Recognition of rock–coal interface in top coal caving through tail beam vibrations by using stacked sparse autoencoders

2.1. SSAE

A SAE neural network is an unsupervised learning algorithm that does not require labeled training examples unlike other neural networks. Applying back propagation sets the target values to be equal to the inputs. The schematic of a SAE with $n$ inputs and $m$ units in the hidden layer is shown in Fig. 1.

Fig. 1Schematic of a SAE

In an autoencoder, the overall cost function is as follows:

where $x^{\left(i\right)}$ is the raw input, $m$ is the number of inputs, $y^{\left(i\right)}$ is the raw output, $h_{W,b}\left(x^{\left(i\right)}\right)$ is the output of activation function, $\lambda$ is the relative importance of the second term.

In a SAE, we can discover some correlations of input features by placing constraints on the network. Sparsity $\rho$ is imposed to constrain the hidden units as follows:

where ${\alpha }_j^2$ denotes the activation of hidden unit $j$ in the SAE when the network is given a specific $x^{\left(i\right)}$. The parameter is the average activation of hidden unit $j$. Moreover, we make the two parameters equal as follows:

Typically, this parameter holds a very small value, usually 0.05. Thus, we need the activation of the hidden unit to be close to 0. We add a penalty term to penalize the situation of ${\widehat{\rho }}_j$ deviating significantly from to optimize the objective. The penalty term is as follows:

Then, the overall cost function is:

The detailed establishment of SSAE, pretraining, and fine-tuning can be carried out in the following steps (Fig. 2):

Step (1): A SAE is trained on the raw input $x^{\left(k\right)}$. for learning of primary features $h^{\left(1\right)\left(k\right)}$. The structure of the first SAE is $[n,s_2,n]$, corresponding to $n$ inputs, $s_2$ units in hidden layers, and $n$ outputs.

Step (2): This trained SAE is then adopted to obtain the primary feature activations $h^{\left(1\right)\left(k\right)}$ for each input $x^{\left(k\right)}$.

Fig. 2Establishment of SSAE

Step (3): $h^{\left(1\right)\left(k\right)}$ is then used as the “raw input” to the second SAE for learning the secondary features $h^{\left(2\right)\left(k\right)}$. The second SAE structure is described by $[s_2,s_3,s_2]$, corresponding to $s_2$ inputs, $s_3$ units in hidden layer, and $s_2$ outputs.

Step (4): To obtain the secondary feature activations $h^{\left(2\right)\left(k\right)}$, each $h^{\left(1\right)\left(k\right)}$ is fed into the second SAE.

Step (5): Treat the secondary features as “raw inputs” of a sigmoid classifier to map digit labels.

Step (6): Combine the three layers and a classifier layer to form the SSAE model.

Step (7): Back-propagation is conducted to improve the results by adjusting the parameters of all layers simultaneously in a process called fine-tuning.

Step (8): Step (7) is performed repeatedly until the set training times are achieved.

2.2. Batch gradient descent

Batch gradient descent is an efficient algorithm for searching the optimal solution. One iteration of batch gradient descent is as follows:

Step 1: The following assumptions are set: $\mathrm{\Delta }{W}^{\left(l\right)}:=0$, $\mathrm{\Delta }{b}^{\left(l\right)}:=0$ for all $l$.

where $\mathrm{\Delta }{W}^{\left(l\right)}$ is a matrix with the same dimension as $W^{\left(l\right)}$ and $\mathrm{\Delta }{b}^{\left(l\right)}$ is a vector with the same dimension as $b^{\left(l\right)}$.

Step 2: For $i=1:m\text{,}$ back-propagation is used to compute ${\nabla }_{W^{\left(l\right)}}J(W,b;x,y)$ and ${\nabla }_{b^{\left(l\right)}}J(W,b;x,y)$. The following expressions are set:

where $W^{\left(l\right)}$ is the weights, and $b^{\left(l\right)}$ is the bias term.

Step 3: $W^{\left(l\right)}$ and $b^{\left(l\right)}$ are updated as below:

where $\lambda$ is the weight decay parameter. The above-mentioned steps of batch gradient descent are repeated to reduce the cost function for training the neural network.

3.1. Acquisition of the vibration signal of tail beam

The vibration signal acquisition of a tail beam is the first step for identification of rock-coal interface. Obtaining the vibration signal by sensors is the most common method used for identification. In this study, an acceleration sensor (4508 type) was employed. Table 1 displays the acceleration sensor parameters, and Fig. 5 presents the vibration sensor.

