NOx prediction method of domain adaptive physical information network based on linear dynamic operator

Abstract

The invention relates to the field of NOx prediction, in particular to a NOx prediction method of a domain adaptive physical information network based on a linear dynamic operator. Comprising the following steps: S1, acquiring historical working condition data and current working condition data of a thermal power plant unit, performing data cleaning, and performing feature selection on a cleaned data set; s2, inputting the historical working condition data and the current working condition data obtained in the S1 into a linear dynamic operator neural network model; s3, carrying out distribution alignment on the hidden layer state variables under the historical working condition and the current working condition in the S2, and constructing a domain adaptation loss function; s4, establishing a differential equation model according to a NOx generation mechanism in the coal combustion process, discretizing the differential equation model through a forward Euler method to construct a physical information regularization item, and physically constraining the neural network in S2; and S5, training the linear dynamic operator neural network model in the step S2, and inputting the current working condition data obtained in the step S1 into the trained model to obtain a final NOx prediction value.

Description

Technical Field

[0001] The present invention relates to the field of NOx prediction, in particular to a NOx prediction method based on a domain-adaptive physical information network of a linear dynamic operator. Background Art

[0002] Thermal power plants generate electricity primarily by burning fossil fuels. During this combustion process, high-temperature reactions between nitrogen and oxygen produce nitrogen oxides (NOx), which are harmful gases that pose a threat to the atmosphere and human health. Therefore, monitoring and predicting NOx concentrations is a key part of environmental protection measures for thermal power plants.

[0003] With the transformation of energy structure, thermal power units will gradually become the main regulating power source, which is characterized by deep peak regulation and frequent start-stop operations. When performing deep peak regulation operations, thermal power units need to quickly adjust their loads to adapt to the needs of the power grid. This load change is usually accompanied by fluctuations in the output power and heat load of the thermal power units, which may cause large changes in the temperature and pressure of the combustion chamber, resulting in the inability of the thermal power units to continue to work at a fixed operating point. The system therefore exhibits multi-state operating characteristics, and as the operating conditions change, the distribution of process data will also show significant differences, which poses a great challenge to the prediction of NOx emissions.

[0004] The parameters (weights and biases) in a neural network are so numerous and their interactions are so complex that it is difficult to directly understand the specific functions or effects of each parameter. These parameters process input data through multiple layers of nonlinear transformations, making their impact on the final output highly abstract and indirect, resulting in a lack of intuitive interpretability. The core element of a linear dynamic operator neural network is a linear infinite impulse response dynamic operator described by a rational transfer function. The parameters in the network correspond to the coefficients of the numerator and denominator polynomials in the rational transfer function. The interpretability of a linear dynamic operator neural network lies in its ability to describe and predict system behavior using known dynamic system theory, where rational transfer functions provide an intuitive way to explain how a system responds to external inputs.

[0005] Deep learning has attracted great attention in various fields due to its powerful nonlinear modeling capabilities. However, typical deep learning is constructed as a black-box agent model, which usually requires a large amount of labeled data, which is often unavailable in many scientific applications. Physically-Informed Neural Networks (PINNs) use known partial differential equations to constrain the training of neural networks with relatively small amounts of data.

[0006] The maximum mean difference (MMD) is a method used to measure the difference between two data sets, which can quantify the distribution difference of NOx data under different operating conditions. By calculating the MMD value between the NOx data distribution under different operating conditions, the degree of difference between them can be quantified. Based on this difference, the model or prediction algorithm can be adjusted to better adapt to the data distribution under different operating conditions, thereby improving the accuracy of NOx prediction. Summary of the invention

[0007] In order to solve the problem of difficult NOx prediction under deep peak regulation and wide-range variable operating conditions, the present invention provides a NOx prediction method based on a domain adaptive physical information network of a linear dynamic operator.

