Fuzzy width hearth temperature model prediction control method

Abstract

The invention provides a fuzzy width hearth temperature model predictive control method, which relates to the technical field of hearth temperature model predictive control, and comprises the following steps: constructing a hearth temperature predictive model; obtaining a correction output variable according to the hearth temperature prediction model; according to a gradient particle swarm optimization algorithm and the correction output variable, solving an objective function of MPC corresponding to the hearth temperature prediction model to determine an optimal manipulated variable set; determining an optimal control law of the MPC according to the optimal manipulated variable set; according to the optimal control law, a control variable to be input is input into the hearth temperature prediction model, an initial controlled variable is obtained, the control variable is the secondary air volume, and the controlled variable is the hearth temperature; and correcting and compensating the initial controlled variable according to the prediction error at the current moment to obtain a final controlled variable. According to the method, the problems of high calculation complexity and low precision of the existing MPC control facing the FT in the MSWI process are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of furnace temperature model predictive control, and particularly to a fuzzy width furnace temperature model predictive control method. Background Art

[0002] The acceleration of the global urbanization process has made the problem of municipal solid waste (MSW) increasingly prominent, which has become a major environmental challenge faced globally. Improperly treated MSW will release harmful gases and pollutants, thus aggravating air pollution and the greenhouse effect. In addition, the leachate from solid waste landfills may pollute groundwater, endangering human health and ecological safety. The treatment method of MSW directly affects environmental protection and resource utilization, and has become an urgent problem to be solved globally. Due to its advantages such as reduction, harmlessness and resource utilization, municipal solid waste incineration (MSWI) has become a key technology to promote the global urban renewable energy cycle, sustainable development and environmental protection. However, harmful gases and particles such as dioxins and heavy metals may be released during the incineration process, so advanced combustion control technologies need to be adopted to ensure that the emissions meet environmental protection standards. In summary, it is necessary to develop a large-scale, integrated and intelligent MSWI control system, and optimize the incineration process through efficient intelligent control technologies to achieve the intelligent, low-carbon, harmless and efficient sustainable development of MSWI.

[0003] As a key controlled variable in the MSWI process, the furnace temperature (FT) helps to achieve complete incineration of solid waste, reduce the generation and emission of harmful gases, and optimize the heat energy recovery efficiency. However, the diversity of MSW components leads to calorific value fluctuations and equipment aging, etc., which require frequent adjustment of process variables, bringing uncertain disturbances to the stable control of FT. The automatic combustion control (ACC) system has been widely used in countries such as Europe, America and Japan. Although the ACC system introduced into China has undergone many years of industrial applications, the control technology of MSWI plants in China still relies on manual control by domain experts. Therefore, in the face of the challenges of lack of experience accumulation and foreign technology blockade, it is necessary to combine years of practical experience to study FT intelligent control algorithms with Chinese local characteristics.

[0004] However, the existing MPC control for the FT in the MSWI process still faces the following challenges: (1) The high uncertainty of complex nonlinear systems makes it difficult to construct a prediction model, which requires the use of modeling algorithms with strong uncertainty handling and nonlinear mapping capabilities to solve. (2) As a meta-heuristic optimization algorithm, PSO has a powerful global search ability, but its computational complexity is high, making it difficult to meet the real-time requirements of MPC. In addition, poor initial particle positions may lead to premature convergence of PSO to local optimal solutions, reducing the optimization performance. (3) In a complex dynamic environment, it is difficult to maintain the accuracy and reliability of the surrogate model, resulting in the deviation of the MPC control law from the optimal solution or even control errors. Although existing research has explored the online update mechanism of the surrogate model, most are based on offline data or heuristic methods and fail to fully utilize the knowledge and data accumulated during the operation of the system. (4) The current surrogate models in MPC mainly focus on reducing computational consumption, do not effectively utilize the knowledge of particle distribution to assist in solving the control law, and lack a secure solution strategy based on sample and particle archive databases, unable to ensure the stability and security of the control output. Summary of the Invention

[0005] In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a fuzzy-width furnace temperature model predictive control method.

[0006] To achieve the above object, the present invention provides the following solution:

[0007] A fuzzy-width furnace temperature model predictive control method, comprising:

[0008] Construct a furnace temperature prediction model, wherein the furnace temperature prediction model is an IT2FBLS prediction model, and the IT2FBLS prediction model includes: an input layer, an IT2FNN layer, an enhancement layer, and an output layer;

[0009] Obtain a corrected output variable according to the furnace temperature prediction model;

[0010] Solve the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable to determine the optimal set of manipulated variables;

[0011] Determine the optimal control law of the MPC according to the optimal set of manipulated variables;

[0012] According to the optimal control law, input the control variable to be input into the furnace temperature prediction model to obtain the initial controlled variable, wherein the control variable is the secondary air volume, and the controlled variable is the furnace temperature;

[0013] Correct and compensate the initial controlled variable according to the prediction error at the current moment to obtain the final controlled variable.

