A method and system for rapid evacuation performance evaluation and optimization of occupant space distribution

Abstract

The application relates to a kind of evacuation performance rapid evaluation and personnel space distribution optimization method and system, it is related to intelligent evacuation evaluation technical field, the technical problems that current evacuation simulation method is long in time, cannot be solved according to target performance initiative optimization personnel distribution, its method includes: obtaining building information and current personnel distribution;Input forward prediction network obtains total evacuation time and exit utilization rate;If not reach preset threshold, then with target performance as condition input reverse generation network generates density distribution map;After probability sampling and physical constraint correction, obtain optimized personnel distribution;Iterative evaluation until reach standard by returning forward network.The application has the following effects: the time consumption of evacuation evaluation is compressed to second-level response, realizes personnel distribution initiative reverse optimization, improves evacuation efficiency and exit utilization balance.

Description

Technical Field

[0001] This invention relates to the field of intelligent evacuation assessment technology, and in particular to a method and system for rapid assessment of evacuation performance and optimization of personnel spatial distribution. Background Technology

[0002] With the continuous expansion of large public buildings, the density of people in places such as subway stations, commercial complexes, and transportation hubs has increased significantly. In the event of an emergency, achieving efficient evacuation of people is a core issue in building safety. Total evacuation time and exit utilization rate are key indicators for measuring evacuation effectiveness; unreasonable personnel distribution can lead to localized congestion and severely prolong evacuation time. Therefore, accurately assessing and optimizing the spatial distribution of people is crucial for improving emergency evacuation capabilities.

[0003] Currently, physical mechanism-based microscopic evacuation simulation software, such as Pathfinder and AnyLogic, is widely used in engineering practice. This type of software constructs passable areas and exits by inputting a building floor plan, specifying the number of people and their initial positions, and iteratively calculates the movement trajectory of each person at time steps according to preset behavioral rules until all people have left the building. Finally, it outputs evacuation time and exit usage data. This technology has become a commonly used tool for performance-based assessment of building fire protection.

[0004] However, the core drawback of the aforementioned simulation methods lies in the contradiction between computational time and the need for real-time decision-making. Microscopic simulations require path planning and collision handling for each individual at each time step, and the computational load increases significantly with the number of people, with a single assessment often taking tens of minutes or more. In emergency scenarios, the on-site situation changes rapidly, and managers need to obtain assessment results within seconds to adjust evacuation strategies. Minute-level response delays cause the simulation results to be severely out of sync with the actual situation on-site. If different personnel distribution schemes need to be tried, the time cost of multiple trial and error will accumulate exponentially, making such methods only suitable for pre-emptive offline analysis and unable to meet the fundamental requirement of real-time emergency decision-making for response speed. Summary of the Invention

[0005] In order to reduce the evacuation assessment time to the second level, realize proactive reverse optimization of personnel distribution, and improve evacuation efficiency and exit utilization balance, this application provides a method and system for rapid evacuation performance assessment and personnel spatial distribution optimization.

[0006] Firstly, this application provides a method for rapid assessment of evacuation performance and optimization of personnel spatial distribution, employing the following technical solution: Obtain basic scene information and current spatial distribution of personnel for the target building. Basic scene information includes building structure, exit location and width, and total number of personnel. Input the basic information of the scene and the current spatial distribution of people into the forward prediction deep neural network to predict the total evacuation time and exit utilization rate. Determine whether the total evacuation time and exit utilization rate have reached the preset target thresholds; If the target is reached, output the current spatial distribution of personnel. If the target is not met, a deep neural network is generated in reverse with the target total evacuation time and target exit utilization rate corresponding to the preset target threshold, and the building structure, exit location and width are input to generate a continuous personnel density distribution map. The density distribution map is sampled in a density-weighted manner, and after spatial exclusion and physical feasibility correction, a discrete personnel location distribution that conforms to the building structure constraints is obtained as the optimized personnel spatial distribution. The optimized spatial distribution of personnel is used as the new current spatial distribution of personnel. It is then fed back into the positive prediction deep neural network for re-evaluation. The above prediction, judgment, generation and post-processing steps are iteratively executed until the total evacuation time and exit utilization rate meet the preset target thresholds.

[0007] By adopting the above technical solutions, this method uses forward and inverse deep neural networks to form a closed-loop iteration of evacuation performance assessment and personnel distribution optimization, breaking through the minute-level latency bottleneck of traditional micro-simulation and achieving second-level rapid response; the inverse network integrates physical constraints to ensure the feasibility of generating density maps; gradient-driven iteration accurately converges to the target threshold, taking into account real-time performance, physical feasibility and optimization efficiency.

[0008] Secondly, this application provides a system for rapid assessment of evacuation performance and optimization of personnel spatial distribution, employing the following technical solution: A rapid evacuation performance assessment and personnel spatial distribution optimization system includes a memory, a processor, and a program stored in the memory and executable on the processor. When the program is loaded and executed by the processor, it implements the rapid evacuation performance assessment and personnel spatial distribution optimization method as described in the first aspect. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to an embodiment of this application. Detailed Implementation

[0010] The present application will be further described in detail below with reference to the accompanying drawings.

[0011] Reference Figure 1 This application discloses a method for rapid assessment of evacuation performance and optimization of personnel spatial distribution, comprising: Step S1: Obtain the basic scene information of the target building and the current spatial distribution of personnel. The basic scene information includes the building structure, exit location and width, and total number of personnel.

[0012] The basic scenario information refers to a structured dataset representing the static physical attributes of an evacuation scenario. It consists of three core parameters: building structure, exit location and width, and total number of people. These parameters describe the physical boundaries and accessibility constraints of the evacuation environment. Building structure refers to the static physical entities that constitute the spatial boundaries of the building's evacuation environment. Specifically, it includes the geometric contours, spatial coordinates, and topological connections of impassable areas such as walls, columns, and fixed obstacles. In digital representation, it is typically represented by a binary mask depicting the distribution of passable and obstructed areas. Exit location refers to the spatial coordinates of the evacuation exit in the building's two-dimensional physical coordinate system, representing the horizontal and vertical coordinates of the geometric center point or bounding box of the exit area in the building's global coordinate system. Exit width refers to the minimum horizontal distance between the effective access boundaries of evacuation exits, measured in length units. It represents the upper limit of physical accessibility for people per unit time and is encoded as a key physical constraint parameter in the data channel. Total number of people refers to the total number of people requiring evacuation in the current scenario, represented as an absolute scalar quantity, reflecting the overall size of the group to be evacuated. Current spatial distribution of people refers to the distribution of the position coordinates of a group of people in the two-dimensional plane space of a building at the current moment. It can be characterized by discrete point set coordinates or continuous density field, reflecting the actual spatial aggregation and distribution pattern of people in the built environment.

[0013] The necessary procedures are as follows: First, digital acquisition and analysis of the building environment are performed: by parsing the IFC standard format data files of the Building Information Modeling (BIM) system, or reading the DXF / DWG format vector graphics files of computer-aided design (CAD) drawings, spatial boundary elements in the building layers are extracted, and the geometric data of polylines or closed polygons of walls, columns, and fixed obstacles are identified to determine the boundary topology of the accessible and obstructed areas inside the building. Simultaneously, the position coordinates (X, Y coordinate values ​​in a Cartesian coordinate system) and opening size annotation parameters of evacuation exit elements are extracted to obtain the effective passage width values ​​for each exit. For scenarios without digital drawings, the internal geometric contours of the building are obtained through 3D LiDAR point cloud scanning, and structural boundary lines are extracted through point cloud segmentation and planar projection processing.

[0014] Secondly, real-time perception and data acquisition of personnel status: By accessing the real-time video stream of the video surveillance system, deep learning-based pedestrian detection algorithms (such as YOLOv5 or Faster R-CNN architecture) are used to detect and track human targets in the video frames. Image pixel coordinates are mapped to two-dimensional plane coordinates in the building's physical coordinate system using camera calibration parameters. The total number of effectively detected targets is calculated to obtain the total number of personnel, and the location coordinates of each person are recorded to form discrete point set distribution data. Alternatively, Bluetooth Low Energy Beacon (BLE Beacon) or Ultra-Wideband (UWB) positioning base station networks deployed in the building space are used to receive wireless signals emitted by mobile terminals carried by personnel. Based on Received Signal Strength Indication (RSSI) ranging or Time Difference of Arrival (TDOA) positioning algorithms, the real-time coordinates of personnel are calculated, and the total number and spatial distribution of personnel are summarized and statistically analyzed.

[0015] Subsequently, a uniform-scale raster discretization process is performed: spatial resolution parameters are set (e.g., 0.1 m / pixel to 0.5 m / pixel), and the raster matrix size (number of pixels) is calculated based on the physical dimensions of the building plan (building length and width, unit: meters), establishing a two-dimensional raster coordinate system. The vector-form building structure boundary lines are converted into a binary raster image aligned with the physical space using a rasterization algorithm. Pixel values ​​in obstacle areas are set to 1 (or a specific encoded value of 255), while pixel values ​​in passable areas are set to 0, forming building structure channels. The physical coordinates of the exit location are mapped to the raster index through coordinate transformation, and exit area pixels are marked in the form of a binary mask, forming the exit location channel; the physical dimension (meters) of the exit width is encoded as a scalar value associated with the exit mask and expanded into a constant channel consistent with the spatial dimensions of the raster image (exit area pixels are assigned the actual width value, and other areas are set to 0), forming the exit width channel. The total number of people is used as a global scalar parameter and is extended into a two-dimensional numerical layer (the total number of people is filled in the whole image) with the same spatial size as the raster image through a broadcast mechanism, forming a people size channel.

