Furnace temperature control method based on improved interval type-2 fuzzy width neural network

Abstract

The application provides a furnace temperature control method based on an improved interval two fuzzy width neural network, comprising the following steps: constructing an FT controller module based on the IT2FBNN, designing an incremental learning strategy and a structure simplification strategy, constructing an incremental learning module and a structure simplification module based on the incremental learning strategy and the structure simplification strategy respectively, adjusting the structure of the FT controller module based on the incremental learning module and the structure simplification module, designing a selective parameter updating strategy based on the gradient descent method, constructing a selective parameter updating module, and adjusting the parameters of the FT controller module based on the selective parameter updating module. The furnace temperature control method based on the improved interval two fuzzy width neural network can realize furnace temperature control and is convenient to use.

Description

Technical Field

[0001] This invention relates to the field of urban solid waste treatment technology, and in particular to a furnace temperature control method based on an improved interval type II fuzzy width neural network. Background Technology

[0002] The existing MSWI plant mainly adopts the "3T+E" principle, of which 1T is to keep the furnace temperature (FT) stable above 850℃. However, the fluctuation of feed composition, uncertainty of feed amount and unknown equipment loss in the MSWI process bring uncertainty interference to the stable control of FT. Therefore, it is necessary to study the control problem of FT in the MSWI process. Considering the time-varying characteristics of the MSWI process and the structural complexity of the Interval Type II Fuzzy Width Neural Network (IT2FBNN), the design of the IT2FBNN controller also needs to consider the following difficulties: (1) The number of controller parameters is large, and updating all of them will lead to high complexity in the parameter learning process, making it difficult to achieve fast tracking response, and the updating of irrelevant parameters may even lead to a decrease in the performance of the controller; (2) There are many types of IT2FBNN parameters, and the gradient descent update algorithm of parameters within and between layers is not clear; (3) The incremental learning (IL) mechanism of the enhanced node is an effective means to improve the adaptive ability of FBNN and alleviate the rule explosion problem, but IL has not been reported in the research on IT2FBNN controller. In addition, the high structural complexity of the controller also leads to the phenomenon of structural redundancy. Therefore, it is essential to design a furnace temperature control method based on an improved interval type-II fuzzy width neural network. Summary of the Invention

[0003] The purpose of this invention is to provide a furnace temperature control method based on an improved interval type II fuzzy width neural network, which can achieve furnace temperature control and is easy to use.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A furnace temperature control method based on an improved interval type-II fuzzy width neural network includes the following steps:

[0006] Step 1: Construct an FT controller module based on IT2FBNN;

[0007] Step 2: Design incremental learning strategy and structural simplification strategy, and build incremental learning module and structural simplification module based on incremental learning strategy and structural simplification strategy respectively, and adjust the structure of FT controller module based on incremental learning module and structural simplification module;

[0008] Step 3: Design a selective parameter update strategy based on gradient descent, construct a selective parameter update module, and adjust the parameters of the FT controller module based on the selective parameter update module.

[0009] Optionally, in step 2, an incremental learning strategy is designed, and an incremental learning module is constructed based on the incremental learning strategy, specifically as follows:

[0010] The augmentation nodes of the FT controller module are incrementally learned based on a dynamic incremental learning algorithm. The squared system error is used as the evaluation index for whether to add additional augmentation nodes. The rule for incrementing nodes at the current time is defined as follows:

[0011]

[0012] In the formula, ε1 is the threshold for determining whether to perform an increment, and h| J+1 (t) and w e | J+1 (t) represents the output and connection weights of the augmented node after the increment, respectively:

[0013] h| J+1 (t)=[h1(t),L,h J (t),h J+1 (t)] (11)

[0014] w e | J+1 (t)=[w e1 (t),L,w eJ (t),w eJ+1 (t)] T (12)

[0015] In the formula, h J+1 (t)=tanh(z(t)w J+1 (t)+β J+1 (t)); w J+1 (t), β J+1 (t) and w eJ+1 The parameters for adding enhanced nodes have the following values:

[0016] w J+1 (t)=rand(0,1),β J+1 (t)=rand(0,1),w eJ+1 =0 (13)

[0017] In the formula, rand(0,1) represents a random number whose value is uniformly distributed within the interval [0,1].

