# Gas Concentration Monitoring Prewarning Based on Adaptive Prediction and Feature Extraction

Authors: Dingwen Dong
Journal: Computational Intelligence and Neuroscience
 (2023)

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## Abstract

This study presents a reliable method for predicting gas concentration and implementing prewarning analysis. Gas monitoring data are decomposed into intrinsic mode functions (IMFs) with different time scales by using empirical mode decomposition (EMD), which represents the intrinsic features of gas concentration on different time scales. The prediction accuracy is evaluated by the prediction effectiveness, and the IMF phase space parameters and the Gaussian process regression (GPR) hyperparameters are dynamically adjusted to achieve adaptive prediction. Combined with singular value decomposition (SVD) to extract the intrinsic features of gas monitoring data, a prediction and prewarning model is established. The case study shows that the prediction accuracy of the adaptive model is significantly higher than that of direct GPR prediction and that it solves the problem of low prediction accuracy at mutational points in gas concentration time series. The degree of influence of the production process on the variation in gas concentration is quantitatively determined to improve the reliability of prewarning applications.


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## Body

## 1. Introduction

Mine gas disasters have threatened the safe production of coal mines in China, and in recent years, gas accidents have become frequent and caused numerous casualties and property losses. Safety monitoring and prewarning are effective means to prevent and control gas accidents in Chinese coal mines, and gas monitoring data provide the measured value of the real-time mine gas concentration, which is derived from sensors. Because of the harsh environment of underground coal mines, data detection and transmission are affected by steam, coal dust, electromagnetic interference, improper sensor correction, etc., so noisy data are common. With a short monitoring cycle, the gas concentration time series composed of monitoring data has highly complex and nonlinear features. Gas concentration prediction and prewarning are large data processing problems and are applied in the domain of mining safety monitoring and control. Through accurate prediction and reliable prewarning, the abnormal status of gas concentration in high-risk areas can be identified in advance. By taking timely measures to reduce the gas concentration, the influence of frequent power cuts caused by gas overruns on production efficiency can be avoided, and gas explosion accidents caused by gas concentration overruns can be prevented. The research results are important for coal mines to achieve safe and efficient production.In terms of gas concentration prediction, some scholars have adopted chaos theory [1], machine learning [2–4], fuzzy mathematics [5], and grey theory [6] to research the short-term methods for gas concentration prediction. Common existing problems are the low prediction accuracy or prediction failure at the mutational points in the gas concentration time series, as the main factors impacting the variation in gas concentration in short-term prediction are production process factors. Due to the complexity of gas emission into the working face of an underground coal mine, the production process factors have not been considered in prediction modelling, which leads to the low reliability of gas concentration prewarning. Although the author’s previous research [7–9] achieved good prediction accuracy, the accuracy is occasionally low at the mutation point of the gas concentration time series. In terms of gas concentration prewarning, the representative research methods mainly include numerical calculation prewarning [10] and probability prewarning [11]. Some studies provide useful references for algorithm performance improvement, model optimization, and prewarning information system design [12–14]. However, for the determination of prewarning results, most studies focus on direct judgement based on industrial technical regulations; these methods [10–14] do not consider the production process factors that mainly affect the real-time variation in gas concentration and cannot be used to quantitatively analyse the variation in gas concentration caused by the production process. Thus, the reliability of the application is difficult to ensure. Therefore, to achieve more accurate prediction, it is very important to quantitatively determine the impact of the production process on gas concentrations and realize reliable gas concentration prewarning. Presently, there are no practical studies on the quantitative research and application of gas concentration variation caused by the production process.Gas monitoring data integrate the variation law of gas concentration under the influence of the production process. Under the conditions of “two standards and one mining” or “two mining and one standard” production arrangements that are widely employed in coal mines in China, the initial gas concentration during a production shift is large and then gradually decreases to a stable level during the subsequent maintenance or preparation shift. Therefore, the variation in gas concentration affected by the production process can be determined through feature extraction to assist the prewarning analysis in periods of abnormal increases in gas concentration. This study aimed at the low prediction accuracy at the inflection point of the gas concentration time series and the low prewarning reliability because of the lack of consideration of the main factors affecting the variation in gas concentrations. The motivation of this paper is to solve the problem of low prediction accuracy by adaptively optimizing the hyperparameters of the GPR prediction model for different time-frequency characteristic series, considering the production and ventilation factors that mainly affect the variation in gas concentrations, and dynamically determining a prewarning index and threshold through feature extraction to improve the reliability of prewarning by combining EMD and SVD. EMD has achieved good results in nonlinear time series analysis in the fields of price prediction [15], fault diagnosis [16], data denoising [17], etc. EMD can process and obtain the intrinsic features of complex time series; the gas concentration time series can be decomposed into components on different scales, and the establishment of prediction models for these components will reduce the complexity of prediction problems, so it is a good auxiliary method to improve the prediction accuracy. With its ability to handle high-dimensional data and complex nonlinear problems, GPR is also a popular topic in application research on time series prediction [18–20]. SVD is a matrix decomposition and transformation method that is widely employed in signal processing and data compression and is suitable for extracting the intrinsic features of signals from sequences with obvious time-frequency features [21, 22], such as gas concentration monitoring data sequences. The singular value of gas concentration monitoring data can reflect the variation and its time characteristics in a production cycle; it can provide an important quantitative basis for gas concentration prewarning. This paper investigates a gas concentration adaptive prediction method based on feature reconstruction and hyperparametric optimization to solve the problem of low prediction accuracy at the mutation point of gas concentration time series and extract the intrinsic features of gas monitoring data with SVD to achieve reliable prewarning. The content of this paper includes the time-frequency analysis of gas monitoring data, the establishment of a gas concentration prediction model and a prewarning model, and the implementation of case analyses.


## 2. Time-Frequency Feature Analysis of Gas Monitoring Data

The EMD method is used to extract the IMFs from gas concentration time series. The fluctuation and trend components of different dimensions are decomposed through a repeated screening process to generate IMFs with different time-frequency features, each IMF represents a dimensional fluctuation composition. For the gas concentration time seriesct,t=1,2,⋯, after decomposition, it can be expressed as follows:(1)ct=∑i=1simfit+rst,where imfit is the IMF component and rst is the remainder, which represents the average trend of the gas concentration time series.


## 3. Gas Concentration Prediction

### 3.1. Phase Space Reconstruction

After EMD processing of the gas concentration time series, an IMF setimfit,t=1,2,⋯, which can construct an m dimension vector space by determining a suitable embedding dimension m and time delay t, is obtained for each IMF component; xit=imfit,imfit+τ,⋯,imfit+m−1τt=1,2,⋯,n represents the points in m dimension phase space; n (n=N−m−1τ) denotes the number of phase points; N is the length of the gas concentration time series, which describes the gas concentration’s variation track in phase space. Only if the parameters m and τ are suitable (the values of the two parameters are generally less than 12), does the reconstructed phase space have the same properties as the original time series. Considering the highly complex features of the gas concentration time series, m and τ are dynamically determined in the process of prediction to obtain the best prediction accuracy. When m and τ are determined, there is a prediction function f• in the phase space, which makes y=xt+τ=fxt, and f• is constructed with GPR thereafter.


