Open-air area radon exhalation rate prediction method based on VMD-LSTM-ELMAN

Abstract

The application provides an open area radon emission rate prediction method based on VMD-LSTM-ELMAN, first, the radon emission rate historical data is decomposed into three components with different characteristic information by VMD, then the data training and prediction are carried out by selecting the LSTM model, the ELMAN neural network model and the normal distribution model, and the environmental factors affecting the radon emission are taken as the prediction index to input the model, so that the influence of the environmental index on the radon emission can be more truly reflected, the model prediction result can accurately reflect the emission law of the radon emission, and the prediction precision is high. The radon emission rate prediction model is established by jointly using VMD, LSTM and ELMAN, the lagging effect of the environmental index on the radon emission rate is specially considered, the radon emission rate value curve is decomposed and the change trend is predicted, and guidance is provided for radon prevention and control and environmental management.

Description

Technical Field

[0001] This invention relates to the field of radon emission monitoring technology, and in particular to a method for predicting radon emission rates in open areas based on VMD-LSTM-ELMAN. Background Technology

[0002] Radon is a colorless, odorless, radioactive inert gas. Listed by the World Health Organization as the second leading cause of lung cancer, it commonly leaches from underground engineering sites, mines, tourist caves, nuclear facilities, tailings ponds, and surfaces such as building materials, soil, and the ground. The spread and migration of radon causes significant radioactive pollution to the surrounding environment, seriously impacting human health. Therefore, radon prediction and early warning are of paramount importance.

[0003] Many scholars have conducted research on radon prediction. Khaled F. Al-Shboul et al. trained and tested their model using global soil radionuclide levels and the Rn-ER dataset. They compared the results of descriptive statistics with qualitative results using artificial neural networks (ANN) and gene expression programming (GEP) models to estimate radon release rates based on the content of natural radionuclides in the soil. They found that the ANN model had higher accuracy and precision than the best-performing GEP model. Adil Aslam Mir et al. studied the prediction of radon anomalies caused by seismic activity using different ensemble and individual machine learning methods on real-time radon time-series data under different scenarios. They found that reinforced trees and radial kernel support vector machines proved to be better regression models for predicting soil radon concentration anomalies during seismic activity. Adil Aslam Mir et al., when processing soil radon concentration (SRGC) time series data, compared different methods including mean, median, mode, predicted mean matching (PMM), and hot-deck interpolation. They found that the IBFI estimation dataset provides a more suitable model, and model generation and prediction based on IBFI-estimated time series produce more accurate predictions. Hao Duong Van et al. conducted a study to optimize machine learning models, namely artificial neural networks (ANNs), to accurately predict radon diffusion in Vietnam, and concluded that ANNs performed very well in predicting radon diffusion with low performance index values. Tran Dinh Bao et al. designed a simple single-hidden-layer artificial neural network (ANN) model to predict radon release during ore dressing and mining in radioactive mines. Compared with the two-hidden-layer ANN, random forest, and support vector machine models applied to Sin Quyen copperdeposit, it has lower computational cost, can be trained and referenced, and achieves the best results.

[0004] However, the above prediction methods do not consider the lag effect of environmental indicators on radon emission rates, ignore external factors, have large errors, and are difficult to effectively reflect the fluctuation trend of radon emission rates. The prediction results are inaccurate and cannot guide management units to carry out effective radon prevention and control.

[0005] In view of this, it is necessary to design an improved method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN to solve the above problems. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting radon release rate in open areas based on VMD-LSTM-ELMAN. The method uses VMD to decompose historical radon release rate data into three components with different physical meanings. By selecting LSTM model, ELMAN neural network model and normal distribution model for data training and prediction, the method can accurately reflect the radon release pattern and ensure prediction accuracy, making it better applicable to actual radon release prediction work.

[0007] To achieve the above-mentioned objectives, this invention provides a method for predicting radon leaching rates in open-air areas based on VMD-LSTM-ELMAN, comprising the following steps:

[0008] S1. Obtain historical radon exhalation rate monitoring data for the area to be predicted to form the original dataset for the time series.

[0009] S2. Normalize the original dataset from step S1 and use VMD to decompose it into three sets of modal components with different feature information.

[0010] S3. Divide the three modal components of step S2 according to the feature information, and select one of the LSTM model, ELMAN neural network model or normal distribution model for data training and prediction respectively; finally, add the three sets of predicted values ​​according to the time series, and then perform data inverse normalization to obtain the predicted value of radon exhalation rate in the region to be predicted.