[0018] Optionally, in step 3, a structural simplification strategy is designed, and a structural simplification module is constructed based on the structural simplification strategy, specifically as follows:

[0019] Using the utilization rate as an evaluation metric, a simplified strategy for enhancing nodes is designed, and the utilization rate of enhancing nodes within one period is calculated. for:

[0020]

[0021] In the formula, T del The set period for deletion judgment, The number of times the activation strength of the j-th enhancement node is judged as weak within this period is calculated as follows:

[0022]

[0023] In the formula,

[0024]

[0025] In the formula, h j (t del ) is the t-th del The output value of the j-th augmentation node at time j is the activation strength of the augmentation node, and ε2 is the threshold for judging the strength of the activation of the augmentation node.

[0026] The rule for removing augmented nodes at the current moment is defined as follows:

[0027]

[0028] In the formula, h| J-1 (t)=tanh(z(t)w J-1 (t)+β J-1 (t)); w J-1 (t), β J-1 (t) and w eJ-1 To enhance the parameter vector after node deletion, ε3 is the threshold for judging the uselessness of deletion;

[0029] Perform parameter compensation on the node with the closest Euclidean distance to the node to be enhanced but removed. Let the index of the node to be removed be d, and the index of the node to be compensated be d. The compensation process is as follows:

[0030]

[0031] In the formula, h d (t) represents the output value of the removed enhancement node, h d (t) represents the output value of the node being compensated before compensation. and These are the corresponding parameter values ​​of the nodes after compensation.

[0032] Optionally, in step 4, a selective parameter update strategy based on gradient descent is designed, a selective parameter update module is constructed, and the parameters of the FT controller module are adjusted based on the selective parameter update module, specifically as follows:

[0033] The gradient descent method is used to update the parameters of the FT controller module, and the loss function is defined as follows:

[0034]

[0035] In the formula, y * (t) represents the current furnace temperature setpoint. This represents the actual furnace temperature at the current moment.

[0036] The parameters to be updated in the FT controller module include inter-layer parameters and intra-layer parameters. Among them, the inter-layer parameters include the connection weight matrix W(t) = [w1(t),L,w] between the IT2FNN layer and the enhancement layer. J [(t)] and bias term vector β(t) = [β1(t),L,β J (t)] T The connection weight vector w between the IT2FNN layer and the output layer f (t) and the connection weight vector w between the enhancement layer and the output layer e (t), where the in-layer parameter is the lower bound vector of the uncertainty center in the IT2FNN layer. c (t) and upper bound vector The width vector σ(t) and the consequent connection weight vector δ(t) are replaced by the parameter W;

[0037] The gradient of the loss function with respect to each parameter is calculated as follows:

[0038] The calculation process for interlayer parameters is as follows:

[0039]

[0040]

[0041]

[0042]

[0043] in,

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050] In the formula, Jacobian information for the controlled object;

[0051] The Fourier Transform (FT) model is constructed using a linear regression decision tree algorithm, and its Jacobian information is as follows:

[0052]

[0053] The gradient formula for the interlayer parameters is calculated as follows:

[0054]

[0055]

[0056]

[0057]

[0058] For the intra-layer parameters, the gradient calculation process is as follows:

[0059]

[0060]

[0061]

[0062]

[0063] in,

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072]

[0073] The gradient formula for the intralayer parameters is calculated as follows:

[0074]

[0075]

[0076]

[0077]

[0078] Design an adaptive selective parameter update strategy based on weights and rule activation strength, and calculate the upper and lower bound activation strength thresholds of the rules respectively. and f th (t) and the consequent connection weight threshold of each subsystem in the IT2FNN layer. for:

[0079]

[0080]

[0081] In the formula, I is the number of subsystems in the IT2FNN layer, M is the number of fuzzy rules in each subsystem, s is the number of input features of IT2FBNN, and α1, α2 and α3 are the parameter selection ratios of the corresponding parameters.

[0082] Threshold parameters f th (t) and With parameter vector c (t), Compare each parameter in δ(t) individually, and select the parameters in the parameter vector that are greater than the corresponding mean as the updatable parameters, as follows:

[0083]

[0084] In the formula, When the value is 1, the corresponding parameter is an updatable parameter;

[0085] Let the vector of updatable parameters between layers be denoted as c ′(t), And δ′(t), choose parameters c ′(t) and The width corresponding to the membership function that is updated together is taken as the updatable width, denoted as σ′(t);

[0086] Update the updatable parameters in both inter-layer and intra-layer parameters as follows:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] In the formula, η1 is the learning rate of the inter-layer parameters and η2 is the learning rate of the intra-layer parameters.