### 3.2. GPR Prediction Model

The Gaussian process is a kernel learning method with probabilistic meaning. For each IMF decomposed from the gas concentration time series by EMD, after phase space reconstruction, there is a gas concentration training sample setD=xt,ytt=1,⋯n, in which x is the m dimension input vector and y is the corresponding output vector. For an IMF, the training sample is as follows:(2)D=imf1imf1+τ⋯imf1+m−1τimf2imf2+τ⋯imf2+m−1τ⋮⋮⋱⋮imfnimf2+τ⋯imfn+m−1τ,imf1+mτimf2+mτ⋮imfn+mτ,where X=xt,t=1,⋯n is the m×n input matrix and D=X,y. Therefore, the prediction function can be described as a regression problem(3)y=fx+ε,where ε i.i.d. N0,σn2, the prior distribution of y is as follows:(4)yX,K∼N0,KX,X+σn2I,where KX,X is the covariance matrix, in which each kX,X is the covariance function or kernel function, σn2 is the sequence variance, and I is the unit matrix. For a series of test input samples X∗, the joint probability distribution of its target value and function values is expressed as follows:(5)yf∗∼N0,KX,X+σn2IKX,X∗KX∗,XKX∗,X∗.K=KX,X, and K∗=KX∗,X∗. If there is only a test sample, k∗=kx∗ is employed to represent the covariance between the test sample and the n training sample, and the GPR prediction is expressed as follows:(6)f∗X,y,X∗∼Nmf∗,covf∗,(7)mf∗=k∗TK+σn2I−1y,(8)covf∗=kx∗,x∗−k∗TK+σn2I−1k∗.The superscriptT expresses the matrix transposition operations. The kernel function of the Gaussian process model is the Gaussian kernel function, which is expressed as follows:(9)kimfp,imfq=σf2exp−imfp−imfq22l2+σn2δpq,where δpq is a Kronecker delta, and it is one if p = q and zero otherwise. θ=l,σf2,σn2 is a hyperparameter that is directly related to the training process of the model. Thus, the value of the hyperparameters will affect the prediction accuracy. Then, the gas prediction value y^=mf∗ is the average approximation of the prediction samples’ posterior probability distribution. The sum of all the IMF prediction values is the gas concentration prediction value.


### 3.3. Adaptive Prediction Model and Algorithm Description

In order to ensure higher prediction accuracy, it is necessary to dynamically adjust the model parameters, including the GPR hyperparameters and the IMFs’ phase space parameters, that is, continuously evaluate the prediction effectiveness during the model training process, and dynamically adjust the model parameters to obtain the highest prediction accuracy. This is how we realize the adaptive prediction driven by the monitoring data.


#### 3.3.1. Prediction Effectiveness Evaluation

During the prediction process, as the real-time monitoring data are continuously obtained, the training and prediction samples of the gas concentration are continually updated. For the IMF’s prediction calculation, because of different time-frequency features, each IMF’s prediction accuracy is inconsistent. To improve the prediction accuracy, the prediction effectiveness is adopted to evaluate its accuracy; it is defined as follows:y^t is set as the prediction value at time point t, et=yt−y^t is the absolute error of prediction, yt is the actual on-time monitoring value, assuming 1,N is the sample interval, and N+1,N+M is the prediction sample interval, which contains M prediction points. Then, the prediction effectiveness is defined as follows:(10)Mt=1M∑t=N+1N+MAt.If0≤et/yt≤1, then At=1−et/yt. Otherwise, et/yt>1. At=0, where At is the fitting degree of prediction or prediction accuracy at time point t.


#### 3.3.2. Hyperparametric Optimization

In the GPR model, the values of the hyperparameters affect the prediction accuracy. In addition, due to the high complexity and nonlinear features of gas concentration time series, their value needs to be dynamically determined. In the training process of the GPR model,l is the length factor of the sequence, and its theoretical recommended value is l = 1; the variation range is 0,3; σf2 is the signal variance, which is obtained by real-time calculation with gas monitoring data updating; σn2 is the white noise variance, where the recommended value is σn2 = 0.5 and its variation range is [0, 1] [18]. By using the Monte Carlo simulation principle, according to l∼U0,3, σn2∼N0,1, and the optimal hyperparameters can be dynamically determined by random sampling. For each pair of l and σn2, model training is carried out, test samples are created, and the prediction effectiveness is calculated. Then, the optimal hyperparameters corresponding to the maximum value of prediction effectiveness are obtained.


#### 3.3.3. Parameter Optimization of Phase Space Reconstruction

Before prediction, several test samples are chosen to predict and dynamically adjust the IMFs’ phase space parametersth≤tw≤2h and τ, which are used to determine the best phase space parameters. The phase space reconstruction parameters of embedding dimension m and time delay τ directly determine the prediction accuracy of the model. In theory, these parameters can be calculated by using the chaotic system method. However, considering the highly complex and nonlinear features of gas concentration time series, the method cannot use fixed values of th≤tw≤2h and τ to reconstruct each period of monitoring data and to obtain the best prediction results. Therefore, the determination of th≤tw≤2h and τ should be a dynamically adaptive process. Based on previous research [9], the optimum value of th≤tw≤2h is between 4 and 12, and that of τ is between 1 and 7. Therefore, with real-time gas monitoring data updating, m=4 and τ=1 are set as the initial values for training the model for each pair of th≤tw≤2h and τ, and the prediction effectiveness of the test samples is calculated. m and τ are set with a certain step, and the prediction accuracy of the test samples is compared. There is a pair of parameters corresponding to the highest prediction accuracy, which is the best embedding dimension th≤tw≤2h and time delay τ.


#### 3.3.4. Algorithm Description

Based on the methods above, the algorithm steps of the self-adaptive prediction model are summarized as follows, and the calculation process is shown in Figure1.(1)
For the gas concentration time seriesct, the EMD method is used to decompose it and obtain its IMF sets imf1,imf2,⋯,imfs(2)
For eachimfi,i=1,2,⋯,s, its phase space parameters are reconstructed, the initial embedding dimension is mi=m0i, the initial time delay is τi=τ0i, their initial iteration step is 1, and the number optimization calculation steps is j=1,2,⋯,Pj, where Pj is the product of the adjustment steps of mi and τi;(3)
For eachimfi, GPR hyperparameters lijv and σnijv2 are randomly obtained to execute pN (k=1,2,⋯,pN) times during model training, and the test samples are input to calculate the prediction results and its prediction effectiveness Mijv. The optimal hyperparameters lij and σnij2 are obtained when the maximum value of Mijv is reached;(4)
Step (3) is repeatedp times to obtain the optimal parameters for phase space reconstruction li and σni2 when the maximum value of Mijv is reached(5)
For eachfi∗ of the prediction sample, a calculation is performed, and its prediction value f^i∗ is obtained(6)
Steps (2), (3), (4), and (5) are executeds times, and the final gas concentration prediction result y^=∑i=1sf^i∗ is obtained.Figure 1
Calculation process.


## 3.1. Phase Space Reconstruction

After EMD processing of the gas concentration time series, an IMF setimfit,t=1,2,⋯, which can construct an m dimension vector space by determining a suitable embedding dimension m and time delay t, is obtained for each IMF component; xit=imfit,imfit+τ,⋯,imfit+m−1τt=1,2,⋯,n represents the points in m dimension phase space; n (n=N−m−1τ) denotes the number of phase points; N is the length of the gas concentration time series, which describes the gas concentration’s variation track in phase space. Only if the parameters m and τ are suitable (the values of the two parameters are generally less than 12), does the reconstructed phase space have the same properties as the original time series. Considering the highly complex features of the gas concentration time series, m and τ are dynamically determined in the process of prediction to obtain the best prediction accuracy. When m and τ are determined, there is a prediction function f• in the phase space, which makes y=xt+τ=fxt, and f• is constructed with GPR thereafter.


## 3.2. GPR Prediction Model

The Gaussian process is a kernel learning method with probabilistic meaning. For each IMF decomposed from the gas concentration time series by EMD, after phase space reconstruction, there is a gas concentration training sample setD=xt,ytt=1,⋯n, in which x is the m dimension input vector and y is the corresponding output vector. For an IMF, the training sample is as follows:(2)D=imf1imf1+τ⋯imf1+m−1τimf2imf2+τ⋯imf2+m−1τ⋮⋮⋱⋮imfnimf2+τ⋯imfn+m−1τ,imf1+mτimf2+mτ⋮imfn+mτ,where X=xt,t=1,⋯n is the m×n input matrix and D=X,y. Therefore, the prediction function can be described as a regression problem(3)y=fx+ε,where ε i.i.d. N0,σn2, the prior distribution of y is as follows:(4)yX,K∼N0,KX,X+σn2I,where KX,X is the covariance matrix, in which each kX,X is the covariance function or kernel function, σn2 is the sequence variance, and I is the unit matrix. For a series of test input samples X∗, the joint probability distribution of its target value and function values is expressed as follows:(5)yf∗∼N0,KX,X+σn2IKX,X∗KX∗,XKX∗,X∗.K=KX,X, and K∗=KX∗,X∗. If there is only a test sample, k∗=kx∗ is employed to represent the covariance between the test sample and the n training sample, and the GPR prediction is expressed as follows:(6)f∗X,y,X∗∼Nmf∗,covf∗,(7)mf∗=k∗TK+σn2I−1y,(8)covf∗=kx∗,x∗−k∗TK+σn2I−1k∗.The superscriptT expresses the matrix transposition operations. The kernel function of the Gaussian process model is the Gaussian kernel function, which is expressed as follows:(9)kimfp,imfq=σf2exp−imfp−imfq22l2+σn2δpq,where δpq is a Kronecker delta, and it is one if p = q and zero otherwise. θ=l,σf2,σn2 is a hyperparameter that is directly related to the training process of the model. Thus, the value of the hyperparameters will affect the prediction accuracy. Then, the gas prediction value y^=mf∗ is the average approximation of the prediction samples’ posterior probability distribution. The sum of all the IMF prediction values is the gas concentration prediction value.


