Probability density distribution driven virtual sample generation method for dioxin detection

Abstract

The present invention provides a probability density distribution driven virtual sample generation method for dioxin detection. First, principal component analysis PCA is used to perform feature dimension reduction on a small sample of DXN modeling, kernel density estimation is performed on the obtained principal components, and candidate virtual principal components are generated according to the distribution estimation results, and the virtual principal components obtained by orthogonal sampling are reconstructed to obtain DXN virtual sample input; then, random forest RF and random weight neural network RWNN are used to construct an integrated mapping model to obtain DXN virtual sample output; finally, a comprehensive learning particle swarm optimization algorithm is used to optimize various parameters that affect the "quality" of virtual samples, and obtain virtual samples that optimize the generalization performance of the DXN prediction model. The present invention can obtain virtual sample inputs that are more in line with the expected distribution of data, improve the generalization performance of the mapping model, and optimize the quantity and quality of virtual samples.

Description

Technical Field

[0001] The present invention relates to the technical field of dioxin emission concentration detection, and in particular to a probability density distribution driven virtual sample generation method for dioxin detection. Background Art

[0002] Dioxin (DXN) compounds emitted during the municipal solid waste incineration (MSWI) process are highly toxic pollutants and are the main cause of the "NIMBY" phenomenon of MSWI plants. As a complex compound, DXN cannot be detected in real time and can only be detected by high-cost, long-term offline testing. Therefore, real-time online detection of the emission concentration of the highly toxic substance DXN is an urgent problem that needs to be solved.

[0003] like Figure 1 As shown in the figure, the DXN produced by the MSWI process is contained in three products: ash, fly ash and flue gas. The flue gas can be divided into the following according to the emission stage: flue gas G1 when DXN is produced, flue gas G2 after DXN is adsorbed and flue gas G3 discharged to the atmosphere. Mechanistically, the sources of DXN include incomplete combustion of solid waste and de novo synthesis reaction generation (de novo synthesis). Generally, in order to ensure the effective decomposition of toxic organic matter such as DXN, the flue gas temperature in the solid waste incineration stage should reach at least 850°C and maintain for 2 seconds. In order to reduce the concentration of DXN in the exhaust flue gas, slaked lime and activated carbon need to be sprayed into the reactor in the flue gas treatment stage to adsorb DXN and certain heavy metals. In addition, the DXN memory effect inherent in the ash accumulation in the waste heat boiler and flue gas treatment stage also leads to an increase in the DXN emission concentration. The process variables in the above different stages are collected and stored by the on-site distributed control system (DCS) with a period of seconds. In addition, the easily detectable gases (CO, HCL, SO 2 、NO x and HF, etc.) concentrations can be detected in real time through the CEMS system and are correlated with the DXN concentration. However, incineration companies or environmental protection departments usually use offline direct chemical analysis methods to detect the DXN concentration in the flue gas G3 on a monthly / quarterly basis or as needed with a longer uncertain period. This method requires a special laboratory and related laboratory analysis equipment, the detection cost is very high, and it takes a long time. Online indirect detection methods based on indicators / associated substances have been studied and applied to a certain extent; however, this method requires first detecting the concentration of indicators / associated substances in the flue gas, and then indirectly calculating the DXN emission concentration based on the mapping model. Similarly, this method requires expensive and complex online laboratory analysis equipment, and there is a lag time of hours. Therefore, it is necessary to construct a soft sensor for DXN emission concentration to realize its online measurement.

[0004] In summary, the DXN concentration in flue gas G3 is jointly affected by hundreds of process parameters such as furnace temperature, flue gas flow, and HCL concentration of the MSWI process. Moreover, these big data collected by the DCS system at a time scale of seconds only cover the parameter combination space under steady-state operating conditions. Obviously, the MSWI process has been running in steady-state mode for a long time, resulting in most of the data corresponding to very similar conditions, which makes the available DXN effective modeling samples very scarce and the sample distribution is very uneven. In addition, the high cost and long cycle of offline detection of DXN lead to the lack of modeling truth. The cost and risk of obtaining non-steady-state, abnormal, or even fault data of the MSWI process through experiments are extremely high and are usually not allowed. Therefore, the DXN modeling of the MSWI process faces the dilemma of "big data and small samples".

[0005] The small sample problem cannot be simply understood as the absolute small number of samples, but rather a relative concept related to sample input, etc. Its essence is that the sample contains insufficient information required for modeling. In essence, small samples cannot fully reflect the actual data distribution due to their sparse distribution due to the limited number of samples, and they also exhibit problems such as imbalanced distribution. Therefore, models built based on small samples are often one-sided and biased, and their prediction results are difficult to truly reflect the actual output. At present, existing methods such as support vector machines, gray models, kernel regression, and Bayesian networks are difficult to further improve the prediction accuracy of the model when the number of samples is extremely scarce and the distribution is imbalanced.

[0006] The virtual sample generation (VSG) technology, first proposed in the field of pattern recognition, generates an appropriate number of virtual samples by extracting potential information in the gaps between small sample data, thereby expanding the number of modeling samples to improve the model's prediction performance. Researchers usually combine prior knowledge to generate effective virtual samples to improve the generalization performance of the model; however, since it is difficult and time-consuming to obtain domain-specific prior knowledge, researchers in various fields mostly focus on how to extract knowledge from small samples to generate virtual samples. In view of the problems that the traditional feature interpolation used to obtain virtual sample input destroys the expected distribution of samples due to information "holes", different mapping models used to obtain virtual sample outputs have difficulty in balancing accuracy and randomness, and VSG hyperparameters are difficult to select, it is urgent to further study the probability density distribution driven virtual sample generation method for dioxin emission concentration prediction. Summary of the invention

[0007] The purpose of the present invention is to provide a probability density distribution driven virtual sample generation method for dioxin detection, which can obtain virtual sample input that is more in line with the expected data distribution and improve the generalization performance of the mapping model to optimize the quantity and quality of virtual samples.

