A Multi-Model-Based Method for Predicting CO2 Emission Concentrations in MSWI Processes

Abstract

The application provides a multi-model-based MSWI process CO2 emission concentration prediction method, and belongs to the field of CO2 emission concentration prediction, and comprises the following steps: a linear main model is constructed by using an ARIMA algorithm; CO2 emission concentration prediction is performed by using the linear main model to obtain a main model prediction result; a non-linear compensation model is constructed by using an LSTM algorithm with the difference between the main model prediction result as an input value, and a prediction compensation result is obtained; and the main model prediction result and the prediction compensation result are added to obtain a target CO2 emission concentration prediction result. Through the combination of the ARIMA algorithm and the LSTM algorithm, prediction compensation is performed on the basis of the main model prediction by using a neural network model, so that high-precision prediction of the CO2 emission concentration is realized.

Description

Technical Field

[0001] This invention relates to the field of CO2 emission concentration prediction, and in particular to a multi-model-based method for predicting CO2 emission concentration in MSWI processes. Background Technology

[0002] The main methods for treating municipal solid waste include recycling, landfill, and incineration. Among these, municipal solid waste incineration, also known as MSWI, has become a widely adopted technology due to its significant advantages in harmlessness, volume reduction, and resource recovery, achieving reduction rates of 70% and 90%, respectively. MSWI processes emit flue gas containing pollutants such as CO2, NOx, and dioxins. Predicting CO2 concentration is essentially a time series modeling problem, and many researchers have studied CO2 emission concentration prediction. The Differential Integrated Moving Average Autoregressive Model (ARIMA) is a classic time series prediction model suitable for non-stationary data, effectively fitting the linear characteristics in time series data. Long Short-Term Memory Recurrent Neural Networks (LSTM) have strong nonlinear modeling capabilities. However, research shows that using only ARIMA or LSTM models cannot achieve high-precision predictions.

[0003] However, existing technologies do not employ both ARIMA and LSTM models for multi-step prediction of CO2 emission concentrations. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a multi-model-based method for predicting CO2 emission concentrations in MSWI processes. By combining the ARIMA and LSTM algorithms, a neural network model is used to compensate for the predictions based on the master model, thereby achieving high-precision prediction of CO2 emission concentrations.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A multi-model-based method for predicting CO2 emission concentrations from MSWI processes, comprising:

[0007] Construct a linear master model using the ARIMA algorithm;

[0008] CO2 emission concentration was predicted using a linear master model, and the prediction results of the master model were obtained.

[0009] Using the residual of the prediction result of the main model as the input value, the LSTM algorithm is used to construct a nonlinear compensation model and predict the compensation result;

[0010] The target CO2 emission concentration prediction result is obtained by adding the prediction result of the master model and the prediction compensation result.

[0011] Preferably, the linear master model is constructed using the ARIMA algorithm, including:

[0012] The Z-Score method was used to process outliers in the pre-collected CO2 dataset to obtain a preprocessed dataset.

[0013] The stationarity of the preprocessed dataset is tested using the extended Dickie-Fowler test to obtain the sequence stationarity results; the sequence stationarity results include: sequence stationarity and sequence non-stationarity;

[0014] When the sequence stationarity result is that the sequence is non-stationary, a difference operation is performed on the preprocessed dataset to obtain a stationary sequence and the difference order.

[0015] Based on the stationary sequence, the autoregression order and moving average order of the stationary sequence are determined using the Bayesian information criterion.

[0016] The difference order, the autoregression order, and the moving average order are input into the ARIMA algorithm to obtain the linear master model.

[0017] Preferably, using the residual of the prediction result of the main model as the input value, the LSTM algorithm is used to construct a nonlinear compensation model and predict the compensation result, including:

[0018] Calculate the prediction residual between the main model prediction result and the preset true value;

[0019] The predicted residuals are standardized using the minimum-maximum normalization method to obtain a standard input sequence.

[0020] The standard input sequence is propagated forward using the LSTM algorithm to obtain the forward output;

[0021] Based on the forward output, a preset loss function is calculated to obtain error data;

[0022] Based on the error data, the training parameters of the LSTM algorithm are updated using backpropagation until the prediction of the standard input sequence ends, thus obtaining the nonlinear compensation model and the prediction compensation result.

[0023] Preferably, a linear master model is used to predict CO2 emission concentrations, and the master model prediction results are obtained, including:

[0024] Calculate the standardized residuals of the linear master model, and determine whether the linear master model satisfies a normal distribution by using a residual scatter plot to obtain an applicability judgment result; the applicability judgment result includes: conforming to a normal distribution and not conforming to a normal distribution;

[0025] When the applicability judgment result is that it conforms to a normal distribution, the Durbin-Watson test is used to test the validity of the linear master model to obtain the autocorrelation detection result; the autocorrelation detection result includes: having obvious autocorrelation and not having obvious autocorrelation.

[0026] When the linear master model has significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result.

[0027] Preferably, based on the stationary sequence, the autoregressive order and moving average order of the stationary sequence are determined using the Bayesian information criterion, including:

[0028] The stationary sequence is centered and subjected to Fourier transform to obtain a centered sequence; the formula used for the centered process is as follows: y d For the centered sequence; y s The stationary sequence is described above. For y s The j-th element in; The number of samples in the centered sequence; the formula used for the Fourier transform includes: as well as f nextpow2 (·) to satisfy the condition The smallest integer n p N FFT The number of points in the Fourier transform; f is the length of the stationary sequence; fft For the centered sequence; For y d The j-th element in f fft The g-th element in;

[0029] Based on the centered sequence, the formula is used. and formula Calculate the autocorrelation coefficient; f fft The j-th element in c; acf The centered sequence; It is the g-th element of the centered sequence;

[0030] Based on the autocorrelation coefficient, using the formula Calculate the autoregressive covariance sequence; c AR The autoregressive covariance sequence is described above. For y d Length;

[0031] The autoregression order is calculated based on the autoregressive covariance sequence.

