=Paper=
{{Paper
|id=Vol-3126/paper41
|storemode=property
|title=Fuzzy logic in control systems for potentially explosive objects
|pdfUrl=https://ceur-ws.org/Vol-3126/paper41.pdf
|volume=Vol-3126
|authors=Victor Volkov,Natalia Makoyed
}}
==Fuzzy logic in control systems for potentially explosive objects==
https://ceur-ws.org/Vol-3126/paper41.pdf
Fuzzy Logic in Control Systems for Potentially Explosive Objects
Victor Volkov1, Natalia Makoyed2
1
Odessa I.I.Mechnikov National University, Dvoryanskaya str.,2, Odessa, 65082, Ukraine
2
Odessa National Academy of Food Technologies, Kanatnaya str., 112, Odessa, 65039, Ukraine
Abstract
Main principles of the decision-making on hazards of industrial explosions are formulated.
Classical mathematical models often are not applicable for the decision-making on hazards of
industrial explosions, because explosive objects in most cases are very complicated systems.
The model of decision-making under risk, that is based on the probability theory and the
probability logic, is not effective also. Thus application of the model of decision-making under
uncertainty, that is based on the fuzzy-set theory and fuzzy logic, is preferable for complicated
industrial and transport potentially explosive objects. Application of the fuzzy logic is the first
basic principle of the decision-making on hazards of industrial explosions. But fuzzy logic in
this case has to be used in combination with the exact mathematical theory of combustions
and explosions combined with correct application of experimental data. That is the second
basic principle of the decision-making on hazards of industrial explosions. This approach
provides an opportunity to avoid involvement of evaluators (experts) and thus to avoid all
problems connected with evaluators and their interaction and cooperation with decision-
makers. Mathematical model for decision-making in decision support systems (DSS) for
automated control of potentially explosive objects is developed. This model is based on
combination of the fuzzy logic and classical mathematical methods from the mathematical
theory of combustions and explosions (primarily the theory of stability of combustion and
detonation waves). That makes it possible to create an adequate mathematical support for the
mentioned above DSS. Suitable DSS is developed for the enterprises of the grain storing and
processing, which are explosive objects.
Keywords 1
Decision-making, uncertainty, fuzzy logic, mathematical model, fuzzy logic, explosion,
explosive object, combustion, detonation
1. Introduction Nowadays the progress in computing
machinery and telecommunicational equipment
enlarged greatly the human potentialities in
The explosion prevention is one of the most
sphere of making of the high-quality decisions
topical and most difficult problems of the present-
for solving different problems. It concerns also the
day industry and up-to-date transport. There are
problems of hazards, prevention and mitigation of
lots of reasons for such state of affairs. Among
industrial and transport explosions.
these reasons there are the complications of
The basic idea of the present-day organization
technological processes, the emergence of new
of explosion protection is to prevent the
combustible materials and explosives, the
occurrence of accidental fires [2-4]. Naturally, if
chemicalization of industry, etc. But one of the
a fire does not occur, then an explosion is
main reasons is the insufficient efficiency of
impossible. Therefore, in the process of solving
automatic and automated systems for preventing
the fire safety problem, the problem of explosion
and suppressing explosions [1].
safety is simultaneously fully solved. Thus, the
ISIT 2021: II International Scientific and Practical Conference
«Intellectual Systems and Information Technologies», September
13–19, 2021, Odesa, Ukraine
EMAIL: viktor@te.net.ua (A.1); natamakoyed@gmail.com (A.2)
ORCID:0000-0002-3990-8126(A.1); 0000-0002-4591-555X(A.2)
©️ 2021 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
problem of explosion safety is not solved as a resources and time. Therefore such numerical
separate problem, but only within the fire safety simulations cannot be used for DSS in automated
problem. Thereby modern automated control control systems for explosive objects, because the
systems for explosive objects are aimed at the time for decision making is strictly limited.
prevention or suppression of accidental fires and Analytical criteria [1, 12] for the flame instability
spontaneous combustion [3-5]. But this approach are also only very rough estimates [1, 17].
has at least two significant drawbacks: Finding of the explosion induction distance
For a relatively low probability of makes it possible to answer the question about the
ignition, the possibility of an explosion in the possibility of the combustion-to-explosion
case of fire may be great [1,2,6]; this is true transition for almost all kinds of channels and
first of all for enterprises where explosive dust- tubes [1], which simulate a variety of potentially
air mixtures are formed during the production explosive and detonative objects [1, 18].
