MSGSE-NSCF-based urban solid waste incineration NOx emission prediction method

Abstract

The invention provides an urban solid waste incineration NOx emission prediction method based on MSGSE-NSCF, and the method comprises the steps: obtaining a key variable and nonlinear dependence of NOx emission, and constructing a non-stationary cross converter; constructing a non-stationary gated spectrum enhancement sub-module and a gated convolution attention fusion sub-module, extracting space-time enhancement representation, and realizing time-frequency domain feature fusion modeling; performing hyper-parameter verification to obtain reasonable parameters of the model; according to the NOx emission prediction method based on the non-stationary cross converter and the multi-scale time-frequency feature enhancement, the non-linear dependence, the original structure and the dynamic change of data can be reserved, the non-stationary time sequence is modeled, the output scale is kept, and the NOx emission concentration is obtained. In addition, time domain-frequency domain and global-local cooperative enhancement can be achieved, selective modeling of periodicity and key frequency components is enhanced, and an accurate NOx emission prediction result is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of municipal solid waste incineration, and particularly relates to a municipal solid waste incineration NOx emission prediction method based on MSGSE-NSCF. BACKGROUND

[0002] The global urbanization process is accelerating with the development of science and technology, which brings convenience to residents' life, but also produces a large amount of municipal solid waste (MSW), which will breed bacteria and even destroy the environment for a long time. How to effectively solve the environmental problems caused by MSW accumulation has always been a research hotspot. At present, the main treatment technologies of MSW include landfill, composting and incineration. Among them, the first two technologies have defects such as large site demand, high technical requirements and long processing period, and municipal solid waste incineration (MSWI) has the advantages of reduction, harmlessness and resource utilization, and is the mainstream technology in the world. For example, in developing countries, MSWI accounts for 70%. However, the process will produce residues such as slag, fly ash and flue gas. Among them, the slag can be used as building materials after treatment, the fly ash containing a large amount of harmful substances needs to be treated as hazardous waste, and the pollutants such as NOx, CO, SO2 and HCL in the flue gas need to meet the corresponding environmental protection standards to achieve harmless emission.

[0003] NOx is one of the pollutants that environmental protection departments pay special attention to, and its harm includes causing ozone layer depletion, causing acid rain and photochemical smog. The MSWI process often uses selective non-catalytic reduction (SNCR) technology to reduce NOx to nitrogen (N2). Due to the differences in MSW characteristics and management technology at home and abroad, it is difficult for automatic combustion conditions in developed countries to be applied in China, resulting in that MSWI power plants in developing countries often use manual operation technology. Although the continuous emission monitoring system (CEMS) can detect the concentration of NOx in real time and has a mature proportional-integral-derivative (PID) control loop, field experts in the industry need to consider the fluctuation of multiple controlled variables and flue gas indicators to manually intervene and operate, that is, to adjust the operation variables such as air distribution and material distribution and the amount of ammonia water addition according to the change trend of NOx concentration in a certain period of time. Therefore, it is necessary to build a NOx emission prediction model under the time sequence characteristics.

[0004] Currently, the existing researches on the NOx prediction model of MSWI process include non-time series prediction methods and time series prediction methods. Although the existing mechanism model and data-driven model can accurately realize the prediction of NOx concentration, these researches do not consider the inherent non-stationary characteristics of the MSWI process. Influenced by the MSW composition and humidity, the combustion air wind speed and temperature, and the urea solution addition amount, the time series of variables such as NOx emission concentration has strong nonlinearity. Therefore, the above methods have the following problems in the modeling process: 1) non-time series method and general data-driven method: strong pretreatment is made on the original time series, the non-stationary nature is weakened, and the original distribution is difficult to preserve. 2) pure time series deep model, such as part transformer, convolution, RNN, etc.: insufficient comprehensive description of non-stationary, time-frequency coordination and spatial dependence. 3) NSCF, i.e. non-stationary cross transformer, has been improved through non-stationary attention and convolution, but still has the problems of insufficient frequency domain feature mining, redundant attention calculation and inter-layer data transformation, high complexity, and gradual fading of original structure information in deep layer transmission. SUMMARY

[0005] In order to overcome the shortcomings of the prior art, the purpose of the present application is to provide a municipal solid waste incineration NOx emission prediction method based on MSGSE-NSCF, which can preserve the non-linear dependence, original structure and dynamic change of data, model non-stationary time series and maintain the output scale, and also can realize the collaborative enhancement of time domain-frequency domain and global-local, enhance the selective modeling of periodicity and key frequency components, and obtain accurate NOx emission prediction results.

[0006] To achieve the above purpose, the present application provides the following scheme: a municipal solid waste incineration NOx emission prediction method based on MSGSE-NSCF, comprising: obtaining original emission data of municipal solid waste incineration, analyzing key variables and non-linear dependence of NOx emission in the original emission data by using mutual information method, and constructing a non-stationary cross transformer based on Crossformer to preserve the original time series information of the original emission data; based on the non-stationary cross transformer and the original time series information, constructing a non-stationary gated spectral enhancement sub-module and a gated convolution attention fusion sub-module to obtain a multi-scale time-frequency feature enhancement module, so as to extract a space-time enhanced representation and realize time-frequency domain feature fusion modeling; based on the multi-scale time-frequency feature enhancement module, defining a history step, a segmentation step, a segmentation sequence merging step and a module number to obtain hyperparameters, and performing hyperparameter verification to obtain reasonable model parameters; according to the reasonable model parameters, constructing an emission prediction model based on the non-stationary cross transformer and the multi-scale time-frequency feature enhancement module to perform feature alignment and fusion and prediction output, so as to obtain the NOx emission concentration.

[0007] Optionally, the original emission data of municipal solid waste incineration is acquired, the key variables and nonlinear dependence of NOx emission in the original emission data are analyzed by using mutual information method, and a non-stationary cross transformer is constructed based on a Crossformer to retain the original time sequence information of the original emission data, including: The process of municipal solid waste incineration is acquired to obtain original emission data, the source of NOx, the type of NOx and the influence of process variables on NOx in the original emission data are analyzed by using mutual information method to obtain key variables and nonlinear dependence; Based on the Crossformer model architecture, an encoder and a decoder are designed to obtain an initial model, based on the initial model, a standardization operation is performed on the original emission data, and an overall non-stationary factor is calculated to obtain an original time sequence; The original time sequence is segmented to obtain a segmented time sequence and a corresponding segmented non-stationary factor, the segmented time sequence is segmented and merged, and the segmented stationary factor is linearly mapped to complete the structure optimization of the initial model to obtain a non-stationary cross transformer to retain the original time sequence information of the original emission data.

[0008] Optionally, the encoder includes a non-stationary attention layer for focusing on the dynamic changes of time sequence, a one-dimensional convolution layer for extracting short-term local features, and a cross-attention layer for modeling the dynamic association between multiple variables, and the decoder includes a double-layer attention layer for simultaneously focusing on the local prediction continuity and the global trend consistency, a cross-attention layer for associating the prediction results and the historical data, and an output de-normalization layer for explaining the prediction results.

