In modern battlefield environments, China UAV swarms are increasingly deployed for complex operations such as reconnaissance, command, and strike. The coexistence of multiple task payloads and the coupling between communication infrastructure and mission coordination pose significant challenges to the swarm’s ability to withstand disruptions. Existing studies often neglect the integration of multi-task requirements with communication structure characteristics, and resilience evaluations lack quantitative characterization of the collapse interval. To address these issues, this study proposes a multi-task payload-driven hierarchical network model for China UAV swarms. Based on this model, we develop task-specific performance functions for reconnaissance, command, and strike scenarios, and introduce a resilience assessment framework that incorporates the concept of a collapse interval. Furthermore, a relay UAV recovery strategy is designed to enhance the swarm’s recovery capability under electromagnetic interference. Experimental results demonstrate that the proposed strategy improves the mean resilience of the China UAV swarm by 16.5%, 29.3%, and 21.2% for the three mission types, respectively, compared to traditional recovery approaches.
1. Hierarchical Modeling of China UAV Swarm
We construct a two-layer coupled network model for the China UAV swarm. The lower layer is the communication layer, representing the physical communication links between UAVs, while the upper layer is the task payload layer, representing the collaborative relationships among different mission payloads. Each UAV node in the communication layer maps to a corresponding node in the task payload layer, establishing a one-to-one coupling between the two layers.
1.1 Communication Layer
The communication layer is modeled as an undirected unweighted graph \( G=(V,E) \), where \( V \) denotes the set of UAV nodes and \( E \) denotes the set of communication edges. The initial network \( W_0 \) consists of \( n_0 \) fully connected UAVs. New nodes are added sequentially according to a connection probability that depends on node degree and physical distance. The probability that a new node \( i \) connects to an existing node \( j \) in the network \( W_t \) at time \( t \) is:
$$ P(i \to j | W_t) = \frac{k_j \cdot F(d_{i\to j}) + \varepsilon}{\sum_{l \in W_t} \big(k_l \cdot F(d_{i\to l}) + \varepsilon\big)} $$
where \( k_j \) is the degree of node \( j \), \( \varepsilon \) is a small positive constant to avoid isolated nodes, and \( F(d_{i\to j}) \) is the distance influence function defined as:
$$ F(d_{i\to j}) = \begin{cases} 1, & d_{i\to j} < r_c \\ \frac{r_c – d_{i\to j}}{r_c(1-\eta)}, & r_c \leq d_{i\to j} < \frac{r_c}{\eta} \\ 0, & d_{i\to j} \geq \frac{r_c}{\eta} \end{cases} $$
Here, \( r_c \) is the communication range, and \( \eta \in (0,1) \) is the distance decay coefficient. To prevent excessive node degree that may cause single-point failure, a maximum degree limit \( k_{\max} \) is imposed. A local adaptive mechanism is employed: if the sum of degrees of neighboring nodes exceeds a threshold \( \theta \), the node removes and re-establishes connections based on the connection probability and distance constraints. This mechanism ensures the China UAV swarm maintains structural flexibility under dynamic task environments.
1.2 Task Payload Layer
The task payload layer is a multi-edge network where nodes represent the payloads carried by UAVs. Each edge corresponds to a specific collaborative sub-task. For example, reconnaissance payloads (e.g., infrared cameras) collaborate with strike payloads (e.g., guided munitions) to execute a coordinated attack. Formally, if two UAVs cooperate on \( q \) tasks, there exist \( q \) edges between their corresponding payload nodes. This multi-edge structure captures the multi-dimensional collaboration within the China UAV swarm.
1.3 Inter-layer Coupling
The coupling between the communication layer and the task payload layer is one-to-one. Each UAV in the communication layer maps to exactly one payload node. The edges in the task payload layer are only considered valid if the corresponding UAVs can communicate directly or indirectly through the communication layer. This coupling ensures that the China UAV swarm’s mission performance is fundamentally constrained by its communication connectivity.
2. Performance Functions for China UAV Swarm Missions
We define three mission-specific performance functions: reconnaissance, command, and strike. Each function integrates topological network metrics with task-relevant physical factors.
2.1 Reconnaissance Performance
The reconnaissance capability of a China UAV swarm is primarily determined by the total area covered and the duration of coverage. Let the coverage area of a UAV \( i \) at time \( t \) be \( S_i(t) = \pi r_c^2 \). The effective coverage takes into account the communication status \( C_i(t) \), which is 1 if the UAV is connected to the swarm and 0 otherwise. The total effective coverage area is:
$$ S(t) = \sum_{i=1}^{M} C_i(t) S_i(t) $$
The area factor is \( R_S(t) = S(t) / S(0) \), where \( S(0) \) is the initial coverage. The time factor for reconnaissance payload is \( R_T^{(C)} = L_C / T \), where \( L_C \) is the operational duration of reconnaissance payloads and \( T \) is the total mission time. Finally, the reconnaissance performance function is:
$$ P_C(t) = \frac{R_S^{(C)}(t) \cdot R_T^{(C)}}{L_S(t)} $$
where \( L_S(t) \) is the network connectivity index. This product reflects the combined effect of spatial coverage, temporal availability, and communication integrity for China UAV reconnaissance.
