Non-Uniform Input-Based Adaptive Growing Neural Gas for Unstructured Environment Map Construction

Abstract

The research and development of special robots such as excavation robots is an important way to achieve safe and efficient production in coal mines. Affected by the unstructured environment such as complex working conditions and unsteady factor disturbances, the real-time construction of section environment maps that can accurately describe the environment and facilitate trajectory planning and decision making has become a key scientific problem to be solved as soon as possible. Therefore, non-uniform input based adaptive growing neural gas for unstructured environment map construction has been proposed. Considering complex load identification, real-time location identification, and the types of unsteady disturbance factors and working conditions, a set of environment identification models has been established based on a large amount of underground measured data training. These models can express whether the section environment has changed, as well as the type and magnitude of the change, to realize the overall knowledge extraction and parametric representation of the unstructured environment. Then, in order to solve the problems of inaccurate topology, excessive aging of connecting edges, and excessive deletion of nodes in non-uniform input environment, an adaptive growing neural gas algorithm based on non-uniform input environment (AGNG-NU) is proposed. Featured by a dynamic response deletion mechanism and adaptive adjustment mechanism of neuron parameters, the generated nodes and their topology can be dynamically adjusted according to the density of regional sample points. Several sets of non-uniform input environments are set to test the algorithm. The experimental results show that the topological maps established by AGNG-NU express clearer environmental information and, at the same time, the accuracy and distribution are improved by 8% and 15%, respectively, compared with the basic GNG algorithm. The accuracy and the distribution have also been significantly improved compared with other common SOM and GCS algorithms.

1. Introduction

The status of coal as China’s basic energy source is unshakable [1], and it will still play a role as the main energy source in the future. At present, the state regards intelligent mining of coal mines as a key research and development task and proposes that, by 2030, the key coal mining areas will basically realize unmanned working faces [2].

Coal mining and excavation are the two most dangerous links in coal mine production. Compared with coal mining, the intelligent development of excavation lags behind. The core problem that restricts the development of roadheading robots is that the cutting surface environment is unstructured during the tunneling operation, and there are unsteady factors (such as the dirt band and changes in coal and rock properties of the roof, floor, and at the boundary of the cross-section) [3], so that the environmental information of the cross-section cannot be sensed autonomously. The lack of identification and model description of the unstructured environment will have an impact on the excavation process and section forming, and even lead to dangerous situations such as component damage, motor overload, or shutdown. Therefore, how to parameterize the occurrence time, type, and magnitude of environmental abrupt changes, establish an unstructured unified cross-section environmental identification model, and reflect the dynamic adaptation characteristics of the environmental expression are the key problems to ensure the tunneling operation and intelligent development.

The identification and map construction of the unsteady factor disturbance in the tunnel section can be decomposed into three aspects: acquisition, processing, and expression of environmental information. In terms of the acquisition and processing, the identification of cross-section cutting conditions is one of the most important technologies for the intelligentization of the tunneling process [4]. In the early 1960s, the study of the function of coal and rock identification began. The existing methods include: gamma ray method, sound detection method, dust detection method, cutting force response method, vibration detection method, radar detection method, active power detection method, thermal infrared detection method, image detection method, etc. [5], mainly used in coal mining face. However, the acquisition of section environment information is mainly used to judge the internal geological structure of the tunnel section. In Ref. [6], an identification method of the dirt band based on multi-sensor information was proposed, but it lacked a unified representation method for normal media and unsteady disturbances, and the establishment of an environmental model was not systematically considered and not used as an input signal for map construction.

In terms of environmental information expression, metric maps, topological maps, and hybrid maps [7,8] are the three most mainstream methods of map expression, among which metric map is divided into grid map and geometric feature map. In Ref. [9], a grid map of cross-section was established, and the automatic cutting trajectory was planned according to the cross-sectional grid map. However, it was mentioned in the literature that whether there were obstacles inside each unit was assumed to be known during trajectory planning. Grid maps are not conducive to expressing environmental information, as there is a lack of connections between grids, and the accuracy of grid maps is often low. A topological map is a map that represents relative spatial relationships, describing key landmarks in the environment and the connections between them.

Neural gas is an artificial neural network inspired by the self-organizing map (SOM). Neural gas is a simple algorithm for finding optimal data representations based on feature vectors which is able to connect simple abstract models in different ways to better solve and optimize real-world problems [10]. In Refs. [11,12,13], for robot navigation, the information detection of the environment and positioning is realized, and finally the algorithm is used to build a map model of the unknown exploration environment. The detection process relies on the sensors on the robot, and through the analysis of the information returned by the sensors, the accuracy of robot positioning is often difficult. In Refs. [14,15,16], for feature parameter extraction, such as hand detection and gesture recognition, the authors utilize the algorithm for vector quantization, compress the network parameters, and perform feature screening based on the uniqueness of individual features for evaluation in the database. In Refs. [17,18], for embedded or wireless network, with the clustering of big data streams, a slim model is proposed for minimizing computational complexity, time, and space constraints of the hardware and increasing accuracy. However, for an unstructured environment map, firstly, the environment must be accurately identified; secondly, for the dynamically identified environment, the environment map can be quickly and accurately established, and the non-structural characteristics of the environment can be reflected through the topological structure of the map. The above methods and models cannot solve this problem.