[0008] To achieve the above object, the present invention provides the following solutions:

[0009] A probability density distribution driven virtual sample generation method for dioxin detection comprises the following steps:

[0010] S1, generate virtual sample input based on simplified feature PDF: use principal component analysis PCA to reduce the feature dimension of the small sample of DXN modeling, perform kernel density estimation on the obtained principal components, and then generate candidate virtual principal components according to the distribution estimation results, and reconstruct the virtual principal components obtained by orthogonal sampling to obtain DXN virtual sample input;

[0011] S2, generate virtual sample output based on integrated mapping model: use random forest RF and random weight neural network RWNN to build an integrated mapping model to obtain DXN virtual sample output;

[0012] S3, based on CLPSO optimization of the hyperparameters of the virtual sample generation process: the comprehensive learning particle swarm optimization algorithm is used to optimize the principal component contribution rate, KDE smoothing index, number of candidate virtual principal components and virtual samples, mapping model parameters and model integration weight parameters that affect the "quality" of virtual samples, so as to obtain virtual samples that optimize the generalization performance of the DXN prediction model.

[0013] Furthermore, in step S1, generating a virtual sample input based on the simplified feature PDF specifically includes:

[0014] S101, based on PCA simplified features:

[0015] For the DXN small sample training set R train The d-dimensional input features Conduct principal component analysis: First, according to the formula Center the samples separately and then arrange them into d×N train The matrix Next, calculate its covariance matrix And perform eigenvalue decomposition, the eigenvalue order is: λ 1 ≥λ 2 ≥...≥λ d ; Then, according to the set variance contribution rate threshold θ pca By Calculate the number of principal components d′; finally, take λ 1 ≥λ 2 ≥...≥λ d′ The corresponding d′ eigenvectors form the projection matrix U train =(u 1 ,u 2 ,...,u d′ ) and calculate the sample matrix after dimensionality reduction, as follows:

[0016]

[0017] Among them, X train Input for DXN training set, is the input of the training set after dimensionality reduction, and each sample contains d′ features, that is, Accordingly, X train The d′ principal components of in,

[0018] S102, generate candidate virtual principal components based on KDE:

[0019] Based on PCA feature reduction X train principal component Perform kernel density estimation, taking the i-th principal component For example, calculate Kernel density estimation of for,

[0020]

[0021] Among them, h kde is the smoothing index of kernel density estimation; K(·) is the kernel function; N train For the training set X train The number of samples in the medium;

[0022] Optional The Gaussian function shown is used as the kernel function, and the variance of the Gaussian distribution corresponding to each sample point is h kde , the mean is the sample value but The calculation is,

[0023]

[0024] Based on the kernel density estimation results of the above principal components, a candidate virtual principal component that conforms to the principal component distribution is generated;

[0025] S103, reconstructing a virtual sample input based on sampling:

[0026] According to X train The candidate virtual principal components generated by estimating the principal component distribution of In order to obtain more combination modes to the greatest extent, virtual principal components that are correlated with each other are obtained by randomly orthogonally sampling each candidate virtual principal component. The generation method is:

[0027]

[0028] Among them, rand represents [1,N vpc ] in random integer;

[0029] therefore, The generation method of is described as: randomly select one principal component from each of the d′ virtual candidate principal components to form a d′-dimensional virtual sample input

[0030] For the principal components of the generated virtual sample input Perform PCA reconstruction to obtain virtual sample input X vs , calculate the virtual sample input As follows:

[0031]

[0032] in, Input X for the training set train The mean vector of .

[0033] Furthermore, in step S102, based on the kernel density estimation result of the principal component, a candidate virtual principal component that conforms to the principal component distribution is generated, specifically: N is generated based on the inversion method vpc Kernel density The virtual candidate principal components include the following steps:

[0034] 1) For the composition One of the Gaussian functions generate Candidate virtual principal component values in, Right now The mean is The variance is h kde Normal distribution of

[0035] 2), for the composition N train Each Gaussian function generates a Candidate virtual principal component values ​​can be obtained to meet the principal component Candidate virtual principal components of probability distribution

[0036] 3), for the principal component Generate candidate virtual principal components respectively There is no corresponding relationship between the candidate virtual principal components.

