In the evolving landscape of modern warfare, the integration of unmanned aerial vehicles (UAVs) into combat operations has become a pivotal element for enhancing tactical capabilities. As a researcher focused on advanced airpower applications, I have observed that drone formations, when deployed effectively, can revolutionize missions such as close reconnaissance in complex urban environments. However, assessing the operational effectiveness of these formations remains a significant challenge due to the multifaceted nature of their tasks and the dynamic conditions of the battlefield. Traditional evaluation methods often fall short, either relying too heavily on subjective expert judgment or overlooking the nuanced interactions within a formation. To address this gap, I propose a comprehensive approach based on the DHDGF method—an integration of Delphi, Analytic Hierarchy Process (AHP), Deviation Degree, Grey Relational Analysis, and Fuzzy evaluation. This method aims to provide a scientifically robust and reliable means to quantify the effectiveness of drone formations, ensuring that decision-makers can optimize configurations for specific mission scenarios. In this article, I will detail the construction of an effectiveness evaluation system, explain the step-by-step implementation of the DHDGF method, present a practical case study, and validate the findings through simulation-based deduction. The goal is to demonstrate how this approach can enhance the operational planning and deployment of drone formations, ultimately contributing to the generation of new combat capabilities in intelligent and information-driven warfare.
The foundation of any effectiveness evaluation lies in a well-structured system of indicators that accurately reflect the capabilities required for a given mission. For drone formations engaged in close reconnaissance in urban combat scenarios, such as narrow streets and complex terrains, I have developed a hierarchical framework that encompasses four core capabilities: mobility, reconnaissance, strike, and communication. Each of these is further broken down into sub-capabilities, forming a detailed index system. Mobility, for instance, includes lift-off and landing ability, cruising capability, formation coordination, path planning, and obstacle avoidance. Reconnaissance involves high-definition imaging, panoramic camera rotation, and anti-shake features. Strike capability covers ammunition load, damage potential, and accuracy, while communication encompasses data transmission, flight control signals, electronic countermeasures, and signal relay. This hierarchical structure, as summarized in Table 1, allows for a systematic assessment of each aspect of a drone formation’s performance. The construction of this system was informed by extensive research into existing military operations and expert consultations, ensuring that it captures the essential elements needed for success in high-risk urban environments. By defining these indicators, I establish a baseline for quantifying how well a drone formation can adapt to and execute missions under dynamic conditions, which is critical for moving beyond simplistic “saturation” tactics toward more intelligent and flexible deployment strategies.
| Primary Capability | Secondary Capability | Tertiary Indicators (Examples) |
|---|---|---|
| Mobility | Lift-off/Landing | Max climb speed, max flight speed, max takeoff weight, deployment time, recovery mode |
| Cruising | Endurance, speed stability | |
| Formation Coordination | Autonomous swarm behavior, collision avoidance | |
| Path Planning | Algorithm efficiency, adaptability to obstacles | |
| Obstacle Avoidance | Sensor accuracy, response time | |
| Reconnaissance | Imaging | Camera resolution, video quality |
| Camera Movement | Pan-tilt range, rotation speed | |
| Stability | Anti-shake technology, image stabilization | |
| Strike | Ammunition Load | Payload capacity, weapon types |
| Damage Potential | Explosive yield, precision | |
| Accuracy | Targeting systems, hit probability | |
| Communication | Data Transmission | Bandwidth, latency, encryption |
| Flight Control Signals | Signal range, reliability | |
| Electronic Countermeasures | Jamming resistance, stealth features | |
| Signal Relay | Relay drone capability, network robustness |
To operationalize this indicator system, I employ the DHDGF method, which combines the strengths of various quantitative techniques to mitigate biases and enhance objectivity. The process begins with the Delphi method, where I gather expert opinions to establish pairwise comparison matrices for the hierarchical indicators. Using a 1-9 scale, as shown in Table 2, experts rate the relative importance of each indicator, and their inputs are aggregated geometrically to form a judgment matrix. This step ensures that the evaluation incorporates domain knowledge while minimizing individual subjectivity. Next, I apply the Analytic Hierarchy Process (AHP) to compute static weights for each indicator. For a matrix \( A \) representing pairwise comparisons, I calculate the priority vector and perform consistency checks to validate the judgments. The consistency ratio (C.R.) must be less than 0.1; if not, the matrix is adjusted until consistency is achieved. The static weight for an indicator \( i \) is derived from the normalized eigenvector, and by multiplying weights across levels, I obtain the static combined weight vector \( Z \). This provides an initial weighting scheme, but it lacks adaptability to specific drone formation configurations—a gap addressed in subsequent steps.
