A fish population dynamic monitoring method and system based on a reaction diffusion model

Abstract

The embodiment of the application discloses a fish population dynamic monitoring method and system based on a reaction diffusion model, the method comprising: acquiring fish school echo signals of a target water area collected by an underwater sonar device in real time to generate three-dimensional point cloud data representing spatial density distribution of the fish school; performing maximum minimum angle triangular mesh division on the three-dimensional point cloud data; in each triangular mesh unit in a non-crossing triangular mesh structure, calculating an instantaneous convection velocity field induced by the aggregation behavior of the fish school according to a fish school density difference between adjacent units and a unit center distance, and the convection velocity direction is from a unit with lower density to an adjacent unit with higher density; taking the instantaneous convection velocity field as the only convection driving term of the reaction diffusion model, combining a preset diffusion coefficient to construct a dynamic partial differential equation; and adopting a finite volume method to numerically solve the dynamic partial differential equation and output a predicted fish population density spatio-temporal evolution result. The application improves the real-time performance and accuracy of dynamic monitoring.

Description

Technical Field

[0001] This invention relates to the field of aquatic ecological monitoring and numerical modeling technology, and in particular to a method and system for monitoring fish population dynamics based on a reaction-diffusion model. Background Technology

[0002] Fish population dynamics monitoring is a core foundation for aquatic biological resource management, ecological early warning, and the construction of germplasm resource farms. Under the backdrop of the ten-year fishing ban in the Yangtze River, accurate and dynamic monitoring and assessment of fish resource recovery has become a crucial link in scientifically evaluating the effectiveness of the ban and guiding the optimization of protection measures. Traditional methods mainly rely on underwater sonar imaging and fishing gear techniques ("driving, blocking, spearing, and casting"). While the former can obtain real-time fish density distribution, it only provides a "static snapshot" and cannot reveal the spatiotemporal evolutionary patterns of the population; the latter is time-consuming and labor-intensive, and significantly interferes with fish behavior, making large-scale, continuous monitoring difficult.

[0003] The reaction-diffusion model, a classic framework for describing population dispersal and growth, has been introduced into aquatic ecological numerical simulations in recent years. Its core equations characterize random swimming through the diffusion term, directional migration through the convection term, and birth and death through the reaction term. However, existing models generally use external water flow data when constructing the convection field, treating fish schools as passively drifting "plankton." This assumption neglects intrinsic behavioral mechanisms such as fish schooling, predator avoidance coordination, and foraging tendencies, leading to insufficient accuracy and lagging dynamic responses in predicting key phenomena such as sudden fish swarming and abrupt changes in migration paths.

[0004] Therefore, there is an urgent need for a new method for monitoring fish populations that does not require external flow field assistance, fully integrates sonar perception with population behavior mechanisms, and achieves self-consistent dynamic prediction. Summary of the Invention

[0005] This invention provides a method and system for monitoring fish population dynamics based on a reaction-diffusion model, which improves the real-time performance and accuracy of dynamic monitoring.

[0006] This invention provides the following solution:

[0007] According to the first aspect, a method for monitoring fish population dynamics based on a reaction-diffusion model is provided. The method includes: acquiring echo signals of fish schools in a target water area in real time using an underwater sonar device, and performing point cloud processing on the echo signals to generate three-dimensional point cloud data characterizing the spatial density distribution of the fish school; performing triangular mesh division on the three-dimensional point cloud data to maximize the minimum angle, generating a non-intersecting triangular mesh structure covering the fish school distribution area; calculating the instantaneous convective velocity field induced by the fish school's own aggregation behavior in each triangular mesh cell of the non-intersecting triangular mesh structure based on the difference in fish school density between adjacent cells and the distance between the cell centers, wherein the direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density; using the instantaneous convective velocity field as the only convective driving term of the reaction-diffusion model, and constructing a dynamic partial differential equation in combination with a preset diffusion coefficient; numerically solving the dynamic partial differential equation using the finite volume method, and outputting the predicted spatiotemporal evolution results of the fish population density.

[0008] According to one achievable method in an embodiment of the present invention, the step of performing point cloud processing on the echo signal to generate three-dimensional point cloud data representing the spatial density distribution of the fish school includes: performing multibeam intensity integration on the echo signal, and calculating the three-dimensional spatial coordinates of each echo point based on the echo delay and sound velocity to form weighted three-dimensional point cloud data representing the local density of the fish school.

[0009] According to one achievable method in an embodiment of the present invention, the triangular mesh division for maximizing the minimum angle adopts an incremental insertion algorithm. Performing the triangular mesh division for maximizing the minimum angle on the three-dimensional point cloud data includes: using the convex hull of the point cloud in the three-dimensional point cloud data as the initial mesh, inserting and removing intersecting edges point by point, ensuring that the minimum interior angle of any triangle is not less than the minimum angle of other possible triangles at the same vertex.

[0010] According to one achievable method in an embodiment of the present invention, the step of calculating the instantaneous convective velocity field induced by the aggregation behavior of the fish swarm based on the density difference between adjacent units and the distance between the unit centers includes: obtaining the average density of the current unit and all adjacent units sharing the same edge; calculating the density difference between the current unit and each adjacent unit based on the average density, and measuring the Euclidean distance between the centroids of the two units; when the density of the adjacent unit is higher than that of the current unit, determining the velocity contribution weight according to the density difference, adjusting the contribution intensity according to the reciprocal of the Euclidean distance, multiplying the contribution weight and the contribution intensity to obtain a scalar contribution value, and generating a contribution vector along the direction from the centroid of the current unit to the centroid of the adjacent unit; and normalizing all contribution vectors after vector summation to obtain the instantaneous convective velocity field of the unit.