[0096] According to specific embodiments provided by the present invention, the following technical effects are disclosed: The furnace temperature control method based on an improved interval type-two fuzzy width neural network provided by the present invention includes constructing an FT controller module based on IT2FBNN, designing an incremental learning strategy and a structural simplification strategy, constructing an incremental learning module and a structural simplification module based on the incremental learning strategy and the structural simplification strategy respectively, adjusting the structure of the FT controller module based on the incremental learning module and the structural simplification module, designing a selective parameter update strategy based on gradient descent, constructing a selective parameter update module, and adjusting the parameters of the FT controller module based on the selective parameter update module. This method can effectively reduce the amount of computation and reduce the negative effects caused by irrelevant parameter updates by screening the updated parameters, enabling the controller to self-organize and determine a suitable compact controller structure. Stability analysis has also been performed. This method can achieve furnace temperature control and is easy to use. Attached Figure Description

[0097] Figure 1 This is a schematic diagram of the modeling strategy for the furnace temperature control method based on an improved interval type II fuzzy width neural network in an embodiment of the present invention;

[0098] Figure 2a A constant furnace temperature tracking curve;

[0099] Figure 2b Error curve for constant furnace temperature tracking;

[0100] Figure 2c A graph showing the change in a constant value control quantity;

[0101] Figure 2d A comparison graph of constant value tracking methods;

[0102] Figure 3 The graph shows the change in the number of enhancement nodes in the constant value experiment;

[0103] Figure 4a Update the ratio curve for the lower bound of the uncertainty center;

[0104] Figure 4b Update the ratio curve for the upper bound of the uncertainty center;

[0105] Figure 4c A graph showing the update ratio of the subsequent connection weights. Detailed Implementation

[0106] The purpose of this invention is to provide a furnace temperature control method based on an improved interval type II fuzzy width neural network, which can achieve furnace temperature control and is easy to use.

[0107] The control strategy diagram of this application is as follows: Figure 1 As shown;

[0108] Figure 1 middle, y represents the furnace temperature at time t; * (t) represents the furnace temperature setpoint at time t; e(t) represents the system error value at the current time; e1 and e2 are controller inputs, where e1 = e(t) is the system error at time t, and e2 = Ve(t) is the change in system error at time t; Vu(t) is the increase in secondary air volume of the system at time t, i.e., the controller output; Z -1 This represents a one-step delay, and its operational relation satisfies Z. -1 u(t) = u(t-1); u(t) is the control variable of the system at time t, i.e., the secondary air volume value at the current time; W(t) and β(t) are the connection weight matrix and bias term vector between the IT2FNN layer and the enhancement layer, respectively; wf(t) is the connection weight vector between the IT2FNN layer and the output layer; w e (t) represents the connection weight vector between the enhancement layer and the output layer; the above W(t), β(t), w f (t) and w e (t) is defined as the interlayer parameter in this paper; c(t), σ(t) and δ(t) are the lower bound vector, upper bound vector, width vector, and consequent connection weight vector of the uncertainty center in the IT2FNN layer, respectively, and are defined as in-layer parameters in this paper. f th (t) and They are parameter vectors c (t), The updatable parameter of δ(t) is used to determine the threshold. c ′(t), σ′(t) and δ′(t) are vectors of updatable parameters selected by the SPU strategy; η1 is the learning rate of inter-layer parameters; η2 is the learning rate of intra-layer parameters; z(t) is the output of the IT2FNN layer; h(t) is the output of the enhancement layer; Φ1(t) and Φ2(t) are parameter vectors composed of all inter-layer parameters and intra-layer updatable parameters, respectively; ε1 and ε3 are the thresholds for incremental learning and useless rate. r represents the useless rate of the j-th augmentation node. unuse This is the useless rate vector for all augmented nodes.

[0109] The method includes the following steps:

[0110] In step 1, the FT controller module is constructed based on IT2FBNN, specifically as follows:

[0111] A Fourier Transform (FT) controller module is constructed based on IT2FBNN, which includes an input layer, an IT2FNN layer, an enhancement layer, and an output layer.