[0037] Furthermore, in step S2, generating a virtual sample output based on the integrated mapping model specifically includes:

[0038] S201, build RF mapping model based on DXN small sample:

[0039] The DXN training set obtains K different sub-training sets through Bootstrap sampling and random feature segmentation to construct K decision trees, and integrates their results to obtain prediction results. For regression problems, when constructing a decision tree, the optimal segmentation features and split point values ​​of node q are obtained according to the following formula:

[0040]

[0041] S202, build RWNN mapping model based on DXN small sample:

[0042] Use DXN small sample training set R train Steps to construct the RWNN mapping model: First, randomly set the connection weights between the input layer and the hidden layer neurons W = {w 1 ,w 2 ,...,w I} and the bias value b={b 1 ,b 2 ,...,b N} T ; Then, the hidden layer output matrix H is calculated as follows ori ,

[0043]

[0044] Among them, h ni =Γ map (w i ,b n ,x n ) is the hidden layer node value; I is the number of neurons in the hidden layer of RWNN n L Γ map Represents a mapping function with sigmoid function as activation function;

[0045] Finally, the generalized inverse matrix is ​​used to calculate the connection weight β between the hidden layer and the output layer neurons, as follows:

[0046] β=(H ori ) + y train (20)

[0047] Among them, (H ori ) + H ori The generalized inverse matrix of ; the constructed RWNN mapping model is

[0048] S203, generating a virtual output based on the integrated mapping model:

[0049] Based on the RF and RWNN mapping models, a DXN integrated mapping model is obtained to generate a virtual sample output; by adjusting the RF and RWNN mapping model parameters and the integration weights of the two, a more adaptable integrated mapping model is obtained, and then a virtual sample output is generated;

[0050] Calculate virtual output based on RF mapping model for,

[0051]

[0052] Calculate the virtual output based on the RWNN mapping model for,

[0053]

[0054] Furthermore, based on and Get virtual output y vs for,

[0055]

[0056] Thus, we obtain the virtual sample R vs ={X vs ,y vs}.

[0057] Furthermore, the step S3, based on CLPSO, optimizes the hyper parameters of the virtual sample generation process, specifically including:

[0058] The optimization objective is described as:

[0059]

[0060] Among them, f(z,R train ,R valid ) represents the RMSE value of the model constructed by the mixed sample consisting of the virtual sample and the small sample training set on the validation set; f mix (·) represents the prediction model constructed by mixed samples; z={θ pca ,h kde ,N vpc ,N vs ,n T ,m S ,n L ,ω mod} represents the decision variables of the optimization problem, including 8 parameters of the virtual sample generation process; z∈Ω represents the feasible domain space of the decision variables;

[0061] Based on the optimization objective, CLPSO is used to calculate the PCA principal component contribution rate θ pca , KDE smoothing index h kde, Number of dummy variables N vpc , the number of virtual samples N vs , mapping model parameter n T ,m S ,n L and model combination weight ω mod Solve and obtain the optimal virtual sample.

[0062] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects: the probability density distribution driven virtual sample generation method for dioxin detection provided by the present invention, first, generates the input of the virtual sample based on the simplified feature PDF, including: performing principal component analysis (PCA) on the small sample input features to obtain the sample principal components that are independent of each other after dimensionality reduction, and then performing kernel density estimation (KDE) on them respectively, generating virtual candidate principal components according to the distribution estimation results respectively, and then obtaining virtual principal components through orthogonal sampling, and reconstructing to obtain the virtual sample input; the above strategy reduces the dimension of the small sample features through PCA to reduce the correlation between the original features, and can also reduce the influence of noise, and generates virtual variables according to the KDE estimation results to ensure the distribution consistency of the virtual samples in the low-dimensional space, and orthogonal sampling After that, virtual sample inputs are generated through reconstruction to obtain as many different combination patterns as possible, overcoming the problems of "holes" in the spatial distribution of virtual sample inputs and ignoring the correlation between input attributes. Then, an integrated mapping model is constructed by combining the RF model with high prediction accuracy and small fluctuation with the RWNN model with general prediction accuracy and wide range to generate virtual sample outputs, thereby improving the adaptability of the model to different data sets. Finally, the comprehensive learning particle swarm optimization (CLPSO) algorithm is used to optimize the parameters of the virtual sample generation process to obtain virtual samples that optimize the generalization performance of the soft sensor model. These parameters include PCA principal component contribution rate, KDE smoothing index, number of virtual principal components and virtual samples, mapping model parameters and model integration weights, so as to generate the optimal number of "high-quality" virtual samples. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0064] Figure 1 This is the process flow chart of MSWI;

[0065] Figure 2 It is a schematic flow chart of a probability density distribution driven virtual sample generation method for dioxin detection of the present invention;

[0066] Figure 3 It is a schematic diagram for comparing different principal component probability density estimation curves of the present invention;

[0067] Figure 4 A schematic diagram of the spatial distribution of virtual sample inputs of the present invention;

[0068] Figure 5 This is a comparison bar chart of the probability distribution of the DXN virtual sample output of the present invention. DETAILED DESCRIPTION

[0069] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] The purpose of the present invention is to provide a probability density distribution driven virtual sample generation method for dioxin detection, which can obtain virtual sample input that is more in line with the expected data distribution and improve the generalization performance of the mapping model to optimize the quantity and quality of virtual samples.

[0071] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0072] like Figure 2 As shown, the probability density distribution driven virtual sample generation method for dioxin detection provided by the present invention comprises the following steps:

[0073] S1, generate virtual sample input based on simplified feature PDF: use principal component analysis PCA to reduce the feature dimension of the small sample of DXN modeling, perform kernel density estimation on the obtained principal components, and then generate candidate virtual principal components according to the distribution estimation results, and reconstruct the virtual principal components obtained by orthogonal sampling to obtain DXN virtual sample input;

[0074] S2, generate virtual sample output based on integrated mapping model: use random forest RF and random weight neural network RWNN to build an integrated mapping model to obtain DXN virtual sample output;

[0075] S3, based on CLPSO optimization of the hyperparameters of the virtual sample generation process: the comprehensive learning particle swarm optimization algorithm is used to optimize the principal component contribution rate, KDE smoothing index, number of candidate virtual principal components and virtual samples, mapping model parameters and model integration weight parameters that affect the "quality" of virtual samples, so as to obtain virtual samples that optimize the generalization performance of the DXN prediction model.