[0016] Furthermore, perform raster mapping and encoding of the current spatial distribution of personnel: map the collected set of discrete personnel location coordinates to the same raster coordinate system through coordinate transformation, count the number of personnel falling into each raster cell, and generate a continuous personnel density distribution matrix (Density Map), where each pixel value represents the personnel density (persons / square meter) of the corresponding physical area. Alternatively, one-hot encoding can be used to mark the raster cells containing personnel (set to 1 for occupied areas and 0 for unoccupied areas). For scenarios with uncertain personnel locations, Gaussian kernel convolution smoothing is used to transform the discrete point set into a continuous density heatmap. The standard deviation of the kernel function is set according to the spatial scale occupied by personnel (e.g., 0.3 meters) to form personnel distribution channels.

[0017] Furthermore, multi-channel data tensor construction is performed: the above-mentioned building structure channel, exit location channel, exit width channel, personnel scale channel, and personnel distribution channel are stacked (concatenate operation) on the feature dimension to form a five-channel (or more channels, depending on the implementation) image data structure, realizing unified encoding of spatial geometric information and statistical features.

[0018] Finally, spatial scale normalization and output preparation are performed: the scale factor (unit: meters / pixel) between physical length units (meters) and raster pixel indices is recorded, and the building's physical coordinates are transformed to a dimensionless normalized coordinate range (e.g., mapped to the [0,1] interval, where the lower left corner of the building corresponds to (0,0) and the upper right corner corresponds to (1,1)) through linear mapping. This normalization scale factor is encoded as an additional channel or metadata parameter to ensure a reversible mapping relationship between the physical space and the data space.

[0019] Step S2: Input the basic scene information and the current spatial distribution of people into the forward prediction deep neural network to predict the total evacuation time and exit utilization rate.

[0020] Among them, the forward prediction deep neural network refers to an end-to-end regression model built on a deep convolutional neural network, used to establish a nonlinear mapping relationship between the physical state of the evacuation scene and evacuation performance indicators. This network takes multi-channel scene data as input, and through hierarchical feature extraction and multi-scale fusion, outputs predicted evacuation time and exit utilization parameters. The specific network architecture design and training optimization process can be found in the detailed explanation of subsequent steps S21 to S24. The total evacuation time refers to the time span from the start of evacuation to the last person leaving the building space through an exit, measured in seconds, and is a comprehensive indicator representing the overall evacuation efficiency. Exit utilization rate refers to the actual usage efficiency parameter of each evacuation exit during the evacuation process, specifically including the number of people evacuated through each exit (the number of people leaving the building through a specific exit) and the usage time of each exit (the time required for the exit to complete the evacuation of all passing personnel), used to represent the load balance of exit resources and the actual utilization of passage capacity. Specifically, the export utilization rate can be defined as the ratio of the actual number of people evacuated from each export to the theoretical maximum evacuation capacity, or the ratio of the usage time of each export to the rated evacuation time, which is used to characterize the load balance of export resources.

[0021] The necessary procedures are as follows: First, perform multi-channel data input preparation: receive the multi-channel data tensor constructed and normalized in step S1. This tensor integrates multi-layer feature information representing the building structure, exit location and width, total number of people and current spatial distribution of people to form an image data structure that matches the network input specifications.

[0022] Subsequently, deep feature extraction and multi-scale fusion are performed: multi-channel input tensors are fed into a forward prediction deep neural network, hierarchical convolutional feature extraction is performed through the network backbone structure, channel attention mechanism is introduced to enhance the weights of key region features, and cross-scale fusion of deep semantic features and shallow spatial details is achieved through a feature pyramid structure to obtain feature representations containing rich spatial context information.

[0023] Furthermore, multi-head regression prediction is performed: based on the fused multi-scale features, parallel predictions of evacuation time and exit status are performed separately through the multi-head regression structure at the network end. Specifically, global features are processed by pooling and fully connected layers to generate a scalar prediction of the total evacuation time; exit area features are processed by spatial positioning and regression to generate predictions of the number of evacuees and usage time at each exit, which together constitute the exit utilization parameter set.

[0024] Finally, the prediction results are output in a structured format: the total evacuation time and the utilization parameters of each exit obtained by reasoning are output in the form of structured data to form the evacuation performance evaluation results under the current spatial distribution of personnel. This serves as the basis for the target threshold judgment in the subsequent step S3, realizing an efficient mapping from scene physical description to evacuation performance indicators.

[0025] Step S3: Determine whether the total evacuation time and exit utilization rate have reached the preset target threshold.

[0026] Among them, the preset target threshold refers to the set of evacuation performance benchmark values ​​set in advance according to building safety specifications, emergency management needs or evacuation optimization goals, including the target total evacuation time threshold and the target exit utilization rate threshold, which are used to quantitatively evaluate whether the evacuation performance under the current spatial distribution of personnel meets the expected requirements.

[0027] The necessary procedures are as follows: The system receives the total evacuation time value predicted in step S2 and the set of exit utilization parameters. The predicted total evacuation time is compared with a preset target total evacuation time threshold. Simultaneously, the exit utilization parameters are checked for compliance with a preset target exit utilization threshold, where the target exit utilization threshold represents the minimum acceptable level of load balance and passage efficiency at each exit.

[0028] When the total evacuation time is less than or equal to the preset target total evacuation time threshold, and the utilization rate parameters of each exit meet the preset target exit utilization rate threshold, it is determined that the evacuation performance under the current personnel spatial distribution conditions has reached the preset target threshold. Step S4 is executed, and the current personnel spatial distribution is output as the result that meets the evacuation performance requirements.

[0029] When the total evacuation time exceeds the preset target total evacuation time threshold, or when any exit utilization parameter fails to meet the preset target exit utilization threshold, it is determined that the preset target threshold has not been reached. Step S5 is executed, using the target total evacuation time and target exit utilization corresponding to the unmet preset target threshold as constraints to trigger the reverse generation process.

[0030] This judgment step, based on a preset evacuation performance benchmark, assesses the conformity of the positive prediction results, forming a decision node that determines subsequent process branches, thus achieving a closed-loop connection from performance evaluation to optimized execution.

[0031] Step S4: If the condition is met, output the current spatial distribution of personnel.

[0032] The necessary procedures are as follows: When step S3 determines that both the total evacuation time and exit utilization rate have reached the preset target thresholds, the result output process is triggered. The current spatial distribution of personnel is confirmed as an effective solution that meets the preset evacuation performance index requirements. It is then transformed from internal processing status into result data that can be published to external systems. This data is transmitted to the optimization decision output module through a unified data interface or pushed to a visualization interface for displaying the building's floor plan spatial distribution. This serves as the basis for evacuation layout that can be directly adopted in the current scenario, completing the result publication and convergence exit of this evacuation performance assessment and personnel spatial distribution optimization process.

[0033] Step S5: If the target is not met, then the target total evacuation time and target exit utilization rate corresponding to the preset target threshold are used as conditions to generate a deep neural network in reverse with the input of building structure, exit location and width, and generate a continuous personnel density distribution map.

[0034] Among them, the inverse generative deep neural network is a neural network model that takes target performance parameters and building structure as input conditions, learns the inverse mapping relationship through a deep learning generative architecture, and outputs a continuous population density distribution map that satisfies the constraints. The continuous population density distribution map is a heat map that represents the distribution of people within a building space. It reflects the population density in different areas in a continuous numerical form, providing a quantitative basis for population evacuation route planning and spatial configuration.

[0035] The necessary procedures are as follows: When the total evacuation time exceeds the preset upper limit or the exit utilization rate falls below the preset lower limit, the reverse optimization generation process is initiated. First, the target total evacuation time and target exit utilization rate corresponding to the preset target threshold are extracted and encoded together with the building structure, exit location, and width into a conditional feature vector.

[0036] The conditional vector is input into a trained inverse generative deep neural network. Based on the architecture constructed in steps S51 to S53, the network parses the target constraints through a conditional encoder, reconstructs spatial features layer by layer through the generator backbone network, and finally outputs a continuous population density distribution map that matches the building layout. During the generation process, the network uses a physical constraint mask to ensure that the output does not exceed the accessible area of ​​the building and meets the continuity requirements of the exit boundary.

[0037] The generated continuous personnel density distribution map represents the optimized personnel spatial allocation scheme. Its density distribution, validated by a forward prediction network, can reproduce the target evacuation time and target exit utilization rates, thus achieving a reverse mapping from performance targets to spatial allocation. This distribution map serves as the foundational data for subsequent evacuation plan development, guiding actual personnel scheduling and spatial optimization.

[0038] Step S6: The density distribution map is sampled by density weighting, and after spatial exclusion and physical feasibility correction, the discrete personnel location distribution that meets the building structure constraints is obtained as the optimized personnel spatial distribution.

[0039] Among them, probability-guided sampling: a weighted random sampling method based on the density values ​​of each grid cell in the continuous population density distribution map as probability weights, preferentially selecting location points from high-density areas to generate an initial discrete set of pedestrian locations. Spatial exclusion correction: by forcibly ensuring that the distance between any two pedestrian locations is not less than a preset social distance threshold, the conflict resolution process of eliminating excessive population gathering is eliminated.

