Forest fire identification and prediction method based on bidirectional coupling mechanism

By combining the bidirectional coupling mechanism of the deep learning model FCN and the Rothermel physical model, the problems of limited training data and accumulated prediction errors in forest fire identification and prediction are solved, high-precision fire identification and fire intensity prediction are achieved, and full-cycle emergency decision-making is supported.

CN120635730AActive Publication Date: 2025-09-12NORTH CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY
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Patent Information

Application Number
CN202511154994.7
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-08-18
Publication Date
2025-09-12
Estimated Expiration
2045-08-18

AI Technical Summary

Technical Problem

Existing technologies in forest fire identification and fire spread prediction have problems such as limited training data, insufficient model generalization ability, lack of interpretability, and accumulated prediction errors.

Method used

A method based on a bidirectional coupling mechanism is adopted, combining the deep learning model FCN and the Rothermel physical model. Fire scene segmentation is achieved through an improved fully convolutional network FCN, and the Rothermel model is used to predict fire spread. The initial boundary of the Rothermel model is dynamically corrected through the FCN recognition results. Different features and parameter optimizations are applied in stages to achieve collaborative optimization of recognition and prediction.

Benefits of technology

It significantly improves the accuracy of fire identification and fire prediction, reduces errors, provides full-cycle forest fire identification and prediction support, and helps emergency decision-making to reduce disaster losses.

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Abstract

The invention discloses a forest fire identification and prediction method based on a bidirectional coupling mechanism, which belongs to the technical field of disaster prediction and comprises the following steps of data preprocessing, fire source identification, fire behavior prediction, coupling optimization and staged application. According to the system, a bidirectional coupling mechanism of a full convolutional network FCN and a Rothermel model is innovatively constructed, and collaborative optimization of fire identification and spreading prediction is realized. Wherein the FCN takes ResNet50 as a backbone network, and accurately outputs a discretized boundary of a fire area by dynamically adjusting jump connection and a self-adaptive upsampling coefficient in combination with a cross entropy and Dice combination loss function so as to provide a reliable initial boundary for prediction; and meanwhile, a Rothermel physical rule is utilized to constrain the FCN to reduce an identification error, and a differential cooperation strategy is implemented for four stages (T1-T4) of the fire, so that the fire identification and prediction precision and stability in a complex scene are remarkably improved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of disaster prediction, and in particular is a forest fire identification and prediction method based on a bidirectional coupling mechanism. Background Art

[0002] Forest fires pose a serious threat to the environment, causing not only direct economic losses but also profoundly impacting regional ecological restoration and the global carbon cycle. Therefore, how to reduce disaster losses through efficient and accurate early fire detection technology and scientific spread prediction modeling to support emergency decision-making has become a key issue in the field of disaster prevention and mitigation.

[0003] At present, many scholars at home and abroad have made contributions to improving the recognition efficiency and prediction accuracy of forest fire identification and fire spread prediction. In the field of forest fire identification, Li Yi proposed a fast and efficient fire detection model based on MobileNetV3 and anchor-free structure. This model has better performance and speed on public fire datasets and is suitable for real-time fire detection and embedded device applications; WuS proposed a multi-scale fire image detection method combining convolutional neural network (CNN) and Transformer. In the field of fire spread prediction, M.Byari proposed a suitable multi-scale CA modeling method based on 3D geometric units. The proposed method is used as part of the entire forecasting system to predict wildfire spread. Edigley et al. used a two-stage prediction scheme to adjust unknown parameters for the input data describing the fire scene in the forest fire simulation model to reduce the high uncertainty of the fire scene input data.

[0004] Based on the above research, deep learning models have been widely used in the field of forest fire identification. However, due to factors such as limited training data, insufficient model generalization, and a lack of interpretability (fires are often accompanied by complex phenomena such as smoke and varying lighting), single deep learning models often perform poorly in practical applications. In the field of fire spread prediction, the Rothermel model, as the most commonly used and widely accepted physical model, can return the fire spread rate under specific conditions. However, this model requires high precision in its input parameters, and its uncertainty can lead to cumulative prediction errors. Summary of the Invention

[0005] To overcome the problems mentioned in the aforementioned background technology, this paper proposes a forest fire identification and prediction method based on a bidirectional coupling mechanism. This method deeply integrates a deep learning model (FCN) with the Rothermel physical model, leveraging their complementary strengths to achieve high fire identification accuracy and low fire intensity prediction error.

