Manifold regularization-fused physical information neural network NOx concentration prediction method

Abstract

The invention relates to the field of NOx prediction, in particular to a manifold regularization-fused physical information neural network NOx concentration prediction method. Comprising the following steps: S1, carrying out data acquisition on NOx concentration and related variables of a thermal power generating unit, and preprocessing and cleaning the NOx concentration and the related variables; s2, compressing the NOx concentration and related data collected in the step S1 from a high dimension to a low dimension for representation by using an encoder, constructing a graph Laplacian regular term, and calculating according to the graph Laplacian regular term to obtain a manifold regular term # imgabs0 #; s3, establishing a depth operator network model in the submerged space, taking the data represented in the low dimension in the S2 as branch network input, taking the time sequence as backbone network input, and taking NOx concentration as output; s4, analyzing a NOx generation mechanism of the thermal power generating unit, establishing a NOx concentration mechanism equation to restrain the depth operator network model, and constructing a physical information neural network and a total loss function; and S5, training the model formed in the steps S2-S4, and predicting the NOx concentration by using the trained model.

Description

Technical Field

[0001] The present invention relates to the field of NOx concentration prediction, and in particular to a physical information neural network NOx concentration prediction method integrating manifold regularization. Background Art

[0002] Under the background of "dual carbon", large-scale grid-connected power generation of new energy has impacted the power grid. Deep peak-shaving operation requires thermal power units to frequently adjust power generation to respond to changes in grid demand, resulting in frequent fluctuations in combustion conditions, which in turn significantly affects the generation of NOx and causes NOx emissions exceeding the standard.

[0003] In the prediction of NOx concentration in thermal power units, although deep learning models have been widely used due to their excellent nonlinear fitting ability, their low interpretability caused by their black box nature limits their applicability in certain applications that require high transparency. In contrast, models based on physical mechanisms are more reliable due to their rigorous theoretical basis and high interpretability, but their prediction accuracy is often affected to a certain extent due to simplified assumptions about complex combustion processes. Therefore, a new NOx prediction model that can adapt to a wide range of variable operating conditions in deep peak regulation is needed. Physical Information Neural Network (PINN) improves the prediction accuracy of the model and enhances the interpretability of the model by integrating the high fitting ability of deep learning and the constraints of physical laws.

[0004] Due to its inherent limitations, traditional machine learning models are unable to fully capture the complex dynamic laws inherent in the system, especially when faced with multivariable, nonlinear and frequently changing dynamic conditions. Deep operator networks (DeepONet) can learn and approximate complex nonlinear relationships. They can not only handle scalar-to-scalar mappings, but also directly model complex relationships from input to output. At the same time, by dynamically updating the parameters of physical information items through real-time data and embedding physical information into DeepONet as a regularization term, the model can better adapt to the changing operating conditions under deep peak regulation and improve the accuracy of NOx concentration prediction.

[0005] In addition, power plant data usually has high-dimensional characteristics. A small number of observations can cause the data set to become sparse, making it difficult to fully represent the input / output distribution space, and high-dimensional data often contains redundant features, which may significantly delay the network optimization process. The above challenges can be effectively addressed by applying dimensionality reduction technology, which can remove redundant information and make the data set more dense and representative, thereby accelerating model training and improving model performance. However, the local structure of the data may be lost during the dimensionality reduction process, resulting in the model being unable to accurately reflect the neighboring relationships in the original high-dimensional data. The use of graph Laplace regularization terms can retain these local structures in low-dimensional space, ensuring that the reduced-dimensional data can still accurately reflect the essential characteristics of the original data. Therefore, the physical information neural network method that integrates manifold regularization can establish an accurate NOx concentration prediction model, which is crucial for achieving refined control of the system and green production. Summary of the invention

[0006] In order to solve the problem of difficulty in NOx prediction under high-dimensional data, the present invention provides a NOx concentration prediction method integrating physical information neural network with manifold regularization.