[0040] Physical constraint correction: A verification mechanism that eliminates invalid coordinates based on building structure obstacle boundaries and supplements vacant positions with additional sampling according to the original density distribution. Optimized personnel spatial distribution: A feasible discrete personnel location configuration scheme that meets building physical constraints and social distancing requirements after probability-guided sampling, spatial exclusion correction, and physical constraint correction.

[0041] The necessary procedures are as follows: The continuous crowd density distribution map generated in step S5 is received, and post-processing of probability-guided sampling and physical constraint correction is performed on the density distribution map to obtain a discrete crowd location distribution as the optimized crowd spatial distribution. This post-processing includes three stages: probability-guided sampling, spatial exclusion correction, and physical constraint correction. First, probability-guided sampling converts the continuous density distribution into an initial discrete location set that satisfies the total crowd size. Then, spatial exclusion correction adjusts the location coordinates to ensure that the distance between any two pedestrian locations is not less than a preset social distance threshold. Finally, physical constraint correction removes invalid coordinates falling into obstacle areas and performs supplementary sampling to form a feasible discrete crowd location distribution that conforms to building structure constraints, has no spatial conflicts, and has a complete number of people, which serves as the output of the optimized crowd spatial distribution. Specific implementation methods for each stage of the above post-processing can be found in subsequent steps S61 to S63.

[0042] Step S7: The optimized spatial distribution of personnel is used as the new current spatial distribution of personnel. The optimized distribution is then returned to the input positive prediction deep neural network for re-evaluation. The above prediction, judgment, generation and post-processing steps are iteratively executed until the total evacuation time and exit utilization rate meet the preset target threshold.

[0043] The iterative optimization process involves feeding the optimized spatial distribution of people back to the forward prediction network for re-evaluation. This closed-loop optimization mechanism, through multiple iterations of the prediction-judgment-generation-post-processing process, gradually approaches the preset target threshold. Convergence judgment is the process of determining whether the total evacuation time and exit utilization rate corresponding to the current spatial distribution of people simultaneously meet the preset target threshold conditions, serving as the basis for terminating the iteration. Closed-loop feedback involves returning the optimized spatial distribution of people from the post-processing output as new input to the forward prediction network, forming a cyclical technical architecture from prediction and evaluation to reverse generation and then to re-evaluation. Re-evaluation involves inputting the updated current spatial distribution of people into the forward prediction deep neural network to re-infer the predicted values ​​of total evacuation time and exit utilization rate.

[0044] The necessary process is as follows: Receive the optimized personnel spatial distribution output in step S6, and update it to the new current personnel spatial distribution; input the distribution into the forward prediction deep neural network (see steps S21 to S24 for specific network construction and training), and re-predict the total evacuation time and exit utilization rate under the current configuration through forward inference, and perform a re-evaluation.

[0045] The total evacuation time and exit utilization rate obtained from the reassessment are compared with the preset target thresholds. If the total evacuation time does not exceed the preset upper limit and the exit utilization rate is not lower than the preset lower limit, the convergence condition is met, the iteration is terminated, and the current spatial distribution of personnel is output as the final optimization scheme. If the threshold is not met, the input parameters of the generation model are adjusted. By modifying the target total evacuation time, target exit utilization rate, or exit load weight coefficient, the input conditions of the inverse generation deep neural network are adjusted, and the inverse generation and post-processing process of steps S5 to S6 is re-executed to form a closed-loop feedback loop.

[0046] Repeat the above prediction, judgment, generation, and post-processing steps, and gradually adjust the spatial distribution of personnel through iterative optimization until the total evacuation time and exit utilization rate simultaneously meet the preset target thresholds, or reach the preset maximum number of iterations. For specific implementation methods of the above iterative optimization and convergence determination, please refer to subsequent steps S71 to S75.

[0047] The construction and training of a forward prediction deep neural network includes: Step S21: Construct a feature extraction network with a deep convolutional network as the backbone to extract basic scene information and spatial features of the current spatial distribution of people.

[0048] In this context, deep convolutional networks refer to hierarchical feature extraction architectures built upon residual learning mechanisms. In one specific embodiment of this invention, ResNet50 is used as the backbone network. This network consists of multiple stacked residual blocks, each containing a Bottleneck structure (i.e., a combination of three convolutional layers: 1×1 convolution for dimensionality reduction, 3×3 convolution for feature extraction, and 1×1 convolution for dimensionality enhancement, combined with shortcut connections to achieve identity mapping). This structure is used to alleviate the vanishing gradient problem in deep networks and compress the number of computational parameters.

[0049] As another optional implementation of the present invention, ResNet34 can be used as the backbone network, and a Bottleneck structure (i.e., a combination of 1×1-3×3-1×1 convolutions) can be introduced within each residual block. By adjusting the network depth and the number of channels, the number of computational parameters can be reduced while maintaining feature extraction capabilities. Those skilled in the art will understand that the Bottleneck structure is common in ResNet50 and higher networks, but introducing this structure on top of ResNet34 and making corresponding channel adjustments is also an optional implementation of the present invention. This implementation can also effectively extract spatial features from evacuation scenes.

[0050] Spatial features refer to the hierarchical tensor representation containing edge, texture and semantic information extracted from multi-channel input data such as building structure, exit location and width, and spatial distribution of people through convolution operations.

[0051] The necessary procedures are as follows: First, the multi-channel data tensor constructed in step S1 (including building structure channel, exit location channel, exit width channel, personnel size channel, and personnel distribution channel) is received, with a uniform spatial size of H×W (H is the grid height, W is the grid width, unit: pixels). This tensor is then input into the first convolutional layer of the ResNet34 backbone network (usually a 7×7 convolution with a stride of 2, followed by a 3×3 max pooling with a stride of 2) to obtain the primary feature map.

[0052] Subsequently, the feature maps are sequentially processed through the stages defined by the network. Each stage consists of several Bottleneck residual modules connected in series. Within each Bottleneck module, the input features are first compressed by a 1×1 convolution (reducing the dimensionality to 1 / 4), then extracted by a 3×3 convolution, and finally restored by a 1×1 convolution (increasing the dimensionality). The input is then element-wise added to the original input of the Shortcut Connection and output after ReLU activation. As the network depth increases, the spatial resolution of the feature maps decreases layer by layer (downsampling is achieved through convolutions with a stride of 2), while the number of channels increases layer by layer, thereby extracting a hierarchical spatial feature representation from low-level geometric features (edges, obstacle contours) to high-level semantic features (evacuation bottleneck areas, crowd gathering patterns).

[0053] Step S22: Integrate an attention mechanism into the feature extraction network to enhance the feature weights of the preset key evacuation areas, and integrate a multi-scale feature fusion structure to adapt to the feature extraction needs of building spaces of different sizes.

[0054] In this step, the attention mechanism specifically refers to the Squeeze-and-Excitation (SE) channel attention mechanism. This mechanism obtains channel descriptors by compressing the spatial dimension through global average pooling, learns the dependencies between channels through fully connected layers, and generates channel weight coefficient vectors to achieve weighted enhancement of key information channels. The multi-scale feature fusion structure refers to the Feature Pyramid Network (FPN), which fuses deep low-resolution semantic features with shallow high-resolution location features layer by layer through lateral connections to generate a multi-scale feature map pyramid. Pre-defined critical evacuation areas refer to bottleneck areas in the building space that have a decisive impact on evacuation efficiency, including but not limited to narrow passages, stairwell entrances and corners, and exit connections.

[0055] The necessary procedures are as follows: At the outputs of each stage of the ResNet34 backbone network (typically layers C3, C4, and C5, corresponding to downsampling factors of 8, 16, and 32), SE attention modules are inserted respectively: global average pooling is performed on the input feature map to compress the H×W×C feature map into a 1×1×C channel descriptor vector (Squeeze operation); then, two fully connected layers (dimensionality reduction layer + dimensionality increase layer, activated by Rectified Linear Unit (ReLU) in between, and activated by Sigmoid in the dimensionality increase layer) are used to generate the weight coefficient vector of each channel (Excitation operation); this weight vector is multiplied by the channel dimension of the original feature map (Scale operation) to enhance the channel features that are sensitive to the response of key evacuation areas (such as around the exit and narrow passages) and suppress redundant background channels.

[0056] After obtaining the SE-weighted multi-layer feature maps (denoted as P3, P4, and P5, with spatial dimensions of H / 8×W / 8, H / 16×W / 16, and H / 32×W / 32, respectively), an FPN structure is constructed: starting from the top layer (P5), element-wise addition is performed by upsampling by 2x (nearest neighbor interpolation or deconvolution) and lateral connections (i.e., feature maps adjusted by adjusting the number of channels after 1×1 convolution) to generate a fused feature layer (denoted as M4); this process is repeated, and M4 is upsampled and fused with P3 to generate M3; finally, a multi-scale feature pyramid containing M3, M4, and M5 is formed. This pyramid simultaneously preserves deep semantic information (such as "this is the exit area") and shallow spatial details (such as "the person is specifically located in a certain grid"), adapting to the feature extraction needs of different sized building spaces (from small office cubicles to large airport terminals).

[0057] Step S23: Set a multi-head regression structure at the output of the feature extraction network. The multi-head regression structure has parallel output branches, including at least the total evacuation time output branch, the number of evacuees at each exit output branch, and the usage time of each exit output branch, to obtain the basic architecture of the positive prediction deep neural network.