[0009] Optionally, the construction process of the non-stationary gated spectral enhancement sub-module includes: The output of the non-stationary attention layer is divided into multiple scale windows to obtain a multi-scale window, a one-dimensional real fast Fourier transform is performed on the multi-scale window to obtain a frequency domain representation, and based on the frequency domain representation, a learnable shared weight is introduced in the spectrum to obtain an enhanced frequency domain representation; Based on the enhanced frequency domain representation, the mean of each frequency component is calculated on the channel to obtain an average frequency response intensity, and the average frequency response intensity is input into a lightweight gating network to obtain a frequency domain weight to suppress noise frequency bands and enhance key frequency bands; wherein the lightweight gating network is composed of two layers of full connection, ReLU and Sigmoid; Inverse Fourier transform is performed on the frequency domain weight, and window merging is performed on the multi-scale window to obtain a window merging result, and then the window merging result is summed and averaged to obtain a time domain representation.

[0010] Optionally, the construction process of the gated convolution attention fusion sub-module includes: Based on the original timing information and the frequency domain representation, the cross attention layer is used to capture the interdependence between multiple variables to obtain a spatial enhancement representation, and complete spatial dependence modeling; Based on the spatial enhancement representation, a one-dimensional convolution including three branches is constructed, the one-dimensional convolution is used to extract short-term local patterns, medium-term local patterns and long-term local patterns to obtain branch outputs, and then the branch outputs are spliced, channel compressed and fused to obtain a multi-scale convolution; The spatial enhancement representation and the multi-scale convolution are spliced, and then input into a gated weight generation network to obtain fusion weights, and then the spatial enhancement representation and the multi-scale convolution are adaptively weighted according to the fusion weights to obtain gated enhancement and fusion features; Based on the gated enhancement and the fusion features, the one-dimensional convolution is used for linear mapping, and the residual connection is used for steady-state enhancement, and then the self-attention is introduced to the fusion features to complete global context supplement, obtain a spatiotemporal enhancement representation, and realize time-frequency domain feature fusion modeling.

[0011] Optionally, based on the multi-scale time-frequency feature enhancement module, a history step, a segmentation step, a segmentation sequence merging step and a module number are defined to perform hyperparameter verification to obtain reasonable model parameters, including: Based on the multi-scale time-frequency feature enhancement module, a history step, a segmentation step, a segmentation sequence merging step and a module number are defined; According to the history step and the segmentation step, the initial segmentation number and the remaining data are calculated, and it is judged whether the remaining data is zero, if not, data padding is performed; According to the segmentation step and the segmentation sequence merging step, it is judged whether the segmentation merging needs to be filled, and according to the judgment result, the segmentation step and the segmentation sequence merging step are reset; The coupling relationship between the history step, the segmentation step, the segmentation sequence merging step and the module number is traversed and verified to complete hyperparameter verification to obtain reasonable model parameters.

[0012] Optionally, according to the reasonable model parameters, an emission prediction model based on the non-stationary cross transformer and the multi-scale time-frequency feature enhancement module is constructed to perform feature alignment and fusion and prediction output to obtain the NOx emission concentration, including: According to the reasonable model parameters, an emission prediction model based on the non-stationary cross transformer and the multi-scale time-frequency feature enhancement module is constructed; Based on the emission prediction model, the linear mapping is performed on the output of each multi-scale time-frequency feature enhancement module to unify the module dimension and scale. The output of the multi-scale time-frequency feature enhancement module is weighted and fused, and the weighted and fused result is de-normalized to restore the original data scale, to obtain the NOx emission concentration.

[0013] The present application discloses the following technical effects by providing a city solid waste incineration NOx emission prediction method based on MSGSE-NSCF: 1. Combining experience selection and data driving, using mutual information method to quantitatively screen variables, avoiding linear hypothesis of Pearson correlation, retaining nonlinear dependence, and enhancing data interpretability and usability.

[0014] 2. The non-stationary cross transformer NSCF can better model non-stationary time series and keep the output scale through non-stationary attention, convolution and de-normalization.

[0015] 3. Change the traditional single-line transmission of "front layer output feeding back layer" to "cross-layer merging based on original", and construct the input based on "original sequence + non-stationary factor", so that the information fidelity is higher, and the original structure and dynamic change are maintained.

[0016] 4. Through the non-stationary gating spectrum enhancement NSGSE, the distribution learned by the non-stationary factor is restored and linked with the frequency domain weight, the expression of key frequency band is improved, the multi-window decomposition covers different time scales, the frequency domain gating suppresses noise and retains main trend, and the output is more stable and robust.

[0017] 5. Through the gating convolution attention fusion GCAF, from "single attention or single convolution" to "attention-convolution-gating-self-attention" cascade, the expression depth of complex coupled time series is improved, the cross attention modeling of multivariate space dependence is realized, the multi-scale convolution captures local patterns and edge changes, the gating weight adaptively allocates information sources, and the self-attention strengthens the global context.

[0018] 6. Through hyperparameter verification, the mathematical relationship between historical step, segmented step, segmented sequence merging step and number of multi-scale time-frequency feature enhancement modules is explicitly constrained, and the training instability and precision decline caused by excessive padding and insufficient segmentation are avoided.

[0019] The technical solutions of the present application will be further described in detail below by means of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions in the embodiments or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0021] Figure 1 Method flowchart provided for the embodiment of the present application; Figure 2 Other variables provided for the embodiment of the present application and the MI value diagram of flue gas NOx concentration; Figure 3 NSCF model Encoder structure architecture diagram provided for the embodiment of the present application; Figure 4 NSCF model Decoder structure architecture diagram provided for the embodiment of the present application; Figure 5 MSGSE-NSCF model structure architecture diagram provided for the embodiment of the present application; Figure 6 Non-stationary gating spectral network structure architecture diagram provided for the embodiment of the present application; Figure 7 Multi-scale gating convolutional network structure architecture diagram provided for the embodiment of the present application; Figure 8 PCA principal component projection curve diagram of different data provided for the embodiment of the present application; Figure 9 Similarity curve diagram of input sequence and original sequence obtained in different ways provided for the embodiment of the present application; Figure 10 Intermediate result visualization diagram of non-stationary gating spectral enhancement sub-module provided for the embodiment of the present application; Figure 11 Gating convolutional attention fusion network weight visualization diagram provided for the embodiment of the present application; Figure 12 Hyperparameter verification module experimental result diagram provided for the embodiment of the present application; Figure 13 Feature alignment fusion prediction module experimental result diagram provided for the embodiment of the present application; Figure 14 MSGSE-NSCF model prediction output visualization diagram provided for the embodiment of the present application. DETAILED DESCRIPTION

[0022] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0023] In order to make the above objectives, characteristics and advantages of the present application more apparent, comprehensible and easier to be understood, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0024] As shown in Figure 1 The present application provides a MSGSE-NSCF-based urban solid waste incineration NOx emission prediction method, which comprises the following steps: Step 1: Obtain the original emission data of urban solid waste incineration, analyze the key variables and nonlinear dependence of NOx emission in the original emission data by using mutual information method, and construct a non-stationary cross transformer based on Crossformer to retain the original time sequence information of the original emission data. Specifically, it comprises: 1.1 Obtain the process of urban solid waste incineration to obtain the original emission data, analyze the NOx source, NOx type and process variable influence on NOx of the original emission data by using mutual information method, and obtain the key variables and nonlinear dependence.