[0006] The present invention adopts the following technical solution: a forest fire identification and prediction method based on a bidirectional coupling mechanism, which includes the following steps: A forest fire identification and prediction method based on a bidirectional coupling mechanism, characterized in that the method comprises the following steps: Fire source identification: Fire scene segmentation is achieved using an improved fully convolutional network (FCN). The FCN uses ResNet50 as the backbone network and integrates ConvBlock and IdentityBlock. It optimizes feature fusion by dynamically adjusting the number of skip connections and adaptive upsampling coefficients to output the discretized boundaries of the fire area. Fire Prediction: Based on NASA meteorological data and fire source identification results, the Rothermel model is used to predict fire spread; Coupling optimization: Repair edge breaks in FCN output boundaries, establish a collaborative mechanism between FCN and Rothermel models, dynamically correct the initial boundaries of the Rothermel model based on FCN recognition results, and use Rothermel physical rules to constrain FCN recognition errors; Phased application: Fire spread is divided into four stages: early ignition T1, accelerated spread T2, stable combustion T3, and decay T4. In stage T1, FCN is used to reduce noise interference. In stages T2-T3, FCN texture features are combined with Rothermel dynamic parameter adjustment. In stage T4, FCN is used to identify burnt areas to correct Rothermel prediction bias.

[0007] Furthermore, in the data preprocessing, a dedicated dataset was constructed containing aerial fire images and laboratory combustion data; the aerial images covered forest scenes, and the laboratory data included 10 sets of outdoor steel wool burning experiments. The annotations were generated using the LabelImg tool in PASCAL VOC format XML files, and the dataset was divided into training and test sets in a ratio of 0.85:0.15.

[0008] Furthermore, the FCN includes a head module, which reduces the feature map channels to the number of categories through a 1×1 convolution layer, restores the original size through bilinear interpolation, and sets an auxiliary classifier to extract features from Layer 3 of ResNet to accelerate training.

[0009] Furthermore, the Rothermel model inputs combustible density, wind speed, and slope parameters, and outputs the spread rate and burned area. The model can be simplified as follows: , R is the fire spread rate; I R is the reaction intensity of the flame zone; ζ is the dimensionless fire spread rate, P b is the density of the combustible bed; ε is the effective heat coefficient; Q ig is the pre-combustion heat, where the wind speed correction factor ΦW and slope correction factor Φ S Calculated using the following formula: , , Among them, U is the wind speed, is the fuel bed stacking ratio, For the optimal stacking ratio, is the fuel bed density, C, B, E is a constant, is the slope correction coefficient, is the slope angle, K 1 is the forest fire model coefficient, The spreading rate at different angles θ .

[0010] Furthermore, the morphological processing of edge break repair in the coupled optimization includes a closing operation to repair small holes and a dilation operation to fill edge breaks.

[0011] Furthermore, in the staged application module: in the early fire stage T1, FCN suppresses the noise of star-shaped fire point identification through deep features, and the Rothermel model predicts the area of ​​the next stage based on circular diffusion features; from the diffusion acceleration stage T2 to the stable combustion stage T3, the flame area forms a continuous thermal radiation belt, FCN captures the high-frequency texture features of the flame, and the Rothermel model adjusts the prediction trajectory based on real-time wind speed and terrain parameters; in the decay stage T4, FCN identifies the combustible burnout area and corrects the Rothermel model's prediction deviation of the split fire area.

[0012] Furthermore, the Rothermel model contains a parameter optimization unit, which dynamically adjusts the wind speed correction coefficient through UKF. and slope correction factor .

[0013] Furthermore, the Rothermel predicted trajectories for the four fire spreading stages are not only used as the final prediction results, but also input into the FCN as spatial priors through backpropagation to guide the image segmentation process at the next moment.

