Joint optimization method and system for mountain forest fire risk low-altitude monitoring network

Abstract

The present application is a joint optimization method and system for mountain forest fire risk low-altitude monitoring network, the method comprising the steps of: S1, risk perception and task planning, obtaining multi-source geographic spatial data and meteorological data of the target forest area, evaluating the fire risk level of each sub-region based on the data, and setting different unmanned aerial vehicle inspection frequencies according to different risk levels; S2, infrastructure and operation joint optimization modeling, establishing a two-stage optimization decision model; S3, model solving and scheme output, using an optimization algorithm to solve the two-stage optimization decision model to obtain the optimal nest layout scheme, task area allocation scheme and corresponding unmanned aerial vehicle flight route plan. The present application significantly improves the long-term economy and robustness of the monitoring network, and realizes the normalization, precision and economic efficiency of the monitoring and early warning of mountain forest fire risk.

Description

Technical Field

[0001] This invention relates to the fields of unmanned aerial vehicle (UAV) applications and forestry safety monitoring technology, and in particular to a joint optimization method and system for low-altitude monitoring networks for forest fire risk. Background Technology

[0002] Timely monitoring of forest fire risk is crucial for forest fire prevention. Currently, the main monitoring methods include manual ground patrols, lookout tower observations, and satellite remote sensing. Manual patrols rely on the experience of patrol personnel, which is not only inefficient and has limited coverage, but also struggles to cope with complex terrain and severe weather, resulting in a significant delay in the detection of initial fires. While lookout tower observations offer a wide field of view, they are limited by their location and terrain obstructions, creating blind spots, and the infrastructure construction and maintenance costs are high. Satellite remote sensing technology can achieve large-scale monitoring, but its long revisit cycle makes it difficult to respond promptly to forest areas obscured by clouds or small-scale fires, failing to meet the needs of routine and precise monitoring.

[0003] In recent years, drone technology has been explored for application in forestry monitoring due to its high mobility and flexibility. Existing solutions typically employ single or multiple drones to patrol specific forest areas. However, these solutions have significant limitations: First, the limited endurance of drones severely restricts the duration and scope of a single operation, making it difficult to support continuous monitoring tasks across large forest areas. Second, existing solutions primarily focus on path planning for individual tasks, failing to address the construction of long-term monitoring networks at the system level, particularly lacking consideration for the synergistic optimization between the layout of ground infrastructure (such as drone nests) and drone flight paths. More importantly, forest weather conditions (such as temperature, humidity, and wind speed) are complex and variable, directly affecting fire risk levels and drone operational efficiency. Existing drone monitoring solutions are mostly based on deterministic environmental assumptions, failing to effectively address the challenges posed by weather uncertainty to the long-term operating costs and reliability of monitoring systems. This results in a lack of robustness in system planning, making it difficult to maintain efficiency and economy in changing environments. Summary of the Invention

[0004] To address the technical problems existing in the prior art, this invention provides a joint optimization method and system for a low-altitude monitoring network for forest fire risk. It aims to solve the technical problems of high long-term operating costs, low resource allocation efficiency, and poor robustness of the monitoring network caused by uncertain meteorological conditions, the disconnect between drone nest layout and drone flight path planning, and the lack of a systematic long-term planning perspective. This will enable normalized, precise, economical and efficient monitoring and early warning of forest fire risk.

[0005] The method of this invention is implemented using the following technical solution: a joint optimization method for a low-altitude monitoring network for forest fire risk, comprising the following steps:

[0006] S1. Risk perception and mission planning: acquire multi-source geospatial data and meteorological data of the target forest area, assess the fire risk level of each sub-area based on the data, and set differentiated drone inspection frequencies according to different risk levels.

[0007] S2. Joint optimization modeling of infrastructure and operations: A two-stage optimization decision model is established. The first stage determines the spatial location and number of UAV nests. The second stage optimizes the flight path and task scheduling sequence of UAVs from each nest to their assigned task area for various future operation scenarios. The model takes minimizing the total expected cost of the system over its entire life cycle as the objective function.

[0008] S3. Model Solving and Scheme Output: An optimization algorithm is used to solve the two-stage optimization decision model to obtain the optimal nest layout scheme, task area allocation scheme, and corresponding UAV flight path plan.

[0009] The present invention employs the following technical solution: a joint optimization system for a low-altitude forest fire risk monitoring network, comprising:

[0010] The data acquisition and processing module is used to acquire and process geographic information, meteorological and vegetation data to perform risk perception and task planning.

[0011] The optimization decision module communicates with the data acquisition and processing module and is used to construct and solve a two-stage optimization decision model.

[0012] Multiple drone nests are deployed in the forest area according to the nest layout scheme output by the optimization decision module, and are used for drone take-off and landing, energy supply and mission reception and distribution;

[0013] The drone swarm is configured to take off from its nest and execute the flight path plan generated by the optimization decision module to complete the inspection of the designated task area.

[0014] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0015] 1. This invention significantly improves the long-term economic efficiency and robustness of the monitoring network. By adopting a two-stage decision-making model that jointly optimizes the nesting layout and UAV flight routes, this model considers the operating costs under various possible weather scenarios at the strategic level (nesting location selection) and the tactical level (flight planning), and makes integrated decisions by minimizing the long-term expected total cost. This technical feature makes the system planning scheme no longer the "optimal solution" for a single deterministic environment, but a "robust solution" that can effectively cope with weather uncertainties. This avoids system performance overload or resource idleness caused by environmental fluctuations, reduces long-term operating costs from the source, and enhances the adaptability of the system.

[0016] 2. This invention achieves precise and efficient allocation of monitoring resources. Because the method of this invention includes risk perception and differentiated task planning steps based on multi-source data, it can scientifically divide inspection areas and set different inspection frequencies according to fire risk levels. This technical feature transforms the macro strategy of "risk classification" into executable operation instructions, enabling limited UAV resources to be prioritized for high-risk areas. This overcomes the resource misallocation problem in the traditional uniform inspection mode, thereby significantly improving resource utilization efficiency while ensuring monitoring effectiveness. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method of the present invention;

[0018] Figure 2 This is a map showing the boundary of the forest park and the division of the task area in this embodiment;

[0019] Figure 3 (a) is a schematic diagram of the position perturbation and rebalancing operator;

[0020] Figure 3 (b) is a schematic diagram of the repair operator;

[0021] Figure 4 (a) is a schematic diagram of the task order perturbation operator;

[0022] Figure 4 (b) Schematic diagram of the battery threshold perturbation operator;

[0023] Figure 5 This is a display map showing the location of the hive and mission area;

[0024] Figure 6 This is a diagram showing multiple return points for aircraft nests;

[0025] Figure 7 This is a diagram showing the return point of a single aircraft nest;

[0026] Figure 8 It is a 2D comparison map of the boundary area flight path planning;

[0027] Figure 9 It is a 3D image comparing flight trajectories in the boundary area;

[0028] Figure 10 It is a 2D comparison map of internal area flight path planning;

[0029] Figure 11 It is a 3D image comparing the flight trajectories of the internal regions. Detailed Implementation

[0030] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0031] Example

[0032] like Figure 1 As shown, the joint optimization method for the low-altitude forest fire risk monitoring network in this embodiment includes the following steps:

[0033] S1. Risk perception and mission planning: acquire multi-source geospatial data and meteorological data of the target forest area, assess the fire risk level of each sub-area based on the data, and set differentiated drone inspection frequencies according to different risk levels.

