Urban solid waste incineration process furnace temperature robust prediction method
By assuming that the noise in the training data follows a skewed t-distribution, the model is optimized using maximum likelihood estimation and expectation condition maximization algorithms, and a robust furnace temperature prediction model is established. This solves the problem of inaccurate furnace temperature prediction during urban solid waste incineration and achieves real-time and accurate temperature prediction.
Patent Information
- Application Number
- CN202411065150.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-05
- Publication Date
- 2026-02-24
- Estimated Expiration
- 2044-08-05
AI Technical Summary
Existing technologies struggle to accurately predict furnace temperatures during urban solid waste incineration, especially when outliers exist in data collection and recording, leading to inaccurate predictions.
A robust furnace temperature prediction model is established by assuming a skewed t-distribution in the training data and optimizing the output weights and hyperparameters of the model through maximum likelihood estimation and expectation condition maximization algorithms.
The robustness of the furnace temperature forecasting model to abnormal data has been improved, enabling real-time and accurate forecasting of furnace temperature during urban solid waste incineration.
Smart Images
Figure CN119026466B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of furnace temperature prediction, specifically relating to a robust prediction method for furnace temperature in urban solid waste incineration processes. Background Technology
[0002] Municipal solid waste refers to solid waste generated in daily life or in activities that provide services for daily life. However, due to the strong coupling, large lag, and large inertia of the incineration process, it is difficult to accurately predict furnace temperature changes by relying solely on on-site thermocouples. Therefore, it is necessary to construct a data-driven furnace temperature prediction model to achieve accurate prediction of furnace temperature changes. In addition, data acquisition, data recording, and data storage may all lead to outliers with unknown distributions in the historical operation data of the incineration process. Moreover, the distribution of such outliers is usually asymmetric, thus requiring the furnace temperature prediction method to be robust to such outliers. Summary of the Invention
[0003] To address the aforementioned shortcomings in the existing technology, this invention provides a robust method for predicting furnace temperature during urban solid waste incineration, which solves the problem of inaccurate furnace temperature prediction in the existing technology.
[0004] To achieve the aforementioned objectives, the present invention employs the following technical solution: a robust prediction method for furnace temperature in urban solid waste incineration processes, comprising the following steps:
[0005] S1. Establish an initial furnace temperature model based on the preset training set;
[0006] S2. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, a furnace temperature prediction model is established by iteratively optimizing the set of output weights and hyperparameters of the model through maximum likelihood estimation and expectation condition maximization algorithms.
[0007] S3. Predict the furnace temperature during the incineration process using a furnace temperature prediction model.
[0008] Furthermore: In S1, the training set X and y are training samples;
[0009] The expression for the initial furnace temperature model is as follows:
[0010]
[0011] In the formula, x is the output of the noise included in the initial furnace temperature model. n As the input to the initial furnace temperature model, x n ∈X, y n The output of the initial furnace temperature model, y n ∈y, h(x)n ) represents the hidden layer output matrix of the model, β represents the output weight matrix, and ε represents the output weight matrix. n Let N be the noise contained in the nth sample, and N be the number of training samples.
[0012] Further: S2 includes the following sub-steps:
[0013] S21. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, we introduce latent variables and use a hierarchical approach to represent the output probability density function of the initial furnace temperature model.
[0014] S22. Based on the output probability density function of the initial furnace temperature model, and according to Bayes' theorem, establish the posterior distribution of the output weights of the initial furnace temperature model under the condition of a given complete dataset.
[0015] S23. Perform logarithmic calculation on the posterior distribution of the output weights of the furnace temperature model, and establish a general formula for calculating the set of output weights and hyperparameters of the model based on the maximum a posteriori estimation algorithm.
[0016] S24. Solve the general formula for calculating the set of output weights and hyperparameters of the model using the ECM algorithm (Expectation Conditional Maximization), and iteratively update the set of output weights and hyperparameters of the model. When the expected rate of change meets the termination condition, establish a furnace temperature prediction model based on the final output weights and hyperparameters of the model.
[0017] Further: In S21, it is assumed that the prior distribution of noise in the training data follows a skewed t-distribution, and the expression for the probability density function p(ε) of the noise is as follows:
[0018] p(ε)=ST(0,σ 2 ,λ,v)
[0019] In the formula, σ 2 σ is the scale parameter. 2 ∈(0,+∞), λ is the skew parameter, λ∈R, R is a real number, v is the degree of freedom parameter, v∈(0,+∞).