[0032] The stationary sequence is filtered to obtain a filtered sequence; the formula used for the filtering process is: For x filter The j-th element in; For y s The j-th element in n a and n b All are control variables;

[0033] Based on the filtered sequence, the formula is used. Calculate the moving average covariance sequence; c MA The moving average covariance sequence; For c acf The first to the (q+1)th elements in the array; For y d The i-th element in;

[0034] The moving average order is calculated based on the moving average covariance sequence.

[0035] Preferably, the standard input sequence is forward-propagated based on the LSTM algorithm to obtain the forward output, including:

[0036] Calculate the forgetting process value and forgetting output value of the forgetting gate in the LSTM algorithm;

[0037] Based on the forgotten output value, calculate the input process value, input-output value, and cell state update value of the input gate in the LSTM algorithm;

[0038] Based on the input and output values, calculate the output process value of the output gate in the LSTM algorithm and the forward output.

[0039] Preferably, the standardized residuals of the linear master model are calculated, and the applicability judgment result is obtained by using a residual scatter plot to determine whether the linear master model satisfies a normal distribution. This includes:

[0040] The standardized residuals are sorted in ascending order to obtain an ascending residual sequence;

[0041] Calculate the horizontal axis coordinates based on the ascending residual sequence;

[0042] A residual scatter plot is drawn based on the ascending residual sequence and the horizontal axis coordinates;

[0043] If all data points in the residual scatter plot are near the preset reference line, then the applicability judgment result of the linear master model is determined to conform to the normal distribution.

[0044] Preferably, when the linear master model exhibits significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result, including:

[0045] Based on the stationary sequence, the predicted value is calculated using the linear master model;

[0046] The predicted value is updated to the last element of the stationary sequence, and the first element of the stationary sequence is removed to obtain the updated stationary sequence. The process returns to the step "Calculate the predicted value using the linear master model based on the stationary sequence" until all data in the stationary sequence are the predicted value, at which point the update stops and the master model prediction result is obtained.

[0047] The present invention discloses the following technical effects:

[0048] This invention provides a multi-model-based method for predicting CO2 emission concentration in MSWI processes. By using a linear master model and a nonlinear compensation model to predict CO2 emission concentration in multiple steps, this method solves the problem of large prediction deviations in CO2 emission concentration in MSWI processes and achieves accurate prediction of CO2 emission concentration. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 This is a flowchart of CO2 emission concentration prediction provided in an embodiment of the present invention;

[0051] Figure 2 MSWI process flow diagram provided for embodiments of the present invention;

[0052] Figure 3 A diagram illustrating the CO2 emission prediction strategy provided in this embodiment of the invention;

[0053] Figure 4 The ARIMA master model prediction strategy provided in this embodiment of the invention;

[0054] Figure 5 The prediction strategy of the LSTM compensation model provided in the embodiments of the present invention;

[0055] Figure 6 LSTM cell diagram provided for embodiments of the present invention;

[0056] Figure 7The residual QQ diagram provided for embodiments of the present invention;

[0057] Figure 8 The prediction results are provided for different prediction steps in the embodiments of the present invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] The purpose of this invention is to provide a multi-model-based method for predicting CO2 emission concentrations in MSWI processes. By combining the ARIMA and LSTM algorithms, a neural network model is used to compensate for the predictions made by the master model, thereby achieving high-precision prediction of CO2 emission concentrations.

[0060] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Figure 1 The flowchart for predicting CO2 emission concentration provided in the embodiments of the present invention is as follows: Figure 1 As shown, this invention provides a multi-model-based method for predicting CO2 emission concentrations in MSWI processes, including:

[0062] Step 100: Construct a linear master model using the ARIMA algorithm;

[0063] Step 200: Predict CO2 emission concentration using the linear master model and obtain the master model prediction results;

[0064] Step 300: Using the residual of the prediction result of the main model as the input value, construct a nonlinear compensation model and predict the compensation result using the LSTM algorithm;

[0065] Step 400: Add the prediction result of the master model and the prediction compensation result to obtain the target CO2 emission concentration prediction result.

[0066] Furthermore, a linear master model is constructed using the ARIMA algorithm, including:

[0067] The Z-Score method was used to process outliers in the pre-collected CO2 dataset to obtain a preprocessed dataset.

[0068] The stationarity of the preprocessed dataset is tested using the extended Dickie-Fowler test to obtain the sequence stationarity results; the sequence stationarity results include: sequence stationarity and sequence non-stationarity;

[0069] When the sequence stationarity result is that the sequence is non-stationary, a difference operation is performed on the preprocessed dataset to obtain a stationary sequence and the difference order.

[0070] Based on the stationary sequence, the autoregression order and moving average order of the stationary sequence are determined using the Bayesian information criterion.

[0071] The difference order, the autoregression order, and the moving average order are input into the ARIMA algorithm to obtain the linear master model.

[0072] Preferably, using the residual of the prediction result of the main model as the input value, the LSTM algorithm is used to construct a nonlinear compensation model and predict the compensation result, including:

[0073] Calculate the prediction residual between the main model prediction result and the preset true value;

[0074] The predicted residuals are standardized using the minimum-maximum normalization method to obtain a standard input sequence.

[0075] The standard input sequence is propagated forward using the LSTM algorithm to obtain the forward output;

[0076] Based on the forward output, a preset loss function is calculated to obtain error data;

[0077] Based on the error data, the training parameters of the LSTM algorithm are updated using backpropagation until the prediction of the standard input sequence ends, thus obtaining the nonlinear compensation model and the prediction compensation result.

[0078] Preferably, a linear master model is used to predict CO2 emission concentrations, and the master model prediction results are obtained, including:

[0079] Calculate the standardized residuals of the linear master model, and determine whether the linear master model satisfies a normal distribution by using a residual scatter plot to obtain an applicability judgment result; the applicability judgment result includes: conforming to a normal distribution and not conforming to a normal distribution;

[0080] When the applicability judgment result is that it conforms to a normal distribution, the Durbin-Watson test is used to test the validity of the linear main model to obtain the autocorrelation detection result; the autocorrelation detection result includes: having obvious autocorrelation and not having obvious autocorrelation.