[0034] S2. Joint optimization modeling of infrastructure and operations: A two-stage optimization decision model is established. The first stage determines the spatial location and number of UAV nests. The second stage optimizes the flight path and task scheduling sequence of UAVs from each nest to their assigned task area for various future operation scenarios. The model takes minimizing the total expected cost of the system over its entire life cycle as the objective function.

[0035] S3. Model Solving and Scheme Output: An optimization algorithm is used to solve the two-stage optimization decision model to obtain the optimal nest layout scheme, task area allocation scheme, and corresponding UAV flight path plan.

[0036] Specifically, the multi-source geospatial data and meteorological data in step S1 include multiple data such as digital elevation model, temperature, vegetation index, slope, aspect, altitude, topographic humidity index, distance from road and distance from settlement.

[0037] Specifically, the diverse future operation scenarios in step S2 are typical scenarios generated by clustering analysis of historical meteorological data.

[0038] Specifically, the two-stage optimization decision model in step S2 is a two-stage stochastic programming model.

[0039] Specifically, in step S3, the optimization algorithm is a variable neighborhood search algorithm.

[0040] Specifically, step S3 also includes: when optimizing the UAV flight path, a path coverage algorithm is used to optimize the scanning heading based on the geometric features and terrain undulations of each mission area to minimize flight energy consumption.

[0041] Specifically, the path coverage algorithm is the rotating ox-plowing method.

[0042] Specifically, the implementation scenario, data source, and parameter settings of this embodiment are as follows.

[0043] In a preferred embodiment of the present invention, a forest park is selected as the empirical research area. The basic data used in this embodiment include:

[0044] This paper selects the core area of ​​the park as the empirical research area. This area has a minimum elevation of 198 m and a maximum elevation of 1757 m, with high forest coverage, significant topographic relief, diverse vegetation types, and marked local climate differences. It exhibits typical characteristics of a highly heterogeneous mountain forest region, making it suitable as a verification scenario for drone-based forest fire monitoring methods. The experiment uses a 30 m spatial resolution GDEMV3 digital elevation model as the spatial analysis basis, generating a total of 222,104 raster cells. All path planning and energy consumption calculations are based on this high-resolution raster data to ensure consistency in spatial data processing. The empirical area defined in this study is mainly composed of continuous mountain forests, with no large water bodies (such as lakes or reservoirs) on the surface. This ensures that subsequent optimization algorithms can continuously perturb and optimize the drone nest location within the spatial scope of the study area, thereby focusing on verifying the ability to handle the core contradiction between infrastructure layout and an uncertain operating environment.

[0045] Regarding the configuration of the UAV platform, parameter settings must strictly serve the accuracy target of fire point identification. First, regarding the ground sampling distance, this study will use the UAV monitoring... The focal length was determined to be no greater than 2 cm to achieve centimeter-level identification of early fire points. This was based on a Hasselblad L1D-20c camera (focal length) mounted on the selected DJI Matrice4 RTK platform. Pixel size ),pass With flight altitude ,focal length and pixel size The calculation formula is as follows: Calculations show that, in order to satisfy Requirements for setting relative flight altitude (Calculations show that the theoretical maximum permissible altitude is approximately 199 meters; this setting is to allow for safety and image quality margins.) Secondly, regarding aerial photography parameters, to meet the requirements of higher-precision 3D modeling and fire point identification, the forward and lateral overlap were increased to 80% and 70%, respectively. Considering the above flight altitude and overlap requirements, and based on the calculation of the ground coverage width of the image, the final shooting interval was determined to be 30 meters, thus systematically ensuring the resolution and quality of data acquisition.

[0046] Based on this, and combining the energy consumption model with measured performance data from the DJI Matrice 4, key parameters such as battery capacity, flight speed, and energy consumption per unit distance in each direction were determined, and a refined energy consumption calculation model suitable for three-dimensional undulating terrain was constructed. As shown in Table 1, all parameters are integrated into the UAV energy consumption model and path planning algorithm, ensuring that energy consumption under different headings, speeds, and terrain conditions can be accurately quantified under a unified and reproducible physical benchmark. This provides a reliable engineering basis for subsequent route optimization, system scale design, and parameter sensitivity analysis.

[0047] Table 1 Key parameters of the UAV platform

[0048]

[0049] In terms of cost accounting, various economic parameters were determined based on the list in Table 2, including the cost of the data center construction, battery procurement cost, electricity price, and annual data system fee, to construct a cost model covering the entire lifecycle of construction and operation. All cost parameters were incorporated into the ten-year total cost objective function to ensure that different system configuration schemes could be compared and analyzed under a unified and transparent economic benchmark, thereby providing a reliable basis for subsequent system optimization and sensitivity analysis.

[0050] Table 2 Model Cost Parameter Benchmark

[0051]

[0052] For ease of subsequent description, the main mathematical model symbols involved in this invention will first be uniformly explained. Table 3 below lists the main sets, parameters, and decision variables used in this embodiment.

[0053] Table 3

[0054]

[0055]

[0056] Specifically, in this embodiment, the specific process of risk perception and task planning is as follows:

[0057] First, the task area was divided based on the acquired data. In this stage, based on the administrative boundary vector data of the forest park, a mask extraction was performed using a 30-meter resolution digital elevation model (DEM) in ArcGIS software to obtain the spatial range of the core experimental area actually used in this study, such as... Figure 2 As shown on the left. To construct the basic unit for spatial analysis, a uniform, regular grid of 1 km × 1 km was laid out within the core experimental area, as follows. Figure 2 As shown on the right. The generation of this grid follows these guidelines: using the center points of the cells in the NDVI raster data at a spatial resolution of 1 km as geometric control points, ensuring that each grid cell is strictly aligned with the meteorological-vegetation data. Subsequently, through spatial overlay analysis, grids that do not intersect with the experimental area boundary are removed, and some grids that cross the boundary are pruned and merged, ultimately resulting in 186 task areas that fully cover the study area, as shown below. Figure 2The right side is marked with a red outline. These task areas will serve as the basic spatial units for fire risk assessment, nest deployment, and UAV path optimization. Their geometric centers will also serve as unified sampling points for the terrain and meteorological-vegetation attributes of the area, thus ensuring the spatial consistency of multi-source data.

