1. Introduction
Coal resource is an important basic energy source in China. From 2015 to 2019, the average annual coal production in China accounted for about 68% of the total energy production [
1]. However, coal mine safety accidents have caused serious economic losses and also seriously endangered the lives of miners. Gas explosions are an important cause of coal mine safety accidents, which may cause many miners to die or can destroy the whole coal mine [
2]. According to statistics, from 2007 to 2017, gas explosions accounted for 50% of coal mine safety accidents in China. From 2004 to 2015, 10,298 persons died from gas explosion accidents, accounting for 29.7% of deaths in various coal mine accidents [
3,
4]. Therefore, the prevention of gas explosion accidents should be the top priority of coal mine safety accident prevention in China. How to reduce such hazards and to achieve safe coal mining is a major problem. It is of great significance to improve the ability of gas disaster prediction by strengthening the study of gas disaster prediction and early warning technology.
In recent years, researchers have found that the gas concentration generally rises abnormally before incidents of coal mine gas explosions [
5]. Therefore, in order to predict gas concentration accurately and prevent gas accidents effectively, researchers have proposed some gas prediction methods. Models of gas concentration or gas outburst forecasts are largely based on BP neural networks [
6,
7,
8], LSTM neural networks [
9], the SVR algorithm [
10,
11], the ELM algorithm [
12], the Gaussian process regression algorithm [
13], and some other mathematical or statistical methods [
14,
15,
16]. These methods always use the time-series data collected by the gas sensors to establish the regression prediction model of gas concentration. However, we note that the number of the actual gas data collected by the sensors exceeding the warning threshold is scarce, so the traditional warning models cannot learn the rule for when the gas concentration rises abnormally, thus it is difficult to achieve the effect of warning in advance.
In this study, we consider gas early warning prediction as a binary classification issue. Specifically, the sensing data are divided into one of two classes, early warning class and non-early warning class, based on a pre-defined early warning threshold. It is reasonable that regarding gas early warning prediction as a binary classification issue, owing to in practical coal mining production, it is not necessary to accurately predict gas concentration over a period of future time, but should judge whether it has a high risk to impact safety production or not. Several previous studies support this system of construction, e.g., Ruta and Chen [
17] constructed a methane concentration warning model by combining multiple classification models with optimization approach to provide a relatively accurate warning for the future 3 min’ methane emission; Zhang et al. [
18] developed a gas outburst early warning system by adopting an entropy-weight Bayes inference model. These models seem to be effective, however, they all ignore an important data character, i.e., these kind of data are always extremely imbalanced.
To deal with class imbalanced data, some different solutions have been proposed, and they can be roughly divided into two groups: data level and algorithm level. Data level generally adopts resampling strategies to increase instances belonging to the minority class, or to decrease instances from the majority class, and further re-balances the data distribution [
19,
20,
21]. Several popular resampling algorithms include random undersampling (RUS) [
22], random oversampling (ROS) [
22] and the synthetic minority oversampling technique (SMOTE) [
23] etc. ROS tends to be overfitting, RUS is apt to lose some key information related with classification, while SMOTE is inclined to propagate noises. In recent years, some advanced sampling algorithms have also been proposed to address the problems mentioned above. For example, Xie et al. [
24] proposed a GL algorithm which first takes advantage of the mixture-Gaussian model to estimate the distribution of minority instances, and then oversamples minority class based on the estimated results. As for the algorithm-level strategy, it mainly includes cost-sensitive learning [
25,
26] and the threshold moving technique [
27,
28]. Cost-sensitive learning designates different penalties for training errors belonging to different classes, further balancing the training errors of different classes. The threshold moving technique firstly trains a classification model, and then moves classification hyperplane towards majority class to repair the bias.
To promote the modeling quality of the early warning model on skewed gas concentration data, in this study we proposed a new class imbalance learning solution called the probability density machine (PDM), which adopts a KNN-PDE K nearest neighbors probability density estimation (KNN-PDE)-alike algorithm [
29] to approximately estimate the probability density of each instance, and then directly compares the probability density of an instance on each class to decide which category that instance belongs to. The PDM algorithm has a good adaptability to the skewed data distribution. The PDM algorithm can directly achieve a good warning effect on gas concentration monitoring data, even without resampling any instances. The effectiveness and superiority of the PDM is verified on six gas concentration monitoring data sets collected from a coal mine in China.