[0081] When the linear master model has significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result.

[0082] Specifically, based on the stationary sequence, the autoregressive order and moving average order of the stationary sequence are determined using the Bayesian information criterion, including:

[0083] The stationary sequence is centered and subjected to Fourier transform to obtain a centered sequence; the formula used for the centered process is as follows: y d For the centered sequence; y s The stationary sequence is described above. Indicates y s The j-th element in; The number of samples in the centered sequence; the formula used for the Fourier transform includes: as well as f nextpow2 (·) to satisfy the condition The smallest integer n p N FFT The number of points in the Fourier transform; f is the length of the stationary sequence; fft For the centered sequence; Indicates y d The j-th element in f fft The g-th element in;

[0084] Based on the centered sequence, the formula is used. and formula Calculate the autocorrelation coefficient; f fft The j-th element in c; acf The centered sequence; It is the g-th element of the centered sequence;

[0085] Based on the autocorrelation coefficient, using the formula Calculate the autoregressive covariance sequence; c AR The autoregressive covariance sequence is described above. For y d Length;

[0086] The autoregression order is calculated based on the autoregressive covariance sequence.

[0087] The stationary sequence is filtered to obtain a filtered sequence; the formula used for the filtering process is: For x filter The j-th element in; For y s The j-th element in n a and n b All are control variables;

[0088] Based on the filtered sequence, the formula is used. Calculate the moving average covariance sequence; c MA The moving average covariance sequence; c acf The first to the (q+1)th elements in the array; For y d The i-th element in;

[0089] The moving average order is calculated based on the moving average covariance sequence.

[0090] Further, the standard input sequence is forward-propagated based on the LSTM algorithm to obtain the forward output, including:

[0091] Calculate the forgetting process value and forgetting output value of the forgetting gate in the LSTM algorithm;

[0092] Based on the forgotten output value, calculate the input process value, input-output value, and cell state update value of the input gate in the LSTM algorithm;

[0093] Based on the input and output values, calculate the output process value of the output gate in the LSTM algorithm and the forward output.

[0094] Specifically, the standardized residuals of the linear master model are calculated, and the applicability judgment result is obtained by using a residual scatter plot to determine whether the linear master model satisfies a normal distribution, including:

[0095] The standardized residuals are sorted in ascending order to obtain an ascending residual sequence;

[0096] Calculate the horizontal axis coordinates based on the ascending residual sequence;

[0097] A residual scatter plot is drawn based on the ascending residual sequence and the horizontal axis coordinates;

[0098] If all data points in the residual scatter plot are near the preset reference line, then the applicability judgment result of the linear master model is determined to conform to the normal distribution.

[0099] Furthermore, when the linear master model exhibits significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result, including:

[0100] Based on the stationary sequence, the predicted value is calculated using the linear master model;

[0101] The predicted value is updated to the last element of the stationary sequence, and the first element of the stationary sequence is removed to obtain the updated stationary sequence. The process returns to the step "Calculate the predicted value using the linear master model based on the stationary sequence" until all data in the stationary sequence are the predicted value, at which point the update stops and the master model prediction result is obtained.

[0102] refer to Figure 2 The MSWI process flow includes:

[0103] 1) Storage and Fermentation Stage: MSW (municipal biochemical waste) is transported to the unloading workshop of the MSWI power plant, dumped into a solid waste pool for mixing, and fermented in the solid waste pool for 3 to 7 days to increase its calorific value. After fermentation, it is transferred to a hopper via a grab bucket to prepare for the next stage;

[0104] 2) Solid Waste Combustion Stage: The feeder pushes the MSW into the combustion chamber for complete combustion. The MSW passes through drying, Combustion 1, Combustion 2, and the burnout grate in sequence; the required combustion air is injected into the furnace through primary and secondary air fans via air preheating; the ignition burner is used to ignite the incinerator; the auxiliary burner is used to supplement the heat required for the combustion process. The residue after complete combustion is sent to the slag pool by a slag remover and then transported by truck to a designated department for further processing.

[0105] 3) Waste heat exchange stage: The high-temperature flue gas from the solid waste combustion stage simply passes through the denitrification system to reduce the NOx concentration, and then enters the waste heat exchange stage through the induced draft fan. The high-temperature flue gas passes through the superheater, evaporator and economizer in succession. Water is required during the process, and it exchanges heat with the liquid water in the boiler drum to generate high-temperature steam and generate flue gas G1;

[0106] 4) Steam power generation stage: The high-temperature steam obtained in the waste heat exchange stage enters the steam turbine generator to generate electricity in the power plant. This stage is crucial for realizing resource reuse.

[0107] 5) Flue gas treatment stage: Flue gas G1 enters the deacidification reactor. Activated carbon and slaked lime are added to the activated carbon tank and slaked lime tank respectively for pollutant adsorption. After washing with reclaimed water, it enters the bag filter for dust removal. Some fly ash re-enters the reactor through the mixer, and the remaining fly ash enters the fly ash tank. The flue gas G2 generated after dust removal enters the final stage through the induced draft fan. The hammering equipment in the process improves the dust removal efficiency by removing accumulated ash, and the waste is removed by the ash conveyor.

[0108] 6) Flue Gas Emission Stage: The flue gas G2 obtained in the flue gas purification stage is directly discharged into the atmosphere through the chimney. Flue gas G3 contains CO, CO2, dioxins, and NO. xPollutants such as SO2, HCl and particulate matter.