Based on the above analysis, non-uniform input-based adaptive growing neural gas (AGNG-NU) for unstructured environment map construction is proposed in this paper. Firstly, considering the complex load, the real-time identification position, and the types of unsteady disturbance factors and working conditions, the environment identification method of tunnel section is studied and the model is established. Then, taking the characteristic parameters of the above environment recognition model as input, the topology environment map is established by AGNG-NU. Featuring a dynamic response deletion mechanism and adaptive adjustment mechanism of neuron parameters, the generated nodes of AGNG-NU and their topology can be dynamically adjusted according to the density of regional sample points. Finally, the simulation experiments proved that AGNG-NU achieved a better accuracy and distribution and has actually been applied in the construction of tunnel section environment map.

2. Environment Identification Method and Model Establishment of Tunnel Section

Considering the nonlinear relationship between the hardness of coal and rock and the cutting power required by the external load of the cutting head, the environment recognition model of unstructured cross-section is established, as shown in Figure 1. This uses the cutting motor voltage, cutting motor current, driving cylinder pressure, the cutting arm vibration acceleration, lifting cylinder stroke, and rotation cylinder stroke as the input, and the normalized environmental information parameter and the collection point location parameters as the output. Aiming at the characteristics of the load under the disturbance of various unsteady factors, the BP neural network is trained based on a large amount of underground measured data to identify the type of coal and rock hardness inside the section, whether it changed, and the degree of change. The cutting head positioning model is used to calculate in real-time and identify the location of environmental changes within the section. The environment recognition model is designed to realize the acquisition and representation of unstructured environmental information.

2.1. Load Identification Method of Cutting Head Based on Training of Measured Data

During the cutting process of the roadheader, the load on the cutting head is affected by a variety of factors. The changes of these factors are often accompanied by changes in multiple working parameters. Therefore, it is impossible to establish an accurate mathematical model between these working parameters and the cutting head load.

The cutting motor voltage $U$, cutting motor current $I$, driving cylinder pressure $P$, and cutting arm vibration acceleration $Acc$ are used as four neurons in the input layer, the output layer of the neuron network is set to have one neuron, and the corresponding output is the hardness of coal rock $f$. A BP neural network has the function of realizing any complex nonlinear mapping. A three-layer BP neural network can realize arbitrary nonlinear function approximation and can complete multi-sensor information fusion.

In the designed BP neural network prediction controller, the selected training function is Levenberg–Marquardt, the training algorithm is trainlm, the activation function of the hidden layer is the logarithmic sigmoid activation function logsig, and the activation function of the output layer is the linear activation function purelin. The target error of training is set as $1\times {10}^{-3}$, which is far higher than the requirement of cutting control accuracy in engineering [19], and the maximum number of iterations is set to 1000 times.

In order to determine the number of neurons in the hidden layer of the network, 500 groups of sample data are selected to train the neural network with different numbers of neurons in the hidden layer. The results of the training errors are shown in Figure 2.

It can be seen from Figure 2 that the minimum value of reaching the set target error occurs when the number of neurons in the hidden layer is 10. Therefore, the number of neurons in the hidden layer of the BP neural network is set to 10 and the training of the BP neural network is started. Then, 100 groups of samples are taken to test the network, and the training and testing results of the BP neural network are shown in Figure 3.

It can be seen from Figure 3 that the training and testing results of the BP neural network can achieve the set target, and the error decreases faster and the number of iterations is lower.

Through the BP neural network method trained by the measured data, the fusion criterion of the underground multi-sensor information and the normalized parameter of coal rock hardness is obtained, as shown in

Table 1. The normalized parameter of coal rock hardness in different cutting conditions.

Cutting Condition	Softer Media and Coal	Coal-Rock Inclusions	Full Rock Roof
Normalization parameter of coal and rock hardness	0~0.377	0.377~0.852	0.852~1

below.

According to Table 1, it can be determined that different coal rock hardness corresponds to the range of 0 to 1, and the correspondence between coal rock hardness of tunnel section and coal rock hardness normalized parameter of multi-sensor information is established. It enables the identification of the tunnel section environment.

2.2. The Cutting Head Positioning Model

The relationship between the ordinate of the cutting head in the section and the stroke of the lifting cylinder $l_1$ is shown in Formula (1).

$$Z=(L+\Delta l)\sin \left\{{\cos }^{-1}\left[\frac{L_1^2+L_2^2-{(L_0+l_1)}^2}{2L_1{L}_2}\right]-{\varphi }_0+{\theta }_0\right\}$$

(1)

where $Z$ is the ordinate of the cutting head in the section; $\Delta l$ is the elongation of the telescopic cylinder of the cutting head; $L$ is the length of the cutting arm; ${\theta }_0$ is the angle between the cutting arm and the connect of cutting arm vertical swing center and the hinge point of lifting cylinder and the cutting arm; $L_2$ is the distance between the cutting arm vertical swing center and the hinge point of lifting cylinder and the cutting arm; $L_1$ is the distance between the cutting arm vertical swing center and the hinge point of lifting cylinder and the frame; and ${\varphi }_0$ is the angle between the horizontal line and the connect of the cutting arm vertical swing center and the hinge point of lifting cylinder and the frame.