[0058] The multi-head regression structure refers to setting multiple parallel and independent prediction branches at the end of the network. Each branch is responsible for regressing evacuation performance indicators in a specific dimension, avoiding feature confusion when a single output head is used for multi-task prediction. The total evacuation time output branch is a fully connected network that outputs a scalar value, predicting the total time (in seconds) from the start of evacuation to the last person leaving. The evacuation number output branches for each exit and the usage time output branches for each exit output vector values ​​(both with dimension N) corresponding to the number of exits N. The former represents the number of people leaving through each exit (in people), and the latter represents the time required for each exit to complete evacuation (in seconds).

[0059] The necessary procedures are as follows: Based on the multi-scale feature pyramid obtained in step S22 (taking M3 as an example, with dimensions H / 8×W / 8×256), the spatial dimensions are first compressed using global average pooling to generate a compact feature vector of 1×1×256. This vector is then input in parallel into three independent fully connected branches: 1. Total evacuation time branch: Consists of two fully connected layers (hidden layer) ReLU activation; output layer (linear activation), direct regression scalar value , which represents the predicted total evacuation time.

[0060] 2. Evacuation numbers at each exit branch: Output layer dimension set to (Export quantity), through the fully connected layer ( (Sigmoid or linear activation) output vector ,in Indicates the first The projected number of evacuees for each exit.

[0061] 3. Time branches for each exit: The output layer dimension is also [missing information]. Through an independent fully connected layer ( ReLU activation) output vector ,in Indicates the first Forecast usage time for each export.

[0062] The three branches share common feature extraction parameters from the backbone network, but have independent regression weights, enabling multi-task parallel prediction and together forming the complete basic architecture of a forward predictive deep neural network (denoted as EvacuNet).

[0063] Step S24: Based on the large-scale evacuation simulation dataset, a hybrid loss function adapted to multi-index parallel regression is used to supervise the training of the infrastructure, resulting in a trained positive prediction deep neural network.

[0064] Large-scale evacuation simulation datasets refer to paired datasets generated in diverse building scenarios using physical simulation methods such as social force models or cellular automata. These datasets include inputs on personnel distribution and outputs on evacuation time and exit utilization rates. A hybrid loss function is a composite loss function consisting of a weighted combination of smooth L1 loss and standard L1 loss, used to balance regression errors of indicators of different orders of magnitude. This indicates the training batch size. This represents the threshold parameter for Smooth L1 loss.

[0065] The necessary procedures are as follows: Constructing a training dataset: Based on microscopic simulation, evacuation simulations are performed in parameterized generated building scenes, recording the input scene parameters and output labels (total evacuation time). Number of exporters Export times ).

[0066] The mixed loss function is defined as follows: For total evacuation time prediction, a Smooth L1 Loss is used to balance the impact of outliers: .

[0067] in, For the first The predicted total evacuation time for each sample. For the corresponding true value, It is usually set to 1.0 second.

[0068] For the prediction of the number of evacuees and the usage time at each exit, the standard L1 Loss is adopted: .

[0069] .

[0070] in, and The first The first sample The predicted number of exits versus the actual number of evacuees. and These are the predicted and actual usage times, respectively, in seconds.

[0071] The final mixed loss function is a weighted sum: .

[0072] in , , Preset weighting coefficients (e.g.) ).

[0073] The Adam optimizer was used (initial learning rate 0.001). ), to minimize With the goal of training EvacuNet under end-to-end supervision, a trained positive prediction deep neural network is obtained.

[0074] The construction and training of inverse generative deep neural networks include: Step S51: Construct an image generation model based on a generative adversarial network, wherein the generator adopts an encoder-decoder structure and preserves spatial detail information through skip connections, and the discriminator adopts a preset local region discrimination structure.

[0075] In this context, Generative Adversarial Networks (GANs) refer to adversarial training frameworks that control the generation process using conditional vectors, comprising a generator and a discriminator. The encoder-decoder structure is a U-shaped network structure where the generator extracts high-level semantic features from the input conditions through downsampling encoding, and then reconstructs the spatial image through upsampling decoding. Skip Connections are cross-layer feature direct connections established between corresponding layers of the encoder and decoder. The pre-defined local region discrimination structure in this step specifically refers to the PatchGAN discriminator, which divides the input image into multiple local patches and determines the authenticity of each patch.

[0076] The necessary procedures are as follows: Constructing conditional generative adversarial networks as the core framework for inverse generative deep neural networks: Generator construction: Employs the U-Net architecture, comprising encoding and decoding paths. The encoding path consists of four downsampling blocks, each containing two downsampling operations. Convolution (ReLU activation) followed by Max pooling (step size 2) gradually modulates the input condition map (size). Compression to low-dimensional feature representation ( The decoding path consists of four upsampling blocks, each block first passing through... Transposed convolution achieves a 2x improvement in spatial resolution, followed by concatenation along the channel dimension with the feature maps of the corresponding layers in the encoding path (transmitted via skip connections), and then processed twice. Convolution processing.

[0077] Discriminator Construction: A PatchGAN local map discriminant network structure is adopted, consisting of 5 convolutional layers (convolutional kernels) Step size 2, channel number increases layer by layer: Except for the last layer, all layers use Leaky ReLU activation (slope 0.2). The last layer outputs a single-channel feature map (size as shown). Each output value represents the probability that the corresponding local region of the input image is a real sample.

[0078] Step S52: Using the target evacuation performance index, building structure, exit location and width as input conditions, output a continuous personnel density distribution map. The target evacuation performance index includes the target total evacuation time and the target exit utilization rate.

[0079] Among them, the target evacuation performance index refers to the evacuation performance parameters that the user or system presets to achieve, including the target total evacuation time (denoted as...). (unit: seconds) and target export utilization rate (denoted as Dimension A continuous population density distribution map is a heat map represented by a two-dimensional grayscale image, where the value of each pixel represents the population density intensity (unit: people / square meter) at the corresponding building location, and is in the form of a continuously differentiable tensor.

[0080] The necessary procedures are as follows: 1. Construct a conditional input tensor: This will include the target total evacuation time. Vector of target export utilization Concatenate into a global condition vector This is then expanded into a two-dimensional tensor with the same spatial dimensions as the building structure diagram via a broadcast mechanism. The binary mask of the building structure, the exit location mask, the exit width encoded map, and the aforementioned global condition tensor are stacked along the channel dimension to form a multi-channel conditional input (dimension). , (Number of channels).

[0081] 2. The multi-channel conditional input is fed into the U-Net generator constructed in step S51: the encoding path progressively extracts the coupled features of "target performance + building structure"; the decoding path fuses multi-layer features through skip connections, progressively upsampling to the original spatial resolution. The generator ultimately outputs a single-channel continuous personnel density distribution map. (size ), where each pixel value Indicates position The predicted population density at the location was normalized to Sigmoid activation. After the interval, it can be mapped to the actual density range. ( (This is the preset maximum personnel density).

[0082] Step S53: During the training process, a loss function consisting of adversarial loss and structural similarity loss is used to constrain the training of the image generation model, thereby obtaining the trained inverse generation deep neural network.

[0083] Among them, Adversarial Loss refers to a loss function defined based on the game process between the generator and the discriminator, which measures the generator's ability to deceive the discriminator. Structural Similarity Loss (SSIMLoss) is a loss term constructed based on image brightness, contrast, and structural similarity measures, used to overcome the structural ambiguity problem caused by traditional pixel-level L1 / L2 loss. This represents the average value of the discriminator's patch-level discrimination output on the input image.

[0084] The necessary procedures are as follows: During the training phase, a real-world population density distribution map ( ) and generator output Pairwise input discriminator. The adversarial loss is defined as a least-squares loss: .

[0085] in, This represents the expectation operation. This represents the mean value of the discriminator's discrimination of local patches in the input image.

[0086] Define structural similarity loss: .

[0087] The SSIM value is obtained through a sliding window (such as...). The Gaussian kernel is calculated in a local region of the image: . , These are the mean values ​​within the window. , They are variance, For covariance, , For stability constants (e.g.) and ).

[0088] The total loss function is a weighted fusion: .

[0089] Usually taken By alternately optimizing the discriminator and generator, and training until convergence, a reverse-generative deep neural network (denoted as DistribuNet) is obtained.

[0090] In the training framework of step S53, structural similarity loss effectively overcomes the structural blurring and distortion problems caused by traditional pixel-level loss by constraining the similarity between the generated image and the real image in terms of brightness, contrast, and structural patterns. Combined with adversarial loss to constrain the overall statistical distribution of the generated image, it can generate a visually clear and statistically reasonable personnel density distribution map. However, structural similarity loss essentially measures the overall structural similarity of the image. For certain local areas with key evacuation functions in the evacuation density generation task, such as bottleneck areas like narrow passages and stair corners, their high-frequency density details are easily smoothed or diluted during the global optimization process of structural similarity loss, resulting in insufficient density distribution accuracy in these key areas, which in turn affects the accuracy of evacuation time prediction and exit utilization assessment. At the same time, although the physical constraint channel introduced in step S5B can explicitly constrain the density legality of wall boundaries and blind spots from the input layer, its scope of action is limited to the hard constraints of the building's physical boundaries and cannot provide targeted guidance for the density distribution accuracy within bottleneck areas.