[0014] Compared with the prior art, the present invention has the following beneficial effects: Based on traditional fire recognition technology, the present invention replaces the backbone network from VGG / GoogLeNet with ResNet. Through dynamic feature fusion and auxiliary classifiers, an FCN model that can adapt to a variety of flame colors is constructed, effectively improving the robustness of the fire recognition module.

[0015] This paper, for the first time, explores the bidirectional coupling mechanism between forest fire identification and fire spread prediction. By leveraging the FCN and Rothermel models, the paper proposes a two-way synergy: Firstly, the FCN's recognition results are used to dynamically correct the Rothermel model's initial boundaries; secondly, the Rothermel model's physical rules are applied to inversely constrain the FCN's misidentified regions. This synergy, with error complementation, enables a linkage between identification and prediction, significantly improving both fire identification and fire spread prediction accuracy.

[0016] The present invention integrates fire identification and fire spread prediction, and divides the spread of fire into four stages based on the characteristic differences of fire spread. A system-adaptive processing method is formulated for each stage. At the same time, the trajectory predicted by Rothermel is not only used as the prediction result, but can also be reversely input into the FCN as a spatial prior to guide the segmentation process of the image at the next moment or stage, thereby constructing an identification and prediction scheme applicable to the entire cycle of forest fires, which helps to support emergency decision-making and reduce disaster losses. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Error comparison of FCN before and after correction by Rothermel model. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the forest fire identification and prediction method of the present invention is further described in detail below through embodiments and in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate the present invention and are not intended to limit the present invention.

[0019] A method for identifying and predicting forest fires based on a bidirectional coupling mechanism, comprising the following steps: data preprocessing, fire source identification, fire intensity prediction, coupling optimization, and phased application.

[0020] Data preprocessing, constructing a dedicated dataset containing aerial fire images and laboratory combustion data. First, high-resolution aerial fire images were collected to record the dynamic characteristics of flame propagation under different wind conditions. The aerial fire images covered a variety of scenes (including 62 coniferous forests, 48 ​​broad-leaved forests, and 34 mountain mixed forests) and meteorological conditions (32 cloudy days, 86 sunny days, wind speed 0-8m / s), and included different flame colors (58 yellow, 42 red) and smoke interference samples (26); secondly, outdoor steel wool burning experiments were carried out and combustion data were collected to provide basic samples for multi-feature analysis of flames; finally, a hybrid intelligent strategy was used to annotate the collected data (including aerial fire images and laboratory combustion data) to construct a dedicated dataset. The specific data annotation steps include: LabelImg for initial target annotation (the label is set to "fire"), improved U-Net network for semi-automatic contour extraction, manual verification to ensure boundary accuracy, and generation of XML format annotation files. For fire source identification, an improved fully convolutional network (FCN) is used to segment fire scenes and output the discrete boundaries of the fire area. In the improved FCN overall architecture, ResNet50 is innovatively used as the backbone network, and some improvements are also introduced to the FCN head module. The ResNet50 module, as the backbone network of the fully convolutional network, is divided into five main stages. Each stage contains a different number of residual blocks. These residual blocks are divided into two types: convolutional residual blocks (ConvBlock) and identity residual blocks (IdentityBlock). Convolutional residual blocks are used to increase network depth, while identity residual blocks are used to maintain the dimensional identity of feature maps. A batch normalization layer (BN) is placed before each residual block to normalize the input data. Among the five stages of ResNet50, Stage1 contains a 7x7 convolution layer and a maximum pooling layer for initial feature extraction. The number of residual blocks contained in Stage2-Stage5 are 3, 4, 6, and 3 respectively. The first residual block of Stage2 contains a convolution layer with a stride of 2 (for downsampling), while the first residual block of Stage3-Stage5 has a stride of 1. This residual structure can effectively avoid the gradient vanishing problem. The FCN head module is a key component for achieving pixel-level semantic segmentation in a fully convolutional network. The main functions of the FCN head module are: reducing the dimension of the number of feature map channels through a 1×1 convolution layer and restoring the size of the feature map using bilinear interpolation. In the present invention, an auxiliary classifier is introduced into the FCN head module to extract intermediate features from Layer3 of ResNet. The model convergence is accelerated through a multi-task learning mechanism to enhance the gradient back propagation effect. At the same time, the pre-training strategy of "ImageNet pre-training + COCO dataset fine-tuning" is adopted, combined with the combined loss function of cross entropy loss and Dice loss, and data enhancement methods such as random rotation and scaling to solve the imbalance problem of the ratio of flame and background pixels, and improve the robustness to multi-color flames and complex environments.