[0014] Preferably, the calculation expression of the corrected output variable is as follows:

[0015]

[0016] υ(t) is the error vector for solving the corrected output variable, is the initial controlled variable, and y(t) is the actual output value, is the predicted value of the prediction model at the future i p -th moment, H p is the prediction horizon of MPC, that is, the maximum value of i p , and y p (t + i p ) is the corrected output value of the prediction model at the future i p -th moment.

[0017] Preferably, the calculation expression of the initial controlled variable is as follows:

[0018]

[0019] Among them, h(t) is the output vector of the enhancement layer of the furnace temperature prediction model, G is the number of nodes in the fuzzy mapping layer of the prediction model, g = 1, …, G represents the g-th node, L is the number of nodes in the enhancement layer, l = 1, …, L represents the l-th enhancement node, z g (t) and h l (t) are the output values of the g-th node in the fuzzy mapping layer and the l-th enhancement node in the enhancement layer, respectively, is the initial controlled variable, w f (t) = [w f1 (t), …, w fG (t)] T is the weight vector between the output of the IT2FNN layer and the output layer, where w fG (t) is the G-th weight scalar in this weight vector; w e (t) = [w e1 (t), …, w eL (t)] T is the weight vector between the output of the enhancement layer and the output layer, where w eL (t) is the L-th weight scalar in this weight vector.

[0020] Preferably, the optimal set of manipulated variables is determined by solving the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable:

[0021] Solve the error vector according to the corrected output variable;

[0022] Based on the error vector, calculate the current optimal control sequence according to GD;

[0023] Update the operating variable according to the optimal control sequence to obtain the updated operating variable;

[0024] Determine whether the current moment reaches the threshold. If it reaches, construct an SSDB for the updated operating variable set corresponding to the current moment, initialize the KDD model, and determine the updated operating variable set corresponding to the current moment as the initial value of the PSO particle;

[0025] According to the initial value of the PSO particle, use the PSO algorithm to calculate the output value that minimizes the KDD model;

[0026] Determine the excellent solution of the PSO process according to the output value that minimizes the KDD model, construct a PADB, and continuously update the PADB;

[0027] Determine the candidate solution set according to the PADB and the SSDB;

[0028] Determine the optimal set of manipulation variables according to the candidate solution set.

[0029] Preferably, the formula for SSDB is:

[0030]

[0031] Preferably, the KDD model is constructed based on the system state information and historical knowledge in the SSDB using a Gaussian process regression model, as follows:

[0032] J SSDB ~N(μ0,Σ0)

[0033] where μ0 = [μ0(u1),…,μ0(u K )] is the mean function, K is the number of samples in the SSDB, and Σ0 is the covariance matrix.

[0034] Preferably, the step of minimizing the output value of the KDD model using the PSO algorithm according to the initial value of the PSO particle includes:

[0035] Determine the velocity and position of the current particle;

[0036] Determine the output value of the KDD model according to the velocity and position of the current particle;

[0037] where the calculation formulas for the velocity and position of the current particle are:

[0038]

[0039] where v i,o(t + 1) is the velocity of the o-th dimension of the i-th particle, a i,o (t + 1) is the position of the o-th dimension of the i-th particle, ω(t), c1, and c2 are the first weight parameter, the second weight parameter, and the third weight parameter respectively, and r1 and r2 are random numbers with values in the range of [0, 1].

[0040] The present invention discloses the following technical effects:

[0041] The present invention provides a fuzzy-width furnace temperature model predictive control method, including: constructing a furnace temperature prediction model, and obtaining a corrected output variable according to the furnace temperature prediction model; solving the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable to determine an optimal set of manipulated variables; determining an optimal control law of the MPC according to the optimal set of manipulated variables; according to the optimal control law, inputting a control variable to be input into the furnace temperature prediction model to obtain an initial controlled variable, where the control variable is the secondary air volume and the controlled variable is the furnace temperature; correcting and compensating the initial controlled variable according to the prediction error at the current moment to obtain a final controlled variable. First of all, the present invention uses an interval type-2 fuzzy-width learning system (IT2FBLS) to construct a prediction model of the MPC, enhancing the non-linear modeling and uncertainty processing capabilities. Secondly, in the rolling optimization process, a collaborative strategy of gradient descent and PSO is introduced to ensure fast convergence and improve the global search performance, and a knowledge-data-driven (KDD) surrogate model is constructed using the system sample database (SSDB) and the particle archive database (PADB) to reduce the computational consumption. Finally, combined with the designed manipulated variable (MV) baseline solution strategy, the safety and reliability of the control output are improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0043] Figure 1 It is a flowchart of a fuzzy-width furnace temperature model predictive control method provided by an embodiment of the present invention;

[0044] Figure 2 It is a schematic diagram of the KDD-GPSO-FBMPC control strategy provided by an embodiment of the present invention;

[0045] Figure 3 It is a flowchart of the KDD-GPSO-FBMPC algorithm provided by an embodiment of the present invention. Detailed implementation mode

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0047] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation modes.

