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Article

Application of Back-Propagation Neural Network in the Post-Blast Re-Entry Time Prediction

1
School of Resources & Civil Engineering, Northeastern University, Shenyang 110819, China
2
Laboratory 3SR, CNRS UMR 5521, Grenoble Alpes University, 38000 Grenoble, France
*
Author to whom correspondence should be addressed.
Knowledge 2023, 3(2), 128-148; https://doi.org/10.3390/knowledge3020010
Submission received: 27 February 2023 / Revised: 17 March 2023 / Accepted: 21 March 2023 / Published: 23 March 2023

Abstract

:
Predicting the post-blast re-entry time precisely can improve productivity and reduce accidents significantly. The empirical formulas for the time prediction are practical to implement, but lack accuracy. In this study, a novel method based on the back-propagation neural network (BPNN) was proposed to tackle the drawbacks. A numerical model was constructed and 300 points of sample data were recorded, with consideration to fresh air volume, occupational exposure limit, toxic gas volume per kg of explosives and roadway length. The BPNN model with six neurons in a hidden layer was then developed and prediction performance was discussed in terms of four indicators, namely, the root mean square error (RMSE), the coefficient of determination (R2), the mean absolute error (MAE) and the sum of squares error (SSE). Furthermore, one representative empirical formula was introduced and calibrated for the comparison. The obtained results showed that the BPNN model had a more remarkable performance, with RMSE of 21.45 (R2: 0.99, MAE: 10.78 and SSE: 40934), compared to the empirical formula, with RMSE of 76.89 (R2: 0.90, MAE: 42.06 and SSE: 526147). Hence, the BPNN model is a superior method for predicting the post-blast re-entry time. For better practical application, it was then embedded into the software.

1. Introduction

The number of underground mines is increasing due to the depletion of resources on the surface. The drill and blast (D&B) and tunnel boring machines (TBM) have been used in underground mines for excavation. Although TBM has been adopted at sites such as San Manual Mine and Stillwater Mine [1], many difficulties, including cutter wear and rock popping, etc., have hindered its development [2]. Consequently, D&B is still the main excavation method due to its flexibility and economy [3,4]. However, one of the shortcomings of D&B is that it emits a substantial amount of toxic gases, including carbon monoxide (CO), nitric oxide (NO) and nitrogen dioxide (NO2). Among them, CO is the primary research object, due to its stability and large quantity [5]. For the purposes of improving cleaning efficiency and enhancing the production capacity, ventilation has been identified as one of the most effective methods and has been used widely [6].
The ventilation time taken to reduce the toxic gas concentration below the occupational exposure limit is defined as the post-blast re-entry time [5]. Additionally, a report has shown that most mines have more than four blasts per day, so estimating the post-blast re-entry time as accurately as possible will avoid the loss of significant amounts of production time [7]. Several methods have been studied and applied. For example, many mines have relied on the fixed-time interval to determine when the miners can re-enter the heading face to work continuously [8]. However, it should be noted that this may lead to a number of associated safety and health issues for workers. In order to improve accuracy, some empirical formulas were developed by using the flow balance, fitting the data obtained from numerical simulations, site tests, and laboratory experiments [4,7,9,10,11,12,13,14,15]. Despite the considerable advantages of empirical formulas, such as being simple, convenient, and timesaving, the calculation is less universal so that some parameters such as the dilution efficiency factor, need to be calibrated according to the particular mine where the concentration data can be monitored [15].
As opposed to the empirical formulas, artificial intelligence (AI) technologies have a good history of performance in prediction [16]. The technique has gained popularity in many fields, including UCS of rock [17,18], shear strength of rockfill material [19], backbreak in open-pit mines [20], ozone concentration [21] and carbon monoxide concentration [22]. Additionally, the AI technologies have the ability to consider several factors, and the results can be obtained directly based on the optimized AI model. AI can also avoid the above-mentioned limitations of the empirical formula. However, AI technologies have rarely been implemented into the re-entry time prediction, to the author’s knowledge.
Gathering reliable sample data is necessary for the construction of AI models [23]. Field data is of course the most reliable type, but one that is not easy to access, due to the harsh environment in the mines [24]. On the contrary side, numerical simulation has gained worldwide attention in the study of the migration behaviors of blasting production in the underground roadway, owing to the superiority of visualization, data richness and ease of operation [25,26,27,28]. However, the length of these models is typically short, as numerical simulation requires a high level of computational performance, especially for long roadways with a significant amount of nodes. The Ventsim software, which is based on the Hardy Cross algorithm, and which has been used to study the post-blast re-entry time in some complex roadways with affordable computation time [15,29], was thus selected to calculate the time under various conditions in this study.
Therefore, this paper aims to develop a BPNN model for predicting the post-blast re-entry time. The rest of this study is organized as follows. The section titled “Model process and data preparation” introduces the construction of models used, as well as the process of database establishment, including the selection and analysis of parameter ranges. The section titled “Methodology” describes the algorithm of BPNN as well as the process of calibrating the empirical formula in detail, in addition to four indicators adopted to evaluate the performance of proposed models. The section titled “Results and discussions” contains the description of building the architecture of the BPNN and a performance comparison of both models for the time prediction. The section titled “Algorithm embedding” exhibits one software developed based on the proposed models. In the last section, the main conclusions and future development are given.