Fig. 54508 type acceleration sensor

During top coal caving, coal or rock strikes the tail beam supported by a hydraulic supporter to produce vibration. Vibration waves vary because of different size and hardness of coal and rock. Detection of tail beam vibration can successful identify and differentiate coal and rock. The installation position of the sensor is important for collecting signals. After analyzing the actual working scene, we noted that the main impact locations of coal and rock are the beam and tail chute, respectively, of the hydraulic supporter. Accordingly, we set the sensors at these two places. After many experiments, we found that the sensor is easily buried by falling coal and stone when the sensor is installed in the tail chute. Moreover, the continuous spraying of water for dust-proofing may have damaged sensors during coal caving. The running conveyor chute also generated considerable interference during signal acquisition, thereby negatively affecting the next step of the analysis. Hence, the end of the hydraulic support beam is an ideal location for sensor installation. Then, we chose the tail beam back to acquire vibration signals. The final self-designed experimental system and specific installation location of the sensor are shown in Fig. 6(a) and 6(b), respectively.

The experimental data acquisition system also includes a portable vibration sound wave signal detector with a data acquisition front end, wireless routers, and software system. Vibration signals were obtained by the data acquisition front end, transmitted to the wireless broadband router by cables, and then sent to a notebook for data storage and analysis. Afterward, we exported the data from the software system. All the data were acquired in the No. 1306 working platform in the Xinglongzhuang coal mine of Yanzhou Mining Company. The working pattern involved one knife and one caving. Caving step distance determination was 0.8 m, and coal thickness was 7.34 m to 8.90 m. The frequency of sampling was set as 2560 Hz, and each pattern’s sampling time was 160 ms. A total of 4096 sampling points were obtained for each pattern, and 4000 sample points were saved for each pattern to avoid possible errors of uncertainty.

Fig. 6a) Experimental system; and b) specific installation location of the sensor

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3.2. Feature extraction

Features must be extracted from the data exported from the pulse to enable the use of pattern recognition training and rock-coal interface prediction. Obtaining the final recognition results is hence a highly important task.

Many signal processing approaches can obtain desirable features from primary vibration signals and widely used in many industries, such as the FT [27, 28], WT [29], and EMD [30]. However, the signal was submerged in a strong background noise and non-stationary signals because of difficulty extracting useful features. For example, a signal based on the local characteristic time scales could be decomposed into several IMFs by EMD. However, it exists the problem of mode mixing. Thus, EEMD [29] was presented to solve this problem. Compared with EMD, EEMD adds a certain amount of Gaussian white noise to the original signal to solve mode mixing each time before decomposing. EEMD is highly useful for non-stationary and non-linear signals.

The followings are the summary of EEMD (Fig. 7):

Step 1: The standard deviation of the added noise $Nstd$ and the ensemble number $NE$ is initialized. The experiments show that the proposed model obtained better recognition when we set $NE=$ 300 and $Nstd=$ 0.2.

Step 2: Different white noises with different standard deviation are added to the original signal.

where $x_m\left(t\right)$ signifies the added signal, $x\left(t\right)$ represents the original signal, and $n\left(t\right)$ denotes the nth added white noise.

Step 3: The added noise signal is decomposed by EMD into $N$ IMFs.

Step 4: If $n<NE$, $n=n+1$ and steps (2) and (3) are repeated; otherwise, the next step is performed.

Step 5: Each IMF is calculated by the ensemble mean $c_i\left(t\right)$ of the $N$ trials as follows:

Fig. 7EEMD flowchart

By using the EEMD algorithm, we decomposed the primary vibration signal to 11 IMFs (Fig. 8).

But the IMFs obtained by EEMD are not always the intrinsic mode functions. This is because when the EEMD decomposed the signal, the addition of white noise leads to the high frequency components maybe actually white noise, but not the intrinsic mode functions and should be deleted. Significance test and orthogonality check are conducted, and the significances shows that the first four IMFs have no significance relationship with the results. We removed the first four IMFs and the correctness of it is proved by the experiments in Section 3.3.2.