[0048] As Figure 1 shown, the present invention provides a fuzzy-width furnace temperature model predictive control method, including:

[0049] Step 100: Construct a furnace temperature prediction model, where the furnace temperature prediction model is an IT2FBLS prediction model, and the IT2FBLS prediction model includes: an input layer, an IT2FNN layer, an enhancement layer, and an output layer;

[0050] Step 200: Obtain a corrected output variable according to the furnace temperature prediction model;

[0051] Step 300: Solve the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable to determine the optimal set of manipulated variables;

[0052] Step 400: Determine the optimal control law of the MPC according to the optimal set of manipulated variables;

[0053] Step 500: According to the optimal control law, input the control variable to be input into the furnace temperature prediction model to obtain an initial controlled variable, where the control variable is the secondary air volume and the controlled variable is the furnace temperature;

[0054] Step 600: Correct and compensate the initial controlled variable according to the prediction error at the current moment to obtain the final controlled variable.

[0055] Specifically, this embodiment discloses the background overview corresponding to the above steps:

[0056] MSWI process process overview: The MSWI process goes through 6 main stages: solid waste fermentation, solid waste combustion, waste heat exchange, steam power generation, flue gas purification, and flue gas emission. Among them, the solid waste combustion stage is the key stage of the MSWI process, which can be divided into three processes: drying, combustion, and burnout.

[0057] (1) Drying process: The surface moisture of MSW gradually evaporates as the temperature in the furnace rises and is completely evaporated when the temperature reaches 100°C. With the further increase of the furnace temperature, its internal moisture is gradually released and absorbs a large amount of heat energy. Therefore, the total moisture content of MSW is related to the calorific value entering the furnace, which in turn affects the combustion state and even the operating conditions of the entire process.

[0058] (2) Combustion process: The stage from the ignition of MSW through strong light and heat emission until the end of the oxidation reaction, including strong oxidation, pyrolysis, and atomic group collision reactions. Therefore, the reactions involved in the combustion process are complex and variable, strongly coupled with each other, and have the characteristics of multi-reaction synchronous operation. Obviously, the combustion air volume and grate speed are crucial for a stable combustion process.

[0059] (3) Afterburning process: The process from the end of combustion to the complete stop of combustion. After the combustion process, the combustible components in MSW are mainly coke, and then under the action of primary air and high temperature, gasification reactions occur. After that, the inert substances gradually increase until all the MSW on the grate becomes ash, thereby weakening the combustion until it completely stops.

[0060] In summary, the stable operation of this stage is closely related to FT, which in turn affects the subsequent stages.

[0061] Model Predictive Control (MPC):

[0062] MPC obtains the optimal control law within a finite time domain at each moment by repeatedly solving the optimization problem in each control iteration. The solution of the optimization problem is usually completed based on the accurate prediction of the system dynamics by the prediction model. The nonlinear system is generally described by the following nonlinear autoregressive exogenous model with exogenous input, as follows:

[0063]

[0064] where Ω(·) is an unknown nonlinear function, y and u are the output and input of the system respectively, n y and n u are the maximum lags of the system output and input

[0065] As an iterative control strategy, MPC estimates the current and future states by minimizing the constrained objective function and solves the following optimization problem for a finite prediction time domain. The specific description of MPC is as follows:

[0066] First, measure or estimate the current state, construct and solve the optimization problem within a finite time domain, as follows:

[0067]

[0068] where, and are the reference trajectory vector and the predicted output vector of the control system, respectively is the MV increment vector, H p and H u respectively represent the prediction horizon and the control horizon set by the system (i.e., the step sizes of the predicted values and the control law sets in each iteration of the system, and satisfy H p > H u ; and are the weight parameter matrices of the objective function respectively; J(t) is the objective function of MPC

[0069] Next, solve equation (2) to obtain the optimal control sequence Δu at time t * (t) = [Δu * (t|t), …, Δu * (t + H u -1|t)].

[0070] Furthermore, apply its first term as the increment of the MV at the next moment, as follows:

[0071] u(t + 1) = u(t) + Δu * (t|t) (3)

[0072] Finally, enter the next moment and repeat the above process until the iteration ends to achieve rolling optimization

[0073] System knowledge description of industrial processes:

[0074] Derived from the sampling data in actual process control, each sample contains a specific MV value and the corresponding MPC objective function value. In this paper, this sample set is defined as SSDB, which provides a detailed description of the global characteristics and variation laws of the system by recording the dynamic characteristics and the response behavior of the objective function under different input conditions, enabling the surrogate model to more accurately simulate the system dynamics. At the same time, taking the minimum objective function value in SSDB as the baseline value, it serves as a conservative stability option for the MPC controller when the surrogate model makes unreliable predictions

[0075] PSO algorithm and particle distribution knowledge:

[0076] The PSO algorithm is a global optimization algorithm based on swarm intelligence. By simulating the foraging behavior of bird flocks, it realizes information sharing and mutual cooperation among individuals, enabling the entire group to gradually approach the optimal solution. Its basic process is as follows: First, a group of particles is randomly initialized in the search space, and each particle contains two vectors: position and velocity. Then, for each particle, the fitness value is calculated according to the objective function to evaluate the quality of the current solution of the particle. Next, the particle with the historical best position is updated as pbest, and the particle with the global best position is updated as gbest. The velocity and position of each particle are updated through the update algorithm. The particles in pbest and gbest are called elite particles. Finally, when the maximum number of iterations or the global optimal solution is reached and the accuracy requirement is met, the algorithm stops. For the PSO algorithm for rolling optimization, the MV of the control system is often determined by the positions of the elite particles.

