SCR denitration system outlet NOx concentration distribution PDF prediction method

Abstract

The invention relates to the technical field of SCR denitration systems, and particularly provides an SCR denitration system outlet NOx concentration distribution PDF prediction method. The method comprises the following steps: S1, acquiring NOx concentrations of F different actual point locations of an outlet of the SCR denitration system and historical data of each input variable influencing a NOx concentration distribution probability density function of the outlet of the SCR denitration system, and storing the acquired information to construct a historical data set; s2, estimating a NOx concentration distribution probability density function of the outlet of the SCR denitration system according to the obtained historical data set; s3, representing the probability density function, estimated in the S2, of the NOx concentration distribution at the outlet of the SCR denitration system by using a primary function; and S4, establishing a nonlinear prediction model between the input variable and the first n-1 weight vectors, and predicting the NOx concentration distribution probability density function at the outlet of the SCR denitration system at the next moment.

Description

Technical Field

[0001] The invention relates to the technical field of SCR denitration systems, and in particular provides a method for predicting the NOx concentration distribution PDF at an outlet of an SCR denitration system. Background Art

[0002] Coal-fired power plant boilers play an important role in my country's energy supply, and the nitrogen oxides (NOx) emitted by boiler combustion are one of the main pollutants in the atmosphere, which has long affected air quality and, in turn, human health. In response, my country has implemented strict supervision on the emission of atmospheric pollutants from thermal power units.

[0003] Since the SCR denitration system has nonlinearity, hysteresis of the NOx measurement device and uneven distribution of cross-sectional NOx concentration, and the unit's NOx will fluctuate more during the load change process, especially when the flue gas cross-sectional NOx concentration is unevenly distributed under low load operation, the uniform ammonia injection cannot guarantee the uniformity of the NOx concentration at the outlet of the SCR flue gas denitration system, resulting in the SCR flue gas denitration system having problems such as excessive local NOx concentration at the outlet cross-section, low denitration efficiency and high ammonia escape rate. Therefore, a method is needed to predict the NOx concentration distribution PDF at the outlet of the SCR flue gas denitration system, and use the predicted NOx concentration distribution PDF at the outlet of the SCR flue gas denitration system as an important parameter for ammonia injection feedforward, and participate in the closed-loop control of the total amount of ammonia injection, so as to solve the problem of excessive local NOx concentration at the outlet cross-section caused by measurement hysteresis and uneven distribution of NOx concentration at the outlet of the SCR flue gas denitration system, thereby ensuring the SCR denitration efficiency and reducing the ammonia escape rate. The existing method for predicting the NOx concentration at the outlet of the SCR flue gas denitrification system is mainly to perform point value prediction on the outlet NOx concentration, which cannot reflect the NOx concentration distribution characteristics at the outlet of the SCR flue gas denitrification system and cannot effectively guide the precise ammonia injection, resulting in low denitrification efficiency of the SCR flue gas denitrification system, excessive NOx concentration in the local outlet section, high ammonia escape rate and excessive ammonia injection, which has an adverse effect on the catalyst life. Summary of the invention

[0004] The object of the present invention is to provide a method for predicting the NOx concentration distribution PDF at the outlet of an SCR denitration system, by which the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system is predicted to reflect the NOx concentration distribution characteristics at the outlet of the SCR flue gas denitration system.

[0005] The present invention adopts the following technical solution: a method for predicting the NOx concentration distribution PDF at the outlet of an SCR denitration system, comprising: S1: Obtain the NOx concentrations at F different actual points at the outlet of the SCR denitration system, as well as the historical data of each input variable that affects the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system, and store the acquired information to construct a historical data set; S2: Estimate the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system based on the historical data set; S3: Using basis functions to represent the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system estimated by S2; S4: Establish a nonlinear prediction model between the input variables and the first n-1 weight vectors to predict the NOx concentration distribution probability density function at the outlet of the SCR denitrification system at the next moment.

[0006] In some embodiments, in step S1, the historical data set includes: NOx concentration at F different actual points at the outlet of the SCR denitrification system ; As well as the unit load L, the flue gas temperature T at the inlet of the SCR denitrification system, the flue gas flow rate S at the inlet of the SCR denitrification system, the oxygen content O at the inlet of the flue gas of the SCR denitrification system, the NOx concentration B at the inlet of the SCR denitrification system, and the ammonia injection amount of the M partitions of the ammonia injection grid .

[0007] In some embodiments, step S2 includes: S201: Estimate the NOx concentration at N different estimated points at the outlet of the SCR denitration system, where N>F, and obtain the NOx concentration at N different estimated points at the outlet of the SCR denitration system ; S202: Perform kernel density estimation based on the NOx concentrations at N different estimated points at the outlet of the SCR denitration system obtained in step S201 to obtain a probability density function of the NOx concentration distribution at the outlet of the SCR denitration system: in, is the kernel function and h is the bandwidth.

