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Abstract

The automated search system of safe routes for output of miners from the mine during emergencies

While writing the given abstract the master's work has not been completed yet. The final date of the work completed is December, 2012. The text of master's work and materials on this topic can be received from the author or her research guide after the indicated date.

Содержание

Introduction

Coal mine - a complex production system with very dangerous operating conditions, where there are not only random variation of geological and other natural conditions, and violations of mining safety, refusal techniques, technologies and other violations of adverse events. Despite the safety precautions taken, a mining accident is inevitable. The use of computer systems and software development makes it possible to qualitatively new solutions to complex problems of mining production and documentation of all the technical services of mining enterprises.

1. Theme urgency

Mining deals with many thousands of years mankind. Ukraine's coal industry is a potentially dangerous branch of the national economy. Due to the increasing depth of the development, extension of existing mines, conveyor lines and power cable networks, with an increase in methane and energy consumption of machines and equipment the risk of accidents in coal mines is still quite high. The main objective of occupational safety in the mines in the event of an emergency is to ensure the safe exit of people on the breath of fresh air and the surface as quickly as possible. Human life is priceless, so the rescue people in case of accidents on mine production is an integral part of the coal industry.

2. Goal and tasks of the research

Purpose - determine the optimum safe route out of the miners making great length during an emergency.

Main tasks of the research:

  1. Investigation of ways to represent the workings of chasing in the form of a graph.
  2. Developing a model of emergency in the workings.
  3. Research methods for finding the optimal route out miners on the model of emergency in the workings.

3. Expected scientific innovation.

Developing a model of emergency in the mines, the development of methods for determining the optimal route, taking into account the model of an emergency.

3. The practical importance.

The developed models and analytical technology will enable the process to improve the safe evacuation of miners from the mine working great length during an emergency, that is the task of national importance.

5. The mathematical formalization.

We believe that mining production can be represented in the form of cylindrical channels with variable cross-section S (z), where z - coordinate measured along the channel axis. Without loss of generality, we assume that the fire in mine workings predvigaetsya at νn, z coordinate equal to the fire, take νnt and set the temperature of the fire T(x, y, νn, t) a given function. Heated in the hearth fire, the ventilation flow is distributed on the development of the mountain with a velocity u. On the surface of the channel there is a heat exchange with the mountain range by Newton's law. Before starting a fire air temperature and the surface rocks of the array is assumed constant - T(x, y, z, 0 ) = T0 = const и Tpor = T0.

pic1

where div and grad - divergence and gradient operators;

λ, c, ρ – thermal conductivity, heat capacity and density of the air;

α – coefficient of heat transfer of air in a channel with a surface excavation ∂Ω;

Ω – a cylindrical region with a cross-section S (z);

ƒ(x, y, t) – a monotone decreasing function of time t - ƒ (x, y, 0) = T 0;

n – unit vector outward normal to ∂Ω; [10]

6. Submission of mining.

Mine workings can be represented using a directed graph. Mining operations are conducted on a specific system and planners using planogram development of mining operations. This displays the planogram on the plans of mining operations for each stratum on which the work is underway. The development of mining operations carried out at a certain time interval (t) and in a certain place of the mineral, ie, carried out in time and space. This information is displayed on the surveying of mining plans in the form prodviganiya each generation over time.

Model of excavation on the plane is a graph (network of routes, Figure 1). The path in the graph - a sequence of vertices (without repetitions) in which any two adjacent vertices are adjacent, and each vertex is at once the end of one arc and the beginning of the next arc. Weighted graph - a graph, some elements of which (vertices, edges or arcs) compared the number of numbers - notes have different names: weight, length, value. The path length in a weighted (connected) graph - is the sum of the lengths (weights) of those edges that make up the path. The distance between the peaks - the length of the shortest path.

Necessary to determine the optimal algorithm for finding paths in the graph, which reflects the model of the excavation, taking into account the dynamics of an emergency.