[0058] Specifically, in this embodiment, the specific implementation process of the UAV energy consumption model is as follows:

[0059] The energy consumption of drones primarily stems from overcoming air resistance and gravity. To accurately quantify the energy consumption of drones in complex mountainous terrain, this paper establishes an energy consumption model for drone operation in three-dimensional terrain based on measured physical parameters of the DJI Matrice 4 drone and referencing dynamic models. This model decomposes the drone's spatial motion into three basic modes: horizontal uniform cruise, vertical uniform ascent, and vertical uniform descent, and derives the energy consumption per unit distance for each mode. Let the total thrust of the drone be... The rotor radius is air density is The front area is The air drag coefficient is The total weight of the drone is The drone's width is .

[0060] The drone at a constant speed During vertical ascent, the first term in equation (1) represents the power component overcoming gravity, and the second term represents the rotor-induced power. Energy consumption per unit distance. for:

[0061] (1)

[0062] The drone at a constant speed When descending vertically, gravity does positive work, and the energy consumption per unit distance is... for:

[0063] (2)

[0064] Drones with speed Energy consumption per unit distance during horizontal cruising for:

[0065] (3).

[0066] Specifically, in this embodiment, the specific implementation process of the fire risk measurement model is as follows:

[0067] To construct a fire risk field and classify risk levels, this invention specifically uses the following model to calculate the Fire Risk Index (FRI) for each task area:

[0068] To achieve differentiated inspections based on fire risk, a systematic risk assessment and classification of the task area is required. This embodiment constructs a spatially continuous forest fire risk area based on multi-source geographic information and remote sensing data, and divides the task area into high-risk and low-risk categories according to the risk level, thereby providing a quantitative basis for setting the frequency of differentiated inspections.

[0069] With mission area Using this as the basic unit, the following 8 risk factors are extracted:

[0070] Topographic factors: slope aspect ,slope ,altitude Topographic humidity index

[0071] Human factors: distance from the road Distance from residential areas

[0072] Environmental factors: temperature Vegetation Index

[0073] First, the original observed values ​​of each factor were mapped to discrete risk levels {1, 2, 3, 4, 5} (1 being the lowest risk and 5 the highest risk) based on their correlation with fire risk. Among these, six factors—aspect, slope, altitude, topographic humidity index, temperature, and vegetation index—were analyzed using the methods of Zhang et al.

[28] The proposed empirical grading standard is used to assign values; considering the special characteristics of the spatial distribution of road networks and residential areas, the two factors of distance from roads and distance from residential areas are used for data-driven adaptive grading using the Jenks Natural Breaks method to avoid misjudgment that may be caused by fixed thresholds in heterogeneous areas.

[0074] Based on this, the weights of each factor are determined using the analytic hierarchy process (AHP) to construct the task region. Fire risk index :

[0075] (4)

[0076] Obtain each region Value (range) After that, it was divided into five levels according to the equidistant five-point system; The area is defined as a high-risk area. Based on this, the following risk area delineation rules are established:

[0077] (5)

[0078] Based on this classification result, a differentiated drone inspection strategy is formulated: high-risk areas Execute within each 7-day work cycle A complete monitoring session was conducted in low-risk areas. implement This is a complete monitoring, and The required frequency of inspections in each area can be uniformly expressed as follows:

[0079] (4)

[0080] The specific implementation process of the heading optimization model for the rotary ox-plowing method is as follows:

[0081] After determining the risk level and inspection frequency of the task area, an optimal full-coverage UAV scanning path needs to be planned for each area. Traditional "ox-plowing" scanning, using a fixed heading, is inefficient in mountainous and forested areas with significant terrain undulations. Therefore, this embodiment proposes a rotating "ox-plowing" method for the heading optimization pre-calculation module: for each task area... In the discrete set of candidate heading angles Within the system, the coordinate system is rotated to align the scanning direction with the current candidate heading, thereby generating plowing paths for different headings. By traversing all candidate headings, their total flight energy consumption is calculated and compared, and the heading that minimizes energy consumption is ultimately selected as the optimal scanning heading angle for that region. This optimizes energy consumption per unit area.

[0082] The mathematical model and calculation process are described below, involving the following auxiliary variables: raster coordinates. Coordinates after rotation Number of rows scanned using the ox-plowing method Average line width Horizontal flight distance Vertical flight distance , The grid step size is 30m. All of this embodiment... ;

[0083] (7)

[0084] (8)

[0085] (9)

[0086] (10)

[0087] Equations (7) and (8) complete the coordinate transformation, and the subsequent scanning direction is always along the new horizontal axis. The direction is determined, thus transforming arbitrary directional scanning into horizontal scanning, simplifying path generation. Equation (9) gives the "number of rows plowed by the ox". , The larger the value, the longer the projection length and the more rows, which can directly reflect the impact of rotation on the number of round trips. Then, the average number of pixels per row is calculated to estimate the inter-row turning distance. The GDEMV3 digital elevation model used in this study has a spatial resolution of 30 meters, meaning each grid cell corresponds to a 30-meter × 30-meter area on the ground surface. Equation (10) first places the rotated task area in... In the direction, it is divided into sections with a spacing of 30 meters. The process involves counting the number of grid cells in each row, summing the grid cell counts for all rows, and then averaging the results to obtain the average width. ;

[0088] (11)

[0089] (12)

[0090] (13)

[0091] (14)

[0092] (15)

[0093] (16)

[0094] Based on the above geometric quantities, the task area can be estimated. exist The total horizontal flight distance in the direction, in equation (11), the first term is the in-line movement, and the second term is the inter-line turning back; both terms follow The changes quantify the impact of heading on flight distance. After generating the coverage path, the drone will follow a path... A sequence of ordered waypoints flight, It includes plane coordinates and elevation information.

[0095] Based on the elevation changes between consecutive waypoints, the total descent and total ascent distances can be accumulated separately: In equation (12), The total descent distance is obtained by summing the absolute values ​​of the descending segments. In equation (13), This represents the ascending segment; the total ascending distance is obtained by directly summing the segments. Equation (14) is the core evaluation index of the rotating ox-plowing method: the total energy consumption of the task area, and the goal is to minimize this value. Similarly, Equation (15) calculates the total operation time required to complete the scan, which can be used for feasibility verification and resource capacity balancing of subsequent nest operation cycles. Finally, by traversing the discrete candidate heading angle set, the heading that minimizes energy consumption is selected as the optimal scanning direction, and Equation (16) outputs the optimal heading angle. .

[0096] The specific implementation process of the joint optimization model for drone nest location and drone flight path is as follows:

[0097] After constructing the aforementioned basic models (energy consumption model, risk model, and path optimization model), this invention ultimately integrates a complete joint optimization model for drone nest location and drone flight path. This model is a two-stage stochastic programming model considering multi-cycle operations.

[0098] 1. Multi-cycle operation timeframe

[0099] To ensure the long-term and stable operation of the forest fire risk monitoring network, this embodiment constructs a multi-scale operational time framework, decomposing the ten-year planning period into operable periodic scheduling units. Specifically, the entire operational period (approximately 3650 days) is divided into 521 fixed operational cycles, each lasting 7 days, forming a cycle set. The choice of 7 days as the basic scheduling cycle is based on the following two considerations: From the perspective of monitoring needs, the revisit cycle of current high-resolution remote sensing fire risk products usually exceeds 7 days, making it difficult to effectively capture rapid changes in local weather conditions. [9] Compressing the monitoring cycle to within 7 days helps improve the timeliness of response to fire risk dynamics; from an operational management perspective, a weekly scheduling rhythm facilitates the regular arrangement of tasks and the systematic allocation of resources.