[0112] Taking time t as an example, the process of the controller calculating the control quantity at this iteration time is described according to the forward calculation order: First, based on the system error e(t) and the system error increment Ve(t), the output of each layer of IT2FBNN is calculated; then, it is determined whether the conditions of controller IL and SS are met, and the structure of the controller is optimized; then, the inter-layer parameter gradient is calculated, and the updatable parameters within the layer are filtered by the intra-layer parameter threshold, and updated for them and the inter-layer parameters; finally, the control quantity is output to the MSWI process to obtain the actual FT value and e(t) and Ve(t) at time t+1, and the above process is repeated to achieve stable tracking of the FT setpoint;

[0113] The input layer maps data to the IT2FNN layer, with inputs being e(t) and Ve(t), denoted as:

[0114]

[0115] In the formula, e(t-1) represents the value of the system error at the previous time step;

[0116] The IT2FNN layer sends its output to the enhancement layer, which includes I groups of IT2FNN subsystems. Taking the i-th subsystem as an example, the calculation process is as follows:

[0117] The input is fuzzified using an interval type II membership function with an uncertain center, as follows:

[0118]

[0119] In the formula, and Let be the lower and upper bounds of the membership value of the m-th rule corresponding to the s-th input in the i-th subsystem, where s = 1, 2; m = 1, ..., M, and M is the number of fuzzy rules in the IT2FNN subsystem. and These are the lower bound, upper bound, and width of the uncertainty center for the m-th membership function corresponding to the s-th input, respectively.

[0120] The t-norm product operator is used to perform fuzzy calculations on the upper and lower bounds of the membership values ​​to obtain the activation strength of each rule. Then, the BMM algorithm is used to reduce the bounds to obtain the upper and lower bounds of the output values, which are:

[0121]

[0122] In the formula, z i (t) and These are the lower and upper bounds of the output of the i-th subsystem, respectively. and Let be the upper and lower bounds of the activation intensity of the m-th fuzzy rule, respectively. Output weights for the consequent of the m-th rule. The consequent connection weight for the m-th rule corresponding to the s-th input;

[0123] The output of the i-th subsystem is:

[0124]

[0125] The output of the IT2FNN layer, composed of the I group of subsystems, is:

[0126] z(t)=[z 1 (t),L,z I (t)] (5)

[0127] The enhancement layer receives the output of the IT2FNN layer as its input and performs a nonlinear transformation. It consists of J groups of enhancement nodes. Taking the j-th enhancement node as an example (j = 1, ..., J), the output is:

[0128] h j (t)=tanh(z(t)w j (t)+β j (t)) (6)

[0129] In the formula, and β j (t) represents the connection weights and bias terms, respectively;

[0130] The output of the enhancement layer, consisting of J groups of enhancement nodes, is:

[0131] h(t) = [h1(t),L,h J (t)] (7)

[0132] The output layer linearly combines the outputs of the IT2FNN layer and the enhancement layer to obtain the final output of the controller, which is the secondary wind increment, as follows:

[0133]

[0134] In the formula, w f (t)=[w f1 (t),L,w fI (t)] T and w e (t)=[w e1 (t),L,w eJ (t)] T Let A(t) be the weight vector between the output of the IT2FNN layer, the output of the enhancement layer, and the output layer, respectively; and let W be the output value vector between the IT2FNN layer and the enhancement layer. f,e (t) is the parameter w f (t) and w e A vector consisting of all elements of (t);

[0135] The secondary air volume at the current moment is obtained by adding the secondary air volume from the previous moment to the secondary air volume at the current moment. This secondary air volume is constrained by an empirically set fluctuation range, which is as follows:

[0136]

[0137] In the formula, u max and u min These are the maximum and minimum values ​​of the secondary air volume, set based on experience, as shown in Table 1.

[0138] In addition, regarding w f (t) and w e To solve for (t), this invention provides a one-time algorithm based on pseudo-inverse ridge regression for approximate solving of intra-layer parameters for regression or classification tasks, as follows:

[0139]

[0140] In the formula, This is a matrix consisting of the output values ​​of the IT2FNN layer and the enhancement layer for all samples. Let I be the identity matrix, J be the number of IT2FNN layer subsystems, λ be the number of enhancement layer nodes, and λ be the regularization coefficient. S is a matrix consisting of the actual output values ​​of all samples, where S is the total number of samples and K is the number of output features.