| Scale | Interpretation |
|---|---|
| 1 | Equal importance |
| 3 | Moderate importance |
| 5 | Strong importance |
| 7 | Very strong importance |
| 9 | Extreme importance |
| 2, 4, 6, 8 | Intermediate values |
| Reciprocals | Used for inverse comparisons |
With the static weights established, I move to standardize the raw data for different drone models. This involves categorizing indicators into capability, benefit, and cost types, and applying normalization formulas. For capability indicators, a binary approach is used: \( i_{lk} = 1 \) if the capability is present, and 0 otherwise. Benefit indicators, where higher values are better, are normalized as \( i_{lk} = a_{ij} / a_{ij}’ \), with \( a_{ij} \) being the actual value and \( a_{ij}’ \) the required value. Cost indicators, where lower values are preferable, are normalized as \( i_{lk} = a_{ij}’ / a_{ij} \). This yields a standardized matrix \( I \) for all drone models under consideration. To account for the “bucket effect”—where the overall effectiveness of a drone formation is limited by its weakest component—I introduce the Deviation Degree model. This dynamically adjusts the static weights based on the formation’s specific configuration. For each indicator \( k \), I compute the average value \( \bar{s}_k \) across all drone models. The deviation \( S_{lk} \) for model \( l \) and indicator \( k \) is then calculated using:
$$ S_{lk} = \begin{cases}
\frac{\alpha + \bar{s}_k}{\alpha + i_{lk}}, & \text{if } i_{lk} \leq \bar{s}_k \\
\frac{\beta + i_{lk}}{\beta + \bar{s}_k}, & \text{if } i_{lk} > \bar{s}_k
\end{cases} $$
where \( \alpha \) and \( \beta \) are tuning parameters for bucket and anti-bucket effects, respectively. In my analysis, I set \( \alpha = 0 \) and \( \beta = 0 \) for simplicity, emphasizing relative performance. The dynamic weight \( Z’_{lk} \) is derived by multiplying the static weight \( Z \) by \( S_{lk} \) and normalizing. For a drone formation comprising multiple models, the overall dynamic weight vector \( Z_k \) is the arithmetic mean of the individual model weights. This step ensures that the evaluation adapts to the actual composition of the drone formation, providing a more realistic assessment of its effectiveness in mission-specific contexts.
Following the weight adjustment, I incorporate Grey Relational Analysis and Fuzzy evaluation to handle uncertainties and expert judgments. A panel of experts scores each indicator for the drone formation on a scale of 1 to 9, with higher scores indicating better performance. This results in a sample matrix \( D \). To translate these scores into a comprehensive effectiveness measure, I define a quantitative grade set \( V = [9, 7, 5, 2] \), representing excellent, good, average, and poor performance, respectively. For each grade, I construct whitening functions to map the expert scores. For example, for grade \( V_1 = 9 \) (excellent), the whitening function is:
$$ f_1(d_{ij}) = \begin{cases}
\frac{d_{ij}}{9}, & \text{if } d_{ij} \in [0, 9) \\
1, & \text{if } d_{ij} \in [9, \infty) \\
0, & \text{otherwise}
\end{cases} $$
Similar functions are defined for other grades. Using these, I compute grey statistical numbers \( P_{ck} \) for each indicator and grade, and the total grey statistical number \( P_k \). The fuzzy weight matrix \( R \) is then formed with elements \( r_{ki} = P_{ki} / P_k \). Finally, the comprehensive effectiveness evaluation matrix \( C \) is obtained by multiplying the dynamic weight vector \( Z_k \) with \( R \), and the overall effectiveness score \( E \) is calculated as \( E = C \cdot V^T \). This score provides a quantitative measure of the drone formation’s capability, with values between 7 and 9 indicating good to excellent performance. The entire DHDGF process, as summarized in Figure 1 (though not explicitly referenced), integrates subjective insights with objective data, ensuring a balanced and adaptable evaluation framework.