[0091] Therefore, based on the basic training framework described in step S53, this application further introduces a bottleneck region density reconstruction loss term based on a spatial attention mechanism, and strengthens the network's learning ability of the bottleneck region density features through a differentiated weighting strategy. Specifically, the training of the inverse generative deep neural network also includes: Step S54: Based on the building structure, identify bottleneck areas according to preset bottleneck identification rules. The preset bottleneck identification rules include: identifying areas where the passage width is less than a first preset width threshold as narrow passage areas, and identifying areas where the personnel confluence radius at stair entrances, corners and exits is less than a second preset radius threshold as confluence bottleneck areas. The bottleneck area is a specific implementation of the preset evacuation key area in step S22.

[0092] The bottleneck region refers to a critical local area where the flow rate of people is significantly restricted during evacuation due to spatial geometric constraints. The first preset width threshold (denoted as...) This refers to the critical width value (e.g., 1.2 meters) for determining a narrow passage. The second preset radius threshold (denoted as...) The radius (e.g., 2.0 meters) is the critical radius value for determining a congestion bottleneck. The congestion radius of people refers to the geometric distance from the nearest obstacle to a potential congestion point such as a stairwell entrance, corner, or exit junction.

[0093] The necessary procedures are as follows: Receive building structure binary mask ( (1 represents an obstacle, and 0 represents passage). First, the geometric skeleton of the passable area of ​​the building is extracted through morphological operations. Then, the distance from each passable pixel to the nearest obstacle is calculated using distance transformation. Multiply by spatial resolution (meters / pixel) to obtain the actual distance map .

[0094] Narrow passage identification: Traverse the passable area and identify passages with a width (twice the local minimum distance) less than... Connected regions are marked as narrow channel regions. .

[0095] Bottling bottleneck identification: For predefined key locations such as stairwell entrances, corners, and exit junctions, calculate the distance from each center point to the nearest obstacle, using these locations as the center. As the confluence radius. If Then the radius around the center point The circular area within the range is marked as the confluence bottleneck area. .

[0096] Final bottleneck area for and The union of the values ​​is output as a binary mask (the pixel value in the bottleneck area is 1, and the rest are 0).

[0097] Step S55: Generate a spatial attention weight map based on the bottleneck region. In the spatial attention weight map, pixels belonging to the bottleneck region are assigned a first preset weight value, and pixels not belonging to the bottleneck region are assigned a second preset weight value. The first preset weight value is greater than the second preset weight value.

[0098] The Spatial Attention Weight Map refers to a two-dimensional weight matrix with the same spatial dimensions as the density distribution map, denoted as... (size The first preset weight value (denoted as...) This refers to a high weighting coefficient (e.g., 10.0) for pixels in the bottleneck region. The second preset weighting value (denoted as...) ) refers to the baseline weight coefficient (e.g., 1.0) for pixels in non-bottleneck areas.

[0099] The necessary process is as follows: Based on the binary mask of the bottleneck region obtained in step S54 (The bottleneck region is 1, and the rest are 0), a spatial attention weight map is generated by judging each element: .

[0100] in Indicates pixel coordinate index, Indicates the weighted graph in The value of the position.

[0101] Step S56: Calculate the density deviation between the generated density distribution map and the real density distribution map at each pixel position, multiply the density deviation by the spatial attention weight map element by element, and calculate the mean of the weighted density deviation to obtain the density reconstruction loss term.

[0102] Density deviation refers to the generation of density distribution maps. Compared with the actual density distribution map The numerical difference at the corresponding pixel position is denoted as Element-wise multiplication is an operation that multiplies the values ​​at corresponding positions of two tensors of the same size. It is denoted as... The density reconstruction loss term is denoted as... .

[0103] The necessary procedures are as follows: First, calculate the pixel-level density deviation map. (Using absolute difference form): .

[0104] in and These represent the generated image and the real image, respectively. Density value at location.

[0105] Then Spatial attention weight map generated in step S55 Perform element-wise multiplication to obtain the weighted bias plot: .

[0106] Finally, sum all pixels in the weighted bias map and divide by the total number of pixels ( ), thus obtaining the density reconstruction loss term: .

[0107] Step S57: The density reconstruction loss term is weighted and summed with the adversarial loss and structural similarity loss from step S53 according to the preset loss weight coefficients to form the final training loss function; the preset loss weight coefficients include the adversarial loss weight, the structural similarity loss weight, and the density reconstruction loss weight, and the sum of each weight coefficient is 1.

[0108] Here, the final training loss function is defined. The weighted sum of the three losses: .

[0109] The weighting coefficients satisfy the normalization constraint: .

[0110] Typical configuration is By minimizing The parameters of the generator and discriminator are jointly optimized.

[0111] Step S58: Based on the final training loss function, the inverse generation deep neural network is subjected to constrained training, so that the density reconstruction loss term enhances the preservation of high-frequency density details in the bottleneck region after differential adaptive modulation from step S5C to step S5D.

[0112] High-frequency density details refer to local areas in the density distribution map that change dramatically (such as high-density peaks at the bottleneck or density gradients at the outlet).

[0113] The necessary procedures are as follows: During training, for training samples containing bottleneck regions, the density reconstruction loss term constructed in steps S54 to S56 generates a larger gradient signal for the pixels in the bottleneck region during backpropagation. This gradient signal, when backpropagated through the decoder network, acts on the affine transformation parameters (scaling factors) described in steps S5C to S5D. With bias coefficient This prompts the network to adjust its various layers. , The value allows the bottleneck region to obtain a larger feature activation value at the decoder output, which is then represented by a sharper peak and a steeper gradient on the density distribution map.

[0114] Specifically, when the generation density value of a bottleneck region is lower than the true value, Through high weight A strong gradient is generated and passed to the affine transformation parameters of the corresponding decoder layer via the chain rule, updating the scaling coefficients of that region. To amplify the characteristic response, or adjust the bias coefficient To improve the basic density level.

[0115] In step S59, the density reconstruction loss term and the physical constraint channel in the multi-channel conditional input in step S5B work together: the physical constraint channel explicitly constrains the density of the wall boundary in step S5D to zero and the density of the blind spot from the input layer, and the density reconstruction loss term guides the density distribution accuracy of the bottleneck area from the training layer, so as to achieve the physical legitimacy and evacuation function rationality of the generated image.

[0116] The Physical Constraint Channel refers to the explicit physical constraint map introduced in step S5B, which encodes geodesic distance and line-of-sight occlusion information. Physical Legality means that the generated personnel density distribution satisfies the building's physical boundary constraints (zero density in wall areas). Evacuation Function Rationality means that the aggregation pattern reflected by the density distribution conforms to the laws of evacuation dynamics (high-density queues form in bottleneck areas).

[0117] The necessary procedures are as follows: In the input layer, physical constraint channels (such as setting the wall mask to 0 and the passable area to 1) are used as hard constraints. Through the forward propagation of the encoder-decoder, the density at the wall boundary is forced to be zero in the generation stage of step S5D to ensure physical validity.

[0118] The density reconstruction loss term (steps S56-S58) provides soft constraints from the training optimization level: by using weighted loss, the network is forced to output a high-density distribution in the bottleneck region that is consistent with the real evacuation process, thus compensating for the lack of guidance on density numerical accuracy in the physical constraint channel.

[0119] The two work together in a “hard constraint at the input layer + soft guidance at the training layer” model: physical constraints ensure that the channel does not violate physical rules (no one passes through the wall), and density reconstruction loss term ensures that it meets the evacuation function (a reasonable high-density queue is formed in the narrow channel).

[0120] Generating a continuous population density distribution map includes: Step S5A: Obtain the preset physical constraint map of the target building. The preset physical constraint map at least encodes the geodesic distance from each spatial location to the nearest exit and the line-of-sight occlusion status of each spatial location.

[0121] The pre-defined physical constraint map is denoted as... Geodesic distance refers to the shortest path length along the surface of a building's accessible area from a given location to the nearest exit, denoted as . (Unit: meters)

[0122] Line-of-sight occlusion status is denoted as This refers to whether there is an unobstructed line of sight from a certain location to the exit (0 indicates obstruction, 1 indicates visibility).

[0123] The necessary procedures are as follows: Based on a binary mask of the building structure, the geodesic distance map is first calculated: using the Fast Marching Method or Dijkstra's algorithm, with each exit location as the source point, the shortest path length from each pixel to the nearest exit is calculated in the passable area, generating a geodesic distance matrix of the same size as the building raster map. The range is .

[0124] Subsequently, a view occlusion map is calculated: for each passable pixel, a view is emitted to each exit (Bresenham line algorithm). If the view is blocked by a wall pixel, the view occlusion value of that pixel for that exit is marked as 0; otherwise, it is marked as 1. Combining all exits, the maximum visibility is taken as the view occlusion state value for that pixel, generating a value range of... Line of sight occlusion diagram .

[0125] Will and Stacking along the channel dimension forms a pre-defined physical constraint graph. .

[0126] Step S5B: The preset physical constraint map is used as an explicit physical constraint channel, and is superimposed on the building structure, exit location and width, target total evacuation time and target exit utilization rate in the channel dimension to form a multi-channel condition input.

[0127] Explicit physical constraint channels refer to the physical constraint graphs integrated into the network input as independent channels. Channel dimension stacking refers to the feature concatenation operation performed on the channel axes of the deep learning tensor, denoted as... .