[0007] The present invention adopts the following technical solution: a physical information neural network NOx concentration prediction method integrating manifold regularization, comprising: S1: Collect data on NOx concentration and related variables of thermal power units, and perform preprocessing and cleaning; S2: Use the encoder to compress the NOx concentration and related data collected in S1 from high dimensions to low dimensions, and construct the graph Laplace regularization term. The manifold regularization term is calculated based on the graph Laplace regularization term. ; S3: Establish a deep operator network model in latent space, use the low-dimensional data in S2 as the branch network input, the time series as the backbone network input, and the NOx concentration as the output; S4: Analyze the NOx generation mechanism of thermal power units, establish the NOx concentration mechanism equation to constrain the deep operator network model, construct the physical information neural network, and the total loss function; S5: Train the model composed of S2~S4, and use the trained model to predict the NOx concentration.

[0008] In some embodiments, in step S1, the relevant variables include: Oxygen content, coal supply, primary air, secondary air and furnace temperature.

[0009] In some embodiments, step S2 includes: S21: After the data collected in S1 are sequentially input into two fully connected layers and one activation layer, a low-dimensional representation of the input features is obtained; S22: Construct the graph Laplacian matrix L, construct the adjacency matrix W according to the data set, and the W in the adjacency matrix W ij Reflecting data points and The similarity between them is calculated using a Gaussian kernel. ij : in, and is the high-dimensional input data of NOx concentration related variables, is the Gaussian kernel parameter; Then construct the degree matrix D, which is a diagonal matrix where ; The graph Laplacian matrix L is defined as , the manifold regularization term is: in represents the trace of the matrix, and z is the data after dimensionality reduction.

[0010] In some embodiments, in step S3, the deep operator network model includes: A branch network, wherein the branch network includes a first fully connected layer, a ReLu activation function layer, a second fully connected layer, a ReLu activation function layer, and a third fully connected layer connected in sequence, wherein the number of hidden layers of the first fully connected layer and the second fully connected layer is 128, the number of hidden layers of the third fully connected layer is 64, and the input of the branch network is a low-dimensional representation of a NOx concentration-related variable; A backbone network, wherein the backbone network includes a fully connected network and a ReLu activation function layer, the number of hidden layers in the fully connected layer is 64, and the input of the backbone network is a low-dimensional representation of a NOx concentration-related variable; An element-level multiplication operation is performed on the branch network output and the trunk network output to obtain a predicted value of NOx concentration: is the predicted NOx concentration at time point t, p is the width of the network, that is, the dimension of the output of the branch network and the trunk network, and · represents element-wise multiplication.

[0011] In some embodiments, step S4 includes: S41: Select the coal feed rate 、ash carbon content 、Fly ash carbon content The current total air volume A is the input variable, and the carbon content in the furnace is , the molar concentration of CO 、NOx concentration and NO original emission mass concentration As a state variable, the output variable is the original NOx emission mass concentration ; The NOx mechanism model is: in, is the model dynamic parameter; S42: NOx mechanism model Parameters are identified and real-time operation data of NOx concentration and related variables of thermal power plant units are cached. Whenever the data reaches 2000 groups, Parameters are updated; S43: The NOx mechanism model is discretized by the forward Euler method to construct the physical information regularization term, and the deep operator network model is physically constrained; S44: The total loss function of the physical information neural network NOx concentration prediction method fused with manifold regularization is calculated as: in is the weight of the physical information regularization term, is the weight of the graph Laplace regularization term; Given a set of data at N time points, The loss function is: is the value of the actual NOx concentration at time point t, is the predicted NOx concentration at time point t.

[0012] In some embodiments, step S5 includes: S51: Perform model training to minimize the loss function of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model; S52: Input the real-time operation data into the model trained in S51 to obtain the output value of NOx concentration at the current moment.