[0011] As a further improvement of the present invention, in step S3, the model selection principle for the prediction of the three sets of modal components is as follows: the imf1 component with nonlinear characteristics and non-periodicity is predicted using the LSTM model, the imf2 component with fluctuating characteristics and periodicity is predicted using the ELMAN neural network model, and the imf3 component, which is randomly distributed around 0 and has poor regularity, is predicted using the normal distribution model.

[0012] As a further improvement of the present invention, when the imf2 component is predicted using the ELMAN neural network model, external environmental factors affecting the radon exhalation rate are simultaneously input as prediction indicators.

[0013] As a further improvement of the present invention, in step S2, when using VMD for mode decomposition, a variational model is first constructed, and then an augmented Lagrangian function is introduced to transform the constrained variational problem into an unconstrained variational problem for solution. The alternating direction multiplier algorithm is used for iterative updates until the convergence condition is met, and the mode components are output.

[0014] As a further improvement to the present invention, the process of using the LSTM model to predict the imf1 component is as follows:

[0015] Input gate: Stores the current state information and calculates the input gate i. t The value and the candidate state value of the input cell at time t

[0016] i t =σ·(W i ·[h t-1 ,x t ]+b i (1)

[0017]

[0018] In the formula: W i W c Represents the corresponding weight, b i With b c This represents the corresponding bias;

[0019] Forget gate: controls the information to be forgotten; calculates the activation value f of the forget gate at time t. t :

[0020] f t =σ·(W f ·[h t-1 ,x t ]+b f (3)

[0021] In the formula: W f ,b f Let represent the weights and biases of the forget gate, respectively, and σ represent the ReLU function;

[0022] Update cell state: Based on the calculation results of the input gate and forget gate, obtain the cell state update value C at time t. t :

[0023]

[0024] Output gate: Controls the output information, updating the value C based on the cell state. t The output gate is obtained. t The calculation formula is as follows:

[0025] o t =σ·(W o ·[h t-1 ,x t ]+b o (5)

[0026] h t =o t *tanh(C t (6)

[0027] In the formula: W o and b o h represents the weights and biases of the output gate. t This is the final output result at the current moment, and the output results constitute the predicted value y1 sequence.

[0028] As a further improvement of the present invention, when using the ELMAN neural network model to predict the imf2 component, the mathematical model of the ELMAN neural network is as follows:

[0029]

[0030] In the formula: k is the current state, Y(k), X(k), u(k-1), X c (k) represents the m-dimensional output node vector, the n-dimensional intermediate layer node unit vector, the r-dimensional input vector, and the n-dimensional feedback state vector, respectively; ω3, ω2, and ω1 represent the connection weights from the hidden layer to the output layer, from the input layer to the hidden layer, and from the connection layer to the hidden layer, respectively; b i Let G(·) be the threshold of the hidden layer and the output layer, G(·) be the activation function of the output neuron (using the tan-sigmoid function), and F(·) be the transfer function of the hidden layer neuron (using the sigmoid function).

[0031] The ELMAN neural network uses the sum of squared errors function as the learning index function.

[0032]

[0033] In the formula: The target output vector forms the predicted value y2 sequence.

[0034] As a further improvement of this invention, when using a normal distribution model to predict the imf3 component, the imf3 component is first tested for normality, and the mean μ and standard deviation σ of the imf3 component are calculated. Then, the probability density function formula of the normal distribution is used to calculate the probability density function value f(x) of a given imf3 component data point x. A set of predicted values ​​y3 sequence is generated using these probability density function values.

[0035]

[0036] In the formula: f(x) is the probability density at x, μ is the mean, and σ is the standard deviation.

[0037] As a further improvement to the present invention, the process of using VMD for mode decomposition is as follows:

[0038]

[0039] In the formula: x is the original dataset after normalization; K is the number of intrinsic mode decompositions (3); δ(t) is the impulse function; * is the convolution symbol; {ω k}={ω1,…,ω K} represents the center frequency of the modal function; {u k}={u1,…,u K} represents the decomposed modal components;

[0040] By introducing the augmented Lagrangian function, the above constrained variational problem is transformed into an unconstrained variational problem to be solved. Equation (11) is then transformed as follows:

[0041]

[0042] In the formula: α is the quadratic penalty factor; λ is the Lagrange multiplier;

[0043] Iteratively update u using the alternating direction multiplier algorithm k ,ω k and λ:

[0044]

[0045]

[0046]

[0047] In the formula: Γ is the update factor;

[0048] Until the convergence condition (15) is satisfied, the final modal components are output.