[0076] Among them, virtual sample generation (VSG) usually uses domain prior knowledge combined with known small samples. The definition of virtual samples is as follows: for a given training sample (x, y), the sample (Tx, y) obtained by transforming T T (x)) is also a reasonable sample, so the newly obtained sample (Tx, y T (x)) is the virtual sample generated by transforming T.

[0077] Principal Component Analysis (PCA): PCA can reduce the feature dimension of data while minimizing the loss of information in the data. Its essence is to use orthogonal transformation to map high-dimensional samples in low-dimensional space, so that the correlated sample features in the high-dimensional space are converted into low-dimensional uncorrelated features, which are called principal components.

[0078] For the d-dimensional sample set D = {x 1 ,x 2 ,...,x n}, First, all samples are centered as follows:

[0079]

[0080] This gives the matrix Then, calculate the sample covariance matrix Perform eigenvalue decomposition on it and sort the eigenvalues: λ 1 ≥λ 2 ≥...≥λ d According to the given variance contribution rate threshold θ pca , calculate the number of principal components d′ as follows,

[0081]

[0082] Finally, take λ 1 ≥λ 2 ≥...≥λ d′ The corresponding d′ eigenvectors form the projection matrix U=(u 1 ,u 2 ,...,u d′ ), and then calculate the sample after dimensionality reduction As shown below,

[0083]

[0084] Therefore, the sample set D is obtained by feature dimensionality reduction. Obviously, the sampling density of the sample set after dimensionality reduction is higher and the noise interference is reduced.

[0085] Kernel Density Estimation (KDE): The probability density function (PDF) of a random variable describes the probability of a random number appearing. For VSG, if the PDF of the data population is known, a reasonable virtual sample can be accurately generated. KDE is a non-parametric estimation method that estimates the PDF of an unknown population through samples. It does not need to assume in advance that the data conforms to a certain distribution state, but instead uses a smooth peak function ("kernel") to fit known sample points to obtain a probability density estimation curve for the population data. Let X = {x 1 ,x 2 ,...,x n} are n independent and identically distributed sample points, and the PDF of the population is f X (x), then its kernel density is estimated as,

[0086]

[0087] Among them, x i is the sample value; K(·) is the kernel function, and the commonly used kernel function is the Gaussian function, as follows,

[0088]

[0089] KDE can be understood as follows: each sample point conforms to the distribution of the kernel function K(·), n kernel functions are calculated, and the kernel density estimation function can be obtained by linearly superimposing and normalizing them.

[0090] Comprehensive learning particle swarm algorithm: Standard particle swarm algorithm (PSO) is a swarm intelligence optimization algorithm. The core is that particles update their speed and position iteratively according to the guidance of global optimal and individual optimal to find the optimal solution. Its speed and position are updated as follows:

[0091]

[0092]

[0093] in, and They represent the current coordinate and optimal coordinate of particle p in the nth dimension in the tth iteration respectively; g n (t) represents the coordinate of the nth dimension of the optimal particle in the population in the tth iteration; w inertia is the inertia weight, which indicates the search step length; and Obeys uniform distribution between [0,1]; c self and c society is the learning factor, which represents the degree to which the particle search direction is affected by the individual and global optimal positions.

[0094] According to the optimization objective function, the fitness value of the particle is calculated to update the individual and global optimal values ​​of the population, as shown in the following formula:

[0095]

[0096]

[0097] in, represents the individual optimal position pbest of the pth particle, g = (g 1 ,g 2 ,...,g n ) represents the global optimal position gbest, d k represents the best particle in the population of this generation, where

[0098] The comprehensive learning PSO (CLPSO) improves the updating process of particle velocity. It maintains a sample pool for each particle. Each dimension of the particle is learned with reference to the particles in the sample pool. It can maintain population diversity and alleviate the problem of premature convergence of the standard particle swarm.

[0099]

[0100] Where c is the learning factor; It obeys the uniform distribution between [0,1]; is the reference sample of particle p in the nth dimension.

[0101] When the individual optimum of the particle is N refresh If it is still not updated after iterations, the learning sample pool of the particle is updated. Each dimension of the particle can be updated according to the probability P c p Learn from any two particles in the population and select the better particle as its learning example through the competition mechanism, which is expressed as,

[0102]

[0103] Among them, P c p is the learning probability of particle p, which is updated according to the following formula,

[0104]

[0105] Among them, rank p Represents the fitness ranking of the individual optimal fitness of particle p in the population.

[0106] Based on the above principle, the present invention proposes a probability density distribution driven virtual sample generation method for dioxin emission concentration prediction. In a specific embodiment, Figure 2 In, R train ={X train ,y train} represents the DXN small sample data training set, where X train and train Respectively represent the input and output of the DXN training set; Represents X train d′ principal components after PCA simplification; Kernel density estimation function representing simplified features; Represents the candidate virtual principal components generated by the kernel density estimation function; represents the virtual principal component obtained after sampling the candidate virtual principal component; X vs express The virtual sample input obtained after reconstruction; and Respectively represent the R train Constructed RF and RWNN mapping models; vs represents the DXN virtual sample output generated by the integrated mapping model; f mix (·) indicates that R train With R vs ={X vs ,y vs The prediction model is constructed based on the mixed sample composed of valid represents the small sample validation set; z = {θ pca ,h kde ,N vpc ,N vs ,n T ,m S ,n L ,ω mod} represents the decision variables for optimizing the virtual sample generation process, where θ pca 、h kde 、N vpc 、N vs 、n T 、m S 、n L and ω mod They represent the principal component contribution rate, KDE smoothing index, the number of candidate virtual principal components and virtual samples, mapping model parameters and model integration weight respectively; Ω represents the feasible domain of the decision variable.