[0020] Further: In S21, the probability density function p(y) of the output of the initial furnace temperature model n ;x n ,β,σ 2 The specific expression for (λ, v) is:
[0021]
[0022] In the formula, γ n and τ nLet δ be a latent variable, v∈(0,+∞). λ As the first intermediate parameter, The mean is h(x) n )β+δ λ γ n Standard deviation is The normal distribution Let Γ(·,·) be a truncated normal distribution with a cutoff interval of (0,∞), and let Γ(·,·) be a gamma distribution.
[0023] Further: In S22, the posterior distribution p(β;T,σ) of the output weights of the initial furnace temperature model 2 The expression for ,λ,v) is as follows:
[0024]
[0025] In the formula, ST(h(x) n )β,σ 2 ,λ,v) is the position parameter h(x n )β, with scale parameter σ 2 A skewed t-distribution with skewness parameter λ and degrees of freedom v. The prior distribution of the output weights is expressed as follows:
[0026]
[0027] In the formula, L represents the number of neurons in the hidden layer of the furnace temperature model, and σ 2 β The variance of the prior distribution of the output weights.
[0028] Furthermore: In S23, the set of output weights and hyperparameters of the model. The general formula for calculation is as follows:
[0029]
[0030] In the formula, lnp(β;T,σ) 2 ,λ,v) represents the posterior logarithmic result of the output weights of the furnace temperature model. To find the parameters β and σ corresponding to the maximum value of the function 2 ,λ,v,
[0031] Furthermore: In S24, the set of output weights and hyperparameters of the model in the k-th iteration. The specific method for iterative updates is as follows:
[0032] SA1, Calculate the expected function of the posterior distribution logarithm of the output weights of the furnace temperature model;
[0033] SA2, based on the set of output weights and hyperparameters of the model under the given k-th iteration, update the set of output weights and hyperparameters of the model under the k-th iteration according to the expectation function.
[0034] Furthermore: in the SA1, the expectation function The specific expression is as follows:
[0035]
[0036] In the formula, c3 is a constant. The second intermediate parameter is expressed as follows:
[0037]
[0038]
[0039] in,
[0040] In the formula, DG(·) represents the digamm function;
[0041] In SA2, update and The specific expression is as follows:
[0042]
[0043]
[0044] In the formula, h T (x n ) represents the transpose of the hidden layer output matrix of the model. This is the output weight matrix for the (k+1)th iteration. Let be the variance of the prior distribution in the (k+1)th iteration;
[0045] renew The specific expression is as follows:
[0046]
[0047] In the formula, This represents the scaling parameter in the (k+1)th iteration.
[0048] renew The specific method is as follows: Let and Calculated using the following formula The value of this value is used as the skew parameter in the (k+1)th iteration.
[0049]
[0050] In the formula, This represents the scaling parameter in the (k+1)th iteration.
[0051] renew The specific method is as follows: Let and Calculated using the following formula The value of this value is used as the degree of freedom parameter in the (k+1)th iteration.
[0052]
[0053]
[0054] Further: In S24, the expression for the expected rate of change satisfying the termination condition is specifically as follows:
[0055]
[0056] Here, κ is a positive number that approaches 0.
[0057] The beneficial effects of this invention are as follows: This invention provides a robust prediction method for furnace temperature in urban solid waste incineration. By acquiring process data of urban solid waste incineration in real time, a training set is established for the collected process data, and a furnace temperature prediction model based on a robust stochastic configuration network is established. The prior distribution of asymmetric outliers in the incineration process operation data is simulated by a skewed t-distribution with heavy-tailed characteristics. The output weights of the furnace temperature prediction model are solved by the maximum likelihood estimation method, thereby improving the robustness of the furnace temperature prediction model to outlier data and realizing real-time and accurate prediction of furnace temperature in urban solid waste incineration. Attached Figure Description
[0058] Figure 1 This is a flowchart of a robust prediction method for furnace temperature in urban solid waste incineration processes according to the present invention. Detailed Implementation
[0059] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0060] like Figure 1 As shown, in one embodiment of the present invention, a robust prediction method for furnace temperature in urban solid waste incineration processes includes the following steps:
[0061] S1. Establish an initial furnace temperature model based on the preset training set;
[0062] S2. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, a furnace temperature prediction model is established by iteratively optimizing the set of output weights and hyperparameters of the model through maximum likelihood estimation and expectation condition maximization algorithms.