[0049]

[0050] In the formula: e > 0 represents the discrimination precision.

[0051] As a further improvement of the present invention, the prediction indicators include cumulative rainfall, daily average temperature and daily temperature difference. Considering that the influence of the prediction indicator values ​​on radon release is lagging, the environmental data of day t is used as the prediction indicator for day t+1 and input into the model.

[0052] The beneficial effects of this invention are:

[0053] 1. The present invention provides a method for predicting radon exhalation rates in open areas based on VMD-LSTM-ELMAN. First, VMD is used to decompose historical radon exhalation rate data into three components with different physical meanings. This suppresses noise components in the signal, avoids mode aliasing, and effectively separates the main features of radon exhalation, facilitating targeted prediction and improving prediction accuracy. Then, by using an LSTM model, an ELMAN neural network model, and a normal distribution model for data training and prediction, the method accurately reflects the radon exhalation pattern and ensures better prediction accuracy. This invention establishes a radon exhalation rate prediction model by jointly employing VMD, LSTM, and ELMAN, specifically considering the lag effect of environmental indicators on radon exhalation rates. It decomposes the radon exhalation rate numerical curve and predicts its changing trend, making it suitable for predicting radon exhalation in open areas and providing guidance for radon control and environmental governance.

[0054] 2. When predicting three components with different characteristic information, this invention uses a Long Short-Term Memory (LSTM) neural network model to predict the trend-oriented and non-periodic components. This model accurately captures the long-term and short-term dependencies in the sequence, which is beneficial for predicting long-term radon extrusion trends. The ELMAN neural network model is used to predict the fluctuating and periodic components, taking into account the lag effect of environmental indicators on radon extrusion rates. Due to its multi-layered structure, non-linear activation function, and feedback connections, the ELMAN neural network can better capture the complex non-linear relationships between data, more closely reflecting the actual impact of environmental indicators on radon extrusion. The random fluctuation component without a clear trend is treated as noise, and its frequency conforms to a normal distribution. A normal distribution model is used for prediction, reducing the prediction model error. Compared to a single model, the VMD-LSTM-ELMAN composite model proposed in this invention provides prediction results closer to the actual radon extrusion situation. It not only reflects the overall trend and non-linear characteristics of the radon extrusion rate but also fully considers randomness and uncertainty, improving the stability of the prediction model by reducing the dispersion and fluctuation range of the model error. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the process for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN, as described in this invention.

[0056] Figure 2 This is a graph showing the radon exudation rate monitoring data in Example 1.

[0057] Figure 3 The image shows the three sets of modal component data after VMD modal decomposition in Example 1.

[0058] Figure 4This is a comparison chart of the predicted value y1 sequence and the radon exudation rate data imf1 component in Example 1.

[0059] Figure 5 This is a comparison chart of the predicted value y2 sequence and the radon exudation rate data imf2 component in Example 1.

[0060] Figure 6 This is a graph showing the normal distribution type of the imf3 component and the mean and standard deviation data in Example 1.

[0061] Figure 7 This is a comparison chart of the predicted value y3 sequence and the radon exudation rate data imf3 component in Example 1.

[0062] Figure 8 This is a comparison chart of the radon exhalation rate prediction values ​​for Example 1 and Comparative Examples 1-2 using different models with the actual 35-day monitoring values. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] It should also be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and / or processing steps closely related to the present invention are shown in the accompanying drawings, while other details that are not closely related to the present invention are omitted.

[0065] Additionally, it should be noted that the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0066] Please see Figure 1 As shown, a method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN includes the following steps:

[0067] S1. Obtain historical radon exhalation rate monitoring data for the area to be predicted to form the original dataset for the time series.

[0068] S2. Normalize the original dataset from step S1 and use VMD to decompose it into three sets of modal components with different feature information.

[0069] S3. Divide the three modal components of step S2 according to the feature information, and select one of the LSTM model, ELMAN neural network model or normal distribution model for data training and prediction respectively; finally, add the three sets of predicted values ​​according to the time series, and then perform data inverse normalization to obtain the predicted value of radon exhalation rate in the region to be predicted.