[0008] The present invention adopts the following technical solution: a NOx prediction method based on a domain-adaptive physical information network of a linear dynamic operator, comprising: S1: Obtain historical and current operating data of thermal power plant units, then clean the data and perform feature selection on the cleaned data set; S2: Input the historical working condition data and current working condition data obtained in S1 into the linear dynamic operator neural network model to obtain the hidden layer state variables under the historical working condition and the current working condition and , and calculate the final prediction value of the linear dynamic operator neural network model, and construct the loss function between the true value and the predicted value ; S3: hidden layer state variables under historical working conditions and current working conditions in S2 and Perform distribution alignment and construct domain adaptation loss function ; S4: A differential equation model is established based on the NOx generation mechanism during coal combustion, and the differential equation model is discretized by the forward Euler method to construct a physical information regularization term. , physically constrain the neural network in S2; S5: According to S2-S4 , and The linear dynamic operator neural network model in S2 is trained, and the current operating condition data obtained in S1 is input into the trained model to obtain the final NOx prediction value.

[0009] In some embodiments, step S1 includes: S11: Obtain historical operating data and current operating data of thermal power plant units, and perform data cleaning; S12: Feature selection is performed on the data cleaned in S11, and the mutual information between each characteristic variable and the NOx concentration at the SCR inlet is calculated. The characteristic variables with less correlation are deleted, and the n characteristic variables with the largest mutual information are selected as the input variables for the final prediction modeling.

[0010] In some embodiments, the data cleaning in step S11 includes: first using The outliers are determined by the criterion and filled with the mean of the two values ​​before and after the outliers; the missing values ​​are then processed by the mean filling method; finally, the wavelet denoising method is used to smooth the data.

[0011] In some embodiments, in step S12, n=25.

[0012] In some embodiments, step S2 includes: S21: Historical operating data obtained from S12 and current operating data Input the linear power layer to obtain the hidden layer state variables under historical and current conditions and , the formula is as follows: Where a, b are the coefficients of the numerator and denominator polynomials, respectively, q is the delay operator, is the linear motion operator; S22: The output of the linear power layer and The input fully connected layer is mapped to a high-dimensional space, and the mapping function is as follows: in and are weights and biases respectively, is the activation function; S23: Output the fully connected neural network , mapped to the output value through the linear power layer : ; S24: Neural network prediction value With the true value The loss function is: in, is the i-th predicted value, is the ith true value of NOx concentration, is the number of historical operating condition samples.

[0013] In some embodiments, step S3 includes: The hidden layer state variables under historical conditions and current conditions are and The distribution of the hidden layer state variables under the historical working condition and the current working condition are aligned through the maximum mean difference, and the domain adaptation loss is calculated: in, and is the i-th data output by the linear power layer in S21, and is the i-th data output by the fully connected layer in S22, is the number of samples of the current working condition.

[0014] In some embodiments, in step S4, the differential equation model is: Among them, XN i It is one of the continuous intermediates, which constitute the first i parallel branches, is the mole fraction of nitrogen compounds in the primary fuel, is the amount of fuel, is the mole fraction of the intermediate compound, is the mole fraction of oxygen, and are the NOx generation rate and reduction rate, For XN i The reaction rate constant, e i and f i is the reaction order of the intermediate compound and the amount of fuel; is the oxidation reaction rate constant of NOx, g i and h i is the reaction order of the intermediate compound and the amount of oxygen; is the reduction reaction rate constant of NOx, m i and n i is the reaction order of the intermediate compound and NOx; is the pre-exponential factor of the reaction, is the activation energy of the reaction, R is the ideal gas constant, R=8.137J / mol, and T is the reaction temperature in K.

[0015] In some embodiments, step S4 includes: The differential equation model is discretized by the forward Euler method, and the physical information regularization term is constructed by the residual between the differential equation model and the neural network prediction value. , physically constrain the neural network in S3; in, is discrete time, is the ith NOx concentration value calculated by the mechanism model.

[0016] In some embodiments, step S5 includes: S51: The total loss function of the domain-adapted physical information network for computing the linear dynamics operator is: in is the weight of the physical information regularization term, is the weight of the domain adaptation regularization term; S52: Perform model training to minimize the total loss function L of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model.