2. Model Process and Data Preparation

2.1. Model Construction

The research object is one cross-section of the roadway at a depth of approximately 580 m below the surface. The section’s size and its corresponding 3-D model constructed in Ventsim are shown in Figure 1. It is a three-core arch structure with an area of 14.04 m2. The width, wall height and arch height are 3.95 m, 2.8 m and 0.95 m, respectively. Facilities such as cables and supports inside the roadway were not taken into consideration. The amount of explosives used each time are about 40 kg and the temperature is around 300 K. It is worth pointing out that the ventilation duct was placed off the roadway in this software for the convenience of real-time viewing of ventilation performance.

2.2. Database Generation

Four parameters, namely, average velocity within the roadway, occupational exposure limit, toxic gas volume per kg of explosives and length of roadway, have frequently been considered when calculating the relevant time [11,15]. Hence, these four parameters were also used for developing the BPNN model in this study. Due to the fact that the fresh-air volume of the ventilation duct has a considerable impact on the average velocity within the roadway, the minimal average velocity in the excavation roadway was set at 0.25 m/s and the highest average velocity was set at 4 m/s in the mining area, given in the safety regulations for metal and nonmetal mines of China [30]. As a consequence, the average velocity ranged from 0.25 m/s to 4 m/s in this study. Moreover, some indexes for assessing occupational exposure limit have been proposed, depending upon the actual requirements. For example, time weight average (TWA) is defined as the average permissible concentration within a normal 8 h workday and 40 h work-week. Short term exposure limit (STEL) considers the permissible concentration limit for up to 15 min with the serious implementation of the TWA. Table 1 shows the TWA and STEL of different countries for CO. It can be seen that China has the strictest regulations for exposure concentration, so 24 ppm was used as the monitoring standard rather than the 16 ppm level found in some regulations [31]. Taking all of the above factors into account, the occupational exposure limits in this study were taken to be between 24 ppm and 50 ppm, in order to meet a variety of requirements.
Toxic gas production is susceptible to a variety of influencing factors, such as the sort of explosives [32], the environment of the roadway [33], the type of blasting design, the method of detonation, and so on [34]. Therefore, the amount of toxic gases produced in each detonation varies slightly. The #2 rock emulsion explosive was adopted in this study. The toxic gas volume per kg of explosives in the underground roadway is from 36 L/kg to 42 L/kg, as given by Wang [35]. In addition, the length of the roadway is increased with the continuous construction of excavation engineering. Herein, the range from 200 m up to 1500 m was studied. Figure 2 presents the minimum, lower quartile, median, upper quartile and maximum for each parameter in boxplots. It illustrates that each parameter shows a uniform distribution.
A total of 300 input samples were generated based on the ranges mentioned above, and then these models with specific parameter values were constructed and simulated in Ventsim software to predict the post-blast re-entry time. In total, 300 pieces of data were archived herein as described in Appendix A. The correlation matrix of the dataset is presented in Figure 3. The distributions and correlation coefficients for any two parameters are presented in the lower and upper of this figure, respectively. For the lower, it is clear that the relationship between the inputs and outputs is nonlinear where only the relationship of velocity versus time reveals a distribution similar to a negative exponential. For the upper, the darker the blue, the stronger the negative correlation. Conversely, the lighter the red, the weaker the positive correlation. As can be observed, the correlation coefficient between the four input parameters is low, as they are independent of each other. Additionally, both length and velocity show statistically significant relationships with the time, after significance tests. Despite the fact that gas and limit have lower correlation coefficients, these parameters still remain valid for the subsequent comparative analysis with the empirical formula.