[0107] In the step S1, generating a virtual sample input based on the simplified feature PDF specifically includes:

[0108] S101, based on PCA simplified features:

[0109] For the DXN small sample training set R train The d-dimensional input features Perform principal component analysis: First, center the samples according to formula (1), and then arrange them into d×Ntrain The matrix Next, calculate its covariance matrix And perform eigenvalue decomposition, the eigenvalue order is: λ 1 ≥λ 2 ≥...≥λ d ; Then, according to the set variance contribution rate threshold θ pca Calculate the number of principal components d′ by formula (2); finally, take λ 1 ≥λ 2 ≥...≥λ d′ The corresponding d′ eigenvectors form the projection matrix U train =(u 1 ,u 2 ,...,u d′ ) and calculate the sample matrix after dimensionality reduction, as follows:

[0110]

[0111] Among them, X train Input for DXN training set, is the input of the training set after dimensionality reduction, and each sample contains d′ features, that is, Accordingly, X train The d′ principal components of in,

[0112] S102, generate candidate virtual principal components based on KDE:

[0113] Based on PCA feature reduction X train principal component Perform kernel density estimation, taking the i-th principal component For example, according to formula (4) Kernel density estimation of for,

[0114]

[0115] Among them, h kde is the smoothing index of kernel density estimation; K(·) is the kernel function; N train For the training set X train The number of samples in the medium;

[0116] Theoretically kde should be close to 0, but if h kde Too small, because the number of small samples is very limited, the neighborhood (xh kde ,x+h kde ) will have too few real sample points involved in fitting;

[0117] Optional The Gaussian function shown is used as the kernel function, and the variance of the Gaussian distribution corresponding to each sample point is h kde , the mean is the sample value but The calculation is,

[0118]

[0119] Based on the kernel density estimation results of the above principal components, candidate virtual principal components that conform to the principal component distribution are generated; specifically, N vpc Kernel density The virtual candidate principal components include the following steps:

[0120] 1) For the composition One of the Gaussian functions generate Candidate virtual principal component values in, Right now The mean is The variance is h kde Normal distribution of

[0121] 2), for the composition N train Each Gaussian function generates a Candidate virtual principal component values ​​can be obtained to meet the principal component Candidate virtual principal components of probability distribution

[0122] 3), for the principal component Generate candidate virtual principal components respectively There is no corresponding relationship between the candidate virtual principal components.

[0123] S103, reconstructing a virtual sample input based on sampling:

[0124] According to X train The candidate virtual principal components generated by estimating the principal component distribution of In order to obtain more combination modes to the greatest extent, virtual principal components that are correlated with each other are obtained by randomly orthogonally sampling each candidate virtual principal component. The generation method is:

[0125]

[0126] Among them, rand represents [1,N vpc ] in random integer;

[0127] therefore, The generation method of is described as: randomly select one principal component from each of the d′ virtual candidate principal components to form a d′-dimensional virtual sample input

[0128] For the principal components of the generated virtual sample input Perform PCA reconstruction to obtain virtual sample input X vs , calculate the virtual sample input As follows:

[0129]

[0130] in, Input X for the training set train The mean vector of .

[0131] In step S2, generating a virtual sample output based on the integrated mapping model specifically includes:

[0132] S201, build RF mapping model based on DXN small sample:

[0133] The DXN training set obtains K different sub-training sets through Bootstrap sampling and random feature segmentation to construct K decision trees, and integrates their results to obtain prediction results. For regression problems, when constructing a decision tree, the optimal segmentation features and split point values ​​of node q are obtained according to the following formula:

[0134]

[0135] S202, build RWNN mapping model based on DXN small sample:

[0136] Use DXN small sample training set R train Steps to construct the RWNN mapping model: First, randomly set the connection weights between the input layer and the hidden layer neurons W = {w 1 ,w 2 ,...,w I} and the bias value b={b 1 ,b 2 ,...,b N} T ; Then, the hidden layer output matrix H is calculated as follows ori ,

[0137]

[0138] Among them, h ni =Γ map (w i ,b n ,x n) is the hidden layer node value; I is the number of neurons in the hidden layer of RWNN n L Γ map Represents a mapping function with sigmoid function as activation function;

[0139] Finally, the generalized inverse matrix is ​​used to calculate the connection weight β between the hidden layer and the output layer neurons, as follows:

[0140] β=(H ori ) + y train (20)

[0141] Among them, (H ori ) + H ori The generalized inverse matrix of ; the constructed RWNN mapping model is

[0142] S203, generating a virtual output based on the integrated mapping model:

[0143] Based on the RF and RWNN mapping models, a DXN integrated mapping model is obtained to generate a virtual sample output; by adjusting the RF and RWNN mapping model parameters and the integration weights of the two, a more adaptable integrated mapping model is obtained, and then a virtual sample output is generated;

[0144] Calculate virtual output based on RF mapping model for,

[0145]

[0146] Calculate the virtual output based on the RWNN mapping model for,

[0147]

[0148] Furthermore, based on and Get virtual output y vs for,

[0149]

[0150] Thus, we obtain the virtual sample R vs ={X vs ,y vs}.