[0070] Specifically, in step S3, the model selection principle for the three sets of modal component predictions is as follows: the imf1 component, which has trend, nonlinear characteristics, and is non-periodic, is predicted using an LSTM model; the imf2 component, which has fluctuation characteristics and is periodic, is predicted using an ELMAN neural network model; and the imf3 component, which is randomly distributed around 0 and has poor regularity, is predicted using a normal distribution model. Those skilled in the art should understand that imf1, imf2, and imf3 are merely component names, and the actual selection of the prediction model should be based on the characteristic information of the component.

[0071] The process of using the LSTM model to predict the imf1 component is as follows:

[0072] Input gate: Stores the current state information and calculates the input gate i. t The value and the candidate state value of the input cell at time t

[0073] i t =σ·(W i ·[h t-1 ,x t ]+b i (1)

[0074]

[0075] In the formula: W i W c Represents the corresponding weight, b i With b c This represents the corresponding bias;

[0076] Forget gate: controls the information to be forgotten; calculates the activation value f of the forget gate at time t. t :

[0077] f t =σ·(W f ·[h t-1 ,x t ]+b f (3)

[0078] In the formula: W f ,b f Let represent the weights and biases of the forget gate, respectively, and σ represent the ReLU function;

[0079] Update cell state: Based on the calculation results of the input gate and forget gate, obtain the cell state update value C at time t. t :

[0080]

[0081] Output gate: Controls the output information, updating the value C based on the cell state. t The output gate is obtained. t The calculation formula is as follows:

[0082] o t =σ·(W o ·[h t-1 ,x t ]+b o (5)

[0083] h t =o t *tanh(C t (6)

[0084] In the formula: W o and b o h represents the weights and biases of the output gate. t This is the final output result at the current moment, and the output results constitute the predicted value y1 sequence.

[0085] Long Short-Term Memory (LSTM) neural network models are a special type of recurrent neural network that solves the gradient vanishing and exploding problems in long-term time series analysis. They are suitable for processing and predicting important events with very long intervals and delays in time series. This invention uses an LSTM model to predict trending components, accurately capturing long-term and short-term dependencies in the sequence, which is beneficial for predicting long-term radon emission trends.

[0086] When predicting the IMF2 component using the ELMAN neural network model, external environmental factors affecting the radon exhalation rate are simultaneously input as prediction indicators. The mathematical model of the ELMAN neural network is as follows:

[0087]

[0088] In the formula: k is the current state, Y(k), X(k), u(k-1), X c (k) represents the m-dimensional output node vector, the n-dimensional intermediate layer node unit vector, the r-dimensional input vector, and the n-dimensional feedback state vector, respectively; ω3, ω2, and ω1 represent the connection weights from the hidden layer to the output layer, from the input layer to the hidden layer, and from the connection layer to the hidden layer, respectively; b iLet G(·) be the threshold of the hidden layer and the output layer, G(·) be the activation function of the output neuron (using the tan-sigmoid function), and F(·) be the transfer function of the hidden layer neuron (using the sigmoid function).

[0089] The ELMAN neural network uses the sum of squared errors function as the learning index function.

[0090]

[0091] In the formula: The target output vector forms the predicted value y2 sequence.

[0092] The ELMAN neural network is a typical global feedforward, locally recursive network model. It possesses stronger computational power than feedforward neural networks and is better suited for solving rapid optimization problems. This invention uses the ELMAN neural network model to predict components with fluctuating and periodic characteristics, while also considering the lag effect of environmental indicators on radon emission rates. Due to its multi-layered structure, nonlinear activation function, and feedback connections, the ELMAN neural network can better capture the complex nonlinear relationships between data, thus more accurately reflecting the impact of environmental indicators on radon emission.

[0093] When using a normal distribution model to predict the IMF3 component, first, a normal distribution type test is performed on the IMF3 component, and the mean μ and standard deviation σ of the IMF3 component are calculated. Then, the probability density function formula of the normal distribution is used to calculate the probability density function value f(x) of a given IMF3 component data point x. Using these probability density function values, a set of predicted values ​​y3 sequence is generated.

[0094]

[0095] In the formula: f(x) is the probability density at x, μ is the mean, and σ is the standard deviation.