[0011] According to one embodiment of the present invention, the preset diffusion coefficient is pre-calibrated based on at least one of fish species, temperature, or water depth, or adaptively estimated using historical sonar data.

[0012] According to one embodiment of the present invention, the preset diffusion coefficient is set as a nonlinear function of the local amplitude of the convective velocity field. When the velocity amplitude in the convective velocity field exceeds a preset threshold, the diffusion coefficient is adaptively amplified according to the square of the amplitude.

[0013] According to one achievable method in an embodiment of the present invention, the step of numerically solving the dynamic partial differential equation using the finite volume method and outputting the predicted spatiotemporal evolution results of fish population density includes: using the non-intersecting triangular mesh structure as the control volume of the finite volume method, with the centroid of each triangular mesh cell in the non-intersecting triangular mesh structure as the representative point; calculating the diffusion flux, convection flux, and reaction source term for each control volume, wherein the diffusion flux is approximated along the shared edge based on the density gradient of adjacent cells, the convection flux is interpolated along the shared edge using an upwind scheme based on the convective velocity field, and the reaction source term is calculated based on the current density of the cell according to a preset growth model; using an explicit time-progression method, updating the density values ​​of all control volumes sequentially based on the diffusion flux, convection flux, and reaction source term in each time step, and using the updated density field as the basis for calculating the convective velocity field in the next time step; repeating the above explicit time-progression steps until the preset simulation duration is reached, and outputting the spatiotemporal distribution results of fish population density for each time step.

[0014] According to the second aspect, a fish population dynamic monitoring system based on a reaction-diffusion model is provided. The system includes: an echo signal acquisition unit configured to acquire echo signals of fish schools in a target water area collected in real time by an underwater sonar device, and to perform point cloud processing on the echo signals to generate three-dimensional point cloud data characterizing the spatial density distribution of the fish school; a mesh structure generation unit configured to perform triangular mesh division on the three-dimensional point cloud data to maximize the minimum angle, generating a non-intersecting triangular mesh structure covering the fish school distribution area; and a convection velocity field calculation unit configured to calculate the non-intersecting triangular mesh structure... Within each triangular mesh cell in the structure, the instantaneous convective velocity field induced by the fish's own aggregation behavior is calculated based on the difference in fish density between adjacent cells and the distance between the cell centers. The direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density. The differential equation construction cell is configured to use the instantaneous convective velocity field as the only convective driving term of the reaction-diffusion model and construct a dynamic partial differential equation in combination with a preset diffusion coefficient. The prediction result generation cell is configured to numerically solve the dynamic partial differential equation using the finite volume method and output the predicted spatiotemporal evolution results of the fish population density.

[0015] According to a third aspect, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the first aspects.

[0016] According to a fourth aspect, an electronic device is provided, comprising: one or more processors; and a memory associated with the one or more processors, the memory being used to store program instructions that, when read and executed by the one or more processors, perform the steps of the method described in any one of the first aspects.

[0017] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0018] This invention transforms the three-dimensional density point cloud of fish swarms generated in real time by underwater sonar into a triangular mesh that maximizes the minimum angle. Based on the density difference and centroid distance between adjacent mesh cells, it calculates the instantaneous convective velocity field induced by the fish swarm's aggregation behavior, using this as the sole convective driving term in a reaction-diffusion model. Combined with dynamic solving using the finite volume method, this achieves the intrinsic coupling between the fish swarm's active behavior and the diffusion process. This method can self-consistently predict the spatiotemporal evolution of population density without relying on external water flow data, significantly improving the modeling accuracy and real-time performance of fish swarm aggregation, migration, and dynamic response behaviors. It provides an efficient and autonomous new technological path for fishery resource monitoring, ecological early warning, and intelligent fishery management.

[0019] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a system architecture diagram applicable to the embodiments of the present invention;

[0022] Figure 2 A flowchart of a fish population dynamics monitoring method based on a reaction-diffusion model provided in an embodiment of the present invention;

[0023] Figure 3 This is a structural block diagram of a fish population dynamics monitoring system based on a reaction-diffusion model provided in an embodiment of the present invention.

[0024] Figure 4 A schematic block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0026] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0027] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0028] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0029] To facilitate understanding of the present invention, the system architecture on which the present invention is based will be described first. Figure 1 An exemplary system architecture to which embodiments of the present invention can be applied is shown, such as Figure 1 As shown, the system architecture may include: user equipment and a fish population dynamics monitoring system based on a reaction-diffusion model located on the server side.

[0030] Users can input fish school echo signals through their user devices, which then transmit these signals to a reaction-diffusion model-based fish population dynamics monitoring system on the server side. The reaction-diffusion model-based fish population dynamics monitoring system can employ the method provided in this embodiment of the invention to dynamically monitor the fish school echo signals and obtain the spatiotemporal evolution results of fish population density. The server can then send these spatiotemporal evolution results of fish population density to the user terminal, where the user terminal will perform subsequent related operations.

[0031] User devices can include, but are not limited to, smart mobile terminals, wearable devices, and PCs (Personal Computers). Smart mobile devices can include mobile phones, tablets, laptops, PDAs (Personal Digital Assistants), and connected cars. Wearable devices can include smartwatches, smart glasses, virtual reality devices, augmented reality devices, and mixed reality devices (i.e., devices that support both virtual and augmented reality).

[0032] Fish population dynamics monitoring systems based on reaction-diffusion models can be configured as standalone servers, server clusters, or cloud servers. Cloud servers, also known as cloud computing servers or cloud hosts, are a hosting product within the cloud computing service ecosystem, designed to address the management difficulties and weak service scalability inherent in traditional physical hosts and Virtual Private Servers (VPS) services. Besides... Figure 1 In addition to the architecture shown, the fish population dynamics monitoring system based on the reaction-diffusion model can also be set up on a computer terminal with strong computing power.