[0025] 1.2 Based on the Crossformer model architecture, design the encoder and decoder to obtain the initial model, based on the initial model, perform standardization operation on the original emission data, and calculate the overall non-stationary factor to obtain the original time sequence.

[0026] The encoder comprises a non-stationary attention layer for focusing on the dynamic changes of time sequence, a one-dimensional convolution layer for extracting short-term local features, and a cross-attention layer for modeling the dynamic association between multiple variables. The decoder comprises a double-layer attention layer for simultaneously focusing on the local prediction continuity and global trend consistency, a cross-attention layer for associating the prediction results and historical data, and an output de-standardization layer for explaining the prediction results.

[0027] 1.3 Segment the original time sequence to obtain segmented time sequence and corresponding segmented non-stationary factor, segment and merge the segmented time sequence, and linearly map the segmented stationary factor to complete the structure optimization of the initial model, and obtain the non-stationary cross transformer to retain the original time sequence information of the original emission data.

[0028] Step 1 is specifically as follows: (1) MSWI process description: The MSWI process mainly consists of six parts: solid waste fermentation, solid waste combustion, waste heat exchange, steam power generation, flue gas purification, and flue gas emission. Among them: 1) solid waste fermentation: the garbage transport vehicle transports the collected MSW to the MSWI power plant, and after weighing and metering, it is poured into the solid waste pool, mixed and stirred by the grab bucket, and then transferred to the fermentation pool. After 3-7 days of fermentation and dehydration, it is ensured to reach the low calorific value of MSWI; 2) solid waste combustion: the grab bucket grabs the fermented and dehydrated MSW into the hopper, which is pushed by the chute at the bottom of the feeder into the incinerator, and is treated in turn through drying, combustion 1, combustion 2 and burning out four stages. The ash produced in the incineration process is sent to the slag pool after water cooling in the slag extractor; 3) waste heat exchange: the high-temperature flue gas generated in the incineration process is extracted by the induced draft fan into the waste heat exchange system, and is sequentially passed through the superheater, evaporator and coal economizer, and exchanges heat with the liquid water in the boiler drum to generate high-temperature steam; 4) steam power generation: the high-temperature steam generated by the waste heat exchange system drives the steam turbine generator to generate electricity; 5) flue gas treatment: the flue gas treatment process includes denitration (removal of NOx), desulfurization (removal of HCl, HF, SO2, etc.), heavy metal removal (removal of Pb, Hg, etc.), dioxin (DXN) adsorption and dust removal, etc. Process, so that the incineration flue gas meets the emission standard; 6) flue gas emission: the purified flue gas G2 is extracted by the induced draft fan to the chimney and discharged into the atmosphere.

[0029] Analysis of influencing factors of NOx: The MSWI process involves complex chemical and physical reactions, and the main sources of NOx generation include: 1) nitrogen-containing compounds in MSW react with oxygen; 2) N2 in primary and secondary air is oxidized under high temperature conditions; 3) combustion-supporting fuel pyrolysis under high temperature conditions. In addition, process variables such as furnace temperature, flue gas residence time in the furnace, primary air volume, secondary air volume, etc. will affect the formation of NOx. NOx can be divided into nitric oxide (NO) and nitrogen dioxide (NO2), of which NO accounts for the majority. Currently, NO is mainly divided into thermal, instantaneous and fuel types according to the generation mechanism. Studies have shown that among the three NO generation mechanisms, fuel-type NO is the main part of NO generation in the MSWI process. Currently, the MSWI power plant mainly reduces the generation of NOx through SNCR technology.

[0030] In this context, due to the highly complex characteristics of the MSWI process and the strong coupling between variables, the traditional Pearson correlation analysis is difficult to fully reveal the real dependence relationship between the time series of each variable. Therefore, in order to achieve accurate prediction of NOx concentration, it is crucial to identify the key variables closely related to NOx concentration. On this basis, based on the operation data of a certain MSWI plant from 8:00 to 24:00 on a certain day, and combined with expert experience, 81 variables that have a greater impact on NOx concentration are preliminarily selected, as shown in Table 1 below. In order to further quantify the correlation degree between each variable and NOx, mutual information (MI) is used for analysis. The larger the MI value, the stronger the dependence between the variable and NOx, and the more significant the correlation. The MI analysis results of each variable and NOx are shown in Table 2. Figure 2

[0031] Table 1 Factors affecting NOx concentration

[0032]

[0033] As can be seen from the above, there is a significant nonlinear relationship between some variables and NOx concentration, and traditional time series modeling methods are difficult to fully capture the dynamic dependence relationship between variables. In order to more effectively capture the potential interaction information between variables, it is necessary to use a modeling strategy that integrates local and global, time domain and frequency domain to build a time series prediction model, thereby improving the modeling ability of NOx emissions.

[0034] (2) Non-Stationary Crossformer (NSCF) The NSCF model introduces a non-stationary attention module, a one-dimensional convolution module, and a de-normalization module on the basis of the Crossformer architecture, so as to more effectively model the non-stationary characteristics in multivariate time series and improve the overall prediction performance. First, the non-stationary attention module is introduced to solve the problem of time series non-stationarity fading during the training process of Crossformer. It constructs a lightweight MLP network, calculates the non-stationary factor using the input time series, the mean and standard deviation after standardization, and embeds it into the calculation process of attention, thereby restoring the non-stationary characteristics of the time series. Second, the one-dimensional convolution module is introduced to enhance the model's ability to extract local features of time series. Through multi-scale convolution operation, the local features of time series are extracted, and the richness of feature expression is improved. Finally, the de-normalization module is introduced to restore the model prediction output to the original scale.

[0035] (2.1) NSCF-Encoder: Figure 3 is the structure of the Encoder layer of the NSCF model. As shown in Figure 4 ​As shown, the Encoder layer of the NSCF model includes non-stationary attention, one-dimensional convolution, and cross-attention calculation. Among them, the non-stationary attention plays a crucial role in the recovery process of the non-stationary characteristics of the time series. The specific steps are as follows: First, the input time series is standardized, as shown in the following formula: ; ; ; In the formula, is the mean, is the standard deviation, is the standardized time series, and H is the length of the time series.