[0017] Compared with the prior art, the present invention has the following beneficial effects: The present invention establishes a neural network model based on a linear dynamic operator to increase the interpretability of the model; discretizes the mechanism model through the forward Euler method to construct a physical information regularization term, and physically constrains the neural network, thereby reducing dependence on large amounts of data; and aligns the distribution of hidden layer state variables under historical working conditions and current working conditions through the maximum mean difference, constructs a domain adaptation loss, and reduces the distribution difference between working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 The domain adaptation physical information network NOx prediction flow chart of the linear dynamic operator proposed in the present invention; Figure 2 The block diagram of the domain-adapted physical information network NOx prediction of the linear dynamic operator proposed in the present invention; Figure 3 This is a schematic diagram of a boiler model with relevant variables required by the present invention. DETAILED DESCRIPTION

[0019] 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.

[0020] like Figure 2 As shown, the present invention provides a method comprising the following steps: S1: Obtain the historical and current operating data of the thermal power plant units, then clean the data and perform feature selection based on the mutual information method.

[0021] Furthermore, the step S1 includes: S11: Get the historical and current operating data of the thermal power plant units. First use The outliers are determined by the criterion and filled with the mean of the two values ​​before and after the outliers; the missing values ​​are then processed by the mean filling method; finally, the wavelet denoising method is used to smooth the data.

[0022] S12: Feature selection is performed on the data cleaned in S11, and the mutual information between each characteristic variable collected by the sensor and the NOx concentration at the SCR inlet is calculated. The characteristic variables with less correlation are deleted, and the 25 characteristic variables with the largest mutual information are selected as the input variables for the final prediction modeling.

[0023] Historical operating data including samples ,in , Represents the historical operating conditions. is the corresponding output; Indicates the characteristic data of the current working condition, and is the number of samples in the training set and the test set.

[0024] S2: Input the historical working condition data and current working condition data obtained in S1 into the linear dynamic operator neural network model, which consists of two linear dynamic layers and one fully connected layer, to obtain the hidden layer state variables under the historical working condition and the current working condition. and , and calculate the final prediction value of the linear dynamic operator neural network model, and construct the loss function between the true value and the predicted value .

[0025] Furthermore, the step S2 comprises: The neural network based on linear dynamics operator consists of two linear dynamics layers and one fully connected layer. The core element of the linear dynamics layer is a linear infinite impulse response dynamic operator described by a rational transfer function.

[0026] S21: Historical operating data obtained from S12 and current operating data Input the linear power layer to obtain the hidden layer state variables under historical and current conditions and , the formula is as follows: Where a, b are the coefficients of the numerator and denominator polynomials, respectively, q is the delay operator, is the linear motion operator.

[0027] in is a linear dynamic operator, which is described as follows: In the formula, , Time index t The input and output sequence values, or , and It is a delay operator The polynomial in , that is: Polynomial and The coefficient of , It is adjustable. and They are polynomials , The number of times.

[0028] During the back propagation Received vector , is the loss L about The partial derivative of . Given , It is necessary to calculate the derivative of the loss L to align the differentiable inputs b, a, and x. The reverse operation has the following structure: Numerator coefficient and the denominator coefficient The j-th components of are: Equivalent to With sensitivity The shift of is used for dot product operation. Similarly, Equivalent to With sensitivity The dot product operation is performed by shifting . , , , .

[0029] The back propagation process of the input time series u can be expressed as: in Represents a t-length vector time reversal, .

[0030] S22: The output of the linear power layer and The input fully connected layer is mapped to a high-dimensional space, and the mapping function is as follows: in and are weights and biases respectively, is the activation function.

[0031] S23: Output the fully connected neural network , mapped to the output value through the linear power layer : .

[0032] S24: Neural network prediction value With the true value The loss function is: in, is the i-th predicted value, is the ith true value of NOx concentration, is the number of historical operating condition samples.

[0033] S3: hidden layer state variables under historical working conditions and current working conditions in S2 and Perform distribution alignment and construct domain adaptation loss function .

[0034] The hidden layer state variables under historical and current conditions are transformed by domain adaptation method. and The distribution of the hidden layer state variables under the historical working condition and the current working condition are aligned through the maximum mean difference, and the domain adaptation loss is calculated: in, and is the i-th data output by the linear power layer in S21, and is the i-th data output by the linear power layer in S21, is the number of samples of the current working condition.