[0109] Furthermore, as a typical industrial process, the MSWI process generates greenhouse gases such as CO2 during its operation, making the control and reduction of carbon emissions crucial. Combustion efficiency (CE) reflects the completeness of combustion; specifically, it is the ratio of the actual heat available to heat the combustion products when a specified amount of fuel is burned in the combustion chamber to the lower heating value released when the fuel achieves complete combustion under adiabatic conditions. As a quantitative indicator of combustion status, its calculation formula is as follows:

[0110]

[0111] Where, γ CO Indicates the concentration of CO. This represents the CO2 concentration. The combustion efficiency of the MSWI process is related to both CO and CO2 concentrations. Rapid and accurate prediction of CO2 emission concentration in the MSWI process allows for timely control of changes in the MSWI process's emission concentration (CE), helping to reduce MSWI operating costs. For the MSWI process, comprehensive and accurate prediction of CO2 emissions is a prerequisite for developing emission mitigation strategies. Affected by frequent fluctuations in operating conditions and other factors, CO2 emission concentration data contains both linear and nonlinear characteristics. Therefore, this embodiment provides a prediction method capable of simultaneously fitting the linear and nonlinear characteristics of the data.

[0112] refer to Figure 3 The multi-step prediction strategy based on ARIMA and LSTM algorithms adopted in this embodiment includes three parts: a master model based on ARIMA, a compensation model based on LSTM long short-term neural network, and output ensemble. Wherein, y ori y represents the raw CO2 emission concentration data for the MSWI process; y represents the data after outlier handling; p, d, and q are the autoregression order, differencing order, and moving average order of the ARIMA model, respectively; f ARIMA (·) and f LSTM (·) represent the constructed ARIMA model and LSTM model, respectively; and Represent the predicted values ​​of the ARIMA master model, the LSTM compensation model, and the ARIMA-LSTM hybrid model, respectively; r and r str These are the residual sequence predicted by the ARIMA model and the normalized sequence, respectively; r t str This represents the ARIMA model residual at time t; c represents the predicted value at time t+n; n represents the prediction step size; t and h tThis represents the cell state and hidden state of the LSTM network at time t.

[0113] refer to Figure 4 The main model prediction strategy includes: input dataset y ori After outlier handling, stationarity testing, differencing, and parameter determination, a single-step prediction strategy is employed to obtain the output of the ARIMA master model.

[0114] refer to Figure 5 The compensation model prediction strategy includes: calculating the output of the ARIMA master model. Compared with real data y ori The residuals, after standardization, are input into the LSTM model, which employs a multi-input multi-output iterative multi-step prediction strategy to obtain the predicted values ​​of the LSTM compensated model.

[0115] Furthermore, the integrated output strategy includes: combining the predictions from the ARIMA master model... The predicted values ​​of the LSTM compensation model The predicted values ​​are obtained by combining and adding the results.

[0116] Specifically, the ARIMA model, or Autoregressive Moving Average, essentially uses historical information from the data itself to predict future values. The AR model, or Autoregressive model, considers the influence of past observations on the current value, and its advantage lies in handling data with long historical trends, but it cannot handle data with outliers or high noise levels. The MA model, or Moving Average model, calculates the impact of past prediction errors on the current value and can be used to handle noisy data. The ARIMA model combines the advantages of both models, and its expression is as follows:

[0117]

[0118] Among them, s constant For the constant term, y t Let y be the value of y at time t, and s be the value of y at time t. AR Let s be the AR coefficient. MA It is the MA coefficient, ε t It is the error term at time t; and They represent s respectively AR and s MA The first element in the expression; t represents time.

[0119] Furthermore, the modeling of the ARIMA master model can be divided into six steps: outlier handling, stationarity testing, differencing, determining model parameters, model testing, and outputting model predictions. These steps are described in detail below:

[0120] 1) Outlier handling: Let the CO2 dataset be denoted as y ori ={y1,y2…y t This embodiment uses the Z-Score method to handle outliers that may be caused by equipment malfunctions or environmental problems. Z-Score is a method used to measure the relative distance of a data point to its mean and standard deviation. score The score is calculated using the following formula:

[0121]

[0122] Among them, z score The z-score value. Indicates y ori length, f std (·) indicates the standard deviation.

[0123] When z of a certain sample score When the absolute value of a value exceeds the empirically set value of 3, it is considered an outlier and the entire data record is deleted. Here, the dataset after processing outliers is denoted as y.

[0124] 2) Stationarity test: This embodiment uses the augmented Dickey-Fuller test (ADF) to determine the stationarity of the time series data.

[0125]

[0126] in, The length of y is represented by m. ORT for Normalized column vectors Represents the first to Nth elements in y. total -1 element, s adf It is merely an intermediate variable and has no specific meaning. ORT and s adf The calculation formula is as follows:

[0127]

[0128] Among them, ||·|| and (·) T These represent modulo and transpose, respectively. The calculation is as follows:

[0129]

[0130] Where I is the identity matrix.

[0131] Calculate the polynomial coefficients s coeff Covariance s cov The calculation formula is as follows:

[0132]

[0133] Among them, s coeff S represents the polynomial coefficients. cov For covariance, Indicates the second to the third in y Each element.

[0134] Calculate the test statistic s test The formula is as follows:

[0135] s test =(s coeff -1) / f sqrt (s cov )

[0136] Among them, s test To test the statistic, f sqrt (·) indicates taking the square root.

[0137] Calculate the critical value s for hypothesis testing value The distance is obtained by looking up a table. The two smallest sample sizes N1 and N2 and their corresponding critical values ​​s at the significance level α value1 and s value2 .

[0138] The value of N was calculated using linear interpolation. total -1 and the critical value s at the significance level α value The following system of equations is obtained:

[0139]

[0140] Where, k s Let b be the slope. s This is the intercept.

[0141] Solving this system of equations yields k. s and b s and in sample size And the critical value s at significance level α value :

[0142]

[0143] If s test <s value A positive result indicates that the sequence is stationary; conversely, a negative result indicates that the sequence is not stationary.

[0144] 3) Difference: If the sequence y is non-stationary, a difference operation is needed to achieve stationarity. Perform a first difference operation on the dataset according to the following formula:

[0145] Δy t =y t -y t-1

[0146] Where, Δy t This is the value after the difference.