[0077] The definition of the particle distribution knowledge of PSO is as follows:

[0078] Particle distribution knowledge: It comes from the archiving of the position information of elite particles and the corresponding fitness function values during the rolling optimization of the PSO algorithm. In this paper, this archiving set is defined as PADB, which saves the position of each elite particle and its corresponding fitness function value in the search space, reveals the possible efficient regions in the search space, and provides heuristic guidance for future search processes. At the same time, PADB contains possible optimal control sequences, and the baseline from SSDB is compared through the baseline solution strategy to obtain potentially high-precision optimal control sequences.

[0079] System knowledge and particle distribution knowledge, as two important data sources, respectively provide the interpretation and support for the system behavior and optimization process of the algorithm proposed in this paper. These two types of knowledge complement and cooperate through different information dimensions, providing information support for the update of the subsequent surrogate model and the optimal solution of MPC, which is beneficial to engineering applications.

[0080] Furthermore, as Figure 2 shown, a fuzzy-width furnace temperature model predictive control method can be divided into modules according to the control strategy, which can be divided into:

[0081] (1) IT2FBLS prediction module: Based on the IT2FBLS model, it predicts the state and future trends of the system. The type-2 fuzzy system in it captures the uncertainties in the system, and BLS extracts breadth features to achieve fast modeling and accurate prediction of complex nonlinear systems.

[0082] (2) KDD-GPSO Rolling Optimization Module: Through the collaborative rolling optimization of GD and PSO, and by using its various sub-modules in each control stage, it can find a safe global optimal solution while ensuring the rapid convergence of the system error. The following will describe it from the perspectives of module composition and control stage respectively.

[0083] From the perspective of the composition of each sub-module included in the KDD-GPSO rolling optimization module, the functions of each sub-module are as follows:

[0084] (1) GPSO Sub-module: In the gradient control stage, GD is used to provide a local optimal solution, and the current MV is used as the initial value of PSO in the switching stage; in the PSO control stage after switching, the knowledge data-driven sub-module and the MV baseline solution sub-module are used for global optimization, thereby improving control accuracy and robustness.

[0085] (2) Knowledge Data-driven Sub-module: Build a surrogate model through historical data containing system dynamic knowledge and update it dynamically to adapt to system state changes, reducing the frequent calls to IT2FBLS and plant models during the calculation of the objective function and reducing computational consumption.

[0086] (3) MV Baseline Solution Sub-module: Build a baseline solution and compare it with the current solution to ensure the safety of control input in a high-uncertainty environment and prevent unstable or dangerous MVs during the control process.

[0087] From the perspective of each sub-control stage included in the KDD-GPSO rolling optimization module, the operation of the algorithm includes the following three stages in chronological order: gradient control stage, GPSO switching stage, and PSO control stage. Its operation process is as follows: First, in the gradient control stage, calculate the system error at the current time t and determine whether the current time has reached the switching time t n , if not, update the MV using the GD algorithm in the KDD-GPSO rolling optimization module until t = t n ; then, when t = t n enter the switching stage, use the PSO algorithm as the rolling optimization strategy of MPC, and use the MV corrected by GD at the current time as the initial value of the particle position of the PSO algorithm; in addition, sample near the current MV and calculate its corresponding objective function value to build the SSDB, and build the KDD model as the surrogate model of PSO through the knowledge data-driven sub-module; finally, enter the PSO control stage, sample the new sample at the previous time and update the SSDB, use the knowledge data-driven sub-module to update the KDD model using the updated SSDB, use the excellent solutions generated by PSO to build or update the PADB, combine the constructed SSDB, and use the MV baseline strategy solution sub-module to calculate the optimal control law until the control iteration process ends.

[0088] Furthermore, as Figure 3 shown, the IT2FBLS prediction module includes an input layer, an IT2FNN layer, an enhancement layer, and an output layer. Taking the t-th moment as an example, the prediction process of the prediction model for the system at this iteration moment is described according to the forward calculation order:

[0089] Input layer, the input of this layer is X(t) in Equation (1), which directly maps the input variables to the IT2FNN layer without any operation.

[0090] IT2FNN layer, receives the input layer vector and sends the output of this layer to the enhancement layer and the output layer respectively. It contains G IT2FNN subsystems. Taking the g-th IT2FNN subsystem as an example, its calculation process is described.

[0091] First, the input vector is fuzzified using an interval type-2 membership function with an uncertain center as follows:

[0092]

[0093] where x i is the i-th element of X(t); and are the lower and upper bounds of the membership degree value of the i-th input corresponding to the j-th rule in the g-th subsystem (i = 1,..., I; j = 1,..., J); J is the number of fuzzy rules of the IT2FNN subsystem; and are the lower bound, upper bound, and width of the uncertain center of the j-th membership function corresponding to the i-th state input respectively.