[0063] S3. Predict the furnace temperature during the incineration process using a furnace temperature prediction model.
[0064] To comprehensively improve the robustness of the incineration process furnace temperature prediction model to asymmetric outliers and its adaptability to fluctuations in solid waste composition, this invention proposes a robust SCN modeling method to establish the furnace temperature prediction model. The model is initialized using the SC-III algorithm, assuming that the prior distribution of outliers in the training data follows a skewed t-distribution assumption, and the hyperparameters of the model are iteratively optimized using maximum likelihood estimation and expectation condition maximization algorithms.
[0065] In S1, for a given training set X and y are training samples;
[0066] The expression for the initial furnace temperature model is as follows:
[0067]
[0068] In the formula, x is the output of the noise included in the initial furnace temperature model. n As the input to the initial furnace temperature model, x n ∈X, y n The output of the initial furnace temperature model, y n ∈y, h(x) n ) represents the hidden layer output matrix of the model, β represents the output weight matrix, and ε represents the output weight matrix. n Let N be the noise contained in the nth sample, and N be the number of training samples.
[0069] S2 includes the following steps:
[0070] S21. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, we introduce latent variables and use a hierarchical approach to represent the output probability density function of the initial furnace temperature model.
[0071] S22. Based on the output probability density function of the initial furnace temperature model, and according to Bayes' theorem, establish the posterior distribution of the output weights of the initial furnace temperature model under the condition of a given complete dataset.
[0072] S23. Perform logarithmic calculation on the posterior distribution of the output weights of the furnace temperature model, and establish a general formula for calculating the set of output weights and hyperparameters of the model based on the maximum a posteriori estimation algorithm.
[0073] S24. Solve the general formula for calculating the set of output weights and hyperparameters of the model using the ECM algorithm, and iteratively update the set of output weights and hyperparameters of the model. When the expected rate of change meets the termination condition, establish a furnace temperature prediction model based on the final output weights and hyperparameters of the model.
[0074] In this embodiment, since the distribution of outliers or noise in the operation data of complex industrial processes is usually unbalanced, the present invention uses a skewed t-distribution with heavy-tailed characteristics as the prior distribution of noise. In step S21, it is assumed that the prior distribution of noise in the training data follows a skewed t-distribution, and the expression of the probability density function p(ε) of the noise is as follows:
[0075] p(ε)=ST(0,σ 2 ,λ,v)
[0076] In the formula, σ 2 σ is the scale parameter. 2 ∈(0,+∞), λ is the skew parameter, λ∈R, R is a real number, v is the degree of freedom parameter, v∈(0,+∞).
[0077] The original output probability density function of the initial furnace temperature model is expressed as:
[0078] p(y n ;x n ,β,σ 2 ,λ,v)=ST(h(x n )β,σ 2 ,λ,v)
[0079] To facilitate subsequent calculations, this invention introduces latent variables to obtain a complete dataset T = {X,y,γ,τ}, and establishes the probability density function of the output of the initial furnace temperature model. In step S21, the probability density function p(y...) of the output of the initial furnace temperature model... n ;x n ,β,σ 2 The specific expression for (λ, v) is:
[0080]
[0081] In the formula, γ n and τ n Let δ be a latent variable, v∈(0,+∞). λ As the first intermediate parameter, The mean is h(x) n )β+δ λ γ n Standard deviation is The normal distribution Let Γ(·,·) be a truncated normal distribution with a cutoff interval of (0,∞), and let Γ(·,·) be a gamma distribution.
[0082] In S22, the posterior distribution p(β;T,σ) of the output weights of the initial furnace temperature model. 2 The expression for ,λ,v) is as follows:
[0083]
[0084] In the formula, ST(h(x) n )β,σ 2 ,λ,v) is the position parameter h(x n )β, with scale parameter σ 2 A skewed t-distribution with skewness parameter λ and degrees of freedom v. The prior distribution of the output weights is expressed as follows:
[0085]
[0086] In the formula, L represents the number of neurons in the hidden layer of the furnace temperature model. The variance of the prior distribution of the output weights.