[0021] Fire intensity prediction, taking a wildfire in 2025 as an example, the Rothermel equation can be simplified as follows: , R is the fire spread rate; I R is the reaction intensity of the flame zone; ζ is the dimensionless fire spread rate, P b is the density of the combustible bed; ε is the effective heat coefficient; Q ig is the pre-combustion heat, where the wind speed correction factor Φ W and slope correction factor Φ S Calculated using the following formula: , , Among them, U is the wind speed, is the fuel bed stacking ratio, For the optimal stacking ratio, is the fuel bed density, C, B, E is a constant, is the slope correction coefficient, is the slope angle, K 1 is the forest fire model coefficient, The spreading rate at different angles θ In order to improve the adaptability of the model under complex terrain and meteorological conditions, a parameter optimization unit based on UKF is introduced in the fire prediction module. The system converts the observed changes in the position of the fire front into a spread rate and compares it with the model prediction value to construct an observation model. UKF dynamically updates the wind speed correction coefficient and the slope correction coefficient according to the residual of each cycle to achieve adaptive matching between the model and the actual environment, thereby improving the overall prediction accuracy and stability. The longitude and latitude of a fire are selected, and the fire spread rate in different directions is predicted and output based on the Rothermel model. According to the directional spread characteristics and based on the different stages of the fire, the fire spread area can be approximated as a circle or an ellipse. For the area calculation of the predicted area, in order to reduce the systematic error caused by insufficient regional identification, the closed curve integral method is used to calculate the area of ​​the fire area, and the symmetric difference is used to calculate the area of ​​the fire area. : The error between the predicted fire area and the actual area is obtained; in order to avoid the calculation accuracy failure caused by the non-smooth curve, the Green formula Based on the shoelace formula To solve the predicted fire area A and the actual fire area B, the fitness function of the area obtained by the two integral methods is used to evaluate the stability of the model , Table 1 shows the errors of the Rothermel prediction model under two approximation methods.

[0022] Table 1 Errors of the Rothermel prediction model under two approximation methods

[0023] Coupling optimization, the coupling mechanism between the FCN and Rothermel models, is the core of the joint model's error compensation. This is achieved through optimization at the data interface layer and bidirectional feedback correction, enabling coordinated optimization of recognition and prediction. Morphological post-processing is introduced at the data interface layer to expand and smooth the discretized boundaries of the FCN output, repairing small holes and filling broken edges. This improves the continuity of the initial fire line and reduces the Rothermel model's sensitivity to segmentation noise. Considering that flame edges often exhibit discontinuities due to smoke, lighting, and occlusion, the Rothermel model's physical constraints (such as wind speed and slope restrictions on spread direction) are utilized to correct for FCN misidentifications. Furthermore, Rothermel estimates combustion intensity using fuel sample data. When the FCN-identified area does not match the fuel distribution, the fire line position is recalculated using weighted averaging. This prevents amplification of step-by-step errors while maintaining consistency with physical conditions. Specifically, when the FCN mistakenly identifies a burned area as background due to smoke obstruction, the physical constraints provided by Rothermel compensate for this area through a boundary correction mechanism. Conversely, when the FCN captures a tiny fire point that the physical model fails to predict in time, the segmentation results can be fed back into Rothermel to drive boundary updates in the propagation equation. This forms a closed-loop, bidirectionally coupled system that leverages the fine-grained spatial recognition capabilities of the FCN while leveraging the physical reliability of Rothermel in temporal evolution.

