Incremental modeling method for boiler combustion system based on variational mode decomposition algorithm
By employing variational mode decomposition algorithm and incremental modeling method based on multi-kernel learning, the problems of decreased model prediction accuracy and insufficient generalization ability in boiler combustion system modeling were solved. This enabled accurate prediction of boiler efficiency, NOx emissions, and reheat steam temperature, thereby improving the model's learning efficiency and reliability.
Patent Information
- Application Number
- CN202210990704.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-18
- Publication Date
- 2025-10-24
- Estimated Expiration
- 2042-08-18
AI Technical Summary
Existing boiler combustion system modeling methods suffer from decreased prediction accuracy, lack of self-learning ability, and insufficient generalization ability and multi-step prediction accuracy when faced with changes in coal quality or unit load.
An incremental modeling method based on variational mode decomposition algorithm is adopted, combined with multi-kernel learning and particle swarm optimization algorithm with adaptive inertia weight. The dynamic correspondence between input and output features is optimized through time delay analysis and variational mode decomposition to establish a multi-kernel least squares support vector machine model, and an online update strategy is used to optimize the model parameters.
This improved the accuracy of predicting boiler efficiency, NOx emissions, and reheat steam temperature trends over a future period, as well as the model's learning efficiency. It also enhanced the model's local fitting performance and global generalization ability, ensuring the model's reliability.
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Figure CN115495975B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of thermal automatic control, and particularly relates to a boiler combustion system incremental modeling method based on a variational mode decomposition algorithm. BACKGROUND
[0002] The boiler combustion system is a complex high-dimensional input-output dynamic system, and also has characteristics such as nonlinearity and large lag. For such an object, the traditional modeling method is too single in consideration, and therefore the traditional modeling method is not suitable for the overall analysis modeling of the boiler combustion system. A model capable of correctly reflecting the dynamic characteristics of the boiler combustion system is the basis for subsequent combustion optimization, and therefore how to establish an accurate and effective boiler combustion system model is a problem to be solved.
[0003] At present, the research on the combustion optimization of coal-fired boilers mostly adopts support vector machine and neural network modeling methods, but the currently widely used modeling methods still have the following problems: firstly, when the model mismatch problem occurs due to the change of coal quality or the change of unit load, the prediction accuracy of the model lacking self-learning ability will continuously decrease, and the reliability of the model cannot be always guaranteed; secondly, the support vectors of the least squares support vector machine model do not have sparsity, resulting in low generalization ability of the model; thirdly, the commonly used modeling methods have good performance in single-step prediction simulation, but the accuracy greatly decreases in multi-step prediction simulation, that is, the model does not learn the correct dynamic corresponding relationship between the input features and the output features. SUMMARY
[0004] The application provides a boiler combustion system incremental modeling method based on a variational mode decomposition algorithm, which can improve the accuracy of predicting the change trend of the boiler efficiency, the NOx emission and the reheat steam temperature of the boiler combustion system in the future period of time.
[0005] Technical scheme: In order to achieve the above object, the application provides a boiler combustion system incremental modeling method based on a variational mode decomposition algorithm, which comprises the following steps:
[0006] S1: selecting the input and output variables of the model, and screening the data through a data preprocessing method;
[0007] S2: according to the corresponding relationship between the input features and the output features, determining the lag time between the input variables and the output variables by using the control variable method and the cross-validation method, and organizing the training samples according to the lag time;
[0008] S3: setting the target decomposition number K of the signal f(t), and obtaining the intrinsic mode function set and the corresponding center frequency set and the Lagrange multiplier and using Fourier transform to convert into frequency domain
[0009] S4: secondary optimization solution is carried out on , and then new modal function and corresponding instantaneous frequency
[0010] S5: step S4 is repeated for all modal functions to update;
[0011] S6: Lagrange multiplier is updated;
[0012] S7: after each optimization, decomposition accuracy is judged, if iteration is terminated, otherwise, it returns to step S4 to repeat iteration until accuracy meets the requirements.