[0147] After performing i differentiating operations, the sequences are combined in chronological order to form a difference sequence, denoted as [i, i]. For this sequence Perform the ADF test again. If the sequence is still non-stationary, continue the differencing operation until it becomes stationary. Denote this stationary sequence as y. s .

[0148] 4) Determine model parameters: After determining the parameter difference order d, continue to determine the parameters for the sequence y. s The parameters are the autoregressive order p and the moving average order q. The Bayesian information criterion (BIC) is used to determine the parameters to prevent excessive model complexity. Different combinations of parameters p and q are iterated, and their s... BIC The value is calculated according to the following formula:

[0149]

[0150] in, For y s The sample size, k is the number of estimated parameters in the model, k = p + q + 2, ln(l A ) is the maximum log-likelihood of the model fit, s BIC This represents the BIC value under different combinations of p and q.

[0151] The calculation process for estimating the AR coefficient is as follows:

[0152] First, y s The centralized processing is performed using the following formula:

[0153]

[0154] Among them, y d This represents the sequence after centering.

[0155] Next to y d Perform a Fourier transform to obtain f fft :

[0156]

[0157] Where, N FFT f is the number of points in the Fourier transform. fft For y d The result of performing the Fourier transform, f represents conjugationnextpow2 (·) indicates that a condition is met. The smallest integer n p .

[0158] The autocorrelation coefficient c is calculated according to the following formula. acf :

[0159]

[0160] Among them, c acf This is the autocorrelation coefficient.

[0161] Calculate the covariance sequence of the AR process:

[0162]

[0163] Among them, c AR For the covariance of the AR process, For y d The length.

[0164] Calculate the AR coefficient:

[0165]

[0166] Among them, f tp (·) denotes the Toeplitz matrix, and |a:-1:c| represents the absolute value of a vector that decreases by -1 each time until it reaches c. c AR The (q+1)th to (q+p)th elements in the array.

[0167] To determine the stability of the AR model polynomial, this embodiment sets a threshold u. ARMA If the following conditions are met, the AR model polynomial is considered unstable and s needs to be reset. AR =0.

[0168] |s AR |≥1-u ARMA

[0169] Among them, u ARMA is the threshold for judging the polynomial of the AR model, and |·| represents the absolute value.

[0170] The calculation process for estimating the MA coefficient is as follows:

[0171] First, consider the sequence y. s Filtering yields x filter :

[0172]

[0173] Where, x filter For y sThe filtered vector x represents filter The j-th element in.

[0174] The constant s is calculated according to the following formula. constant :

[0175]

[0176] in, For x filter The length.

[0177] The covariance sequence c of the MA process is calculated according to the following formula. MA :

[0178]

[0179] Among them, c MA The covariance of the MA process, c acf The first to q+1 elements in the middle.

[0180] Set MA coefficients s MA The variable s is 0. MA1 Used to store the MA coefficients obtained from previous iterations, with a convergence tolerance of u. tol When the conditions are met At that time, the following cycle will begin:

[0181] Settings MA1 =s MA The variance of the white noise e(t) is var e(t) The calculation formula is as follows:

[0182]

[0183] Let l = q, and calculate the MA coefficient s according to the following formula. MA :

[0184]

[0185] Then execute l = l - 1, and continue calculating the above expression until l = 0, at which point the calculation stops. This process continues until... Obtain the MA coefficients s MA ,in s MA1 The j-th element in.

[0186] Determine the stability of the MA model polynomial. If the condition |s MA |≥1-u ARMA If so, the MA model polynomial is considered unstable and s needs to be reset. MA =0.

[0187] To support non-seasonal differencing operations, it is necessary to modify s AR The formula is as follows:

[0188] s ARd =f conv ((1,-s AR ),(1,-1))

[0189] Among them, f conv (·) indicates that a convolution operation is performed.

[0190] Let l = max(p,q) + 1, and calculate the predicted value at time j according to the following formula:

[0191]

[0192] in Indicates y predict The l-th element in y represents the first to max(p,q) elements in y, and represents s. ARd The second to the last element.

[0193] Then execute l = l + 1, and continue executing the following formula until l > (2 * max(p, q)):

[0194]

[0195] in, This represents the predicted value at time l during model estimation, and max(·) represents finding the maximum value. s ARd The second to the last element.

[0196] Finally, we get y new :

[0197]

[0198] Where y new It has no practical significance and is merely an intermediate variable.

[0199] Next, the residual r is inferred. e Let l = max(p, q) + 1, r e =0. The residual is calculated using the following formula:

[0200]

[0201] Where, r e Represents the residuals during model estimation. Indicates y new The l-th to l-max(p,q) elements in the array. Indicates r eThe (l-1)th to (l-max(p,q)th elements in the array.

[0202] Then execute l = l + 1, and continue executing the above formula until... Finally, we get r. e .

[0203] Distribution constant variance v constant :

[0204] v constant =(1,var e(t) )

[0205] Calculate the log-likelihood value using the following formula:

[0206]

[0207] in, Indicates v constant The j-th element, e j This represents the j-th element in e.

[0208] The BIC values ​​under different parameter combinations are calculated, and the parameter combination with the smallest BIC value is finally determined.

[0209] 5) Model Validation: After determining the parameters, the residual QQ plot (residual scatter plot) is used to determine whether the residual sequence follows a normal distribution, thus validating the model's applicability. First, the standardized residual r of the model is calculated. std The formula is as follows:

[0210] r std =r e / f sqrt (var e(t) )

[0211] Where, r std This represents the standard deviation used in model estimation.

[0212] Next, for r std Sort in ascending order to get r stdup Calculate the x-axis coordinate of the drawing object. qq for:

[0213]

[0214] Determine the coordinates of the plotting point in the residual QQ plot as (x qq r stdup If the deviation between the data points and the straight line is small, and most of them fall on the straight line, it proves that the data conforms to a normal distribution. The straight line mentioned above is the red line in the QQ plot, called the "reference line" or "fitting line," and its function is to determine whether the residual data follows a normal distribution.