[0151] The step S3, based on CLPSO, optimizes the hyper parameters of the virtual sample generation process, specifically includes:

[0152] The optimization objective is described as:

[0153]

[0154] Among them, f(z,R train ,R valid ) represents the RMSE value of the model constructed by the mixed sample consisting of the virtual sample and the small sample training set on the validation set; f mix (·) represents the prediction model constructed by mixed samples; z={θ pca ,h kde ,N vpc ,N vs ,n T ,m S ,n L ,ω mod} represents the decision variables of the optimization problem, including 8 parameters of the virtual sample generation process; z∈Ω represents the feasible domain space of the decision variables;

[0155] Based on the optimization objective, CLPSO is used to calculate the PCA principal component contribution rate θ pca , KDE smoothing index h kde , Number of dummy variables N vpc , the number of virtual samples N vs , mapping model parameter n T ,m S ,n L and model combination weight ω mod Solve and obtain the optimal virtual sample.

[0156] The industrial verification process is as follows:

[0157] 1. Description of evaluation indicators

[0158] For a data set X = {x 1 ,x 2 ,...,x N}, define the indicator and To evaluate the sparseness of the sample space distribution, as follows,

[0159]

[0160]

[0161] in, and Respectively represent the average and minimum Euclidean distances between a sample and its k nearest neighbors; x n,i Represents x n The i-th k nearest neighbor of nst Indicates the number of neighbors of the set sample; E(x n ,x n,i ) represents x n and x n,iThe Euclidean distance is calculated as follows:

[0162]

[0163] in,

[0164] Define the index η to evaluate the distribution similarity between the sample and the entire data. Dataset S 1 ,S 2 The distribution similarity of is calculated as follows,

[0165]

[0166] Among them, N attr Represents the dataset S 1 ,S 2 The number of attributes; and Respectively and The probability distribution of Represents the dataset S 1 ,S 2 The Hellinger distance of attribute i, which is a type of F-divergence, is used to measure the similarity of two probability distributions. The formula is as follows:

[0167]

[0168] The root mean square error RMSE is used as the model performance evaluation indicator, as follows:

[0169]

[0170] 2. Industrial process and data description

[0171] The industrial data used comes from a grate-furnace-based MSWI incineration enterprise in Beijing, covering 34 valid DXN emission concentration detection samples recorded from 2012 to 2018; the original variable 314 dimensions is reduced to 119 dimensions after preprocessing, and 1 dimension is output, namely the DXN emission concentration.

[0172] 3. Experimental results

[0173] A simulation experiment is carried out for the experimental data, where the parameters of CLPSO are set as shown in Table 1.

[0174] Table 1 Parameter settings of virtual sample generation process based on CLPSO

[0175]

[0176] Table 1 gives the P num 、N iter and N refreshThe setting values ​​of CLPSO, namely the number of population particles, the number of iterations and the learning sample update threshold, and θ pca ,h kde ,N vpc ,N vs ,n T ,m S ,n L and ω mod The maximum and minimum values ​​of , that is, the optimization range of the decision variable z.

[0177] 1) Generate virtual sample input results based on simplified feature PDF

[0178] The principal component analysis of the DXN training set is performed. After principal component analysis of the 119-dimensional training set input features, the cumulative variance contribution rate of the first 10 principal components reaches 91.94%, of which the cumulative variance contribution rate of the first 3 principal components is close to 60%. The cumulative variance contribution rate of the principal components θ is calculated by CLPSO. pca Optimization of parameters, θ pca The optimization result is 65.92%, and finally four principal components are selected as simplified features, and their actual cumulative variance contribution rate is 66.94%.

[0179] The probability density estimation based on KDE is performed on the 4-dimensional simplified features. It can be seen that the probability density estimation curve can fit its probability distribution histogram well. Among them, the smoothing index h kde The optimization result is 0.891.

[0180] Generate candidate virtual principal components based on the kernel density estimation results, and then obtain virtual principal components through sampling. Figure 3 The probability density estimation curves of the principal components of the original DXN training set, candidate virtual principal components, and virtual principal components are shown.

[0181] Depend on Figure 3 It can be seen that the candidate virtual principal components generated based on the kernel density estimation results and the virtual principal components obtained after sampling have good consistency with the probability distribution of the simplified features of the original training set, but the degree of fit for the principal component 2 with more frequent oscillations is low.

[0182] In addition, the number of candidate virtual principal components N is vpc and the number of virtual principal components N vs The optimization of N vpc and N vs The optimization results are 33 and 196 respectively.

[0183] The virtual principal components are reconstructed to obtain virtual sample inputs. Tables 2 and 3 show 7 training sample inputs and 7 virtual sample inputs generated from them (randomly selected), respectively.

[0184] Table 2 Training sample input

[0185]

[0186]

[0187] Table 3 Virtual sample input

[0188]

[0189] It can be seen from Tables 2 and 3 that the generated DXN virtual sample input can effectively fill the gap of small sample input and can expand the small sample input space to a certain extent. However, there are characteristic values ​​in the virtual sample that are contrary to the physical meaning of the data. For example, the value of feature 118 of virtual sample 5 in Table 3 is -19.6, and its physical meaning is urea supply, which is obviously wrong.

[0190] The spatial expansion rate and spatial sparsity of the generated virtual sample input are analyzed. Table 4 shows the evaluation indicators of the virtual samples.