[0141] In the iterative control process of this paper, the successive acquisition of samples makes it impossible to solve the inter-layer parameters using formula (10). In addition, for the randomly given initial parameters of the controller, it is necessary to update the updatable parameters within the layer to obtain optimized control performance. The ridge regression algorithm based on pseudo-inverse is obviously not suitable for solving the intra-layer parameters. This invention uses an iterative optimization method to update the inter-layer and intra-layer parameters.

[0142] In step 2, an incremental learning strategy is designed, and an incremental learning module is constructed based on the incremental learning strategy, specifically as follows:

[0143] The time-varying nonlinear characteristics of the MSWI process require the controller to have the ability to adapt to dynamic changes.

[0144] The augmentation nodes of the FT controller module are incrementally learned based on a dynamic incremental learning algorithm. The squared system error is used as the evaluation index for whether to add additional augmentation nodes. The rule for incrementing nodes at the current time is defined as follows:

[0145]

[0146] In the formula, ε1 is the threshold for determining whether to perform an increment, and h| J+1 (t) and w e | J+1 (t) represents the output and connection weights of the augmented node after the increment, respectively:

[0147] h| J+1 (t)=[h1(t),L,h J (t),h J+1 (t)] (12)

[0148] w e | J+1 (t)=[w e1 (t),L,w eJ (t),w eJ+1 (t)] T (13)

[0149] In the formula, h J+1 (t)=tanh(z(t)w J+1 (t)+β J+1 (t)); w J+1 (t), β J+1 (t) and w eJ+1 The parameters for adding enhanced nodes have the following values:

[0150] w J+1 (t)=rand(0,1),β J+1 (t)=rand(0,1),w eJ+1=0 (14)

[0151] In the formula, rand(0,1) represents a random number whose value is uniformly distributed within the interval [0,1].

[0152] In step 3, a structural simplification strategy is designed, and a structural simplification module is constructed based on the structural simplification strategy, specifically as follows:

[0153] The monotonic increment of boost nodes will inevitably increase network redundancy and reduce controller interpretability. A boost node simplification strategy is designed using the utilization rate as an evaluation metric, removing redundant nodes to obtain a compact network structure. The utilization rate of boost nodes within one cycle is then calculated. for:

[0154]

[0155] In the formula, T del The set period for deletion judgment, The number of times the activation strength of the j-th enhancement node is judged as weak within this period is calculated as follows:

[0156]

[0157] In the formula,

[0158]

[0159] In the formula, h j (t del ) is the t-th del The output value of the j-th augmentation node at time j is the activation strength of the augmentation node, and ε2 is the threshold for judging the strength of the activation of the augmentation node.

[0160] Taking the j-th augmenting node as an example, the rule for removing augmenting nodes at the current time is defined as follows:

[0161]

[0162] In the formula, h| J-1 (t)=tanh(z(t)w J-1 (t)+β J-1 (t)); w J-1 (t), β J-1 (t) and w eJ-1 To enhance the parameter vector after node deletion, ε3 is the threshold for judging the uselessness of deletion;

[0163] To ensure the stability of the simplified IT2FBNN, parameter compensation is performed on the node with the closest Euclidean distance to the deleted and enhanced nodes. Let the index of the deleted node be d, and the index of the compensated node be d. The compensation process is as follows:

[0164]

[0165] In the formula, h d (t) represents the output value of the node whose enhancement was removed. The output value of the node to be compensated and enhanced before compensation. and These are the corresponding parameter values ​​of the nodes after compensation;

[0166] The addition or removal of enhancement nodes can affect the dimensionality of inter-layer parameters, and reasonable parameter value compensation is required to minimize the impact of this process on the stability of the control system.

[0167] In step 4, a selective parameter update strategy based on gradient descent is designed, a selective parameter update module is constructed, and the parameters of the FT controller module are adjusted based on the selective parameter update module, specifically as follows:

[0168] The gradient descent method is used to update the parameters of the FT controller module, and the loss function is defined as follows:

[0169]

[0170] In the formula, y * (t) represents the current furnace temperature setpoint. This represents the actual furnace temperature at the current moment.