[0033] It should be understood that Figure 1 The user equipment and fish population dynamics monitoring system based on the reaction-diffusion model shown are merely illustrative. Depending on implementation needs, any number of user equipment and fish population dynamics monitoring systems based on the reaction-diffusion model can be included.

[0034] Figure 2 This is a flowchart of a fish population dynamics monitoring method based on a reaction-diffusion model provided in an embodiment of the present invention. The method can be... Figure 1 The fish population dynamics monitoring system based on the reaction-diffusion model in the system shown is executed. For example... Figure 2 As shown, the method may include the following steps:

[0035] Step 201: Acquire the echo signal of the fish school in the target water area in real time by the underwater sonar equipment, and perform point cloud processing on the echo signal to generate three-dimensional point cloud data representing the spatial density distribution of the fish school.

[0036] Step 202: Perform triangular meshing on the three-dimensional point cloud data to maximize the minimum angle, generating a non-intersecting triangular mesh structure covering the fish distribution area.

[0037] Step 203: In each triangular grid cell of the non-intersecting triangular grid structure, the instantaneous convective velocity field induced by the fish's own aggregation behavior is calculated based on the difference in fish density between adjacent cells and the distance between the cell centers. The direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density.

[0038] Step 204: Using the instantaneous convection velocity field as the sole convection driving term in the reaction-diffusion model, construct a dynamic partial differential equation in combination with a preset diffusion coefficient.

[0039] Step 205: Solve the dynamic partial differential equation numerically using the finite volume method and output the predicted spatiotemporal evolution results of fish population density.

[0040] As can be seen from the above process, this invention transforms the three-dimensional density point cloud of fish swarms generated in real time by underwater sonar into a triangular mesh that maximizes the minimum angle. Based on the density difference and centroid distance between adjacent mesh cells, it calculates the instantaneous convective velocity field induced by the fish swarm's aggregation behavior, using this as the sole convective driving term in the reaction-diffusion model. Combined with dynamic solution using the finite volume method, this achieves the intrinsic coupling between the fish swarm's active behavior and the diffusion process. This method can self-consistently predict the spatiotemporal evolution of population density without relying on external water flow data, significantly improving the modeling accuracy and real-time performance of fish swarm aggregation, migration, and dynamic response behavior. It provides an efficient and autonomous new technological path for fishery resource monitoring, ecological early warning, and intelligent fishery management.

[0041] The following describes in detail each step of the above process and the effects that can be further produced, with reference to the embodiments. First, with reference to the embodiments, step 201, namely, "acquiring the echo signal of the fish school in the target water area in real time by the underwater sonar device, and performing point cloud processing on the echo signal to generate three-dimensional point cloud data representing the spatial density distribution of the fish school", will be described in detail.

[0042] Underwater sonar equipment detects the spatial distribution of fish in target waters in real time by emitting sound pulses and receiving the echo signals reflected by schools of fish. Sonar systems typically employ a multi-beam design, emitting fan-shaped sound waves to cover a wide area of ​​water, with each beam independently recording a complete sequence of echo intensity over time. This echo signal contains rich information about the location and density of fish schools; higher intensity indicates a larger reflective area and correspondingly higher density of fish in the local area.

[0043] The echo signal is processed into point cloud data. First, intensity integration is performed on the echo sequence of each beam to accumulate and form a weighted value reflecting the local fish biomass. Then, based on the echo propagation delay and the real-time measured sound velocity, the three-dimensional spatial coordinates of each reflection point are accurately calculated, thus converting the original one-dimensional time-series signal into weighted three-dimensional point cloud data. Each point cloud data point not only records its spatial location but also carries a density weight, forming a continuous digital representation of the spatial density distribution of the fish population.

[0044] The following describes in detail step 202, namely, "performing a triangular mesh division that maximizes the minimum angle on the three-dimensional point cloud data to generate a non-intersecting triangular mesh structure covering the fish distribution area," with reference to an embodiment.

[0045] A triangular meshing process maximizing the minimum angle is performed on 3D point cloud data to transform discrete point clouds into structured geometric topology, supporting subsequent spatial computation and physical modeling. The process first calculates the convex hull boundary of the point cloud, forming an initial closed surface enclosing the entire fish swarm distribution. Based on this, an incremental insertion algorithm is used to construct triangular meshes point-by-point, ensuring that the shape of each triangular unit is as close to equilibrium as possible. Each time a new point is inserted, the system identifies the existing set of triangles containing that point, constructs a local cavity, and then generates a new triangle group by reconnecting the boundary points. After each connection, the algorithm checks and removes intersecting edges while optimizing the distribution of triangle interior angles, ensuring that the minimum interior angle of any triangle is not less than the minimum angle of other possible configurations at the same vertex. This constraint of maximizing the minimum angle guarantees the geometric quality of the mesh units, avoiding overly sharp or blunt distorted triangles.

[0046] As an feasible approach, the triangular meshing that maximizes the minimum angle employs an incremental insertion algorithm, which includes: using the convex hull of the point cloud as the initial mesh, inserting and removing intersecting edges point by point, ensuring that the minimum interior angle of any triangle is not less than the minimum angle of other possible triangles at the same vertex.

[0047] Specifically, the convex hull is formed by connecting the outermost points of the point cloud, creating a minimal convex polygon or polyhedron, which serves as the starting point for mesh generation. During the point-by-point insertion phase, the algorithm selects an unprocessed point from inside the convex hull or on its boundary and inserts it into the current mesh. The insertion process first locates all existing triangles containing the point and merges their outer edges to form a polygonal cavity. Subsequently, the system connects the newly inserted point to each boundary vertex of the cavity, generating a new set of triangles and completing the local mesh update.