[0128] The necessary procedures are as follows: Constructing a multi-channel conditional input tensor Its channel structure is as follows: Channel 1: Binary Mask for Building Structure (0-1, obstacle / passable); Channel 2: Binary mask at the exit position (0-1, mark the exit area); Channel 3: Exit Width Coding Diagram (Each exit area is filled with the actual width value, the rest are 0); Channel 4: Geodetic Distance Map (Normalization to) ); Channel 5: Line of Sight Obstruction Diagram (0-1 continuous values); Channel 6: Total Target Evacuation Time (Global scalar broadcast to full map size); Channel 7 to Channel Target export utilization vector (Each element is broadcast as an independent channel).

[0129] The above channels are stitched together in the depth dimension to form a shape of size [missing information]. Multi-channel conditional input.

[0130] In step S5C, the multi-channel condition input is used to generate a deep neural network. After feature encoding by the encoder built into the deep neural network, the total evacuation time and the target exit utilization rate are encoded into scaling and bias coefficients by a preset multilayer perceptron in the decoder stage of the deep neural network. Affine transformation is performed on the feature maps of each layer of the decoder to achieve differentiated modulation of the local pixel density generation of the global evacuation performance target.

[0131] In this step, affine transformation specifically refers to the scaling and shifting operations performed on the feature map, mathematically expressed as follows: ( This indicates element-wise multiplication. (This indicates element-wise addition). Differentiated modulation refers to dynamically adjusting the characteristic response intensity of different decoder layers based on global conditions.

[0132] The necessary procedures are as follows: The multi-channel conditional input is first compressed using a U-Net encoder to generate a high-level semantic feature map. (Dimensions as follows) In the decoder stage, for the first... Each decoder level ( (corresponding to a progressively higher resolution), the following modulation is performed: Total evacuation time of the target Vector of target export utilization Concatenate into a condition vector (size ), input a preset multilayer perceptron (MLP). This MLP is for the first Layer output layer-specific scaling factor With bias coefficient (All are vectors, with dimension equal to the number of channels in the feature map of that layer) ).

[0133] For the Intermediate feature maps generated by the layer decoder (size Perform affine transformation: .

[0134] in This indicates that the channel dimensions are multiplied element-wise (scaling operation). This represents element-wise addition (offset operation). By applying this transformation layer by layer, the global sparse performance target is achieved through differentiated modulation of the local pixel density generation.

[0135] Step S5D involves generating a continuous personnel density distribution map that satisfies preset physical boundary constraints and global target constraints by combining the physical constraint channels in the multi-channel condition input after differential modulation.

[0136] Among them, the preset physical boundary constraints refer to the hard constraint that the personnel density at the boundaries of building walls and obstacles must be zero. Global target constraints refer to the fact that after the generated density distribution is inferred by the forward prediction network, the predicted evacuation time and exit utilization rate should approach the target value.

[0137] The necessary procedures are as follows: In the final layer of the decoder (the first layer) (layer), feature map modulated by affine transformation (size )pass Convolutional reduction to a single channel, followed by Sigmoid activation to generate an initial density map. (range Subsequently, the physical constraint channel (building structure mask) in step S5B will be... (as a hard constraint mask) ,right Apply physical boundary constraints: .

[0138] This means the density of the forced obstacle area is zero. The final output is a continuous population density distribution map. It satisfies physical legitimacy (the density of the wall area is zero) and global objective constraints (verified by the forward prediction network in step S2, its predicted evacuation performance is close to the target value).

[0139] The affine transformation of the feature maps of each layer of the decoder is performed layer by layer, including: Step S5C1: Concatenate the total evacuation time and the target exit utilization rate into a global condition vector.

[0140] Wherein, the global condition vector is denoted as It is used to encode global information about the desired evacuation effect.

[0141] Necessary process description: Let the total evacuation time be a scalar. (Normalization to) (or original value), the target export utilization rate is a vector. (Each element represents a utilization value between 0 and 1). Concatenate the two along the feature dimension: .

[0142] The resulting vector dimension is This serves as the input for subsequent MLP operations.

[0143] In step S5C2, the global condition vector is input into a preset multilayer perceptron. The preset multilayer perceptron outputs a set of layer-specific scaling coefficients and layer-specific bias coefficients for each layer of the decoder. The layer-specific scaling coefficients and the layer-specific bias coefficients of each layer are independent of each other.

[0144] The pre-defined multi-layer perceptron (MLP) is a small, fully connected network independent of the U-Net main network, used to map the global conditional vector to affine transformation parameters for each layer. Level-specific scale coefficients are denoted as... Level-specific bias coefficients are denoted as... .

[0145] The necessary procedures are as follows: Assume the decoder has a total of Levels (such as) Resolution from Gradually upsampled to ). Build Each subnetwork is a separate MLP subnetwork (or a single MLP outputting all parameters). For input: For the layer( ):

[0146] The output dimension of each MLP is equal to the number of channels in the feature map of that layer. Each MLP parameter is trained independently to ensure that different resolution levels obtain modulation parameters suitable for their own scale.

[0147] Step S5C3: In the first layer of the decoder, the channel dimension scaling operation is performed on the feature map of the layer using the layer-specific scaling coefficient corresponding to the layer to obtain the first-layer scaled feature map; the channel dimension offset operation is performed on the first-layer scaled feature map using the layer-specific bias coefficient corresponding to the layer to obtain the first-layer modulation feature map.

[0148] Here, the First Level refers to the first upsampling layer with the lowest spatial resolution in the decoder, corresponding to the deepest semantic features. Channel-wise Scaling involves multiplying each channel of the feature map by a scalar coefficient. Channel-wise Shifting involves adding a scalar bias to each channel of the feature map.

[0149] The necessary procedures are as follows: Let the first level be ( The input feature map is (size The level-specific scaling factor is a vector. The level-specific bias coefficients are vectors. .

[0150] Execute channel dimension scaling: .

[0151] in For channel index, For the first The scaling factor for the channel, this operation transmits the vector via a broadcast mechanism. Expand to Multiply the dimensions element by element.

[0152] Execution channel dimension offset: .

[0153] income This is the first-level modulation feature map.

[0154] In step S5C4, from the second to the last layer of the decoder, the channel dimension scaling operation is performed on the feature map of each layer using the layer-specific scaling coefficient corresponding to each layer to obtain the scaled feature map of each layer; the channel dimension offset operation is performed on the scaled feature map of each layer using the layer-specific bias coefficient corresponding to each layer to obtain the modulation feature map of each layer.

[0155] The second to last level refers to the subsequent upsampling layers in the decoder that immediately follow the first level, up to the output layer. The scaled feature maps of each level are denoted as... The modulated feature maps of each level are denoted as follows: .

[0156] The necessary procedures are as follows: For the Hierarchy ( (Resolution doubles layer by layer): Receive from the first Hierarchical upsampling features (via The tensor obtained by concatenating the encoder's corresponding layer features (interpolated or transposed convolution) with skip connections is a function of interpolation or transpose convolution. (size ).

[0157] Similar to step S5C3, utilize the level-specific scaling factor of this level. (dimension) Scaling the channel dimensions: .

[0158] Then utilize the level-specific bias coefficient Perform offset: .

[0159] As the layer deepens (resolution increases), and Gradually shifting from controlling the global density level to regulating local details, the process achieves a layer-by-layer penetration of global target constraints into the generation of local pixels.

[0160] In step S5C5, the level-specific scaling factor and level-specific bias factor of each level are determined through joint training of a preset multilayer perceptron and an inverse generative deep neural network.

[0161] Joint training refers to the synchronous optimization of the MLP parameter generation network and the U-Net main generation network during end-to-end training.

[0162] The necessary procedures are as follows: During the training phase, the MLPs at each level described in step S5C2 (total) Each one is output. and The U-Net generator and the U-Net itself form an integrated computational graph. The loss function (defined in steps S53 and S57) When the gradient of the ) is backpropagated through the U-Net decoder to the affine transformation nodes of each layer, it is further passed to the corresponding MLP subnetwork to update its weight parameters.

[0163] Specifically, when the density reconstruction loss in the bottleneck region generates a gradient, this gradient is backpropagated through the decoder layer to that layer. and This triggers the update of MLP parameters, enabling MLP learning to map specific global conditional vectors into affine parameters that can produce specific density distributions.

[0164] Density-weighted sampling of the density distribution map, followed by spatial exclusion and physical feasibility corrections, yields a discrete distribution of personnel locations that conforms to building structural constraints, including: Step S61: Based on the density values ​​of each pixel in the continuous population density distribution map, perform weighted random sampling to generate an initial discrete pedestrian location set that satisfies the total population size.

[0165] Weighted random sampling refers to a sampling method that randomly selects locations from a raster image using pixel density values ​​as probability weights. The initial discrete pedestrian position set is denoted as... Each point represents the location of a candidate pedestrian.

[0166] The necessary procedures are as follows: Receive the continuous population density distribution map generated in step S5D (size First, the density map is normalized to a probability mass function (PMF): .

[0167] Based on this probability distribution, random sampling is performed, with the number of samples equal to the total number of people. Each sampling is based on Select raster coordinates And convert the coordinates to physical coordinates: .

[0168] in , For grid in , Physical dimensions (meters / pixel) of the orientation. Collect all sampled coordinates to form an initial set. .

[0169] Step S62: Perform spatial exclusion correction on the initial discrete pedestrian location set to ensure that the distance between any two pedestrian locations is not less than the preset social distance threshold.

[0170] Spatial repulsion correction refers to the optimization process of eliminating overlapping positions of people and ensuring minimum spacing by iteratively adjusting position coordinates or removing conflict points. The pre-defined social distance threshold is denoted as... This refers to the minimum permissible distance (usually 0.3 to 0.5 meters) set to avoid overcrowding.