## 3.3. Adaptive Prediction Model and Algorithm Description

In order to ensure higher prediction accuracy, it is necessary to dynamically adjust the model parameters, including the GPR hyperparameters and the IMFs’ phase space parameters, that is, continuously evaluate the prediction effectiveness during the model training process, and dynamically adjust the model parameters to obtain the highest prediction accuracy. This is how we realize the adaptive prediction driven by the monitoring data.


### 3.3.1. Prediction Effectiveness Evaluation

During the prediction process, as the real-time monitoring data are continuously obtained, the training and prediction samples of the gas concentration are continually updated. For the IMF’s prediction calculation, because of different time-frequency features, each IMF’s prediction accuracy is inconsistent. To improve the prediction accuracy, the prediction effectiveness is adopted to evaluate its accuracy; it is defined as follows:y^t is set as the prediction value at time point t, et=yt−y^t is the absolute error of prediction, yt is the actual on-time monitoring value, assuming 1,N is the sample interval, and N+1,N+M is the prediction sample interval, which contains M prediction points. Then, the prediction effectiveness is defined as follows:(10)Mt=1M∑t=N+1N+MAt.If0≤et/yt≤1, then At=1−et/yt. Otherwise, et/yt>1. At=0, where At is the fitting degree of prediction or prediction accuracy at time point t.


### 3.3.2. Hyperparametric Optimization

In the GPR model, the values of the hyperparameters affect the prediction accuracy. In addition, due to the high complexity and nonlinear features of gas concentration time series, their value needs to be dynamically determined. In the training process of the GPR model,l is the length factor of the sequence, and its theoretical recommended value is l = 1; the variation range is 0,3; σf2 is the signal variance, which is obtained by real-time calculation with gas monitoring data updating; σn2 is the white noise variance, where the recommended value is σn2 = 0.5 and its variation range is [0, 1] [18]. By using the Monte Carlo simulation principle, according to l∼U0,3, σn2∼N0,1, and the optimal hyperparameters can be dynamically determined by random sampling. For each pair of l and σn2, model training is carried out, test samples are created, and the prediction effectiveness is calculated. Then, the optimal hyperparameters corresponding to the maximum value of prediction effectiveness are obtained.


### 3.3.3. Parameter Optimization of Phase Space Reconstruction

Before prediction, several test samples are chosen to predict and dynamically adjust the IMFs’ phase space parametersth≤tw≤2h and τ, which are used to determine the best phase space parameters. The phase space reconstruction parameters of embedding dimension m and time delay τ directly determine the prediction accuracy of the model. In theory, these parameters can be calculated by using the chaotic system method. However, considering the highly complex and nonlinear features of gas concentration time series, the method cannot use fixed values of th≤tw≤2h and τ to reconstruct each period of monitoring data and to obtain the best prediction results. Therefore, the determination of th≤tw≤2h and τ should be a dynamically adaptive process. Based on previous research [9], the optimum value of th≤tw≤2h is between 4 and 12, and that of τ is between 1 and 7. Therefore, with real-time gas monitoring data updating, m=4 and τ=1 are set as the initial values for training the model for each pair of th≤tw≤2h and τ, and the prediction effectiveness of the test samples is calculated. m and τ are set with a certain step, and the prediction accuracy of the test samples is compared. There is a pair of parameters corresponding to the highest prediction accuracy, which is the best embedding dimension th≤tw≤2h and time delay τ.


### 3.3.4. Algorithm Description

Based on the methods above, the algorithm steps of the self-adaptive prediction model are summarized as follows, and the calculation process is shown in Figure1.(1)
For the gas concentration time seriesct, the EMD method is used to decompose it and obtain its IMF sets imf1,imf2,⋯,imfs(2)
For eachimfi,i=1,2,⋯,s, its phase space parameters are reconstructed, the initial embedding dimension is mi=m0i, the initial time delay is τi=τ0i, their initial iteration step is 1, and the number optimization calculation steps is j=1,2,⋯,Pj, where Pj is the product of the adjustment steps of mi and τi;(3)
For eachimfi, GPR hyperparameters lijv and σnijv2 are randomly obtained to execute pN (k=1,2,⋯,pN) times during model training, and the test samples are input to calculate the prediction results and its prediction effectiveness Mijv. The optimal hyperparameters lij and σnij2 are obtained when the maximum value of Mijv is reached;(4)
Step (3) is repeatedp times to obtain the optimal parameters for phase space reconstruction li and σni2 when the maximum value of Mijv is reached(5)
For eachfi∗ of the prediction sample, a calculation is performed, and its prediction value f^i∗ is obtained(6)
Steps (2), (3), (4), and (5) are executeds times, and the final gas concentration prediction result y^=∑i=1sf^i∗ is obtained.Figure 1
Calculation process.


## 3.3.1. Prediction Effectiveness Evaluation

During the prediction process, as the real-time monitoring data are continuously obtained, the training and prediction samples of the gas concentration are continually updated. For the IMF’s prediction calculation, because of different time-frequency features, each IMF’s prediction accuracy is inconsistent. To improve the prediction accuracy, the prediction effectiveness is adopted to evaluate its accuracy; it is defined as follows:y^t is set as the prediction value at time point t, et=yt−y^t is the absolute error of prediction, yt is the actual on-time monitoring value, assuming 1,N is the sample interval, and N+1,N+M is the prediction sample interval, which contains M prediction points. Then, the prediction effectiveness is defined as follows:(10)Mt=1M∑t=N+1N+MAt.If0≤et/yt≤1, then At=1−et/yt. Otherwise, et/yt>1. At=0, where At is the fitting degree of prediction or prediction accuracy at time point t.


## 3.3.2. Hyperparametric Optimization

In the GPR model, the values of the hyperparameters affect the prediction accuracy. In addition, due to the high complexity and nonlinear features of gas concentration time series, their value needs to be dynamically determined. In the training process of the GPR model,l is the length factor of the sequence, and its theoretical recommended value is l = 1; the variation range is 0,3; σf2 is the signal variance, which is obtained by real-time calculation with gas monitoring data updating; σn2 is the white noise variance, where the recommended value is σn2 = 0.5 and its variation range is [0, 1] [18]. By using the Monte Carlo simulation principle, according to l∼U0,3, σn2∼N0,1, and the optimal hyperparameters can be dynamically determined by random sampling. For each pair of l and σn2, model training is carried out, test samples are created, and the prediction effectiveness is calculated. Then, the optimal hyperparameters corresponding to the maximum value of prediction effectiveness are obtained.


## 3.3.3. Parameter Optimization of Phase Space Reconstruction

Before prediction, several test samples are chosen to predict and dynamically adjust the IMFs’ phase space parametersth≤tw≤2h and τ, which are used to determine the best phase space parameters. The phase space reconstruction parameters of embedding dimension m and time delay τ directly determine the prediction accuracy of the model. In theory, these parameters can be calculated by using the chaotic system method. However, considering the highly complex and nonlinear features of gas concentration time series, the method cannot use fixed values of th≤tw≤2h and τ to reconstruct each period of monitoring data and to obtain the best prediction results. Therefore, the determination of th≤tw≤2h and τ should be a dynamically adaptive process. Based on previous research [9], the optimum value of th≤tw≤2h is between 4 and 12, and that of τ is between 1 and 7. Therefore, with real-time gas monitoring data updating, m=4 and τ=1 are set as the initial values for training the model for each pair of th≤tw≤2h and τ, and the prediction effectiveness of the test samples is calculated. m and τ are set with a certain step, and the prediction accuracy of the test samples is compared. There is a pair of parameters corresponding to the highest prediction accuracy, which is the best embedding dimension th≤tw≤2h and time delay τ.