[0100] The model concentrates monitoring resources during the daytime hours when fire risk is highest and monitoring efficiency is optimal, setting the effective daily operating time to 12 hours (06:00–18:00). Therefore, the total effective operating time for each 7-day cycle can be expressed as:

[0101] (17)

[0102] Within this timeframe, the monitoring tasks to be completed within each cycle are determined by the risk classification results: high-risk areas Required to be executed Secondary full-coverage scan, low-risk areas Required to be executed The second full-coverage scan requires all drone operations to be completed within an 84-hour effective time window. This multi-period time framework transforms long-term, ten-year operational decisions into 521 relatively independent periodic scheduling sub-problems. This not only ensures the continuity and periodicity of monitoring work but also significantly reduces the complexity of individual decisions through time-dimensional decomposition, thus laying a temporal foundation for the subsequent construction of a two-stage stochastic programming model.

[0103] 2. Strategic Level: Nest Location Decision

[0104] The overall objective of the first phase is to minimize the long-term total expected cost of the nesting network over the ten-year planning period. This objective function includes deterministic nesting construction costs and expected operating costs based on the probability distribution of weather scenarios, seeking the optimal trade-off between deterministic infrastructure investment and expected expenditures under uncertain weather conditions.

[0105] (18)

[0106] Expected operating costs The following is obtained by taking a probability-weighted average of the minimum operating costs under all possible weather scenarios:

[0107] (19)

[0108] In the formula Given a set of typical meteorological scenarios generated by clustering, this formula quantifies the statistical expectation of the long-term operating cost of the system under meteorological uncertainty.

[0109] 3. Tactical Level: UAV 3D Flight Path Planning

[0110] For a given nest layout With meteorological scenes The tactical level aims to minimize the total cost in the current period. It consists of two parts: the first part is the cost of electricity consumption, of which The unit price of electricity For this scene The first part is the total energy consumed during all drone flights; the second part is the battery depreciation cost, with each charge equivalent to consuming one cycle of the battery's lifespan.

[0111] (20)

[0112] Equations (21) and (22) indicate that each task area must be inspected within each cycle, and only one nest can be responsible for one area. Furthermore, tasks can only be assigned to nests that have already been constructed.

[0113] (twenty one)

[0114] (twenty two)

[0115] in, As the result of the first phase of decision-making, when At that time, the nest Not constructed, all corresponding allocation variables ;

[0116] The total operation time of the avionics in Equation (23) consists of three parts: the total scanning time of all assigned areas, the total flight time to and from these areas, and the time spent charging the battery. Equation (24) ensures that the total operation time must be completed within the effective operation time window of the 7-day cycle:

[0117] (twenty three)

[0118] (twenty four)

[0119] Equation (25) ensures that the total energy consumed to complete all assigned tasks does not exceed the total energy that the nest can replenish through battery charging. For each nest, the energy balance constraint is to ensure flight safety; the energy consumed by the UAV in performing a single mission (i.e., going to an area to perform a scan and return) must ensure that the remaining battery charge after its return is not lower than a safe threshold. Equation (26) is a statement of safety requirements:

[0120] (25)

[0121] (26)

[0122] The total energy consumption of the second-stage objective function (20) The total energy consumption of all nests performing tasks is calculated using the following formula (27):

[0123] (27).

[0124] Specifically, in this embodiment, the implementation process of the improved variable neighborhood search algorithm is as follows:

[0125] To efficiently solve the aforementioned two-stage stochastic programming model, this embodiment designs an improved two-stage cooperative variable neighborhood search algorithm. The core of this algorithm lies in decomposing the complex joint optimization problem into two consecutive stages: layout optimization and operational scheduling. Through systematic neighborhood perturbation and switching, an effective balance is achieved between global exploration and local optimization. The overall algorithm process includes initialization, scene clustering, heading pre-calculation, and the core VNS loop.

[0126] Overall solution process and initialization:

[0127] The initialization module provides standardized input for the entire optimization process, ensuring the algorithm runs on a unified and complete data foundation. First, the geospatial data is preprocessed: three layers of data are read: a 30-meter resolution digital elevation model, the boundary vector of the study area, and candidate drone nest locations. A unified coordinate system is established and resampled to the same spatial resolution. Data integrity checks are performed to ensure no missing data, closed boundaries, and that all candidate points are within the valid area. Subsequently, all model parameters are loaded and validated, including UAV technical parameters and economic cost parameters. These parameters are centrally managed to avoid numerical inconsistencies across different modules of the algorithm. Based on the preprocessed data, the task area is divided and its attributes are calculated: a uniform-area grid is generated using the study area boundary as the basic task unit. For each valid task area, various fire risk factors corresponding to its center location are extracted, and the fire risk index is calculated based on the fire risk measurement model. Areas are then classified as high-risk or low-risk according to preset thresholds. Simultaneously, the elevation information of each area is recorded, and the Euclidean distance between each area and all candidate drone nest locations is calculated. Finally, the timeframe and operational configuration were established: 521 7-day work cycles were defined for the ten-year operation period, and the cycle counter and date mapping were initialized. All generated intermediate data (such as task area lists, risk levels, distance matrices, parameter tables, etc.) were stored in a standardized format to ensure that the entire optimization framework has good repeatability and portability.

[0128] Scene clustering and heading angle pre-calculation:

[0129] To characterize the long-term changing patterns of meteorological and vegetation conditions, this embodiment uses a three-level clustering method to extract typical meteorological scenarios from historical data over many years.

[0130] The first-level clustering is performed by month: Monthly temperature and Normalized Differential Vegetation Index (NDVI) raster data for N consecutive years (N ≥ 15) are organized into 12 data cubes. After standardizing the data for each month, the K-means clustering algorithm is used, and the elbow rule (the second difference of the sum of squared observation errors (SSE)) is applied to automatically determine the optimal number of clusters for that month. This step achieves the classification of samples from the same month over many years, preserving extreme differences in temperature and vegetation greenness between different years within the same month.

[0131] The second-level clustering builds upon the first-level results: for each "year-month" combination, the spatial frequency of each first-level cluster within the study area is calculated, forming a frequency vector. This frequency vector is then used to construct a matrix from all "year-month" samples, and K-means clustering is performed again. The elbow rule is used to determine the number of clusters, resulting in a set of intermediate scenarios. Each intermediate scenario represents a cross-year, cross-month weather-vegetation combination pattern, compressing the data size while avoiding the ambiguity of seasonal characteristics that might result from direct cross-month clustering.