3. Methodology

3.1. BPNN Algorithm

BPNN is a classical supervised learning method fusing the feedforward neural network and the back-propagation algorithm. It has been used in many fields and achieved excellent performance because of its capabilities of outstanding nonlinear fitting and generalization. For instance, Li et al. [23] have successfully used a BPNN model to predict the stress values when evaluating pillar stability. Zhao et al. [36] applied an integrated model based on the traditional BPNN to predict air pollution concentration and demonstrated that the method is more practical. Hence, BPNN was chosen in this study for predicting the post-blast re-entry time. There are five steps, namely, initialization of weights and biases, feedforward propagation of data, back-propagation of error, optimization of weights and biases and judgment of termination conditions.
At first, weights w and biases θ at the hidden layer and output layer are initialized with random numbers. The magnitude of each weight stands for the degree of influence of the connected neurons on the output, while the bias represents the level of difficulty in generating activation. After that, the accumulation of yj in the hidden layer and zk in the output layer can be calculated by the following formulas, respectively:
y j = f ( i = 1 n ( w i j × x i ) θ j )   ( i = 1 , 2 , n ; j = 1 , 2 , m )
z k = f ( j = 1 m ( w j k × y j ) θ k )   ( j = 1 , 2 , m ; k = 1 , 2 , l )
where f is an activation function; x, y and z are the output values of the input layer, hidden layer and output layer, respectively; and n, m and l represent the number of neurons at the input layer, hidden layer and output layer, respectively.
Afterward, the back-propagation is performed. The neuron error in the hidden layer and the output layer are Ej and Ek, respectively. As the error is the functions of weights, the tuning weights ∆wij between the input layer and the hidden layer as well as the tuning weights ∆wjk between the hidden layer and the output layer are as follows:
Δ w i j = η E j w i j
Δ w j k = η E k w j k
where η is the learning rate.
Subsequently, the updated weights wij (t + 1) and wjk (t + 1) are given as:
w i j ( t + 1 ) = w i j ( t ) + Δ w i j
w j k ( t + 1 ) = w j k ( t ) + Δ w j k
where t represents the number of iterations.
Finally, the process of training is conducted until the convergence conditions are satisfied, or otherwise, these steps (except for the initialization) are looped. In total, the framework of this research based on the BPNN model can be found in Figure 4.

3.2. Calibrating Empirical Formula

The schematic of ventilation in the longitudinal profile of the roadway is presented in Figure 5. It is given that the length of the working area and roadway are L0 and L, respectively. The area of roadway is S. The fresh air volume discharged from the ventilation duct is Q and the toxic gases concentration uniformly distributed in the working area of volume V is C0 at the initial moment. According to the flow balance, the amount of toxic gases removed after Δ t time of ventilation is Q × Δ t . Hence, the concentration C after T time of ventilation can be calculated by the following:
C = l i m n C 0 ( V Q Δ t V ) n = l i m Δ t 0 C 0 ( 1 Q Δ t V ) T Δ t = C 0 e T Q V
where n is the ratio of T to Δ t .
Moreover, Equation (7) can be further written by taking the logarithm as:
T = V Q ln C 0 C
Furthermore, some other empirical formulas shown in Table 2 have been developed by using different techniques such as mathematical derivation, data fitting and formula calibration. Among them, the empirical formula given by [15] was selected for comparison with the BPNN model because it provides some optimization based on Equation (8) and is more representative than others.
To acquire dilution efficiency factor fd in the formula given by [15], the sample with the post-blast re-entry time of 86 s, velocity of 3.79 m/s, length of 474 m, gas production of 36.2 L/kg and exposure limit value of 34 ppm was randomly picked. Some other parameters, namely the working space Vw, fresh air quantity Q and gas concentration C need to be calculated as follows, respectively:
V w = G × b x 0
Q = u × A
C = 28 × G × b 29 × l × A G × b
l = 15 + G 5
where G is the mass of the explosive, kg; b is the toxic gas volume per kg of explosives, m3/kg; x0 is the peak concentration of gas at the entrance monitored, ppm; and l is the throwing distance of toxic gas, m.
After that, the dilution efficiency factor of 0.73 can be obtained. The final empirical formula, which was employed to calculate the post-blast re-entry time and then compared to the BPNN, is given below:
T = V w 0.73 Q ln ( C C T )

3.3. Performance Indicators for the Assessment of Models

Four performance indicators, the root mean square error (RMSE), the coefficient of determination (R2), the mean absolute error (MAE) and the sum of squares error (SSE) were chosen to evaluate the performance of the models developed in this study [37]. Among them, RMSE is taken to measure the deviation between the actual value and the predicted value, where the smaller the value, the better the model’s performance. R2 is available to represent the goodness of fit of the model to the sample data. The closer it is to 1, the stronger the fit is. MAE can reflect the extent of actual prediction error, with smaller values indicating that the prediction is closer to the actual value. SSE is the accumulation of squared error between the predicted value and the actual value. A larger value means a worse quality model when the number of samples is the same. They are defined by the following:
RMSE = 1 n i = 1 n ( T i m e o , i T i m e p , i ) 2
R 2 = 1 i = 1 n ( T i m e o , i T i m e p , i ) 2 i = 1 n ( T i m e o , i T i m e o ¯ ) 2
MAE = 1 n i = 1 n | T i m e o , i T i m e p , i |
SSE = i = 1 n ( T i m e o , i T i m e p , i ) 2
where n is the number of samples; Timeo,i, Timep,i are the post-blast re-entry time of actual value and the predicted value, respectively; and T i m e o ¯ represents the mean value of actual post-blast re-entry time.