## 3.3.4. Algorithm Description

Based on the methods above, the algorithm steps of the self-adaptive prediction model are summarized as follows, and the calculation process is shown in Figure1.(1)
For the gas concentration time seriesct, the EMD method is used to decompose it and obtain its IMF sets imf1,imf2,⋯,imfs(2)
For eachimfi,i=1,2,⋯,s, its phase space parameters are reconstructed, the initial embedding dimension is mi=m0i, the initial time delay is τi=τ0i, their initial iteration step is 1, and the number optimization calculation steps is j=1,2,⋯,Pj, where Pj is the product of the adjustment steps of mi and τi;(3)
For eachimfi, GPR hyperparameters lijv and σnijv2 are randomly obtained to execute pN (k=1,2,⋯,pN) times during model training, and the test samples are input to calculate the prediction results and its prediction effectiveness Mijv. The optimal hyperparameters lij and σnij2 are obtained when the maximum value of Mijv is reached;(4)
Step (3) is repeatedp times to obtain the optimal parameters for phase space reconstruction li and σni2 when the maximum value of Mijv is reached(5)
For eachfi∗ of the prediction sample, a calculation is performed, and its prediction value f^i∗ is obtained(6)
Steps (2), (3), (4), and (5) are executeds times, and the final gas concentration prediction result y^=∑i=1sf^i∗ is obtained.Figure 1
Calculation process.


## 4. Gas Concentration Prewarning

### 4.1. SVD Processing

After EMD processing, the gas monitoring data are decomposed into anm×n matrix M; then, by using SVD processing, it can obtain the singular value vector σ1,σ2,⋯,σr of matrix M, σ1≥σ2≥⋯≥σr≥0, and r≤minm,n; M is considered the weighted sum of the feature vectors’ exterior products, and the weight is a singular value. The larger the singular value is, the higher the percentage of the corresponding feature vector. Thus, the singular value can reflect the intrinsic feature of the gas monitoring data and be used for feature extraction. According to this principle, the singular value extracted from the gas monitoring data are derived from the time-frequency feature signal of the sequence. Therefore, it can represent the variation degree of the gas concentration under the influence of the main influencing factors of the time scale.


### 4.2. Feature Extraction Model of Gas Monitoring Data

In the gas concentration prewarning stage, it is necessary to quantitatively determine the variation characteristics of the gas concentration affected by the production process, which can be summed up as quantifying two indexes through feature extraction: the variation and the time when the gas concentration tends to stabilize after production stops. The modelling process is as follows.


#### 4.2.1. Feature Extraction from Monitoring Data

Forct, one day is selected as a unit of processing and divided into nd×3 sequences cj1t,cj2t,cj3t by the work shifts, where j=1,2,⋯,nd. Then, each sequence is decomposed with EMD to build nd×3 feature matrix groups Ms=Mj1,Mj2,Mj3. For each feature matrix in Ms, the vectors of the singular values T1=σjr1,σjr2,σjr3 are calculated by using SVD, r1=r2=r3=ceillog2lenx−1, and the mean of the singular value in nd days is calculated. The vectors of the singular value T¯1=σ¯r1,σ¯r2,σ¯r3 are constructed to show the average variation trend of the gas concentration for 3 work shifts in one day.Similarly, we dividect per hour, obtain nd×24 sequences cj1t,cj2t,⋯,cj24t and j=1,2,⋯,nd, and decompose each sequence with EMD to build nd×24 feature matrix groups Mh=Mj1,Mj2,⋯,Mj24. Then, each feature matrix in Mh is decomposed with SVD; the vectors of the singular value T2=σjr1,σjr2,⋯,σjr24, where r1=r2=⋯=r24=ceillog2lenx−1, and the mean of the singular value in nd days is calculated; the vectors of the singular value T¯2=σ¯r1,σ¯r2,⋯,σ¯r24 are constructed to show the average variation trend of the gas concentration per hour over the course of a day.


#### 4.2.2. Threshold Calculation of Prewarning Parameters

The vectors of the singular value for work shiftsT¯1=σ¯r1,σ¯r2,σ¯r3 are merged into the sequences σk, k=1,2,⋯,nr and nr=r1+r2+r3. This singular value sequence contains the feature value of the gas monitoring data, which can be described as the average trend of the gas concentration for 3 work shifts in one day that are affected by the production process and σ1 is the maximum feature value of the gas concentration. Then, the first-order difference of σk and ∆σk=σk−σk−1, where k=2,⋯,nr, is calculated since the elements of the singular value sequence gradually decline, thus, σk>0. According to the flow and diffusion feature of mine gas in a ventilation roadway, when the production activity is over, there are two other work shifts without production activity, and the gas concentration will gradually decrease to a stable level. Therefore, there is an inflection point on the curve of the sequence ∆σk, which can be considered a mutation of the gas concentration originating from the influence of the production process. In the period before the inflection point, the variation in the gas concentration decreases, and the reduction gradually increases due to the influence of production stoppage. In the period after the inflection point, the gas concentration decreases to a stable level and the reduction also decreases; correspondingly, σk∗ in σk is obtained at the inflection point of the first-order difference curve. ∆c∗=σ1−σk∗, that is, the average variation in gas concentration affected by the production process is calculated.Similarly, for each vector of singular values inT¯2=σ¯r1,σ¯r2,⋯,σ¯r24, the first element of the sequence, which is the maximum singular value, is used as the feature value of the gas concentration per hour; the values are combined into a sequence, and then the first-order difference of the sequence is calculated. The time at the inflection point of the first-order differential curve is the time when the gas concentration decreases to a stable level. The time difference tr between the time of the production shift termination and the time when the gas concentration tends to stabilize is calculated.


### 4.3. Algorithm Steps and Flow

The details of the algorithm steps are presented as follows:(1)
ct is divided into nd×3 sequences cj1t,cj2t,cj3t by the work shifts, EMD processing is executed, and nd×3 feature matrix groups Ms are executed. Simultaneously, the feature matrix groups Mh are calculated.(2)
For each feature matrix inMs, the singular value and average per day are calculated, T¯1=σ¯r1,σ¯r2,σ¯r3, and then it is merged into σk, k=1,2,⋯,nr and nr=r1+r2+r3, where σ1 is the maximum feature value. For Mh, we obtain T¯2=σ¯r1,σ¯r2,⋯,σ¯r24.(3)
ForT¯1, its first-order difference sequence σk, corresponding to its maximum value, is calculated, the feature value σk∗ is obtained; and ∆c∗=σ1−σk∗, which is the average variation in the gas concentration affected by the production process. For each sequence T¯2, the first elements are combined, the first-order difference is calculated, and then the time difference tr is obtained.


### 4.4. Determination of the Prewarning Level

The main reason for the abnormal increase in gas concentration within one day is that the amount of gas emission increases during the production process or the air volume in the ventilation roadway decreases. The abnormal variation in air volume can usually return to a normal state within 1 hour, but the abnormal variation in gas concentration affected by the production process may last for several hours. Therefore, the premise of the prewarning problem can be summarized as obtaining or calculating the following prewarning parameters: the current prediction valuey^; the overrun alarm value of the gas concentration ws at a certain type of monitoring point determined by the technical regulations of the coal industry in China, y^<ws; the maximum feature value of the gas monitoring data σ1; the average increment of the gas concentration affected by the production process ∆c∗; the duration of the abnormally high gas monitoring value th; and the average time for the gas concentration to decrease to a stable level from the end of the production shift tr. The prewarning level of the gas concentration is determined according to the following method:(1)
Level I. Wheny^<σ1, the real-time monitoring value does not exceed the overall level of the gas monitoring data in the period of modelling, it is regarded as normal, and no prewarning is given. In contrast, the value is regarded as a high gas concentration, th and ∆y, which express the maximum difference of the real-time monitoring value sequence in the last 1 hour as calculated. If th≥ 30 min and ∆y>∆c∗, the real-time monitoring value exceeds the overall level of the data samples from the model and has a continuous increasing trend in a short time; hence, this is an abnormal situation and is labelled as prewarning level I. It is necessary to pay attention to the current gas concentration dynamics and to determine the reasons for the increase in the gas concentration according to the variation in the air volume in the ventilation roadway. tw is set as the alert time threshold, th≤tw≤1h.(2)
Level II. Wheny^>=σ1 and y^<ws, th and tr are calculated. If th≥tr and ∆y>∆c∗, the real-time monitoring value exceeds the overall level of the data samples from the modelling and has a long-term trend; this is an abnormal situation and is labelled as prewarning level II. It is necessary to take measures to reduce the gas concentration, and tr≤tw≤th.