[0024] The method was applied in stages, and four typical time nodes were selected based on the flame area growth rate and movement characteristics: T1 (early ignition stage, flame area accounts for <5%), T2 (diffusion acceleration stage, area accounts for 15%-20%), T3 (stable combustion stage, area accounts for 30%-35%) and T4 (decline stage, area accounts for 25%-30%).

[0025] During T1, flames primarily appear as scattered, star-shaped fire points with blurred edges and significant interference from ambient noise and dynamic flickering. Traditional edge detection methods (such as the Canny operator) often cause flame outlines to break due to noise. However, FCN, relying on deep feature learning, reduces noise sensitivity to a certain extent. However, due to the small size of the fire points, localization accuracy remains limited. During this stage, the flame area is concentrated and approximately circular. Using the Rothermel model, combined with experimental parameters and the fire contour for physical constraints, the system effectively improves the recall rate of small target fire points. The predicted area output by the Rothermel algorithm is converted into a spatial prior mask, which is then fed into the FCN as an additional input channel along with the original image at the next moment. This guides the FCN to focus more on small fire points within the prediction range, reducing false detections in background areas and improving the recall rate and boundary coherence of small target fire points. During T2, the flames gradually form continuous thermal radiation bands with distinct turbulent texture characteristics, and their diffusion tends to accelerate due to wind direction. During this phase, the FCN's feature extraction advantages are fully demonstrated. The pre-trained ResNet-50 model effectively captures the high-frequency texture features of the flames, but factors such as occlusion and thick smoke can still cause missed or misjudged edges. The flame area at this stage tends to be elliptical. Rothermel combines real-time updates of fuel load, wind speed, and slope parameters to continuously correct FCN errors caused by image noise or occlusion. The prediction results are also converted into a probabilistic prior map, where regions closer to the ellipse center are assigned higher prior probabilities. This prior map is element-wise multiplied with the FCN's deep feature map, effectively embedding physical prediction information into the spatial attention mechanism. This guides the FCN to focus more on valid areas within the prediction range during the next segmentation step, avoiding missed or overdetected areas due to noise or occlusion. At T3, the fire enters a stable spread state, with clear flame boundaries and a complete thermal radiation zone. The influence of terrain slope on fire spread becomes increasingly significant. The FCN primarily leverages high-frequency texture features extracted by ResNet-50 (such as turbulent fluctuation patterns) to capture flame dynamics. The Rothermel model, on the other hand, observes that the curvature variation coefficient of the flame spread region begins to decrease, and the fire gradually transitions from an irregular shape to a nearly circular shape, spreading in multiple directions. By providing real-time feedback on fuel and environmental parameters, the Rothermel model effectively suppresses error accumulation caused by fluctuations in FCN recognition accuracy, achieving high-precision predictions during the stable spread phase. The prediction results are also fed back to the FCN as a spatial prior, making the next-step segmentation process more stable under physical constraints and effectively preventing error accumulation. At T4, after the combustibles in the center of the fire gradually burned out, the flames began to fragment into multiple irregular shapes, and the fire spread rate significantly slowed. At this point, the FCN identified burned areas using a grayscale threshold (<50) and marked them as "non-burning zones." It then scanned with a 128×128 multi-scale sliding window to accurately locate scattered fire points.Because the Rothermel model has difficulty identifying burned-out areas at the microscale, its prediction error increases. Therefore, the FCN and Rothermel collaboratively compensate for this, maintaining high overall model accuracy. The feedback results serve as local priors, weighting and amplifying these local areas in the next input, thus compensating for Rothermel's shortcomings at the microscale.

[0026] The initial recognition errors of the FCN neural network were 60%, 36%, 29% and 31% respectively, while the prediction errors after correction by the Rothermel model were significantly reduced to 30%, 7.2%, 4.95% and 7.05%. Figure 1 As shown in Table 2, adding the FCN fire identification network to the Rothermel model to correct for fire area improves its prediction accuracy. Under the same conditions, the prediction accuracy using the FCN is 5% to 20% higher than that without the FCN, as shown in Table 2.