[0036] Second, the MLP is constructed to learn the non-stationary factors from the mean and statistical information, and then recover the non-stationary characteristics of the input time series, as shown in the following process: ; In the formula, represents the non-stationary factor learning based on the MLP, and are the non-stationary factors.

[0037] To recover the non-stationary characteristics of the input time series in the self-attention calculation, the calculated non-stationary factors and are introduced into the self-attention calculation, thereby obtaining the non-stationary attention, as shown below.

[0038] ; In the formula, is the query matrix, is the key matrix, is the value matrix, is the standardized query matrix, is the standardized key matrix, is the standardized value matrix.

[0039] Next, to capture the time series features, the input time series and its non-stationary factors are equally divided by dimension segmentation embedding, as shown in the following formula: ; In the formula, is the compilation operation, is the segmented time series, for the segmented non-stationary factor .

[0040] In Figure 4 , the first Encoder layer takes , and as inputs, and the non-stationary attention is calculated as follows: ; where is the non-stationary attention calculation, is the non-stationary attention output of the first Encoder layer.

[0041] The j-th Encoder layer takes the output of the j-1-th Encoder layer , and as inputs, and the corresponding non-stationary attention is calculated as follows: ; ; ; ; where is the 1D convolution calculation, is the 1D convolution network output of the j-1-th Encoder layer, is the cross-attention calculation, is the cross-attention output of the j-1-th Encoder layer, and are the segmented input sequence and non-stationary factor of the j-th Encoder layer, is the segmented merging of and , is the non-stationary attention output of the j-th Encoder layer.

[0042] Finally, the outputs of all Encoder layers are saved in a list for subsequent Decoder layer calls, as follows: ; where is the storage of the Encoder layer output.

[0043] (2.2) NSCF-Decoder Figure 4 is the Decoder layer structure of the NSCF model. As Figure 4As shown, Decoder layer includes double-layer attention and cross-attention calculation, wherein: h is a learnable embedding vector, represents the output result of the double-layer attention calculation of the learnable embedding vector; represents the output of the first Decoder layer, which is also the input of the second Decoder layer; represents the output of the jth Decoder layer, which is also the input of the j+1th Decoder layer; represents the input the output result of the double-layer attention calculation; represents the result of summing all Decoder layer outputs.

[0044] In the first layer decoder, a random learnable embedding vector h is created for double-layer attention calculation after the output of the first encoder layer cross-attention calculation, as shown in the following formula: ; ; In the formula, represents double-layer attention calculation.

[0045] The output of the jth Decoder layer above the previous layer is the input, which is calculated after double-layer attention calculation, and then combined with the output of the corresponding Encoder layer to calculate cross-attention, as shown in the following formula: ; ; Finally, the outputs of all Decoder layers are fused and the fusion result is de-normalized, as shown in the following formula.

[0046] ; ; In the formula, is the predicted output of the NSCF model, is the de-normalization operation.

[0047] (3) MSGSE-NSCF modeling strategy: As shown in Figure 5 , the MSGSE-NSCF modeling strategy mainly includes: segmented time series merging and reconstruction module, multi-scale time-frequency feature enhancement module, hyperparameter verification module, and feature alignment fusion prediction module.

[0048] As shown in Figure 5 , is the original input time series of the model, H represents the length of the time series, and C represents the number of variables; is the input segmented time series of the bth multi-scale time-frequency feature enhancement module, where ; is the input segmented non-stationary factor of the bth multi-scale time-frequency feature enhancement module; is the input non-stationary factor of the multi-scale time-frequency feature enhancement module; is the initial setting value of the time series historical data step L, is the setting value of L after verification; is the initial setting value of the time series segmentation step S, is the setting value of S after verification; is the initial setting value of the segmented time series merging step W, is the setting value of W after verification; is the initial setting value of the number B of multi-scale time-frequency feature enhancement modules, is the setting value of B after calibration; is the output feature of the non-stationary gating spectrum enhancement submodule in the bth multi-scale time-frequency feature enhancement module; is the output feature of the bth multi-scale time-frequency feature enhancement module; is the prediction output of the model, and T represents the prediction output step.

[0049] The functions of each module are as follows: Segmented time series merging and reconstruction module: aims to optimize the time sequence information fusion strategy of the multi-scale time-frequency feature enhancement module. This module analyzes the transmission and merging mechanism of the segmented time series between the multi-scale time-frequency feature enhancement modules, selects to merge based on the initial time series and the segmented non-stationary factor, and ensures that the original structure and dynamic change characteristics of the time sequence data are preserved as much as possible during the interlayer transmission process.

[0050] The multi-scale time-frequency feature enhancement module enhances the model's periodic feature modeling capability in the frequency domain through a non-stationary gated spectral enhancement (NSGSE) sub-module. The network restores the original distribution characteristics of the input time sequence through non-stationary attention calculation, and constructs learnable spectral weights in multiple frequency scales in a windowed manner to achieve multi-scale frequency domain modeling and selective enhancement of the input sequence, thereby effectively extracting key periodic patterns and suppressing noise interference. The GCAF (Gated Convolutional Attention Fusion) sub-module enhances the model's ability to capture global and local features of the time sequence. Specifically, cross-attention calculation is used to fuse frequency domain information to enhance time domain feature modeling, and a multi-scale gated convolutional network is used to extract local features of the time sequence and perceive feature changes of the input sequence with different receptive fields to enhance the model's ability to depict local patterns, trend changes, and edge information. A gating mechanism is used to weight and fuse convolutional features at different scales to enhance the model's selective expression ability of key local patterns. After fusing various features, a self-attention mechanism is introduced to further enhance the modeling capability of global context information and improve the model's expression and generalization ability in long sequence processing.

[0051] The hyperparameter verification module directly determines the model's segmentation and merging mechanism for time series data, which in turn affects the time series feature capture process during model training. This module verifies the rationality of hyperparameter configuration by analyzing the calling order and internal mathematical relationship of key hyperparameters in the modeling process, using whether the original sequence can be evenly segmented and whether the proportion of padded data exceeds half of the original sequence as judgment conditions.

[0052] The feature alignment and fusion prediction module linearly maps the output features of each multi-scale time-frequency feature enhancement module to unify their scales and dimensions, ensuring consistency during the fusion process. Then, the output features of all multi-scale time-frequency feature enhancement modules are weighted and fused to enhance the richness of feature expression. Finally, the fused features are restored to the original dimension through inverse normalization operation, and the final prediction result is output.

[0053] (4) Segmented time series merging and reconstruction module: In the NSCF model, the Encoder layer and the Decoder layer adopt a hierarchical progressive structure, wherein the input of the jth Encoder layer is the output of the (j-1)th Encoder layer, and the input of the jth Decoder layer is the output of the (j-1)th Decoder layer and the output of the jth Encoder layer. With the increase of the number of Encoder-Decoder layers, the input time series undergoes multiple nonlinear transformations and reconstructions, and the key information in the original time series data is gradually weakened or even lost, thereby reducing the accuracy of feature representation. The model is more susceptible to information dilution effect, thereby reducing the prediction accuracy and increasing the error accumulation risk.