The rest of this study is organized as follows.
Section 2 reviews the corresponding methods related with the gas concentration prediction.
Section 3 describes the procedure of data collection, data preprocessing and instance generation. In
Section 4, we firstly analyze why imbalanced data distribution always hurts the performance of predictive models in context of Gaussian Naive Bayes (GNB) as our proposed PDM algorithm inherits from GNB [
30,
31], and then based on the analysis, we describe the proposed KNN-PDE-alike and PDM algorithms in detail.
Section 5 analyzes and discusses the experimental results. Finally,
Section 6 concludes this paper.
2. Related Works
In recent years, researchers focused more and more attentions on the gas concentration and gas outburst prediction in coal mine safe production, and have presented some solutions.
Zhang et al. [
6] noted that gas disasters are related to many factors, including crustal stress, coal structural performance, geological structure, gas content, etc. They combined the GM (1, 1) grey prediction model and BP neural network to predict the gas emission value, and acquired an improved result in comparison with only adopting any one single model. A similar method was proposed by Wang et al. [
7], which also adopted an artificial neural network to handle various factors and various nonlinear relationships in geological conditions, and acquired an excellent prediction result about gas outburst. To avoid the BP neural network falling into local minimization, Wu et al. [
8] combined genetic algorithm (GA) and the simulated annealing algorithm (SA) as a new genetic algorithm to improve the generalization of the neural network, and further improve prediction accuracy of gas outburst.
Lyu et al. [
9] first fused the gas information of multiple sensors inside the coal mine, and then used the LSTM model based on encoder-decoder to construct multivariant regression and predict the short-term gas concentration. Wu et al. [
10] firstly used the t-distributed stochastic neighbor embedding (t-SNE) algorithm to perform non-linear dimensionality reduction in coal mine gas-related multi-dimensional monitoring data, then extracted the spatial feature data of the monitoring data, and finally used the support vector regression (SVR) algorithm to predict the top corner gas concentration. Meng et al. [
11] also adopted SVR to predict mine gas emission rate and found it outperforms artificial neural networks. Wu et al. [
12] decomposed the time series of gas concentration into many time-frequency components by using the wavelet analysis algorithm, and then constructed the prediction model of gas concentration by adopting the extreme learning machine (ELM). Dong et al. [
13] combined the Bayesian network method, chaotic phase space reconstructive technology, and Gaussian process regression model to construct a gas concentration prediction model that can produce competitive prediction results.
The above-mentioned related studies considered the sophisticated geological factors which have a strong association with coal mine exploration, but a weak association with the process of coal mines production; or they regarded multiple different groups of sensing and monitoring data, and adopt multivariant regression to construct the prediction model. In this paper, we focus on a single variance, i.e., the gas concentration monitoring data acquired from a single sensor. We wish to analyze each single time-series and discover the regular temporal patterns from each time-series. In addition, we note in gas concentration monitoring sequence, the high concentration corresponds significantly less points, thus the data hold extremely imbalanced distribution. However, all existing models almost ignore this problem, which may be a great risk to subsequent modeling. It is also an important consideration in our study.
6. Conclusions
In this study, we focused on the early warning issue of gas concentration in coal mine production. Specifically, we consider it as an imbalanced binary-class classification issue, and in the context of the Naive Bayes theory, we propose a novel class imbalance learning algorithm called the probability density machine. By six real gas concentration monitoring data sets acquired from a coal mine in Datong city, Shanxi Province, China, the effectiveness and superiority of the proposed PDM algorithm was verified.
The contributions of this study can be concluded as follows:
- (1)
We consider the early warning issue of gas concentration in coal mine production as a classification issue, and note its characteristics of class imbalance and sophisticated distribution;
- (2)
In context of the Naive Bayes theory, we analyzed why imbalanced data distribution can hurt predicted models in theory;
- (3)
A novel class imbalance learning algorithm called the probability density machine was used to promote the accuracy of early warning of gas concentration in coal mine production.
In future work, except the gas concentration data, other synchronously occurring sensing or monitoring data will also be considered to be added into the predicting model for the purpose of improving the predicting accuracy.