In the following data processing, these remained IMFs were used as inputs for the proposed model in the working pattern recognition. Before importing these features to the SSAE model, we first conduct preprocessing. Such step must first be accomplished because the input vectors cannot exceed the defined scope of the hidden and output layers. Through this manner, we can full apply the value of each input and render the operation more convenient and fast. In fact, the normalized method is first used to limit the input absolute value to between 0 and 1, then the standard normal state method is adopted to transform the input into a standard normal distribution.

In these studies, 4000 groups of samples were obtained for each pattern and 8000 groups in total. In the following experiments, a 10-fold cross validation method was employed, and samples were randomly divided into 10 portions. Nine portions were utilized to train the proposed model, whereas 1 portion was used for testing. Each subsample was tested once, and the average of the results of the 10 experiments was regarded as the final test result. In each experiment, 7200 samples were adopted for training, and 800 samples were used for testing.

Fig. 8Signal, decomposed components by EEMD, and trend term (RES): a) coal, b) rock

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3.3. Construction of a SSAE model

To establish the proposed model, we carried out numerous experiments using the control variable method and determined basic parameters, such as learning rate and sparsity parameter. Parameters are obtained by comparing with different recognition accuracy rates of input features, classifiers, and structures.

3.3.3. Comparison among algorithms with different hidden layer structures

In this experiment, we set the number of first autoencoder hidden units to vary from 50 to 1000 at intervals of 50. The number of the second autoencoder hidden units varied from 5 to 50 at intervals of 5. A total of 200 kinds of different structures were assessed to find the most suitable structure for the proposed model (Fig. 9).

Fig. 9Recognition accuracy rates for different hidden layer structures: a) coal, b) rock, c) average

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Fig. 9(a), (b) and (c) refer to the accuracy rates of coal, rock, and the average of coal and rock, respectively. Fig. 9(a) shows that when the number of hidden units of the first SAE was set to 150 and the number of hidden units of the second SAE was set to 40, the accuracy of the coal reached the maximum value (98.12 %), followed by the proposed method structure of [11, 50, 30, 2] (97.95 %) and the structure of [11, 200, 50, 2] (97.85 %). Meanwhile, Fig. 9(b) reveals that the structure of [11, 200, 40, 2] enabled the recognition accuracy of rock to reach the maximum (100 %), followed by the proposed method structure of [11, 50, 30, 2] (99.98 %). Fig. 9(c) shows that the average identification of coal and rock achieved the maximum (98.96 %) when the structure was [11, 50, 30, 2].

3.3.4. Comparison among algorithms with and without pretraining

Pretraining plays an important role in the recognition of SSAE model, and the comparison of the proposed model with and without pretraining (Fig. 10).

As shown in the Fig. 10, the proposed model with pretraining works better than without pretraining, their average accuracy rates were 98.96 % and 91.93 %, respectively, and 7.03 % was improved by pretraining. This result was relatively easy to understand. Without pretraining, the network can only fine-tune the unpretrained parameters, which usually comprise some random initial points. This notion explains why the network may be confined to the local optima. With pretraining, the network could be fine-tuned on the pretrained parameters that will obtain the global optima. Thus, pretraining SSAE is a necessary step.

Fig. 10Comparison of the algorithms with and without pretraining

3.4. Comparison and discussion

For efficient performance assessment, we compared our algorithm with other four algorithms. The four algorithms include SVM, BP neural network (BP-NN), deep network (DN), one SAE-DN. For the SAE-DN, weights were pretrained only by one SAE. For the BP-NN, weights were optimized only in the back-propagation during neural network training. To be objective and fair, the environment of simulation for the five models were rendered similar. The average results of 10 experiments are presented in Fig. 12. Obviously, SSAE operated more effectively than the other algorithms. The testing accuracy of coal, rock, and the average of the two were 97.95 %, 99.98 %, and 98.96 %, respectively. The SVM algorithm was inferior to the other methods in both the recognition of coal and rock, with accuracy rates of only 88.95 % and 79.62 %, respectively, and an average recognition accuracy of 84.29 %. The SAE-DN algorithm did not achieve a satisfactory recognition of rock (89.24 %) but performed effectively for the recognition of coal (90.83 %). The DN algorithm (91.37 %, 92.44 %, and 91.90 %) was superior to BP-NN (89.09 %, 91.45 %, and 90.47 %) but inferior to SSAE in coal and rock recognition.

Fig. 11Comparison of the algorithms with different classifiers

Fig. 12Results from different methods