Analysis of algorithms currently used to find the shortest paths between vertices of the graph revealed Warshall algorithm, Dijkstra, Ford. All algorithms are characterized by different computational results allow us to solve our problem, but the most effective is Dijkstra's algorithm [9].

pic1

Fig. 1. Model of excavation on the plane.

7. Dijkstra's algorithm.

The algorithm uses three arrays of N (= number of vertices of the network) numbers each. The first array S contains a label with two values: 0 (the top is not considered) and 1 (the top is considered), the second array B contains the distance - the shortest distance from the current to the corresponding vertex, and the third array contains the number of vertices - k - th element of C [k] is the penultimate number of vertices in the current shortest path from Vi в Vk. Distance matrix A [i, k] gives the length of the arc A [i, k]; if this arc is not, then A [i, k] is assigned to a large number of B is equal to "infinity machine"[10].

1) (initialization). In a series from 1 to N zeros to fill the array S; i fill an array of numbers C; move i - th row of the matrix A in array B, S [i]: = 1; C [i]: = 0 (i - number of starting vertices)

2) (collective pitch). Find a minimum of unmarked ( those k, for which S [k] = 0) and let the minimum is reached on the index j, B [j] <= B [k] then the following operations:

S[j]:=1;

if B[k] > B[j]+A[j, k], then ( B[k]:=B[j]+A[j, k]; C[k]:=j )

That mean, if path Vi ... Vk longer, then Vi...Vj Vk. If all S[k] noted, the length of the path from Vi to Vk is equal to B[k].

3) 3) (issue of response). The path from Vi до Vk is given in reverse order the following procedure:

3.1. z:=C[k];

3.2. To give z;

3.3. z:=C[z].If z = О, then stop, otherwise go to 3.2.

To run the algorithm N times should see an array of N elements of B, ie, Dijkstra's algorithm has quadratic complexity. This algorithm is working in weighted environments, as well as update the nodes in finding the best path for them.

There are algorithms more efficient than the procedure of repetitive Dijkstra algorithm. These algorithms belong to Floyd, and Danzig. For the problem of finding the optimal path in the mine they are somewhat inferior to Dijkstra's algorithm because it has a cubic complexity, are used when the weight of the arcs have negative values, the execution speed is lower than in Dijkstra's algorithm.

Figure 2 shows the animation of the construction of safe withdrawal of the optimal path the miners from the mine during an emergency. O shows the route the miners during an emergency, fire accident, as well as danger zones. You have selected a safe route for people to view the source area of ??the accident, as well as zagazirovanyh sites that are dangerous to the miners. The blue arrow shows the shortest path motion miners during an emergency, but this way is not safe. Green arrows laid the optimal route the output of the mine people, taking into account security and optimality.

Пример оптимального пути вывода людей из шахты во время аварийной ситуации.

Figure 2. - Example of the optimal path from the output shaft of people during an emergency.
(Animation: volume - 61 KB size - 600x368, number of frames - 12, the delay between shots - 30 ms delay between the last and first frames - 100 ms, the number of cycles of repetition - 7)

Conclusion

Based on the above can be concluded that the search of safe routes for people from the mine during an emergency arises the problem of uncertainty of the initial, intermediate and output information, solving problems of ventilation, drainage and tactical activities of the PLA. To find the optimal path is chosen Dijkstra's algorithm, as well as defining the parameters considered and the criteria for a model of emergency situations.

When looking for optimal ways of working need to be considered output suitable openings for emergency evacuation, and travel time on them, taking into account the geometric (length, cross-sectional area, the angle of inclination), process (temperature, water content, the degree of clutter technological equipment and industrial waste) and emergency (possible increase in air temperature and zagazirovanie workings fire gases) characteristics.

Need for additional methodological approaches, appropriate methodology, algorithms and software for solving these problems in order to supply it to the mine and improve problem solving with a view of determining the time factor (and not a mean value of estimated parameters and the occurrence of an emergency situation regardless of the time).

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