[0087] In S23, the set of model output weights and hyperparameters. The general formula for calculation is as follows:
[0088]
[0089] In the formula, lnp(β;T,σ) 2 ,λ,v) represents the posterior logarithmic result of the output weights of the furnace temperature model. To find the parameters β and σ corresponding to the maximum value of the function 2 ,λ,v,
[0090] Because the set of output weights and hyperparameters of the model is unknown, the above equation has no analytical solution. Therefore, this invention uses the ECM algorithm to solve for the set of output weights and hyperparameters of the model.
[0091] In this embodiment, the expectation function is obtained by performing a logarithmic operation on the posterior distribution of the output weights of the initial furnace temperature model. The specific operation is as follows:
[0092]
[0093] In the formula, c1 and c2 are constants, and η n =(y n -h(x n )β) / σ.
[0094] In S24, the set of output weights and hyperparameters of the model in the k-th iteration is... The specific method for iterative updates is as follows:
[0095] SA1, Calculate the expected function of the posterior distribution logarithm of the output weights of the furnace temperature model;
[0096] SA2, based on the set of output weights and hyperparameters of the model under the given k-th iteration, update the set of output weights and hyperparameters of the model under the k-th iteration according to the expectation function.
[0097] In SA1, the expectation function The specific expression is as follows:
[0098]
[0099] In the formula, c3 is a constant. The second intermediate parameter is expressed as follows:
[0100]
[0101]
[0102] in,
[0103] In the formula, DG(·) represents the digamm function;
[0104] In SA2, update and The specific expression is as follows:
[0105]
[0106] In the formula, h T (x n ) represents the transpose of the hidden layer output matrix of the model. This is the output weight matrix for the (k+1)th iteration. Let be the variance of the prior distribution in the (k+1)th iteration;
[0107] In this embodiment, the above equation maximizes the expected function with respect to β and Establish.
[0108] renew The specific expression is as follows:
[0109]
[0110] In the formula, This represents the scaling parameter in the (k+1)th iteration.
[0111] In this embodiment, the above equation maximizes the expected function with respect to σ. 2 Establish.
[0112] renew The specific method is as follows: Let and Calculated using the following formula The value of this value is used as the skew parameter in the (k+1)th iteration.
[0113]
[0114] In the formula, Let be the scaling parameter in the (k+1)th iteration. The above equation is established by maximizing the expectation function with respect to λ.
[0115] renew The specific method is as follows: Let and Calculated using the following formula The value of this value is used as the degree of freedom parameter in the (k+1)th iteration.
[0116]
[0117]
[0118] In this embodiment, the above equation is established by maximizing the expected function with respect to v.
[0119] In S24, the expression for the expected rate of change satisfying the termination condition is specifically as follows:
[0120]
[0121] Wherein, κ is a positive number approaching 0, and in this embodiment, it takes the value 10. -4 .
[0122] In this embodiment, the maximum number of hidden layer neurons in the furnace temperature prediction model is 50, the maximum number of model configurations is 200, the skewness parameter of the skewed t-distribution is 0.1, the scale parameter is 0.1, the degrees of freedom is 5, and the prior variance of the output weights is 0.15.
[0123] The furnace temperature prediction model has 600 training data points and 200 test data points. There are 49 input feature variables and 1 output variable. After 50 experiments, the results are presented as mean ± standard deviation, as follows:
[0124] The tested RMSE was 4.91 ± 0.19℃.
[0125] The measured MAE was 3.91 ± 0.15℃;
[0126] The R² coefficient was 92.64 ± 0.56.
[0127] Therefore, the furnace temperature prediction model designed in this invention can accurately calculate the furnace temperature.
[0128] The beneficial effects of this invention are as follows: This invention provides a robust prediction method for furnace temperature in urban solid waste incineration. By acquiring process data of urban solid waste incineration in real time, a training set is established for the collected process data, and a furnace temperature prediction model based on a robust stochastic configuration network is established. The prior distribution of asymmetric outliers in the incineration process operation data is simulated by a skewed t-distribution with heavy-tailed characteristics. The output weights of the furnace temperature prediction model are solved by the maximum likelihood estimation method, thereby improving the robustness of the furnace temperature prediction model to outlier data and realizing real-time and accurate prediction of furnace temperature in urban solid waste incineration.
[0129] In the description of this invention, it should be understood that the terms "center," "thickness," "upper," "lower," "horizontal," "top," "bottom," "inner," "outer," and "radial," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying the relative importance or the number of technical features implicitly specified. Therefore, a feature defined by "first," "second," and "third" may explicitly or implicitly include one or more of that feature.
