Soft-sensing modeling method for NOx emission of coal-fired boiler based on gaussian process active learning

Abstract

The application discloses a kind of soft measurement modeling methods of coal-fired boiler NOx emission based on Gaussian process active learning, comprising the following steps: S1, collection boiler operation data and generate sample set, select sample from sample set and construct training set using batch Gaussian process active learning, train the soft measurement model constructed in advance;S2, the NOx emission of a certain sampling time is predicted using the trained soft measurement model, and whether the sampling value and its corresponding sample input is added to the training set is decided according to the prediction variance;S3, if the capacity of training set does not exceed the preset value, the soft measurement model is retrained using training set;S4, further reduce the scale of training set using batch Gaussian process active learning, retrain the soft measurement model.The soft measurement modeling method of coal-fired boiler NOx emission based on Gaussian process active learning of the application can effectively reduce the calculation burden in modeling process and overcome the overfitting problem of soft measurement model.

Description

Technical Field

[0001] This invention relates to a soft measurement modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning, belonging to the field of soft measurement technology for coal-fired boilers. Background Technology

[0002] In recent years, under the backdrop of my country's deepening efforts in energy conservation and emission reduction, reducing exhaust emissions has become an urgent task for major thermal power plants. Statistics show that by the end of 2020, thermal power capacity accounted for approximately 56.6% of my country's total installed capacity, holding a dominant position. NOx and SO2 produced by coal-fired boilers are major sources of air pollution, causing serious harm to the ecological environment. NOx, a collective term for nitrogen oxides, is typically produced during the combustion of coal-fired boilers; excessive emissions can cause smog, acid rain, and tropospheric ozone pollution. Therefore, national environmental protection departments have increasingly stringent requirements for NOx emissions from thermal power plants, with the current emission standard being 50 mg / m³. 3 The generation of NOx depends on the combustion process, meaning that optimizing the combustion process can reduce the NOx content in emissions. Currently, NOx emission concentration detection mainly relies on continuous emission monitoring systems (CEMS). However, CEMS operates in harsh environments, requires regular cleaning, is prone to malfunction, and cannot predict future NOx emission concentrations. Therefore, exploring soft measurement models for NOx emissions can not only improve detection stability without increasing hardware costs but also predict future trends in NOx emission concentrations, thereby enabling real-time combustion optimization of coal-fired boilers when combined with optimization algorithms.

[0003] With the development of industrial data science, soft sensing technology is often used to infer or estimate important variables in industrial processes that are difficult or impossible to measure in real time, thereby improving the real-time performance and reliability of engineering process control. Soft sensing technology can use easily measurable input variables from coal-fired boilers to build models, providing a software solution for NOx emission prediction. Currently, data-driven algorithms such as neural networks, core vector machines, extreme learning machines, and support vector machines are widely used in soft sensing modeling of NOx emissions from coal-fired boilers. Existing soft sensing modeling methods for NOx emissions focus on using various machine learning techniques to improve the accuracy of soft sensing models, such as introducing dynamic error correction and using GRU recurrent neural networks suitable for time series modeling. Compared to the improved model accuracy brought by the above modeling strategies, improving the quality of the training set samples and determining an appropriate sample size can further improve the model's generalization ability, thereby leading to improved model accuracy. Extensive research revealed the following problems with existing soft sensing methods for NOx emissions from coal-fired boilers: Firstly, current soft sensing modeling lacks a sample selection strategy to improve the quality of the training set and determine an appropriate sample size, instead blindly using all historical operating data to construct the soft sensing model, leading to overfitting or underfitting. Secondly, existing soft sensing models can only provide estimates of NOx emissions from coal-fired boilers, without indicating the reliability of the results, making it difficult to provide reasonable suggestions for optimizing the operating parameters of coal-fired boilers. Thirdly, existing soft sensing modeling uses static models to predict NOx emissions, making it impossible to further optimize and adjust the soft sensing model based on samples with low prediction reliability. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a soft measurement modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning, which can effectively overcome the overfitting problem of soft measurement models, and also provide reliability detection of prediction results, optimization and adjustment of soft measurement models, and soft measurement model reconstruction schemes.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0006] A soft-sensor modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning includes the following steps:

[0007] S1. Collect boiler operation data and generate a sample set. Then, use batch Gaussian process active learning to select samples from the sample set to build a training set. Then, use the training set to train the pre-built NOx emission soft measurement model to obtain the trained NOx emission soft measurement model.