4. Results and Discussion

4.1. Building the Architecture of the BPNN

An excellent BPNN model, one which has the best weights obtained from the training phase, can predict the post-blast re-entry time precisely. In this study, the BPNN model built on MATLAB was trained and tested with 210 samples (70%) and 90 samples (30%), respectively. The changes in RMSE and R2 were recorded while the model had a different number of neurons at the hidden layer, as shown in Table 3. It can be summarized that the model with six neurons in the hidden layer performed best in which the lowest RMSE of 12.6171 and the highest R2 of 0.9975 can be acquired. At the same time, it also has a remarkable performance in the testing phase. Hence, this model was served as the final post-blast re-entry time prediction model and the schematic diagram is presented in Figure 6.

4.2. Performance Comparison between BPNN and Formula

The BPNN and empirical formula previously developed were run to predict the post-blast re-entry time in the training set and the test set. The models’ performance, including RMSE, R2, MAE and SSE, was summarized in Table 4. As can be seen in this table, the BPNN model has a better performance in both the training set and the test set than does the empirical formula. The average prediction error of BPNN in the test set is only 10.78 s, which is approximately a quarter of the empirical formula. Additionally, the goodness of fit of BPNN is closer to 1, indicating that it can better account for the relationship between the inputs and output than can the empirical formula. It should be noted that the delay caused by the empirical formula each time will accumulate with the increasing number of detonations. To reduce the losses, the BPNN model should be adapted to predict the post-blast re-entry time.
In order to compare the performance of both models more exactly, the regression diagrams in the training phase and the testing phase are described in Figure 7. The horizontal axes represent the actual time. The vertical axes render the prediction value obtained from the BPNN and the empirical formula. The slope of diagonal lines with the black color is 1. Other radical lines with deviations of 10% and 30% from the diagonal lines are also drawn in this diagram. Taken as a whole, the BPNN model has a higher accuracy than does the empirical formula in both sets, because the data points are closer to the diagonal line, whereas some data points obtained from the empirical formula are far outside of the line of 30%, especially in the testing phase. It can also be seen that most of them are larger than the actual time when the ventilation time required is larger than 400 s. At the same time, the BPNN in the testing phase has a larger error than in the training phase, but these data points are almost limited to the radical line of 10%. Hence, the BPNN model can offer more stable performance and more accurate results.
Figure 8 illustrates the error distributions of both models in the training phase and testing phase and some statistical indicators, i.e., the minimum of error (Errormin), the maximum of error (Errormax), the mean of error (Errormean) and the standard deviation of error (ErrorSt.D) are contained in this figure as criteria. The horizontal axes represent the error values between the actual time and the predicted time. The vertical axes are the count within a specified error range. Accordingly, the higher the error bar near the origin and the lower the statistical indicators are, the smaller the model error. As can be realized, the BPNN shows promising results because the region of horizontal axes of the first bar is only from 0 to 10 in the BPNN model when the count of the first bar is almost equal in both models. Additionally, it can be observed that the empirical formula has similar performance in both the training phase and the testing phase.

5. Algorithm Embedding

Given the complicated environment on the site and the inconvenience of running code in the engineering practice, some scientists have performed a lot of work on the application of construction schedule methods, such as the use of software. Song et al. [38] developed a universal engineering construction system simulation software for the construction schedule visualization simulation of hydraulics and hydropower. Wang et al. [10] embedded a ventilation time function in existing software to replace the empirical values for the construction processes and schedule arrangement. In this study, the trained BPNN model was embedded into an existing software module named Simulation Software for Post-blast Re-entry to enhance the performance and facilitate practical use in the central control room located on the surface (see Figure 9). It can be seen that the prediction time obtained from the BPNN model is displayed as both numeric and bar values. Additionally, some optimizations have been applied to the software based on this study. For example, the standard concentration can be input more flexibly according to the requirements rather than using the fixed one. The dilution efficiency factor in the empirical formula was also appended to this software to provide more reference information for users in the period of decision-making. Furthermore, the software can also be utilized to support the formulation of a preliminary schedule. To respond to the call to develop an intelligent mine, interfacing with the mine’s integrated system will be the object in future research.