[0132] The third-level clustering aims to further merge similar patterns and generate a comprehensive set of typical scenarios for final planning. The intermediate scenario frequency vector from the second-level output is used as input for a final K-means clustering operation, with an upper limit of 10 clusters. This results in a set of 6–10 comprehensive typical scenarios, with the frequency of each scenario's occurrence in historical records used as its probability of occurrence. This three-level clustering process runs fully automatically, requiring only the original raster data and a few configuration parameters as input. The resulting set of "scene-probability" pairs... It can effectively characterize various combinations of temperature and vegetation states that have occurred in history and their frequency of occurrence, providing a reliable uncertainty input for two-stage stochastic programming models.

[0133] For each task area The optimal heading angle is calculated to minimize scan energy consumption. This process involves calculating the optimal heading angle for each candidate heading angle. Evaluation: First, calculate the corresponding horizontal energy consumption, ascent energy consumption, and descent energy consumption. Then, based on the rotating ox-plowing model in Section 2.4, determine the total energy consumption required to perform a full-coverage scan in this flight direction. The heading angle that minimizes total energy consumption is selected as the optimal heading angle. The optimal heading angle for each task area will be stored in the database for subsequent periodic traversal and path planning.

[0134] Based on the two-stage stochastic programming model constructed above, the overall solution process follows the framework of "strategic site selection first, scenario assessment later". First, all standardized input data are loaded, including the task area and its risk level, candidate nesting sites, spatial distance matrix, typical scenario set generated by clustering historical data and its corresponding probabilities, and all technical and economic parameters.

[0135] The solution process corresponds to a two-stage structure in the model: The first stage uses an optimization algorithm to perform a global search across the candidate point set to determine the final location of the hub. This decision must satisfy spatial coverage constraints and aim to minimize the total expected cost. The second stage evaluates each candidate location and calculates its expected operating cost, which is the probabilistic weighted sum of operating costs under various weather scenarios. Since accurately solving the optimal scheduling problem for each scenario is computationally inefficient, this framework employs a fast heuristic estimator based on greedy rules for approximate calculation. This estimator can quickly generate feasible task allocation and charging scheduling plans for any given location and weather scenario, and estimate the corresponding operating costs.

[0136] The optimization algorithm ultimately outputs the drone nesting scheme with the lowest expected total cost. For this optimal scheme, detailed offline scheduling simulations can be run to verify its operational performance under various typical weather scenarios, and corresponding drone inspection paths and charging scheduling strategies can be generated, providing decision-making references for actual operations. This overall process achieves efficient acquisition of high-quality, robust planning schemes by decomposing the complex stochastic programming problem into several manageable steps and leveraging a collaborative mechanism of outer-layer optimization and inner-layer evaluation.

[0137] Core design of the variable neighborhood search algorithm:

[0138] 1. Decoding scheme

[0139] To address the coexistence of continuous location decision-making and discrete task scheduling in this problem, a hybrid encoding strategy is designed to fully represent the solution structure. The nest location is encoded using integer coordinate vectors to ensure that each coordinate point lies within the effective area of ​​the digital elevation model. Each coordinate corresponds to a valid row and column number in the digital elevation model; task scheduling uses grouped sequence encoding, maintaining an independent task execution order list for each nest and preserving the task-nest affiliation; battery management parameters use real number encoding, with a return threshold set independently for each nest. This hybrid encoding method maintains the physical feasibility of the solution and provides a clear and operable data interface for subsequent operators such as position perturbation, task rearrangement, and parameter adjustment.

[0140] 2. Core Operator Design

[0141] The algorithm's performance is guaranteed by a set of core perturbation operators. During the layout optimization phase, the position perturbation operators randomly adjust the nest coordinates according to preset small, medium, and large perturbation intensities to balance local depth search and global exploration. This operator incorporates boundary wrapping and terrain verification mechanisms to ensure that the new coordinates are always valid. Figure 3 (a) Figure 3As shown in (b), when the system detects a severe load imbalance between nests, the rebalancing operator is triggered, automatically migrating low-load nests to the vicinity of high-load areas, aiming to indirectly balance task allocation through spatial adjustment.

[0142] After a perturbation or rebalancing operation, the repair operator, based on the "nearest neighbor" principle, reassigns all task regions to the latest nest set to quickly restore the feasibility of the solution. Following repair, the rapid evaluation module calculates the operational cost of the new solution, providing a quantitative basis for algorithmic decision-making.

[0143] Once the parameter tuning phase begins, the task sequence perturbation operator starts working, optimizing the task execution sequence within each nest through swapping, reversing, or rearranging operations, while maintaining task affiliation. In conjunction with this, the battery threshold perturbation operator fine-tunes the return-to-home battery threshold for each nest within a safe range, seeking the optimal balance between energy efficiency and mission reliability. The overall process and data interaction during the parameter tuning phase are as follows: Figure 4 (a) Figure 4 As shown in (b).

[0144] 3. Search Strategy and Convergence Mechanism

[0145] The algorithm employs a standard variable neighborhood search framework, executed in two phases: the first phase focuses on nest layout, primarily using location perturbations and secondarily on rebalancing; the second phase focuses on operational parameters, with task order and battery threshold perturbations as the core, to repair the feasibility of the solution guaranteed throughout the process. An adaptive neighborhood switching strategy is used within each phase: if a perturbation produces a better solution, it is accepted and reset to a mild perturbation mode; otherwise, the perturbation intensity is gradually increased to escape local optima. The entire search is completed within a fixed number of iterations (160 in the first phase and 40 in the second phase), ultimately outputting the historical best solution, achieving controllable computational overhead while ensuring solution quality.

[0146] Experimental verification and result analysis

[0147] To verify the effectiveness, superiority, and practicality of the technical solution of this invention, a comprehensive test and comparative analysis were conducted based on the aforementioned forest park embodiment. The key experimental results are as follows.

[0148] 1. Algorithm Performance Comparison

[0149] To systematically verify the comprehensive performance of the improved Variable Neighborhood Search (VNS) algorithm proposed in this invention, simulated annealing (SA) and genetic algorithm (GA) were selected as benchmarks for comparison. To ensure the fairness of the comparison and the robustness of the conclusions, all comparison algorithms were run under the same initial conditions (including fire risk field, 7-day operation cycle, hardware parameters, and candidate hive locations). Given the complexity of the problem-solving process, each algorithm was run independently 5 times, and the average of the results was taken as the performance index of the algorithm to objectively evaluate its stability and average optimization performance. Performance evaluation focused on three dimensions: economy, energy efficiency, and timeliness, with specific indicators as follows:

[0150] (1) Overall economic efficiency: The optimal score is used for measurement. This indicator is the best operating cost obtained in 5 runs (calculated by formula (20)). It comprehensively reflects the energy consumption and battery depreciation. The lower the value, the better the economic efficiency.

[0151] (2) Energy efficiency: This includes two indicators: total energy consumption and total number of flights. Total energy consumption is obtained by weighting and accumulating the three-dimensional energy consumption model of UAVs (1)–(3) according to each weather scenario; total number of flights is the number of times all UAVs are dispatched in a single cycle. Reducing the number of flights can directly reduce battery cycle loss and corresponding depreciation costs.