[0013] S8: for the modal signal obtained by decomposition, a new combined kernel function is constructed based on the kernel function weighted linear combination method of multi-core learning, which is constructed by Gaussian kernel function and polynomial kernel function:
[0014] K(x i ,x j )=aK RBF (x i ,x j )+(1-a)K POLY (x i ,x j ) (1)
[0015] Wherein, K RBF (x i ,x j ) represents Gaussian kernel function, K POLY (x i ,x j ) represents polynomial kernel function, a is the kernel function weight coefficient, and the value range is [0, 1];
[0016] S9: the particle swarm optimization algorithm with adaptive inertia weight is used to calculate the optimal kernel parameters and kernel function weight coefficients of each model;
[0017] S10: based on multi-kernel least square support vector machine (MKLSSVM) algorithm, the dynamic model as shown in formula (2) is established, and the prediction value y k of each modal signal model at next time is calculated:
[0018]
[0019] Wherein, α i represents the Lagrange operator corresponding to the sample point, K(x,x i ) is a multi-core function, b is a bias;
[0020] S11: According to the prediction value of the modal signal at the same time, the output feature prediction value at the time is reconstructed:
[0021]
[0022] Wherein, k represents the number of modal signal, m represents the number of modal signal.
[0023] S12: Calculate the deviation between the model prediction value and the measured value at the current time obtained in step S7, and update the model parameters online when the deviation exceeds the threshold, and finally realize accurate prediction of each output feature at future time.
[0024] Further, the input features of the prediction model in step S1 include control variables and state variables, the control variables include the coal supply amount of each layer coal feeder, the opening degree of each layer secondary air damper, the opening degree of combustion air damper and the oxygen amount after economizer, and the state variables include unit operation load and total fuel amount into the furnace; the output variables of the prediction model include boiler efficiency, NOx emission and reheated steam temperature.
[0025] Further, the model cross validation method in step S2 means that the control variable method is used to adjust the lag time of each input feature in turn, and then based on the cross validation method, the original data set is divided into 10 sample sets with the same size, one sample set is taken as the training sample and the other 9 sample sets are taken as the test sample, and finally the lag time corresponding to the minimum root mean square error and average absolute error of the prediction result is taken as the final lag time. After the lag time is determined, the training sample is organized accordingly, for example, the lag time between a certain input variable and an output variable is Td, and the input variable at sampling time t-Td and the output variable at time t are combined to form a training sample.
[0026] Further, in step S3, Transformed into frequency domain The Fourier transform method used at this time can be expressed as:
[0027]
[0028] Wherein, And Correspond to u i Fourier transform of f(t) and λ(t); β is a quadratic penalty term, which is used to ensure the reconstruction accuracy of the signal; λ(t) is a Lagrange multiplier, which is used to maintain the strictness of the constraint condition.
[0029] Further, the quadratic optimization solving method in step S4 is to first let ω k), and then convert it into an integral form on the non-negative interval:
[0030]
[0031] Then solving the quadratic optimization problem can obtain:
[0032]
[0033] Similarly, the solution of the instantaneous frequency can be converted into:
[0034]
[0035] Further, the update formula thereof is:
[0036]
[0037] Further, the updating method of the Lagrange multiplier in the step S6 is:
[0038]
[0039] Further, the model prediction value in the step S10 refers to the prediction value of each modal signal of the output feature obtained by the variational modal decomposition algorithm.
[0040] Further, the model prediction value in the step S11 includes a boiler efficiency prediction value, a NOx emission prediction value and a reheat steam temperature prediction value.
[0041] Further, the online updating method of the model parameter in the step S12 is:
[0042] According to the Mahalanobis distance to judge the similarity between samples and select two groups of samples with the smallest Mahalanobis distance in the original sample set, then replace the group of samples with more recent time series in the two groups of samples with new samples, and the updated decision function coefficient is
[0043]
[0044] Wherein, α=[α1,α2,…,α n ] T is the Lagrange multiplier vector, H1 is a matrix composed of the kernel function and the penalty coefficient of each updated sample point, y is the updated output vector, is a unit column vector.
[0045] The application provides a kind of incremental modeling method of boiler combustion system based on variational modal decomposition algorithm, on the basis of multi-kernel least square support vector machine adaptive algorithm, in combination with input feature incremental optimization method based on time delay analysis and output feature signal decomposition optimization method based on variational modal decomposition algorithm, the data-driven modeling of boiler combustion system is realized, and it is verified that the modeling method can accurately predict the change trend of boiler efficiency, NOx emission and reheat steam temperature of boiler combustion system in future period.