[0008] In some embodiments, step S201 includes: Assume that the distance between the i-th estimated point and the j-th actual point is , then the influence weight of each actual point on the estimated point can be obtained according to the Gaussian function of the distance between the estimated point and the actual point. The weight is expressed as: According to the weight, the NOx concentration at the i-th estimation point can be expressed as: in, is the NOx concentration at the jth actual point.

[0009] In some embodiments, in step S202, the bandwidth is calculated using the following formula.

[0010] in, To estimate the standard deviation of the data, the kernel function is a Gaussian kernel function, as shown below: in, is the bandwidth smoothing parameter, which affects the shape of the distribution.

[0011] In some embodiments, step S3 includes: S301: Select basis function ; S302: Determine a weighted representation of a basis function. S303: Determine the weight of each basis function according to the NOx concentration distribution probability density function at the outlet of the SCR denitration system and all basis functions.

[0012] In some embodiments, in step S301, The Gaussian RBF basis function is used as the basis function of the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system to approximate the root mean square of the output probability density function, and its expression is: Among them, Y is the NOx concentration information at the estimated point, l Indicates l network nodes, n is the total number of network nodes, and Respectively represent l The center value and width of each network node function.

[0013] In some embodiments, in step S302, the root mean square probability density function of the NOx concentration distribution at the outlet of the SCR denitration system output at time k is expressed in the form of a weighted sum of basis functions, and the expression is: in, is the basis function vector composed of the first n-1 basis functions, is the weight vector composed of the weights corresponding to the first n-1 basis functions. is the nth basis function, is the weight corresponding to the nth basis function, is the approximation error.

[0014] In some embodiments, in step S303, the weight vector is determined by the following steps: The nth weight Use weight vector Nonlinear function It is expressed as: in, , , , , ; After neglecting the approximation error, we can get: Multiply both sides on the left , and for both ends in the interval When the matrix When it is non-singular, the weight vector is obtained by inverting the matrix: .

[0015] In some embodiments, step S4 includes: S401: Select input variable and input the current time into the variable , and the weight vector corresponding to the current moment Combined as the comprehensive input of the nonlinear model, denoted as ; S402: Select a random weight neural network for training, randomly select a set of input layer weights and biases within a given range, and use the collected historical data set to train the random weight neural network so that the random weight neural network outputs With the actual output The error between them is minimal; S403: Obtaining the optimal output weight by obtaining the generalized inverse of the H matrix; S404: Establishing a nonlinear dynamic mapping relationship between basis function weights and input variables; S405: Predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system at the next moment.

[0016] Compared with the prior art, the present invention has the following beneficial effects: Compared with the prior art, the present invention is based on the relevant theories of random distribution control, utilizes the actual operating data of the coal-fired unit and the SCR denitrification system, and represents the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system through basis functions; establishes a nonlinear prediction model between the input variables and the first n-1 weight vectors to realize the prediction of the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system, and provides support for the precise ammonia injection for realizing the random distribution control of the NOx concentration at the outlet of the SCR denitrification system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic flow chart of a method for predicting the probability density function of NOx concentration distribution at the outlet of an SCR denitration system according to the present invention; Figure 2 for Figure 1 Detailed process diagram; Figure 3 It is a schematic diagram of the actual point position and estimated point position of the NOx concentration at the outlet of the SCR denitration system according to the present invention; Figure 4 This is a diagram showing the effect of estimating the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system at a certain moment by kernel density estimation of the present invention; Figure 5 It is a modeling prediction diagram of the probability density function of NOx concentration distribution at the outlet of the SCR denitration system at a certain moment according to the present invention. DETAILED DESCRIPTION

[0018] The present invention proposes a method for predicting the NOx concentration distribution PDF at the outlet of an SCR denitration system, which will be further described below in conjunction with the accompanying drawings.

[0019] As attached Figure 1 And attached Figure 2 As shown, the method for predicting the NOx concentration distribution PDF at the outlet of the SCR denitration system of the present invention uses the actual operation data of the coal-fired unit and the SCR denitration system to express the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system by using the basis function; a nonlinear prediction model between the input variable and the first n-1 weight vectors is established to realize the prediction of the NOx concentration distribution probability density function at the outlet of the SCR denitration system, including the following steps: S1: Obtain the historical data of NOx concentrations at F different actual points at the outlet of the SCR denitrification system and the input variables that affect the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system from the DCS, and store the acquired information to construct a historical data set.

[0020] The historical data set includes the NOx concentration at F different actual points at the outlet of the SCR denitrification system. , and the unit load L, the flue gas temperature T at the inlet of the SCR denitrification system, the flue gas flow rate S at the inlet of the SCR denitrification system, the oxygen content O at the inlet of the flue gas of the SCR denitrification system, the NOx concentration B at the inlet of the SCR denitrification system, and the ammonia injection amount of the M partitions of the ammonia injection grid .