[0171] The parameters to be updated in the FT controller module include inter-layer parameters and intra-layer parameters. Among them, the inter-layer parameters include the connection weight matrix W(t) = [w1(t),L,w] between the IT2FNN layer and the enhancement layer. J [(t)] and bias term vector β(t) = [β1(t),L,β J (t)] T The connection weight vector w between the IT2FNN layer and the output layer f (t) and the connection weight vector w between the enhancement layer and the output layer e (t), where the in-layer parameter is the lower bound vector of the uncertainty center in the IT2FNN layer. c (t) and upper bound vector The width vector σ(t) and the consequent connection weight vector δ(t) are replaced by the parameter W;

[0172] The gradient of the loss function with respect to each parameter is calculated as follows:

[0173] The calculation process for interlayer parameters is as follows:

[0174]

[0175]

[0176]

[0177]

[0178] in,

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] In the formula, Jacobian information for the controlled object;

[0186] The Fourier Transform (FT) model is constructed using a linear regression decision tree algorithm, and its Jacobian information is as follows:

[0187]

[0188] The gradient formula for the interlayer parameters is calculated as follows:

[0189]

[0190]

[0191]

[0192]

[0193] For the intra-layer parameters, the gradient calculation process is as follows:

[0194]

[0195]

[0196]

[0197]

[0198] in,

[0199]

[0200]

[0201]

[0202]

[0203]

[0204]

[0205]

[0206]

[0207]

[0208]

[0209] The gradient formula for the intralayer parameters is calculated as follows:

[0210]

[0211]

[0212]

[0213]

[0214] As shown above, the IT2FBNN controller has numerous parameters. Tuning all parameters would increase computational complexity and cost, which is detrimental to controller stability. Considering that samples are acquired one by one during the iterative control process, parameter selection and update methods based on sensitivity or contribution are difficult to apply. Therefore, an adaptive selective parameter update strategy based on weights and rule activation strength is designed, calculating the upper and lower bound activation strength thresholds of the rules respectively. and f th (t) and the consequent connection weight threshold of each subsystem in the IT2FNN layer. for:

[0215]

[0216]

[0217] In the formula, I is the number of subsystems in the IT2FNN layer, M is the number of fuzzy rules in each subsystem, s is the number of input features of IT2FBNN, and α1, α2 and α3 are the parameter selection ratios of the corresponding parameters.

[0218] Threshold parameters f th (t) and With parameter vector c (t), Compare each parameter in δ(t) individually, and select the parameters in the parameter vector that are greater than the corresponding mean as the updatable parameters, as follows:

[0219]

[0220] In the formula, When the value is 1, the corresponding parameter is an updatable parameter;

[0221] Let the vector of updatable parameters between layers be denoted as c ′(t), And δ′(t), choose parameters c ′(t) and The width corresponding to the membership function that is updated together is taken as the updatable width, denoted as σ′(t);

[0222] Update the updatable parameters in both inter-layer and intra-layer parameters as follows:

[0223]

[0224]

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231] In the formula, η1 is the learning rate of the inter-layer parameters, and η2 is the learning rate of the intra-layer parameters;

[0232] This method employs a gradient descent-based SPU strategy, which not only updates inter-layer parameters but also selectively updates intra-layer parameters, thereby improving control performance.

[0233] Assume the number of parameters of the i-th IT2FNN subsystem is N. i The forward propagation time complexity of the IT2FBNN controller is O(n log n). forward When the controller uses the PFT policy to update, the time complexity of its backpropagation update parameters is O(n). When the controller uses the SPU strategy, the time complexity of its backpropagation parameter update is O(n). Where 0 ≤ ρ1, ρ2, ρ3 ≤ 1. Clearly, Compared to the PFT strategy, the method used in this paper avoids the risk of irrelevant parameter updates and reduces unnecessary computational costs.

[0234] This invention provides an embodiment with a practical MSWI process experiment to verify the effectiveness of the proposed IT2FBNN;

[0235] The experiment uses the integral of squared error (ISE), the integral of absolute error (IAE), and the maximum deviation from setpoint (Devmax) as control performance indicators to quantitatively evaluate the system's transient response, stability, and anti-interference capability.

[0236] In the formula, t0 and t f Let t be the initial time and number of iterations for the controller iteration, and e(t) be the system error at time t.