[0152] (3) Operation timeliness: Characterized by the maximum working time (i.e. the longest nest operation time required to complete all inspection tasks in a single cycle). This indicator directly reflects whether the scheduling scheme meets the time constraint of the 7-day cycle (84 hours).

[0153] Table 4 Comparison of core performance indicators of different algorithms

[0154]

[0155] The optimal results of each algorithm in 5 runs are shown in Table 4. VNS achieved optimal values ​​in all four metrics: its optimal operating cost (335.63) was 0.80% and 1.65% lower than GA and SA, respectively; and its total energy consumption (2.507 × 10⁻⁶) was lower than GA and SA, respectively. 8 The energy consumption per joule (J) decreased by 1.18%–1.49%; the total number of flights (509) decreased by 6–8; and the maximum operating time (71.2 hours) was shortened by 2.0–6.1 hours, a reduction of 2.76%–7.90%. This indicates that VNS has advantages in improving economic efficiency, reducing energy consumption, reducing equipment wear and tear, and ensuring scheduling feasibility.

[0156] In summary, the improved VNS algorithm achieves an effective balance between global exploration and local optimization by combining the outer layer's variable neighborhood perturbation of the nest layout with the inner layer's heading optimization based on the rotating ox-plowing method. This results in superior solution quality and stability compared to traditional heuristic algorithms, providing an efficient and reliable solution tool for the collaborative planning of forest fire risk monitoring networks.

[0157] 2. System Scale Decision and Cost Analysis

[0158] To determine the optimal system size for the monitoring network, it is first necessary to define a reasonable range for the number of drone nests. This study conducts a preliminary assessment based on the total area of ​​the mission region, the maximum coverage radius of a single drone sortie (determined by battery capacity and safe return threshold), and a basic coverage model. Preliminary analysis shows that when the number of nests is less than 5, some peripheral mission areas will exceed the maximum effective operating radius of the drones, failing to meet the basic requirement of full coverage; while when the number is more than 8, construction costs will increase significantly, and the cost savings due to increased coverage overlap have shown a clear trend of diminishing marginal returns. Therefore, to achieve a balance between ensuring the feasibility of full coverage and controlling the potential for cost increases, four representative and reasonably ranged nest sizes of 5, 6, 7, and 8 were selected for refined comparative analysis and optimization to scientifically determine the optimal number.

[0159] Based on the previously demonstrated high-performing VNS algorithm as the solver, this embodiment evaluates the four scale schemes mentioned above with the core objective of minimizing the total expected cost over a ten-year period. First, it assesses whether each scheme meets the hard constraint on operation time set in Section 2 (all inspection tasks must be completed within a 7-day cycle). As shown in Table 5, the longest single-cycle time for the 5-nest scheme (8.05 days) exceeds the 84-hour constraint and is therefore deemed infeasible. The longest cycles for the 6, 7, and 8-nest schemes are all less than 7 days, thus meeting the feasibility requirements.

[0160] Table 5. Order cycle time performance for different cluster sizes

[0161]

[0162] Table 6. Cost Breakdown Over Ten Years for Different Nest Sizes

[0163]

[0164] Among the feasible 6, 7, and 8 nesting configurations, the optimal scale needs to be further determined based on economic factors. A ten-year total cost analysis (Table 6) shows that the 6 nesting configurations minimized long-term total costs. Battery depreciation costs accounted for the highest proportion (44.01%), becoming the key factor affecting total costs. Although the average operating time of the 7 and 8 nesting configurations was slightly shorter, and the operating costs (the sum of battery depreciation and electricity costs) decreased slightly due to fewer flights, the resulting operating cost savings were extremely limited (the 7 and 8 nesting configurations saved RMB 18,200 and RMB 28,600 respectively compared to the 6 nesting configuration), far from enough to offset the additional construction costs incurred by the increased number of nests (the construction costs of the 7 and 8 nesting configurations increased by RMB 215,100 and RMB 430,200 respectively compared to the 6 nesting configuration).

[0165] In summary, the six nesting schemes achieve the optimal balance between construction investment and long-term operating expenses while strictly meeting the time constraints, thus minimizing the total cost over the system's lifecycle. Therefore, this study determines six nesting schemes as the optimal system size. The following sections will provide a detailed visualization and in-depth analysis of this optimal scheme.

[0166] After determining the optimal spatial layout of the six nests and the allocation of mission areas, specific flight routes need to be planned for each nest and its assigned mission area. This embodiment will use multi-scale visualization to display the generated route network and its safety assurance design from both global and local perspectives.

[0167] First, examine the system's spatial configuration from a global perspective. Figure 5 The diagram illustrates the spatial hierarchy of all six nests (triangle markers) and their respective task areas (dots of the same color). This visually reflects the output of the optimization model in the first phase: while ensuring coverage of all task areas, it achieves a balanced distribution of workload among the nests, laying the structural foundation for subsequent route planning.

[0168] After determining the task area responsible for each nest, a system security system needs to be established. Figure 6 The overlay displays a network of return-to-home points (pentagram markers) pre-defined for the entire system. It's important to clarify the function of these return-to-home points: they are pre-defined locations in the model based on the geometry of the mission area and the drone's endurance, used to mark the power management boundaries where the drone should begin its return journey. Figure 7 The No. 3 nest was shown in a magnified view.

[0169] After determining the optimal spatial layout of the six nests and the allocation of mission areas, specific flight paths need to be planned for each mission area. To fully demonstrate the adaptability of the flight path planning method to different mission scenarios, this embodiment selects four typical areas and compares them through two-dimensional and three-dimensional visualization.

[0170] like Figure 8 The figure shows the two-dimensional trajectory planning results for Region 5 (high-risk boundary area) and Region 2 (low-risk boundary area). The left side represents the high-risk area (Region 5), with its complete coverage path marked in red, corresponding to a higher monitoring frequency of "4 inspections per cycle." The right side represents the low-risk area (Region 2), with its complete coverage path marked in blue, corresponding to a lower monitoring frequency of "2 inspections per cycle," visually reflecting the significant difference in trajectory planning under differentiated inspection strategies. The figure clearly shows the nest location, mission start and end points, the optimal scan path generated by the rotating ox-plowing method, and the return point. As a boundary area, its nest layout is geographically constrained, and trajectory planning must balance coverage integrity and boundary safety constraints. Figure 9 The flight trajectories of the same two boundary areas are further shown in a 3D view. Figure 9 The left side shows the 3D flight path of high-risk area 5. Figure 9 The right side shows the 3D flight path of low-risk area 2. The 3D view intuitively reveals how the UAV's flight path undulates and conforms to the terrain in complex boundary terrain. The flight path adaptively adjusts with changes in terrain, demonstrating the effectiveness of the rotary tillage method in 3D space.