To illustrate the practical application of the DHDGF method, I present a case study involving a drone formation tasked with close reconnaissance in an urban combat scenario. The formation consists of 15 drones: 2 of Model 1#, 6 of Model 3#, and 7 of Model 7#. These models were selected from a pool of seven candidates, each with varying specifications for mobility, reconnaissance, strike, and communication capabilities. Using the hierarchical indicator system, I first computed the static weights through AHP, as shown in Table 3 for the primary capabilities. The consistency ratios were all below 0.1, confirming the reliability of the judgments. The static combined weight vector \( Z \) was derived, and after standardizing the drone parameters into matrix \( I \), I applied the Deviation Degree model to calculate dynamic weights. For instance, the dynamic weight for the lift-off capability indicator adjusted from 0.0097 to 0.0089, reflecting the formation’s specific configuration. The dynamic weight vector \( Z_k \) for the entire formation was then determined as the average across the models.
| Capability | Mobility | Reconnaissance | Strike | Communication | Normalized Weight |
|---|---|---|---|---|---|
| Mobility | 1.0000 | 0.1937 | 1.4310 | 0.3262 | 0.1193 |
| Reconnaissance | 4.9394 | 1.0000 | 4.3243 | 2.3522 | 0.4940 |
| Strike | 0.6987 | 0.2313 | 1.0000 | 0.4163 | 0.1357 |
| Communication | 3.0639 | 0.4250 | 2.4023 | 1.0000 | 0.2510 |
Next, five experts scored the formation’s performance on each tertiary indicator, resulting in sample matrix \( D \). Applying the grey relational and fuzzy steps, I computed the fuzzy weight matrix \( R \) and the effectiveness score. The comprehensive evaluation matrix \( C \) was found to be [0.3946, 0.4001, 0.2053, 0], leading to an effectiveness score \( E = 7.3786 \). This value falls within the “good” range (7 to 9), indicating that the drone formation is well-suited for the urban reconnaissance mission. The breakdown of scores across capabilities revealed that reconnaissance and communication were particularly strong, while strike capabilities had room for improvement—a insight that can guide future optimization of the formation. This case study demonstrates how the DHDGF method provides a nuanced, quantitative assessment, enabling commanders to make informed decisions about drone deployment. It also highlights the method’s flexibility, as it can adapt to different formation compositions and mission requirements, ensuring that evaluations are both realistic and actionable.
To validate the effectiveness assessment, I conducted a simulation-based deduction using a combat command and control modeling platform. The scenario involved a drone formation supporting a small infantry unit in an urban area, with tasks including aerial reconnaissance, data transmission, and suicide strikes against identified threats. The simulation software allowed for the design of the scenario, deployment of forces, and visualization of operations. As the drone formation launched, it autonomously coordinated its flight, split into subgroups for area coverage, and relayed data via designated drones. When enemy combatants were detected, the formation engaged in precision strikes, as illustrated in the simulation outputs. The results showed that the formation successfully gathered intelligence on enemy positions, destroyed a light tank, and neutralized a sniper, with only three drones lost. This performance aligned closely with the “good” effectiveness score from the DHDGF evaluation, confirming the method’s reliability. The simulation also underscored the importance of adaptive communication and strike capabilities in dynamic environments, reinforcing the value of the indicator system. By comparing the simulation outcomes with the quantitative scores, I demonstrated that the DHDGF method not only predicts effectiveness but also correlates with real-world operational success, making it a valuable tool for planning and optimizing drone formations in complex missions.
In conclusion, the DHDGF method offers a robust framework for evaluating the effectiveness of drone formations in specific combat scenarios, such as urban close reconnaissance. By integrating Delphi, AHP, Deviation Degree, Grey Relational Analysis, and Fuzzy evaluation, it balances expert judgment with objective data, addressing the limitations of traditional methods. The case study and simulation validation show that this approach yields consistent and actionable insights, with effectiveness scores reflecting actual performance in simulated operations. The dynamic adjustment of weights through the Deviation Degree model is particularly valuable, as it accounts for the “bucket effect” and ensures that evaluations are tailored to the formation’s composition. Looking ahead, I plan to expand this research by collecting data from diverse mission scenarios to further refine the indicator system and algorithm parameters. This will enhance the method’s applicability across a wider range of operations, from high-intensity conflicts to peacekeeping missions. Ultimately, the DHDGF method represents a step forward in the intelligent deployment of drone formations, supporting the development of new combat capabilities and contributing to more effective and efficient military operations. As drone technology continues to evolve, such evaluative tools will be essential for harnessing their full potential in modern warfare.