and the data is resampled to 10-second periods to compress redundancy and improve the signal-to-noise ratio. Simultaneously, a multi-period sliding window sampling strategy is introduced to enhance sample diversity: the 6-hour long time series data is divided into multiple sample segments according to a certain length sliding window (e.g., every 30 minutes, overlapping by 10 minutes), and the dynamic changes within each segment are extracted for use as the training sample set. During the sliding window partitioning process, the rate of change and variance of each data segment are calculated, and sample segments with drastic dynamic changes are selected for modeling (statically stable segments are used for model validation), thereby strengthening the model's learning of dynamic characteristics. After the above preprocessing is completed, a clean and rich training dataset and an independent test dataset are obtained, which are used for subsequent parameter identification and model output verification, respectively.

[0270] After data preparation, an improved Particle Swarm Optimization (IPSO) algorithm is deployed for parameter identification of the unit model. Due to real-time requirements, the identification program is deployed on the power plant simulation server and uses processed historical data obtained through the DCS interface for offline calculations. Newly identified parameters can be uploaded to the DCS for model updates, achieving online closed-loop processing. The improved PSO algorithm incorporates adaptive inertia weights and mutation operations to balance global search and local exploitation. First, the particle encoding method is set according to the structure of the unit model being identified (e.g., boiler-turbine system model), with each particle containing a parameter vector θ to be identified. The initial search range of parameters is determined using engineering experience, and an initial particle swarm is randomly generated within this range. Prior calibration values ​​can be used to perturb the initial swarm to improve the diversity of initial solutions. During algorithm operation, each particle calculates the mean square error (MSE) of the model simulation based on the collected input and output data as its fitness function, continuously updating its velocity and position through iteration. The improved PSO algorithm records the globally optimal fitness value during the iteration process to monitor the convergence progress. As the generation number increases, the error of each particle gradually decreases and tends to stabilize. By setting appropriate convergence criteria (such as a maximum iteration number of 100 generations or an error reduction threshold), the algorithm stops after convergence. Finally, a set of optimal parameters θ obtained from the identification is output and stored for later use. The entire identification calculation process is very short (can be completed within minutes), meeting the needs of rapid identification in engineering fields.

[0271] The identified parameters are applied to the unit's simulation model system, and independent data segments not used in training are selected to validate the model's output. Specifically, the test data segment reserved in step 2 (one hour of data from 17:00–18:00 on March 15, 2025) is used as the model input to drive the simulation, obtaining the model's predicted main outputs (power generation, main steam pressure, etc.) and comparing them with actual measured values. In this example, the evaluation is directly quantified using error indicators. Table 4 lists the root mean square error (RMSE) of the model's predicted values ​​relative to the measured values, the goodness of fit (FIT%, the higher the better), and the maximum error bandwidth, among other indicators.

[0272] Table 4 Identification Error Table index Power generation Main steam pressure RMSE 5.2MW 0.12MPa FIT% (Fitness) 98.7％ 97.5％ Maximum error bandwidth ±1.5% power ±1.2% pressure

[0273] As shown in Table 4, the model obtained by the improved PSO identification has very small prediction errors for the unit's key outputs: the power generation RMSE is only about 5MW, and the main steam pressure RMSE is about 0.12MPa; the FIT of both outputs is close to 98%, indicating that the model can explain more than 98% of the output variations. The maximum deviations between the predicted and measured values ​​are controlled within ±1.5% and ±1.2% of the rated values, respectively, fully meeting the engineering control accuracy requirement of "no more than ±2%".

[0274] Although the aforementioned identification model has met the established accuracy requirements, an online correction mechanism for model mismatch still needs to be considered in actual operation. When the model prediction error index exceeds the threshold (e.g., RMSE exceeds the set value or the deviation continues to exceed 2%), the system automatically triggers a local disturbance test and a rapid re-identification process: applying a small-amplitude step signal or random disturbance to the relevant control channels, acquiring new dynamic response data without affecting unit safety, and using an improved PSO algorithm to locally identify and adjust key parameters. Through multiple iterative fine-tuning, adaptive convergence of model parameters is achieved. Once the model correction is complete, a feedback loop of model prediction error → control quantity correction is introduced: the control system monitors the difference between the model output and the measured value in real time, and appropriately biases the control command (feedforward correction of fuel or water quantity) according to the error trend to offset the impact of model error on control. Finally, the closed-loop control scheme with the identification model is tested in the unit simulation environment: the results show that the control system based on the real-time correction model has better performance than the original control logic, mainly reflected in smaller main steam pressure deviation, reduced steam temperature fluctuation, and faster adjustment speed when the load changes. For example, in the same load disturbance experiment, the control scheme introducing model feedback kept the main steam pressure deviation within ±0.5MPa, while the deviation of traditional PID control once exceeded ±1MPa; at the same time, overshoot and settling time were reduced. This proves that model-driven adaptive control is a significant improvement over the original control logic. If significant drift in model parameters is found during long-term operation, this mechanism can also be regarded as an early fault diagnosis method. Parameter changes can reflect equipment performance degradation or sensor malfunctions, thus reminding maintenance personnel to carry out maintenance.

