In recent years, the multi-rotor drone industry has experienced rapid growth, leading to increased operational complexity and a higher risk of accidents. Analyzing the causes of multi-rotor drone accidents is crucial for developing effective prevention strategies. This study investigates multi-rotor drone accident cases and establishes a Fault Tree Analysis-Bayesian Network (FTA-BN) model to systematically analyze accident causes. By combining the logical structure of FTA with the probabilistic reasoning of BN, this approach enables a comprehensive assessment of multi-rotor drone accident factors, facilitating targeted risk mitigation.
The FTA model is constructed with the multi-rotor drone accident as the top event, intermediate events including mid-air collision, crash, and loss of contact, and basic events representing various causal factors. The model captures the logical relationships between events using AND and OR gates. Subsequently, the FTA model is transformed into a BN model, where nodes correspond to events, and conditional probabilities reflect the logical gates. This transformation allows for quantitative analysis using Netica software, including posterior probability inference and sensitivity analysis. The results highlight key contributing factors to multi-rotor drone accidents, providing insights for safety improvements.
The methodology begins with data collection from 382 multi-rotor drone accident cases, sourced from aviation safety databases, surveys, and literature. The FTA model for multi-rotor drone accidents includes one top event, ten intermediate events, and twenty-one basic events. The intermediate events are categorized into three types: multi-rotor drone mid-air collision, multi-rotor drone crash, and multi-rotor drone loss of contact. Loss of contact is treated separately due to uncertainties in post-incident states, which could involve collision or crash. The basic events encompass factors such as environmental conditions, human errors, and system failures. The logical relationships are defined using AND and OR gates, as illustrated in the FTA diagram. For instance, an AND gate requires all input events to occur for the output event to happen, while an OR gate requires at least one input event.
The transformation from FTA to BN involves mapping FTA events to BN nodes: basic events become root nodes, intermediate events become intermediate nodes, and the top event becomes the leaf node. The prior probabilities of root nodes are derived from the frequency of basic events in the accident dataset. For example, if a basic event occurs in 108 out of 382 cases, its prior probability is calculated as $$ P(X_i) = \frac{108}{382} \approx 0.283 $$. The conditional probabilities for intermediate and leaf nodes are determined based on the logical gates from the FTA model. For an AND gate with inputs \( E_1, E_2, \ldots, E_n \) and output \( S \), the conditional probability is defined as:
$$ P(S = 1 | E_1 = 1, E_2 = 1, \ldots, E_n = 1) = 1 $$
$$ P(S = 1 | \text{otherwise}) = 0 $$
For an OR gate, the conditional probability is:
$$ P(S = 1 | E_1 = 0, E_2 = 0, \ldots, E_n = 0) = 0 $$
$$ P(S = 1 | \text{otherwise}) = 1 $$
This ensures that the BN model accurately represents the causal structure of multi-rotor drone accidents.
The BN model topology consists of 21 root nodes, 10 intermediate nodes, and 1 leaf node, connected by directed edges. The root nodes represent basic events like obstacle presence, system failures, and environmental factors. The intermediate nodes aggregate these factors into higher-level events, such as loss of power or signal loss. The leaf node represents the overall multi-rotor drone accident. The BN model is implemented in Netica for parameter learning and analysis. The prior probabilities of root nodes are inputted, and the software computes the probabilities of intermediate and leaf nodes through probabilistic inference.
| Root Node | Description | Prior Probability |
|---|---|---|
| X1 | Obstacle in flight path | 0.283 |
| X2 | Unreasonable automatic path planning | 0.252 |
| X3 | Obstacle avoidance system failure | 0.194 |
| X4 | Lack of pilot experience | 0.124 |
| X5 | Fog | 0.126 |
| X6 | Low light conditions | 0.134 |
| X7 | Bird strike | 0.121 |
| X8 | Unreasonable load | 0.256 |
| X9 | Illegal modification | 0.217 |
| X10 | Pilot operation error | 0.277 |
| X11 | Strong wind | 0.210 |
| X12 | Heavy rain | 0.190 |
| X13 | Motor natural wear | 0.188 |
| X14 | Motor high-intensity operation | 0.266 |
| X15 | Propeller wear | 0.186 |
| X16 | Inadequate maintenance inspection | 0.193 |
| X17 | Ground station equipment failure | 0.259 |
| X18 | Out of communication range | 0.374 |
| X19 | Weak signal | 0.161 |
| X20 | Strong magnetic interference | 0.129 |
| X21 | Automatic return system failure | 0.347 |
Parameter learning in the BN model involves calculating the probabilities of intermediate and leaf nodes. For example, the probability of the top event (multi-rotor drone accident) is derived as 100% when the model is conditioned on accident occurrence. The intermediate events show the following probabilities: multi-rotor drone mid-air collision at 26.9%, multi-rotor drone crash at 45.5%, and multi-rotor drone loss of contact at 28.0%. These values indicate that crashes are the most common accident type for multi-rotor drones, followed by loss of contact and mid-air collisions. The BN model allows for posterior probability inference by setting the leaf node to 100% and updating the probabilities of root nodes. This reveals how each basic event contributes to multi-rotor drone accidents under the condition that an accident has occurred.