[0054] To solve the above problems, the improvements proposed by the present application are as follows: Firstly, the original input is subjected to data preprocessing to obtain the input data of the first multi-scale time-frequency feature enhancement module (corresponding to the 1st Encoder-Decoder layer of NSCF, b=1), as shown in the following formula: ; In the formula, is the segmented time series, is the segmented non-stationary factor, is the calculated non-stationary factor, D is the feature dimension of the model, is the number of segments of the input sequence of the first multi-scale time-frequency feature enhancement module, is a data preprocessing operation.

[0055] Secondly, the transmission mode of the reconstructed input data in the model training process is changed. The input of the bth multi-scale time-frequency feature enhancement module (corresponding to the jth Encoder-Decoder layer of NSCF, is no longer the output of the previous layer, but is constructed in the following way: 1) segmenting and merging the input segmented time series of the (b-1)th multi-scale time-frequency feature enhancement module; 2) linearly mapping the input segmented non-stationary factor of the (b-1)th multi-scale time-frequency feature enhancement module; 3) taking the segmented and merged input sequence , the linearly mapped segmented non-stationary factor , and the non-stationary factor as the input of the bth multi-scale time-frequency feature enhancement module at the same time, as shown in the following formula: ; ; In the formula, , , The number of segments of the sequence is input into the bth multi-scale time-frequency feature enhancement module, is a linear mapping.

[0056] Finally, the input of the multi-scale time-frequency feature enhancement module is uniformly expressed as follows: ; Therefore, after the above merging and reconstruction, the input of each multi-scale time-frequency feature enhancement module is constructed based on the original sequence, which enhances the effective preservation of the original time sequence information in the feature transmission process of the model. This way not only enhances the integrity of the time sequence feature expression, but also helps to alleviate the information decay problem in the deep network, thereby improving the prediction accuracy and stability of the model.

[0057] 2. Based on the non-stationary cross transformer and the original time sequence information, a non-stationary gated spectral enhancement sub-module and a gated convolution attention fusion sub-module are constructed to obtain a multi-scale time-frequency feature enhancement module to extract a spatio-temporal enhanced representation and realize time-frequency domain feature fusion modeling. 2.1 The construction process of the non-stationary gated spectral enhancement sub-module includes: For the output of the non-stationary attention layer, multi-window division is performed to obtain a multi-scale window, one-dimensional real fast Fourier transform is performed on the multi-scale window to obtain a frequency domain representation, and based on the frequency domain representation, a learnable shared weight is introduced in the spectrum to obtain an enhanced frequency domain representation.

[0058] Based on the enhanced frequency domain representation, the mean of each frequency component is calculated on the channel to obtain an average frequency response intensity, the average frequency response intensity is input into a lightweight gating network to obtain a frequency domain weight to suppress noise bands and enhance key bands; wherein the lightweight gating network is composed of two layers of full connection, ReLU and Sigmoid.

[0059] For the frequency domain weight, inverse Fourier transform is performed, and window merging is performed on the multi-scale window to obtain a window merging result, and then the window merging result is summed and averaged to obtain a time domain representation.

[0060] 2.2 The construction process of the gated convolution attention fusion sub-module includes: Based on the original time sequence information and the frequency domain representation, the cross attention layer is used to capture the interdependence between multiple variables to obtain a spatial enhanced representation and complete spatial dependence modeling.

[0061] Based on the spatial enhanced representation, a one-dimensional convolution including three branches is constructed, the one-dimensional convolution is used to extract short-term local patterns, medium-term local patterns and long-term local patterns to obtain branch outputs, and then the branch outputs are spliced, compressed and fused in channels to obtain a multi-scale convolution.

[0062] The spatial enhancement representation and the multi-scale convolution are spliced, input into a gating weight generation network to obtain fusion weights, and then the spatial enhancement representation and the multi-scale convolution are adaptively weighted according to the fusion weights to obtain a gated enhancement and fusion feature.

[0063] Based on the gated enhancement and the fusion feature, linear mapping is performed by using the one-dimensional convolution, steady-state enhancement is performed by using a residual connection, self-attention is introduced to the fusion feature, global context is supplemented, a spatiotemporal enhancement representation is obtained, and time-frequency domain feature fusion modeling is realized.

[0064] The step 2 is specifically as follows: (2.1) Non-stationary gated spectrum enhancement sub-module: As shown in Figure 6 , in order to better restore the non-stationary change characteristics of time series, capture the periodic change characteristics of time series, and reduce data noise, a non-stationary gated spectrum network based on Fast Fourier Transformation (FFT) is constructed here. By setting different window sizes (such as 16, 32, 64), the frequency domain dependence relationship of the non-stationary attention output feature in the short term, medium term and long term is captured, so as to enhance the expression ability of the model to key information.

[0065] As can be seen from Figure 6 , first, the output sequence of the non-stationary attention is divided by a window size of , as shown in the following formula: ; ; In the formula, is the subsequence obtained after window division, is the number of subsequences, , is the window division of .

[0066] Next, the time series of each sub-window is one-dimensionally real FFT along the time dimension, and all subsequences are converted from the time domain to the frequency domain, as shown in the following formula: ; In the formula, is the time series obtained after FFT, is the FFT algorithm.

[0067] Secondly, a learnable shared weight is created to enhance the learning of , as shown in the following formula: ; where, denotes element-wise multiplication, .

[0068] Then, the average frequency response strength is obtained by taking the modulus of the complex spectrum of each frequency component and calculating the mean value in the channel dimension, which is used as the input of the lightweight gating network. This network extracts frequency domain features using two fully connected layers and generates frequency domain weights through a Sigmoid activation function, which can be used to adaptively adjust the importance of different frequency channels, effectively suppressing noise frequencies and enhancing the expression ability of key frequency components, as shown in the following formula: ; ; ; where, is the average frequency response strength of the mth window, is the gating weight of the mth window, 、 、 and are the learnable parameters of the lightweight gating network, is the ReLU function, is the Sigmoid function.

[0069] Next, all sub-sequences are converted back to the time domain by Fourier inverse transform, and window merging is performed, as shown in the following formula: ; ; where, is the sub-sequence obtained by Fourier inverse transform, is the gating spectrum enhancement network output of the bth multi-scale time-frequency feature enhancement module when the time sequence division window is win, is the window merging of all Fourier inverse transform obtained sub-sequences.

[0070] Finally, the sum of the outputs of all gating spectrum enhancement networks is taken and averaged to obtain the final output, as shown in the following formula: ; where, .

[0071] (2.2) Gating convolution attention fusion sub-module: The non-stationary attention calculation of NSCF mainly realizes the data feature capture and non-stationary characteristic recovery of time series in the time dimension, but it does not consider the dependency between different variables. In order to enhance the perception ability of the model to the collaborative features of multiple variables, a cross-attention mechanism is introduced to capture the dependency of multivariate time series in the spatial dimension, as follows: ; In the formula, .

