Моделирование эвакуации пассажиров и экипажа из воздушных судов при пожаре на земле

Полный текст

1.     Introduction

Aviation incidents involving fires on board of aircrafts are regularly recorded in Russia and worldwide [1–3]. Such incidents often result in injuries and even victims among passengers and crew members. Nevertheless, in nearly all cases, they cause substantial material damage [4].

© 2026 Baklashov, A. S., Filimonyuk, L. Y.

                               This work is licensed under a Creative Commons “Attribution-NonCommercial 4.0 International” license.

Strict guidelines exist [5] that regulate the actions of the crew and passengers during aircraft evacuation. However, these guidelines are typically applicable in certain key details only to specific aircraft types and cannot be effectively implemented in a general context [6].

At the same time, it is important to note that analysis of statistical data reveals a notable trend driven by the increasing adoption of onboard decision support systems [7]. The relative proportion of “sudden” accidents, where there is virtually no time for decision-making, has been rising over the years compared to “anticipated” accidents, which allow sufficient time for preparing the aircraft for landing and subsequent evacuation [8].

In this field of research, we cannot ignore works about crowds in confined spaces [9, 10] and their behavior dictated by people’s psychological features [11–13]. However, these works don’t take into account the features of enclosed spaces such as the cabin of the aircraft.

Both domestic and international researchers conducted studies on modeling fire dynamics in confined spaces [14–17]. However, these works are primarily useful for analyzing individual hazardous factors. Some of the models considering people’s interaction neglect the effects of physical connection and inertial forces between agents [18, 19]. This limitation can be addressed through the application of integrated model research findings [20–23], although these models, in turn, do not account for the unique characteristics of fires occurring on board of aircrafts.

This determines the relevance of research focused on developing integrated models that allow simultaneous consideration of diverse hazardous factors during emergency landings (e.g., the spread of carbon monoxide, high combustion temperatures, flooding in water landings, and others). Such models can be employed to analyze the aircraft evacuation process under various scenarios of hazardous factor spreading, thereby allowing the development of optimal action sequences for each specific situation.

1.1.      Structure of the paper

The article includes several sections, each addressing a specific aspect of the research:

The section “Theoretical Basis” defines models of spreading fire and carbon monoxide, and mathematical model of people evacuation from the plane.

The section “Results” presents the graphs obtained by application of the model in specific conditions.

The section “Discussion” summarizes the experimental findings.

The section “Conclusion” outlines the main outcomes and discusses directions for future research.

2.      Theoretical Basis

2.1.     Problem statement

The specific problem addressed in this study is the development of new models for the dynamics of fire propagation and the evacuation process of aircraft crew and passengers, taking into account their physical interactions. It also includes development of the integrated model that combines the processes of fire, smoke, and temperature spread with evacuation.

2.2.            Proposed mathematical models of the spread of fire hazards on board an aircraft

2.2.1.        Fire propagation model

We propose to use the mathematical framework of multidimensional cellular automata for describing the fire propagation process.

The aircraft, including the volume of the passenger cabin and the cockpit, is discretized into cubic cells. This yields a three-dimensional grid 𝐴 = {𝑎_𝑖𝑗𝑘 ∣ 0 ≤ 𝑖 < 𝑛, 0 ≤ 𝑗 < 𝑚, 0 ≤ 𝑘 < 𝑙}, where 𝑛, 𝑚, 𝑙 denote the number of cubes along the horizontal, vertical, and height axes, respectively; 𝑐_𝑖𝑗𝑘 represents the elementary cube (EC) at coordinates (𝑖,𝑗,𝑘). Let

• 𝐹_𝑡 be the set of ECs where combustion is occurring at the given time instant.
• 𝑉_𝑡 be the set of ECs where the material has fully burned out, preventing any further combustion.
• 𝑀_𝑡 be the set of ECs where combustion is fundamentally possible due to the presence of combustible material but has not yet initiated at time 𝑡.
• 𝑁 be the set of ECs where fire is impossible (non-combustible material).