process [6,7], as well as for coal mines [6,8,9]; Algebraic formulae for estimations of the
It is not always possible to detect and explosive induction distance and the time of the
suppress a fire on time [4, 7, 10]. combustion-to-explosion transition are obtained
So for lots of enterprises and for many kinds of analytically [1] and are in good agreement with
equipment the fire safety problem sometimes some experimental data. The comparative
can’t be solved properly, i.e. it is impossible to simplicity of the formulas obtained makes it
guarantee almost complete absence of fires. This possible to evaluate the possibilities and time of
is critical if there is a danger of explosion. the transition from combustion to explosion
These cases have to be specifically diagnosed, without significant expenditure of the
because the damages and personnel casualties computational time and computer resources. This
from explosions are much greater than from fires. is important for on-line control of potentially
In such cases it’s necessary to have additional explosive objects and makes such control less
safety “mechanism” to prevent explosions. One of expansive [1, 17]. But analytical estimations of
the main parts of such mechanism should be a the explosive induction distance are still too
decision support system (DSS) for the decision- inaccurate because of wall roughness and
making on the explosion safety problems. obstacles in channels and tubes. These roughness
The main theoretical problems for this and obstacles significantly reduce explosion
decision-making are: induction distance Xs and the time of the shock
1. Problem of the flame stability. wave formation (i.e. the time of the explosion
2. Finding of the explosion induction induction) τ [1, 10, 17].
distance. Finding the time of the explosion induction is
3. Finding the time of the explosion closely related to finding of the explosion
induction. induction distance. Solving of this problem helps
Solving of the flame stability problem allows to decide, what measures can be taken to prevent
to answer the question about the possibility of the an explosion timely or to minimize the possible
combustion-to-explosion transition in principle. consequences of an explosion.
Only instable flames accelerate and generate Although a simple mathematical model of the
shock or detonation waves [11]. This problem is transition of combustion to explosion is
solved analytically [1, 12] and numerically [10, constructed [1, 10] and this model is simple (for
13]. The scientific studies [10, 13] are done first calculations) and universal (it is applicable to the
of all in connection with deflagration-to- combustion of both homogeneous gas mixtures
detonation transition [10] and are based on and heterogeneous media, i.e. dust-air mixtures,
numerical simulations of premixed gas aerosols, sprays, etc.), it cannot be used directly in
combustion. But these numerical simulations are DSS for the decision-making on the explosion
always connected with finite perturbations, while safety problems. That is because of roughness and
stability of flames should be researched in relation inaccuracy of results, obtained by using this
to small perturbations (Darrieus-Landau model [1, 10, 17, 18], based on classical
instability). Besides, deflagration explosions are mathematical methods and rather primitive
more frequent than detonations, though physical models.
detonations are more dangerous and destructive. The aim of the present research is the
In addition, numerical simulations of the flame development of a mathematical model that is
stability [14] and deflagration-to-detonation based on fuzzy logic and makes it possible to
transition [13,15,16] require significant computer create an adequate mathematical support for DSS
of automated control systems for explosive
objects.
making uses uncertain estimates of evaluators
2. Main principles and mathematical (experts), based on their theoretical knowledges,
practical experiences, their intuition and so on.
modeling of the decision-making Due to the large number of considerations
on hazards of industrial explosions involved in many decisions, computer-based DSS
can be developed to assist decision makers in
As shown above classical models for the considering the implications of various courses of
decision-making [19] on hazards of industrial thinking. This may help to reduce the risk of
explosions often are not applicable. different human errors.
Taking into account the foregoing, it’s
necessary to offer effective methodology for
2.1. Main principles constructing intellectual, universal enough DSS
using the model of decision-making under
Thus for the constructing of DSS on the uncertainty (i.e. under conditions of “fuzziness”)
explosion-proof problems it is possible to use on the explosion-proof problems. But fuzzy logic
only two kinds of mathematical models: in such DSS must be used in combination with the
The model of decision-making under risk. exact mathematical theory of combustions and
The model of decision-making under explosions combined with correct application of
uncertainty. experimental data (accounting sometimes on the
The model of decision-making under risk is “fuzziness” of those data). That is the second
based on the probability theory and the probability basic principle of the decision-making on hazards
logic. of industrial explosions.
The model of decision-making under This approach provides an opportunity to
uncertainty is based on the fuzzy-set theory and avoid involvement of evaluators and to avoid all
fuzzy logic. problems connected with evaluators and their
It is proved that application of the latter model interaction and cooperation with decision-makers
is preferable for complicated industrial and [21, 22].
transport systems [1, 17].
Thus application of the fuzzy logic is the first 2.2. Main principles
basic principle of the decision-making on hazards
of industrial explosions.
