# Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis

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## Abstract

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## 1. Introduction

- Reliability analysis of a single drone. In this case, a drone is a system from the point of view of reliability analysis. The components of the drone are considered system components and impact its operation and reliability [5]. There are many investigations of drone components. These components can be divided into two groups. The first group comprises the hardware and mechanical components of drones, for example, the propellers [6], motors and power system [7,8,9], communication platform and sensors [8,10,11,12], and mechanical components [13]. The other group of components consists of the software used for drone mission support, for which the methods of software reliability are applied [14,15,16,17]. There is one more direction for drone reliability improvement: the development of machine-learning-based and AI-based methods to improve some of a drone’s components’ functioning [18,19,20,21,22]. However, in these studies, the proposed methods do not evaluate drone reliability directly and consider reliability as one of the positive characteristics of developed methods.
- Reliability evaluation of a drone mission. In these studies, as a rule, the problem of the fulfillment or non-fulfillment of the assigned mission by the drone is considered and this mission result is evaluated by reliability or risk. Many of the developed methods focus on the tasks of planning or optimizing the flight path [23,24,25]. However, reliability and risk are not considered according to the reliability of engineering designs. An important tendency in reliable drone missions is the application of artificially intelligent and machine learning methods in the mission’s development and support [26,27,28]. A discussion of reliability analysis methods for drone missions is in some papers: redundancy of drone components [29], maintenance [30], prognostic and health management [31], importance analysis [32], safety [33], and defense [34] analysis.
- Reliability analysis of drone swarm (fleet) or multi-UAVs. A drone swarm (in some publications it is called a “fleet”) is group of drones that implement one mission or are joined by one control center [35]. In some studies, this concept is named “multi-UAVs” [36]. From the point of view of reliability analysis, the reliability of a drone swarm is influenced by many factors such as: its structure or topology [32,37], type of redundancy [38], drone characteristics [39], heterogeneity [40], and others.

## 2. Reliability Analysis of Drone Swarm Review

- The swarm structure, which can include one fleet (drome swarm) or more than one drone fleet (multi-fleets drone swarm).
- The heterogeneous or homogenous types of swarms; in the case of homogenous drone swarms, all drones have similar characteristics and properties.
- The presence of a reserved fleet of drones in the overall structure of drone swarm.
- The number of states in swarm performance: a mathematical model of a Binary-state system (BSS) allows the representation of two states in swarm performance (failure and functioning) and a mathematical model of a Multi-state system (MSS) [43,44] allows for the investigation of degradation in swarm performance.

## 3. Structure Function-Based Approach of Reliability Analysis

#### 3.1. Structure Function

#### 3.2. Availability Defined Based on a Structure Function

#### 3.3. Importance Analysis of UAV Fleets

#### 3.4. Hand-Calculated Example

## 4. Typical Structures of Drone Swarms

- Homogenous irredundant drone swarm;
- Homogenous hot stable redundant drone swarm;
- Heterogeneous irredundant drone swarm;
- Heterogeneous hot stable redundant drone swarm.

#### 4.1. Homogenous Irredundant Drone Swarms

#### 4.2. Homogenous Hot Stable Redundant Drone Swarms

#### 4.3. Heterogeneous Irredundant Drone Swarm

_{r}is the number of drones of type r. The availability of a heterogeneous irredundant drone swarm with decentralized control (Figure 12a) ${A}_{HeID}$ according to definitions of a structure function for this swarm (32) and availability (4) is:

_{r}is the number of drones of type r; ${p}_{s}$ is the probability of the functioning of the drone $s$.

#### 4.4. Heterogeneous Hot Stable Redundant Drone Swarm

_{r}-out-of-l

_{r}system with a structure function which is similar to the structure function (21). The working state of the swarm is possible if each drone type implements a specified activity. The structure function of this type of heterogeneous drone is a series system of K components which are k

_{r}-out-of-l

_{r}systems:

_{r}-out-of-l

_{r}systems. The K fleets are an interconnected series and, in series, are connected with the CU ${x}_{n}$:

## 5. Conclusions

- Homogenous irredundant drone swarm;
- Homogenous hot stable redundant drone swarm;
- Heterogeneous irredundant drone swarm;
- Heterogeneous hot stable redundant drone swarm.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**The publications in the domain of drone swarm reliability analysis according to Scopus resources.