[0048] If edges intersect after insertion, the algorithm immediately detects and removes these intersecting edges, restoring the flatness and non-intersecting state of the mesh through local edge flipping operations. Simultaneously, during each triangle generation or optimization, the system rigorously compares the minimum interior angle of the current triangle with the minimum interior angle of other possible triangle configurations with the same vertex, ensuring that the final retained configuration has the largest minimum interior angle value. Through this iterative insertion, local reconnection, and angle optimization, until all point cloud data points are incorporated into the mesh, a triangular mesh structure covering the entire fish population distribution area, without intersections, and with a high-quality shape is ultimately formed.

[0049] The resulting triangular mesh structure covers the entire fish distribution area. All triangles are non-intersecting, and edges intersect only at vertices or common edges, forming continuous, non-overlapping, and seamless patches. This structure not only preserves the original spatial features of the point cloud but also establishes clear adjacency relationships, providing a stable and efficient computational mesh foundation for subsequent cell-based density gradient analysis and flux calculations.

[0050] The following describes in detail step 203, namely, "In each triangular grid cell of the non-intersecting triangular grid structure, the instantaneous convective velocity field induced by the fish's own aggregation behavior is calculated based on the difference in fish density between adjacent cells and the distance between the cell centers, wherein the direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density," with reference to the embodiments.

[0051] Within each triangular mesh cell, the system first calculates the mean fish density of that cell and identifies all neighboring cells sharing edges. By comparing the mean density of the current cell with that of each neighboring cell, the density difference is obtained, and the Euclidean distance between the centroids of the two cells is measured. These density differences, along with the centroid distance, constitute a quantitative indicator of the local spatial heterogeneity of the fish population.

[0052] Based on the natural aggregation behavior of fish, they tend to actively swim from low-density areas to high-density areas to gain a defensive or foraging advantage. This invention translates this biological mechanism into a physical driving signal. Specifically, when the density of an adjacent cell is higher than that of the current cell, the system determines the weight of the velocity contribution according to the magnitude of the density difference and adjusts the contribution intensity according to the reciprocal of the centroid distance, thereby generating an instantaneous velocity vector along the centroid line from the low-density cell to the high-density cell.

[0053] The algorithm iterates through all neighboring cells of the current cell, calculates the positive velocity contribution vector for each cell, and then accumulates these vectors. After accumulation, the total vector is normalized to obtain the final instantaneous convective velocity of the cell. This velocity field is entirely induced by the density gradient of the fish swarm itself, without relying on any external water flow or human assumptions, thus achieving intrinsic modeling of the active behavior of the population.

[0054] As an feasible approach, the instantaneous convective velocity field induced by the aggregation behavior of fish swarms is calculated based on the density difference between adjacent units and the distance between the unit centers. This includes: obtaining the average density of the current unit and all adjacent units sharing a common edge; calculating the density difference between the current unit and each adjacent unit based on the average density, and measuring the Euclidean distance between the centroids of the two units; when the density of an adjacent unit is higher than that of the current unit, determining the velocity contribution weight according to the density difference, adjusting the contribution intensity according to the reciprocal of the Euclidean distance, multiplying the contribution weight and the contribution intensity to obtain a scalar contribution value, and generating a contribution vector along the direction from the centroid of the current unit to the centroid of the adjacent unit; and normalizing all contribution vectors after vector summation to obtain the instantaneous convective velocity field of the unit.

[0055] Specifically, at the start of the calculation, the system first locates the currently processed triangular mesh cell and obtains the sum of the density weights of all point cloud data within that cell, dividing this sum by the number of points in the point cloud to obtain the cell's mean density. Next, it traverses the cell's three edges, identifying all adjacent triangular cells that share each edge. The mean density of the point cloud within each adjacent cell is also calculated. In this way, each cell and its adjacent cells obtain a defined scalar density value, laying the foundation for subsequent difference calculations.

[0056] The system calculates the difference between the current cell and the average density of each adjacent cell, resulting in a positive or negative density difference. Simultaneously, it calculates the geometric centroid coordinates of two triangular cells, i.e., the average of the coordinates of their three vertices. Based on these centroid coordinates, the Euclidean distance formula is used to accurately measure the linear spatial distance between the centroids of the two cells. This distance reflects the physical interval between adjacent cells and directly affects the intensity attenuation of behavior-driven events.

[0057] Velocity contribution calculation is triggered only when the density of adjacent cells is higher than that of the current cell. The contribution weight is proportional to the density difference; a larger difference indicates a stronger attraction from higher density cells. The contribution intensity is proportional to the inverse of the centroid distance; the closer the distance, the more significant the effect. The system constructs a unit direction vector from the current cell's centroid to the centroid of adjacent cells, multiplies the weight by the intensity, and generates a directed velocity contribution vector. This vector runs along the centroid line from the low-density cell to the high-density cell and is accumulated in the total velocity contribution of the current cell.

[0058] After traversal, the current cell may accumulate multiple velocity contribution vectors from different high-density neighboring cells. The system performs vector summation on these vectors to obtain a resultant vector. The resultant vector is then normalized, preserving its direction while controlling its amplitude within a reasonable range, to generate the final instantaneous convective velocity for that cell. This velocity is entirely induced by the density gradient of the fish swarm itself, pointing towards the local high-density region, and its amplitude is adjusted by a combination of gradient and proximity, forming a dynamic and continuous convective velocity field that provides intrinsic driving force for the reaction-diffusion model.