6. Conclusions

Determining the post-blast re-entry time is essential in the excavation field of tunnel and mining to prevent the occurrence of poisoning and asphyxiation incidents. In this paper, a BPNN model was proposed with consideration of four parameters most used in former studies. An empirical formula was calibrated to compare the performance with the proposed BPNN model. It found that the BPNN model with six neurons in the hidden layer outperforms the others. Furthermore, the results show that the BPNN model has a higher reliability and accuracy (RMSE: 21.45; R2: 0.99; MAE: 10.78; SSE: 40934) compared with the empirical formula (RMSE: 76.89; R2: 0.90; MAE: 42.06; SSE: 526147). In order to facilitate the engineering use of the BPNN model developed in this study, the model has been embedded in one software application. The operator can not only set schedules for production tasks in advance but also can perform some ventilation optimization by adjusting parameters in this software to facilitate the cleaning efficiency of toxic gases.
This study provides an effective tool for the prediction of post-blast re-entry time in excavation engineering. However, some other influence factors, such as the temperature and the interactions between the wall roughness and the velocity of airflow, etc., may also affect the results; a fact which should be considered to achieve a better agreement between the predicted results and the actual situations. This will be discussed in future research.

Author Contributions

Conceptualization, J.Z. and C.L.; methodology, C.L.; software, J.Z.; validation, J.Z.; formal analysis, J.Z.; investigation, J.Z. and T.Z.; resources, J.Z.; data curation, J.Z.; writing—original draft preparation, J.Z.; writing—review and editing, T.Z. and C.L.; visualization, J.Z.; supervision, T.Z. and C.L.; project administration, J.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Length/(m)Gas/(L/kg)Velocity/(m/s)Limit/(ppm)Time/(s)
146940.47 1.31 38.52 246
292139.53 2.57 31.90 140
3147540.77 2.33 32.69 185
489337.50 0.38 32.40 1040
539340.27 1.34 24.62 246
624338.16 2.37 37.60 121
725640.40 3.25 33.73 90
843940.02 2.10 41.43 152
932440.61 0.69 29.08 448
1034741.58 1.77 44.34 166
1151038.91 2.31 31.86 145
1247436.20 3.79 33.98 86
1395436.09 3.50 38.44 107
14114537.83 1.59 30.45 246
15138136.61 1.99 40.52 201
1696739.21 1.72 34.15 221
1738541.72 3.21 36.36 94
1860138.99 1.03 36.23 336
1997736.35 1.92 30.20 200
20102838.84 2.40 38.10 169
2195740.69 2.92 41.64 129
2273337.23 3.53 25.00 101
23145941.48 3.54 49.79 120
2430736.69 0.77 31.24 401
2536341.33 0.79 39.60 377
2653537.85 3.66 46.26 89
27135837.93 1.17 42.51 337
28149040.42 2.49 34.57 174
2989139.11 3.62 35.44 109
30138836.72 3.89 36.69 104
31128738.94 1.65 39.18 270
3286541.51 1.08 30.82 354
33108938.02 0.30 27.91 1419
3427141.53 0.42 37.10 679
3579938.20 3.26 26.70 121
36105640.83 0.92 35.32 456
37121839.50 1.45 24.92 289
38126141.46 2.26 41.85 193
3954039.51 3.22 41.22 102
40116036.17 0.55 42.26 729
4145441.63 2.36 45.01 131
4287539.01 0.47 47.88 723
43134336.12 1.73 26.25 270
44141441.35 1.38 38.31 299
4560640.44 3.77 26.08 92
46100241.98 1.80 48.54 219
47144937.53 2.19 47.50 193
4826639.80 2.53 45.38 115
4930241.93 3.31 25.87 95
50138341.23 0.85 45.80 471
51103340.59 1.70 37.31 240
52113438.15 2.47 40.43 157
5353041.75 0.88 28.33 395