[0094]

[0095] where, z g and are the lower and upper bounds of the output of the g-th subsystem respectively; and are the upper and lower activation strengths of the j-th fuzzy rule in the k-th subsystem respectively; is the consequent output weight of the j-th rule; is the consequent connection weight of the i-th input corresponding to the j-th rule.

[0096] Furthermore, the output of the g-th subsystem is obtained as:

[0097]

[0098] Finally, the output of the IT2FNN layer is obtained by combining G groups of subsystems as:

[0099] z = [z1 ,…,z G (7)

[0100] An enhancement layer that receives the output of the IT2FNN layer as the input of this layer and performs a non - linear transformation. It consists of L groups of enhancement nodes. Taking the l - th enhancement node as an example (l = 1,…,L), its output is:

[0101]

[0102] Among them, and are respectively the connection weight vector and the bias term coefficient between the IT2FNN layer and the l - th enhancement layer.

[0103] An output layer that obtains the final output of the model by linearly combining the outputs of the IT2FNN layer and the enhancement layer, as follows (initial calculation expression of the controlled variable):

[0104]

[0105] Among them, h(t) is the output vector of the enhancement layer of the furnace temperature prediction model, G is the number of nodes in the fuzzy mapping layer of the prediction model, g = 1,…,G represents the g - th node, L is the number of nodes in the enhancement layer, l = 1,…,L represents the l - th enhancement node, z g (t) and h l (t) are respectively the output values of the g - th node in the fuzzy mapping layer and the l - th enhancement node in the enhancement layer, is the initial controlled variable, w f (t)=[w f1 (t),…,w fG (t)] T is the weight vector between the output of the IT2FNN layer and the output layer, where w fG (t) is the G - th weight scalar in this weight vector; w e (t)=[w e1 (t),…,w eL (t)] T is the weight vector between the output of the enhancement layer and the output layer, where we L (t) is the L - th weight scalar in this weight vector.

[0106] Taking the calculated by Equation (9) as the input of the IT2FBLS model at the next moment, and repeating Equations (4) - (9), the outputs at future times t + 1,...,t + H p can be calculated, where Hp is the prediction horizon.

[0107] As a width learning model, the pre-training process of IT2FBLS is to input large-scale sample data simultaneously and solve the connection weights between the IT2FNN layer, the enhancement layer, and the output layer at one time. For the solution of the initial values of parameters w f and w e , this paper realizes it through the ridge regression approximation algorithm as follows:

[0108]

[0109] Among them, I is the identity matrix, ξ is the regularization coefficient, is the true output value of all samples, and N s is the number of samples in the data set.

[0110] Furthermore, to reduce the deviation between the output value of the prediction model and the true value, the IT2FBLS prediction module introduces a feedback correction mechanism after the prediction model outputs . By calculating the prediction error υ(t) at the current moment, it is used to compensate a series of prediction model outputs within the subsequent prediction time domain. Among them, the calculation expression of the corrected output variable is:

[0111]

[0112] y(t) is the true output of the plant.

[0113] The predicted value y p (t) = [y p (t + 1), …, y p (t + H p )] T will be used as the system predicted value in the subsequent online optimization control module, so as to solve the optimization problem and calculate the optimal control law.

[0114] Furthermore, the 3KDD - GPSO rolling optimization module combines GD and PSO to minimize the MPC objective function. At the initial moment of control, rolling optimization is carried out through GD. When the switching condition is met, the rolling optimization is replaced by PSO. Samples are taken within the current MV range calculated by GD to construct the SSDB, and this range is determined as the initial values of the particles of PSO. It should be noted that in this paper, the PSO algorithm is not directly used to solve the optimal control sequence, but is used to construct the PADB, combined with the MV baseline solution sub-module, to obtain the control sequence that balances safety and efficiency.

[0115] Next, taking t n as the switching time, the specific implementation process is described in stages according to the time axis order.

[0116] The moment of this stage is \(t\in[t_0,t n \), and the rolling optimization is carried out by using the GD algorithm in the GPSO sub-module:

[0117] To facilitate the subsequent solution, the weight parameter matrix \(W\) of the objective function in Equation (2) is simplified y and \(W u The diagonal elements in are \(\rho_1\gt0\) and \(\rho_2\gt0\) respectively. The output \(y p (t)\) after feedback correction is used for the calculation of the error vector, and the corresponding objective function is rewritten as:

[0118] \(J(t)=\rho_1[r(t)-y p (t)] T [r(t)-y p (t)]+\rho_2\Delta u(t) T \Delta u(t)\ (12)

[0119] Starting from the moment \(t_0\), the optimal control sequence \(\Delta u * (t)\) is solved iteratively by using GD, as follows:

[0120]

[0121] Among them, η＞0 is the learning rate of GD.