[0072] In addition, in order to further improve the deep feature extraction ability of the model to the spatial dimension of multivariate time series, this paper proposes to construct a multi-scale gated convolutional network, which includes three parallel convolution branches with receptive fields of , and , to realize the feature extraction of input time series in short-term, medium-term and long-term scales. At the same time, a gating mechanism is introduced to adaptively fuse the feature representations of different scales, so as to realize the dynamic selection and enhancement of time series features. This network not only improves the feature extraction depth of the model, but also improves the modeling ability of complex time series dependency, and its structure is shown as Figure 7 .

[0073] Firstly, a parallel convolutional network with different receptive fields is constructed to perform multi-scale feature extraction, as follows: ; ; ; In the formula, , and are one-dimensional convolution outputs with convolution kernel of 7, 5 and 3; , and are one-dimensional convolution calculations with convolution kernel of 7, 5 and 3.

[0074] Next, the output features of different scales are spliced to realize multi-scale information fusion, as follows: ; In the formula, , is feature splicing.

[0075] Then, the 1x1 convolutional network is used to compress and weight the results of the above formula to reduce the feature dimension and adaptively integrate multi-scale information, as follows: ; In the formula, , is a one-dimensional convolution calculation with a convolution kernel of 1.

[0076] Secondly, the input sequences and are spliced in the gated feature interaction network, so that the gated network can simultaneously perceive the complete information of the two groups of time sequence features, thereby capturing their similarities, differences and complementary relationships, as follows: ; In the formula, .

[0077] Next, the fusion weight is calculated by the gated weight generation unit to adaptively adjust the importance of the input features in the fusion process, as shown in the following formula: ; In the formula, , is the weight calculation.

[0078] Then, based on the adaptive gated weight, the feature dynamic fusion is realized, as shown in the following formula: ; ; ; In the formula, is the gated enhanced feature, is the gated complementary feature, is the gated fusion feature.

[0079] Secondly, the gated fusion feature is linearly mapped by a 1x1 convolutional network to alleviate the distribution difference after the fusion of different branches, as follows: ; In the formula, .

[0080] Next, to preserve the original information of the input sequence and improve the stability of the fusion process, the residual connection structure shown below is introduced: ; ; In the formula, .

[0081] Finally, the output features of the multi-scale gated convolutional network are calculated by self-attention, and the output of the bth multi-scale time-frequency feature enhancement module is obtained, as follows: ; In the formula, Self-attention is calculated.

[0082] 3. Based on the multi-scale time-frequency feature enhancement module, define the history step, the segmentation step, the segmentation sequence merging step, and the module number to obtain the hyperparameters, and perform hyperparameter verification to obtain the reasonable model parameters. Specifically, it includes: 3.1 Based on the multi-scale time-frequency feature enhancement module, define the history step, the segmentation step, the segmentation sequence merging step, and the module number.

[0083] 3.2 According to the history step and the segmentation step, calculate the initial segmentation number and the remaining data, and judge whether the remaining data is zero. If not, perform data padding.

[0084] 3.3 According to the segmentation step and the segmentation sequence merging step, judge whether the segmentation merging needs to be filled, and according to the judgment result, reset the segmentation step and the segmentation sequence merging step.

[0085] 3.4 Traverse the coupling relationship between the history step, the segmentation step, the segmentation sequence merging step, and the module number to complete the hyperparameter verification and obtain the reasonable model parameters.

[0086] Step 3 specific examples are as follows: Hyperparameter verification module: Since the input data of each multi-scale time-frequency feature enhancement module is based on the preset segmentation and merging reconstruction method, its performance is largely dependent on the setting of key hyperparameters such as time series segmentation step. Therefore, this place introduces a hyperparameter verification module to realize the systematic verification and constraint of key hyperparameters.

[0087] In the model data preprocessing process, usually according to the initial setting value of the time series history data step L and the initial setting value of the time series segmentation step S , the initial segmentation number and the remainder of the input sequence are calculated as follows: ; ; In the formula, is the remainder calculation.

[0088] Due to the problem of data that cannot be divided by a certain probability in the above calculation process, time series segmentation processing models such as Crossformer usually perform data padding and other operations according to algorithm rules. However, the introduction of padding data may affect the stability of the model training process, thereby reducing the model prediction accuracy. In order to avoid the above situation, it is necessary to ensure 0, otherwise re-enter the hyperparameters and .

[0089] In the present application, in the calculation process of traversing all multi-scale time-frequency feature enhancement modules, the input (segmented time series ) of the bth multi-scale time-frequency feature enhancement module needs to be segmented and merged according to the hyperparameters and , and the specific steps are as follows: By taking the remainder of the segment number of the time series and , it is determined whether data needs to be filled.

[0090] ; 1) If , it indicates that no data needs to be filled in the segmented time series merging process, and the segment number of the input time series of the bth multi-scale time-frequency feature enhancement module is calculated as follows: ; At the same time, it is determined whether the condition is met and whether the last multi-scale time-frequency feature enhancement module has been executed, and if the condition is met, it indicates that the hyperparameters or are set too large and need to be re-entered.

[0091] 2) If , it indicates that data needs to be filled in the segmented time series merging process. The number of time series segments to be filled is calculated as follows: ; The segment number of the input time series of the bth multi-scale time-frequency feature enhancement module after further filling is updated as follows: ; At the same time, it is determined whether the condition is met and whether the last multi-scale time-frequency feature enhancement module has been executed, and if the condition is met, it indicates that the hyperparameters or are set too large and need to be re-entered.

[0092] 4. According to the reasonable parameters of the model, a discharge prediction model based on a non-stationary cross transformer and the multi-scale time-frequency feature enhancement module is constructed to perform feature alignment and fusion and output prediction, and the NOx emission concentration is obtained. Specifically, it includes:​​​ 4.1 According to the reasonable parameters of the model, an emission prediction model based on a non-stationary cross transformer and the multi-scale time-frequency feature enhancement module is constructed.

[0093] 4.2 Based on the emission prediction model, linear mapping is performed on the output of each multi-scale time-frequency feature enhancement module to unify the module dimension and scale.

[0094] 4.3 The outputs of the multi-scale time-frequency feature enhancement modules are weighted and fused, and the result after weighted fusion is de-normalized to restore the original data scale to obtain the NOx emission concentration.

[0095] Step 4 is specifically illustrated as follows: (1) Feature alignment and fusion prediction module: Since the model adopts a segmented time series modeling structure, the output features of each multi-scale time-frequency feature enhancement module differ in dimension. To facilitate subsequent calculations, the outputs of each module are first linearly mapped to achieve dimension alignment, as follows: ; In the formula, represents linear mapping.