54149537.79 3.83 28.24 114
55130238.35 2.76 29.16 163
5677936.96 2.51 29.41 152
5793136.44 1.63 43.76 224
5848739.94 1.22 44.68 257
5924636.57 1.04 40.81 282
6032236.89 3.92 42.72 74
61111436.37 3.69 27.95 120
6237339.85 3.13 30.66 98
63132240.91 3.38 37.06 136
6459141.14 3.61 29.78 94
65136339.36 2.08 36.44 228
6646737.42 1.89 24.50 182
6777136.16 1.30 27.20 290
6831741.21 2.79 39.35 107
6973839.38 1.75 47.09 205
7080937.48 1.40 28.99 254
7191637.14 1.46 34.98 244
72104841.88 3.02 40.39 138
7395239.93 2.24 46.67 167
7423638.77 0.34 43.09 831
7552036.46 0.61 34.48 558
7656636.22 0.94 30.24 372
77133238.68 1.91 44.88 242
78122137.90 0.32 37.69 1332
7994637.95 2.94 45.17 126
8075940.64 2.03 30.86 183
8193638.12 1.19 36.65 307
82127938.09 2.96 43.64 149
8340636.83 3.60 45.72 85
8464236.32 3.86 44.55 88
8535237.98 2.87 27.74 110
8644939.46 0.50 25.21 652
87121138.54 3.55 35.19 117
88137337.21 0.64 49.75 618
8948937.68 1.69 49.96 187
9085537.75 3.56 39.77 106
91123141.73 2.56 47.25 166
9222541.01 2.23 27.08 133
93129240.32 1.18 26.87 379
9444640.91 1.84 30.32 177
9580441.65 0.49 32.07 717
96142438.79 3.72 30.41 111
9786038.52 1.52 25.46 250
98124640.86 3.64 25.66 118
9949538.49 2.67 35.65 120
10070838.59 3.85 32.11 89
101118039.75 3.03 49.13 134
102103837.36 1.00 26.04 409
10357640.05 3.05 38.77 107
104129736.15 2.32 35.23 194
105106341.38 2.82 26.29 150
106106837.06 3.63 31.65 117
10781439.68 1.16 34.36 309
10879437.80 2.38 43.72 146
109111938.47 3.45 33.32 111
11041337.38 0.68 43.97 463
11120341.79 1.15 49.04 242
11221040.52 2.59 42.10 109
11322039.48 0.86 39.39 331
114144441.80 0.39 24.58 1284
11574836.07 2.97 40.02 123
116137839.56 1.78 32.32 269
11729136.30 1.82 37.94 164
11878439.28 3.78 49.33 91
119136841.60 2.95 29.82 161
12085040.00 2.39 44.80 157
12167739.98 3.95 38.14 91
122128236.47 3.99 48.92 111
12393441.57 2.06 25.12 202
12470336.62 1.33 32.90 283
12569040.24 3.67 36.56 90
126134839.19 2.90 48.34 135
127147039.83 1.06 27.33 404
12825138.96 3.58 28.37 84
12987340.39 1.61 42.60 241
13042936.25 3.07 28.74 107
131122638.05 1.98 33.57 214
13226137.70 2.09 33.15 145
13354540.81 1.93 44.59 173
13469841.19 0.75 27.54 496
135145439.65 2.63 42.47 161
136112937.65 2.25 37.27 172
13733240.72 1.21 31.49 251
13856841.50 2.52 42.80 128
139112440.20 1.11 44.38 345
14092640.99 3.70 46.63 98
14188041.16 2.13 37.73 183
142125136.02 3.17 31.03 136
14371837.60 0.81 35.02 430
144117841.13 0.46 43.84 883
145124139.14 0.93 40.18 461
14644437.78 3.23 36.48 100
147132737.31 1.27 32.94 363
14835739.35 3.52 33.11 87
14962940.09 0.82 33.24 404
150125638.44 1.09 46.88 397
151143436.40 1.10 38.93 378
15268240.68 2.98 24.08 122
15365736.49 2.28 25.25 153
15465240.35 0.62 40.60 555
155134038.24 0.99 31.36 468
156135340.62 3.48 43.30 113
15788636.54 2.48 24.79 159
158115540.74 3.28 47.30 121
15943438.86 0.96 46.46 326
16054838.39 3.75 25.96 90
16178940.37 1.02 48.75 340
162117040.46 2.75 29.28 146
16399237.41 2.74 38.98 142
16468836.67 1.86 48.96 178
165131237.43 1.79 41.01 254
166148036.52 0.45 31.70 966
167115039.43 1.26 48.29 314
16837840.84 0.26 48.50 1113
16945937.28 2.71 39.97 116
17060939.57 0.76 45.92 417
17155036.02 2.61 37.48 129
172113941.68 3.84 39.56 102
17381241.28 2.29 47.80 155
17455539.16 0.27 32.53 1254
17571037.05 0.28 41.56 1213
17633736.10 2.02 46.21 147
17774341.06 0.95 42.05 381