[0275] To apply the aforementioned model and identification method in practical engineering, the model and algorithm need to be encapsulated and integrated online. This example encapsulates the complete modular simulation model of the unit and the improved PSO identification algorithm into a standard dynamic link library (DLL) component, providing input and output conforming to the functional block interface specification. This model-algorithm component is integrated into the simulation host or DCS open platform at the unit site, achieving online computation through interaction with a real-time database. After deployment, an automatic rolling identification mechanism is established: a timed scheduler automatically executes the data acquisition and parameter identification process every certain period (e.g., hourly). The specific process is a closed-loop cycle of "data acquisition → parameter identification → model update → control optimization": at the end of each hour, the DCS automatically extracts the operating data of the most recent hour and performs preprocessing, then calls the PSO algorithm to update the model parameters, writing the new parameters online into the model system; simultaneously, the control system reads the updated model for control calculations in the next cycle. This rolling operation allows the model parameters to continuously self-correct as operating conditions change, maintaining high accuracy and adaptability. To further demonstrate the effectiveness of the improved PSO algorithm proposed in this invention, it is compared with other optimization algorithms. The iteration curve is shown below. Figure 7 As shown. By Figure 8 It can be seen that the improved PSO has the fastest convergence speed and the highest accuracy, significantly outperforming the other three algorithms.

[0276] To further verify the superiority of the improved PSO algorithm, Table 5 summarizes the performance indicators of the identification models obtained by each algorithm on the test data, including the NRMSE (Normalized Root Mean Square Error) of the power generation output, the FIT goodness of fit, and the maximum error percentage.

[0277] Table 5 Comparison of metrics for different algorithms algorithm NRMSE (Power) FIT (%) Maximum error Does it meet ±2%? Improve PSO 1.1% 98.5 ±1.5% yes Standard PSO 2.3% 95.0 ±2.8% Basically satisfied DE (Differential Evolution) 2.7% 93.4 ±3.2% no GA (Genetic Algorithm) 4.6% 89.8 ±5.0% no

[0278] As shown in the table above, the improved PSO algorithm achieved the best identification performance in this example: its model output was only about 1.1% of the measured NRMSE, with a goodness of fit close to 98.5% and a maximum error within ±1.5%, fully meeting the engineering accuracy requirements. The standard PSO was second, with an NRMSE of about 2.3%, barely controlled within ±3%, basically meeting the requirements but slightly inferior in accuracy. In contrast, the identification accuracy of the GA and DE algorithms was significantly lower, with NRMSEs in the 3-5% range and maximum errors exceeding the ±2% control tolerance, thus failing to meet the high-precision control requirements. This further verifies the effectiveness of the invention from an algorithmic perspective.

[0279] The above description is merely a preferred embodiment of this disclosure and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in the embodiments of this disclosure is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the above-described inventive concept. For example, technical solutions formed by substituting the above-described features with (but not limited to) technical features with similar functions disclosed in the embodiments of this disclosure.

Claims

1. A method for identifying model parameters of ultra-supercritical units based on an improved particle swarm optimization algorithm, characterized in that, include: Step 1: Divide the ultra-supercritical unit into a boiler system, a turbine system, and a feedwater system; The boiler system includes a combustion chamber, water-cooled walls, a superheater, a reheater, an economizer, and an air preheater; the steam turbine system includes a high-pressure cylinder, an intermediate-pressure cylinder, and a low-pressure cylinder; and the feedwater system includes a feedwater pump, a deaerator, and a heater. Step 2: Construct mathematical models of the boiler system, steam turbine system, and feedwater system to determine the parameters to be identified for the ultra-supercritical unit. Step 3: Collect multiple operating data of the ultra-supercritical unit under dynamic operating conditions, process all operating data, and obtain the processed data sequence; Step 4: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, the parameters to be identified for the ultra-supercritical unit, and the processed data sequence, an improved particle swarm optimization algorithm is used to determine the initial optimal parameters. Step 5: Based on the mathematical models of the boiler system, steam turbine system, and feedwater system, as well as the processed data sequence, the initial optimal parameters are further identified to obtain the identified parameters.

2. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In step 2, the mathematical model of the boiler system is constructed as follows: ； in, for The first derivative in time, for The first derivative in time, The pressure response time constant is The temperature response time constant, This refers to the pressure gain of the fuel input to the boiler system. The temperature gain of fuel input to the boiler system; Input of coal quantity per unit time; This is the pressure reduction coefficient of the steam turbine intake. Main steam flow rate; Main steam pressure; Main steam temperature; Among them, the parameters to be identified in the boiler system ; The mathematical model of the steam turbine system is as follows: ； in, This represents the turbine output power in the time domain. for The first derivative over time; Main steam pressure, Indicates the pressure-load transfer gain. This represents the mechanical response inertia of a steam turbine; Among them, the parameters to be identified in the steam turbine system ; The mathematical model of the water supply system is expressed as follows: ； in, This refers to the boiler feedwater flow rate. for The first derivative in time, for The second derivative in time; The water supply regulation signal is the model input. It is the second-order inertial time constant; To control the delay time; For water supply system gain; Among them, the parameters to be identified in the water supply system ; The parameters to be identified for ultra-supercritical units include , and .

3. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 2, characterized in that, Step 3 specifically includes the following steps: Step 3.1: Collect multiple operating data of the ultra-supercritical unit under typical dynamic operating conditions. The operating data includes various sampling data, namely, the amount of coal input per unit time. Boiler feedwater flow rate Main steam pressure Main steam temperature Steam turbine output power and water supply regulation signal ; Step 3.2: Set up a common timeline, specifying the times on the common timeline. When any sample data in the running data is missing, linear interpolation is used to calculate the time. Sampling data Specifically, this is achieved through the following formula: ； in, Indicates a moment on the common timeline The first sampled data on the right, express At the corresponding time, Moments on the public timeline The first sampled data on the left, express The corresponding moment; The sampled data corresponding to all moments on the common time axis constitute the first sampling sequence; Step 3.3: Set a data threshold interval, remove sampled data that are not in the data threshold interval in the first sampling sequence, calculate the mean of the first data at the left time step and the first data at the right time step of the sampled data, obtain the neighbor mean, use the neighbor mean as the new sampled data, and then obtain the second sampling sequence; The mean of the data within the sliding window is calculated by sliding a preset sliding window over the second sampling sequence. with standard deviation Specifically, this is achieved through the following formula: ； ； Where L represents the length of the sliding window. Represents the time in the sliding window. Indicating the second sampling sequence Data at any given time; exist At that time, the time in the second sampling sequence Data Replace with ,exist At that time, retain After each data point in the second sampling sequence undergoes the above processing, the third sampling sequence is obtained. Step 3.4: For the data in the third sampling sequence, calculate the difference between the data at two adjacent time points to obtain multiple differences. Obtain the difference that is greater than or equal to a preset threshold, and obtain the corresponding data in the third sampling sequence to form the fourth sampling sequence. Step 3.5: Smooth the data in the fourth sampling sequence to obtain the filtered data, specifically achieved through the following formula: ； in, This represents the data in the fourth sampling sequence. Indicates time Filtered data, As a smoothing factor, Indicates time Filtered data; The filtered data is normalized using the following formula to obtain normalized data, which is then used to form the processed data sequence. ； in, This represents the normalized data. This represents the minimum value of all filtered data. This represents the maximum value of all filtered data.

4. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 3, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Set multiple particles and the maximum number of iterations. Set the initial iteration count d=0; randomly generate multiple sets of identification parameters for ultra-supercritical units, and use these parameters as the initial positions of the particles. The particle velocity is initialized to obtain the initial velocity. The initial position of each particle is taken as the initial optimal position of the individual. Step 4.2: Set the initial iteration count as the current iteration count d, and the initial position as the current position. Use the initial velocity as the current velocity. The initial optimal position of an individual is used as the current optimal position of the particle. ; Step 4.3: For each particle, according to The processed data sequence, mathematical models of the boiler system, turbine system, and feedwater system were used to calculate the predicted main steam pressure. Predicting the main steam temperature Predicting the output power of the steam turbine And predict boiler feedwater flow ; Step 4.4: Based on , , , Calculate the overall objective function value; Step 4.5: For each particle, among the total objective function value corresponding to the current individual optimal position and the total objective function value of the particle at the current iteration number, find the one with the smallest value and take its corresponding position as the new individual optimal position. Among the total objective function values ​​of all particles, find the one with the smallest value and take its corresponding position as the global optimal position. ; Step 4.6: At all total objective function values In the middle, get the first with the smallest value. Each particle is considered an elite particle, and all other particles are considered ordinary particles. Current velocity of elite particles The update is performed using the following formula: ； in, This represents the velocity of the elite particles in the updated (d+1)th iteration. Indicates the elite velocity decay factor; Step 4.7: Calculate the inertia weight at the current iteration number. Learning factors and learning factors ; Calculate the inertia weight at the current iteration number. Specifically, this is achieved through the following formula: ； in, , Given the maximum and minimum values ​​of the inertia weights, It is a non-linear decreasing factor; Calculate the learning factor at the current iteration number. and learning factors Specifically, this is achieved through the following formula: ； in, Represents learning factor initial value, Represents learning factor The final value, Represents learning factor initial value, Represents learning factor The final value; Step 4.8: Calculate the hybrid guidance probability at the current iteration number. Specifically, this is achieved through the following formula: ； in, As the initial value of the probability, This is the final probability value. It is a non-linear adjustment factor; according to Determine the mixing guidance vector of ordinary particle z. Specifically, this is achieved through the following formula: ； in, This represents the current optimal position of an ordinary particle z. Step 4.9: According to , , and The current velocity of ordinary particles The initial update is performed using the following formula: ； in, This represents the velocity of a normal particle in the (d+1)th iteration after the initial update. and It is a random vector. This represents the current position of the ordinary particle z; Step 4.10: Obtain the total objective function value from all elite particles. The smallest elite particle is designated as the elite optimal particle, based on the current position of the elite optimal particle. ,right After another update, the final velocity of the ordinary particle is obtained. Specifically, this is achieved through the following formula: ； in, For elite guidance strength, It is a random vector; Step 4.11: Calculate the updated positions of elite particles Position updated with ordinary particles Specifically, this is achieved through the following formula: ； ； Step 4.12: For any particle among elite particles and ordinary particles, if The total objective function value after dM iterations If the difference is greater than or equal to the stagnation threshold, the updated position of the particle will be taken as the final position of the particle. like The total objective function value of the global optimal position after dM iterations If the difference is less than the stagnation threshold, the updated position of the particle is locally perturbed using the following formula to obtain the perturbed position, which is then taken as the final position of the particle. ； ； in, This represents the position after the ordinary particle is disturbed. This represents the position of the elite particles after perturbation. For the disturbance amplitude, Let be a multidimensional standard normal random vector with a mean of 0 and a covariance matrix that is the identity matrix. ; Step 4.13: In If the difference between the total objective function value of the global optimal position in the current iteration number and the total objective function value of the global optimal position in the dM iterations is less than a preset threshold, then the global optimal position is used as the initial optimal parameter, and step 5 is executed. exist If the difference between the total objective function value of the global optimal position at the current iteration number and the total objective function value of the global optimal position at the dMth iteration number is greater than or equal to a preset threshold, then proceed to step 4.

14. Step 4.14: If the variance of the final positions of all particles is less than a preset variance threshold, and the total objective function value corresponding to the global optimal position does not decrease in R iterations, then increment the current iteration number by one, and use the final position of the elite particle as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used to randomly initialize the position and velocity of the ordinary particles, and then the process returns to step 4.

3. If the variance of the final positions of all particles is greater than or equal to a preset variance threshold, or if the total objective function value corresponding to the globally optimal position decreases in R iterations, then the current iteration number is incremented by one, and the final position of the elite particle is used as the position in the new iteration number. The velocity of the elite particles in the new iteration number is used as the final position of the ordinary particles in the new iteration number. As the velocity of the ordinary particles in the new iteration, return to step 4.

3.

5. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 4, characterized in that, Step 4.3 includes: Based on the processed data sequence The main steam flow rate is calculated based on the regulating valve position. The processed data sequence , , as well as In Substituting into the mathematical model of the boiler system, we obtain and The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain The processed data sequence as well as In Substituting into the mathematical model of the steam turbine system, we obtain .

6. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 4, characterized in that, Step 4.4 includes: Calculate the mean square error Specifically, this is achieved through the following formula: ； Where T represents the processed data sequence ,or ,or The quantity; when m=3, and i are 1, 2, 3 respectively, They are respectively , , , They are respectively , , ; Calculate the total objective function value Specifically, this is achieved through the following formula: ； in, The L1 regularization weighting factor. This is the L2 regularization weight factor.

7. The method for identifying model parameters of ultra-supercritical units based on the improved particle swarm optimization algorithm according to claim 4, characterized in that, Step 5 specifically includes the following steps: Step 5.1: Based on the data sequence after processing the initial optimal parameters, the mathematical model of the boiler system, the mathematical model of the turbine system, and the mathematical model of the feedwater system, obtain the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate. Step 5.2: Based on the predicted main steam pressure, predicted main steam temperature, predicted turbine output power, and predicted boiler feedwater flow rate, as well as the processed data sequence... , , and Calculate the root mean square error (RMSE) and the goodness of fit (FIT). Step 5.3: When RMS is greater than the preset error threshold or FIT is less than the preset fitting threshold, take the initial optimal parameter as the center and generate multiple new sets of ultra-supercritical unit parameters to be identified according to the preset disturbance range, and return to step 4; when RMS is less than or equal to the preset error threshold and FIT is greater than or equal to the preset fitting threshold, take the initial optimal parameter as the parameter identification completed, and complete the parameter identification.

Images