In Formula (1), only $l_1$ is a variable. According to the $l_1$ detected by the cylinder displacement sensor, the ordinate of the cutting head in the section $Z$ can be determined.

The relationship between the abscissa of the cutting head in the section and the stroke of the rotation cylinder $l_2$ is shown in Formula (2).

$$y=\left\{e+\left(L+\Delta L\right)\cos \left[{\cos }^{-1}\left[\frac{L_1^2+L_2^2-{\left(L_0+l_1\right)}^2}{2L_1{L}_2}\right]-{\phi }_0+{\theta }_0\right]\right\}·\sin \left\{{\cos }^{-1}\left[\frac{n^2+r^2-{\left(L_0^{\prime }+l_2\right)}^2}{2nr}\right]-\theta \right\}$$

(2)

where $y$ is the abscissa of the cutting head in the section; $e$ is the distance between the vertical swing center point of the cutting arm and the center of the horizontal rotary table; $r$ is the radius of the rotary table; $n$ is the distance between the center of the horizontal rotary table and the hinge point of horizontal rotation cylinder and the roadheader body; $L_0^{\prime }$ is the distance between the hinge point of rotation cylinder and the roadheader body and the hinge point of rotation cylinder and the horizontal rotary table when the cutting head is in the horizontal middle position; and $\theta$ is the angle between $n$ and $r$ when the cutting head is in the horizontal middle position.

In Formula (2), only $l_2$ is a variable. According to the $l_2$ detected by the cylinder displacement sensor, the abscissa of the cutting head in the section can be determined.

Therefore, as long as the stroke of the vertical lifting cylinder $l_1$ and the stroke of the horizontal rotation cylinder $l_2$ are detected, the specific position of the cutting head in the tunnel section can be determined, and the positioning model of the cutting head is constructed.

3. AGNG-NU

3.1. The Operating Mechanism of the Growing Neural Gas Network

The GNG algorithm is a growing SOM algorithm. It also has four stages, that are competition, collaboration, adaption and neuron growth and deletion. However, compared with the SOM algorithm, the calculation of the GNG algorithm in the collaboration and adaption stages is much simpler. The calculation of the neuron growth is also much simpler compared with the GCS algorithm. The operation mechanism of the GNG algorithm is as follows [20,21,22,23]:

(1)

Competition stage

GNG neurons compete with each other under the stimulation of the input sample $\xi ={({\xi }_x,{\xi }_y)}^T\in X$. The purpose of the competition is to find the neuron closest to the input node and identify it as the winning neuron. As shown in Formula (3), the neuron with the smallest value in Formula (3) wins.

$$\left|\right|\xi -w_i\left|\right|={\left({\xi }_x-w_{ix}\right)}^2+{\left({\xi }_y-w_{iy}\right)}^2$$

(3)

where the serial number of the winning neuron is $i(\xi )$ and its position coordinate is $w_i={(w_{ix},w_{iy})}^T\in X$.

(2)

Collaboration stage

In the collaboration stage, the neuron that wins the competition does not complete the task of constructing the topological map in isolation. Instead, it excites nearby neurons, causing them to excite together with itself, as shown in Figure 4. The domain function is usually used to determine which neurons are excited with the winning neuron, and finally complete the construction of the topological map together. The domain function of the GNG algorithm ${\theta }_{i(x),j}$ is shown in Formula (4).

$${\theta }_{{}_{i(x),j}}=\{{}_{0 j \mathrm{not} \mathrm{connected} \mathrm{to} i}^{1 j \mathrm{connected} \mathrm{to} i}$$

(4)

(3)

Adaption stage

In the adaption stage, the Hebb learning rate can be used, and the weight adjustment method of neurons is that the neurons are adjusted closer to the input node, as shown in Formulas (5)–(8).

$$\Delta w_i(t)=eb(\xi (t)-w_i(t))$$

(5)

$$w_i(t+1)=w_i(t)+\Delta w_i(t)$$

(6)

$$\Delta w_j(t)=en(\xi (t)-w_j(t))$$

(7)

$$w_j(t+1)=w_j(t)+\Delta w_j(t)$$

(8)

where $0\prec eb\prec 1$, $0\prec en\prec 1$, and $en\ll eb$.

(4)

Neuron growth and deletion stage

When the number of input samples increases to a certain value $\lambda$, a new neuron will be inserted. The process is shown in Figure 5. If there is a neuron that cannot always win or has no connected edges, the neuron will be deleted. In addition, if the age of the connecting edge reaches the set maximum age value, the connecting edge will be deleted.

The GNG algorithm completes the analysis and calculation of the input data and establishes a topological structure map after adjusting through the four stages of competition, collaboration, adaptation, and neuron growth and deletion.

3.2. Dynamic Response Deletion Mechanism

For the basic GNG algorithm, when there are non-uniform input signals, that is, the input samples are concentrated in a certain area, the age of the neurons in this area increases faster, and the probability of being deleted will also increase. For the construction of the environment map of the tunnel section, the number of input samples can also express the information of the area. The denser the samples, the slower the cutting speed of the area and the increased hardness of the coal and rock, but the neurons in the area can still be planned in the cutting trajectory and belong to the feasible area. If they are deleted directly, this unstructured environmental feature will not be expressed.