[0215] The Durbin-Waston (DW) test is used to assess the model's effectiveness. A DW test value close to 2 indicates that the residual series has no significant autocorrelation. The formula for calculating its statistic is as follows:

[0216] s DW =((f diff (r std )) T *f diff (r std )) / ((r std ) T *r std )

[0217] Among them, f diff (·) indicates the difference operation, s DW This is the DW test value.

[0218] 6) Model Prediction: An ARIMA model with defined parameters is denoted as an ARIMA(p, d, q) model. An ARIMA model requires initial values ​​to start; the number of initial values ​​is N. start = p + q + 2. Therefore, this embodiment firstly... Get N start Predicted value at time +1 Next, based on Get N start Predicted value at time +2 Continuing in a loop, assuming the length of sequence y is... Finally, the ARIMA model prediction values ​​are obtained. in express The Nth start +1 element.

[0219] refer to Figure 6 The LSTM (Long Short-Term Memory) model is a variant of the Recurrent Neural Network (RNN). It utilizes an alternative method based on the hidden state h at time t-1. t-1 To calculate the hidden state h at time t t This avoids directly calculating the hidden layer values ​​using the previous formulas, solves the gradient problem that occurs in recurrent neural networks, and overcomes the difficulty of RNNs in handling long-order dependencies of data.

[0220] Furthermore, the LSTM compensation model in this embodiment adopts a multi-step prediction strategy based on iterative prediction, and the loss function is the mean squared error (MSE), the formula of which is as follows:

[0221]

[0222] Among them, E t The loss at time t, Let y be the predicted value at time t. t Let be the truth value at time t.

[0223] Furthermore, the LSTM compensation model performs advance... n The prediction steps are as follows:

[0224] 1) Calculate the residual: Input And y, calculate the residuals according to the following formula to obtain the input r of the LSTM model:

[0225]

[0226] 2) Data Standardization: Using the residual data r as input data, standardize it according to the following formula to obtain r0. str :

[0227]

[0228] Among them, f min (·) indicates taking the minimum value, f max (·) indicates taking the maximum value, and a and b represent the lower and upper limits of standardization, respectively.

[0229] Suppose we are performing a prediction for the m-th input window. We input the values ​​of n times before (including time t) to obtain the predicted values ​​for n times after time t. Where r t str R represents the value of r at time t. str The following input is r. t str For example, r t str The corresponding output value should be

[0230] 3) Calculate the process value f of the forgetting gate at time t. t and output value g t The forgetting gate operates on previously remembered values, allowing neurons to selectively remember or forget previous information. The input at time t is r. t str and h at time t-1 t-1 and c t-1 The forgetting gate process value f at time t can be calculated using the following formula. t And the output value g of the forget gate t :

[0231]

[0232] g t =c t-1 f t

[0233] Among them, f t Let g be the process value of the forget gate at time t. t Let σ be the output value of the forget gate at time t, and σ be the sigmoid function. and The weights and biases corresponding to the forget gate of the m-th input window are the Hadamard product, h. t-1 c represents the hidden state at time t-1. t-1 This represents the state of the nerve cells at time t-1.

[0234] 4) Calculate the process value i of the input gate at time t. t and output value c t and cell status update value The input gate operates on the input value at the current time step. Input r t str and h t-1 i is calculated according to the following formula. t , and c t :

[0235]

[0236] Among them, i t The input gate process value at time t, It is the cell state update value at time t, and tanh is the tanh function. and These are the weights and biases corresponding to the input gates of the m-th input window. and It represents the weights and biases corresponding to the updated state of the m-th input window unit.

[0237] 5) Calculate the process value o of the output gate at time t. t and output value h t Enter h t-1 r t str c t According to the following formula, o can be obtained. t and the output value h t :

[0238]

[0239] h t =o t tanh(c t )

[0240] Among them, o t Output the process value of the gate at time t. and It represents the weights and biases corresponding to the output gate of the m-th input window.

[0241] 6) Output layer: Input h t Calculate according to the following formula

[0242]

[0243] Among them, v T b v For the weights and biases of the output layer, This represents the predicted value at time t+n.

[0244] 7) Repeat steps (3)-(7) to calculate all predicted values ​​corresponding to the m-th input window, and then update the parameters.

[0245] 8) A parameter update is required after each prediction of an input window is completed. The LSTM compensation model in this embodiment requires updating 8 weights and 4 biases, as follows:

[0246] 9) This embodiment uses the backpropagation algorithm for gradient update. The derivation of the gradient is as follows:

[0247] For ease of calculation and representation, let L = t + j:

[0248] LSTM has two hidden states, h t and c t Therefore, we define two δ values, namely:

[0249]

[0250] Where E represents the loss function value.

[0251] The final sequence position L and They are respectively:

[0252]

[0253]

[0254] Where diag represents a diagonal matrix, and v represents the weights of the output layer. δ at time L represents h .

[0255] The following formula can be used to calculate the value at any time t.

[0256]

[0257] Only in the above formula Since it is an unknown term, the core issue lies in calculating h from the previous time step. t+1 For the current moment h t Partial derivative:

[0258] Assumption:

[0259]

[0260] The following formula can be used to calculate the value at any time t.

[0261]

[0262] The following formula can be used to calculate the value at any time t.

[0263]

[0264] The model for The total gradient is:

[0265]

[0266] In the next input window The calculation formula is as follows:

[0267]

[0268] Where η represents the learning rate.

[0269] The gradient calculation formulas and update formulas for other parameters are obtained by following the above process.

[0270] 10) Repeat steps (3)-(9) to calculate the predicted value of the next input window and update the network parameters until the entire sequence is predicted, and finally obtain the predicted value of the residual sequence.