[0059] Ultimately, a continuously varying instantaneous convection velocity field is formed across the entire grid region. The direction of this field always points from the lower-density cells to the higher-density neighboring cells, and the amplitude increases with the density gradient. This accurately characterizes the aggregation tendency and dynamic response characteristics of the fish swarm at the local scale, providing a realistic and self-consistent convection term for the subsequent reaction-diffusion equation.

[0060] The following describes in detail step 204, namely, "using the convective velocity field as the only convective driving term in the reaction-diffusion model and constructing a dynamic partial differential equation in combination with a preset diffusion coefficient," with reference to an embodiment.

[0061] Using the convective velocity field as the sole convective driver in the reaction-diffusion model means completely discarding external water flow, wind fields, or artificially set directional migration parameters when constructing partial differential equations. Instead, it relies solely on the instantaneous velocity field induced by the fish's own aggregation behavior as the physical driving force of the convection process. This design achieves intrinsically self-consistent modeling of population dynamics. Every local density change in the fish population is fed back to the convective field in real time, thus affecting the overall evolutionary trajectory and avoiding the parameter uncertainties and dynamic mismatches caused by the introduction of external fields in traditional models.

[0062] The core equations of the reaction-diffusion model consist of three parts: a diffusion term, a convection term, and a reaction term. The diffusion term characterizes the random swimming behavior of the fish population, and the spatial dispersion intensity is controlled by a preset diffusion coefficient. The convection term describes directional migration, and in this invention, it is explicitly defined as the product of the instantaneous convective velocity field and density field calculated in the preceding steps. The reaction term employs a logistic growth model to characterize the natural proliferation and density-dependent mortality of the fish population. The preset diffusion coefficient is calibrated based on the swimming characteristics of the target fish species, water temperature, or historical observation data, and has clear biological significance.

[0063] In constructing the dynamic partial differential equations, the system embeds the convective velocity field into the convective operator in vector form, ensuring its continuous updating over time and space, forming a highly coupled nonlinear equation set. This equation is no longer driven by static parameters, but rather is a living model that evolves continuously with real-time sonar input. It can sensitively respond to sudden aggregation, dispersion, or path changes in fish populations, significantly improving the realism and foresight of population dynamics prediction.

[0064] Specifically, the reaction-diffusion model uses fish population density. As state variables, their dynamic evolution follows the following partial differential equations:

[0065]

[0066] in, For diffusion term, is the diffusion coefficient, which characterizes the intensity of random swimming among individual fish in a school; For convection terms, The instantaneous convective velocity field induced by the fish's own aggregation behavior, calculated in the aforementioned steps, is used as the sole convective driving term of the model. As the response term, the logistic growth model is used to describe the natural population growth and density-dependent effects. The intrinsic growth rate This refers to environmental carrying capacity. In numerical implementation, the diffusion coefficient... It can be preset as a constant or assigned values ​​based on fish species, water temperature, and water depth, or adaptively estimated using historical sonar data. Convection velocity field The growth rate is recalculated at each time step using the real-time density gradient from the sonar. With carrying capacity The determination is based on the biological parameters of the target fish species and the area of ​​the water body.

[0067] As an feasible approach, the diffusion coefficient of the dynamic partial differential equation is set as a nonlinear function of the local amplitude of the convective velocity field. When the convective velocity amplitude exceeds a preset threshold, the diffusion coefficient is adaptively amplified according to the square of the amplitude.

[0068] Specifically, the system first extracts the amplitude of the convective velocity vector within each triangular mesh cell, i.e., the scalar value of the velocity magnitude. Then, this amplitude is input into a predefined nonlinear mapping function, which outputs the corresponding diffusion coefficient value. This nonlinear function is designed to be monotonically increasing, ensuring that the stronger the convection, the larger the diffusion coefficient, thereby mathematically simulating the enhanced spatial disturbance of fish swarms under high aggregation tendencies.

[0069] When the convection velocity exceeds a preset threshold, the system triggers an adaptive amplification mechanism for the diffusion coefficient, with the amplification ratio proportional to the square of the convection amplitude. This square relationship stems from the nonlinear amplification effect of fish swarm behavior: slight aggregation only causes local disturbances, while strong aggregation triggers group tumbling and repositioning, leading to a significant enhancement of random diffusion. The square ratio ensures a rapid response of the diffusion term in high-convective regions, preventing the model from underestimating the spatial expansion rate of the population.

[0070] By setting the parameters described above, the diffusion coefficient is no longer globally uniform or statically layered, but rather a spatially heterogeneous field that dynamically evolves with the local characteristics of the convection field. This design enables the reaction-diffusion equation to automatically enhance diffusion transport in the core region of fish aggregation and maintain mild diffusion in the low-convection edge region, thereby improving the model's ability to represent complex population dynamics.

[0071] The following describes in detail step 205, namely, "using the finite volume method to numerically solve the dynamic partial differential equation and output the predicted spatiotemporal evolution results of fish population density," with reference to an embodiment.

[0072] This invention employs the finite volume method to numerically solve dynamic partial differential equations, using a triangular mesh structure as the basic control volume for discretization. Each triangular mesh cell is considered an independent finite volume, with the centroid of the cell serving as the representative point for the density value. This centroid-based discretization method fully utilizes the superior topology generated by maximizing the minimum angle partitioning, ensuring the geometric stability and accuracy consistency of the numerical computation.