[0008] S2. Use the trained NOx emission soft measurement model to predict the NOx emission at a certain sampling time. If the prediction variance is less than the preset value, it means that the prediction result is highly reliable. Use the sampled value of NOx emission at this time and its corresponding sample to guide the optimization of the operating parameters of the coal-fired boiler. Otherwise, add the sampled value of NOx emission at this time and its corresponding sample to the training set and jump to S3.

[0009] S3. If the training set size does not exceed the preset value, retrain the NOx emission soft measurement model using the training set and jump to S2. If the training set size exceeds the preset value, jump to S4.

[0010] S4 employs batch Gaussian process active learning to further reduce the size of the training set, and then uses the reduced training set to retrain the NOx emission soft measurement model.

[0011] S1 specifically includes the following steps:

[0012] S11. Based on the given NOx sampling period T, m input variables related to NOx emission concentration (denoted as y). and their corresponding delays With order Collect historical operating data of coal-fired boilers and generate a sample set. Where x(kT)∈R d×1 Let y(kT)∈R be the sample input and sample output at sampling time kT, respectively, and R denote the real number field. N is the number of samples;

[0013] The dynamic model for NOx emission concentration is described as follows:

[0014]

[0015] In the formula, f(·) represents the objective function, and i m ∈{i∈Z|d m ≤i≤o m};

[0016] S12. Divide the sample set D into a training set D. L Test set D T With candidate set D U Three parts;

[0017] S13, Based on training set D L A soft measurement model for NOx emissions was established using k-fold cross-validation.

[0018] S14. Based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the NOx emission soft measurement model. The specific process is as follows: According to formula (2), from the candidate set DU Choose n in sequence u One sample, i.e. Add to the training set and retrain the NOx emission soft measurement model using k-fold cross-validation:

[0019]

[0020] In formula (2), i∈{1,2,…,n u} represents the selected i-th sample input, S U It is a set consisting of sample inputs from the candidate set. Performance metrics for actively selecting training samples for batch Gaussian processes. The variance representing the noise present in the training sample set is obtained from the NOx emission soft measurement model, X. u This represents the matrix composed of the selected sample inputs and the training sample inputs;

[0021] S15. Repeat S14 until the error of the NOx emission soft measurement model on the test set reaches its minimum. The NOx emission soft measurement model at this point is the final NOx emission soft measurement model.

[0022] The NOx emission soft measurement model, derived from the model, can predict the current sampling time d as early as possible. * NOx emission concentration after T, where d * The minimum value of a given delay, i.e. Based on the NOx emission soft measurement model, the predicted result y of a sample input x follows the normal distribution:

[0023] y|x,X,y~N(μ(x),σ 2 (x)) (3)

[0024] In formula (3), It is a matrix composed of sample inputs from the training set. It is a column vector composed of sample outputs from the training set, where μ(x) represents the predicted mean of the sample input x, and its specific expression is: σ 2 (x) represents the prediction variance of the sample input x, and its specific expression is: k(·,·) denotes the covariance function; k represents the column vector of the covariance function between X and x, K represents the covariance function matrix of X, and I represents the identity matrix of the same order as the covariance matrix K.

[0025] Performance metrics of batch Gaussian process active learning for selecting training samples The calculation formula is:

[0026]

[0027] Where k(·,·) represents the covariance function, whose hyperparameters are obtained from the NOx emission soft measurement model, k u X represents u The column vector of the covariance function between x and x, K u X represents u The covariance function matrix.

[0028] S2 specifically includes the following steps:

[0029] S21. Based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct (k... * +d * The sample input x corresponding to sampling time T * , where k * T represents the current sampling time;

[0030] S22. Predict NOx emissions using the final obtained soft-measurement model (k) * +d * The NOx emission concentration at sampling time T, and its prediction variance σ 2 (x * Take the following steps:

[0031] If σ 2 (x * If the result satisfies formula (5), it indicates that the prediction result has a high degree of reliability.