[0271] Furthermore, the final output of the ARIMA-LSTM model proposed in this embodiment is obtained by adding the output of the main model and the output of the compensation model, and the calculation formula is as follows:

[0272]

[0273] in, These are the predicted values ​​from the combined model.

[0274] Optionally, the prediction strategy of this embodiment is validated by collecting actual emission data. The dataset is taken from a certain MSWI power plant, and the data within each minute is averaged, resulting in 720 sets, each containing 194 process variables. In this embodiment, a total of 720 sample data points were collected, and 28 samples were ultimately identified as outliers, leaving 692 valid data points.

[0275] An ARIMA model is built for prediction, with N initial values. start In this example, N start The value is set to 5, thus yielding 687 residual data points. The residual sequence is then divided into training, validation, and test sets in a ratio of 11:1:1.

[0276] To evaluate the model's predictive performance, the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) were selected. 2 The calculation formulas for each evaluation indicator, which serves as the evaluation metric for the model, are as follows:

[0277] MAE: Mean Absolute Error: Calculated by averaging the absolute values ​​of the differences between the predicted and actual values ​​for each sample.

[0278]

[0279] Where, n e This represents the number of samples.

[0280] RMSE: Root Mean Square Error; Root Mean Square Error (RMSE)

[0281]

[0282] Coefficient of determination R 2 Goodness of fit. Its value ranges from (0, 1), with a value closer to 1 indicating better model performance. Because its calculation results have upper and lower limits, this method has a more unified standard compared to other methods.

[0283]

[0284] in, Let y be the mean, MSE be the mean squared error, and Var be the variance.

[0285] Furthermore, the Z-Score method is used to handle outliers in the original CO2 dataset. In this embodiment, the Z-Score threshold is set to 3. As a result, a total of 28 samples are identified as outliers, which are then directly deleted to obtain sequence y.

[0286] Next, the ADF test method was used to analyze the stationarity of the sequence y, and the test statistic s was determined. test =-0.4343>s value= -1.9413, therefore the sequence y did not pass the ADF test;

[0287] Therefore, the sequence y is first-differenced, and the stationarity test is performed again. Experimental results show that the test statistic s test =-27.3156<s value = -1.9413, therefore the sequence passed the ADF test, indicating that the first-order difference sequence is stationary, and the difference order d = 1 was determined.

[0288] The BIC criterion was used to determine the model parameters for model order determination. Table 1 shows the BIC values ​​for different p, d, and q.

[0289] Table 1

[0290]

[0291]

[0292] The table shows that the BIC value is minimized when p = 1 and q = 2. At this point, the three parameters p, d, and q of the ARIMA model are all determined, which are 1, 1, and 2 respectively.

[0293] Next, residual testing was performed. The results of the residual testing are as follows: Figure 7 As shown in the figure, the scatter points are all distributed near the fitted line, proving that the residual sequence follows a normal distribution. A DW test is then performed, yielding a DW test value of 2.0122, indicating that the residual sequence is white noise data and the model satisfies the autocorrelation test. Therefore, it can be determined that the ARIMA model has extracted the linear features of the sequence y, while the nonlinear features of the sequence y are contained within the residual sequence.

[0294] Based on the ARIMA master model prediction strategy, the predicted value of the master model can be obtained, and then the residual sequence r can be obtained. The residual sequence of the ARIMA model is fitted using an LSTM model to complete the error correction. The hyperparameters of the LSTM compensation model are shown in Table 2. The LSTM model is used for multi-step prediction with 1, 2, 3, 4, and 5 steps of lead-ahead. To verify the effectiveness of the model, an LSTM multi-step prediction model, an ARIMA model, and a parallel LSTM multi-step prediction model are constructed for comparison. The parameters of the LSTM multi-step prediction model are set as follows: 64 hidden layer units, 350 training epochs, learning rate 0.003, and penalty factor 0.9. The hyperparameters of the parallel multi-step prediction model are consistent with those of the LSTM multi-step prediction model, and the output is weighted by average. To increase the model's credibility and verify the overall stability of the model, 10 repeated experiments are conducted on the three models, and the average value of the model evaluation index is taken. The prediction results on the test set are shown in Table 2. Figure 8 (a) to Figure 8As shown in (e), the evaluation indicators are shown in Table 3. Figure 8 (a) is the prediction result one step ahead; Figure 8 (b) shows the prediction results two steps ahead; Figure 8 (c) shows the prediction results 3 steps ahead; Figure 8 (d) shows the prediction results 4 steps ahead; Figure 8 (e) represents the prediction results 5 steps ahead.

[0295] Table 2

[0296]

[0297]

[0298] Table 3

[0299]

[0300]

[0301] Furthermore, a comprehensive analysis of the predicted effects is conducted. This is combined with... Figure 8 As shown in Table 3, taking the 5-step lead time prediction as an example, the R-value of the ARIMA-LSTM combined model is... 2 The R value is 0.5678, compared to the R values ​​of the LSTM model and the ARIMA / LSTM parallel model. 2 These represent improvements of 11.9% and 32.3%, respectively. The ARIMA-LSTM model proposed in this embodiment demonstrates better prediction performance compared to a single LSTM model. This is because the model combines the advantages of both models, capable of handling both linear and nonlinear features of the data. The poor performance of parallel models stems from their inability to fully utilize the complementary information between models and their inability to handle the complex linear and nonlinear components of time series data.

[0302] Specifically, the prediction performance is analyzed across different time steps. Overall, the prediction accuracy of both the LSTM model and the ARIMA / LSTM parallel model decreases with increasing prediction time steps. Taking a 5-step lead time and a 1-step lead time as examples, the R-value of the LSTM model... 2 The R-value of the ARIMA and LSTM parallel model was reduced by 4.9%. 2 The error rate decreased by 14.9% because the accumulation of errors became increasingly significant as the number of prediction steps increased, ultimately leading to a decline in model performance. The model proposed in this embodiment exhibits stable prediction accuracy and small error fluctuations, outperforming the comparative models.