[0035] S4: A differential equation model is established based on the NOx generation mechanism during coal combustion, and the differential equation model is discretized by the forward Euler method to construct a physical information regularization term. , physically constrain the neural network in S2.

[0036] Further, the step S4 includes: The NOx generation mechanism involved in S4, there are three main ways to generate NOx during the combustion of coal: thermal type, rapid type and fuel type. In power plant boilers, fuel type NOx is the most important, accounting for 75-90% of the total NOx, followed by thermal type, and the least rapid type. Fuel NOx is NOx generated by the thermal decomposition and subsequent oxidation of nitrogen compounds contained in the fuel during the combustion process.

[0037] After the fuel enters the furnace and is heated, the nitrogen organic compounds in the fuel are first thermally decomposed into intermediate products such as hydrogen cyanide (HCN), ammonia (NH4) and cyanide (CN). The intermediate products are oxidized into NOx when encountering oxygen, and can also undergo reduction reaction with the generated NOx, reducing NO to N2.

[0038] Assume XN i is one of the intermediates, then XN i The generation rate can be expressed as: is the mole fraction of nitrogen compounds in the primary fuel, is the amount of fuel, For XN i The reaction rate constant, e i and f i is the reaction order of the intermediate compound and the amount of fuel. The generation rate of NOx is: is the mole fraction of the intermediate compound, is the mole fraction of oxygen, is the oxidation reaction rate constant of NO, g i and h i is the reaction order of the intermediate compound and the amount of oxygen. The reduction rate of NOx is: is the NO mole fraction, is the reduction reaction rate constant of NO, m i and n i is the reaction order of the intermediate compound and NO.

[0039] is the pre-exponential factor of the reaction, is the activation energy of the reaction, R is the ideal gas constant, R=8.137J / mol, and T is the reaction temperature in K.

[0040] The thermal NO generation rate is: Then the differential equation model is: Among them, XN i It is one of the continuous intermediates, which constitute the first i parallel branches, is the mole fraction of nitrogen compounds in the primary fuel, is the amount of fuel, is the mole fraction of the intermediate compound, is the mole fraction of oxygen, and are the NOx generation rate and reduction rate, For XN i The reaction rate constant, e i and f i is the reaction order of the intermediate compound and the amount of fuel; is the oxidation reaction rate constant of NOx, g i and h i is the reaction order of the intermediate compound and the amount of oxygen; is the reduction reaction rate constant of NOx, m i and n i is the reaction order of the intermediate compound and NOx; is the pre-exponential factor of the reaction, is the activation energy of the reaction, R is the ideal gas constant, R=8.137J / mol, and T is the reaction temperature in K.

[0041] In some embodiments, step S4 includes: The differential equation model is discretized by the forward Euler method, and the physical information regularization term is constructed by the residual between the differential equation model and the neural network prediction value. , physically constrain the neural network in S3; in, is discrete time, is the ith NOx concentration value calculated by the mechanism model.

[0042] During the model training process, the loss function of the NOx concentration prediction model is minimized, and the model parameters are updated through the back propagation algorithm to obtain the final trained model.

[0043] S5: According to S2-S4 , and The linear dynamic operator neural network model in S2 is trained, and the current operating condition data obtained in S1 is input into the trained model to obtain the final NOx prediction value.

[0044] S51: The total loss function of the domain-adapted physical information network for computing the linear dynamics operator is: in is the weight of the physical information regularization term, is the weight of the domain adaptation regularization term; S52: Perform model training to minimize the total loss function L of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model.

[0045] Historical operating data Input the trained model to get the output value of NOx concentration under the current working conditions .