**Figure 3.**Drone swarm reliability characteristics according to one paper [38].

**Figure 4.**Drone swarm structural characteristics according to one paper [38].

**Figure 5.**The topologies of a homogenous irredundant drone swarm with decentralized (

**a**) and centralized (

**b**) control.

**Figure 7.**The topologies of homogenous hot stable redundant drone swarms with decentralized (

**a**) and centralized (

**b**) control.

**Figure 8.**The availability of a homogenous hot stable redundant drone swarm with decentralized control.

**Figure 9.**Comparison of the availability of homogenous hot stable redundant drone swarms with decentralized control and CU.

**Figure 10.**The SI of the drone $i$ $S{I}_{i}^{HoRC}$ (

**a**) and the CU $S{I}_{CU}^{HoRC}$ (

**b**) of a homogenous hot stable redundant drone swarm.

**Figure 11.**The BI of the drone $i$ $B{I}_{i}^{HoRC}$ (

**a**) and the CU $B{I}_{CU}^{HoRC}$ (

**b**) of a homogenous hot stable redundant drone swarm.

**Figure 12.**The topologies of heterogeneous irredundant drone swarms with decentralized (

**a**) and centralized (

**b**) control.

**Figure 14.**The topologies of a heterogeneous hot stable redundant drone swarm with decentralized (

**a**) and centralized (

**b**) control.

**Figure 15.**The availability of a heterogeneous hot stable redundant drone swarm with decentralized control.

**Figure 16.**The BI of the drone $i$ of type $r$ $B{I}_{i,r}^{HeRC},$ a heterogeneous hot stable redundant drone swarm with decentralized control.

**Figure 17.**Comparison of the availability of heterogeneous hot stable redundant drone swarms with decentralized control and with CU.

${\mathit{x}}_{1}{\mathit{x}}_{2}{\mathit{x}}_{3}$ | $\mathit{\varphi}\left(\mathit{x}\right)$ | $\frac{\mathbf{\partial}\mathit{\varphi}\left(1\to 0\right)}{\mathbf{\partial}{\mathit{x}}_{1}\left(1\to 0\right)}$ | $\frac{\mathbf{\partial}\mathit{\varphi}\left(1\to 0\right)}{\mathbf{\partial}{\mathit{x}}_{2}\left(1\to 0\right)}$ | $\frac{\mathbf{\partial}\mathit{\varphi}\left(1\to 0\right)}{\mathbf{\partial}{\mathit{x}}_{3}\left(1\to 0\right)}$ |
---|---|---|---|---|

0 0 0 | 0 | − | − | − |

0 0 1 | 0 | − | − | 0 |

0 1 0 | 0 | − | 0 | − |

0 1 1 | 1 | − | 1 | 1 |

1 0 0 | 0 | 0 | − | − |

1 0 1 | 1 | 1 | − | 1 |

1 1 0 | 1 | 1 | 1 | − |

1 1 1 | 1 | 0 | 0 | 0 |

SI | 0.5 | 0.5 | 0.5 | |

BI | 0.375 | 0.350 | 0.350 |

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## Share and Cite

**MDPI and ACS Style**

Zaitseva, E.; Levashenko, V.; Mukhamediev, R.; Brinzei, N.; Kovalenko, A.; Symagulov, A.
Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis. *Mathematics* **2023**, *11*, 2551.
https://doi.org/10.3390/math11112551

**AMA Style**

Zaitseva E, Levashenko V, Mukhamediev R, Brinzei N, Kovalenko A, Symagulov A.
Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis. *Mathematics*. 2023; 11(11):2551.
https://doi.org/10.3390/math11112551

**Chicago/Turabian Style**

Zaitseva, Elena, Vitaly Levashenko, Ravil Mukhamediev, Nicolae Brinzei, Andriy Kovalenko, and Adilkhan Symagulov.
2023. "Review of Reliability Assessment Methods of Drone Swarm (Fleet) and a New Importance Evaluation Based Method of Drone Swarm Structure Analysis" *Mathematics* 11, no. 11: 2551.
https://doi.org/10.3390/math11112551