[0073] During the solution process, the system calculates the diffusion flux, convection flux, and reaction source term for each control volume. The diffusion flux is approximated along the shared edge based on the density gradient of adjacent cells, and flux conservation is achieved through edge-length weighted averaging. The convection flux is determined based on the interpolation of the convective velocity field in the upwind direction, prioritizing the density values ​​of cells on the incoming side to suppress numerical oscillations and maintain the accuracy of the physical transport direction. The reaction source term is directly calculated based on the current density of the cell according to a preset growth model, reflecting the natural proliferation and mortality contributions of the local population.

[0074] Numerical updates employ an explicit time-progression approach. At each time step, the system first traverses all control volumes, i.e., each triangular grid cell, and updates the density based on the calculated diffusion flux, convective flux, and reaction source terms. Specifically, the update formula adds these flux terms and source terms to the current density value, forming the density distribution for the next time step. Diffusion flux characterizes the density redistribution caused by random walks, convective flux reflects the net transport effect of directional migration, and reaction source terms embody local changes in population growth or mortality. The combined contribution of these terms ensures the conservation of equations and physical accuracy.

[0075] By repeating the above time progression process until the preset simulation duration is reached, the system continuously generates a series of density field results arranged in time sequence. These results fully record the entire process of fish population density evolution in three-dimensional space over time, including the formation of aggregation centers, the expansion of migration paths, and the advancement of diffusion fronts. Ultimately, a visualized spatiotemporal evolution prediction output of the population dynamics is generated, providing intuitive and reliable numerical basis for fisheries monitoring and decision-making.

[0076] Specifically, the method of this invention has been tested in practical applications. For example, in a monitoring embodiment of the yellow croaker population in Bohai Bay, a multibeam underwater sonar device was first deployed to collect echo signals from the water area in real time at a frequency of 200 kHz, covering a depth range of 50 m. The echo signals were then processed into point clouds: the density weight was calculated by multibeam intensity integration, and three-dimensional point cloud data was generated based on the time delay Δt and the sound speed of 1500 m / s, with a point cloud density of 10^5 points / frame. Subsequently, the point cloud was divided into triangular meshes that maximized the minimum angle, using the Bowyer-Watson incremental insertion algorithm to ensure that the minimum interior angle of the mesh cell was ≥30°, generating a non-intersecting triangular mesh structure with an average side length of 0.8 m. Within each mesh cell, the mean density ρ_i was calculated, and the instantaneous convective velocity field was calculated using the density difference Δρ between adjacent cells and the Euclidean distance d between the centroids: when Δρ>0, the weight ∝ Δρ, the intensity ∝ 1 / d, and a contribution vector was generated along the centroid direction, which was accumulated and normalized to obtain the v field. Using v as the sole convection-driven term in the reaction-diffusion equation, and combining it with a preset diffusion coefficient D = 0.5 m² / s (adaptively adjusted to be a function of the square of the convection amplitude v, amplifying D when |v| > 0.2 m / s), the equation is constructed. The population density was calculated using the finite volume method: a triangle was used as the control volume to calculate diffusion / convection flow and reaction source terms. An explicit time progression of Δt = 2s was applied to simulate a 1-hour evolution, outputting the spatiotemporal density sequence. This embodiment achieved real-time prediction of fish population density fields. Compared to traditional sonar statistical methods, the aggregation center error was reduced from 51% to 19%, the computation time was <3s (i7 processor), no external water flow data was required, and the accuracy of population migration paths was improved by 32%. This provides efficient and self-consistent dynamic decision support for fisheries patrols and ecological early warning.

[0077] The methods provided in this invention can be applied to various application scenarios, including but not limited to: in marine fisheries, patrol vessels equipped with underwater sonar and edge computing modules can generate real-time predictions of fish migration paths, assisting fishermen in precise fishing and avoiding overfishing areas; in nearshore cage aquaculture farms, the system continuously outputs spatiotemporal evolution results of population density through fixed sonar stations, promptly detecting escape risks or early signs of disease spread, and achieving optimized feeding and early warning intervention; in reservoir ecological management, combined with floating monitoring platforms, models predict the invasion front of alien fish species and the trend of local population compression, providing dynamic decision-making basis for aquatic biodiversity conservation, and significantly improving fishery production efficiency and aquatic ecological sustainability.

[0078] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0079] According to another embodiment, a fish population dynamics monitoring system based on a reaction-diffusion model is provided. For example... Figure 3 As shown, the device 300 includes:

[0080] The echo signal acquisition unit 301 is configured to acquire the echo signal of a school of fish in the target water area in real time collected by the underwater sonar device, and to perform point cloud processing on the echo signal to generate three-dimensional point cloud data characterizing the spatial density distribution of the school of fish.

[0081] The mesh structure generation unit 302 is configured to perform triangular mesh division on the three-dimensional point cloud data to maximize the minimum angle and generate a non-intersecting triangular mesh structure covering the fish distribution area.

[0082] The convection velocity field calculation unit 303 is configured to calculate the instantaneous convection velocity field induced by the fish's own aggregation behavior in each triangular grid cell of the non-intersecting triangular grid structure, based on the difference in fish density between adjacent cells and the distance between the cell centers. The direction of the convection velocity is from the cell with lower density to the adjacent cell with higher density.

[0083] The differential equation construction unit 304 is configured to use the instantaneous convection velocity field as the only convection driving term of the reaction diffusion model and construct a dynamic partial differential equation in combination with a preset diffusion coefficient.

[0084] The prediction result generation unit 305 is configured to use the finite volume method to numerically solve the dynamic partial differential equation and output the predicted spatiotemporal evolution results of fish population density.

[0085] As an implementable approach, the echo signal acquisition unit 301 can be configured to perform multi-beam intensity integration on the echo signal and calculate the three-dimensional spatial coordinates of each echo point based on the echo delay and sound velocity to form weighted three-dimensional point cloud data representing the local density of the fish school when performing point cloud processing on the echo signal to generate three-dimensional point cloud data representing the local density of the fish school.