Claims
1. A robust prediction method for furnace temperature in urban solid waste incineration processes, characterized in that, Includes the following steps: S1. Establish an initial furnace temperature model based on the preset training set; In S1, the training set , X and y For training samples; The expression for the initial furnace temperature model is as follows: In the formula, The output of the initial furnace temperature model contains noise. x n As input to the initial furnace temperature model, x n ∈ X , y n The output of the initial furnace temperature model. y n ∈ y , h ( x n ) represents the hidden layer output matrix of the model. β To output the weight matrix, For the first n The noise contained in each sample N This represents the number of training samples; S2. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, a furnace temperature prediction model is established by iteratively optimizing the set of output weights and hyperparameters of the model through maximum likelihood estimation and expectation condition maximization algorithms. S2 includes the following steps: S21. Assuming that the prior distribution of noise in the training data follows a skewed t-distribution, we introduce latent variables and use a hierarchical approach to represent the output probability density function of the initial furnace temperature model. S22. Based on the output probability density function of the initial furnace temperature model, and according to Bayes' theorem, establish the posterior distribution of the output weights of the initial furnace temperature model under the condition of a given complete dataset. S23. Perform logarithmic calculation on the posterior distribution of the output weights of the furnace temperature model, and establish a general formula for calculating the set of output weights and hyperparameters of the model based on the maximum a posteriori estimation algorithm. S24. Solve the general formula for calculating the set of output weights and hyperparameters of the model using the ECM algorithm, and iteratively update the set of output weights and hyperparameters of the model. When the expected rate of change meets the termination condition, establish a furnace temperature prediction model based on the final output weights and hyperparameters of the model. S3. Predict the furnace temperature during the incineration process using a furnace temperature prediction model.
2. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 1, characterized in that, In step S21, it is assumed that the prior distribution of noise in the training data follows a skewed t-distribution, and the probability density function of the noise is... The specific expression is as follows: In the formula, For scale parameters, , The skew parameter, R is a real number. For the degree of freedom parameter, .
3. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 2, characterized in that, In step S21, the probability density function of the output of the initial furnace temperature model The specific expression is: In the formula, and As a latent variable, , As the first intermediate parameter, , The mean is Standard deviation is The normal distribution The cutoff interval is The truncated normal distribution It has a gamma distribution.
4. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 3, characterized in that, In S22, the posterior distribution of the output weights of the initial furnace temperature model. The specific expression is as follows: In the formula, For position parameters The scale parameter is The skew parameter is The degrees of freedom are v The skewed t-distribution The prior distribution of the output weights is expressed as follows: In the formula, L This represents the number of hidden layer neurons in the furnace temperature model. The variance of the prior distribution of the output weights.
5. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 4, characterized in that, In S23, the set of model output weights and hyperparameters. The general formula for calculation is as follows: In the formula, The posterior distribution logarithm of the weights is used to calculate the output weights for the furnace temperature model. To find the parameter corresponding to the maximum value of the function .
6. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 5, characterized in that, In S24, for the first k The set of output weights and hyperparameters of the model in the next iteration The specific method for iterative updates is as follows: SA1, Calculate the expected function of the posterior distribution logarithm of the output weights of the furnace temperature model; SA2, based on the given first k The set of output weights and hyperparameters of the model in the nth iteration is updated according to the expectation function. k The set of output weights and hyperparameters of the model in each iteration.
7. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 6, characterized in that, In SA1, the expectation function The specific expression is as follows: In the formula, c 3 is a constant. The second intermediate parameter is expressed as follows: in, In the formula, DG(·) represents the digamm function; In SA2, update and The specific expression is as follows: In the formula, This is the transpose of the hidden layer output matrix of the model. For the first k+ The output weight matrix in one iteration For the first k+ The variance of the prior distribution in one iteration; renew The specific expression is as follows: In the formula, For the first k+ Scale parameters in one iteration; renew The specific method is as follows: Let and Calculated using the following formula The value of is used as the first k+ Skew parameters in one iteration ; In the formula, For the first k+ Scale parameters in one iteration; renew The specific method is as follows: Let , , and Calculated using the following formula The value of is used as the first k+ Degrees of freedom parameters in one iteration ; 。 8. The robust prediction method for furnace temperature in urban solid waste incineration process according to claim 7, characterized in that, In S24, the expression for the expected rate of change satisfying the termination condition is specifically as follows: in, It is a positive number that approaches 0.