[0046] 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 NOx prediction method based on a domain-adaptive physical information network of a linear dynamic operator, characterized in that: include: S1: Obtain historical and current operating data of thermal power plant units, then clean the data and perform feature selection on the cleaned data set; S2: Input the historical working condition data and current working condition data obtained in S1 into the linear dynamic operator neural network model to obtain the hidden layer state variables under the historical working condition and the current working condition and , and calculate the final prediction value of the linear dynamic operator neural network model, and construct the loss function between the true value and the predicted value ; S3: hidden layer state variables under historical working conditions and current working conditions in S2 and Perform distribution alignment and construct domain adaptation loss function ; S4: A differential equation model is established based on the NOx generation mechanism during coal combustion, and the differential equation model is discretized by the forward Euler method to construct a physical information regularization term. , physically constrain the neural network in S2; S5: According to S2-S4 , and The linear dynamic operator neural network model in S2 is trained, and the current operating condition data obtained in S1 is input into the trained model to obtain the final NOx prediction value.

2. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 1 is characterized in that: The step S1 comprises: S11: Obtain historical operating data and current operating data of thermal power plant units, and perform data cleaning; S12: Feature selection is performed on the data cleaned in S11, and the mutual information between each characteristic variable and the NOx concentration at the SCR inlet is calculated. The characteristic variables with less correlation are deleted, and the n characteristic variables with the largest mutual information are selected as the input variables for the final prediction modeling.

3. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 2 is characterized in that: The data cleaning in step S11 includes: first using The outliers are determined by the criterion and filled with the mean of the two values ​​before and after the outliers; the missing values ​​are then processed by the mean filling method; finally, the wavelet denoising method is used to smooth the data.

4. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 2 is characterized in that: In step S12, n=25.

5. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 1 is characterized in that: The step S2 comprises: S21: Historical operating data obtained from S12 and current operating data Input the linear power layer to obtain the hidden layer state variables under historical and current conditions and , the formula is as follows: Where a, b are the coefficients of the numerator and denominator polynomials, respectively, q is the delay operator, is the linear motion operator; S22: The output of the linear power layer and The input fully connected layer is mapped to a high-dimensional space, and the mapping function is as follows: in and are weights and biases respectively, is the activation function; S23: Output the fully connected neural network , mapped to the output value through the linear power layer : ； S24: Neural network prediction value With the true value The loss function is: in, is the i-th predicted value, is the ith true value of NOx concentration, is the number of historical operating condition samples.

6. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 1 is characterized in that: The step S3 comprises: The hidden layer state variables under historical conditions and current conditions are and The distribution of the hidden layer state variables under the historical working condition and the current working condition are aligned through the maximum mean difference, and the domain adaptation loss is calculated: in, and is the i-th data output by the linear power layer in S21, and is the i-th data output by the fully connected layer in S22, is the number of samples of the current working condition.

7. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 1 is characterized in that: In step S4, the differential equation model is: Among them, XN i It is one of the continuous intermediates, which constitute the first i parallel branches, is the mole fraction of nitrogen compounds in the primary fuel, is the amount of fuel, is the mole fraction of the intermediate compound, is the mole fraction of oxygen, and are the NOx generation rate and reduction rate, For XN i The reaction rate constant, e i and f i is the reaction order of the intermediate compound and the amount of fuel; is the oxidation reaction rate constant of NOx, g i and h i is the reaction order of the intermediate compound and the amount of oxygen; is the reduction reaction rate constant of NOx, m i and n i is the reaction order of the intermediate compound and NOx; is the pre-exponential factor of the reaction, is the activation energy of the reaction, R is the ideal gas constant, R=8.137J / mol, and T is the reaction temperature in K.

8. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 7 is characterized in that: The step S4 comprises: The differential equation model is discretized by the forward Euler method, and the physical information regularization term is constructed by the residual between the differential equation model and the neural network prediction value. , physically constrain the neural network in S3; in, is discrete time, is the ith NOx concentration value calculated by the mechanism model.

9. The NOx prediction method based on domain-adaptive physical information network of linear dynamic operator according to claim 1, characterized in that: The step S5 comprises: S51: The total loss function of the domain-adapted physical information network for computing the linear dynamics operator is: in is the weight of the physical information regularization term, is the weight of the domain adaptation regularization term; S52: Perform model training to minimize the total loss function L of the NOx concentration prediction model, update the model parameters through the back propagation algorithm, and obtain the final trained model.

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