[0122] For the gradient term, by solving the partial derivative of \(u(t)\) through the shown objective function, we can obtain:

[0123]

[0124] Furthermore, we can get:

[0125]

[0126] Among them, is the Jacobian matrix. Taking the element in its \(n\)-th row and \(m\)-th column (\(n = [1,...,H p , m = [1,...,H u ) as an example, the calculation formula is as follows:

[0127]

[0128] Among them, \(X(t)\) is the model input shown in Equation (1). After calculating \(\Delta u * (t)\), the MV is updated by using Equation (3).

[0129] Furthermore, the optimal set of manipulated variables is determined by solving the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable:

[0130] Solve the error vector υ(t) according to the calibrated output variable;

[0131] Based on the error vector, calculate the current optimal control sequence according to GD;

[0132] Update the manipulated variable according to the optimal control sequence to obtain the updated manipulated variable;

[0133] Determine whether the current time reaches the threshold. If it does, construct an SSDB for the set of updated manipulated variables corresponding to the current time, initialize the KDD model, and determine the set of updated manipulated variables corresponding to the current time as the initial value of the PSO particle;

[0134] According to the initial value of the PSO particle, use the PSO algorithm to calculate the output value that minimizes the KDD model;

[0135] Determine the excellent solution of the PSO process according to the output value of the minimized KDD model, construct a PADB, and continuously update the PADB;

[0136] Determine the candidate solution set according to the PADB and the SSDB;

[0137] Determine the optimal set of manipulated variables according to the candidate solution set.

[0138] Furthermore, the GPSO switching stage:

[0139] The time of this stage is t = t n , sample within the current MV range to construct an SSDB and initialize the KDD model, and determine this range as the initial value of the PSO particle, denoted as a0(t) = u(t n ), where a0(t) is the initial position value of the particle.

[0140] Randomly sample K times near u(t n ), and calculate the corresponding J(t) respectively to obtain K sample points The elements of the sample points can be expressed as:

[0141]

[0142] where, ε k is a random perturbation obeying a uniform distribution.

[0143] All the above sample points will form the SSDB, which is expressed as follows:

[0144]

[0145] The KDD model is constructed based on the system state information and historical knowledge in the SSDB using the Gaussian Process Regression (GPR) model. It serves as a surrogate model for the PSO algorithm to reduce the computational consumption of the PSO and improve the real-time performance of the control system. First, the KDD model is constructed using the samples in the SSDB and the GPR algorithm. It takes the known data as the prior probability distribution that satisfies the multivariate normal distribution. The KDD model is constructed based on the system state information and historical knowledge in the SSDB using the Gaussian process regression model as follows:

[0146] J SSDB ~N(μ0,Σ0)(19)

[0147] where μ0 = [μ0(u1),…,μ0(u K )] is the mean function, K is the number of samples in the SSDB, Σ0 is the covariance matrix, the state information is the value of the current MV and the current error, etc., and the historical knowledge is the value of the MV at the historical moment and the current error, etc.

[0148] Furthermore,

[0149] where the elements of the covariance matrix are the kernel functions between the k i and k j sample points. The mean function often takes a constant value, i.e., μ0 = [0,…,0], and the calculation formula of the kernel function is as follows:

[0150]

[0151] where σ f is the kernel amplitude of the kernel function, and l f is the length ratio of the samples.

[0152] For a new sample point u + in the sample space, the posterior probability distribution of this sample point can be calculated through the prior probability distribution. According to the definition of GPR, the joint Gaussian distribution J SSDB of the known data and the predicted value of GPR also follow a Gaussian distribution and can be expressed as:

[0153]

[0154] where is the covariance of the known samples in the SSDB, is the covariance of the new sample.

[0155] Since the training set is known, calculate SSDB for the given J Conditional distribution is as follows:

[0156]

[0157] wherein, μ is the posterior mean, that is, the predicted value of the KDD model for the new sample u+ is the posterior variance.

[0158] In the subsequent stage, to reduce the performance degradation caused by the mismatch of the KDD model, after updating the SSDB in each control stage, the KDD model will be updated synchronously.

[0159] Remark2: For the MPC rolling optimization problem of FT, the computational cost of J(t) is relatively high. By repeatedly iteratively solving and calculating the objective function multiple times, it will lead to a large amount of computational time required for solving the optimal control law, which is a challenge for the MPC process that requires real-time performance. By using the KDD model as a surrogate model and assisting the PSO algorithm to replace the solution of the actual objective function, the repeated prediction of the IT2FBLS prediction model in the original MPC can be achieved through calculation. When the prediction horizon is H p , the original MPC needs to repeatedly calculate H p times of equations (4)-(9) to achieve the calculation of the objective function in equation (2). Therefore, the introduction of KDD significantly reduces the computational consumption of GPSO.