The direction of fire propagation at time 𝑡 + 1 is governed by the ignition probability 𝑃_𝑖𝑗𝑘^𝑡 of an EC in state 𝐼_𝑡 (a state that subsequently assumes values from the aforementioned sets). The ignition probability of an EC can be determined via the expression:

                                                                   𝑃𝑖𝑗𝑘𝑡 = 𝑣𝑖𝑗𝑘𝑓𝑖𝑗𝑘𝑡  𝑑𝑡/8𝑙,                                                                                    (1)

where 𝑣_𝑖𝑗𝑘 is the fire propagation velocity of the material composing EC 𝑐_𝑖𝑗𝑘; 𝑓_𝑖𝑗𝑘^𝑡 is a parameter characterizing the state of neighboring ECs; and 𝑑𝑡 is the model time step. The parameter 𝑓_𝑖𝑗𝑘^𝑡 is calculated using the formula:

                                                           𝑓𝑖𝑗𝑘𝑡  = 3𝑞𝑡𝑖𝑗𝑘1 + 2𝑞𝑡𝑖𝑗𝑘2 + 𝑞𝑡𝑖𝑗𝑘3,

where 𝑞^𝑡_{𝑖𝑗𝑘1} is the number of ECs sharing a face with the considered EC, where combustion is occurring

at time 𝑡. Their coordinates (see Table 1): (𝑖,𝑗,𝑘 + 1), (𝑖 − 1,𝑗,𝑘), (𝑖,𝑗 − 1,𝑘), (𝑖,𝑗 + 1,𝑘), (𝑖 + 1,𝑗,𝑘),

(𝑖,𝑗,𝑘 − 1);

𝑞^𝑡_{𝑖𝑗𝑘2} is the number of ECs sharing an edge but not a face with the considered EC, where combustion is occurring at time 𝑡. Their coordinates (see Table 1): (𝑖 − 1,𝑗,𝑘 + 1), (𝑖,𝑗 − 1,𝑘 + 1), (𝑖,𝑗 + 1,𝑘 + 1),

(𝑖+1,𝑗,𝑘+1), (𝑖−1,𝑗−1,𝑘), (𝑖−1,𝑗+1,𝑘), (𝑖+1,𝑗−1,𝑘), (𝑖+1,𝑗+1,𝑘), (𝑖−1,𝑗,𝑘−1), (𝑖,𝑗−1,𝑘−1),

(𝑖,𝑗 + 1,𝑘 − 1), (𝑖 + 1,𝑗,𝑘 − 1);

𝑞^𝑡_{𝑖𝑗𝑘3} is the number of ECs sharing a vertex but neither an edge nor a face with the considered

EC, where combustion is occurring at time 𝑡. Their coordinates (see Table 1): (𝑖 − 1,𝑗 − 1,𝑘 + 1),

(𝑖 − 1,𝑗 + 1,𝑘 + 1), (𝑖 + 1,𝑗 − 1,𝑘 + 1), (𝑖 + 1,𝑗 + 1,𝑘 + 1), (𝑖 − 1,𝑗 − 1,𝑘 − 1), (𝑖 − 1,𝑗 + 1,𝑘 − 1),

(𝑖 + 1,𝑗 − 1,𝑘 − 1), (𝑖 + 1,𝑗 + 1,𝑘 − 1).

The parameter 𝑓_𝑖𝑗𝑘^𝑡                     can take one of the values 0, 1, 2, …, 50, determined according to the following principle (see Fig. 1 and Table 2).

Each non-boundary elementary cube has:

• 6 ECs sharing a common face with the considered EC, and each of these six takes the value 3.
• 12 ECs sharing a common edge but not a face with the considered EC, and each of these 12 takes the value 2.
• 8 ECs sharing a common vertex but not a face or edge with the considered EC, and each of these 8 takes the value 1.