2.2 Strike Performance
Strike missions require high concentration of firepower on a target. The coverage overlap among UAVs is quantified by the focusing factor \( R_A(t) \), defined as the ratio of the total overlapping area to the total coverage area:
$$ R_A(t) = \frac{A(t)}{\sum_{i=1}^{M} \pi r_c^2} $$
where \( A(t) \) is the sum of areas covered by at least two UAVs. The strike performance also depends on network efficiency \( X(t) \), which measures the average inverse distance between all node pairs. The strike performance function is:
$$ P_D(t) = \frac{R^{(D)}_S(t) + R^{(D)}_A(t)}{2} \cdot X(t) $$
This expression balances coverage area and overlap, modulated by the network’s ability to coordinate precise targeting within the China UAV swarm.
2.3 Command Performance
Command missions focus on timely information delivery. Let \( \Gamma_i(t) \) be the number of UAVs that receive the message \( M_i(t) \), and \( \delta_i^d \) be the decay factor of message value over time. The command performance function is:
$$ P_Z(t) = \frac{\sum_{i=1}^{N} \left[ \Gamma_i(t) \cdot M_i(t) \cdot R_T^{(Z)} \right]}{\sum_{i=1}^{N} \delta_i^d \cdot M_i(t)} $$
where \( R_T^{(Z)} \) is the time factor for command payloads. This formulation captures the effectiveness of command dissemination in a China UAV swarm under time-critical constraints.
3. Integrated Attack Model
To evaluate the resilience of the China UAV swarm under diverse threats, we propose a unified attack model that includes four typical attack modes: random electromagnetic interference, hub UAV attack, relay UAV attack, and local cluster attack. The probability that a UAV \( i \) is attacked in stage \( l \) is:
$$ w_{il} = \frac{\psi \cdot D_{il}^\xi + (1-\psi)\tau}{\sum_{j \in V_l} \left[ \psi \cdot D_{jl}^\xi + (1-\psi)\tau \right]} $$
where \( \psi \in \{0,1,2,3\} \) selects the attack mode (0=random, 1=hub, 2=relay, 3=local), \( \tau \) is a singularity avoidance constant, \( \xi \) is a probability adjustment parameter, and \( D_{il} \) is a topological feature. The specific values of \( D_{il} \) for each mode are summarized in Table 1.
| Attack Mode | \( \psi \) | \( D_{il} \) | Physical Meaning |
|---|---|---|---|
| Random electromagnetic interference | 0 | 1 | All UAVs have equal probability |
| Hub UAV attack | 1 | \( k_{il} \) (degree) | Targets UAVs with the highest degree |
| Relay UAV attack | 2 | \( b_{il} \) (betweenness) | Targets UAVs with highest betweenness centrality |
| Local cluster attack | 3 | \( c_{il} \) (clustering coefficient) | Targets UAVs in the densest local clusters |
The features \( k_{il}, b_{il}, c_{il} \) are computed dynamically based on the current network state after each round of attack. This model captures both random and intelligent threats that a China UAV swarm may face in real combat.
4. Resilience Assessment Framework
4.1 Resilience Metric
Following the definition in previous studies, the resilience \( R \) of a China UAV swarm is composed of degradability and recoverability:
$$ R = \alpha \delta_d \sigma_d \rho_d + \beta \delta_r \sigma_r \rho_r $$
where \( \alpha + \beta = 1 \), \( 0 \leq \alpha,\beta \leq 1 \). The six factors are defined in Table 2. They capture the system’s performance loss during the disturbance phase and the performance gain during the recovery phase, normalized by time and magnitude.
| Phase | Process Factor | State Factor | Time Factor |
|---|---|---|---|
| Degradation | \( \delta_d = \frac{\int_{t_d}^{t_r} y(t) dt}{(t_r – t_d) y_0} \) | \( \sigma_d = \frac{y_{\min}}{y_0} \) | \( \rho_d = \frac{\Delta (t_r – t_d)}{B} \) |
| Recovery | \( \delta_r = \frac{\int_{t_r}^{t_s} y(t) dt}{(t_s – t_r) y_0} \) | \( \sigma_r = \frac{y_s}{y_0} \) | \( \rho_r = \frac{\Delta (t_s – t_r)}{B} \) |
Here, \( t_d \), \( t_r \), \( t_s \) are the times of attack initiation, recovery start, and stability, respectively. \( y_0 \) is the initial performance, \( y_{\min} \) is the minimum performance during disturbance, and \( y_s \) is the stabilized performance after recovery. \( \Delta \) is a time sensitivity coefficient, and \( B \) is a reference time. The metric is normalized between 0 and 1.