[0303] The beneficial effects of this invention are as follows:

[0304] This invention achieves high-precision prediction of CO2 emission concentration by combining the ARIMA and LSTM algorithms and using a neural network model for prediction compensation based on the main model prediction.

[0305] 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.

[0306] This embodiment 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 CO2 emission concentrations from MSWI processes based on multiple models, characterized in that, include: Construct a linear master model using the ARIMA algorithm; CO2 emission concentration was predicted using a linear master model, and the prediction results of the master model were obtained. Using the residual of the prediction result of the main model as the input value, the LSTM algorithm is used to construct a nonlinear compensation model and predict the compensation result; The target CO2 emission concentration prediction result is obtained by adding the main model prediction result and the prediction compensation result; Constructing a linear master model using the ARIMA algorithm includes: The Z-Score method was used to process outliers in the pre-collected CO2 dataset to obtain a preprocessed dataset. The stationarity of the preprocessed dataset is tested using the extended Dickie-Fowler test to obtain the sequence stationarity results; the sequence stationarity results include: sequence stationarity and sequence non-stationarity; When the sequence stationarity result is that the sequence is non-stationary, a difference operation is performed on the preprocessed dataset to obtain a stationary sequence and the difference order. Based on the stationary sequence, the autoregression order and moving average order of the stationary sequence are determined using the Bayesian information criterion. The difference order, the autoregression order, and the moving average order are input into the ARIMA algorithm to obtain the linear master model; Based on stationary sequences, the autoregressive order and moving average order of the stationary sequences are determined using the Bayesian information criterion, including: The stationary sequence is centered and subjected to Fourier transform to obtain a centered sequence; the formula used for the centered process is as follows: ; y d The centered sequence; y s The stationary sequence is described above. for y s The first in j One element; The number of samples in the centered sequence; the formula used for the Fourier transform includes: , as well as ; To meet the conditions The smallest integer n p ; N FFT The number of points in the Fourier transform; The length of the stationary sequence; f fft The centered sequence; for y d The first in j One element, for f fft The first in g One element; Based on the centered sequence, the formula is used. and formula Calculate the autocorrelation coefficient; for f fft The first in j One element; The centered sequence; The first of the centered sequence g One element; Based on the autocorrelation coefficient, using the formula Calculate the autoregressive covariance sequence; The autoregressive covariance sequence is described above. for y d Length; The autoregression order is calculated based on the autoregressive covariance sequence. The stationary sequence is filtered to obtain a filtered sequence; the formula used for the filtering process is: ; for x filter The first in j One element; for y s The first in j One element, n a and n b All are control variables; Based on the filtered sequence, the formula is used. Calculate the moving average covariance sequence; The moving average covariance sequence; for c acf The first to the second q +1 element; for y d The first in i One element; The moving average order is calculated based on the moving average covariance sequence.

2. The method for predicting CO2 emission concentrations from a MSWI process based on multiple models according to claim 1, characterized in that, Using the residuals of the main model's prediction results as input values, the LSTM algorithm is used to construct a nonlinear compensation model and predict the compensation results, including: Calculate the prediction residual between the main model prediction result and the preset true value; The predicted residuals are standardized using the minimum-maximum normalization method to obtain a standard input sequence. The standard input sequence is propagated forward using the LSTM algorithm to obtain the forward output; Based on the forward output, a preset loss function is calculated to obtain error data; Based on the error data, the training parameters of the LSTM algorithm are updated using backpropagation until the prediction of the standard input sequence ends, thus obtaining the nonlinear compensation model and the prediction compensation result.

3. The method for predicting CO2 emission concentrations from a MSWI process based on multiple models according to claim 1, characterized in that, CO2 emission concentration was predicted using a linear master model, and the prediction results were obtained, including: Calculate the standardized residuals of the linear master model, and determine whether the linear master model satisfies a normal distribution by using a residual scatter plot to obtain an applicability judgment result; the applicability judgment result includes: conforming to a normal distribution and not conforming to a normal distribution; When the applicability judgment result is that it conforms to a normal distribution, the Durbin-Watson test is used to test the validity of the linear main model to obtain the autocorrelation detection result; the autocorrelation detection result includes: having obvious autocorrelation and not having obvious autocorrelation. When the linear master model has significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result.

4. The method for predicting CO2 emission concentrations from a MSWI process based on multiple models according to claim 2, characterized in that, The standard input sequence is forward-propagated based on the LSTM algorithm to obtain the forward output, including: Calculate the forgetting process value and forgetting output value of the forgetting gate in the LSTM algorithm; Based on the forgotten output value, calculate the input process value, input-output value, and cell state update value of the input gate in the LSTM algorithm; Based on the input and output values, calculate the output process value of the output gate in the LSTM algorithm and the forward output.

5. The method for predicting CO2 emission concentrations for a MSWI process based on multiple models according to claim 3, characterized in that, Calculate the standardized residuals of the linear master model, and determine whether the linear master model satisfies a normal distribution through a residual scatter plot to obtain the applicability judgment result, including: The standardized residuals are sorted in ascending order to obtain an ascending residual sequence; Calculate the horizontal axis coordinates based on the ascending residual sequence; A residual scatter plot is drawn based on the ascending residual sequence and the horizontal axis coordinates; If all data points in the residual scatter plot are near the preset reference line, then the applicability judgment result of the linear master model is determined to conform to the normal distribution.

6. The method for predicting CO2 emission concentrations from a MSWI process based on a multi-model approach according to claim 3, characterized in that, When the linear master model exhibits significant autocorrelation, the stationary sequence is predicted using the linear master model to obtain the master model prediction result, including: Based on the stationary sequence, the predicted value is calculated using the linear master model; The predicted value is updated to the last element of the stationary sequence, and the first element of the stationary sequence is removed to obtain the updated stationary sequence. The process returns to the step "Calculate the predicted value using the linear master model based on the stationary sequence" until all data in the stationary sequence are the predicted value, at which point the update stops and the master model prediction result is obtained.

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