[0032] If σ 2 (x * If the NOx emission sample value at this moment and its corresponding sample input satisfy formula (6), add them to the training set and jump to S3;

[0033]

[0034]

[0035] Among them, S T It is the test set D T The set of sample inputs, σ 2 (x) is the prediction variance of the sample input x, and α is the adjustment parameter.

[0036] S3 specifically includes the following steps:

[0037] If the training set size does not exceed 2N L , where N LIf the number of training set samples is the number after S1, the soft sensor model is retrained using the training set and the process jumps to S2; otherwise, the process jumps to S4 to rebuild the soft sensor model.

[0038] S4 specifically includes the following steps:

[0039] S41. Divide the training set of the current NOx emission soft measurement model into training set D. L ′ and candidate set D U ′;

[0040] S42. Based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct a sample set from all the collected operational data. and from set D′-D L Randomly select test set D from ' T ′, test set D T The sample size and the test set D in S12 T The sample size is the same;

[0041] S43, Based on training set D L A soft measurement model for NOx emissions was established using k-fold cross-validation.

[0042] S44. Based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the soft measurement model. The specific process is as follows: According to formula (2), from the candidate set D U Choose n in sequence from ' u One sample was added to the training set, and the NOx emission soft measurement model was retrained using k-fold cross-validation.

[0043] S45. Repeat S44 until the error of the soft measurement model on the test set is minimized. The Gaussian regression model at this point is the final soft measurement model.

[0044] The beneficial effects of this invention are as follows: This invention provides a soft-sensing modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning. By organically combining Gaussian processes and active learning, it aims to reduce the computational burden in the modeling process and improve the predictive performance of the soft-sensing model. Benefiting from the sample selection capability of batch Gaussian process active learning, a set of the most informative samples can be selected as the training set. This not only effectively avoids overfitting or underfitting of the soft-sensing model but also solves the problem of excessive computational burden caused by a large amount of training data in Gaussian processes. Thanks to the prediction distribution provided by the Gaussian model (which is jointly determined by the prediction mean and prediction variance), the predicted value of NOx emissions from coal-fired boilers can be obtained from the prediction mean, while the prediction variance can be used to measure the reliability of the prediction value, thereby achieving reliability detection of the prediction results. Based on the reliability monitoring of the prediction results, this invention can adjust boiler operating parameters based on predictions with higher reliability or further optimize the soft-sensing model using samples with lower prediction reliability. Furthermore, as the predicted NOx emission concentration under coal-fired boiler operating conditions increases, the size of the training set will gradually increase, which will affect the generalization ability of the soft-sensing model. Therefore, when the training set size reaches a certain level, batch Gaussian process active learning can be used to further reduce the training set size and reconstruct the soft sensor model, so as to reduce the computational burden in the modeling process and avoid overfitting of the soft sensor model. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the main process of a soft measurement modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning provided in an embodiment of the present invention;

[0046] Figure 2 This is the iterative error diagram of the active learning of the batch Gaussian process in this invention;

[0047] Figure 3 This is a diagram illustrating the prediction results based on the soft measurement model of this invention. Detailed Implementation

[0048] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present invention more clearly, and should not be used to limit the scope of protection of the present invention. Specific Implementation Example 1

[0050] like Figure 1As shown, this invention discloses a soft-sensor modeling and real-time prediction method for NOx emissions from coal-fired boilers. By organically combining Gaussian processes and active learning, it aims to reduce the computational burden during modeling and improve the predictive performance of the soft-sensor model. Benefiting from the sample selection capability of batch Gaussian process active learning, a set of the most informative samples can be selected as the training set. This not only effectively avoids overfitting or underfitting of the soft-sensor model but also solves the problem of excessive computational burden caused by a large amount of training data in Gaussian processes. Thanks to the prediction distribution provided by the Gaussian model (which is jointly determined by the prediction mean and prediction variance), the predicted value of NOx emissions from coal-fired boilers can be obtained from the prediction mean, while the prediction variance can be used to measure the reliability of the predicted value, thereby enabling the reliability detection of the prediction results.