[0237] The parameters were set as follows: An FT model based on a linear regression decision tree algorithm was constructed as the controlled object. Tracking control experiments were conducted with a constant setpoint (930℃, 1000 iterations) and a variable setpoint (925℃~935℃, 3000 iterations, setpoints at the 1000th and 2000th iterations). Comparative experiments were performed using a self-organizing TS-FNN (SOTS-FNN) controller, an IT2FNN controller, and a self-organizing IT2FNN (SO-IT2FNN) controller. The parameter settings for the IL-SPU-IT2FBNN controller and other controllers are shown in Table 1.

[0238] Table 1 Hyperparameter settings for the IL-SPU-IT2FBNN controller and comparison controller

[0239]

[0240] The experimental results are as follows: The tracking, error, and control variable changes of IT2FBNN for the constant furnace temperature are shown in Figure 2 (a, b, c, d), and the curves comparing the tracking results are as follows. The curves showing the change in the number of enhanced nodes are as follows. Figure 3 As shown in the figure, the parameter selection update ratio diagram within the layer is shown in Figure 4 (a, b, c), and the control performance index comparison is shown in Table 2.

[0241] Table 5. Comparison of Experimental Control Performance of Constant Setpoint under Different Methods

[0242]

[0243]

[0244] As shown in Figures 2-4 and Table 2, the proposed IL-SPU-IT2FBNN controller can quickly approach the setpoint, exhibiting excellent control performance. Its control effect remains relatively stable throughout 1000 iterations without large-scale fluctuations. A magnified view in Figure 2 shows that the IL-SPU-IT2FBNN controller outperforms other controllers in tracking results, tracking error, and fluctuation amplitude. The variation curves of the enhancement nodes indicate that the structural simplification strategy takes effect after the control process stabilizes, allowing the controller to remove useless enhancement nodes while maintaining stability, resulting in a compact controller structure. The SPU strategy reduces the impact of random initial values ​​on the control process. Furthermore, updating only updatable parameters significantly reduces the update frequency of parameters within the layer. Performance comparisons show that, for constant value control experiments, the IT2FBNN type controller outperforms other types of controllers. Moreover, the control performance with the IL strategy is superior, with the IL-SPU-IT2FBNN controller exhibiting the best ISE and IAE compared to other controllers.

[0245] The abbreviations used in this application have the following meanings: FT - furnace temperature; MSW - municipal solid waste; MSWI - municipal solid waste incineration; IL - incremental learning; SS - structural simplification; SPU - adaptive selective parameter update; PFT - fully tuned parameter update; IT2FBNN - interval type II fuzzy width neural network; PID - proportional, integral, and derivative; RBF - radial basis function; FNN - fuzzy neural network; SOFNN - self-organizing fuzzy neural network; BLS - width learning system; FBNN - fuzzy width neural network; IT2FNN - interval type II fuzzy neural network; WWTP - wastewater treatment process; T2FBLS - type II fuzzy width learning system; PCC - Pearson correlation coefficient; SOIT2FNN - self-organizing interval type II fuzzy neural network.

[0246] The present invention provides a furnace temperature control method based on an improved interval type II fuzzy width neural network. This method can effectively reduce the amount of computation and reduce the negative effects caused by irrelevant parameter updates by filtering and updating parameters. It enables the controller to self-organize and determine a suitable compact controller structure. Stability analysis has also been performed. This method can achieve furnace temperature control and is easy to use.