[0171] The necessary procedures are as follows: 1. Set minimum distance threshold (e.g., 0.4 meters). For the initial set Perform iterative corrections: Build spatial indexes (such as KD-Tree) to accelerate nearest neighbor queries; 2. Traverse all points, and for each point... Query its radius Set of neighboring points within (e.g., 1 meter) ; 3. For each neighboring point Calculate Euclidean distance .like Then, they are forcibly separated along the direction of the displacement vectors of the two points: Calculate the unit direction vector: ; Update location: , , for and The Euclidean distance; 4. If the corrected position exceeds the building boundary or falls into the obstacle zone, mark the point as to be removed; 5. Repeat steps 2-4 until the spacing between all point pairs is equal. Or reach the maximum number of iterations.

[0172] 6. The set is obtained after correction. .

[0173] Step S63: Perform a physical feasibility check on the pedestrian location set after spatial exclusion correction, remove invalid location coordinates that fall into the obstacle area, and supplement the missing locations after removal by sampling according to the density distribution map until a complete discrete personnel location distribution that meets the building structure constraints is obtained.

[0174] Physical feasibility verification refers to the process of checking whether pedestrian locations meet the geometrical accessibility constraints of the building. Supplementary sampling refers to the operation of resampling based on the original density distribution map after eliminating invalid locations to make up for the shortfall in the total number of people.

[0175] The necessary procedures are as follows: Set after spatial repulsion correction Point inclusion test with building structure binary mask: for each point Map its coordinates to the raster index Check mask value .like If a point is identified as an obstacle zone, or if a valid path to any exit cannot be planned based on the path planning algorithm, then it is marked as such. Invalid positions are removed.

[0176] Record removal quantity .like Then return to step S61, based on the original density distribution map. (After excluding the probability mass of already retained points and re-normalizing) perform supplementary sampling to generate... At a new location, repeat step S62 for spatial repulsion correction and physical feasibility verification, iterating until... .

[0177] The final collection This refers to the optimized spatial distribution of personnel.

[0178] The physical feasibility verification includes the following sub-steps: Step A1: Input the set of pedestrian locations obtained after spatial exclusion correction into the preset microscopic evacuation simulation model; the preset microscopic evacuation simulation model constructs a pedestrian passable network based on the building structure, and calculates the microscopic evacuation trajectory and microscopic evacuation time of each pedestrian location along the passable network to the corresponding exit.

[0179] Among them, the preset micro-evacuation simulation model refers to a refined evacuation process simulator built based on social force models or cellular automata. The pedestrian walkable network refers to a topological map composed of the skeleton lines of walkable areas. Micro-evacuation trajectory and micro-evacuation time refer to the detailed walking path and required time from a specific starting point to the exit.

[0180] The necessary procedures are as follows: Based on a binary mask of the building structure, the geometric skeleton of the passable area is extracted, and a graph structure is constructed. , where the vertex As a key node in the channel, the edge The edges are traversable connections between nodes, with the edge weight being the Euclidean distance.

[0181] For sets Each pedestrian location Using the A* algorithm to calculate from To the nearest export shortest path and corresponding time If there exists a certain If no effective path can be planned, the location is determined to be physically unreachable.

[0182] Step A2: Based on the micro evacuation trajectory, identify physically inaccessible locations in the pedestrian location set; physically inaccessible locations include: locations outside the passable network, and locations from which a continuous path to any exit cannot be planned within a preset maximum time threshold.

[0183] Physically unreachable positions are denoted as... The preset maximum time threshold is denoted as... This refers to the upper limit of time for determining whether a location is reachable.

[0184] Necessary process description: Microscopic evacuation time calculated in step A1 Based on this, set a time threshold. (e.g., 600 seconds). For each pedestrian location :like Located in the obstacle zone, or If the path planning algorithm fails, the path is considered unreachable and added to the set. .

[0185] Step A3: Remove all physically inaccessible locations from the pedestrian location set to obtain the accessible location set and the number of locations removed.

[0186] Necessary process description: From the current set of pedestrian positions Remove all physically unreachable locations To obtain the set of reachable locations : .

[0187] Record the number of removal locations .

[0188] Step A4: Determine if the number of eliminated locations is greater than zero; if it is greater than zero, then based on the continuous pedestrian density distribution map, conduct supplementary sampling in the adjacent accessible area of ​​the physically inaccessible location to supplement the number of new pedestrian locations corresponding to the number of eliminated locations.

[0189] The Adjacent Reachable Area of ​​a Physically Unreachable Location refers to the passable buffer zone surrounding the unreachable location.

[0190] Necessary process description: If For each unreachable location that is removed Define the radius around it as A circular neighborhood (e.g., 2 meters) is defined, and passable grid cells are searched within this neighborhood to form local candidate regions. The global density distribution map is then used. Multiplying the result by the local candidate region mask yields a local probability distribution. After normalization, weighted random sampling is performed within this region to generate new candidate locations. Repeat this process until replenished. A new location is created, forming a supplementary location set. .

[0191] Step A5: Add the newly added pedestrian locations to the reachable location set to form an updated pedestrian location set.

[0192] Necessary process description: The supplementary location set generated in step A4... With the set of reachable locations merge: .

[0193] at this time The total number of people restored remains constant.

[0194] Step A6: Repeat steps A1 to A5 for the updated pedestrian location set until the number of locations removed in a certain iteration is zero, and output the pedestrian location set at this time as a complete discrete distribution of personnel locations that conforms to the building structure constraints.

[0195] Necessary process description: As a new Enter step A1 and re-execute the physical feasibility check. If physically inaccessible locations still exist in the new iteration, continue with supplementary sampling and merging in steps A4-A5. Iterate until the number of locations removed in a given check is reached. The set of pedestrian locations at this time. This refers to the complete discrete distribution of personnel locations that conforms to the constraints of the building structure.

[0196] Iteratively execute the above prediction, judgment, generation, and post-processing steps until the total evacuation time and exit utilization rate meet the preset target thresholds, including: Step S71: The discrete personnel location distribution obtained in post-processing is transformed into a continuous differentiable personnel distribution representation through a preset differentiable surrogate model.

[0197] Among them, a differentiable surrogate model refers to an approximate function that transforms a discrete point set into a continuous density field and supports gradient backpropagation. A continuous differentiable pedestrian distribution representation is denoted as... This allows the gradient flow to propagate backward from the output to the input.

[0198] The necessary procedures are as follows: Let the set of discrete personnel locations obtained through post-processing be... , Define the differentiable surrogate model as the Gaussian kernel density estimate (KDE): .

[0199] in Given a Gaussian kernel bandwidth (e.g., 0.3 meters), this continuous density field... Rasterize to be consistent with step S1 A grid is formed to represent a continuous and differentiable tensor of personnel distribution (size). ).

[0200] Step S72: Input the continuous differentiable personnel distribution representation into the forward prediction deep neural network to obtain the predicted total evacuation time and the predicted exit utilization rate, calculate the time error between the predicted total evacuation time and the target total evacuation time, and the utilization error between the predicted exit utilization rate and the target exit utilization rate.

[0201] Wherein, time error is denoted as This refers to the difference between the predicted total evacuation time and the target total evacuation time. Utilization error is denoted as... , refers to the vector difference between the predicted export utilization rate and the target export utilization rate.

[0202] The necessary procedures are as follows: The continuously differentiable population distribution representation generated in step S71 is stacked with building structure and exit information, and then input into the trained positive prediction deep neural network (EvacuNet) to obtain the predicted total evacuation time. Vector of predicted export utilization .

[0203] Calculate the time error (L1 norm): .

[0204] Calculate the utilization error (L1 norm average): .

[0205] Total error , as the optimization target.

[0206] Step S73: Propagate the time error and utilization error in reverse along the gradient propagation path from the forward prediction deep neural network, the differentiable surrogate model to the input of the inverse generation deep neural network, to obtain the updated gradient of the input condition parameters of the inverse generation deep neural network.

[0207] The gradient propagation chain refers to the continuous computational graph path that propagates the gradient from the final error back through each computation node to the parameters to be optimized. Input condition parameters refer to the inputs to the inverse generation network, i.e., the total target evacuation time. With target export utilization rate .

[0208] The necessary procedures are as follows: Based on the calculation in step S72 Backpropagation is performed through an automatic differentiation mechanism: 1. The error is backpropagated to its input layer via EvacuNet to obtain the gradient representing the continuously differentiable population distribution. ; 2. The gradient is backpropagated via a differentiable surrogate model to calculate the gradient for each discrete coordinate. The gradient; 3. The gradient is backpropagated to its input via the inverse generation network, ultimately obtaining the input condition parameters. gradient .

[0209] This gradient indicates how the target evacuation time and target exit utilization should be adjusted so that the generated personnel distribution, after positive prediction, is closer to the current target.

[0210] Step S74: Adjust the target total evacuation time and target exit utilization rate of the inversely generated deep neural network input based on the updated gradient, and use the adjusted target total evacuation time and target exit utilization rate as the condition input for the next iteration.

[0211] Gradient descent update refers to the process of adjusting parameters along the negative gradient direction to minimize the loss function. The learning rate is denoted as... This refers to the hyperparameter that controls the update step size each time.

[0212] Necessary process description: Setting the optimization step size (e.g., 0.01). Update the input condition parameters based on the gradient obtained in step S73: .