[0013] Compared with the prior art, the present invention has the following beneficial effects: The present invention performs dimensionality reduction processing on the data through an encoder to reduce the impact of data sparsity and redundant features on prediction accuracy, and uses manifold regularization technology to construct a graph Laplace regularization term to retain key feature information while reducing the dimension; then, a deep operator network model that combines low-dimensional features with time series data is constructed; in addition, a differential equation model is established based on physical mechanisms, and the forward Euler method is used for discretization to construct a physical information regularization term to ensure that the model conforms to physical laws and improve the accuracy of the model through continuous updating of real-time data. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The physical information neural network NOx prediction flow chart of the present invention integrating manifold regularization; Figure 2 This is a block diagram of the physical information neural network NOx prediction based on manifold regularization proposed by the present invention; Figure 3 It is a schematic diagram of the NOx generation principle of the coal-fired boiler of the present invention. DETAILED DESCRIPTION

[0015] In order to facilitate the understanding of the present invention, the present invention will be described more comprehensively and meticulously below in conjunction with the accompanying drawings and preferred embodiments of the present invention, but the protection scope of the present invention is not limited to the following specific embodiments.

[0016] like Figure 2 As shown, the present invention provides a physical information neural network NOx concentration prediction method integrating manifold regularization, comprising the following steps: S1: Collect data on NOx concentration and related variables of thermal power units, and perform preprocessing and cleaning; S2: Use the encoder to compress the NOx concentration-related data collected in S1 from high dimensions to low-dimensional representation, and use the manifold regularization technology to construct the graph Laplace regularization term; S3: The low-dimensional data in S2 is used as the branch network input, the time series is used as the backbone network input, and the NOx concentration is used as the output to establish a deep operator network model in the latent space; S4: Analyze the NOx generation mechanism of thermal power units, establish the NOx concentration mechanism equation, update the mechanism model online according to real-time operation data, and use the mechanism model to construct physical information regularization terms; S5: Train the model composed of S2~S4, and use the trained model to predict the NOx concentration.

[0017] Furthermore, the step S1 includes: Obtain historical data and real-time operation data of NOx concentration and related variables of thermal power plant units. NOx concentration-related variables include oxygen content, coal feed rate, primary air, secondary air, furnace temperature, etc., and perform outlier cleaning, missing value filling and smoothing filtering on the above data.

[0018] Furthermore, the step S2 includes: Assumptions is the high-dimensional input data about NOx concentration related variables, is a low-dimensional representation, where After the feature x is input into two fully connected layers and one activation layer, a low-dimensional representation of the input feature is obtained: in, and Represent the weights of the two fully connected layers, and Represent the bias of the two fully connected layers respectively. The weights and biases are updated by the back-propagation algorithm. Represents the ReLu activation function; Furthermore, to construct the graph Laplace regularization term, we first need to construct the graph Laplace matrix L, and then construct the adjacency matrix W according to the data set, where It reflects the similarity between data points i and j and can be calculated using a Gaussian kernel: in, and is the high-dimensional input data of NOx concentration related variables, is the Gaussian kernel parameter; Then construct the degree matrix D, which is a diagonal matrix where ; The graph Laplacian matrix L can be defined as L=DW; The manifold regularization term can be defined as: in represents the trace of a matrix; Furthermore, the step S3 includes: Assuming that the data collected in S1 is about time series t, the low-dimensional representation of the NOx concentration-related variables can be written as ,in Indicates The values ​​of related variables (such as oxygen content, coal feed rate, primary air, secondary air, furnace temperature, etc.) at time t.

[0019] Furthermore, the branch network extracts useful features from the time series of operating conditions. The mapping of the branch network can be expressed as , is the output of the branch network, which depends on the input function z at n different points The value on .

[0020] The branch network consists of three fully connected layers. First, z is input into the fully connected layer with 128 hidden layers, and then the obtained data is input into the ReLu activation function layer; then, the obtained data is input into the fully connected layer with 128 hidden layers and the ReLu activation function layer in sequence; finally, the obtained data is input into the fully connected layer with 64 hidden layers to obtain the output value of the branch network: , and Represent the weights of the three fully connected layers, , and Represent the bias of the three fully connected layers respectively, Represents the ReLu function.