The connecting edge is used to describe the degree of closeness between two neuron nodes and has the attribute of age. The smaller the age, the closer it is. When the age exceeds the set maximum age value, it means that the connection edge has aged and needs to be deleted.

In the deletion mechanism of the basic GNG algorithm, the value of the maximum age value $max\_age$ is a fixed value. Due to the uneven relationship between the input samples, the age value of the nodes where the sample points are dense will quickly reach the maximum age value and be deleted, that is, where the samples are dense, the generated network nodes are fewer and the topology structure is sparse, which is inconsistent with the actual environment. The presented topology map is not satisfactory enough.

To this end, a dynamic response deletion mechanism is proposed, which dynamically adjusts the maximum age value according to the actual area density, that is, the number of neuron neighbor nodes. The more neighbor nodes, the denser the neurons there, then the maximum age of the node is appropriately set to increase according to the actual situation, so that the speed of the age growth reaching the maximum value in a certain traversal cycle is slowed, and finally the purpose of protecting important nodes is realized. The maximum age setting in the dynamic response deletion mechanism can be represented by Formula (9).

$$max\_ag{e}_i=max\_age\times {\gamma }^{N_i}$$

(9)

where $\gamma$ is adjustment parameter of the maximum age, and its value is greater and close to 1, while $N_i$ is the number of neighbors connected to the $i$th neuron.

Algorithm 1 shows the connecting edge adjustment method based on the dynamic response deletion mechanism. Lines 1 to 4 show that the age value of all edges connected to the winning node is increased by 1; Lines 5 to 10 show that if there is no connecting edge between the winning node and the second closest node, it will add the connecting edge and set the age value to 0; Lines 11 to 19 show the calculation of the maximum age value according to the dynamic response deletion mechanism, and deletion of the edge that exceeds the maximum age. For non-uniform input signals, the topology formed by this method can better represent environmental information.

Algorithm 1 Connecting edge adjustment method based on dynamic response deletion mechanism

Input: connecting edge vector $edges$, connecting edge age vector $ages$, node position vector $nodes$, winning node $s_1$, second closest node $s_2$, points $s_1\_Neighbors$ connected with $s_1$ and the number of the points $Size Of Neighborhood$ Output: connecting edge vector $edges$ 1: FOR $1\le k1\le Size Of Neighbors$ DO 2:  $ages(s_1\_N(k1),s_1)=ages(s_1\_N(k1),s_1)+1$ 3:  $ages(s_1,s_1\_N(k1))=ages(s_1\_N(k1),s_1)$ 4: END FOR 5: $\mathrm{IF} edges(s_1,s_2)=0$ THEN 6:  $edges(s_1,s_2)=1$ 7:  $edges(s_2,s_1)=1$ 8:  $ages(s_1,s_2)=0$ 9:  $ages(s_2,s_1)=0$ 10: END IF 11: $\mathrm{Calculate} max\_ag{e}_{s_1}$ according to Formula (9) 12: $\mathrm{FOR} 1\le k1\le Size Of Neighbors$ DO 13:  $\mathrm{IF} ages(s_1,s_1\_N(k1))>max\_ag{e}_{s_1}$ THEN 14:  $edges(s_1,s_1\_N(k1))=0$ 15:  $edges(s_1\_N(k1),s_1)=0$ 16:  $ages(s_1,s_1\_N(k1))=\mathrm{NaN}$ 17:  $ages(s_1\_N(k1),s_1)=\mathrm{NaN}$ 18:  END IF 19: END FOR 20: $\mathrm{RETURN} edges$

3.3. Adaptive Adjustment Mechanism of Neuron Parameters

As the parameters $eb$ and $en$ for adjusting the position of the neuron node are fixed values, they cannot be adjusted quickly and reasonably with the positional relationship of the input samples. Therefore, an adaptive adjustment mechanism of neuron parameters is proposed to make the node position more suitable for the environment input description so as to form a more reasonable topology between nodes.

The degree of parameter dynamic adjustment is related to the cyclic adjustment mean, that is, the sum of the squares of the position differences between the winning node and its neighbors to the actual input sample divided by the total number of nodes. The cyclic adjustment mean value can be determined by Formula (10).

$$L_{average}=\frac{{\displaystyle \sum _{i=1}^{Size of Neighborhood}{\Vert S_1\_Neighbors(i)-\xi \Vert }^2}+{\Vert S_1\_nodes-\xi \Vert }^2}{Size of Neighborhood+1}$$

(10)

where $Size of Neighborhood$ represents the number of nodes with the edge connected to the winning neuron, $S_1\_Neighbors(i)$ represents the $i$th neuron connected to the winning neuron, $S_1\_nodes$ represents the winning neuron node, and $\xi$ is the actual input sample point.