[0191] Table 4 Evaluation indicators of virtual sample input

[0192]

[0193] As shown in Table 4, the virtual samples of DXN data are 6.53% larger than the input domain of the training set; and They were reduced by 59.5% and 94.4% respectively, indicating that the virtual samples significantly improved the sparse distribution problem of small samples.

[0194] Figure 4 To display the spatial distribution of the generated virtual sample input, features 9, 21 and 45 were selected respectively; it can be seen that the virtual samples can effectively fill the information gaps of small samples, but there are also cases where the edge areas of small samples are not filled.

[0195] The generated virtual sample input can effectively fill the gaps in the probability distribution of small samples; the entire data in the figure is 34 data including training set and test set, and the probability distribution it presents cannot reflect the actual probability distribution of real DXN data. The generated virtual sample shows the characteristics of normal distribution based on the probability distribution characteristics of the original small sample data, which is in line with expectations.

[0196] 2) Generate virtual sample output results

[0197] Based on the DXN training set, the RF and RWNN mapping model is constructed, where the modeling parameter n of the RF and RWNN mapping model is T、m S and n L , and the model ensemble weight ω mod The optimization results are shown in Table 5.

[0198] Table 5 Parameter optimization results based on CLPSO integrated mapping model

[0199]

[0200] Table 5 shows the RMSE values ​​of the integrated mapping model built based on the DXN training set and the RF and RWNN individual mapping models on the validation set. It can be seen that the integrated mapping model has better generalization performance.

[0201] Based on the constructed integrated mapping model, virtual sample outputs are generated for virtual sample inputs. Table 6 shows the actual outputs corresponding to the training sample inputs in Table 2, and Table 7 shows the virtual sample outputs corresponding to the virtual sample inputs.

[0202] Table 6 Training sample output

[0203]

[0204] Table 7 Virtual sample output

[0205]

[0206] Table 7 shows the virtual sample outputs of the RF and RWNN individual mapping models and the integrated mapping model. It can be seen that the RF mapping output value is more stable and the RWNN mapping output value distribution range is wider.

[0207] Furthermore, Table 8 shows the expansion rate of the virtual sample output generated based on the mapping model.

[0208] Table 8 Virtual sample output expansion rate

[0209]

[0210] It can be seen from Table 8 that: the RF mapping output value distribution is concentrated, and its output domain is narrower than the output domain of the training set; the RWNN mapping output value distribution range is wide, but it also causes its output value to exceed the normal range, which is contrary to the actual physical meaning; the integrated mapping model can balance the advantages and disadvantages of the two, so that the mapping output value distribution is wide and does not exceed the reasonable range too much.

[0211] Figure 5The comparison bar chart of the probability distribution of DXN virtual sample output. In the figure, the probability distribution of the mixed sample output composed of virtual samples and training samples maintains some characteristics of small samples and is closer to the normal distribution, which is in line with expectations; however, the lower limit of the virtual sample output exceeds the normal range and needs further screening.

[0212] 3) Prediction model results of mixed samples

[0213] The virtual samples obtained in the experiment and the original training samples are used together to construct the RF prediction model. Table 9 shows the performance indicators of the constructed prediction model.

[0214] Table 9 Results of prediction model constructed with mixed samples

[0215]

[0216] In Table 9, compared with the prediction model constructed with small samples, the RMSE of the mixed sample modeling on the test set is reduced by 13.4%, indicating that the virtual sample improves the prediction performance of the model. In addition, since the DXN data is scarce, the validation set and the training set data are the same, so their RMSE is also the same.

[0217] In summary, the probability density distribution driven virtual sample generation method for dioxin detection provided by the present invention is innovative in the following aspects: 1) the feature simplification of DXN training sample input is performed for the first time, and then the virtual sample input is generated according to its kernel density estimation result, so that the virtual sample input is closer to the expected probability distribution, and its spatial distribution sparsity is reduced and sample "holes" are avoided; 2) the RF and RWNN models are used to construct an integrated mapping model to generate DXN virtual sample output, so as to ensure the accuracy and scalability of the virtual sample output; 3) CLPSO is used to optimize the hyperparameters of the DXN virtual sample generation process, which can simultaneously optimize the quality and quantity of the generated virtual samples; finally, the effectiveness of the proposed method is verified by using real industrial data.