[0021] Furthermore, the goal of the backbone network is to extract information from time points, and the mapping can be expressed as , is the output of the backbone network, t is the time point at which the NOx concentration is predicted.

[0022] The backbone network consists of a fully connected network. t The input is a fully connected layer with 64 hidden layers, and then the obtained data is input into the ReLu activation function layer to obtain the output value of the branch network: They represent the weights of the fully connected layer, represents the bias of the fully connected layer, Represents the ReLu function; Furthermore, the output of the branch network and the output of the trunk network are element-wise multiplied to obtain the predicted value of NOx concentration: is the predicted NOx concentration at time point t, p is the width of the network, i.e., the dimension of the output of the branch network and the trunk network, and · represents element-wise multiplication.

[0023] Furthermore, we give a set N For data at each time point, the loss function can be written as: is the value of the actual NOx concentration at time point t.

[0024] The step S4 comprises: According to the combustion mechanism of coal-fired boilers, a mechanism model of NOx in the furnace is built. Based on the immediate carbon model, a self-generation and self-reduction model in the furnace is established. The self-generation model of NOx in the furnace is composed of immediate carbon nitrogen and volatile nitrogen, and the self-reduction model of NOx in the furnace is composed of immediate carbon and CO. Furthermore, the coal feed rate is selected 、ash carbon content 、Fly ash carbon content and the current total air volume A entering the furnace are input variables. 、NOx concentration and NO original emission mass concentration As a state variable, the output variable is the original NOx emission mass concentration .

[0025] Furthermore, the differential equation of NOx at the furnace outlet is expressed as: The parameters are as follows: , , , , , , , , , ; For the convenience of description, the symbols and terms used are defined as follows: Furthermore, the particle swarm identification method was used to identify the NOx mechanism model. Parameters are identified and real-time operation data is cached. Whenever the data reaches 2000 groups, online particle swarm optimization algorithm is used to optimize the Parameters are updated.

[0026] Define particle inertia weight w The value range is [0.7, 0.9], the learning factor c 1 and c 2The value range is [1.5,2], r 1 and r 2 is a random number between [0,1]. v id and x id Particles pi Location x i and speed v i No. d Quantity, p gd and p bd yes p g and b The d-th component of . The range of each parameter is .

[0027] The NOx mechanism model described in S41 is used to establish the fitness evaluation function: The model parameters As individual particles of the particle swarm algorithm The input data u(k) in the input-output data pair sequence {u(k), Y(k)} stimulates the model and generates the model in the particle The model output is , and then calculate the fitness evaluation function.

[0028] Determining the size of the particle population N p and the number of iterations N D , initialize all particles, each particle Initial position x i and speed v i ; Calculate the fitness value of each particle. If the current fitness of each particle is better than the historical best, update its individual best position. p b , find the particle with the best fitness value in the entire population and set its position as the global best position p g .

[0029] Update the velocity and position of each particle according to the following formula: Furthermore, the mechanism model is discretized through the forward Euler method to construct the physical information regularization term, and the deep operator network model in S3 is physically constrained; Furthermore, the total loss function of the NOx concentration prediction method of the physical information neural network fused with manifold regularization is: in is the weight of the physical information regularization term, is the weight of the graph Laplace regularization term.

[0030] The step S5 comprises: S51: Perform model training to minimize the loss function of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model; S52: Input the real-time operation data into the model trained in S51 to obtain the output value of NOx concentration at the current moment.