[0046] The method of the application is aimed at boiler combustion system, selects the output features of each layer of the boiler, such as coal supply bias, secondary air damper opening, overfire air damper opening, economizer oxygen content, unit load, total coal supply and past time, as input features of the model, selects boiler efficiency, NOx emission and reheat steam temperature as output features of the model, and establishes corresponding data-driven model based on incremental modeling method of variational modal decomposition algorithm, to realize accurate prediction of the change trend of output features in future period. By introducing input feature incremental optimization method based on time delay analysis and output feature signal decomposition optimization method based on variational modal decomposition algorithm, the dynamic correspondence between input features and output features of the model is determined, and the learning efficiency of the model is improved. In addition, by introducing multi-kernel learning, the mapping ability of the kernel function in the support vector machine algorithm is improved, thus the generalization ability of the prediction model is improved. On the basis of the above, the online updating strategy of model parameters is introduced to ensure the reliability of the model. By using the modeling method, the prediction accuracy of the change trend of boiler efficiency, NOx emission and reheat steam temperature in future period can be effectively improved.
[0047] Advantages: compared with the prior art, first, the dynamic modeling of boiler combustion system is realized based on online least square support vector machine and multi-kernel learning, and the particle swarm optimization algorithm with adaptive inertia weight is used to select the optimal kernel function weight coefficient and related kernel parameters, so that the model has better local fitting performance and global generalization ability; second, the dynamic correspondence between input features and output features of the model is determined by combining input feature incremental optimization method based on time delay analysis and output feature signal decomposition optimization method based on variational modal decomposition algorithm, and the learning efficiency of the model is improved, finally the prediction accuracy of the model is effectively improved. BRIEF DESCRIPTION OF DRAWINGS
[0048] Figure 1 It is a schematic diagram of the basic framework of the prediction model of the application;
[0049] Figure 2 It is a single-step prediction performance test diagram of the boiler efficiency prediction model in the specific embodiment of the application;
[0050] Figure 3The single-step prediction performance test chart of the NOx emission prediction model in the embodiment of the present application;
[0051] Figure 4 The multi-step prediction performance test chart of the NOx emission prediction model in the embodiment of the present application;
[0052] Figure 5 The multi-step prediction performance test chart of the NOx emission prediction model in the embodiment of the present application;
[0053] Figure 6 The multi-step prediction performance test chart of the NOx emission prediction model in the embodiment of the present application;
[0054] Figure 7 The multi-step prediction performance test chart of the NOx emission prediction model in the embodiment of the present application. DETAILED DESCRIPTION
[0055] The present application will be further illustrated below in conjunction with the accompanying drawings and specific embodiments, which should be understood as merely illustrating the present application and not limiting the scope of the present application, and after reading the present application, those skilled in the art can make various equivalent modifications to the present application, which all fall within the scope defined by the appended claims of the present application.
[0056] The present application provides a kind of incremental modeling method of boiler combustion system based on variational mode decomposition algorithm, this method is applied to boiler combustion system in the embodiment, such as Figure 1 The basic architecture of the model implementation is given, referring to Figure 1 The specific implementation process of the method is as follows:
[0057] 1) Select the input and output of the prediction model, and perform data preprocessing.
[0058] In the embodiment, based on boiler combustion system, select each layer coal feeder coal supply, each layer secondary air damper opening, combustion air damper opening and oxygen after economizer, a total of 8 control quantities and unit operation load, total fuel into the furnace, a total of 2 state quantities as the input variables of the prediction model, select the boiler efficiency, NOx emission and reheat steam temperature as the output variables of the model, simultaneously introduce the output variables of the previous two time as part of the model input variables, and then establish a dynamic model. After selecting the required data, remove the obviously abnormal data points.
[0059] 2) According to the corresponding relationship between the input characteristics and the output characteristics, the control variable method and the cross-validation method are used to determine the lag time between the input characteristics and the output characteristics.
[0060] In the embodiment, firstly, for each input variable, the time interval of the constructed increment is changed in the interval range of [0, 400s] with a step of 20s, and a total of 20 rounds of ten-fold cross-validation simulation is completed, 500 groups of training samples and 4500 groups of test samples per round. The lag time is determined according to the optimal model performance in the interval range of [0, 400s]. Finally, in the boiler efficiency model, the lag time of the coal feeder coal supply amount is 100s, the lag time of the secondary air damper opening degree is 180s, the lag time of the burnout air damper opening degree is 100s, the lag time of the oxygen content after the economizer is 20s, and the lag time of the total fuel amount into the furnace is 100s; in the NOx emission model, the lag time of the coal feeder coal supply amount is 100s, the lag time of the secondary air damper opening degree is 160s, the lag time of the burnout air damper opening degree is 120s, the lag time of the oxygen content after the economizer is 20s, and the lag time of the total fuel amount into the furnace is 100s; in the reheat steam temperature model, the lag time of the coal feeder coal supply amount is 80s, the lag time of the secondary air damper opening degree is 100s, the lag time of the burnout air damper opening degree is 80s, the lag time of the oxygen content after the economizer is 20s, and the lag time of the total fuel amount into the furnace is 80s.