[0021] S2: Estimate the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system based on historical data, which is implemented in the following way: S201: Estimate the NOx concentration at N (N>F) different estimated points at the outlet of the SCR denitration system. Figure 3 As shown, assuming that the distance between the i-th estimated point and the j-th actual point is , then the influence weight of each actual point on the estimated point can be obtained according to the Gaussian function of the distance between the estimated point and the actual point. The weight can be expressed as: (1) According to the weight, the NOx concentration at the i-th estimation point can be expressed as: (2) in, is the NOx concentration at the jth actual point.

[0022] The NOx concentration at N different estimated points at the outlet of the SCR denitrification system can be obtained .

[0023] S202: Based on the NOx concentrations at N different estimated points at the outlet of the SCR denitration system obtained in step S201, kernel density estimation is performed using a Gaussian kernel function, and the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system can be obtained according to the following formula: (3) in, is the kernel function, h is the bandwidth, and the bandwidth is calculated using the following formula.

[0024] (4) in, To estimate the standard deviation of the data, the kernel function is a Gaussian kernel function, as shown below: (5) in, is the bandwidth smoothing parameter, which affects the shape of the distribution.

[0025] Attached Figure 4It is represented as an estimation effect diagram of the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system at a certain moment through kernel density estimation based on the NOx concentration at the actual and estimated points of the SCR denitrification system outlet.

[0026] S3: Using basis functions to represent the probability density function of the known NOx concentration distribution at the outlet of the SCR denitration system, the specific implementation is as follows: S301: Select a basis function, and use a Gaussian RBF basis function as the basis function of the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system to approximate the root mean square of the output probability density function, and its expression is: (6) Among them, Y is the NOx concentration information at the estimated point, l Indicates l network nodes, n is the total number of network nodes, and Respectively represent l The center value and width of each network node function.

[0027] S302: Determine the weighted representation of the basis function. According to the RBF network approximation principle, the probability density function root mean square of the NOx concentration distribution at the outlet of the SCR denitration system output at time k is represented in the form of the weighted sum of the basis functions. The expression is: (7) in, is the basis function vector composed of the first n-1 basis functions, is the weight vector composed of the weights corresponding to the first n-1 basis functions. is the nth basis function, is the weight corresponding to the nth basis function, is the approximation error.

[0028] S303: Determine the weight of each basis function, ignoring the approximation error for ease of analysis , the nth weight Use weight vector Nonlinear function It is expressed as: (8) in, , , , , .

[0029] After ignoring the approximation error, combining equations (7) and (8) we can obtain: (9) Multiply both sides of equation (9) by , and for both ends in the interval When the matrix When it is non-singular, the weight vector can be obtained by inverting the matrix: (10) The weights of each basis function of the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system are calculated using formula (10).

[0030] S4: Establish a nonlinear prediction model between the input variables and the first n-1 weight vectors to predict the NOx concentration distribution probability density function at the outlet of the SCR denitration system at the next moment. The specific implementation is as follows: S401: Select input variable and input the current time into the variable , and the weight vector corresponding to the current moment Combined as the comprehensive input of the nonlinear model, denoted as .

[0031] S402: Select a prediction model, select a random weight neural network, and its network model is expressed as: (11) Where L is the number of hidden nodes, is the input weight vector connecting the jth hidden unit to the m input nodes, is the output weight vector connecting the output nodes of the jth hidden layer, is the bias of the jth hidden unit, express and The inner product between.

[0032] S403: Train the model by randomly selecting a set of input layer weights and biases within a given range, and train the model using the collected S sets of historical data sets so that the model output With the actual output The error between them is the smallest, and its objective function is: (12) The matrix of formula (11) is expressed as (13) Among them, H is the hidden layer output matrix, is the output weight, and Y is the weighted output of the prediction model. , , .

[0033] S404: The optimal output weight is obtained by obtaining the generalized inverse of the H matrix, and the formula is: (14) S405: Establish a nonlinear dynamic mapping relationship between basis function weights and input variables: (15) S406: Predict the probability density function of NOx concentration distribution at the outlet of the SCR denitration system at the next moment: (16) Attached Figure 5 It is represented as a prediction effect diagram of the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system based on the trained model.

[0034] This patent proposes a method for predicting the PDF of NOx concentration distribution at the outlet of an SCR denitrification system. The probability density function of NOx concentration distribution at the outlet of the SCR denitrification system is weighted by using a basis function through a random distribution algorithm, and a nonlinear relationship between the input variables affecting the NOx concentration distribution at the outlet of the SCR denitrification system and the weight of the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system is established, thereby predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system to reflect the NOx concentration distribution characteristics at the outlet of the SCR flue gas denitrification system. The predicted probability density function of NOx concentration distribution at the outlet of the SCR denitrification system can be used as ammonia injection feedforward to achieve the effect of precise ammonia injection, thereby improving the denitrification efficiency and reducing the ammonia escape rate, which has important practical value.