Table 1 Coordinates of neighboring elementary cubes to the considered one

Upper row of EC			Middle row of EC		Lower row of EC
(i-1, j+1, k+1)	(i, j+1, k+1)	(i+1, j+1, k+1)	(i-1, j+1,              (i, j+1, k)           (i+1, j+1,       k)                                              k)	(i-1, j+1, k-1)	(i, j+1, k-1)	(i+1, j+1, k-1)
(i-1, j, k+1)	(i, j, k+1)	(i+1, j, k+1)	(i-1, j, k)                (i, j, k)             (i+1, j, k)	(i-1, j, k-1)	(i, j, k-1)	(i+1, j, k-1)
(i-1, j-1, k+1)	(i, j-1, k+1)	(i+1, j-1, k+1)	(i-1, j-1, k)           (i, j-1, k)           (i+1, j-1, k)	(i-1, j-1, k-1)	(i, j-1, k-1)	(i+1, j-1, k-1)

Figure 1. Graphical representation of the EC (highlighted in red) and all its neighboring elementary cubes

    𝑓_𝑖𝑗𝑘^𝑡            will be equal to the sum of the values of neighboring burning ECs.

This value is chosen based on the fact that the distance between the centers of ECs sharing a common face with the considered EC is smaller than the distance between the centers of ECs sharing a common edge. At the same time, it is still smaller than between the centers of ECs sharing a common vertex with the considered EC.

For edge ECs, the parameter 𝑓_𝑖𝑗𝑘^𝑡         can take a value from the set {0,1,2,…,35}, and for corner ones — from {0,1,2,…,24}.

The elementary cube transitions from the burning state at moment 𝑡 to the burned state at 𝑡 + 1, if no combustible mass remains in it. For each EC 𝑎_𝑖𝑗𝑘, the mass of combustible substance 𝑚_𝑖𝑗𝑘 and burning speed 𝑣_𝑖𝑗𝑘 are specified.

The mass of the combustible substance of the combustible material 𝑚_𝑖𝑗𝑘 is determined as follows:

𝑚𝑡+1𝑖𝑗𝑘 = 𝑚𝑡𝑖𝑗𝑘 − 𝑣𝑖𝑗𝑘 𝑑𝑡.

Figure 2 shows an example of fire propagation on board a twin-engine aircraft.

2.2.2.         Carbon monoxide propagation model

In the proposed model, the mass of combustible material in each burning EC changes according to the relation

𝑚𝑡+1𝑖𝑗𝑘 = 𝑚𝑡𝑖𝑗𝑘 − 𝑣𝑖𝑗𝑘 𝑑𝑡.

Table 2 Values of the terms in the parameter 𝑓_𝑖𝑗𝑘^𝑡 for neighboring elementary cubes

	Upper row of EC			Middle row of EC			Lower row of EC
1	2	1	2	3	2	1	2	1
2	3	2	3	EC	3	2	3	2
1	2	1	2	3	2	1	2	1

Figure 2. Dynamics of fire propagation on board an aircraft during an engine fire

During combustion, carbon monoxide is emitted. The volume of this emission depends on the type of material being burned. The density of carbon monoxide 𝜇_𝑖𝑗𝑘 in the elementary cube 𝑎_𝑖𝑗𝑘 increases according to the relation:

𝜇𝑡+1𝑖𝑗𝑘 = 𝜇𝑡𝑖𝑗𝑘 + 𝑈𝑖𝑗𝑘𝑣𝑖𝑗𝑘 𝑑𝑡/ℎ3,

where 𝑈_𝑖𝑗𝑘 is the CO emission coefficient of the burning material, ℎ³ is the cell volume.

The propagation of carbon monoxide is determined by the expression:

                                                     𝜇𝑡+1𝑖𝑗𝑘 = 𝜇𝑡𝑖𝑗𝑘 + 𝑑𝑖𝑗𝑘′   ),

𝑠∈𝑆𝑖𝑗𝑘′

where 𝑑_𝑖𝑗𝑘^′                          , 𝑑_𝑠^′ are coefficients regulating the rate of carbon monoxide propagation; 𝜇^𝑡_𝑠 is the density of carbon monoxide for EC.