[0061] 3) Set the target decomposition number K of the signal f(t), and obtain the intrinsic mode function set and the corresponding center frequency set and the Lagrange multiplier and use Fourier transform to convert to the frequency domain
[0062] 4) Solve the quadratic optimization of , and further obtain the new modal function and the corresponding instantaneous frequency
[0063] 5) Repeat step 2) update for all modal functions.
[0064]
[0065] iteration, otherwise return to step S4 and repeat the iteration until the accuracy meets the requirements.
[0066] In this example, the quadratic penalty coefficient is fixed at 1000, and the initial range of the modal signal number is [2, 6]. Iterations are performed sequentially, and the Pearson correlation coefficient between each decomposed modal signal and the original signal is calculated for verification. If the correlation coefficient is less than 0.1, the modal signal is determined to be a false signal or noise signal, and the number of modal signals is excessive. Based on the assumption that no false signals or noise signals are present, the number of signals corresponding to the minimum signal reconstruction error is selected as the modal signal number. That is, the optimal number of modal signals K for NOx emissions, reheat steam temperature, and boiler efficiency is 5, 5, and 3, respectively.
[0067] 8) Construct a multi-kernel function and use the particle swarm optimization algorithm with adaptive inertia weight to calculate the optimal kernel parameters and kernel function weight coefficients of each model.
[0068] Based on the weighted linear combination of Gaussian kernel function and polynomial kernel function, the new multi-kernel function is K(x i ,x j )=aK RBF (x i ,x j )+(1-a)K POLY (x i ,x j ). Among them, K RBF (x i ,x j ) represents the Gaussian kernel function, K POLY (x i ,x j ) represents the polynomial kernel function, a is the kernel function weight coefficient, and its value range is [0,1].
[0069] An adaptive inertia weight particle swarm optimization (AIWPSO) algorithm is used to select the optimal kernel parameters and kernel function weight coefficients. In this embodiment, the related parameters in the AIWPSO algorithm are set as follows: the number of particles is 20, the maximum iteration coefficient is 10, the value range of the learning factor is [0.5, 0.9], the value range of the inertia weight is [0.5, 0.9], the selected range of the kernel parameter σ of the Gaussian kernel function is [0, 2], the selected range of the penalty coefficient C is [100, 2000], and the selected range of the kernel function weight coefficient a is [0, 1]. After calculation, the optimal multi-kernel coefficients of the kernel function of the boiler efficiency modal signal model are 0.9443, 0.2079, and 0.0762, the optimal Gaussian kernel parameters are 1.5196, 1.2840, and 0.1032, and the optimal penalty coefficients are 161.4376, 1605.0980, and 467.1010, respectively. The optimal multi-kernel coefficients of the kernel function of the NOx emission modal signal model are 0.7469, 0.1012, 0.0514, 0.3286, and 0.4431, the optimal Gaussian kernel parameters are 1.4903, 1.2106, 1.4499, 0.0437, and 1.4358, and the optimal penalty coefficients are 1328.3533, 1173.9502, 1506.8085, 709.5959, and 0197.2247, respectively. The optimal multi-kernel coefficients of the kernel function of the reheated steam temperature modal signal model are 0.8852, 0.6224, 0.9542, 0.0553, and 0.3320, the optimal Gaussian kernel parameters are 1.7688, 0.2410, 1.3044, 0.0036, and 1.9198, and the optimal penalty coefficients are 774.5633, 637.3962, 1173.4926, 1584.0753, and 1501.5028, respectively.
[0070] 9) Establishing a prediction model.
[0071] According to The boiler efficiency, NOx emission, and reheated steam temperature modal signal prediction models based on the multi-kernel least squares support vector machine (MKLSSVM) are respectively established, where α i represents the Lagrange operator corresponding to the sample point, K(x, x i ) is a multi-kernel function, and b is a bias. After the modal signal prediction values are reconstructed, the prediction values of the corresponding boiler efficiency, NOx emission, and reheated steam temperature can be obtained.