In the stage of adaptive adjustment of neuron parameters, the value of the parameter $e{b}_i$ which used to adjust the winning neuron to move to the actual input sample is determined by the ratio of the position distance between the winning node and the actual input sample point to the cyclic adjustment mean, as shown in Formula (11); the parameter $e{n}_j$, used to adjust neighbor nodes to move to the actual input sample, is determined by the ratio of the distance between the neighbor nodes to the actual input sample to the cyclic adjustment mean, as shown in Formula (12).

$$e{b}_i=eb\times {\alpha }^{\frac{{\Vert w_i-\xi \Vert }^2}{L_{average}}}$$

(11)

where $\alpha$ is the adjustment parameter of the winning node, and the value is around 1; $w_i$ is the $i$th winning neuron node.

$$e{n}_j=en\times {\beta }^{\frac{{\Vert w_j-\xi \Vert }^2}{L_{average}}}$$

(12)

where $\beta$ is the adjustment parameter of the neighbor node, and the value is around 1; $w_j$ is the $j$th neighbor node connected to the $i$th winning neuron.

Algorithm 2 demonstrates the neuron coordination and adjustment method based on the adaptive adjustment mechanism of neuron parameters. Lines 1 to 3 show finding the two closest points to the input node and all nodes connected to the winning node, reflecting the coordination mechanism of neurons; lines 4 to 10 show neuron adaptive adjustment method so that the winning node and its topological neighbors adaptively move towards the environment input sample point.

Algorithm 2 Neuron coordination and adjustment method based on the adaptive adjustment mechanism of neuron parameters

Input: input signal $\xi (t)$ at time $t$, node position vector $nodes$, winning node $s_1$, points $s_1\_Neighbors$ connected with $s_1$ and the number of the points $Size Of Neighborhood$ Output: node position vector $nodes$ 1: $\mathrm{Calculate} L_{\mathrm{average}}$ according to Formula (10) 2: $\mathrm{Calculate} e{b}_{S_1}(t)$ according to Formula (11) 3: Update coordinates of node $s_1$$\mathrm{to} nodes(s_1)=nodes(s_1)+e{b}_{S_1}(t)(\xi (t)-nodes(s_1))$ 4: $\mathrm{FOR} 1\le k2\le Size Of Neighbors$ DO 5:  $\mathrm{Calculate} e{n}_{S_{1k}}(t)$ according to Formula (12) 6:  $\mathrm{Update} \mathrm{coordinates} \mathrm{of} \mathrm{nodes} s_1\_Neighbors(k)$ to     $nodes(s_1\_N(k2))=nodes(s_1\_N(k2))+e{n}_{S_{1k}}(t)(\xi (t)-nodes(s_1\_N(k2)))$ 7: END FOR 8: $\mathrm{RETURN} nodes$

3.4. Implementation of AGNG-NU

AGNG-NU adopts the dynamic response deletion mechanism, which dynamically sets the maximum age value of different regions according to the density of the input environment in order to solve the defect of mistaken deletion of effective nodes in dense regions. Then, it also adopts the adaptive adjustment mechanism of neuron parameters, so that location weight parameters can be dynamically and adaptively adjusted according to the non-uniform input environment. Finally, with the links of competition, coordination and neuron growth, the construction of the topology map in the non-uniform input environment is realized.

Algorithm 3 shows the AGNG-NU method. Line 1 shows the initialization of the algorithm; lines 2 to 20 show the iterative process of the algorithm, of which lines 3 to 5 show the competition stage, where the closest winning node, the second closest node, and the node connected to the winning node are picked out. Lines 6 to 8 show the coordination, neuron weight adjustment, and deletion stages, in which the winning node and connecting edges are adjusted to make it more approaching the input information. Lines 9 to 19 show the neuron growth stage; when the cycle reaches a certain number of times, a new node is added, which reflects the dynamic growth and adaptation of the topology structure with the increase in input signals.

Algorithm 3 AGNG-NU method

Input: input signal $\xi$, $\mathrm{node} \mathrm{position} \mathrm{vector} nodes$$, \mathrm{connecting} \mathrm{edge} \mathrm{vector} edges$ Output: node position vector $nodes$, $\mathrm{connecting} \mathrm{edge} \mathrm{vector} edges$ 1: Initialize the node position vector, arbitrarily select two neural units $a \mathrm{and} b$, and randomly set the position coordinates $w_a$ and $w_b$ in the space $R^2$, while parameters of other neurons are 0. 2: FOR number of iterations $kk$, $1\le kk\le Num Of Epochs$ DO 3:  Calculate the distance $distances$ between each node in $nodes$ and the input signal $\xi (t)$ 4:  Find the closest neuron node $s_1$ (marked as the winning point) and the second closest point $s_2$ 5:  Find all points $s_1\_Neighbors$ that are connected to $s_1$ in $edges$, and the number is $Size Of Neighborhood$ 6:  Invoke Algorithm 1 to adjust connecting edges of $s_1$$, s_2$ and $s_1\_Neighbors$ 7:  Invoke Algorithm 2 to adjust node positions of $s_1$ and $s_1\_Neighbors$ 8:  Calculate error of $s_1$ $error(s_1)=error(s_1)+{\Vert \xi (t)-nodes(s_1)\Vert }^2$ 9:  $\mathrm{IF} \mathrm{mod}(kk,\lambda )=0$$\mathrm{AND} \mathrm{size}(nodes)<max\_nodes$ THEN 10:  Find the neuron $m$ with the largest error, and its error is $q$; find the neuron $n$ with the largest error in the neurons connected to $m$, and its error is $f$ 11:  Insert a new neuron $s$ $nodes(s)=(nodes(m)+nodes(n))/2$ 12:  $edges(m,n)=edges(n,m)=0$ 13:  $edges(m,s)=edges(s,m)=1$ 14:  $edges(s,n)=edges(n,s)=1$ 15:  $error(m)=\mu \times q$, $error(n)=\mu \times f$, $error(s)=0.5\times (error(m)+error(n))$ 16:  $\mathrm{FOR} 1\le k3\le Num Of Nodes$ DO 17:  $error(k3)=\mu \times error(k3)$ 18:  END FOR 19: END IF 20: END FOR 21: $\mathrm{RETURN}$$nodes,edges$