2.3.       Mathematical model of the evacuation process of people from the aircraft

In the proposed mathematical model of the evacuation process, the following objects will be considered:

Figure 3. Model of the passenger projected onto the xOy plane

1. A finite set of obstacles in the aircraft cabin, each represented by parameters: (𝑥_𝑊,𝑦_𝑊) are the coordinates of the lower left corner, 𝑥_𝑊𝑊 and 𝑦_𝑊𝑊 — their length and width, respectively.
2. A finite set of exits from the aircraft, specified by the coordinates of the lower left corner (𝑥_𝐸,𝑦_𝐸), width and length of the opening 𝑥_𝑊𝐸 and 𝑦_𝑊𝐸. The exit zone outside of the aircraft should be located at some distance from the door opening, as after exiting the aircraft, the passenger in some cases still influences the evacuation process.
3. A finite set of evacuating passengers, which we will consider as a set of their projections onto the xOy plane in the form of circles (see Figure 3). The coordinates of these passengers are the centers of the corresponding circles.
4. A finite set of evacuation zones, each specified by parameters: (𝑥_𝑍,𝑦_𝑍) are the coordinates of the lower left corner of the evacuation zone, 𝑥_𝑊𝑍 and 𝑦_𝑊𝑍 — its length and width, respectively. It is assumed that passengers are located within these zones at the initial moment of evacuation. The parameters considered in the model for passengers (or agents in terms of multi-agent systems theory):

• vector 𝑏(𝑡), specifying the coordinates of the center of the passenger’s projection onto the xOy plane.
• 𝑟 — projection radius.
• 𝑚 — human mass.
• 𝑣(𝑡) — velocity vector of movement.
• 𝑎(𝑡) — acceleration vector of movement. – 𝑣_max — maximum possible speed.
• 𝑎_max — maximum possible acceleration.

Figure 3 shows the passenger’s projection onto the xOy plane.

In the proposed model, the law of motion for passengers is determined by the relations:

𝑏(𝑡 + 𝛥𝑡) = 𝑏(𝑡) + 𝑣(𝑡)𝛥𝑡, 𝑣(𝑡 + 𝛥𝑡) = 𝑣(𝑡) + 𝑎(𝑡)𝛥𝑡,

where 𝛥𝑡 is the model time step.

 

Passenger speeds change during collisions. We will consider collisions as partially elastic impacts. To describe a partially elastic collision, we introduce a restitution coefficient 0 ≤ 𝑅 ≤ 1. We calculate the normal components of the motion velocities to the common tangent plane to the surfaces of the colliding bodies at their contact point (collision plane) after the impact in a partially elastic impact using the formulas:

        𝑝1𝑛 = −𝑅𝑣1𝑛 + (1 + 𝑅)𝑚1𝑣1𝑛 + 𝑚2𝑣2𝑛 , 𝑝2𝑛 = −𝑅𝑣2𝑛 + (1 + 𝑅)𝑚1𝑣1𝑛 + 𝑚2𝑣2𝑛 .                                                             (2)

                                                           𝑚1 + 𝑚2                                                                              𝑚1 + 𝑚2

Here, 𝑣_1𝑛 and 𝑣_2𝑛 are the normal projections of the passengers’ motion velocities to the collision plane before the impact, and 𝑝_1𝑛 and 𝑝_2𝑛 are the normal projections of the passengers’ motion velocities to the collision plane after the impact; 𝑚₁ and 𝑚₂ are the masses of the colliding agents. We assume that the tangential projections of the velocities to the collision plane do not change during the impact.

When a passenger collides with an obstacle, the projection of their motion velocity that is in parallel to the obstacle does not change. The other projection changes its sign to the opposite and decreases its value depending on 𝑅.