As a matter of fact a lot of parameters, which The basis for decision-making on hazards of
are essential for the first model of decision- industrial explosions must use fuzzy estimates for
making, are determined under the statistics such parameters as combustibility of medium, its
processing. But statistics for the explosive ability for detonation, possibility of initiation (by
processes are absent or very imperfect in many different ways) of combustion or detonation,
cases. Moreover, these statistics sometimes are possibility of transition of “slow” burning to
also fuzzy in a way. And though it is always explosive deflagration or even detonation and so
possible to make the probability graph for on. These estimates afford grounds for making
conversions from the explosion-proof state to the decisions on prevention or mitigation of
dangerously/highly explosive one and to build up explosions. Some of those decisions should be
the probability matrix for such conversions, the implemented at the stage of projecting of the
efficiency of this methodology does not look potentially explosive object, the others allow for
high. the possibility of taking operative actions such as
Decision-making under uncertainty should be the inhibitor injection, pressure relief, use of
implemented if all possible states of object flame arresters and protective partitions, etc.
(nature, medium) are known, but their probability Let us consider the fuzzy estimate of the
distribution is not known [19]. Decision-making explosive ability of media.
under uncertainty leads to robust, quasi-rational Data base of the detonation concentration
decision, that means making the best possible limits and of the deflagration concentration limits
choice when information is incomplete. is created. For the estimation of the explosive
Theoretical base for such decisions is fuzzy-set ability a decision maker has to indicate fuel,
theory and fuzzy logic [20]. This kind of decision- oxidizer (if any), fuel concentration, geometrical
form (round tube, flat duct, etc.) for mixture or d
other explosive medium and geometrical sizes, 0 d d cr
physical parameters (first of all initial pressure D d cr (3)
1d d
and initial temperature) of explosive or mixture. cr
The explosive ability of such system is Value of dcr is less than the fire cell size or the
expressed by fuzzy logical variable (fuzzy detonation cell size [10,11]. These sizes are
statement) FA, which is the conjunction of three determined analytically [1, 12] or experimentally
fuzzy statements, namely: [10, 11].
Fuzzy logical variable FC, expressing
maintenance of the explosion concentration μC
limits (the combustion concentration limits
and the detonation concentration limits).
1
Fuzzy logical variable FD, expressing
maintenance of the absence for the explosion
suppressing distance.
Fuzzy logical variable FP, expressing
exceeding of the initial pressure over the
critical one.
That is
FA = FC & FD & FP (1) 0
LCEL UCEL 100 C
Universal set (basic set, basic scale) for fuzzy
logical variable FC is set of values for the fuel Figure 1: The characteristic function C for fuzzy
volumetric concentration C , expressed by logical variable FC
percentage (0 ≤ C ≤ 100). The characteristic
function C for fuzzy logical variable FC is For PEO the value of D determines the
trapezoidal (Figure 1), expressed by formula degree of the belonging of this PEO to the fuzzy
C subset AD of the objects, which are able for
LCEL 0 C LCEL explosion by the geometry of walls. It is a fuzzy
subset of the accurate set U1 of all possible PEO
C 1LCEL C UCEL (2)
with specified fuel and oxidizer and also with
C UCEL
1 UCEL C 100 specified geometry of walls (U1 U). If D 1 ,
100 PEO may be estimated as undoubtedly able for
where LCEL is the lower concentration explosion by the geometry of walls. In the case
explosive limit, UCEL is the upper concentration D 0 , PEO is estimated as disabled for
explosive limit. These limits are determined
analytically [1, 17] or experimentally [10, 11]. explosion.
For a potentially explosive object (PEO) the
value of C defines the degree of the belonging to
μD
the fuzzy subset AC of those PEO, which are able
for explosion by the fuel concentration. It is a
1
fuzzy subset of the accurate set U of all possible
objects of this type with specified fuel and
oxidizer. If C 1 , PEO may be estimated as
undoubtedly able for explosion by the fuel
concentration. In the case C 0 , PEO is
estimated as undoubtedly disabled for explosion.
Universal set for fuzzy logical variable FD is 0
dcr d
set of values for the duct width or the tube
diameter d (d ≥ 0). The characteristic function Figure 2: The characteristic function D for
D for fuzzy logical variable FD is piecewise- fuzzy logical variable FD
linear (Figure 2), expressed by formula
Finally, universal set for fuzzy logical variable mathematical support for these mentioned above
FP is set of values for the initial pressure p. The DSS. Suitable DSS is developed by us for the
characteristic function P for fuzzy logical enterprises of the grain storing and processing.
variable FP is piecewise-linear (Figure 3),
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