[0027] Table 2: Comparison of the accuracy of FCN-Rothermel predictions and traditional Rothermel model predictions

[0028] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A forest fire identification and prediction method based on a bidirectional coupling mechanism, characterized in that: The method comprises the following steps: Data preprocessing and dataset construction; Fire source identification: Fire scene segmentation is achieved using an improved fully convolutional network (FCN). The FCN uses ResNet50 as the backbone network and integrates ConvBlock and IdentityBlock. It optimizes feature fusion by dynamically adjusting the number of skip connections and adaptive upsampling coefficients to output the discretized boundaries of the fire area. Fire Prediction: Based on NASA meteorological data and fire source identification results, the Rothermel model is used to predict fire spread; Coupling optimization: Repair edge breaks in FCN output boundaries, establish a collaborative mechanism between FCN and Rothermel models, dynamically correct the initial boundaries of the Rothermel model based on FCN recognition results, and use Rothermel physical rules to constrain FCN recognition errors; Phased application: Fire spread is divided into four stages: early ignition T1, accelerated spread T2, stable combustion T3, and decay T4. In stage T1, FCN is used to reduce noise interference. In stages T2-T3, FCN texture features are combined with Rothermel dynamic parameter adjustment. In stage T4, FCN is used to identify burnt areas to correct Rothermel prediction bias.

2. A forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1, characterized in that: During the data preprocessing, a dedicated dataset was constructed, including aerial fire images and laboratory combustion data. The aerial images covered forest scenes, and the laboratory data included 10 sets of outdoor steel wool burning experiments. The data were annotated using the LabelImg tool to generate a PASCAL VOC format XML file. The dataset was divided into a training set and a test set in a ratio of 0.85:0.

15.

3. The forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1 is characterized in that: The FCN includes a head module, which reduces the feature map channels to the number of categories through a 1×1 convolution layer, restores the original size through bilinear interpolation, and sets an auxiliary classifier to extract features from Layer 3 of ResNet to accelerate training.

4. The forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1 is characterized in that: The Rothermel model inputs combustible density, wind speed, and slope parameters, and outputs spread rate and burned area. The model can be simplified as follows: , R is the fire spread rate; I R is the reaction intensity of the flame zone; ζ is the dimensionless fire spread rate, P b is the combustible bed density; ε is the effective thermal coefficient; Q ig is the pre-combustion heat, where the wind speed correction factor Φ W and slope correction factor Φ S Calculated using the following formula: , , Among them, U is the wind speed, is the fuel bed stacking ratio, For the best stacking ratio, is the fuel bed density, C, B, E is a constant, is the slope correction coefficient, is the slope angle, K 1 is the forest fire model coefficient, The spreading rate at different angles θ Rothermel predicts the fire spread rate in each direction. Based on the spread characteristics, the fire area is approximately elliptical or circular, and the fire area is calculated by closed curve integration and shoelace formula.

5. The forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1 is characterized in that: The morphological processing of edge break repair in the coupled optimization includes closing operation to repair small holes and dilation operation to fill edge breaks.

6. The forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1 is characterized in that: The phased application module In the early stage of fire T1, FCN suppresses the noise of star-shaped fire point identification through deep features, and the Rothermel model predicts the area of ​​the next stage based on circular diffusion features; From the diffusion acceleration stage T2 to the stable combustion stage T3, a continuous thermal radiation belt is formed in the flame area. The FCN captures the high-frequency texture characteristics of the flame, and the Rothermel model adjusts the predicted trajectory in combination with real-time wind speed and terrain parameters. In the decay stage T4, FCN identifies the combustible burnout area and corrects the prediction bias of the Rothermel model on the split fire area.

7. A forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 1 or 4, characterized in that: The Rothermel model contains a parameter optimization unit, which dynamically adjusts the wind speed correction coefficient through UKF. and slope correction factor .

8. The forest fire identification and prediction method based on a bidirectional coupling mechanism according to claim 6 is characterized in that: The Rothermel predicted trajectories for the four fire spreading stages are not only used as the final prediction results, but also fed back into the FCN as spatial priors to guide the image segmentation process at the next moment.

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