Let us determine the direction of the acceleration vector 𝑎(𝑡) for each passenger, assuming that each strives to reach the nearest aircraft exit as quickly as possible. For this, let us introduce the concept of the optimal (from the passenger’s perspective) velocity vector 𝑣_opt(𝑡), approximating the passenger to the chosen exit and allowing avoidance of collisions with obstacles such as the other passengers and obstacles. Also, the actual speed and direction of the agent’s movement 𝑣(𝑡) may change due to these collisions. Then, it can be considered that passengers move with acceleration 𝑎(𝑡), whose absolute magnitude depends on physical capabilities: |𝑎(𝑡)| = 𝑎_max, and the direction matches with the direction of 𝑣_opt(𝑡) − 𝑣(𝑡). If 𝑣_opt(𝑡) = 𝑣(𝑡), it is considered that the agent moves without acceleration. The absolute magnitude of acceleration is always at its maximum value, except in the cases when the passenger is already moving with maximum speed. It can be explained by the stressful situation and the passenger’s desire to leave the aircraft as quickly as possible.

The absolute magnitude of the optimal velocity 𝑣_opt(𝑡) is bounded above by the agent’s physical capabilities, namely the speed 𝑣_max. If there are no obstacles ahead along the route, then |𝑣_opt(𝑡)| = 𝑣_max. To avoid collision with other agents along the route, the absolute magnitude |𝑣_opt(𝑡)| may decrease.

Let us consider the approach to choosing the vector 𝑣_opt(𝑡). Let 𝑤 be the vector specifying the direction to the nearest exit, accounting for the cabin layout. The vector 𝑤 is an attribute of the space cell where the agent is located and is determined by the positions of obstacles and exit zones. Let ℎ_𝛾 be the distance from the agent’s center to the nearest obstacle in the motion direction at angle 𝛾 to 𝑤, 𝐵 is the given critical distance, 𝑟 is the radius of the passenger’s projection onto the xOy plane.

Consequently, the absolute magnitude of the optimal speed 𝑣_𝛾opt(𝛾) of the passenger in the motion direction at angle 𝛾 to the vector 𝑤 can be calculated by formula:

⎧𝑣max ⎪ 𝑣𝛾opt(𝛾) =      𝑣max(ℎ𝛾−𝑟)                  ⎨         𝐵 ⎪ ⎩0

if ℎ𝛾 ≥ 𝐵 + 𝑟, if 𝑟 ≤ ℎ𝛾 ≤ 𝐵 + 𝑟, if ℎ𝛾 ≤ 𝑟.

Passengers’ physical capabilities vary, so each passenger must have individual values of 𝑣_max and

𝑎max.

Let us introduce the function 𝑔(𝛾):

                                                    𝑔(𝛾) = 𝑣_𝛾opt(𝛾) cos(𝛾),         𝛾 ∈ [−𝜋/2,𝜋/2].                                                               (3)

It can be inferred from formula (3) that the angle 𝛼 between the vectors 𝑣_opt and 𝑤 is defined as the angle at which the function 𝑔(𝛾) is maximal.

The absolute magnitude of 𝑣_opt determined as:

|𝑣opt| = 𝑣𝛾opt(𝛼).

The presented method for choosing 𝑣_opt allows the agent to maneuver between other agents, aiming to avoid collisions and approach the nearest exit faster (assuming the passenger knows where the exit is).

Thus, the choice of the optimal velocity vector 𝑣_opt accounts for the cabin layout and the positions of other agents. This vector must be recalculated for each passenger at each model time step 𝛥𝑡. Agents also exhibit additional properties such as heterogeneity due to differences in their mass and projection radius, as well as goal-directedness, since all presented passengers strive to exit the aircraft cabin.

Furthermore, we have to consider the impact of carbon monoxide spreading on the velocity of agents. This impact can be calculated by formula:

                                       𝑣max′  = ⎧𝑣max,                                                               if 𝜇𝑖𝑗𝑘 ≤ 0.1,

⎨

                                                     ⎩𝑣_max ⋅ max (0.6, 1 − 1.1 ⋅ 𝜇_𝑖𝑗𝑘),           if 𝜇_𝑖𝑗𝑘 > 0.1.

It should be noted that the presented model also includes known attributes such as the angle and range of the agent’s view of the surrounding space, moment of inertia, and head rotation angle. The direction leading the agent to the exit (considering obstacles) is determined by the vector 𝑤. The agent’s view angle can be considered equal to 180°, since 𝛾 ∈ [−𝜋/2,𝜋/2], i.e., the agent analyzes all possible alternatives for movement in the plane ahead.