Compared with traditional algorithms, AGNG-NU can solve the problems of inaccurate topology structure, excessive aging of connecting edges, and excessive deletion of nodes in non-uniform input environment. A dynamic response deletion mechanism is proposed, and the maximum age value is dynamically adjusted according to the density of regional sample points. The generated nodes and their topology can meet the needs of environment description. Meanwhile, an adaptive adjustment mechanism of neuron parameters is proposed to make the node position more suitable for the described feasible area. AGNG-NU can dynamically update and adaptively adjust the topology structure with the input of environmental information, better describe the unstructured characteristics of the environment, and construct an environmental topology map, which is suitable to be applied to the problem of dynamic optimization and decision making based on the environment.

4. Simulation Experiments

In order to verify the effectiveness of AGNG-NU in solving the problem of map construction under such non-uniform input environments, the evaluation indicators are proposed, relevant verification experiments are carried out, and the method is also applied to the construction of the roadheader cutting map.

4.1. Evaluative Indicators

In the construction of environmental maps, most algorithms are tested based on uniform and randomly distributed input samples. However, in practice, the input sample points in most environments are not uniform, especially for the tunneling section; the density of different sample points can reflect the current state of cutting coal and rock. The dense samples collected indicate that hard points are encountered, and the swing speed of the cutting arm decreases. On the contrary, the sparseness of the collection points indicates that the coal rock has low hardness and is easily cut, and the swing speed of the cutting arm is high.

In the process of collecting sample points, this kind of non-uniform distribution will be encountered, that is, the environment is unstructured. However, there is no relevant literature that proposes an evaluation index for map construction under non-uniform input environment [8,24]. Therefore, the evaluation method of map construction is proposed in this paper which is analyzed from the aspects of accuracy and distribution.

(1)

Accuracy

The accuracy indicator is used to measure the closeness of the current network node to the actual input parameters, and it is evaluated by the mean error of the network. The smaller the mean error value, the higher the accuracy of the generated topology network. The calculation formula of accuracy is shown in Formula (13).

$$RMSE=\frac{\Vert error\Vert }{\sqrt{Num of Nodes}}$$

(13)

where $RMSE$ is the mean error, $error$ is the error vector composed by errors of each neuron node, and $Num of Nodes$ is the number of network neuron nodes.

(2)

Distribution

The distribution index is used to evaluate the distribution of the generated network nodes. The denser the environment input is, the more network nodes should be described and the richer the topology structure. Two calculation methods are designed for the distribution index:

(1) The ratio of the number of connected nodes of each winning neuron node to the total number of points is subtracted from the ratio of the number of input nodes in this area to the total number of input points, and the distribution index is obtained by summing and averaging. The smaller the value, the better the distribution, as shown in Formula (14).

$$Dis{t}_1=\frac{{\displaystyle \sum \left|\frac{Size of Neighborhood}{max\_nodes}-\frac{Size of Neighborhood samples}{Num of Samples}\right|}}{max\_nodes}$$

(14)

where $Size of Neighborhood$ is the number of connected neuron neighbor nodes of the winning neuron node, $Size of Neighborhood samples$ is the number of input samples in the region, $\max \_nodes$ is the total number of neuron nodes, and $Num of Samples$ is the total number of input samples.

(2) Divide the overall area into several blocks, calculate the ratio of the number of neuron nodes in this area to its total number, minus the ratio of the number of input nodes in this area to its total number for each block, and the distribution index is obtained by taking the average of the sum. The smaller the value, the better the distribution, as shown in Formula (15).

$$Dis{t}_2=\frac{{\displaystyle \sum \left|\frac{Size of block nodes}{max\_nodes}-\frac{Size of block samples}{Num of Samples}\right|}}{max\_block}$$

(15)

where $Size of block nodes$ is the number of neuron nodes in the divided area, $Size of block samples$ is the number of input samples in the divided area, $max\_nodes$ is the maximum number of neuron nodes, $Num of Samples$ is the number of input samples, and $max\_block$ is the number of divided areas.

4.2. Compared with the Basic GNG Algorithm

In order to verify the effectiveness of the proposed AGNG-NU algorithm and its advantages in the non-uniform input environment, a large number of simulation experiments has been carried out on the Matlab platform with the construction of the tunnel section as the background, which was compared with the basic GNG algorithm. The initial parameters of the simulation are set as follows: the number of loop traversals $Num of Epochs=100$, the total number of sample inputs $Num of Samples=1000$, the maximum age value $max\_age=140$, the maximum number of nodes $max\_nodes=200$, and the weight adjustment parameters $eb=0.085$, $en=0.0045$.