## 4.1. SVD Processing

After EMD processing, the gas monitoring data are decomposed into anm×n matrix M; then, by using SVD processing, it can obtain the singular value vector σ1,σ2,⋯,σr of matrix M, σ1≥σ2≥⋯≥σr≥0, and r≤minm,n; M is considered the weighted sum of the feature vectors’ exterior products, and the weight is a singular value. The larger the singular value is, the higher the percentage of the corresponding feature vector. Thus, the singular value can reflect the intrinsic feature of the gas monitoring data and be used for feature extraction. According to this principle, the singular value extracted from the gas monitoring data are derived from the time-frequency feature signal of the sequence. Therefore, it can represent the variation degree of the gas concentration under the influence of the main influencing factors of the time scale.


## 4.2. Feature Extraction Model of Gas Monitoring Data

In the gas concentration prewarning stage, it is necessary to quantitatively determine the variation characteristics of the gas concentration affected by the production process, which can be summed up as quantifying two indexes through feature extraction: the variation and the time when the gas concentration tends to stabilize after production stops. The modelling process is as follows.


### 4.2.1. Feature Extraction from Monitoring Data

Forct, one day is selected as a unit of processing and divided into nd×3 sequences cj1t,cj2t,cj3t by the work shifts, where j=1,2,⋯,nd. Then, each sequence is decomposed with EMD to build nd×3 feature matrix groups Ms=Mj1,Mj2,Mj3. For each feature matrix in Ms, the vectors of the singular values T1=σjr1,σjr2,σjr3 are calculated by using SVD, r1=r2=r3=ceillog2lenx−1, and the mean of the singular value in nd days is calculated. The vectors of the singular value T¯1=σ¯r1,σ¯r2,σ¯r3 are constructed to show the average variation trend of the gas concentration for 3 work shifts in one day.Similarly, we dividect per hour, obtain nd×24 sequences cj1t,cj2t,⋯,cj24t and j=1,2,⋯,nd, and decompose each sequence with EMD to build nd×24 feature matrix groups Mh=Mj1,Mj2,⋯,Mj24. Then, each feature matrix in Mh is decomposed with SVD; the vectors of the singular value T2=σjr1,σjr2,⋯,σjr24, where r1=r2=⋯=r24=ceillog2lenx−1, and the mean of the singular value in nd days is calculated; the vectors of the singular value T¯2=σ¯r1,σ¯r2,⋯,σ¯r24 are constructed to show the average variation trend of the gas concentration per hour over the course of a day.


### 4.2.2. Threshold Calculation of Prewarning Parameters

The vectors of the singular value for work shiftsT¯1=σ¯r1,σ¯r2,σ¯r3 are merged into the sequences σk, k=1,2,⋯,nr and nr=r1+r2+r3. This singular value sequence contains the feature value of the gas monitoring data, which can be described as the average trend of the gas concentration for 3 work shifts in one day that are affected by the production process and σ1 is the maximum feature value of the gas concentration. Then, the first-order difference of σk and ∆σk=σk−σk−1, where k=2,⋯,nr, is calculated since the elements of the singular value sequence gradually decline, thus, σk>0. According to the flow and diffusion feature of mine gas in a ventilation roadway, when the production activity is over, there are two other work shifts without production activity, and the gas concentration will gradually decrease to a stable level. Therefore, there is an inflection point on the curve of the sequence ∆σk, which can be considered a mutation of the gas concentration originating from the influence of the production process. In the period before the inflection point, the variation in the gas concentration decreases, and the reduction gradually increases due to the influence of production stoppage. In the period after the inflection point, the gas concentration decreases to a stable level and the reduction also decreases; correspondingly, σk∗ in σk is obtained at the inflection point of the first-order difference curve. ∆c∗=σ1−σk∗, that is, the average variation in gas concentration affected by the production process is calculated.Similarly, for each vector of singular values inT¯2=σ¯r1,σ¯r2,⋯,σ¯r24, the first element of the sequence, which is the maximum singular value, is used as the feature value of the gas concentration per hour; the values are combined into a sequence, and then the first-order difference of the sequence is calculated. The time at the inflection point of the first-order differential curve is the time when the gas concentration decreases to a stable level. The time difference tr between the time of the production shift termination and the time when the gas concentration tends to stabilize is calculated.


## 4.2.1. Feature Extraction from Monitoring Data

Forct, one day is selected as a unit of processing and divided into nd×3 sequences cj1t,cj2t,cj3t by the work shifts, where j=1,2,⋯,nd. Then, each sequence is decomposed with EMD to build nd×3 feature matrix groups Ms=Mj1,Mj2,Mj3. For each feature matrix in Ms, the vectors of the singular values T1=σjr1,σjr2,σjr3 are calculated by using SVD, r1=r2=r3=ceillog2lenx−1, and the mean of the singular value in nd days is calculated. The vectors of the singular value T¯1=σ¯r1,σ¯r2,σ¯r3 are constructed to show the average variation trend of the gas concentration for 3 work shifts in one day.Similarly, we dividect per hour, obtain nd×24 sequences cj1t,cj2t,⋯,cj24t and j=1,2,⋯,nd, and decompose each sequence with EMD to build nd×24 feature matrix groups Mh=Mj1,Mj2,⋯,Mj24. Then, each feature matrix in Mh is decomposed with SVD; the vectors of the singular value T2=σjr1,σjr2,⋯,σjr24, where r1=r2=⋯=r24=ceillog2lenx−1, and the mean of the singular value in nd days is calculated; the vectors of the singular value T¯2=σ¯r1,σ¯r2,⋯,σ¯r24 are constructed to show the average variation trend of the gas concentration per hour over the course of a day.


## 4.2.2. Threshold Calculation of Prewarning Parameters

The vectors of the singular value for work shiftsT¯1=σ¯r1,σ¯r2,σ¯r3 are merged into the sequences σk, k=1,2,⋯,nr and nr=r1+r2+r3. This singular value sequence contains the feature value of the gas monitoring data, which can be described as the average trend of the gas concentration for 3 work shifts in one day that are affected by the production process and σ1 is the maximum feature value of the gas concentration. Then, the first-order difference of σk and ∆σk=σk−σk−1, where k=2,⋯,nr, is calculated since the elements of the singular value sequence gradually decline, thus, σk>0. According to the flow and diffusion feature of mine gas in a ventilation roadway, when the production activity is over, there are two other work shifts without production activity, and the gas concentration will gradually decrease to a stable level. Therefore, there is an inflection point on the curve of the sequence ∆σk, which can be considered a mutation of the gas concentration originating from the influence of the production process. In the period before the inflection point, the variation in the gas concentration decreases, and the reduction gradually increases due to the influence of production stoppage. In the period after the inflection point, the gas concentration decreases to a stable level and the reduction also decreases; correspondingly, σk∗ in σk is obtained at the inflection point of the first-order difference curve. ∆c∗=σ1−σk∗, that is, the average variation in gas concentration affected by the production process is calculated.Similarly, for each vector of singular values inT¯2=σ¯r1,σ¯r2,⋯,σ¯r24, the first element of the sequence, which is the maximum singular value, is used as the feature value of the gas concentration per hour; the values are combined into a sequence, and then the first-order difference of the sequence is calculated. The time at the inflection point of the first-order differential curve is the time when the gas concentration decreases to a stable level. The time difference tr between the time of the production shift termination and the time when the gas concentration tends to stabilize is calculated.