[0072] In this embodiment, the prediction bias thresholds of the boiler efficiency, NOx emission, and reheated steam temperature models are respectively set as ±0.01%, ±3 mg / m 3and ±0.5°C. When the model's prediction deviation exceeds the threshold, the model parameters are updated online to ensure model prediction accuracy. The similarity between samples is determined based on the Mahalanobis distance. The two groups of samples with the smallest Mahalanobis distance are selected from the original sample set. The new sample is then used to replace the sample with the one with the earlier time series. The decision function coefficients α and b are then recalculated.
[0073] Based on the above scheme, in order to verify the effectiveness of the method of the present invention, a simulation test was carried out and the following results were obtained: Figures 2 to 4 The following graph compares the prediction performance of the model obtained using the incremental modeling method based on the variational mode decomposition algorithm, the full modeling method based on the least squares support vector machine adaptive model, and the incremental modeling method. It shows that for the NOx emissions prediction model, incremental input feature optimization alone cannot completely solve the "shift" problem of the predicted values. The incremental prediction models for reheat steam temperature and boiler efficiency also have room for improvement in terms of accuracy. After introducing a signal processing method based on the output features of variational mode decomposition, the curve comparison clearly shows that the predicted NOx emissions curve remains largely consistent with the actual value, with no significant lag, indicating that this problem has been effectively solved. The prediction accuracy of the reheat steam temperature and boiler efficiency models has also been significantly improved. The mean absolute error and root mean square error (RMSE), two metrics used to evaluate the model's single-step prediction performance, were significantly reduced. Compared to the full modeling method, the prediction accuracy of the NOx emissions, reheat steam temperature, and boiler efficiency models increased by approximately 67.83%, 86.33%, and 70.83%, respectively. Therefore, combining the incremental optimization method of model input features based on time-lag analysis and the output feature signal processing method based on variational mode decomposition can reduce data complexity, clarify the relationship between input features and output features, and thus solve the problem of low model training efficiency and effectively improve the reliability of model prediction results.
[0074] In this embodiment, a combination of single-step prediction and multi-step iteration is used to achieve multi-step prediction. The multi-step prediction step length P is set to 10, that is, the change trend of the output characteristics within the next 200 seconds is predicted. Figures 5 to 7The prediction performance comparison chart between the model obtained by the incremental modeling method of the present application based on the variational mode decomposition algorithm and the model obtained by the full modeling method of the least squares support vector machine adaptive model. It can be seen that the full prediction model is prone to prediction results with opposite trends when multi-step prediction is performed. Taking the continuous 10-step results of sample numbers 41-50 in the local magnified chart as an example, the full prediction model is completely opposite to the actual situation in predicting the change trend of the NOx emission amount in the next 10 steps, while the incremental prediction model based on the variational mode decomposition always maintains relatively good prediction effect in the test sample set. Similarly, the full model of the reheat steam temperature and the boiler efficiency will all have prediction trend errors in multi-step prediction, and the incremental model based on the variational mode decomposition algorithm has better performance.
[0075] The above results all prove that the incremental modeling method of the boiler combustion system based on the variational mode decomposition algorithm of the present application can establish an accurate data-driven model and accurately predict the change trend of the boiler efficiency, the NOx emission amount and the reheat steam temperature in the future period of time.
