Information Model for Potentially Detonative Object Anastasiya Kovalenko Viktor Volkov Educational department Department of Theoretical Mechanics Odessa National Academy of Food Technologies Odessa I.I. Mechnikov National University Odessa, Ukraine Odessa, Ukraine virgonass@gmail.com viktor@te.net.ua Abstract—Arbitrary potentially detonative object is is equal to m 1; these potentially detonative objects of the 1st considered from the point of view of the system analysis as the level are marked as PDO_1_1, PDO _1_2, ..., PDO _1_ m 1 . complex hierarchical system. The first stages of elaboration of the information model for this complex system are fulfilled: the Some of the PDO_1 (for example, PDO _1_ i 1, PDO- system is structurized, its elements are described with their _1_i 2, ..., PDO _1_i к , where1 ≤ i 1 ≤ ... ≤ ik ≤ m1 ) can also attributes and relationships, and appropriate information be divided into subsystems – potentially explosive objects of structure diagrams are composed. the 2nd level (PDO_2), which are numbered as follows: - PDO_2_ 1_i1_1, PDO_2_ 1_i1_2, ..., PDO_2_ 1_i1_ m2,1; Keywords—detonation, potentially detonative object, PDO_2_ 1_i2_1, PDO_2_ 1_i2_2, ..., PDO_2_ 1_i2_m2,2; …; elementary potentially detonative object, information model, PDO_2_ 1_ik_1, PDO_2_ 1_ik_2, ..., PDO_2_ 1_ik_m2,k. The general number of PDO_2 is equal to m2 = m2,1+ m2,2+…+ structuring m2,k. I.INTRODUCTION Some of the PDO_2 can also be divided into subsystems – potentially explosive objects of the 3rd level (PDO_3) in the Progress in computing machinery and general number of m3, and so on (Fig.1). telecommunicational equipment enlarged greatly the human potentialities in sphere of the decision making for solving different problems. It concerns also the problems of prevention and mitigation of industrial and transport explosions. The explosion prevention is one of the most topical and most difficult problems of the present-day industry and up-to-date transport. There are two kinds of explosions: deflagration explosion (sometimes called simply “explosion”) and detonation. Detonations are more devastating and less studied than deflagration explosions. It is obvious the necessity of creating special program-technical systems to prevent detonations. Such a system (the computer complex) may be the decision support system (DSS). But to construct suitable DSS it is necessary to compose general information model for potentially detonative object of arbitrary type. Constructing of such information model is the main purpose of this study. II. THE MAIN CONTENT An arbitrary potentially detonative object (PDO) can be viewed from the standpoint of system analysis as a complex system. The architecture of this system consists of some components (subsystems) and of the hierarchical relationships between these components. As a matter of fact, hierarchy is the first feature of a complex system, since only systems with a hierarchical structure can be in principle investigated [1]. The first stage for the development of an information model of every system is its structuring. The complex detonative explosive object is considered a potentially detonative object of the zero level with the number 1 (PDO_0). This object can be divided into subsystems; those Fig. 1. The general structure of the complex potentially detonative object subsystems are potentially detonative objects of the 1st level (PDO _1), each of which has its own individual The total number of sublevels in a complex potentially number n 1 (1≤ n1 ≤m1), where the general number of PDO _1 detonative object (which itself is considered an object of the Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) zero level) is not limited in principle and is largely infinite (open), b) of the finite length, half-open (closed at one determined by the developer of the information model. The end), c) finite length, closed (closed at both ends), d) finite developer, in turn, focuses on the specifics of the object and length, closed (closed at both ends). 4. Joint of two different features of the formulation of the problem of ensuring objects of type 1-3 (for example, joint of two tubes with detonation safety. The general structure of a complex different diameters or channel output in the open space). potentially detonative object is shown in Fig.1. The The choice of such potentially detonative objects as numbering of the levels is “top-down”, i.e. the lower level has elementary is due to the following considerations: a larger number. • For objects of type 1-3, mathematical models have It is quite obvious that the generalized structure of a been developed [3-7], allowing to evaluate the complex potentially detonative object can be represented by possibility of the detonation explosion developing in an oriented tree (a connected directed acyclic graph) [2] with each of such objects. a root corresponding to PDO_0. This graph (tree) can be sorted [2]; the outgoing degrees of all vertices, except the • For objects of type 4 there are investigations [5,8] for external ones (i.e., except the terminal nodes or leaves) are at estimating the possibility of the detonation transition from one object of type 1-3 to another. Object of type least 2. 