17883540.17 2.69 25.62 137
179123637.04 1.37 45.22 312
18066238.10 2.86 30.61 123
181121640.22 3.08 40.64 136
182131739.41 3.81 44.18 120
183119538.81 0.63 26.91 649
18472339.88 1.94 28.95 180
18562737.26 0.48 36.27 687
18628437.57 3.14 41.76 92
18736837.09 1.96 38.73 154
18894140.30 3.97 32.74 93
18947938.32 3.32 47.67 93
19098740.10 0.72 35.81 539
191146239.28 0.53 37.40 797
19234238.07 0.60 49.38 479
19328640.12 3.87 47.05 75
194117537.33 3.46 29.20 116
195110941.28 1.64 28.53 270
19622336.39 2.68 32.20 109
19728138.67 2.70 33.36 113
19861638.30 1.29 43.14 250
19997240.89 1.24 24.83 307
20072841.56 2.85 37.52 124
201140437.58 2.84 33.94 143
202118541.85 0.98 35.86 414
203130740.49 0.52 46.05 865
20424141.11 1.47 45.84 191
20575438.25 0.70 39.14 527
20652837.13 2.22 33.44 157
20762141.95 1.87 34.77 192
20869339.09 2.80 43.93 119
209102337.19 2.05 41.06 197
21090136.05 0.91 49.17 387
211101536.24 1.53 46.96 262
212119837.72 1.07 46.76 385
213119036.84 2.15 27.70 190
21431239.60 1.88 40.22 155
215140938.64 0.73 41.26 560
216116539.31 2.34 24.17 171
21741839.73 1.49 36.85 214
21850536.74 1.14 26.50 290
21983038.74 2.21 36.90 166
22064738.89 3.39 45.63 101
221136041.05 2.43 28.04 195
22276437.35 2.45 48.71 136
22338838.02 3.68 42.68 83
224107339.04 0.83 29.62 513
22546439.26 1.55 41.47 205
22630439.05 1.35 48.84 217
227120040.02 1.54 32.28 268
228139339.06 3.09 25.41 157
22982536.77 3.40 37.89 107
230105839.90 1.39 42.89 302
231148538.17 1.62 46.42 268
23264937.94 1.76 39.48 195
23376939.78 0.40 41.68 830
234127139.95 0.57 29.57 774
23571341.36 3.15 46.84 110
236142140.16 3.44 48.00 120
23732739.23 2.99 35.40 100
23896236.94 0.58 28.78 653
23985339.79 3.29 38.64 115
24038336.59 2.78 47.71 108
241105337.56 0.71 47.92 504
24229638.62 0.80 24.37 400
24358137.73 0.41 26.45 872
24458639.70 2.44 24.42 150
24597438.61 2.83 49.88 135
24691141.70 0.29 43.55 1209
24782041.83 3.74 40.85 96
24852538.00 1.32 34.40 261
24987036.81 3.01 34.19 128
250109441.78 2.16 31.28 201
25189640.57 3.18 27.29 125
25242341.04 3.51 34.82 92
253100736.68 0.84 43.51 472
25436539.13 2.60 26.16 121
25539837.88 0.87 29.99 363
256101339.33 2.93 28.16 136
257110439.63 0.37 34.61 1016
258113737.28 3.37 27.00 135
25963238.69 1.85 28.12 198
260126637.63 3.43 24.21 127
26163740.94 2.72 49.58 123
262129941.94 3.90 34.28 115
26361137.46 3.33 31.45 105
26477440.79 1.57 35.61 241
265141937.11 2.55 25.04 194
266103539.72 2.14 31.16 191
267139840.07 1.90 28.58 256
26898238.72 3.35 41.89 115
26927636.99 1.56 25.83 197
27084538.46 1.68 39.68 222
27120538.42 1.42 29.37 208
27250041.43 3.93 27.49 83
273133840.67 0.56 38.56 834
27473138.83 3.06 30.12 116
27556140.54 1.41 45.59 225
27666741.41 1.67 33.78 212
277120536.27 2.41 42.93 172
27848440.15 0.33 30.03 1030
27990638.40 2.17 44.13 162
28021537.51 3.76 36.02 71
281109638.91 3.98 40.72 94
282107940.25 2.00 49.54 184
28384036.42 0.35 44.97 1062
284101841.09 0.65 33.53 614
28551541.31 3.41 43.34 91
286108436.64 3.10 36.06 139
287109936.79 2.64 46.01 142
288146437.01 3.30 44.76 129
28967236.91 1.23 47.46 290
290127741.26 2.62 31.07 168
29140338.22 2.01 27.12 160
292143938.37 3.16 38.35 133
29357138.57 2.11 48.09 154
294125936.91 2.91 35.52 150
29540841.90 2.46 32.49 125
29623037.16 3.20 48.13 89
29799739.58 3.91 26.66 100
298104338.27 3.49 45.42 118
299142940.96 1.44 39.81 288
30059636.86 1.50 42.30 228