| Root Node | Description | Posterior Probability |
|---|---|---|
| X1 | Obstacle in flight path | 0.294 |
| X2 | Unreasonable automatic path planning | 0.263 |
| X3 | Obstacle avoidance system failure | 0.195 |
| X4 | Lack of pilot experience | 0.124 |
| X5 | Fog | 0.126 |
| X6 | Low light conditions | 0.134 |
| X7 | Bird strike | 0.131 |
| X8 | Unreasonable load | 0.257 |
| X9 | Illegal modification | 0.218 |
| X10 | Pilot operation error | 0.284 |
| X11 | Strong wind | 0.216 |
| X12 | Heavy rain | 0.196 |
| X13 | Motor natural wear | 0.200 |
| X14 | Motor high-intensity operation | 0.277 |
| X15 | Propeller wear | 0.197 |
| X16 | Inadequate maintenance inspection | 0.204 |
| X17 | Ground station equipment failure | 0.265 |
| X18 | Out of communication range | 0.383 |
| X19 | Weak signal | 0.162 |
| X20 | Strong magnetic interference | 0.130 |
| X21 | Automatic return system failure | 0.368 |
Sensitivity analysis is conducted to identify the most influential factors on multi-rotor drone accidents. The analysis measures the mutual information between the target node (multi-rotor drone accident) and other nodes, indicating the strength of influence. The mutual information is calculated as:
$$ I(X; Y) = \sum_{x \in X} \sum_{y \in Y} P(x, y) \log \frac{P(x, y)}{P(x)P(y)} $$
where \( X \) is the target node and \( Y \) is another node. The results are normalized as percentages relative to the target node’s mutual information. Additionally, the coefficient of variation for mutual information assesses the stability of each node’s influence. Nodes with higher mutual information and lower coefficients of variation are considered more critical and stable contributors to multi-rotor drone accidents.
| Node | Mutual Information (×10⁻²) | Percentage (%) | Coefficient of Variation (×10⁻²) |
|---|---|---|---|
| S (Target) | 64.400 | 100.00 | 13.716 |
| M2 | 33.708 | 52.30 | 8.356 |
| M3 | 16.665 | 25.90 | 4.326 |
| M1 | 9.303 | 14.40 | 2.453 |
| X21 | 5.148 | 7.99 | 1.368 |
| X13 | 4.158 | 6.46 | 0.943 |
| X2 | 3.997 | 6.21 | 1.064 |
| M6 | 3.997 | 6.21 | 1.064 |
| X16 | 3.288 | 5.11 | 0.670 |
| M10 | 3.057 | 4.75 | 0.625 |
| X15 | 3.056 | 4.75 | 0.627 |
| X1 | 2.562 | 3.98 | 0.598 |
| X14 | 2.294 | 3.56 | 0.538 |
| M9 | 1.626 | 2.53 | 0.435 |
| X7 | 1.331 | 2.07 | 0.286 |
| X18 | 1.330 | 2.02 | 0.286 |
| X10 | 0.089 | 0.139 | 0.018 |
| M7 | 0.083 | 0.129 | 0.018 |
| X11 | 0.083 | 0.129 | 0.018 |
| M8 | 0.038 | 0.060 | 0.008 |
| X12 | 0.033 | 0.051 | 0.007 |
| M5 | 0.009 | 0.014 | 0.002 |
| X17 | 0.009 | 0.014 | 0.002 |
| X3 | 0.004 | 0.007 | 0.001 |
| X8 | 0.003 | 0.005 | 0.001 |
| X9 | 0.003 | 0.005 | 0.001 |
| X19 | 0.002 | 0.002 | 0.000 |
| M4 | 0.001 | 0.002 | 0.000 |
| X20 | 0.001 | 0.001 | 0.000 |
| X4 | 0.000 | 0.001 | 0.000 |
| X6 | 0.000 | 0.000 | 0.000 |
| X5 | 0.000 | 0.000 | 0.000 |
The results from the BN model indicate that the most probable accident type for multi-rotor drones is crash (45.5%), followed by loss of contact (28.0%) and mid-air collision (26.9%). Posterior probability analysis shows that factors such as automatic return system failure (X21), motor natural wear (X13), unreasonable automatic path planning (X2), inadequate maintenance inspection (X16), and propeller wear (X15) have significant increases in probability under accident conditions, making them critical contributors to multi-rotor drone accidents. Sensitivity analysis further confirms that these nodes have high mutual information with the target node, indicating strong influence. For instance, X21 (automatic return system failure) has a mutual information of 5.148×10⁻², accounting for 7.99% of the target node’s mutual information, with a low coefficient of variation (1.368×10⁻²), suggesting stable and high impact on multi-rotor drone accidents.
Discussion of these findings emphasizes the importance of addressing system reliability and maintenance in multi-rotor drone operations. The high posterior probabilities of X13, X21, X2, X16, and X15 suggest that preventive measures should focus on improving automatic systems, conducting regular maintenance, and enhancing path planning algorithms. Environmental factors like communication range (X18) and signal strength (X19) also play a role but have lower sensitivity scores. The FTA-BN model effectively combines qualitative and quantitative analysis, providing a robust framework for multi-rotor drone accident causation studies. Future work could expand the dataset, incorporate real-time data, or apply the model to other drone types.
In conclusion, the FTA-BN model offers a comprehensive approach to analyzing multi-rotor drone accident causes. By integrating FTA’s logical structure with BN’s probabilistic reasoning, the model identifies key risk factors and their interrelationships. The analysis reveals that system failures and maintenance issues are predominant in multi-rotor drone accidents, highlighting areas for safety enhancements. This methodology can be adapted for regulatory guidelines, training programs, and design improvements to reduce multi-rotor drone accident rates. Continued research in this field will further advance the safety and reliability of multi-rotor drone operations.