4 is principally new object in comparison with the Fig. 2 shows a graph image for the structure of a complex information model of potentially explosive object [9]. potentially detonative object. The external vertices (terminal The necessity of considering such object is connected nodes) of the graph (tree) shown in Fig. 3 are vertices 2, with possibility of the detonation attenuation during 4,7,8,9,10,11,12. It is obvious that terminal vertices can be in the transition of detonation wave from tube or channel any level, except zero level. The subsystems corresponding to to open space or from tube or channel to another tube the terminal nodes of the graph in the graph representation of or channel with smaller diameter. the structure of a potentially detonative object, considered as • Any real potentially detonative object can be virtually a complex system, are the elementary components of the modeled by a composition (combination) of these system. These components are called elementary potentially elementary potentially detonative objects. detonative objects (EPDO). • Real potentially detonative objects or their components (subsystems) are easily identified as the above mentioned elementary potentially detonative objects. Any PDO is characterized by physicochemical properties (dynamic properties) and geometry of its borders (walls) (static properties). It is the type of boundary geometry that allows (as was done above) to identify and simultaneously classify EPDO. The above classification of EPDO can be considered a topological classification (as opposed to other types of classification — systemic and parametric). Thus, 10 classes are distinguished. The object of each of these 10 classes of EPDO can be a model of some element (subsystem) of a real explosive system. The details about 9 classes of types 1-3 are outlined before [9]. Note EPDO of class 2 and 3 can simulate not only channels of rectangular cross section and pipes of circular Fig. 2. Graph of the complex potentially detonative object structure cross section, respectively, but also pipes of elliptical cross section. Moreover, if the length of the major semiaxis of the According to [1], the choice of elementary components of ellipse in the section of the pipe slightly exceeds the length of the system under study is relatively arbitrary and is largely its minor axis, then the pipe can be modeled with a circular determined by the researcher himself. However, such section pipe with a radius of a circle equal to the length of the arbitrariness in the choice of the researcher is actually always major axis of the ellipse, i.e. potentially explosive class 3 limited: such a restriction is primarily dictated by the need to facility; if the length of the major semiaxis of the ellipse in have all the information required for solving the task set the section of the pipe significantly exceeds the length of its about each of the elementary components of the system – its minor semiaxis, then the pipe can be modeled with a characteristics, possible states and reactions to the effects of rectangular channel with a rectangle within which this ellipse other components of the system or external influences. In the can be inscribed, and such a channel, in turn, is modeled as case of modeling a potentially detonative object of an one of the potentially explosive objects of class 2. arbitrary nature, one of the following objects should be (to a Consider the completeness of the classification of EPDO. certain extent) considered as an EPDO (model of a real It is quite obvious that the only often-observed common object): 1. Open space; 2. Flat channel: a) infinite (unlocked), element of real PDO not covered by the 10 classes mentioned b) of the finite length, half-open (closed at one end), c) of the above is a round tube with a bend. The detonative hazard of finite length, closed (closed at both ends), d) of the finite pipes even with a smooth bend is significantly higher than for length, open (open at both ends); 3. Round cylindrical tube: a) straight pipes. A detailed consideration of this problem shows possibility of detonation [14]. Algorithms for calculating [8,10,11] that the analysis of the detonation hazard of an these estimations are described before [13, 14]. Relative object simulated by a curved circular tube, in one way or explosion hazard is fuzzy variable for estimation of the another, boils down to an analysis of the detonation hazard of possibility of explosion when ignition already takes place. an object that is simulated by a straight circular tube, i.e. one Relative detonation hazard is fuzzy variable for estimation of the PDO of class 3. But at the same time, the obtained of the possibility of detonation when ignition or deflagrative estimates of the detonation hazard are very approximate. explosion already takes place. Algorithms for calculating of these estimations are also developed before [13, 14]. So the first stage of development of the information model for real PDO is its decomposition, which must be done All kinds of EPDO are described with their attributes and by the rules described above. The indisputable advantages of with the relationships between them and with the complex such decomposition are its naturalness and the possibility of PDO. Information structure diagram [12] for complex PDO is obtaining, along with the assessment of the detonation hazard composed for general case. Information structure diagrams of a complex PDO as a whole, the explosion rating of each of for different kinds of PDO are also built in general terms. its subsystems. However, such a multi-level decomposition of PDO as a complex system is in most cases superfluous. III. CONCLUSIONS In fact, if one particularly evaluates the detonation hazard Arbitrary potentially explosive object is considered from of each technological or technical subsystem of a complex the point of view of the system analysis as the complex PDO, then this object can be considered a simple set of hierarchical system. This system is structurized, elementary EPDO. It should proceed from a simple postulate that the potentially detonative objects are indicated. All kinds of these level of the detonation ability of a complex PDO as a whole objects are described with their attributes and relationships. corresponds (equal to or not less) to the level of the Information structure diagrams are also built. detonation ability which among all the elementary potentially detonative objects this PDO contains is maximum. Then a complex PDO (PDO_0) is represented by a system with only REFERENCES one sublevel containing “equal” EPDO, denoted as EPDO_1, [1] G. 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