## 4.3. Algorithm Steps and Flow

The details of the algorithm steps are presented as follows:(1)
ct is divided into nd×3 sequences cj1t,cj2t,cj3t by the work shifts, EMD processing is executed, and nd×3 feature matrix groups Ms are executed. Simultaneously, the feature matrix groups Mh are calculated.(2)
For each feature matrix inMs, the singular value and average per day are calculated, T¯1=σ¯r1,σ¯r2,σ¯r3, and then it is merged into σk, k=1,2,⋯,nr and nr=r1+r2+r3, where σ1 is the maximum feature value. For Mh, we obtain T¯2=σ¯r1,σ¯r2,⋯,σ¯r24.(3)
ForT¯1, its first-order difference sequence σk, corresponding to its maximum value, is calculated, the feature value σk∗ is obtained; and ∆c∗=σ1−σk∗, which is the average variation in the gas concentration affected by the production process. For each sequence T¯2, the first elements are combined, the first-order difference is calculated, and then the time difference tr is obtained.


## 4.4. Determination of the Prewarning Level

The main reason for the abnormal increase in gas concentration within one day is that the amount of gas emission increases during the production process or the air volume in the ventilation roadway decreases. The abnormal variation in air volume can usually return to a normal state within 1 hour, but the abnormal variation in gas concentration affected by the production process may last for several hours. Therefore, the premise of the prewarning problem can be summarized as obtaining or calculating the following prewarning parameters: the current prediction valuey^; the overrun alarm value of the gas concentration ws at a certain type of monitoring point determined by the technical regulations of the coal industry in China, y^<ws; the maximum feature value of the gas monitoring data σ1; the average increment of the gas concentration affected by the production process ∆c∗; the duration of the abnormally high gas monitoring value th; and the average time for the gas concentration to decrease to a stable level from the end of the production shift tr. The prewarning level of the gas concentration is determined according to the following method:(1)
Level I. Wheny^<σ1, the real-time monitoring value does not exceed the overall level of the gas monitoring data in the period of modelling, it is regarded as normal, and no prewarning is given. In contrast, the value is regarded as a high gas concentration, th and ∆y, which express the maximum difference of the real-time monitoring value sequence in the last 1 hour as calculated. If th≥ 30 min and ∆y>∆c∗, the real-time monitoring value exceeds the overall level of the data samples from the model and has a continuous increasing trend in a short time; hence, this is an abnormal situation and is labelled as prewarning level I. It is necessary to pay attention to the current gas concentration dynamics and to determine the reasons for the increase in the gas concentration according to the variation in the air volume in the ventilation roadway. tw is set as the alert time threshold, th≤tw≤1h.(2)
Level II. Wheny^>=σ1 and y^<ws, th and tr are calculated. If th≥tr and ∆y>∆c∗, the real-time monitoring value exceeds the overall level of the data samples from the modelling and has a long-term trend; this is an abnormal situation and is labelled as prewarning level II. It is necessary to take measures to reduce the gas concentration, and tr≤tw≤th.


## 5. Case Study

### 5.1. Results

According to the method above, a computing program is developed for online application analysis based on safety monitoring and a monitoring system in the Yuan Zigou coal mine in Shaanxi Province, China. The application of mine gas concentration prediction and prewarning on March 6, 2019, 0:00–12:00 is shown as follows: the monitoring period of the safety monitoring and control system in this mine is 30 s, but the interval of actual real-time monitoring data is often uneven. To clearly display the calculation results, the monitoring data were resampled every 1 min, and the lengths of the data samples of the gas concentration were 720 during this period. The gas concentration is expressed as a volume fraction, and the maximum value is 0.64%, the minimum value is 0.011%, and the average value is 0.268%. The gas concentration time series is shown in Figure2.Figure 2
Gas monitoring data.In Figure2, the fluctuation features of the gas concentration time series are obvious, and the frequency of the mutational points is high. According to equation (1), the gas concentration time series are decomposed into IMF components by using EMD, as shown in Figure 3. There are 7 IMF components, of which IMF7 is the remainder, and it presents the average trend of the time series. The waveforms of IMF5 and IMF6 are gentle, and the periodicity is obvious, mainly containing the signal of the gas concentration variation caused by the production process. The waveforms of IMF3 and IMF4 tend to stabilize, but the fluctuation features are obvious and mainly contain the signal of the gas concentration variation caused by the variation in air supply and human operations and management factors in the production scheduling process. IMF1 and IMF2 are high-frequency components and mainly contain the signal of the gas concentration variation caused by other random factors.Figure 3
IMFs of EMD processing.For each IMF, the GPR prediction model is built by reconstructing the phase space, and the process of prediction and calculation is dynamic. When the time equals 0, the gas monitoring data over 8 hours is set as training and test samples. The first 7 hours of data are considered training samples, and the data from the 8th hour are considered the test sample. The 1 hour ahead prediction results are calculated. Continuous prediction is performed, and equations (2)–(5) are applied to execute model training, in which pN = 1000 random samplings of the GPR hyperparameters are executed for each group of phase-space parameters. Then equations (6)–(8) and (10) are applied to calculate the prediction value and its effectiveness. The optimal computation times of m and τ are 63, and the dynamic phase space parameters, the theorized phase space parameters of each IMF, the optimal hyperparameters of the GPR, and the prediction effectiveness are shown in Table 1.Table 1
Phase space parameters and prediction effectiveness.
ParametersIMFimf1imf2imf3imf4imf5imf6imf7mτmτmτmτmτmτmτTheorized parameters115858484836161l0.30.51.40.510.11.2σn20.240.560.780.450.120.090.67Prediction effectiveness0.520.570.610.680.810.920.92Optimization parameters82747373726161l0.3310.7210.6σn20.050.790.540.570.620.320.73Prediction effectiveness0.700.850.880.930.950.980.99As shown in Table1, when the phase space reconstruction parameters and hyperparameters adopt the theoretical value, the GPR prediction has higher accuracy only in IMF6 and IMF7 and lower accuracy in IMF1 and IMF4.For the gas monitoring data, the gas monitoring data sequence is divided into 30 × 3 sequences. For each sequence, equation (1) is employed for decomposition, the number of IMF components is 8, and 480 × 8 feature matrix groups are formed. Then, the feature matrix is decomposed by using SVD, the vectors of the singular value are calculated, and the feature value sequence corresponding to three 8 hour periods is obtained after averaging each day. By merging and calculating the first-order difference, the maximum feature value is 0.60%, and the average increment of gas concentration is 0.265%. Similarly, the vectors of singular values corresponding to 24 hours are calculated. After averaging per day, the first element of the vectors is selected to construct the feature value sequence corresponding to 24 hours. By merging and calculating the first-order difference, it is concluded that the time at which the gas concentration decreases to a stable level is 1 hour after the end of production. The results are shown in Figures 4 and 5. The first-order difference is the first-order difference of the feature value sequence.Figure 4
Gas concentration variation trends by work shift.Figure 5
Gas concentration variation trends per hour.In Figure4, the feature value curve of gas concentration corresponds to the work shifts, the gas concentration in the first work shift has no obvious downward trend, and its overall level is higher than the average value of samples of the gas concentration. At the 9th feature value point, due to the cessation of production activities, the gas concentration begins to rapidly decline. At the 14th feature value point in the second work shift, the gas concentration continues to decrease, and the decreasing range reaches the maximum. Then, the downward trend gradually becomes less obvious and stabilizes in the third shift.The trend curve of the feature value of the gas concentration in Figure5 is similar to that in Figure 4, but the feature value curve is smoother and the maximum of the feature value is slightly larger, as the hourly feature value uses the first element in the singular value vector. The two kinds of results from the first-order difference sequence have the same trend, that is, the shape of the curve before and after the inflection point is similar. These features fully conform to the theoretical characteristics of mine gas flow in a ventilation roadway. The feature value of the gas concentration variation caused by the production process can be used to identify abnormal gas concentrations and to determine the prewarning threshold under normal ventilation conditions.Based on the features extracted from the gas monitoring data, to intuitively compare the prediction and prewarning results, the results from the 300th time point to the 540th time point (5:00 to 9:00) are displayed. The two kinds of prediction results from the the direct GPR model and the adaptive model in this period are shown in Figures6 and 7, respectively, and the prediction effectiveness values are 0.71 and 0.9, respectively.Figure 6
Prediction results of direct GPR.Figure 7
Prediction results of the adaptive model.As shown in Figure6, although the overall fitting degree between the prediction value and the real-time monitoring value is high, the error is obvious, especially at most mutation points, and the overall prediction effectiveness is 0.71. The abovementioned results show that the GPR prediction model cannot achieve good prediction results at all time scales with theoretical phase space reconstruction parameters, or hyperparameters, especially for high-frequency components. These model parameters need to be dynamically adjusted to obtain the best prediction effect.According to Figure7, under optimal parameter combination conditions, the adaptive model has higher prediction accuracy, and the prediction accuracy is lower only in imf1, but it does not affect the overall prediction effectiveness. The overall prediction effectiveness is 0.92. A comparison of the parameter combinations in Table 1 reveals that there is better prediction accuracy in imf6 and imf7 but poor prediction accuracy for imf1–imf5 for the theorized phase space parameters. Thus, the phase space parameters need to be dynamically adjusted, and the dynamic determination of the GPR hyperparameters further improves the prediction accuracy of the IMF components. Given the prediction effectiveness, the total prediction accuracy of the adaptive model increases by 21%. At the mutational points, the prediction effectiveness increases by more than 30%, and the overall prediction results show that the prediction results of the adaptive model have a high degree of fit with the real-time data. The curve of the predicted value is consistent with the variation trend of the actual monitoring value, which realizes self-adaptive prediction.There is no prewarning level II in the period, as the prediction accuracy of the single GPR model is low, and the prewarning results are not shown in Figure6. According to the prewarning results in Figure 7, there is prewarning level I in the time slots, from the sixth time point (1:0) to the 22nd time point (4:40) and from the 54th time point (9:0) to the 68th time point (11:20). In addition, from the 30th time point (5:00) to the 38th time point (7:30), the gas concentration is high but not continuous during shearer operations, and the gas concentration increases with increasing gas emission. Then, when the shearer stops at the end of the working face, the gas concentration decreases again, and this situation is periodic. In this case, the continuous increase in the gas concentration can be controlled as long as the air supply is stable. Before the alarm limit for gas concentration according to the regulations is reached, attention only needs to be paid to the trend and duration of the continuous increase in the gas concentration.