[0213] .

[0214] The updated As new input conditions, the reverse generation and post-processing flow of steps S5-S6 is re-executed.

[0215] Step S75: Repeat the above steps to iteratively update the input condition parameters along the gradient descent direction until the time error and utilization error converge to within the preset error threshold.

[0216] Convergence to a pre-defined error threshold means that optimization is considered complete when the error is less than a set tolerance. The pre-defined error threshold includes a time error threshold. (e.g., 2 seconds) and utilization error threshold (e.g., 0.1).

[0217] Necessary process description: Setting the convergence threshold and Repeat the closed-loop iteration of steps S71-S74, generating the personnel distribution in each iteration based on the current condition parameters. Positive prediction Calculation error Backpropagation Update the condition parameters.

[0218] Check convergence conditions: like and If the iteration stops, then stop.

[0219] Or it can reach a preset maximum number of iterations (e.g., 50 times). When the convergence condition is met, the current spatial distribution of people is the final optimized solution that meets the preset target threshold, and the output is used as the final evacuation layout suggestion.

[0220] Based on the same inventive concept, embodiments of the present invention provide a system for rapid assessment of evacuation performance and optimization of personnel spatial distribution, including a memory and a processor, wherein the memory stores information that can be run on the processor to implement, as described above. Figure 1 The procedure for the method shown.

[0221] The embodiments described in this specific implementation are preferred embodiments of this application and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A method for rapid assessment of evacuation performance and optimization of spatial distribution of personnel, characterized in that, include: Obtain basic scene information and current spatial distribution of personnel for the target building. Basic scene information includes building structure, exit location and width, and total number of personnel. Input the basic information of the scene and the current spatial distribution of people into the forward prediction deep neural network to predict the total evacuation time and exit utilization rate. Determine whether the total evacuation time and exit utilization rate have reached the preset target thresholds; If the target is reached, output the current spatial distribution of personnel. If the target is not met, the target total evacuation time and target exit utilization rate corresponding to the preset target threshold are used as conditions. The deep neural network is generated in reverse with the input of building structure, exit location and width to generate a continuous personnel density distribution map. The deep neural network is an image generation model with a generative adversarial network framework, and the discriminator adopts a preset local region discrimination structure. The density distribution map is sampled in a density-weighted manner, and after spatial exclusion and physical feasibility correction, a discrete personnel location distribution that conforms to the building structure constraints is obtained as the optimized personnel spatial distribution. The optimized spatial distribution of personnel is used as the new current spatial distribution of personnel. It is then fed back into the positive prediction deep neural network for re-evaluation. The above prediction, judgment, generation and post-processing steps are iteratively executed until the total evacuation time and exit utilization rate meet the preset target thresholds.

2. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 1, characterized in that, The construction and training of a forward prediction deep neural network includes: A feature extraction network with a deep convolutional network as its backbone is constructed to extract basic scene information and spatial features of the current spatial distribution of people. An attention mechanism is integrated into the feature extraction network to enhance the feature weights of the preset key evacuation areas, and a multi-scale feature fusion structure is integrated to adapt to the feature extraction needs of building spaces of different sizes. A multi-head regression structure is set at the output of the feature extraction network. The multi-head regression structure has parallel output branches, including at least the total evacuation time output branch, the number of evacuees at each exit output branch, and the usage time of each exit output branch, thus obtaining the basic architecture of the positive prediction deep neural network. Based on a large-scale evacuation simulation dataset, a hybrid loss function with adapted multi-index parallel regression is used to supervise the training of the infrastructure, resulting in a trained positive prediction deep neural network.

3. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 2, characterized in that: The deep convolutional network is a ResNet backbone network, which contains the Bottleneck residual module; The attention mechanism is the SE channel attention mechanism; The multi-scale feature fusion structure is a feature pyramid network structure; In the multi-head regression structure, the total evacuation time output branch outputs a scalar value, while the number of evacuees at each exit and the usage time at each exit output branch output vector values ​​corresponding to the number of exits, respectively. The hybrid loss function consists of smoothed L1 loss and L1 loss.

4. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 1, characterized in that, The generator of the inverse deep neural network adopts an encoder-decoder structure and preserves spatial detail information through skip connections; The construction and training of inverse generative deep neural networks include: Using the target evacuation performance index, building structure, exit location and width as input conditions, the output is a continuous personnel density distribution map. The target evacuation performance index includes the target total evacuation time and the target exit utilization rate. During training, a loss function consisting of adversarial loss and structural similarity loss is used to constrain the training of the image generation model, resulting in a trained inverse generative deep neural network.

5. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 4, characterized in that: The generative adversarial network is a conditional generative adversarial network, with the generator adopting the U-Net structure and the discriminator adopting the PatchGAN structure. In the loss function formed by fusing adversarial loss and structural similarity loss, the structural similarity loss is SSIM loss.

6. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 1, characterized in that, Density-weighted sampling of the density distribution map, followed by spatial exclusion and physical feasibility corrections, yields a discrete distribution of personnel locations that conforms to building structural constraints, including: Based on the density values ​​of each pixel in the continuous population density distribution map, weighted random sampling is performed to generate an initial discrete set of pedestrian locations that meets the total population size. Perform spatial exclusion correction on the initial discrete set of pedestrian locations to ensure that the distance between any two pedestrian locations is not less than a preset social distance threshold. A physical feasibility check is performed on the pedestrian location set after spatial exclusion correction, invalid location coordinates that fall into the obstacle area are removed, and the missing locations after removal are supplemented by sampling according to the density distribution map until a complete discrete personnel location distribution that meets the building structure constraints is obtained.

7. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 1, characterized in that, Generating a continuous population density distribution map includes: Obtain the preset physical constraint map of the target building. The preset physical constraint map should at least encode the geodesic distance from each spatial location to the nearest exit and the line-of-sight occlusion status of each spatial location. The preset physical constraint map is used as an explicit physical constraint channel, and is superimposed on the building structure, exit location and width, target total evacuation time and target exit utilization rate in the channel dimension to form a multi-channel condition input; The multi-channel condition input is reverse-generated deep neural network. After feature encoding by the encoder built into the reverse-generated deep neural network, the total evacuation time and target exit utilization rate are encoded into scaling and bias coefficients by a preset multilayer perceptron in the decoder stage of the reverse-generated deep neural network. Affine transformation is performed on the feature maps of each layer of the decoder layer by layer to achieve differentiated modulation of local pixel density generation for global evacuation performance target. After differential modulation, combined with the physical constraint channel in the multi-channel condition input, a continuous personnel density distribution map that satisfies the preset physical boundary constraints and global target constraints is generated.

8. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 7, characterized in that, The affine transformation of the feature maps of each layer of the decoder is performed layer by layer, including: Concatenate the total target evacuation time with the target exit utilization rate to form a global condition vector; The global condition vector is input into a preset multilayer perceptron, which outputs a set of layer-specific scaling coefficients and layer-specific bias coefficients for each layer of the decoder. The layer-specific scaling coefficients and the layer-specific bias coefficients of each layer are independent of each other. In the first level of the decoder, the channel dimension scaling operation is performed on the feature map of the level using the level-specific scaling coefficient corresponding to the level to obtain the first-level scaled feature map; the channel dimension offset operation is performed on the first-level scaled feature map using the level-specific bias coefficient corresponding to the level to obtain the first-level modulation feature map. From the second to the last layer of the decoder, the channel dimension scaling operation is performed on the feature map of each layer by using the layer-specific scaling coefficient corresponding to each layer to obtain the scaled feature map of each layer; the channel dimension offset operation is performed on the scaled feature map of each layer by using the layer-specific bias coefficient corresponding to each layer to obtain the modulation feature map of each layer. The level-specific scaling factor and level-specific bias factor for each level are determined through joint training of a pre-set multilayer perceptron and an inverse generative deep neural network.

9. The method for rapid assessment of evacuation performance and optimization of personnel spatial distribution according to claim 1, characterized in that, Iteratively execute the above prediction, judgment, generation, and post-processing steps until the total evacuation time and exit utilization rate meet the preset target thresholds, including: The discrete personnel location distribution obtained after post-processing is transformed into a continuous and differentiable personnel distribution representation through a preset differentiable surrogate model. The continuous and differentiable personnel distribution representation is input into the forward prediction deep neural network to obtain the predicted total evacuation time and the predicted exit utilization rate. The time error between the predicted total evacuation time and the target total evacuation time, as well as the utilization error between the predicted exit utilization rate and the target exit utilization rate are calculated. The time error and utilization error are propagated backward along the gradient propagation path from the forward prediction deep neural network, the differentiable surrogate model to the input of the inverse generation deep neural network, to obtain the updated gradient of the input condition parameters of the inverse generation deep neural network. The target total evacuation time and target exit utilization rate are adjusted based on the updated gradient to generate the deep neural network input in reverse. The adjusted target total evacuation time and target exit utilization rate are then used as the conditional input for the next iteration. Repeat the above steps to iteratively update the input condition parameters along the gradient descent direction until the time error and utilization error converge to within the preset error threshold.

10. A system for rapid assessment of evacuation performance and optimization of personnel spatial distribution, characterized in that, It includes a memory, a processor, and a program stored in the memory and executable on the processor, which, when loaded and executed by the processor, implements a method for rapid assessment of evacuation performance and optimization of personnel spatial distribution as described in any one of claims 1 to 9.

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