[0096] The IMF3 component, which fluctuates randomly around 0 without a clear trend, is taken as the noise part. Its frequency conforms to the normal distribution type. Using the normal distribution model for prediction reduces the prediction model error.

[0097] This invention employs Variational Mode Decomposition (VMD) to first construct a variational model, then introduces an augmented Lagrangian function to transform the constrained variational problem into an unconstrained variational problem for solution. An alternating multiplier direction algorithm is used for iterative updates until the convergence condition is met, outputting the modal components. Variational Mode Decomposition (VMD) is an adaptive, fully non-recursive method for modal variation and signal processing. It overcomes the endpoint effects and modal component aliasing problems of Empirical Mode Decomposition (EMD), and can reduce the non-stationarity of complex and highly nonlinear time series, decomposing them into relatively stationary subsequences containing multiple different frequency scales. This invention utilizes VMD to decompose historical radon exudation rate data into three components with different physical meanings. This suppresses noise components in the signal, avoids mode aliasing, and effectively separates the main features in the radon exudation process, facilitating subsequent targeted predictions and significantly improving prediction accuracy.

[0098] The process of using VMD for mode decomposition is as follows:

[0099]

[0100] In the formula: x is the original dataset after normalization; K is the number of intrinsic mode decompositions (3); δ(t) is the impulse function; * is the convolution symbol; {ω k}={ω1,…,ω K} represents the center frequency of the modal function; {u k}={u1,…,u K} represents the decomposed modal components;

[0101] By introducing the augmented Lagrangian function, the above constrained variational problem is transformed into an unconstrained variational problem to be solved. Equation (11) is then transformed as follows:

[0102]

[0103] In the formula: α is the quadratic penalty factor; λ is the Lagrange multiplier;

[0104] Iteratively update u using the alternating direction multiplier algorithm k ,ω k and λ:

[0105]

[0106]

[0107]

[0108] In the formula: Γ is the update factor;

[0109] Until the convergence condition (15) is satisfied, the final modal components are output.

[0110]

[0111] In the formula: e > 0 represents the discrimination precision.

[0112] More specifically, when using the ELMAN neural network model to predict the mf2 component, the prediction indicators include cumulative rainfall, daily average temperature, and daily temperature range. Considering the lag in the impact of the prediction indicator values ​​on radon release, the environmental data of day t is used as the prediction indicator input for day t+1. The prediction indicators are specifically ranked by mutual information values ​​to analyze the correlation between variables and obtain the importance of each feature variable. The formula for calculating the mutual information value is:

[0113]

[0114] In the formula: p(a) and p(b) are the probability distributions of variables a and b, respectively, and p(a,b) is the joint probability distribution of variables a and b.

[0115] It should be noted that cumulative rainfall, average daily temperature, and daily temperature range are all affected by the weather. Since the weather forecast period for most areas is at most 40 days, in order to ensure the accuracy of the forecast, the optimal forecast period using this method should not exceed 40 days, which can be used to predict the radon exhalation rate of the area to be predicted within the next 1 to 40 days.

[0116] This invention presents a VMD-LSTM-ELMAN-based method for predicting radon release rates in open areas. By jointly employing VMD, LSTM, and ELMAN to establish a radon release rate prediction model, it specifically considers the lag effect of environmental indicators on radon release rates. The method decomposes the radon release rate curve and predicts its changing trend, making it suitable for predicting radon release in open areas and providing guidance for radon control and environmental management. In practical applications, this method can not only guide radon prevention and control, such as spraying water to reduce radon during upcoming high-temperature weather, but also determine whether structural damage has occurred in the monitored area based on the deviation between the predicted and actual radon release rates. It can also be used for early warning of structural instability accidents.

[0117] Example 1

[0118] This embodiment provides a VMD-LSTM-ELMAN method for predicting radon exhalation rates in open areas; specifically, it includes the following steps:

[0119] S1. Table 1 shows the radon leaching rate monitoring results obtained from the Hunan Provincial Engineering Technology Research Center for Uranium Tailings Dam Decommissioning and Treatment Technology for a certain open-pit uranium tailings dam surface model over 179 consecutive days. The obtained radon leaching rate monitoring results are as follows: Figure 2 As shown.

[0120] Table 1. Radon release rate results of a beach model of an open-pit uranium tailings dam over 179 consecutive days.