The input signal $\xi ({\xi }_x,{\xi }_y,{\xi }_e)$ is the three parameters obtained by the environment identification model of tunnel section, namely ${\xi }_x$ is the ordinate of the cutting head in the section, ${\xi }_y$ is the abscissa of the cutting head in the section, and ${\xi }_e$ is the environment normalization parameter.

In the simulation experiment, the special situation of the existence of obstacles such as dirt band in the environment is considered to form a non-uniform input signal environment. The experimental scene settings are described as follows:

(1)

As shown in Figure 6, the obstacles are set on both sides of the vertical symmetry axis of the topology map distribution and are symmetrical about the vertical symmetry axis.

(2)

The contrast area of the graphic distribution is the left, middle, and right parts, and the two separated parts remain the same without modification.

(3)

Table 2. Experimental environment scale setting table.

Experimental Scene	The Ratio of the Number of Input Points on Left, Middle, and Right Part
1	1:1:1
2	1:3:5
3	5:3:1
4	2:2:5
5	2:5:2
6	1:1:7
7	16:1:1

is the experimental environment scale setting table for seven input points with different distribution ratios.

By changing the distribution of input sample points, the simulation results of taking the average value of 10 experiments are shown in Figure 7, which are seven groups of simulation experiment results, among which (a), (c), (e), (g), (i), (k) and (m) are the topology diagrams obtained by the basic GNG algorithm under the experimental setting conditions, and (b), (d), (f), (h), (j), (l) and (n) are the AGNG-NU simulation diagrams.

It can be seen from the simulation diagrams that in experiment 1, where the input sample points are uniformly distributed, the connecting edges of the GNG algorithm is not as good as that of the AGNG-NU algorithm, but the difference is not obvious enough. However, in experiments 2 to 7, where the input sample points are non-uniformly distributed, the GNG experiments simulation results show more broken lines and large blank areas, while the results of AGNG-NU show that in the area with dense input signals, the more neuron nodes are described, the more abundant the connecting edges between nodes, and the clearer the environmental information expression.

For the evaluation indicators, the distribution data obtained by the basic GNG algorithm and AGNG-NU are shown in

Table 3. Experiment data of distribution indicator.

Experimental Scene	Distribution by Basic GNG	Distribution by AGNG-NU
1	0.00842	0.00790
2	0.03432	0.02921
3	0.03442	0.02924
4	0.03197	0.03087
5	0.03428	0.03087
6	0.05977	0.05689
7	0.07310	0.06667

, and the accuracy data are shown in

Table 4. Experiment data of accuracy indicator.

Experimental Scene	Accuracy by Basic GNG	Accuracy by AGNG-NU
1	0.00652	0.00618
2	0.00606	0.00587
3	0.00630	0.00577
4	0.00649	0.00607
5	0.00601	0.00586
6	0.00606	0.00574
7	0.00535	0.00492

.

It can be seen from Table 3 that, under all experimental settings, the distribution indicator obtained by AGNG-NU is better, and compared with the GNG algorithm, the distribution indicator can be increased by up to 15%. Table 4 shows that the accuracy indicator obtained by AGNG-NU is better, which can be improved by up to 8%. From the comprehensive topological diagrams and evaluation indicators, it can be concluded that the map constructed by AGNG-NU achieves better results than GNG algorithm.

4.3. Compared with Other Algorithms

Experiments comparing AGNG-NU with other classical algorithms such as SOM [25] and GCS [26] are carried out, and two background images are used, one with fewer obstacles and the other with more. The parameters of the three algorithms are set thus: the number of loop traversal is 100, the maximum number of nodes is 100, the total number of input samples is 500, and the sample points are randomly generated in the non-obstacle part. The experimental results are shown in Figure 8, from which it can be clearly seen that the topology maps of GCS and GNG are significantly better than the SOM algorithm. The topological maps generated by GCS and GNG are indistinguishable from the naked eye.

The comparison of the two evaluation indicators of distribution and accuracy obtained by SOM, GCS, and AGNG-NU on map 1 and map 2 is shown in Figure 9. Accuracy1 and Distribution1 are data on map 1, while the other data are on map 2. It can be seen from the comparison histograms that AGNG-NU has the best accuracy and distribution. Compared with the SOM algorithm, the accuracy is improved by 32.31%, and the distribution is improved by 47.20%; compared with the GCS algorithm, the accuracy is improved by 5.71%, and the distribution improved by 2.76%.

SOM has two main limitations. First, the network structure and dimensionality must be determined before learning. This limits the accuracy of the resulting mapping and output. Second, the network capacity is predefined by the number of network nodes and learning parameters. This makes the network unsuitable for continuous learning or learning on non-stationary datasets. For non-uniform input environments, it is impossible to predetermine a neighborhood connectivity architecture that closely matches the data manifold structure, so SOM cannot provide a perfect topology mapping.

Compared with the SOM algorithm, GCS has a self-organizing growth stage. The number of neurons in the GCS algorithm can be increased, and the network that can add nodes in its map space can more accurately approximate the input space.