[0096] Next, the outputs of all multi-scale time-frequency feature enhancement modules are fused, as follows: ; Finally, the de-normalization operation is used to restore to the original data scale to obtain the final prediction result, as follows: ; (2) Industrial data verification: All experiments in this paper are implemented based on Pytorch in the Microsoft Windows 10.0 environment.

[0097] Evaluation index description: In this paper, MSE, MAE and MAPE are selected to evaluate the model performance, as follows: ; ; ; In the formula, represents the true value, represents the predicted value.

[0098] Example 1 Take a MSWI power plant as an example, 13 variables highly correlated with NOx are selected as model inputs through mutual information analysis and domain expert experience, as shown in Table 2 below. Each variable contains 57,426 data points, with a sampling interval of 1s. The data set is divided into 70% training set, 10% validation set and 20% test set.

[0099] Table 2 Input variables of MSGSE-NSCF model

[0100] Experimental results: The MSGSE-NSCF model parameter settings are shown in Table 3: Table 3 MSGSE-NSCF model parameter settings

[0101] Experimental results of the segmented time series merging process reconstruction module: To better represent the effect of this module, the second multi-scale time-frequency feature enhancement module is selected for comparative experiment. The input of the second multi-scale time-frequency feature enhancement module obtained by merging the segmented sequence and the output of the first multi-scale time-frequency feature enhancement module are compared with the original input sequence in terms of features.

[0102] First, the entire batch, space and feature dimensions of , and are flattened at each time step, so that the data shape becomes [C, batch*N*D]; then, principal component analysis (PCA) is performed on all samples in the time step dimension and feature vectors in the spatial dimension to extract the first principal component, as shown in Figure 8 .

[0103] As can be seen from Figure 8 , the PCA curve shape and trend of the input data obtained by merging the segmented sequence and the original input data are basically the same, retaining most of the original data information. Further, first, the original input and , are averaged in the third dimension to obtain the average feature vector of all segmented sequences; then, the cosine similarity of and , is calculated at each time step; finally, the average is taken in the batch dimension to obtain the average similarity curve at each time step, as shown in Figure 9 .

[0104] As can be seen from Figure 9 , the cosine similarity of the input data obtained by merging the segmented sequences with the original input data is closer to 1 than the cosine similarity of the output data calculated by the MSTFFE module with the original input data, proving that merging the segmented sequences based on the original input sequence can retain more original data information in the model training process.

[0105] Experimental results of the multi-scale time-frequency feature enhancement module: 1) Experimental results of the non-stationary gated spectrum enhancement sub-module The experimental results of the non-stationary gated spectrum enhancement sub-module of the first multi-scale time-frequency feature enhancement module are shown in Figure 10 . In Figure 10 , when the window division size is 16, the output waveform of the gated spectrum network fluctuates less than the other two, and the shorter time window size of the sub-sequence leads to the frequency domain transformation mainly capturing low-frequency trends, suppressing high-frequency noise components; when the window division size is 32, the output waveform of the gated spectrum network presents more obvious oscillation, indicating that more medium-frequency and partial high-frequency information is retained; when the window division size is 64, the output curve of the gated spectrum network oscillates with the largest amplitude, indicating complex frequency components of longer time scales, retaining more high-frequency details, and the output waveform is more abundant. By comparing the output curves of different window division sizes, the information extraction ability of the non-stationary gated spectrum enhancement sub-module in different time and frequency scales is verified, providing a multi-band feature time series representation for subsequent time series prediction. After processing by the non-stationary gated spectrum enhancement sub-module, the output curve is basically consistent with the overall trend of the original input curve, indicating that the non-stationary gated spectrum enhancement sub-module effectively retains the main dynamic characteristics of the input data. In addition, due to the suppression and smoothing of high-frequency noise and sharp fluctuations in the frequency domain gating process, the amplitude of the time domain feature values of the output curve is reduced, and the output data is more stable.

[0106] 2) Experimental results of the gated convolution attention fusion sub-module The weight change curve of the gated convolution attention fusion network of the MSGSE-NSCF model is shown in Figure 11 . As can be seen from Figure 11 , the gating weight value fluctuates around 0.501, indicating that the model can adaptively adjust the feature proportion of and at each time step, rather than simply relying on one of them. This dynamic adjustment of the gating weight helps to improve the representation ability of the model, enabling it to retain both local features extracted by multi-scale convolution and global trend information in cross-attention features, demonstrating the effectiveness of information interaction and reconstruction.

[0107] Experimental results of the hyperparameter verification module: Based on the fixed historical input sequence length L=168, the setting values of the time series segmentation step S, the segmented time series merging step W and the number of multi-scale time-frequency feature enhancement modules B are combined for testing. When S=1, W=1 and B=1, it is difficult for the model to fully capture the multi-level time sequence features in the training process. Therefore, the initial values of the hyperparameters S, W and B are all set to 2 in the experimental process. In the experimental process, first, the setting interval of S is calculated; second, for each setting value of S, the corresponding reasonable W interval is analyzed under the condition of B=2; finally, under the determined combination of S and W parameters, the maximum B value that meets the model structure integrity requirement is analyzed, as shown in Figure 12 .

[0108] As can be seen from Figure 12 , when the input sequence length L is fixed, the setting interval of the time series segmentation step S is ; the setting interval of the segmented time series merging step W is ; and the setting interval of the number of multi-scale time-frequency feature enhancement modules B is. The above experimental process further clarifies the coupling relationship between the hyperparameters, providing a basis for model structure design and parameter selection.

[0109] Experimental results of the feature alignment and fusion prediction module: The data change curves of the outputs of each multi-scale time-frequency feature enhancement module after linear mapping and the fused data change curve are as shown in Figure 13 .

[0110] As can be seen from Figure 13 , due to the different input data structures of each module, the output feature curves have certain differences, which proves that the parallel computing architecture enhances the model's perception ability of time sequence features. In addition, the fused feature curve is consistent with the output of each single module in the overall trend, effectively integrating multi-scale features and improving the expression stability and discriminability of time sequence information.

[0111] Comparative analysis: To verify the performance of the proposed method, the present application selects four advanced time series prediction models, namely PatchTST, FITS, iTransformer and ModernTCN, for experimental comparison. All models are run in a unified experimental environment, and the data set division, training round number, optimizer type and the like remain the same. The hyperparameter setting table of each model is as shown in Table 4, and the prediction comparison results are as shown in Table 5. The experimental results prove that the method in the present application is significantly better than the existing methods at multiple prediction steps, showing stronger modeling ability and generalization performance.

[0112] Table 4 Hyperparameter settings of each comparison model

[0113] Table 5 Prediction results of each comparison model

[0114] The output curves of the method proposed in this invention in prediction tasks with different step sizes are as follows: Figure 14 As shown. Figure 14 Visualize the prediction output of the MSGSE-NSCF model. Figure 14 This includes model prediction results at T=32, T=48, T=96, and T=168.