[0051] The present invention specifically includes the following steps:

[0052] Step one involves collecting boiler operation data and generating a sample set. Then, batch Gaussian process active learning is used to select samples from this set to construct a training set. This training set is then used to train the pre-built NOx emission soft measurement model, resulting in a trained NOx emission soft measurement model. The specific steps of step one are as follows:

[0053] S11, based on the given NOx sampling period T and the input variables related to the NOx emission concentration (denoted as y). and their corresponding delays With order Collect historical operating data of coal-fired boilers and generate a sample set. in Let y(kT)∈R be the sample input and sample output at sampling time kT, respectively, and N be the number of samples. The dynamic model of NOx emission concentration is described as follows:

[0054]

[0055] In formula (1), f(·) represents the objective function.

[0056] S12, divide the sample set D into a training set (denoted as D). L There are 20 samples in total), and the test set (denoted as D) T , which has N T (N samples, approximately 0.3N) and the candidate set (denoted as D) U , which has N U The sample consists of three parts (approximately 0.7N).

[0057] S13, based on training set D L A Gaussian regression model (i.e., a soft measurement model for NOx emissions) was established using k-fold cross-validation.

[0058] S14, based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the soft measurement model. The specific process is as follows: According to formula (2), from the candidate set D U Twenty samples were selected sequentially and added to the training set, and the soft measurement model was retrained using k-fold cross-validation.

[0059]

[0060] In formula (2), S U It is a set consisting of sample inputs to the candidate set; This represents the i-th selected sample input; Performance metrics for actively selecting training samples for batch Gaussian processes; The variance representing the presence of noise in the training sample set can be obtained from the soft sensor model; X u This indicates the selected sample input (i.e. The matrix consisting of the training sample inputs.

[0061] The performance metrics of the training samples are as follows:

[0062]

[0063] In formula (3), k(·,·) represents the covariance function, whose hyperparameters can be obtained from the soft measurement model; k u X represents u The column vector of the covariance function between x and k; K u X represents u The covariance function matrix.

[0064] S15, repeat S14 until the error of the soft sensor model on the test set is minimized. The Gaussian regression model at this point is the final soft sensor model. Let N be the number of training set samples at this point. L According to the soft measurement model, the earliest prediction possible is the current sampling time d. * NOx emission concentration after T, where d * The minimum value of a given delay (i.e. Based on the soft sensor model, the predicted result y of a sample input x follows a normal distribution:

[0065] y|x,X,y~N(μ(x),σ 2 (x)) (4)

[0066] In formula (4), It is a matrix composed of sample inputs from the training set; It is a column vector composed of the sample outputs of the training set; μ(x) represents the predicted mean of the sample input x, and its specific expression is: σ 2 (x) represents the prediction variance of the sample input x, and its specific expression is: k(·,·) denotes the covariance function; k represents the column vector of the covariance functions between X and x; K represents the covariance function matrix of X.

[0067] Step two involves using the NOx emission soft measurement model trained in Step one to predict NOx emissions at a specific sampling time. If the prediction variance is less than a preset value, the prediction result is considered to have high reliability. Otherwise, the sampled NOx emission value at this time and its corresponding sample input are added to the training set, and the process proceeds to Step three. The specific steps of Step two are as follows:

[0068] S21, based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct (k * +d * The sample input x corresponding to sampling time T * , where k * T represents the current sampling time;

[0069] S22, using a soft measurement model to predict (k * +d * The NOx emission concentration at sampling time T, and its prediction variance (σ) 2 (x * Take the following steps:

[0070] If σ 2 (x * If the result satisfies formula (5), it indicates that the prediction result has a high degree of reliability.

[0071] If σ 2 (x * If the NOx emission sample value at this moment satisfies formula (6), add it to the training set along with its corresponding sample input, and then proceed to step three:

[0072]

[0073]

[0074] In formulas (5) and (6), S T It is the test set D T The set of sample inputs; σ 2 (x) is the prediction variance of the sample input x; α is the adjustment parameter. Choosing an appropriate adjustment parameter can enable the soft measurement model to obtain better prediction performance. In this embodiment, its value is 0.6.

[0075] Step 3: If the training set size does not exceed the preset value (2N), then... L Retrain the NOx emission soft measurement model using the training set and proceed to step two. If the training set size exceeds the preset value, proceed to step four.