[0121]

[0122]

[0123] S2. The radon exhalation rate results from step S1 are used as the raw data and normalized. The data from the first 144 days are used as training data, and the data from the last 35 days are used as test data. First, VMD is used for mode decomposition, decomposing it into three sets of modal components with different feature information, such as... Figure 3 As shown;

[0124] The process of using VMD for mode decomposition is as follows: set the model parameters: quadratic penalty factor α = 1500, discrimination precision e = 10. -8 The number of modes K = 3;

[0125]

[0126] In the formula: x is the original dataset after normalization; K is the number of intrinsic mode decompositions (3); δ(t) is the impulse function; * is the convolution symbol; {ω k}={ω1,…,ω K} represents the center frequency of the modal function; {u k}={u1,…,u K} represents the decomposed modal components;

[0127] Introducing the augmented Lagrangian function transforms the above constrained variational problem into an unconstrained variational problem to be solved, and equation (2) is transformed as follows:

[0128]

[0129] In the formula: α is the quadratic penalty factor; λ is the Lagrange multiplier;

[0130] Iteratively update u using the alternating direction multiplier algorithm k ,ω k and λ:

[0131]

[0132]

[0133]

[0134] In the formula: Γ is the update factor;

[0135] Until the convergence condition (6) is satisfied, the final modal components are output.

[0136]

[0137] In the formula: e > 0 represents the discrimination precision.

[0138] S3. Divide the three modal components from step S2 according to the feature information, and select one of the following models for data training (the first 144 days of data are used for training) and prediction (the last 35 days of data are used for prediction) respectively. Finally, add the three sets of predicted values ​​according to the time series, and then perform data inverse normalization to obtain the predicted value of radon exhalation rate in the region to be predicted.

[0139] The process of using the LSTM model to predict the imf1 component is as follows: the parameters are set as follows: the initial learning rate is 0.005 and the maximum number of iterations is 500.

[0140] Input gate: Stores the current state information and calculates the input gate i. t The value and the candidate state value of the input cell at time t

[0141] i t =σ·(W i ·[h t-1 ,x t ]+b i (7)

[0142]

[0143] In the formula: W i W c Represents the corresponding weight, b i With b c This represents the corresponding bias;

[0144] Forget gate: controls the information to be forgotten; calculates the activation value f of the forget gate at time t. t :

[0145] f t =σ·(W f ·[h t-1 ,x t ]+b f (9)

[0146] In the formula: W f ,b f Let represent the weights and biases of the forget gate, respectively, and σ represent the ReLU function;

[0147] Update cell state: Based on the calculation results of the input gate and forget gate, obtain the cell state update value C at time t. t:

[0148]

[0149] Output gate: Controls the output information, updating the value C based on the cell state. t The output gate is obtained. t The calculation formula is as follows:

[0150] o t =σ·(W o ·[h t-1 ,x t ]+b o (11)

[0151] h t =o t *tanh(C t (12)

[0152] In the formula: W o and b o h represents the weights and biases of the output gate. t This is the final output result at the current time. The output results constitute the predicted value y1 sequence, such as... Figure 4 The figure shown is a comparison between the predicted value y1 sequence and the radon exhalation rate data imf1 component.

[0153] When predicting the imf2 component using the ELMAN neural network model, external environmental factors affecting the radon release rate are also input as prediction indicators.

[0154] The importance ranking of each feature variable is obtained by calculating the mutual information value to analyze the correlation between variables. The formula for calculating the mutual information value is as follows:

[0155]

[0156] In the formula: p(a) and p(b) are the probability distributions of variables a and b, respectively, and p(a,b) is the joint probability distribution of variables a and b.

[0157] As can be seen from Table 2, the feature importance of cumulative rainfall, average daily temperature, and daily temperature range is greater than 0.5. Therefore, the feature variables of cumulative rainfall, average daily temperature, and daily temperature range are used as the input for prediction.

[0158] Table 2 Importance of characteristic variables affecting radon precipitation

[0159]

[0160]

[0161] The mathematical model of the ELMAN neural network is as described in formula (14), and the model parameters are set as follows: maximum training iterations are 1000, learning rate is 0.01, and minimum error is 1e. -6 ,

[0162]

[0163] In the formula: k is the current state, Y(k), X(k), u(k-1), X c (k) represents the m-dimensional output node vector, the n-dimensional intermediate layer node unit vector, the r-dimensional input vector, and the n-dimensional feedback state vector, respectively; ω3, ω2, and ω1 represent the connection weights from the hidden layer to the output layer, from the input layer to the hidden layer, and from the connection layer to the hidden layer, respectively; b i Let G(·) be the threshold of the hidden layer and the output layer, G(·) be the activation function of the output neuron (using the tan-sigmoid function), and F(·) be the transfer function of the hidden layer neuron (using the sigmoid function).