[0160] Furthermore, minimizing the output value of the KDD model by using the PSO algorithm according to the initial values of the PSO particles includes:

[0161] Determine the velocity and position of the current particle;

[0162] Determine the output value of the KDD model according to the velocity and position of the current particle;

[0163] where the time of this stage is t∈[t n ,t f , and the PSO algorithm in the GPSO sub-module is used for rolling optimization, and the initial particle value is u(t n ). Use PSO to minimize the output value of the KDD model Assume that the number of particles in the population is I, and the dimension of each particle is O (O = H u ); taking the o-th dimension of the i-th particle as an example, the calculation formulas for the velocity and position of the current particle are:

[0164]

[0165] where v i,o ​(t + 1) is the velocity of the $i$-th particle in the $o$-th dimension, $a$ i,o (t + 1) is the position of the $i$-th particle in the $o$-th dimension, $\omega(t)$, $c_1$, and $c_2$ are the first weight parameter, the second weight parameter, and the third weight parameter respectively, and $r_1$ and $r_2$ are random numbers with values in the range $[0, 1]$. The output result of the rolling optimization is determined by the position of the particle. Define $p$ i (t) and $g(t)$ as the positions of the single best particle and the global best particle at time $t$, respectively, and their relationship with is as follows:

[0166]

[0167] Note that due to the influence of the random factors $r_1$ and $r_2$ on the movement of the particle, the position of the particle is uncertain; at the same time, since the KDD model is introduced as a surrogate model, the reliability of the PSO solution depends on the accuracy of the KDD model. To avoid system oscillations or instability caused by model mismatch and modeling errors, here $p$ obtained by PSO i (t) and $g(t)$ are not directly used as the solution of the MV at the next moment, but $p$ i (t) and $g(t)$ are used as excellent solutions found during the operation of PSO, stored in the PADB as the selection basis for solving the optimal control law, and guide the search of subsequent particles. The construction of the PADB is as follows:

[0168]

[0169] Among them, $p$ i (t), $p$ i (t + 1), …, $g$ will be used as possible MV candidates.

[0170] Through reasonable update and maintenance strategies, the archive can maintain the diversity of solutions and avoid the over - concentration of solutions in a certain part of the search space. The archive provides global information for the flight direction of the particles, guiding the particles to search in a better region.

[0171] After each iteration of the control process ends, the new excellent solutions $\{p$ + , $J(p$ + )$\} generated by PSO will be used to update the PADB, and the update rule is as follows:

[0172] If $\{p$ + , $J(p$ + )$\} is dominated by the solutions in the PADB, then $\{p$ + , $J(p$ + )$\} is discarded;

[0173] If $\{p$ + , $J(p$ +)} dominates some solutions in PADB, then remove the dominated solutions from the archive, and add {p + , J(p + )} to the archive.

[0174] If {p + , J(p + )} and the solutions in PADB do not dominate each other, then directly add {p + , J(p + )} to PADB.

[0175] In fact, SSDB comes from the random sampling of the system near MV, while PADB comes from the exploration of PSO in space. They respectively reflect two types of states in MV solution: stable but conservative and potentially high performance. To improve the performance of the control system as much as possible without sacrificing safety, the proposed MV baseline solution sub-module is used to safely and effectively solve the control law, which is specifically described as follows.

[0176] First, denote the minimum value of the objective function in SSDB as and take the corresponding MV as the "baseline", as follows:

[0177]

[0178] where u baseline is the value baseline of MV at the current moment.

[0179] Next, screen the potentially high-performance solutions from PADB, and verify the safety of each of them to ensure that it meets the system's constraint conditions and safety requirements. The safety constraints of the system are shown in (2), and for the convenience of subsequent description, denote it as

[0180] For the solutions that meet the safety constraint , compare their objective function values with the baseline solution, and form a candidate solution set with all the solutions that meet the above conditions:

[0181]

[0182] where u PADB =[u PADB (t|t),…,u PADB (t + H u - 1|t)] (28)

[0183] Finally, if Ξ candidate is a non-empty set, then select the first element of the solution with the optimal performance from the candidate solution set as the MV for the next iteration; if Ξ candidateis an empty set. To ensure security, a conservative baseline solution is adopted as the MV for the next iteration, as follows:

[0184]

[0185] After each control iteration is completed, the SSDB will obtain new samples {u + , J +}, which are used to update the SSDB, i.e., Ξ SSDB . As can be seen from the above, in the PSO control stage, the performance of the MPC rolling optimization depends on the reliability of the KDD model in the knowledge data-driven submodule. To reduce the impact of model mismatch and prediction error on the MV solution, after each control iteration process is completed and Ξ SSDB is updated, the parameters of the KDD model will be updated to improve the model prediction performance. The KDD model parameters involved include the parameters θ = [θ1, θ2] in the mean function and the covariance matrix, and the maximum likelihood estimation (MLE) is used to θ estimate them. First, since each sample in the SSDB follows a multivariate normal distribution, the likelihood function is defined as follows:

[0186]

[0187] where μ0 is the mean function, which contains the hyperparameter θ1; ∑0 is the covariance function, which contains the hyperparameter θ2.

[0188] Next, using MLE, the log marginal likelihood of the KDD model is obtained:

[0189]

[0190] where the first term is a complexity penalty term, which is used to measure and penalize the complexity of the model; the second term is a negative quadratic term, whose value depends on the SSDB and serves as a data fitting measure; the third term is a constant term and is independent of the data.