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Figure 1. Geometry of researched model.
Figure 1. Geometry of researched model.
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Figure 2. Boxplots of input parameters.
Figure 2. Boxplots of input parameters.
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Figure 3. Correlation between input and output parameters.
Figure 3. Correlation between input and output parameters.
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Figure 4. Flowchart of the research process.
Figure 4. Flowchart of the research process.
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Figure 5. Schematic of ventilation.
Figure 5. Schematic of ventilation.
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Figure 6. Proposed BPNN model for predicting time.
Figure 6. Proposed BPNN model for predicting time.
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Figure 7. Regression diagrams of both models in the training and testing phase: (a) BPNN in training phase; (b) empirical formula in training phase; (c) BPNN in testing phase; and (d) empirical formula in testing phase.
Figure 7. Regression diagrams of both models in the training and testing phase: (a) BPNN in training phase; (b) empirical formula in training phase; (c) BPNN in testing phase; and (d) empirical formula in testing phase.
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Figure 8. Prediction error comparison of both models in the training and testing phase: (a) BPNN in training phase; (b) empirical formula in training phase; (c) BPNN in testing phase; and (d) empirical formula in testing phase.
Figure 8. Prediction error comparison of both models in the training and testing phase: (a) BPNN in training phase; (b) empirical formula in training phase; (c) BPNN in testing phase; and (d) empirical formula in testing phase.
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Figure 9. Interface of simulation software for predicting time.
Figure 9. Interface of simulation software for predicting time.
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Table 1. Occupational exposure limit for CO in different countries [13].
Table 1. Occupational exposure limit for CO in different countries [13].
TWA/ppmSTEL/ppm
ASM-250100
NIOSH REL35200
NOHSC30200
OSHA PEL35200
CHINA1624
Note: ASM-2 is Instructions Technique Complementary to Mining Safety Actions (Spain); NIOSH is the National Institute for Occupational Safety and Health; NOHSC is the National Occupational Health and Safety Commission; OSHA is the Occupational Safety and Health Administration.
Table 2. Empirical formulas for time prediction.
Table 2. Empirical formulas for time prediction.
ReferenceEquationWay
[4] C = V G 2 A π D T e ( ( L u T ) 2 4 D T ) Calibration
[7] T = e ( Q 60.119 12.924 ) Calibration
[7] T = 2383.7 Q 1.574 Calibration
[9] C = p 1 T n + p 2 T n 1 + + p n T + p n + 1 Fitting
[9] C = 1048 e ( T 6.464 0.8676 ) 2 Fitting
[10] T = 13.118 e 0.0017 L Fitting
[11] T = n ln ( C C T ) Derivation
[11] T = V Q + Q g ln [ ( Q g + Q B g ) ( Q + Q g ) C ( Q g + Q B g ) ( Q + Q g ) C T ] Derivation
[15] T = V w Q × f d ln ( C C T ) Calibration
Note: T: ventilation time required, min or s; Q: fresh air quantity, m3/s; C: gas concentration at the beginning of ventilation, ppm; p1, p2, …, pn+1: fitting constants; VW: volume of working space, m3; fd: dilution efficiency factor; CT: gas concentration at time T, ppm; VG: volume of gas at the heading and beginning of time, m3; A: area of cross-section of roadway, m2; D: effective axial dispersion factor, m2/s; L: distance away from the heading, m; u: average air velocity, m/s; n: numbers of fresh air which is passing through the working space; Qg: inflow rate of the toxic gases, m3/s; and Bg: concentration of toxic gases in the ventilation duct, %.
Table 3. Performance of BPNN models with different numbers of neurons in the hidden layer.
Table 3. Performance of BPNN models with different numbers of neurons in the hidden layer.
Model NeuronsRMSER2
TrainingTestingTrainingTesting
1216.019621.92490.99590.9922
2355.901237.02020.95020.9776
3472.464660.6010.91630.9401
4561.699650.56170.93930.9583
5612.617121.34210.99750.9926
6714.355121.0260.99670.9928
7814.767721.45770.99650.9925
8914.270322.05160.99680.9921
91013.141921.64390.99730.9924
Note: the line in bold type indicates the best model.
Table 4. Performance comparison of both models.
Table 4. Performance comparison of both models.
IndicatorsTrainingTesting
EmpiricalBPNNEmpiricalBPNN
RMSE61.8112.6176.8921.34
MAE38.347.6642.0610.78
R20.940.990.900.99
SSE7983523342952614740934
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Zhang, J.; Li, C.; Zhang, T. Application of Back-Propagation Neural Network in the Post-Blast Re-Entry Time Prediction. Knowledge 2023, 3, 128-148. https://doi.org/10.3390/knowledge3020010

AMA Style

Zhang J, Li C, Zhang T. Application of Back-Propagation Neural Network in the Post-Blast Re-Entry Time Prediction. Knowledge. 2023; 3(2):128-148. https://doi.org/10.3390/knowledge3020010

Chicago/Turabian Style

Zhang, Jinrui, Chuanqi Li, and Tingting Zhang. 2023. "Application of Back-Propagation Neural Network in the Post-Blast Re-Entry Time Prediction" Knowledge 3, no. 2: 128-148. https://doi.org/10.3390/knowledge3020010

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