[0218] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A probability density distribution driven virtual sample generation method for dioxin detection, characterized in that: The following steps are involved: S1, generate virtual sample input based on simplified feature PDF: use principal component analysis PCA to reduce the feature dimension of the small sample of DXN modeling, perform kernel density estimation on the obtained principal components, and then generate candidate virtual principal components according to the distribution estimation results, and reconstruct the virtual principal components obtained by orthogonal sampling to obtain DXN virtual sample input; S2, generate virtual sample output based on integrated mapping model: use random forest RF and random weight neural network RWNN to build an integrated mapping model to obtain DXN virtual sample output; S3, based on CLPSO optimization of the hyperparameters of the virtual sample generation process: the comprehensive learning particle swarm optimization algorithm is used to optimize the principal component contribution rate, KDE smoothing index, candidate virtual principal components and virtual sample numbers, mapping model parameters and model integration weight parameters that affect the "quality" of virtual samples, so as to obtain virtual samples that optimize the generalization performance of the DXN prediction model; In the step S1, generating a virtual sample input based on the simplified feature PDF specifically includes: S101, based on PCA simplified features: For the DXN small sample training set R train The d-dimensional input features Conduct principal component analysis: First, according to the formula Center the samples separately and then arrange them into d×N train The matrix Next, calculate its covariance matrix And perform eigenvalue decomposition, the eigenvalue order is: λ1≥λ2≥...≥λ d ; Then, according to the set variance contribution rate threshold θ pca By Calculate the number of principal components d′; finally, take λ1≥λ2≥...≥λ d′ The corresponding d′ eigenvectors form the projection matrix U train =(u1,u2,...,u d′ ) and calculate the sample matrix after dimensionality reduction, as follows: Among them, X train Input for DXN training set, is the input of the training set after dimensionality reduction, and each sample contains d′ features, namely Accordingly, X train The d′ principal components of in, S102, generate candidate virtual principal components based on KDE: Based on PCA feature reduction X train principal component Perform kernel density estimation, taking the i-th principal component For example, calculate Kernel density estimation of for, Among them, h kde is the smoothing index of kernel density estimation; K(·) is the kernel function; N train For the training set X train The number of samples in the medium; Optional The Gaussian function shown is used as the kernel function, and the variance of the Gaussian distribution corresponding to each sample point is h kde , the mean is the sample value but The calculation is, Based on the kernel density estimation results of the above principal components, a candidate virtual principal component that conforms to the principal component distribution is generated; S103, reconstructing a virtual sample input based on sampling: According to X train The candidate virtual principal components generated by estimating the principal component distribution of In order to obtain more combination modes to the greatest extent, virtual principal components that are correlated with each other are obtained by randomly orthogonally sampling each candidate virtual principal component. The generation method is: Among them, rand represents [1,N vpc ] in random integer; therefore, The generation method of is described as: randomly select one principal component from each of the d′ virtual candidate principal components to form a d′-dimensional virtual sample input For the principal components of the generated virtual sample input Perform PCA reconstruction to obtain virtual sample input X vs , calculate the virtual sample input As follows: in, Input X for the training set train The mean vector of .

2. The probability density distribution driven virtual sample generation method for dioxin detection according to claim 1, characterized in that: In step S102, based on the kernel density estimation result of the principal component, a candidate virtual principal component that conforms to the principal component distribution is generated, specifically: N is generated based on the inversion method. vpc Kernel density The virtual candidate principal components include the following steps: 1) For the composition One of the Gaussian functions generate Candidate virtual principal component values in, Right now The mean is Variance is h kde Normal distribution of 2), for the composition N train Each Gaussian function generates a Candidate virtual principal component values ​​can be obtained to meet the principal component Candidate virtual principal components of probability distribution 3), for the principal component Generate candidate virtual principal components respectively There is no corresponding relationship between the candidate virtual principal components.

3. The probability density distribution driven virtual sample generation method for dioxin detection according to claim 2, characterized in that: In step S2, generating a virtual sample output based on the integrated mapping model specifically includes: S201, build RF mapping model based on DXN small sample: The DXN training set obtains K different sub-training sets through Bootstrap sampling and random feature segmentation to construct K decision trees, and integrates their results to obtain prediction results. For regression problems, when constructing a decision tree, the optimal segmentation features and split point values ​​of node q are obtained according to the following formula: S202, build RWNN mapping model based on DXN small sample: Use DXN small sample training set R train Steps to construct the RWNN mapping model: First, randomly set the connection weights between the input layer and the hidden layer neurons W = {w1,w2,...,w I } and the bias value b={b1,b2,...,b N } T ; Then, the hidden layer output matrix H is calculated as follows ori , Among them, h ni =Γ map (w i ,b n ,x n ) is the hidden layer node value; I is the number of neurons in the hidden layer of RWNN n L Γ map Represents a mapping function with sigmoid function as activation function; Finally, the generalized inverse matrix is ​​used to calculate the connection weight β between the hidden layer and the output layer neurons, as follows, β = (H ori ) + y train (20) Among them, (H ori ) + H ori The generalized inverse matrix of ; the constructed RWNN mapping model is S203, generating a virtual output based on the integrated mapping model: Based on the RF and RWNN mapping models, a DXN integrated mapping model is obtained to generate a virtual sample output; by adjusting the RF and RWNN mapping model parameters and the integration weights of the two, a more adaptable integrated mapping model is obtained, and then a virtual sample output is generated; Calculate virtual output based on RF mapping model for, Calculate the virtual output based on the RWNN mapping model for, Furthermore, based on and Get virtual output y vs for, Among them, ω mod is the model combination weight; Thus, we obtain the virtual sample R vs ={X vs ,y vs }.

4. The probability density distribution driven virtual sample generation method for dioxin detection according to claim 3, characterized in that: The step S3, based on CLPSO, optimizes the hyper parameters of the virtual sample generation process, specifically includes: The optimization objective is described as: Among them, f(z,R train ,R valid ) represents the RMSE value of the model constructed by the mixed sample consisting of the virtual sample and the small sample training set on the validation set; f mix (·) represents the prediction model constructed by mixed samples; z={θ pca ,h kde ,N vpc ,N vs ,n T ,m S ,n L ,ω mod } represents the decision variables of the optimization, including 8 parameters of the virtual sample generation process; z∈Ω represents the feasible domain space of the decision variables; Based on the optimization objective, CLPSO is used to calculate the PCA principal component contribution rate θ pca , KDE smoothing index h kde 、Number of dummy variables vpc , the number of virtual samples N vs , mapping model parameter n T ,m S ,n L and model combination weight ω mod Solve and obtain the optimal virtual sample.

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