[0164] The ELMAN neural network uses the sum of squared errors function as the learning index function.

[0165]

[0166] In the formula: The target output vector forms the predicted value y2 sequence, as follows: Figure 5 The figure shown is a comparison between the predicted value y2 sequence and the imf2 component of the radon exhalation rate data.

[0167] When using a normal distribution model to predict the IMF3 component, first perform a normal distribution type test on the IMF3 component, and then calculate the mean μ and standard deviation σ of the IMF3 component to obtain... Figure 6 Then, using the probability density function formula (16) of the normal distribution, the probability density function value f(x) of the given imf3 component data point x is calculated, and a set of predicted values ​​y3 is generated using these probability density function values.

[0168]

[0169] In the formula: f(x) is the probability density at x, μ is the mean, and σ is the standard deviation.

[0170] like Figure 7 The figure shown is a comparison between the predicted value y3 sequence and the radon exhalation rate data imf3 component.

[0171] Finally, the predicted values ​​of all components are summed to obtain the sequence y = y1 + y2 + y3, and then denormalized to obtain the final predicted value of radon exhalation rate.

[0172] Comparative Example 1

[0173] Comparative Example 1 provides a method for predicting radon exhalation rate. Compared with Example 1, the difference is that step S2 is not performed, and in step S3, only the LSTM model is used for prediction. The rest is roughly the same as Example 1, and will not be repeated here.

[0174] Comparative Example 2

[0175] Comparative Example 2 provides a method for predicting radon exhalation rate. Compared with Example 1, the difference is that step S2 is not performed, and in step S3, only the ELMAN model is used for prediction. The rest is roughly the same as Example 1, and will not be repeated here.

[0176] The data from radon exhalation rate prediction using different models in Example 1 and Comparative Examples 1-2 were compared with the actual data for the last 35 days. The results are as follows: Figure 8 As shown in Table 3, the modeling performance of different models was analyzed by calculating the MSE (mean squared error), MAPE (mean absolute percentage error), and R2 (the proportion of model-explainable variance to total variance) of each model.

[0177] Table 3. Prediction accuracy of different models in Example 1 and Comparative Examples 1-2

[0178] MSE MAPE R2 LSTM 0.1120 44.49％ -0.3755 ELMAN 0.0996 38.73％ -0.2238 VMD-LSTM-ELMAN 0.0044 7.09％ 0.9456

[0179] From Table 3 and Figure 8 It can be seen that although the LSTM model has a good predictive effect on the radon release rate trend, it cannot predict the fluctuation points, ignores the influence of external factors, and has a large error. The ELMAN model, although considering the influence of external factors, does not take into account the radon release trend and random error. Therefore, it only predicts the fluctuation range, which is consistent with the actual situation, but the numerical value is quite different. The VMD-LSTM-ELMAN model used in Example 1 is the best overall. It can not only make a good prediction on the radon release trend, but also consider the fluctuation caused by the influence of external factors, while ensuring that the prediction error is relatively small.

[0180] In summary, this invention provides a method for predicting radon exhalation rates in open areas based on VMD-LSTM-ELMAN. First, VMD is used to decompose historical radon exhalation rate data into three components with different physical meanings. This suppresses noise components in the signal and effectively separates the main features of the radon exhalation process, thus improving prediction accuracy. Then, by using an LSTM model, an ELMAN neural network model, and a normal distribution model for data training and prediction, the method accurately reflects the radon exhalation pattern and ensures better prediction precision. This invention establishes a radon exhalation rate prediction model by jointly employing VMD, LSTM, and ELMAN, specifically considering the lag effect of environmental indicators on radon exhalation rates. It decomposes the radon exhalation rate numerical curve and predicts its changing trend, making it suitable for predicting radon exhalation in open areas and providing guidance for radon control and environmental management.