[0191] Then, by calculating the partial derivatives, the marginal likelihood is maximized as follows:

[0192]

[0193] where ∑0 is the covariance matrix. Since the mean function is a constant, the parameters to be estimated only include the parameters θ2 = [l f , σ f in ∑0.

[0194] Finally, after the SSDB is updated, through the above calculation process, the parameter update of the KDD model can be realized to improve the prediction performance of the KDD model for MPC and reduce the influence of model mismatch and prediction error on the control system.

[0195] In the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference may be made to each other.

[0196] In this article, specific examples are used to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. At the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A fuzzy-width furnace temperature model predictive control method, characterized in that, Including: Construct a furnace temperature prediction model, where the furnace temperature prediction model is an IT2FBLS prediction model, and the IT2FBLS prediction model includes: an input layer, an IT2FNN layer, an enhancement layer, and an output layer; Obtain a corrected output variable according to the furnace temperature prediction model; Solve the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable to determine the optimal set of manipulated variables; Determine the optimal control law of the MPC according to the optimal set of manipulated variables; According to the optimal control law, input the control variable to be input into the furnace temperature prediction model to obtain an initial controlled variable, where the control variable is the secondary air volume and the controlled variable is the furnace temperature; Correct and compensate the initial controlled variable according to the prediction error at the current moment to obtain the final controlled variable.

2. The predictive control method for the furnace temperature model with fuzzy width according to claim 1, wherein, The calculation expression of the corrected output variable is: υ(t) is the solution error vector for the corrected output variable, is the initial controlled variable, y(t) is the actual output value, is the predicted value of the prediction model for the future i p -th moment, H p is the prediction horizon of MPC, that is, the maximum value of i p , y p (t + i p ) is the corrected output value of the prediction model for the future i p -th moment.

3. A fuzzy-width furnace temperature model predictive control method according to claim 1, characterized in that The calculation expression of the initial controlled variable is: Among them, h(t) is the output vector of the enhanced layer of the furnace temperature prediction model, G is the number of nodes in the fuzzy mapping layer of the prediction model, g = 1, …, G represents the g-th node, L is the number of nodes in the enhanced layer, l = 1, …, L represents the l-th enhanced node, z g (t) and h l (t) are the output values of the g-th node in the fuzzy mapping layer and the l-th enhanced node in the enhanced layer respectively, is the initial controlled variable, w f (t) = [w f1 (t), …, w fG (t)] T is the weight vector between the output of the IT2FNN layer and the output layer, where w fG (t) is the G-th weight scalar in this weight vector; w e (t) = [w e1 (t), …, w eL (t)] T is the weight vector between the output of the enhanced layer and the output layer, where w eL (t) is the L-th weight scalar in this weight vector.

4. The fuzzy width furnace temperature model predictive control method according to claim 1, characterized in that: The solution of the objective function of the MPC corresponding to the furnace temperature prediction model according to the gradient particle swarm optimization algorithm and the corrected output variable to determine the optimal set of manipulated variables: Solve the error vector υ(t) according to the corrected output variable; Based on GD, calculate the current optimal control sequence according to the error vector; Update the manipulated variable according to the optimal control sequence to obtain an updated manipulated variable; Judge whether the current moment reaches the threshold. If it reaches, construct an SSDB with the updated manipulated variable set corresponding to the current moment, initialize the KDD model, and determine the initial value of the PSO particle with the updated manipulated variable set corresponding to the current moment; According to the initial value of the PSO particle, use the PSO algorithm to calculate the output value that minimizes the KDD model; Determine the excellent solution of the PSO process according to the output value that minimizes the KDD model, construct a PADB, and continuously update the PADB; Determine a candidate solution set according to the PADB and the SSDB; Determine the optimal set of manipulated variables according to the candidate solution set.

5. The fuzzy width furnace temperature model predictive control method according to claim 4, characterized in that: The formula of SSDB is:

6. A fuzzy-width furnace temperature model predictive control method according to claim 4, characterized in that The KDD model is constructed based on the system state information and historical knowledge in the SSDB using a Gaussian process regression model, as follows: J SSDB ~N(μ0,Σ0) Among them, μ0 = [μ0(u1), …, μ0(u K )] is the mean function, K is the number of samples in SSDB, and Σ0 is the covariance matrix.

7. The fuzzy width furnace temperature model predictive control method according to claim 4, characterized in that: The use of the PSO algorithm to minimize the output value of the KDD model according to the initial value of the PSO particle includes: Determine the velocity and position of the current particle; Determine the output value of the KDD model according to the velocity and position of the current particle; Among them, the calculation formulas for the velocity and position of the current particle are: where, v i,o (t + 1) is the o-th dimensional velocity of the i-th particle, a i,o (t + 1) is the o-th dimensional position of the i-th particle, ω(t), c1, and c2 are the first weight parameter, the second weight parameter, and the third weight parameter respectively, and r1 and r2 are random numbers with values in the range [0, 1].

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