Claims

1. A furnace temperature control method based on an improved interval type-II fuzzy width neural network, characterized in that, Includes the following steps: Step 1: Construct an FT controller module based on IT2FBNN; Step 2: Design incremental learning strategy and structural simplification strategy, and build incremental learning module and structural simplification module based on incremental learning strategy and structural simplification strategy respectively, and adjust the structure of FT controller module based on incremental learning module and structural simplification module; Step 3: Design a selective parameter update strategy based on gradient descent, construct a selective parameter update module, and adjust the parameters of the FT controller module based on the selective parameter update module; In step 2, an incremental learning strategy is designed, and an incremental learning module is constructed based on the incremental learning strategy, specifically as follows: The augmentation nodes of the FT controller module are incrementally learned based on a dynamic incremental learning algorithm. The squared system error is used as the evaluation index for whether to add additional augmentation nodes. The rule for incrementing nodes at the current time is defined as follows: In the formula, To determine the threshold for incremental adjustments, Vu(t) represents the system's secondary airflow increment at time t, i.e., the controller output; z(t) is the IT2FNN layer output; w f (t) represents the connection weight vector between the IT2FNN layer and the output layer; and The output and connection weights of the augmented node after the increment are as follows: In the formula, ; , and The parameters for adding enhanced nodes have the following values: In the formula, This indicates that the parameter value is a random number that follows a uniform distribution within the interval [0, 1]. In step 2, a structural simplification strategy is designed, and a structural simplification module is constructed based on the structural simplification strategy, specifically as follows: Using the utilization rate as an evaluation metric, a simplified strategy for enhancing nodes is designed, and the utilization rate of enhancing nodes within one period is calculated. , The unusability of the j-th augmentation node is: In the formula, The set period for deletion judgment, The number of times the activation strength of the j-th enhancement node is judged as weak within this period is calculated as follows: In the formula, In the formula, For the first The output value of the j-th booster node at time j is the activation strength of the booster node. A threshold for determining the strength of enhanced node activation; The rule for removing augmented nodes at the current moment is defined as follows: In the formula, ; , and To enhance the parameter vector after node removal, To determine the threshold for the rate of useless deletions; Perform parameter compensation on the node with the closest Euclidean distance to the deleted enhanced node. Let the index of the deleted node be... The index of the compensated node is The compensation process is as follows: In the formula, The output value of the deleted enhancement node, The output value of the node to be compensated and enhanced before compensation. , and These are the corresponding parameter values ​​of the nodes after compensation.

2. The furnace temperature control method based on an improved interval type-II fuzzy width neural network according to claim 1, characterized in that, In step 4, a selective parameter update strategy based on gradient descent is designed, a selective parameter update module is constructed, and the parameters of the FT controller module are adjusted based on the selective parameter update module, specifically as follows: The gradient descent method is used to update the parameters of the FT controller module, and the loss function is defined as follows: In the formula, This is the current furnace temperature setpoint. This represents the actual furnace temperature at the current moment. The parameters to be updated in the FT controller module include inter-layer parameters and intra-layer parameters. Among them, the inter-layer parameters include the connection weight matrix between the IT2FNN layer and the enhancement layer. and bias term vector The connection weight vector between the IT2FNN layer and the output layer The connection weight vector between the enhancement layer and the output layer The in-layer parameters are the lower bound vectors of the uncertainty center in the IT2FNN layer. and upper bound vector Width vector Connecting weight vectors to successors ; The gradient of the loss function with respect to each parameter is calculated as follows: The calculation process for interlayer parameters is as follows: in, In the formula, Jacobian information for the controlled object; The Fourier Transform (FT) model is constructed using a linear regression decision tree algorithm, and its Jacobian information is as follows: For the intra-layer parameters, the gradient calculation process is as follows: In the formula, and These are the lower and upper bounds of the output of the i-th subsystem, respectively. and Let be the upper and lower bounds of the activation intensity of the m-th fuzzy rule, respectively. The output weight for the m-th rule. The consequent connection weight for the m-th rule corresponding to the s-th input; and Let these be the lower and upper bounds of the membership degree value of the m-th rule corresponding to the s-th input in the i-th subsystem. , The number of fuzzy rules in the IT2FNN system. and These are the lower bound, upper bound, and width of the uncertainty center for the m-th membership function corresponding to the s-th input, respectively. Design an adaptive selective parameter update strategy based on weights and rule activation strength, and calculate the upper and lower bound activation strength thresholds of the rules respectively. and and the consequent connection weight threshold for each subsystem in the IT2FNN layer. ,for: In the formula, I represents the number of subsystems in the IT2FNN layer, and M represents the number of fuzzy rules in each subsystem. The number of input features for IT2FBNN , and These represent the parameter selection ratios for the corresponding parameters; Threshold parameters , and With parameter vector , and Each parameter in the vector is compared individually, and the parameters that are greater than their corresponding mean are selected as the updatable parameters, as follows: In the formula, When the value is 1, the corresponding parameter is an updatable parameter; Let the vector of updatable parameters between layers be denoted as , and Select parameters and The width corresponding to the membership functions that are updated together is taken as the updatable width, denoted as . ; Update the updatable parameters in both inter-layer and intra-layer parameters as follows: In the formula, The learning rate is the inter-layer parameter. The learning rate is the parameter within the layer.

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