Since the agent calculates the optimal speed values based on analyzing the situation within the critical zone, the agent’s view range is at least 𝐵.

Part of the energy during impact transfers to rotational motion. In the model, these energy losses are accounted for by the restitution coefficient.

2.4.      Algorithm for modeling the evacuation process

We created an algorithm for modeling emergency situations (an event of fire on the ground in our case) consisting of such steps:

1. Input initial data: cabin dimensions, coordinates of obstacles, exits from the cabin, number of agents and their parameters.
2. Generate agents inside evacuation zones according to seating positions.
3. Calculate 𝑣_opt for each agent.
4. Calculate 𝑎 for each agent.
5. Calculate 𝑣 for each agent.
6. Calculate 𝑏 for each agent.
7. Check for collisions for each pair of agents. If a collision occurs, recalculate velocities.
8. Check collisions with obstacles for each agent. If a collision occurs, recalculate velocities.
9. Check the condition for reaching the emergency exit for each agent. If the agent has reached the exit, exclude them from the list.
10. Collect and store statistics. If no passengers remain in the cabin, proceed to step 12.
11. Proceed to the next model time step. Go to step
12. Display the results of the experiments (graphs of functions).
13. Go to step 1 (upon user request).

The model is created according to this algorithm.

3.     Results

The model was built using Python 3 according to the proposed theoretical basis, the application of the mathematical apparatus of multidimensional cellular automata, and the rules of mathematical models of fire and carbon monoxide propagation. Also, a mathematical model of the evacuation of passengers was implemented.

All of the mentioned models were integrated into the program according to the algorithm suggested in Section 2.4.

The results include graphs of the dependence between the time and passengers evacuated, as well as of the dependence between the time and burned cubes.

The scenario of the model is the combustion of the left engine of an aircraft. One of the model conventions is the fact that the fire begins its propagation from the cabin (exactly from the part of the cabin in front of the left engine).

The graphs introduced for the aircraft models, such as the Embraer E-190 with 100 seats and a full load of passengers and the Airbus A320-100 with 150 seats and also a full load of passengers.

Let us introduce the common parameters of the model for Airbus A320-100 and Embraer E-190.

(see Table 3).

As we can observe, the parameters in question are primarily relevant to passengers and the general model configuration. A uniform distribution is set for the parameters that are calculated at each step of the algorithm.

Also, there are differing parameters to consider (see Table 4).

Figures 4 , 5 display the dynamic of evacuation from the aircraft and fire propagation via displaying the cubic cells that have been burned.

In comparing the scenarios for the Embraer E-190 and Airbus A320-100, it is noted that the bigger

A320, accommodating 50% more passengers and featuring a broader cabin, requires approximately 50 seconds longer for total evacuation (140 seconds against 90 seconds). Meanwhile, the fire extends to 43 additional burned cells, and the time increases to 140 seconds, illustrating how larger cabin volume and passengers’ capacity affect the model. The uniform distribution applied for parameters like 𝑣_𝑚𝑎𝑥, 𝑎_𝑚𝑎𝑥, 𝑟 and 𝑚 makes this model and the result more realistic. These findings highlight the vital role of right exits and evacuation zone locations.

4.     Discussion

The results obtained from the integrated model show that combining cellular automata for fire and carbon monoxide propagation with the dynamics of agent evacuation provides a method to predict the evacuation process from aircraft in the event of a fire on the ground.

For example, in the Embraer E-190 case (Fig. 4), 100 passengers could evacuate in about 90 seconds when only 94 cubic cells was burned. As the maximum count of burning EC is 528, and for this time only 94 of them were burned, this time is enough to evacuate all of the passengers without injuries.