[0031] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A physical information neural network NOx concentration prediction method integrating manifold regularization, characterized in that: include: S1: Collect data on NOx concentration and related variables of thermal power units, and perform preprocessing and cleaning; S2: Use the encoder to compress the NOx concentration and related data collected in S1 from high dimensions to low dimensions, and construct the graph Laplace regularization term. The manifold regularization term is calculated based on the graph Laplace regularization term. ; S3: Establish a deep operator network model in latent space, use the low-dimensional data in S2 as the branch network input, the time series as the backbone network input, and the NOx concentration as the output; S4: Analyze the NOx generation mechanism of thermal power units, establish the NOx concentration mechanism equation to constrain the deep operator network model, construct the physical information neural network, and the total loss function; S5: Train the model composed of S2~S4, and use the trained model to predict the NOx concentration.

2. The physical information neural network NOx concentration prediction method fused with manifold regularization according to claim 1 is characterized in that: In step S1, the relevant variables include: Oxygen content, coal supply, primary air, secondary air and furnace temperature.

3. The NOx concentration prediction method of physical information neural network fused with manifold regularization according to claim 1 is characterized in that: The step S2 comprises: S21: After the data collected in S1 are sequentially input into two fully connected layers and one activation layer, a low-dimensional representation of the input features is obtained; S22: Construct the graph Laplacian matrix L, construct the adjacency matrix W according to the data set, and the W in the adjacency matrix W ij Reflects the similarity between data points i and j, using Gaussian kernel to calculate W ij : in, and is the high-dimensional input data of NOx concentration related variables, is the Gaussian kernel parameter; Then construct the degree matrix D, which is a diagonal matrix where ; The graph Laplacian matrix L is defined as , the manifold regularization term is: in represents the trace of the matrix, and z is the data after dimensionality reduction.

4. The NOx concentration prediction method of physical information neural network fused with manifold regularization according to claim 1 is characterized in that: In step S3, the deep operator network model includes: A branch network, wherein the branch network includes a first fully connected layer, a ReLu activation function layer, a second fully connected layer, a ReLu activation function layer, and a third fully connected layer connected in sequence, wherein the number of hidden layers of the first fully connected layer and the second fully connected layer is 128, the number of hidden layers of the third fully connected layer is 64, and the input of the branch network is a low-dimensional representation of a NOx concentration-related variable; A backbone network, wherein the backbone network includes a fully connected network and a ReLu activation function layer, the number of hidden layers in the fully connected layer is 64, and the input of the backbone network is a low-dimensional representation of a NOx concentration-related variable; An element-level multiplication operation is performed on the branch network output and the trunk network output to obtain a predicted value of NOx concentration: is the predicted NOx concentration at time point t, p is the width of the network, i.e., the dimension of the output of the branch network and the trunk network, and · represents element-wise multiplication.

5. The NOx concentration prediction method of physical information neural network fused with manifold regularization according to claim 1 or 4, characterized in that: The step S4 comprises: S41: Select coal feed rate 、ash carbon content 、Fly ash carbon content And the current total air volume into the furnace A is the input variable, the carbon content in the furnace , the molar concentration of CO 、The molar concentration of NO and NO original emission mass concentration As a state variable, the output variable is the original emission mass concentration of NO ; The NOx mechanism model is: in, is the model dynamic parameter; S42: NOx mechanism model Parameters are identified and real-time operation data of NOx concentration and related variables of thermal power plant units are cached. Whenever the data reaches 2000 groups, Parameters are updated; S43: The NOx mechanism model is discretized by the forward Euler method to construct the physical information regularization term, and the deep operator network model is physically constrained; S44: The total loss function of the physical information neural network NOx concentration prediction method fused with manifold regularization is calculated as: in is the weight of the physical information regularization term, is the weight of the graph Laplace regularization term; Give a set N Data at a point in time, The loss function is: is the value of the actual NOx concentration at time point t, is the predicted NOx concentration at time point t.

6. The physical information neural network NOx concentration prediction method integrating manifold regularization according to claim 1 is characterized in that: The step S5 comprises: S51: Perform model training to minimize the loss function of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model; S52: Input the real-time operation data into the model trained in S51 to obtain the output value of NOx concentration at the current moment.

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