[0171] like Figure 10 As shown, the two-dimensional trajectory planning results for Region 106 (high-risk internal region) and Region 118 (low-risk internal region) are presented. Compared with the boundary regions, the nesting layout in the internal regions is more flexible, and trajectory planning can be more fully optimized based on the principle of optimal energy consumption. Similarly, using a comparison method of high risk on the left (red) and low risk on the right (blue), the impact of risk level on trajectory density and coverage strategy is clearly demonstrated. Figure 11 The flight trajectories of the two interior regions were compared using 3D views. The 3D views further revealed the adaptability of the flight path to the terrain in the vertical dimension. The undulating shape of the flight path in the interior region contrasts with that in the boundary region, demonstrating the planning effectiveness of the method in different spatial locations.

[0172] The side-by-side comparison of the four composite diagrams clearly demonstrates that the trajectory planning model proposed in this embodiment can simultaneously adapt to mission requirements with different risk levels (high risk and low risk) and different spatial locations (boundary areas and interior areas). Furthermore, regardless of whether it is a geographically constrained boundary area or a freely laid-out interior area, the model can generate complete, feasible, and terrain-adaptive flight paths, verifying the robustness and universality of the method.

[0173] 3. Verification of the effectiveness of heading angle optimization

[0174] To verify the effectiveness of the rotating ox-plowing method for optimizing the heading angle, this embodiment, under the optimal six-nest layout, compared the fixed heading (0°, 90°) with the optimized heading angle based on measured terrain data from 186 task areas. The performance under different inspection modes is shown in Table 6. Table 6 lists the total system energy consumption and operation time under two typical inspection modes. Mode ① represents a full-coverage scan of the entire study area (single full-area scan), while Mode ② represents a differentiated inspection strategy (4 inspections per cycle for high-risk areas and 2 inspections per cycle for low-risk areas).

[0175] Table 7 Comparison of traversal energy consumption and operation time at different heading angles

[0176]

[0177] As shown in Table 7, the optimal heading angle achieved the lowest energy consumption in both modes. Compared to the second-best performing 0° heading, energy consumption was reduced by an average of approximately 0.5%; compared to the least efficient 90° heading, energy consumption was reduced by an average of approximately 1.0%. In terms of operation time, the optimal heading angle performed essentially the same as the 0° heading (difference <0.2%), but significantly shortened the operation time by approximately 30% compared to the 90° heading. Based on the above-mentioned savings per task, the cumulative benefits in long-term operation can be further estimated. Using a calculation framework of 52 operation cycles per year, 4 inspections per cycle in high-risk areas, and 2 inspections per cycle in low-risk areas, if the entire system adopts the optimal heading angle instead of the 0° heading, the cumulative energy savings over a ten-year operation period are estimated to be approximately [amount missing]. Joules; compared to a 90° heading, the cumulative energy savings can reach approximately Joules. This indicates that while the rotating ox-plowing method, by adaptively matching the optimal heading for each task area, has limited energy savings in a single task, it generates significant cumulative economic and environmental benefits through continuous energy cost savings and effective delays in battery depreciation during long-term routine operation. This optimization method provides key technical support for efficient track inspection and further verifies the practical value of the heading optimization mechanism proposed in this embodiment in the entire life cycle operation.

[0178] 4. Robustness verification of stochastic programming model

[0179] To verify the superiority of the proposed two-stage stochastic programming (SP) model in addressing weather-fire uncertainty, this embodiment compares it with traditional deterministic programming methods. The experimental design is as follows: First, the deterministic model is solved independently for each of the eight typical weather scenarios, yielding eight scenario-specific optimal layouts (denoted as DE). Then, the two-stage stochastic programming model considering the probability distribution of all scenarios is solved, resulting in a robust layout scheme (denoted as SP). Finally, all nine layout schemes are placed under all eight weather scenarios to re-evaluate their long-term operational performance.

[0180] To quantify the evaluation results, two standard metrics for stochastic programming are introduced:

[0181] Expected Value of Perfect Information (EVPI): This metric reflects the upper limit of the theoretically optimal return achievable with complete weather information (i.e., knowing in advance what scenarios will occur in each period). It is calculated by subtracting the average expected value of the scenario-specific optimal solution from the expected value of the stochastic programming solution.

[0182] Value of Stochastic Solution (VSS): This metric measures the actual improvement of a stochastic programming solution compared to a deterministic solution. It is calculated by subtracting the expected value of the stochastic programming solution from the average performance of the deterministic solution across all scenarios.

[0183] Table 8 selects four key samples for display: the best-performing deterministic solution (DE1), the worst-performing deterministic solution (DE2), the stochastic programming solution (SP), and the theoretically best perfect information solution (PI), forming a complete comparison system.

[0184] Table 8. Performance Comparison Analysis of Deterministic Model and Stochastic Programming Scheme

[0185]

[0186] The stochastic programming solution (SP) exhibits significant robustness and economic advantages. As shown in Table 8, SP outperforms both the optimal and deterministic solutions (DE1 and DE2) across all operational metrics. Specifically, the SP solution reduces the total number of operating days and total energy consumption over ten years by 18.2% and 11.0% respectively compared to the optimal deterministic solution (DE1), effectively mitigating the risk of system overload in other scenarios due to optimization for specific scenarios. Furthermore, the performance gap between the SP solution and the perfect information solution (PI) is extremely small (EVPI value is much smaller than VSS), indicating that the two-stage stochastic programming model can closely approximate the theoretical optimum under uncertain conditions.

[0187] In summary, the two-stage stochastic programming model, by explicitly integrating multiple meteorological scenarios and their probability distributions, generates an optimized solution that can effectively balance conflicting demands under different scenarios. This not only ensures long-term economic viability but also significantly improves the overall robustness of the monitoring system in the face of environmental fluctuations.

[0188] Specifically, this invention also proposes a joint optimization system for a low-altitude forest fire risk monitoring network, comprising:

[0189] The data acquisition and processing module is used to acquire and process geographic information, meteorological and vegetation data to perform risk perception and task planning.

[0190] The optimization decision module communicates with the data acquisition and processing module and is used to construct and solve a two-stage optimization decision model.

[0191] Multiple drone nests are deployed in the forest area according to the nest layout scheme output by the optimization decision module, and are used for drone take-off and landing, energy supply and mission reception and distribution;

[0192] The drone swarm is configured to take off from its nest and execute the flight path plan generated by the optimization decision module to complete the inspection of the designated task area.

[0193] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A joint optimization method for a forest fire danger low-altitude monitoring network, characterized in that, Includes the following steps: S1. Risk perception and mission planning: acquire multi-source geospatial data and meteorological data of the target forest area, assess the fire risk level of each sub-area based on the data, and set differentiated drone inspection frequencies according to different risk levels. S2. Joint optimization modeling of infrastructure and operations: A two-stage optimization decision model is established. The first stage determines the spatial location and number of UAV nests. The second stage optimizes the flight path and task scheduling sequence of UAVs from each nest to their assigned task area for various future operation scenarios. The model takes minimizing the total expected cost of the system over its entire life cycle as the objective function. S3. Model Solving and Scheme Output: An optimization algorithm is used to solve the two-stage optimization decision model to obtain the optimal nest layout scheme, task area allocation scheme, and corresponding UAV flight path plan. 2.The method for joint optimization of forest fire danger low-altitude monitoring network according to claim 1, characterized in that, The multi-source geospatial and meteorological data in step S1 include multiple data such as digital elevation model, temperature, vegetation index, slope, aspect, altitude, topographic humidity index, distance from road and distance from settlement. 3.The method of claim 1, wherein, The specific implementation process of step S1 includes: Based on the acquired data, the task area is divided. In the task area division stage, based on the boundary vector data, the Digital Elevation Model (DEM) is used in the ArcGIS software platform for mask extraction to obtain the actual spatial range of the core experimental area. Construct basic spatial analysis units, and deploy uniform and regular grids within the core experimental area; Through spatial overlay analysis, grids that do not intersect with the boundary of the experimental area are eliminated, and some grids that cross the boundary are clipped and merged to obtain several task areas that fully cover the study area.