### 5.2. Discussions

In this section, compared with other representative methods, the main methods in the relevant literature are applied to process the sample data, calculate the prediction effectiveness, and evaluate the prewarning analysis processes. The results are shown in Tables2 and 3.Table 2
Comparison with other prediction methods.
Relevant researchPrediction modelImplementation processPrediction effectiveness[1]Chaotic time series modelPhase space reconstruction0.69[2]Support vector machine regressionFix the time length to reconstruct the sequence0.77[3]Deep learningDynamically adjust the time length to reconstruct the sequence0.86[4]Recurrent neural networkFix the time length to reconstruct the sequence0.78[5]Grey self-memorizationGrey prediction model0.71[6]Extreme learning machineDynamically adjust the time length to reconstruct the sequence0.83This research methodMultiparameter adaptive adjustment driven by real-time data0.92Table 3
Comparison with other prewarning methods.
Relevant researchPrewarning modelImplementation processPrewarning reliability[10]Subjective indicator prewarningSubjectively set the threshold of indicators derived from regulationsThe determination of threshold is subjective, and abnormality is not recognized[11]Probability prewarningPrewarning analysis based on statistical parametersUses a single statistical analysis and fails to reliably identify anomalies[12]Numerical calculation prewarningSet the threshold of indicators derived from regulations by numerical calculationThe threshold is fixed, and the reliability is unknown[13]Numerical calculation prewarningCompare the results of the abnormal analysis with the alarm values derived from regulationsUsing the alarm value as the threshold, abnormality is not reasonably recognized[14]Probability prewarningPrewarning analysis based on statistical parametersOnly statistical values are linearly superimposed, and the reliability is unknownThis research methodDynamically determine the prewarning threshold based on the adaptive prediction and the quantitative analysis of the production process impactThe abnormal conditions are reasonably and reliably identifiedTable2 shows that the prediction results of this study are better than those of other methods. Compared with other methods, this study fully utilizes the time-frequency characteristics of gas monitoring data and solves the problem of low prediction accuracy in the local high-frequency section of gas concentration time series by adaptively determining the superparameters of the GPR model, which creates the basic conditions for reliable prewarning analysis.Table3 shows that the prewarning reliability of this study is better than that of other methods. Compared with other methods, the function of the main influencing factors on the variation in the gas concentration is quantitatively determined by feature extraction to reasonably and reliably identify the abnormalities, to avoid the problem of unreasonable abnormal identification or unknown reliability of other methods, and to ensure the feasibility and applicability of this method in practical applications.