[0086] As an implementable approach, the triangular meshing that maximizes the minimum angle employs an incremental insertion algorithm. When performing the triangular meshing that maximizes the minimum angle on the three-dimensional point cloud data, the mesh structure generation unit 302 can be configured to: use the convex hull of the point cloud in the three-dimensional point cloud data as the initial mesh, insert and remove intersecting edges point by point, and ensure that the minimum interior angle of any triangle is not less than the minimum angle of other possible triangles at the same vertex.

[0087] As an implementable approach, the convective velocity field calculation unit 303, when calculating the instantaneous convective velocity field induced by the aggregation behavior of the fish swarm based on the density difference between adjacent units and the distance between the unit centers, can be configured as follows: Obtain the average density of the current unit and all adjacent units sharing its edges; calculate the density difference between the current unit and each adjacent unit based on the average density, and measure the Euclidean distance between the centroids of the two units; when the density of an adjacent unit is higher than that of the current unit, determine the velocity contribution weight according to the density difference, adjust the contribution intensity according to the reciprocal of the Euclidean distance, multiply the contribution weight by the contribution intensity to obtain a scalar contribution value, and generate a contribution vector along the direction from the centroid of the current unit to the centroid of the adjacent unit; after normalizing all contribution vectors through vector summation, obtain the instantaneous convective velocity field of the unit.

[0088] As an feasible approach, the preset diffusion coefficient is pre-calibrated based on at least one of the fish species, temperature, or water depth, or adaptively estimated using historical sonar data.

[0089] As an feasible approach, the diffusion coefficient of the dynamic partial differential equation is set as a nonlinear function of the local amplitude of the convective velocity field. When the velocity amplitude in the convective velocity field exceeds a preset threshold, the diffusion coefficient is adaptively amplified according to the square of the amplitude.

[0090] As an feasible approach, the prediction result generation unit 305, when numerically solving the dynamic partial differential equation using the finite volume method and outputting the predicted spatiotemporal evolution results of fish population density, can be configured as follows: The non-intersecting triangular mesh structure is used as the control volume of the finite volume method, with the centroid of each triangular mesh cell in the non-intersecting triangular mesh structure as the representative point; diffusion flux, convection flux, and reaction source term are calculated for each control volume, where the diffusion flux is approximated along the shared edge based on the density gradient of adjacent cells, the convection flux is interpolated along the shared edge using an upwind scheme, and the reaction source term is calculated based on the current density of the cell according to a preset growth model; an explicit time-progression method is adopted, updating the density values ​​of all control volumes sequentially based on the diffusion flux, convection flux, and reaction source term in each time step, and using the updated density field as the basis for calculating the convection velocity field in the next time step; the above explicit time-progression steps are repeated until the preset simulation duration is reached, outputting the spatiotemporal distribution results of fish population density for each time step.

[0091] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. Components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0092] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this invention are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of related data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0093] In addition, embodiments of the present invention also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any of the foregoing method embodiments.

[0094] And an electronic device comprising: one or more processors; and a memory associated with the one or more processors, the memory being used to store program instructions that, when read and executed by the one or more processors, perform the steps of the method described in any of the foregoing method embodiments.

[0095] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in any of the foregoing method embodiments.

[0096] in, Figure 4 An exemplary architecture of an electronic device is shown, which may include a processor 410, a video display adapter 411, a disk drive 412, an input / output interface 413, a network interface 414, and a memory 420. The processor 410, video display adapter 411, disk drive 412, input / output interface 413, network interface 414, and memory 420 can communicate with each other via a communication bus 430.

[0097] The processor 410 can be implemented using a general-purpose CPU, microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solution provided by the present invention.

[0098] The memory 420 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 420 can store the operating system 421 for controlling the operation of the electronic device 400, and the basic input / output system (BIOS) 422 for controlling the low-level operations of the electronic device 400. Additionally, it can store a web browser 423, a data storage management system 424, and a fish population dynamic monitoring system 425 based on a reaction-diffusion model, etc. The aforementioned fish population dynamic monitoring system 425 based on a reaction-diffusion model can be the application program that specifically implements the aforementioned steps in this embodiment of the invention. In summary, when implementing the technical solution provided by this invention through software or firmware, the relevant program code is stored in the memory 420 and is called and executed by the processor 410.

[0099] Input / output interface 413 is used to connect input / output modules to realize information input and output. Input / output modules can be configured as components in the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touch screens, microphones, various sensors, etc., and output devices may include displays, speakers, vibrators, indicator lights, etc.

[0100] Network interface 414 is used to connect a communication module (not shown in the figure) to enable communication and interaction between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0101] Bus 430 includes a pathway for transmitting information between various components of the device, such as processor 410, video display adapter 411, disk drive 412, input / output interface 413, network interface 414, and memory 420.

[0102] It should be noted that although the above-described device only shows the processor 410, video display adapter 411, disk drive 412, input / output interface 413, network interface 414, memory 420, bus 430, etc., in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the present invention, and not necessarily all the components shown in the figures.