4. The joint optimization method of the mountain forest fire danger low-altitude monitoring network according to claim 1, characterized in that, The diverse future operation scenarios in step S2 are typical scenarios generated by clustering analysis of historical meteorological data.

5. The joint optimization method of the mountain forest fire danger low-altitude monitoring network according to claim 1, characterized in that, The two-stage optimization decision model in step S2 is a two-stage stochastic programming model, and the specific implementation process is as follows: Construct a multi-cycle task time framework; The spatial location decision for drone nests aims to minimize the long-term total expected cost of the nest network. This objective function includes deterministic nest construction costs and expected operating costs based on the probability distribution of weather scenarios, seeking the optimal trade-off between deterministic infrastructure investment and expected expenditures under uncertain weather conditions. （18） Expected operating cost By probabilistically averaging the minimum operating cost over all weather scenarios, we obtain: （19） where A typical set of weather scenarios generated for clustering, which quantifies the statistical expectation of the long-term system operation cost under weather uncertainty; Three-dimensional route planning for unmanned aerial vehicles, for a given nest layout and weather scenarios , minimizing the total cost at each period , which is composed of two parts: the first part is the electricity consumption cost, where is the unit electricity price, is the total energy consumed by all the UAVs flying in the scene ; the second part is the battery depreciation cost, which is equivalent to consuming a battery's full cycle life each time it is charged, （20） Equations (21) and (22) indicate that each task area must be inspected in each cycle, and only one nest can be responsible for one area; at the same time, tasks can only be assigned to nests that have actually been built: （21） （22） wherein, is the first stage decision result, when the nest is not built, all the allocated variables ; The total operation time of the avionics in equation (23) consists of three parts: the total scanning time of all assigned areas, the total flight time to and from these areas, and the time spent charging the battery; equation (24) ensures that the total operation time must be completed within the effective operation time window of the cycle: （23） （24） Equation (25) ensures that the total energy consumed to accomplish all the assignments cannot exceed the total energy that can be replenished by the battery charging at the nest; for each nest, the energy balance constraint is that the energy consumed by the UAV to perform a single assignment must ensure that the battery has a remaining capacity above a safety threshold upon return Equation (26) is a safety requirement expression: （25） （26） Total energy consumption of the second stage objective function (20) The total energy consumption of all the nests performing the task is calculated by the following equation (27): （27）。 6. The joint optimization method for the low-altitude forest fire risk monitoring network according to claim 1, characterized in that, In step S3, the optimization algorithm is a variable neighborhood search algorithm, which specifically decomposes the complex joint optimization problem into two stages: continuous layout optimization and operation scheduling. Through systematic neighborhood perturbation and switching, an effective balance is achieved between global exploration and local optimization. The overall process of the algorithm includes initialization, scene clustering, heading pre-calculation, and the core VNS loop.

7. The joint optimization method for the low-altitude forest fire risk monitoring network according to claim 1, characterized in that, Step S3 also includes: when optimizing the UAV flight path, a path coverage algorithm is used to optimize the scanning heading for each task area based on its geometric features and terrain undulations, thereby minimizing flight energy consumption; wherein, the path coverage algorithm is the rotary oxen plowing method.

8. The joint optimization method for the low-altitude forest fire risk monitoring network according to claim 7, characterized in that, The specific implementation process of the rotary ox plowing method is as follows: For each task area In the discrete set of candidate heading angles Within the system, by rotating the coordinate system to align the scanning direction with the current candidate heading, different ox-plowing paths are generated under different headings. By traversing all candidate headings, their total flight energy consumption is calculated and compared, and finally, the heading that minimizes energy consumption is selected as the optimal scanning heading angle for that region. This optimizes energy consumption per unit area. Its mathematical model and calculation process involve the following auxiliary variables: raster coordinates Coordinates after rotation Number of rows scanned using the ox-plowing method Average line width Horizontal flight distance Vertical flight distance , Grid step size 30m; all ; （7） （8） （9） （10） Equations (7) and (8) complete the coordinate transformation, and the subsequent scanning direction is always along the new horizontal axis. Direction: Converts arbitrary direction scanning into horizontal scanning, simplifying path generation; The average number of pixels per row is counted to estimate the inter-row turning distance. The spatial resolution of the GDEMV3 digital elevation model is 30 meters, that is, each grid cell corresponds to a 30-meter × 30-meter area on the ground surface; Equation (10) first rotates the task area in In the direction, it is divided into sections with a spacing of 30 meters. The process involves counting the number of grid cells in each row, summing the grid cell counts for all rows, and then averaging the results to obtain the average width. ; （11） （12） （13） （14） （15） （16） Based on the above geometric quantities, estimate the task area. exist The total horizontal flight distance in the direction, in equation (11), the first term is the in-line movement, and the second term is the inter-line turning back; both terms follow Changes in course are used to quantify the impact of flight distance. After generating the coverage path, the drone will follow a path consisting of... A sequence of ordered waypoints flight, Includes plane coordinates and elevation information; Based on the elevation changes between consecutive waypoints, the total descent and total ascent distances are accumulated respectively: In equation (12), The total descent distance is obtained by summing the absolute values ​​of the descending segments. In equation (13), This represents the ascending segment; the total ascending distance is obtained by directly summing the segments. Equation (14) is the core evaluation index of the rotary ox plowing method: the total energy consumption of the task area, and the goal is to minimize this value; Equation (15) calculates the total operation time required to complete the scan, which is used for feasibility verification and resource capacity balance of subsequent nest operation cycles; By traversing the set of discrete candidate heading angles, the heading that minimizes energy consumption is selected as the optimal scanning direction, and equation (16) outputs the optimal heading angle. .

9. A joint optimization system for a low-altitude forest fire risk monitoring network, characterized in that, include: The data acquisition and processing module is used to acquire and process geographic information, meteorological and vegetation data to perform risk perception and task planning. The optimization decision module communicates with the data acquisition and processing module and is used to construct and solve a two-stage optimization decision model. Multiple drone nests are deployed in the forest area according to the nest layout scheme output by the optimization decision module, and are used for drone take-off and landing, energy supply and mission reception and distribution; The drone swarm is configured to take off from its nest and execute the flight path plan generated by the optimization decision module to complete the inspection of the designated task area.

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