## 5.1. Results

According to the method above, a computing program is developed for online application analysis based on safety monitoring and a monitoring system in the Yuan Zigou coal mine in Shaanxi Province, China. The application of mine gas concentration prediction and prewarning on March 6, 2019, 0:00–12:00 is shown as follows: the monitoring period of the safety monitoring and control system in this mine is 30 s, but the interval of actual real-time monitoring data is often uneven. To clearly display the calculation results, the monitoring data were resampled every 1 min, and the lengths of the data samples of the gas concentration were 720 during this period. The gas concentration is expressed as a volume fraction, and the maximum value is 0.64%, the minimum value is 0.011%, and the average value is 0.268%. The gas concentration time series is shown in Figure2.Figure 2
Gas monitoring data.In Figure2, the fluctuation features of the gas concentration time series are obvious, and the frequency of the mutational points is high. According to equation (1), the gas concentration time series are decomposed into IMF components by using EMD, as shown in Figure 3. There are 7 IMF components, of which IMF7 is the remainder, and it presents the average trend of the time series. The waveforms of IMF5 and IMF6 are gentle, and the periodicity is obvious, mainly containing the signal of the gas concentration variation caused by the production process. The waveforms of IMF3 and IMF4 tend to stabilize, but the fluctuation features are obvious and mainly contain the signal of the gas concentration variation caused by the variation in air supply and human operations and management factors in the production scheduling process. IMF1 and IMF2 are high-frequency components and mainly contain the signal of the gas concentration variation caused by other random factors.Figure 3
IMFs of EMD processing.For each IMF, the GPR prediction model is built by reconstructing the phase space, and the process of prediction and calculation is dynamic. When the time equals 0, the gas monitoring data over 8 hours is set as training and test samples. The first 7 hours of data are considered training samples, and the data from the 8th hour are considered the test sample. The 1 hour ahead prediction results are calculated. Continuous prediction is performed, and equations (2)–(5) are applied to execute model training, in which pN = 1000 random samplings of the GPR hyperparameters are executed for each group of phase-space parameters. Then equations (6)–(8) and (10) are applied to calculate the prediction value and its effectiveness. The optimal computation times of m and τ are 63, and the dynamic phase space parameters, the theorized phase space parameters of each IMF, the optimal hyperparameters of the GPR, and the prediction effectiveness are shown in Table 1.Table 1
Phase space parameters and prediction effectiveness.
ParametersIMFimf1imf2imf3imf4imf5imf6imf7mτmτmτmτmτmτmτTheorized parameters115858484836161l0.30.51.40.510.11.2σn20.240.560.780.450.120.090.67Prediction effectiveness0.520.570.610.680.810.920.92Optimization parameters82747373726161l0.3310.7210.6σn20.050.790.540.570.620.320.73Prediction effectiveness0.700.850.880.930.950.980.99As shown in Table1, when the phase space reconstruction parameters and hyperparameters adopt the theoretical value, the GPR prediction has higher accuracy only in IMF6 and IMF7 and lower accuracy in IMF1 and IMF4.For the gas monitoring data, the gas monitoring data sequence is divided into 30 × 3 sequences. For each sequence, equation (1) is employed for decomposition, the number of IMF components is 8, and 480 × 8 feature matrix groups are formed. Then, the feature matrix is decomposed by using SVD, the vectors of the singular value are calculated, and the feature value sequence corresponding to three 8 hour periods is obtained after averaging each day. By merging and calculating the first-order difference, the maximum feature value is 0.60%, and the average increment of gas concentration is 0.265%. Similarly, the vectors of singular values corresponding to 24 hours are calculated. After averaging per day, the first element of the vectors is selected to construct the feature value sequence corresponding to 24 hours. By merging and calculating the first-order difference, it is concluded that the time at which the gas concentration decreases to a stable level is 1 hour after the end of production. The results are shown in Figures 4 and 5. The first-order difference is the first-order difference of the feature value sequence.Figure 4
Gas concentration variation trends by work shift.Figure 5
Gas concentration variation trends per hour.In Figure4, the feature value curve of gas concentration corresponds to the work shifts, the gas concentration in the first work shift has no obvious downward trend, and its overall level is higher than the average value of samples of the gas concentration. At the 9th feature value point, due to the cessation of production activities, the gas concentration begins to rapidly decline. At the 14th feature value point in the second work shift, the gas concentration continues to decrease, and the decreasing range reaches the maximum. Then, the downward trend gradually becomes less obvious and stabilizes in the third shift.The trend curve of the feature value of the gas concentration in Figure5 is similar to that in Figure 4, but the feature value curve is smoother and the maximum of the feature value is slightly larger, as the hourly feature value uses the first element in the singular value vector. The two kinds of results from the first-order difference sequence have the same trend, that is, the shape of the curve before and after the inflection point is similar. These features fully conform to the theoretical characteristics of mine gas flow in a ventilation roadway. The feature value of the gas concentration variation caused by the production process can be used to identify abnormal gas concentrations and to determine the prewarning threshold under normal ventilation conditions.Based on the features extracted from the gas monitoring data, to intuitively compare the prediction and prewarning results, the results from the 300th time point to the 540th time point (5:00 to 9:00) are displayed. The two kinds of prediction results from the the direct GPR model and the adaptive model in this period are shown in Figures6 and 7, respectively, and the prediction effectiveness values are 0.71 and 0.9, respectively.Figure 6
Prediction results of direct GPR.Figure 7
Prediction results of the adaptive model.As shown in Figure6, although the overall fitting degree between the prediction value and the real-time monitoring value is high, the error is obvious, especially at most mutation points, and the overall prediction effectiveness is 0.71. The abovementioned results show that the GPR prediction model cannot achieve good prediction results at all time scales with theoretical phase space reconstruction parameters, or hyperparameters, especially for high-frequency components. These model parameters need to be dynamically adjusted to obtain the best prediction effect.According to Figure7, under optimal parameter combination conditions, the adaptive model has higher prediction accuracy, and the prediction accuracy is lower only in imf1, but it does not affect the overall prediction effectiveness. The overall prediction effectiveness is 0.92. A comparison of the parameter combinations in Table 1 reveals that there is better prediction accuracy in imf6 and imf7 but poor prediction accuracy for imf1–imf5 for the theorized phase space parameters. Thus, the phase space parameters need to be dynamically adjusted, and the dynamic determination of the GPR hyperparameters further improves the prediction accuracy of the IMF components. Given the prediction effectiveness, the total prediction accuracy of the adaptive model increases by 21%. At the mutational points, the prediction effectiveness increases by more than 30%, and the overall prediction results show that the prediction results of the adaptive model have a high degree of fit with the real-time data. The curve of the predicted value is consistent with the variation trend of the actual monitoring value, which realizes self-adaptive prediction.There is no prewarning level II in the period, as the prediction accuracy of the single GPR model is low, and the prewarning results are not shown in Figure6. According to the prewarning results in Figure 7, there is prewarning level I in the time slots, from the sixth time point (1:0) to the 22nd time point (4:40) and from the 54th time point (9:0) to the 68th time point (11:20). In addition, from the 30th time point (5:00) to the 38th time point (7:30), the gas concentration is high but not continuous during shearer operations, and the gas concentration increases with increasing gas emission. Then, when the shearer stops at the end of the working face, the gas concentration decreases again, and this situation is periodic. In this case, the continuous increase in the gas concentration can be controlled as long as the air supply is stable. Before the alarm limit for gas concentration according to the regulations is reached, attention only needs to be paid to the trend and duration of the continuous increase in the gas concentration.


## 5.2. Discussions

In this section, compared with other representative methods, the main methods in the relevant literature are applied to process the sample data, calculate the prediction effectiveness, and evaluate the prewarning analysis processes. The results are shown in Tables2 and 3.Table 2
Comparison with other prediction methods.
Relevant researchPrediction modelImplementation processPrediction effectiveness[1]Chaotic time series modelPhase space reconstruction0.69[2]Support vector machine regressionFix the time length to reconstruct the sequence0.77[3]Deep learningDynamically adjust the time length to reconstruct the sequence0.86[4]Recurrent neural networkFix the time length to reconstruct the sequence0.78[5]Grey self-memorizationGrey prediction model0.71[6]Extreme learning machineDynamically adjust the time length to reconstruct the sequence0.83This research methodMultiparameter adaptive adjustment driven by real-time data0.92Table 3
Comparison with other prewarning methods.
Relevant researchPrewarning modelImplementation processPrewarning reliability[10]Subjective indicator prewarningSubjectively set the threshold of indicators derived from regulationsThe determination of threshold is subjective, and abnormality is not recognized[11]Probability prewarningPrewarning analysis based on statistical parametersUses a single statistical analysis and fails to reliably identify anomalies[12]Numerical calculation prewarningSet the threshold of indicators derived from regulations by numerical calculationThe threshold is fixed, and the reliability is unknown[13]Numerical calculation prewarningCompare the results of the abnormal analysis with the alarm values derived from regulationsUsing the alarm value as the threshold, abnormality is not reasonably recognized[14]Probability prewarningPrewarning analysis based on statistical parametersOnly statistical values are linearly superimposed, and the reliability is unknownThis research methodDynamically determine the prewarning threshold based on the adaptive prediction and the quantitative analysis of the production process impactThe abnormal conditions are reasonably and reliably identifiedTable2 shows that the prediction results of this study are better than those of other methods. Compared with other methods, this study fully utilizes the time-frequency characteristics of gas monitoring data and solves the problem of low prediction accuracy in the local high-frequency section of gas concentration time series by adaptively determining the superparameters of the GPR model, which creates the basic conditions for reliable prewarning analysis.Table3 shows that the prewarning reliability of this study is better than that of other methods. Compared with other methods, the function of the main influencing factors on the variation in the gas concentration is quantitatively determined by feature extraction to reasonably and reliably identify the abnormalities, to avoid the problem of unreasonable abnormal identification or unknown reliability of other methods, and to ensure the feasibility and applicability of this method in practical applications.


## 6. Conclusion

In this paper, by EMD processing of gas monitoring data, using GPR to predict the IMFs after model optimization, and combining these prediction results, the prediction accuracy is higher than that of raw data’s direct GPR prediction. The IMF of gas monitoring data has obvious fluctuation features on the time scale, which is the basis of model optimization and can improve the overall prediction accuracy. Combined with EMD and SVD processing, the intrinsic features of gas monitoring data can be extracted. The mean singular value clearly reflects the variation in the gas concentration affected by the production process, and its variation features on the time scale are obvious, which is convenient for determining the time when the gas concentration declines to a stable level after production stops and can be used to assist in identifying abnormal gas concentrations.From the prediction results of the case study, the adaptive methods' prediction accuracy is obviously higher than the accuracy of direct GPR prediction at mutational points, and the prediction value mainly has the same trend as the real-time data. This finding shows that IMF phase space reconstruction and GPR hyperparametric optimization can simplify the highly complex nonlinear time series prediction problem, realize adaptive gas concentration prediction, extract the internal features of gas monitoring data with SVD, and improve the reliability of gas concentration prewarning.The determination of the gas concentration prewarning index and its threshold in this study is based on normal mine ventilation. Mine air flow characteristics are complex and abrupt under disaster conditions, and how to scientifically model and reasonably identify gas concentration anomalies needs to be further investigated.



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*Source: 4793258-2023-03-20.xml*