[0076] Step four involves further reducing the training set size using batch Gaussian process active learning, and then retraining the NOx emission soft measurement model using the reduced training set. The specific steps of step four are as follows:

[0077] S41. Divide the training set of the current NOx emission soft measurement model into training set D. L ′ and candidate set D U ′;

[0078] S42. Based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct a sample set from all the collected operational data. and from set D′-D L Randomly select test set D from ' T ′, test set D T The sample size and the test set D in S12 T The sample size is the same;

[0079] S43, Based on training set D L A soft measurement model for NOx emissions was established using k-fold cross-validation.

[0080] S44. Based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the soft measurement model. The specific process is as follows: According to formula (2), from the candidate set D U Choose n in sequence from ' u One sample was added to the training set, and the NOx emission soft measurement model was retrained using k-fold cross-validation.

[0081] S45. Repeat S44 until the error of the soft measurement model on the test set is minimized. The Gaussian regression model at this point is the final soft measurement model. Specific Implementation Example 2

[0083] This embodiment, based on Specific Embodiment 1, takes a 600MW subcritical coal-fired boiler generator unit in a power plant as an example. The dataset consists of operating data of the coal-fired boiler collected by the power plant's DCS system in August 2018, with a sampling period of 60 seconds. After data preprocessing, a total of 32,549 data points were obtained. Based on the NOx generation mechanism and suggestions from power plant staff, the following variables were determined as input variables, including: total coal quantity, furnace negative pressure, furnace load, furnace oxygen content, total furnace air volume, and primary air volume of the coal mill (P). A P B， P C， P D Secondary air volume of coal mill (S) AB S BA S BC S CA S CB S CC There are 15 variables in total. The time delay relationship of the above input variables is shown in Table 1. In this embodiment, historical operating data within 72 hours (a total of 4320 samples) is used to construct a soft measurement model and make real-time predictions of NOx emissions for the next 24 hours.

[0084] Table 1. Distribution of Time Delay and Order

[0085]

[0086]

[0087] like Figure 2 As shown, when the training set size N t The generalization performance of the soft sensor model reaches its optimal level when the value reaches 540. Subsequently, based on the aforementioned soft sensor model and using the prediction scheme provided by this invention, real-time predictions of NOx emissions for the next 24 hours are made, and the prediction results are as follows: Figure 3 As shown, the prediction error (root mean square error) of the soft sensor model trained using all data is calculated to be 3.99; the prediction error (root mean square error) of the soft sensor model built using batch Gaussian process active learning is 3.48; and the prediction error (root mean square error) of using batch Gaussian process active learning combined with real-time operational prediction is 2.91. Based on the above analysis, it can be seen that compared to traditional soft sensor modeling methods, batch Gaussian process active learning can select a set of the most informative samples as the training set, effectively avoiding overfitting or underfitting of the soft sensor model. Furthermore, the solution provided by this invention can achieve real-time prediction of NOx emissions from coal-fired boilers and continuous optimization of the soft sensor model. Through accurate prediction of NOx emissions, real-time optimization of operating parameters can be achieved, thereby reducing air pollutant emissions.

[0088] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A soft-sensor modeling method for NOx emissions from coal-fired boilers based on Gaussian process active learning, characterized in that: Includes the following steps: S1. Collect boiler operation data and generate a sample set. Then, use batch Gaussian process active learning to select samples from the sample set to build a training set. Then, use the training set to train the pre-built NOx emission soft measurement model to obtain the trained NOx emission soft measurement model. S2: Use the trained NOx emission soft measurement model to predict the NOx emission at a certain sampling time. If the prediction variance is less than the preset value, it means that the prediction result is highly reliable. Otherwise, add the sampled value of the NOx emission at this time and its corresponding sample input to the training set, and jump to S3. S3. If the training set size does not exceed the preset value, retrain the NOx emission soft measurement model using the training set and jump to S2. If the training set size exceeds the preset value, jump to S4. S4 employs batch Gaussian process active learning to further reduce the size of the training set, and then uses the reduced training set to retrain the NOx emission soft measurement model.

2. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 1, characterized in that: S1 specifically includes the following steps: S11. Based on the given NOx sampling period T and m input variables related to NOx emission concentration. and their corresponding delays With order Collect historical operating data of coal-fired boilers and generate a sample set. Where x(kT)∈R d×1 Let y(kT)∈R be the sample input and sample output at sampling time kT, respectively, and R denote the real number field. N is the number of samples; The dynamic model for NOx emission concentration is described as follows: In formula (1), f(·) represents the objective function, i m ∈{i∈Z|d m ≤i≤o m }; S12. Divide the sample set D into a training set D. L Test set D T With candidate set D U Three parts; S13, Based on training set D L A soft measurement model for NOx emissions was established using k-fold cross-validation. S14. Based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the NOx emission soft measurement model. The specific process is as follows: According to formula (2), from the candidate set D U Choose n in sequence u One sample, i.e. Add to the training set and retrain the NOx emission soft measurement model using k-fold cross-validation: In formula (2), S represents the selected i-th sample input. U It is a set consisting of sample inputs from the candidate set. Performance metrics for actively selecting training samples for batch Gaussian processes. The variance representing the noise present in the training sample set is obtained from the NOx emission soft measurement model, X. u This represents the matrix composed of the selected sample inputs and the training sample inputs; S15. Repeat S14 until the error of the NOx emission soft measurement model on the test set reaches its minimum. The NOx emission soft measurement model at this point is the final NOx emission soft measurement model.

3. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 2, characterized in that: The NOx emission soft measurement model, derived from the model, can predict the current sampling time d as early as possible. * NOx emission concentration after T, where d * The minimum value of a given delay, i.e. Based on the NOx emission soft measurement model, the predicted result y of a sample input x follows the normal distribution: y|x,X,y~N(μ(x),σ 2 (x))(3) In formula (3), It is a matrix composed of sample inputs from the training set. It is a column vector composed of sample outputs from the training set, where μ(x) represents the predicted mean of the sample input x, and its specific expression is: σ 2 (x) represents the prediction variance of the sample input x, and its specific expression is: k(·,·) denotes the covariance function; k represents the column vector of the covariance function between X and x, K represents the covariance function matrix of X, and I represents the identity matrix of the same order as the covariance matrix K.

4. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 3, characterized in that: Performance metrics of batch Gaussian process active learning for selecting training samples The calculation formula is: Where k(·,·) represents the covariance function, whose hyperparameters are obtained from the NOx emission soft measurement model, k u X represents u The column vector of the covariance function between x and x, K u X represents u The covariance function matrix.

5. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 3, characterized in that: S2 specifically includes the following steps: S21. Based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct (k... * +d * The sample input x corresponding to sampling time T * , where k * T represents the current sampling time; S22. Predict NOx emissions using the final obtained soft-measurement model (k) * +d * The NOx emission concentration at sampling time T, and its prediction variance σ 2 (x * Take the following steps: If σ 2 (x * If the result satisfies formula (5), it indicates that the prediction result has a high degree of reliability. If σ 2 (x * If the NOx emission sample value at this moment and its corresponding sample input satisfy formula (6), add them to the training set and jump to S3; Among them, S T It is the test set D T The set of sample inputs, σ 2 (x) is the prediction variance of the sample input x, and α is the adjustment parameter.

6. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 5, characterized in that: S3 specifically includes the following steps: If the training set size does not exceed 2N L , where N L If the number of training set samples is the number after S1, the soft sensor model is retrained using the training set and the process jumps to S2; otherwise, the process jumps to S4 to rebuild the soft sensor model.

7. The method for soft-sensor modeling of NOx emissions from coal-fired boilers based on Gaussian process active learning according to claim 6, characterized in that: S4 specifically includes the following steps: S41. Divide the training set of the current NOx emission soft measurement model into training set D. L ′ and candidate set D U ′; S42. Based on the given NOx sampling period, the input variables related to NOx emission concentration, and their corresponding time delays and orders, construct a sample set from all the collected operational data. and from set D′-D L Randomly select test set D from ' T ′, test set D T The sample size and the test set D in S12 T The sample size is the same; S43, Based on training set D L A soft measurement model for NOx emissions was established using k-fold cross-validation. S44. Based on the NOx emission soft measurement model, a batch Gaussian process is used to actively learn and select a batch of samples to update the soft measurement model. The specific process is as follows: According to formula (2), from the candidate set D U Choose n in sequence from ' u One sample was added to the training set, and the NOx emission soft measurement model was retrained using k-fold cross-validation. S45. Repeat S44 until the error of the soft measurement model on the test set is minimized. The Gaussian regression model at this point is the final soft measurement model.

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