[0181] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting radon exhalation rate in open-air areas based on VMD-LSTM-ELMAN, characterized in that, Includes the following steps: S1. Obtain historical radon exhalation rate monitoring data for the area to be predicted to form the original dataset for the time series. S2. Normalize the original dataset from step S1 and use VMD to decompose it into three sets of modal components with different feature information. S3. Divide the three modal components from step S2 according to the feature information, and select one of the LSTM model, ELMAN neural network model or normal distribution model for data training and prediction respectively; finally, add the three sets of predicted values ​​according to the time series, and then perform data inverse normalization to obtain the predicted value of radon exhalation rate in the region to be predicted. In step S3, the model selection principle for the prediction of the three sets of modal components is as follows: the imf1 component with nonlinear characteristics and non-periodicity is predicted using the LSTM model, the imf2 component with fluctuation characteristics and periodicity is predicted using the ELMAN neural network model, and the imf3 component, which is randomly distributed around 0 and has poor regularity, is predicted using the normal distribution model. When the IMF2 component is predicted using the ELMAN neural network model, external environmental factors that affect the radon release rate are also input as prediction indicators. The prediction indicators include cumulative rainfall, daily average temperature, and daily temperature range. Considering that the influence of the prediction indicator values ​​on radon release is lagging, the environmental data of day t is used as the prediction indicator input for day t+1.

2. The method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN according to claim 1, characterized in that, In step S2, when using VMD for mode decomposition, a variational model is first constructed, and then an augmented Lagrangian function is introduced to transform the constrained variational problem into an unconstrained variational problem for solution. The alternating direction multiplier algorithm is used for iterative updates until the convergence condition is met, and then the mode components are output.

3. The method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN according to claim 1, characterized in that, The process of using the LSTM model to predict the imf1 component is as follows: Input gate: Remembers the current state information and calculates the input gate. The value and in Input the candidate state values ​​of the cells at any time : （1） （2） In the formula: , Represents the corresponding weight. and This represents the corresponding bias; Forget gate: controls the information that is forgotten, calculated in Activation value of the Forgotten Gate : （3） In the formula: , These represent the weight and bias of the forget gate, respectively. Represents the ReLU function; Update cell state: Based on the calculation results of the input gate and forget gate, obtain Cell state update value at time t : （4） Output gate: Controls the output information, updating values ​​based on cell state. Output gate The calculation formula is as follows: （5） （6） In the formula: and Represents the weights and biases of the output gate. This is the final output result at the current moment, and the output results constitute the predicted value y1 sequence.

4. The method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN according to claim 1, characterized in that, When using the ELMAN neural network model to predict the IMF2 component, the mathematical model of the ELMAN neural network is as follows: （7） In the formula: The current state. , , , They are respectively 3D output node vector, Dimensional intermediate layer node unit vector, 3D input vector sum dimensional feedback state vector, , , These represent the connection weights from hidden layer to output layer, input layer to hidden layer, and connection layer to hidden layer, respectively. The threshold values ​​for the hidden and output layers are... The tan-sigmoid function is used as the activation function for the output neuron. The transfer function for the hidden layer neurons is the sigmoid function; The ELMAN neural network uses the sum of squared errors function as the learning index function. (8) In the formula: The target output vector forms the predicted value y2 sequence.

5. The method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN according to claim 1, characterized in that, When using a normal distribution model to predict the IMF3 component, first perform a normal distribution type test on the IMF3 component, and then calculate the mean of the IMF3 component. with standard deviation Then, using the probability density function formula of the normal distribution, the given IMF3 component data points are calculated. probability density function value Using these probability density function values, a sequence of predicted values ​​y3 is generated: （9） In the formula: Is The probability density at that location, It is the mean. That is the standard deviation.

6. The method for predicting radon exhalation rate in open areas based on VMD-LSTM-ELMAN according to claim 2, characterized in that, The process of using VMD for mode decomposition is as follows: （10） In the formula: This is the original dataset after normalization. The number of intrinsic mode decompositions is 3; It is a pulse function; The symbol for convolution; The center frequency of the modal function; These are the decomposed modal components; By introducing an augmented Lagrangian function, the above constrained variational problem is transformed into an unconstrained variational problem to be solved. Equation (11) is then transformed as follows: （11） In the formula: It is a secondary penalty factor; For Lagrange multipliers; Iterative updates using the alternating direction multiplier algorithm , and : （12） （13） （14） In the formula: For the update factor; Until the convergence condition (15) is satisfied, the final modal components are output. （15） In the formula: To determine accuracy.

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