Claims
1. A method for incremental modeling of a boiler combustion system based on a variational modality decomposition algorithm, characterized in that, The method comprises the following steps: S1: selecting the coal feeder amount of each layer, the secondary air door opening degree of each layer, the combustion air door opening degree, the oxygen amount after the economizer, the load and the total fuel amount as the input variables of the prediction model, and selecting the boiler efficiency, the NOx emission amount and the reheat steam temperature as the output variables of the model; S2: according to the corresponding relationship between the input variables and the output variables, the lag time between the input variables and the output variables is determined by using the control variable method and the cross-validation method, and the training samples are organized according to the lag time; S3: Let f(t) represent a certain model output signal, i.e. boiler efficiency, NOx emission or reheat steam temperature signal, set the target decomposition number of f(t) as K, and get the intrinsic mode function set according to the decomposition number K and the corresponding center frequency set and the Lagrange multiplier set {λ 1 (t)}; convert to the frequency domain using Fourier transform ω represents the signal frequency; S4: solving the quadratic optimization problem to obtain the new modal function and the corresponding instantaneous frequency n is the iteration number; S5: repeating step S4 for updating all modal functions; S6: updating the Lagrange multiplier; S7: After each optimization, the decomposition accuracy is judged. If the iteration is terminated, otherwise, return to step S4 to repeat the iteration until the accuracy meets the requirements. e is the decomposition accuracy threshold. S8: for the modal signals obtained by decomposition, a new combined kernel function is constructed based on the kernel function weighted linear combination method of multi-kernel learning, and the new combined kernel function is constructed by a Gaussian kernel function and a polynomial kernel function: K(x i ,x j ) = aK RBF (x i ,x j ) + (1 - a)K POLY (x i ,x j ) (1) Among them, K RBF (x i ,x j )=exp(-||x i -x j || 2 / 2σ 2 ) represents the Gaussian kernel function, x i and x j are the samples of group i and group j respectively, σ is the kernel parameter, K POLY (x i ,x j )=(x i x j +1) d represents the polynomial kernel function, d is the order of the polynomial kernel function, a is the kernel function weight coefficient, and the value range is [0,1]; S9: the optimal kernel parameters and the kernel function weight coefficients of each model are calculated by using the particle swarm optimization algorithm with adaptive inertia weight; S10: Based on the multi-core least squares support vector machine algorithm, a dynamic model as shown in formula (2) is established, and the predicted value y of each modal signal model at the next time is calculated k : wherein a i represents the Lagrange operator corresponding to the sample point, K(x, x i is a multi-kernel function, b is a bias, N is the number of support vectors, x is an input sample, and x i is the i-th support vector; S11: the output feature prediction value at the moment is reconstructed according to the prediction value of each modal signal at the moment: S12: the deviation between the model prediction value and the measured value at the current moment obtained in step S7 is calculated, when the deviation exceeds the threshold value, the model parameters are updated online, and finally the accurate prediction of the output features at the future moment is realized.
2. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 1, characterized in that, In the step S1, the input variables of the prediction model include control variables and state variables, the control variables include the coal feeder amount of each layer, the secondary air door opening degree of each layer, the combustion air door opening degree and the oxygen amount after the economizer, and the state variables include the unit operation load and the total fuel amount into the furnace.
3. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 1, characterized in that, In the step S2, the method for determining the lag time between the input variables and the output variables is: the control variable method is used to change the lag time of each input feature in turn, then based on the cross-validation method, the original data set is divided into 10 sample sets with the same size, one sample set is taken as the training sample and the other 9 sample sets are taken as the test sample, and finally the lag time corresponding to the minimum root mean square error and the average absolute error of the prediction result is taken as the final lag time.
4. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 1, characterized in that, In said step S3, the Transforming into the frequency domain The Fourier transform method used at this point is represented by: wherein, and correspond to u i Fourier transform of t), f(t) and l(t), u i (t) is the i-th modal function, f(t) is the original signal; β is a quadratic penalty term for ensuring the reconstruction accuracy of the signal; l(t) is a Lagrange multiplier for maintaining the strictness of the constraint condition.
5. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 4, characterized in that, In the step S4, the secondary optimization solving method is to first let the first term in the formula (5) ω←(ω-ω k ), and then convert it into the integral form in the non-negative interval: Then the quadratic optimization problem is solved to obtain: instantaneous frequency The solution of the equation transforms into: and the update formula is: Finally, the variational modal decomposition algorithm obtains the set of intrinsic mode functions {u (t)} in the time domain by performing inverse Fourier transform on k (t)}.
6. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 5, characterized in that, In the step S6, the updating method of the Lagrange multiplier is: wherein and are the Lagrange multiplier values of the (n+1)th and nth iteration, respectively, and τ is the update step size.
7. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 1, characterized in that, In the step S10, the model prediction value refers to the prediction value of each modal signal of the output feature obtained by the variational modal decomposition algorithm, and the prediction value includes the boiler efficiency prediction value, the NOx emission prediction value and the reheat steam temperature prediction value.
8. The incremental modeling method of a boiler combustion system based on a variational modal decomposition algorithm according to claim 1, characterized in that, In the step S12, the online updating method of the model parameters is: the similarity between samples is judged according to the Mahalanobis distance, and the two samples with the minimum Mahalanobis distance are selected in the original sample set, then the sample with a more forward time sequence in the two samples is replaced by a new sample, and the updated decision function coefficient is: where, α = [α1, α2, …, αn]T, and β = [β1, β2, …, βn]T. n ] T is a Lagrange multiplier vector, H1is a matrix composed of the kernel functions and penalty coefficients of the updated sample points, y is an updated output vector, is a unit column vector.
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