The GNG algorithm is also developed from the SOM and GCS algorithms. In comparison, it not only has the advantages of the GCS algorithm in the growth stage and the deletion mechanism to make up for the disadvantages of the SOM algorithm, but also uses the topological domain function and makes a great simplification in determining the calculation method of excited neurons. Featured by dynamic response deletion mechanism and adaptive adjustment mechanism of neuron parameters, the AGNG-NU proposed in this paper has had improvements on the basis of the basic GNG algorithm, in order to be more suitable for unstructured environment.

Therefore, from the comprehensive topology maps and evaluation indicators, it can be concluded that AGNG-NU has better topology map generation performance.

4.4. Construction and Application of Environmental Map of Tunnel Section

The real-time generation and optimization of the tunneling section trajectory in the unstructured environment is the key common problem to be solved as soon as possible to ensure the quality of the section forming and the tunneling operation. The excavation operation scene is shown in Figure 10. Firstly, according to the actual working conditions of roadway construction and the established environmental identification model, real-time environment information of the tunnel section on the excavation operation can be obtained. Secondly, aiming at high efficiency and strong safety, a multi-objective optimization model of cutting trajectory based on topology structure is established, which reasonably integrates the dynamic environment topology map and multi-objective optimization to realize real-time generation and optimization of tunnel section trajectory in an unstructured environment. The construction of the tunnel section environment map is an important prerequisite for the planning of the tunnel section trajectory. The construction of the section environment map based on the AGNG-NU algorithm can improve the quality, real-time, and applicability of the tunnelling section trajectory planning, and achieve efficient and safe tunnelling goals.

Figure 11 shows the simulation diagrams of cutting and forming trajectory planning based on section environment topology. In Figure 11, the red retangles are the obstacles that cannot be cut, the red and green lines are the planned trajectories and the red one is the optimal trajectory. The experimental steps are as follows: (1) Based on the unstructured section environment identification model, the cutting motor voltage, cutting motor current, driving cylinder pressure, cutting arm vibration acceleration, the strokes of the lifting cylinder, and rotation cylinder are collected by sensors to obtain the normalized environmental information parameter and the horizontal and vertical coordinates of the collection point position. (2) Based on the AGNG-NU algorithm, using the obtained parameters as the input signals, the cross-section environment topology maps are constructed under the scenes of different cross-section shapes and dirt band positions. (3) Multiple optimal trajectory sets that meet the efficiency and safety conditions are obtained through multi-objective optimization (the red and green trajectories in the diagrams) [27]. (4) Considering the environmental topology of the section, the special requirements of cutting, and the characteristics of automatic control of large-mass bodies, the decision is made to obtain the red trajectory as the optimal trajectory for section forming. It should be pointed out that, in addition to the dirt band area, if the topology structure is adopted, the trajectory will have lots of small fluctuations, the change of which is negligible compared with the diameter of the cutting head and is within the controllable error range. Therefore, the traditional cutting method is still used. Based on this, a relatively close horizontal or vertical trajectory is planned according to the position of each node.

5. Conclusions

In view of the complex excavation conditions and unstructured cross-section environment disturbed by unsteady factors, in order to realize the robotized operation of coal mine underground tunneling and form a cross-section environment map that can accurately describe the environment and facilitate trajectory planning and decision making in real time, the environment identification model of tunnel section is established. Based on multi-sensor information and a large amount of underground measured data training, the load identification method is proposed to identify the type of coal rock hardness inside the section, whether it changes, and the degree of change. At the same time, the positioning model of the cutting head is used to identify the position of the internal environment change in the section in real time. Finally, it realizes the overall knowledge extraction and parametric characterization of the unstructured environment.

In order to better express environmental information, the AGNG-NU algorithm, which featured a dynamic response deletion mechanism and adaptive adjustment mechanism of neuron parameters, is proposed to solve the problems of inaccurate topology, excessive aging of connecting edges, and excessive deletion of nodes in non-uniform input environment. Moreover, a set of evaluation system for GNG map construction method under non-uniform input environment is proposed, and two evaluation indicators of accuracy and distribution are designed.

It is verified by simulation experiments that the topology map established by AGNG-NU achieves good results in a non-uniform input environment. In the area where the input signal is denser, more nodes are described, the connection lines between nodes are more abundant, and environmental information is clearer. Compared with the basic GNG algorithm, the accuracy is improved by 8%, and the distribution is improved by 15%; compared with other common SOM and GCS algorithms, the accuracy and distribution are also significantly improved. The AGNG-NU algorithm is used to construct the section environment map of the actual tunneling scene, and it is applied to the trajectory planning of the tunnel section in the unstructured environment, and the optimal trajectory suitable for cutting is obtained. The proposed AGNG-NU can adaptively adjust the topology structure with the input of environmental information, better describe the unstructured characteristics of the environment, and build an environmental topology map, which is suitable for solving similar problems of dynamic optimization and decision making based on the environment.

Non-uniform input environments are extremely important for the construction of robot environment maps. These can abstract environmental information as a data input source, respond to environmental input through the autonomous growth of neurons, establish connections with existing neurons in the network, build environmental topological maps, and carry out path planning. In the future, it will be considered that the algorithm can be further optimized from a multi-angle and multi-level representation of environmental information, and the rapid dynamic update of the map and the early warning of environmental hazard information will also be the focus of future research.