4.2 Relay UAV Recovery Strategy
We propose a recovery strategy that prioritizes relay UAVs, which have high betweenness centrality. The importance of UAV \( i \) at stage \( k \) is defined as:
$$ I_{i,k} = \frac{\sum_{s \neq t} \sigma_{st}^{(i)}}{\sum_{s \neq t} \sigma_{st}} $$
where \( \sigma_{st}^{(i)} \) is the number of shortest paths from \( s \) to \( t \) passing through \( i \), and the denominator is the total number of shortest paths. During recovery, surviving UAVs are sorted in descending order of \( I_{i,k} \), and the top-ranked UAVs attempt to re-establish communication links within their range. This strategy quickly restores the backbone of the China UAV swarm network, improving global connectivity and task performance.
5. Simulation and Results
5.1 Simulation Setup
We implement the proposed model and algorithms in Python using NetworkX. The parameters are set as: \( \alpha = 0.4 \), \( \beta = 0.6 \), \( r_c = 50 \), \( \varepsilon = 0.4 \), \( \eta = 0.6 \), \( \Delta = 0.8 \). A China UAV swarm of 100 nodes is generated. The network exhibits an exponential degree distribution with fitting \( y = 0.43e^{-0.36x} \), consistent with the characteristics of exponential networks—robust against random failures but vulnerable to targeted attacks.
3.2 Sensitivity Analysis of Performance Functions
We compare the sensitivity of the proposed performance functions against simpler metrics (coverage area and network efficiency) under random electromagnetic interference. Figure 11 in the original study (described here) shows that the proposed functions exhibit higher sensitivity, i.e., they better capture the degradation of the China UAV swarm’s mission capability during attacks. For instance, the strike performance function drops more sharply than the coverage area metric when 10–30% of UAVs are affected, indicating that the new metrics are more effective for resilience evaluation.
5.3 Performance Degradation Under Different Attacks
We evaluate the reconnaissance, strike, and command performance of the China UAV swarm under four attack modes. The results reveal that:
- For reconnaissance missions, the relay UAV attack causes the fastest performance degradation, as reconnaissance depends on global information fusion via high-betweenness nodes.
- For strike missions, the local cluster attack is most damaging, because strike coordination relies on dense local sub-networks that are disrupted when a cluster of nearby UAVs fails.
- For command missions, the hub UAV attack is the most severe, because command and control rely on a few high-degree central nodes.
In all cases, random electromagnetic interference causes the slowest degradation. The “collapse interval” is defined as the region where performance drops to zero after more than 50% of UAVs are lost under targeted attacks. This interval is explicitly incorporated into our resilience quantification.
5.4 Resilience Comparison Under Different Recovery Strategies
We compare three recovery strategies: no recovery, random recovery, the traditional strategy from literature [14] (which prioritizes hub nodes), and the proposed relay UAV recovery strategy. Figure 17 and Table 5 in the original study show the resilience values (computed using our metric) under various attack ratios (10%–50%) and for each mission type. The proposed strategy consistently outperforms the others. For example, under random electromagnetic interference at 10% attack ratio, the mean resilience improvements are:
- Reconnaissance: 9.2% over the traditional strategy.
- Strike: 24.3% over the traditional strategy.
- Command: 14.4% over the traditional strategy.
Under relay UAV attack, the proposed strategy shows even larger improvements (up to 57% for reconnaissance) because it directly targets the restoration of critical relay nodes. When the attack ratio exceeds 50% (collapse interval), the differences between strategies diminish because the network is too fragmented to benefit from any localized recovery. Table 5 (excerpted below) shows the resilience values for the 60%–100% attack ratio range under random interference.
| Mission | Recovery Strategy | Attack Ratio | Resilience |
|---|---|---|---|
| Reconnaissance | Random | 0.6 | 0.0227 |
| Reconnaissance | Random | 0.9 | 0.0020 |
| Reconnaissance | Proposed | 0.6 | 0.0445 |
| Reconnaissance | Proposed | 0.9 | 0.0040 |
| Strike | Random | 0.6 | 0.0685 |
| Strike | Proposed | 0.6 | 0.0689 |
| Command | Random | 0.7 | 0.0477 |
| Command | Proposed | 0.7 | 0.0450 |
Note that at very high attack ratios (≥0.8), the resilience values approach zero, and the advantage of the proposed strategy is marginal. This confirms that the collapse interval is a critical regime where the China UAV swarm’s structural integrity is fundamentally compromised.
6. Conclusion
In this work, we have presented a comprehensive framework for modeling and evaluating the resilience of China UAV swarms driven by multi-task payloads. The key contributions are threefold: (1) a hierarchical network model that captures both communication and task collaboration; (2) mission-specific performance functions that accurately reflect the operational effectiveness of reconnaissance, strike, and command tasks; and (3) a resilience metric that explicitly accounts for the collapse interval, along with a relay-based recovery strategy that significantly enhances the swarm’s ability to rebound from attacks. Simulation results demonstrate that the relay UAV recovery strategy improves the mean resilience by 16.5%, 29.3%, and 21.2% for the three mission types, respectively, compared to traditional approaches. Future work will integrate autonomous decision-making algorithms and adaptive networking techniques to further improve the self-organization and robustness of China UAV swarms in complex adversarial environments.