[0115] Depend on Figure 14 As can be seen, the MSGSE-NSCF proposed in this paper can effectively predict NOx emission concentrations. Specifically, in short-step prediction tasks, the model can accurately fit short-term fluctuations in NOx concentrations with small errors, indicating that the model has strong modeling and response capabilities for local time-series features. In longer-step prediction tasks, although the model error increases slightly compared to short-term predictions due to the increased prediction span, the overall trend remains consistent with the true value. The model can accurately predict the changing trend and main fluctuation direction of NOx concentrations, demonstrating its good long-term modeling ability and certain generalization performance.

[0116] Therefore, this invention provides a method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF, which can preserve the nonlinear dependence, original structure and dynamic changes of the data, model non-stationary time series and maintain the output scale, and also achieve synergistic enhancement of time domain-frequency domain and global-local, enhance selective modeling of periodic and key frequency components, and obtain accurate NOx emission prediction results.

[0117] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0118] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF, characterized in that, include: The raw emission data of urban solid waste incineration is obtained, and the key variables and nonlinear dependencies of NOx emissions in the raw emission data are analyzed using the mutual information method. A non-stationary cross-transformer is constructed based on the Crossformer to retain the original time-series information of the raw emission data. Based on the non-stationary crossover transformer and the original time-series information, a non-stationary gated spectrum enhancement submodule and a gated convolutional attention fusion submodule are constructed to obtain a multi-scale time-frequency feature enhancement module, so as to extract the spatiotemporal enhancement representation and realize the time-frequency domain feature fusion modeling. Based on the multi-scale time-frequency feature enhancement module, the historical step size, segment step size, segment sequence merging step size, and number of modules are defined to obtain hyperparameters. Hyperparameters are then validated to obtain reasonable parameters for the model. Based on the reasonable parameters of the model, an emission prediction model based on a non-stationary cross-transformer and the multi-scale time-frequency feature enhancement module is constructed to perform feature alignment fusion and prediction output to obtain the NOx emission concentration.

2. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 1, characterized in that, Raw emission data from urban solid waste incineration were obtained. The key variables and nonlinear dependencies of NOx emissions in the raw emission data were analyzed using the mutual information method. A non-stationary cross-transformer was constructed based on the Crossformer to preserve the original time-series information of the raw emission data, including: The process technology of urban solid waste incineration is obtained to acquire raw emission data. The mutual information method is used to analyze the NOx sources, NOx types, and the impact of process variables on NOx in the raw emission data to obtain key variables and nonlinear dependencies. Based on the Crossformer model architecture, an encoder and decoder are designed to obtain an initial model. Based on the initial model, the raw emission data is standardized and the overall non-stationary factor is calculated to obtain the raw time series. The original time series is segmented to obtain segmented time series and corresponding segmented non-stationary factors. The segmented time series are then merged, and the segmented stationary factors are linearly mapped to complete the structural optimization of the initial model, resulting in a non-stationary crossover transformer to preserve the original time series information of the original emission data.

3. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 2, characterized in that, The encoder includes a non-stationary attention layer for focusing on temporal dynamic changes, a one-dimensional convolutional layer for extracting short-term local features, and a cross-attention layer for modeling dynamic associations among multiple variables. The decoder includes a two-layer attention layer for simultaneously focusing on local prediction coherence and global trend consistency, a cross-attention layer for associating prediction results with historical data, and an output denormalization layer for interpreting prediction results.

4. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 3, characterized in that, The construction process of the non-stationary gated spectrum enhancement submodule includes: For the output of the non-stationary attention layer, a multi-window partition is performed to obtain a multi-scale window. A one-dimensional real-number fast Fourier transform is performed on the multi-scale window to obtain a frequency domain representation. Based on the frequency domain representation, learnable shared weights are introduced into the spectrum to obtain an enhanced frequency domain representation. Based on the enhanced frequency domain representation, the mean value of each frequency component is calculated on the channel to obtain the average frequency response intensity. The average frequency response intensity is then input into a lightweight gating network to obtain frequency domain weights, which are used to suppress noise bands and enhance key frequency bands. The lightweight gating network consists of two fully connected layers, ReLU, and Sigmoid. For the frequency domain weights, perform an inverse Fourier transform and merge the multi-scale windows to obtain the window merging result. Then, sum and average the window merging results to obtain the time domain representation.

5. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 4, characterized in that, The construction process of the gated convolutional attention fusion submodule includes: Based on the original time-series information and the frequency domain representation, the cross-attention layer is used to capture the dependencies between multiple variables, resulting in a spatially enhanced representation and completing spatial dependency modeling. Based on the spatial augmentation representation, a one-dimensional convolution with three branches is constructed. The one-dimensional convolution is used to extract short-term local patterns, mid-term local patterns and long-term local patterns to obtain branch outputs. The branch outputs are then spliced, channel compressed and fused to obtain multi-scale convolutions. The spatial augmentation representation and the multi-scale convolution are concatenated and then input into a gated weight generation network to obtain fusion weights. Based on the fusion weights, the spatial augmentation representation and the multi-scale convolution are adaptively weighted to obtain gated augmentation and fusion features. Based on the gated enhancement and the fused features, linear mapping is performed using the one-dimensional convolution, and steady-state enhancement is performed using residual connections. Then, self-attention is introduced into the fused features to complete global context supplementation, thereby obtaining a spatiotemporal enhanced representation and realizing time-frequency domain feature fusion modeling.

6. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 5, characterized in that, Based on the multi-scale time-frequency feature enhancement module, the historical step size, segment step size, segment sequence merging step size, and number of modules are defined for hyperparameter verification to obtain reasonable model parameters, including: Based on the multi-scale time-frequency feature enhancement module, the historical step size, segment step size, segment sequence merging step size, and number of modules are defined. Based on the historical step size and the segmented step size, calculate the initial number of segments and the remaining data, and determine whether the remaining data is zero. If not, perform data filling. Based on the segmentation step size and the segment sequence merging step size, determine whether segment merging needs to be padded, and reset the segmentation step size and the segment sequence merging step size according to the determination result; The coupling relationship between the historical step size, the segmented step size, the segmented sequence merging step size, and the number of modules is traversed and verified to complete the hyperparameter verification and obtain reasonable model parameters.

7. The method for predicting NOx emissions from urban solid waste incineration based on MSGSE-NSCF according to claim 6, characterized in that, Based on the reasonable parameters of the model, an emission prediction model based on a non-stationary cross-transformer and the multi-scale time-frequency feature enhancement module is constructed for feature alignment and fusion and prediction output to obtain NOx emission concentration, including: Based on the reasonable parameters of the model, an emission prediction model based on a non-stationary crossover transformer and the multi-scale time-frequency feature enhancement module is constructed. Based on the emission prediction model, the output of each of the multi-scale time-frequency feature enhancement modules is linearly mapped to unify the module dimensions and scale; The output of the multi-scale time-frequency feature enhancement module is weighted and fused, and then the weighted and fused result is de-standardized to restore the original data scale and obtain the NOx emission concentration.

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