Table 3 Common parameters of the E190 and A320 models

Parameter		Value	Description
Cell size		0.5 m	Size of elementary cube (EC) in meters
Time step 𝛥𝑡		0.05 s	Model time step
Restitution coefficient 𝑅		0.2	Coefficient for collision handling
Critical distance 𝐵		2.0 m	Distance for optimal velocity calculation
Initial temperature		20∘C	Initial EC temperature
Maximum agent velocity 𝑣max		1.2–1.8 m/s (uniform distribution)	Maximum speed of agents
Maximum acceleration 𝑎max		2.0–4.0 m/s2 (uniform distribution)	Maximum acceleration of agents
Reaction time	0–8 s (uniform distribution)		Delay before agent starts moving
Agent radius 𝑟	0.20–0.28 m (uniform distribution)		Radius of projection for agents
Agent mass 𝑚	50–90 kg (uniform distribution)			Mass of agents
	Differing parameters of the E190 and A320 models			Table 4
Parameter	E190 Value			A320 Value
Aircraft model	Embraer E190			Airbus A320-100
Number of passengers	100			150
Cabin length	25.0 m			27.5 m
Cabin width	2.74 m			3.70 m
Cabin height	2.0 m			2.22 m
Grid size	52 x 7 x 6			57 x 9 x 6
Engine fire position	(26, 0, 0)			(28, 0, 0)
Max. burning EC	528			682
Number of exits	4			6
Seat configuration	2+2			3+3

Figure 4. Dynamic of evacuation from the aircraft / fire propagation for Embraer E-190

Figure 5. Dynamic of evacuation from the aircraft / fire propagation for Airbus A320-100

At the same time, the Airbus A320-100 scenario (Fig. 5) took longer, around 140 seconds for 150 passengers with 137 cells affected. These results are obtained because of the larger cabin and more people involved.

The fire spread follows a smoothly growing curve due to the mechanism of neighbor influences in the automata, as does the curve of evacuation in both cases. It follows from this that physical interactions, like passenger collisions handled through restitution coefficients (Eq. (2)), and hazard progression (Eq. (1)) lead to accurate and realistic results of the model.

There are no major deviations in the graphs. The variability of the random starting conditions

(e.g., reaction times 0–8 s) confirming the model’s stability. The suggested approach stands out by its simple adaptation to aircraft specifics and could feed into real decision-support tools to cut down on casualties in the “sudden” incidents.

There is a perspective for the future work, as could be added more data for the output in the model, such as detailed temperature maps, a map of cabin and burned cubes etc. Overall, this research enhances the importance of comprehensive models for aviation safety. This research could reduce sudden accidents by generating results for different scenarios and considering them when designing aircraft.

5.     Conclusion

A complex of mathematical models and algorithms has been developed that enables the simulation of situations arising during aircraft fires, the calculation of the dynamics of hazardous fire factors, and passenger evacuation under the spread of these factors.

The integrated model of the dynamics of hazardous fire factors development and the process of evacuating passengers and crew from the aircraft is built on the basis of the mathematical apparatus of cellular automata and multi-agent systems.

It is proposed to use the integrated model for analyzing the process of leaving the aircraft, taking into account various scenarios of the spread of fire’s hazardous factors, which will allow developing optimal lists of actions for each specific situation.

Об авторах

А. С. Баклашов

Институт проблем управления им. В. А. Трапезникова Российской академии наук

Автор, ответственный за переписку.
Email: baklashov2001@mail.ru
ORCID iD: 0009-0000-9046-3225
ResearcherId: KLZ-4503-2024

Postgraduate Student of V.A. Trapeznikov Institute of Control Sciences of RAS; Junior Researcher of Laboratory of Technical Diagnostics and Fault Tolerance, V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences

ул. Профсоюзная, д. 65, Москва, 117997, Российская Федерация

Л. Ю. Филимонюк

Институт проблем управления им. В. А. Трапезникова Российской академии наук

Email: filimonyukleonid@mail.ru
ORCID iD: 0000-0002-0007-3969
Scopus Author ID: 57189024654
ResearcherId: F-2611-2017

Doctor of Technical Sciences, Leading Researcher of of Laboratory of Technical Diagnostics and Fault Tolerance

ул. Профсоюзная, д. 65, Москва, 117997, Российская Федерация

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