[0035] The above description is only a preferred embodiment of the present invention and is 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 method for predicting the NOx concentration distribution PDF at the outlet of an SCR denitration system, characterized in that: include: S1: Obtain the NOx concentrations at F different actual points at the outlet of the SCR denitration system, as well as the historical data of each input variable that affects the probability density function of the NOx concentration distribution at the outlet of the SCR denitration system, and store the acquired information to construct a historical data set; S2: Estimate the probability density function of NOx concentration distribution at the outlet of the SCR denitrification system based on the historical data set; S3: Using basis functions to represent the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system estimated by S2; S4: Establish a nonlinear prediction model between the input variables and the first n-1 weight vectors to predict the NOx concentration distribution probability density function at the outlet of the SCR denitrification system at the next moment.

2. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 1, characterized in that: In step S1, the historical data set includes: NOx concentration at F different actual points at the outlet of the SCR denitrification system ; As well as the unit load L, the flue gas temperature T at the inlet of the SCR denitrification system, the flue gas flow rate S at the inlet of the SCR denitrification system, the oxygen content O at the inlet of the flue gas of the SCR denitrification system, the NOx concentration B at the inlet of the SCR denitrification system, and the ammonia injection amount of the M partitions of the ammonia injection grid .

3. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 1, characterized in that: The step S2 comprises: S201: Estimate the NOx concentration at N different estimated points at the outlet of the SCR denitration system, where N>F, and obtain the NOx concentration at N different estimated points at the outlet of the SCR denitration system ; S202: Perform kernel density estimation based on the NOx concentrations at N different estimated points at the outlet of the SCR denitration system obtained in step S201 to obtain a probability density function of the NOx concentration distribution at the outlet of the SCR denitration system: in, is the kernel function and h is the bandwidth.

4. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 3, characterized in that: The step S201 includes: Assume that the distance between the i-th estimated point and the j-th actual point is , then the influence weight of each actual point on the estimated point can be obtained according to the Gaussian function of the distance between the estimated point and the actual point. The weight is expressed as: According to the weight, the NOx concentration at the i-th estimation point can be expressed as: in, is the NOx concentration at the jth actual point.

5. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 3, characterized in that: In step S202, the bandwidth is calculated using the following formula. in, To estimate the standard deviation of the data, the kernel function is a Gaussian kernel function, as shown below: in, is the bandwidth smoothing parameter, which affects the shape of the distribution.

6. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 1, characterized in that: The step S3 comprises: S301: Select basis function ; S302: Determine a weighted representation of a basis function. S303: Determine the weight of each basis function according to the NOx concentration distribution probability density function at the outlet of the SCR denitration system and all basis functions.

7. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 6, characterized in that: In step S301, The Gaussian RBF basis function is used as the basis function of the probability density function of the NOx concentration distribution at the outlet of the SCR denitrification system to approximate the root mean square of the output probability density function, and its expression is: Among them, Y is the NOx concentration information at the estimated point, l Indicates l network nodes, n is the total number of network nodes, and Respectively represent l The center value and width of each network node function.

8. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 7, characterized in that: In the step S302, the root mean square probability density function of the NOx concentration distribution at the outlet of the SCR denitration system output at time k is expressed in the form of a weighted sum of basis functions, and the expression is: in, is the basis function vector composed of the first n-1 basis functions, is the weight vector composed of the weights corresponding to the first n-1 basis functions. is the nth basis function, is the weight corresponding to the nth basis function, is the approximation error.

9. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 8, characterized in that: In step S303, the weight vector is determined by the following steps: The nth weight Use weight vector Nonlinear function It is expressed as: in, , , , , ; After neglecting the approximation error, we can get: Multiply both sides on the left , and for both ends in the interval When the matrix When it is non-singular, the weight vector is obtained by inverting the matrix: 。 10. The method for predicting the probability density function of NOx concentration distribution at the outlet of the SCR denitration system according to claim 1, characterized in that: The step S4 comprises: S401: Select input variable and input the current time into the variable , and the weight vector corresponding to the current moment Combined as the comprehensive input of the nonlinear model, record ; S402: Select a random weight neural network for training, randomly select a set of input layer weights and biases within a given range, and use the collected historical data set to train the random weight neural network so that the random weight neural network outputs The actual output The error between them is minimal; S403: Obtaining the optimal output weight by obtaining the generalized inverse of the H matrix; S404: Establishing a nonlinear dynamic mapping relationship between basis function weights and input variables; S405: Predict the NOx concentration distribution PDF at the outlet of the SCR denitration system at the next moment.

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