[0103] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a computer program product. This computer program product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0104] The technical solution provided by this invention has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A method for monitoring fish population dynamics based on a reaction-diffusion model, characterized in that, The method includes: The underwater sonar equipment acquires real-time echo signals of fish schools in the target water area, and performs point cloud processing on the echo signals to generate three-dimensional point cloud data characterizing the spatial density distribution of the fish schools. Perform a triangular mesh division on the three-dimensional point cloud data to maximize the minimum angle, and generate a non-intersecting triangular mesh structure covering the fish distribution area; Within each triangular grid cell of the non-intersecting triangular grid structure, the instantaneous convective velocity field induced by the fish's own aggregation behavior is calculated based on the difference in fish density between adjacent cells and the distance between the cell centers. The direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density. The instantaneous convective velocity field is used as the only convective driving term in the reaction-diffusion model, and a dynamic partial differential equation is constructed by combining it with a preset diffusion coefficient. The dynamic partial differential equation is numerically solved using the finite volume method, and the predicted spatiotemporal evolution of fish population density is output. The calculation of the instantaneous convective velocity field induced by the fish's aggregation behavior, based on the difference in fish density between adjacent units and the distance between the unit centers, includes: Obtain the average density of the current cell and all its neighboring cells with shared edges; Based on the average density, calculate the density difference between the current cell and each adjacent cell, and measure the Euclidean distance between the centroids of the two cells; When the density of an adjacent cell is higher than that of the current cell, the velocity contribution weight is determined according to the density difference, the contribution intensity is adjusted according to the reciprocal of the Euclidean distance, the contribution weight is multiplied by the contribution intensity to obtain a scalar contribution value, and a contribution vector is generated along the direction from the centroid of the current cell to the centroid of the adjacent cell. After summing all contribution vectors and normalizing them, the instantaneous convective velocity field of the element is obtained.

2. The method according to claim 1, characterized in that, The step of performing point cloud processing on the echo signal to generate three-dimensional point cloud data characterizing the spatial density distribution of the fish school includes: The echo signal is integrated by multibeam intensity, and the three-dimensional spatial coordinates of each echo point are calculated based on the echo delay and sound speed to form weighted three-dimensional point cloud data representing the local density of the fish school.

3. The method according to claim 1, characterized in that, The triangular meshing for maximizing the minimum angle adopts an incremental insertion algorithm. The triangular meshing for maximizing the minimum angle in the three-dimensional point cloud data includes: using the convex hull of the point cloud in the three-dimensional point cloud data as the initial mesh, inserting and removing intersecting edges point by point, ensuring that the minimum interior angle of any triangle is not less than the minimum angle of other possible triangles at the same vertex.

4. The method according to claim 1, characterized in that, The preset diffusion coefficient is pre-calibrated based on at least one of the fish species, temperature, or water depth, or adaptively estimated using historical sonar data.

5. The method according to claim 1, characterized in that, The preset diffusion coefficient is set as a nonlinear function of the local amplitude of the convective velocity field. When the velocity amplitude in the convective velocity field exceeds the preset threshold, the diffusion coefficient is adaptively amplified according to the square of the amplitude.

6. The method according to claim 1, characterized in that, The method of numerically solving the dynamic partial differential equation using the finite volume method outputs the predicted spatiotemporal evolution results of fish population density, including: The non-intersecting triangular mesh structure is used as the control volume of the finite volume method, with the centroid of each triangular mesh unit in the non-intersecting triangular mesh structure as the representative point. For each control volume, the diffusion flux, convection flux, and reaction source term are calculated. The diffusion flux is approximated along the shared edge based on the density gradient of adjacent cells, the convection flux is interpolated along the shared edge using an upwind scheme based on the convective velocity field, and the reaction source term is calculated based on the current density of the cell according to a preset growth model. An explicit time-progression method is adopted, in each time step, the density values ​​of all control volumes are updated sequentially based on the diffusion flux, convection flux and reaction source term, and the updated density field is used as the basis for calculating the convection velocity field in the next time step; Repeat the above explicit time progression steps until the preset simulation duration is reached, and output the spatiotemporal distribution results of fish population density at each time step.

7. A fish population dynamics monitoring system based on a reaction-diffusion model, characterized in that, The system includes: The echo signal acquisition unit is configured to acquire the echo signal of a school of fish in the target water area in real time collected by the underwater sonar device, and to perform point cloud processing on the echo signal to generate three-dimensional point cloud data characterizing the spatial density distribution of the school of fish. The mesh structure generation unit is configured to perform triangular mesh division on the three-dimensional point cloud data to maximize the minimum angle, and generate a non-intersecting triangular mesh structure covering the fish distribution area. The convective velocity field calculation unit is configured to calculate the instantaneous convective velocity field induced by the fish's own aggregation behavior in each triangular grid cell of the non-intersecting triangular grid structure, based on the difference in fish density between adjacent cells and the distance between the cell centers. The direction of the convective velocity is from the cell with lower density to the adjacent cell with higher density. The differential equation construction unit is configured to use the instantaneous convective velocity field as the only convective driving term of the reaction-diffusion model and construct dynamic partial differential equations in combination with a preset diffusion coefficient. The prediction result generation unit is configured to numerically solve the dynamic partial differential equation using the finite volume method and output the predicted spatiotemporal evolution results of fish population density. The calculation of the instantaneous convective velocity field induced by the fish's aggregation behavior, based on the difference in fish density between adjacent units and the distance between the unit centers, includes: Obtain the average density of the current cell and all its neighboring cells with shared edges; Based on the average density, calculate the density difference between the current cell and each adjacent cell, and measure the Euclidean distance between the centroids of the two cells; When the density of an adjacent cell is higher than that of the current cell, the velocity contribution weight is determined according to the density difference, the contribution intensity is adjusted according to the reciprocal of the Euclidean distance, the contribution weight is multiplied by the contribution intensity to obtain a scalar contribution value, and a contribution vector is generated along the direction from the centroid of the current cell to the centroid of the adjacent cell. After summing all contribution vectors and normalizing them, the instantaneous convective velocity field of the element is obtained.

8. An electronic device, characterized in that, include: One or more processors; And a memory associated with the one or more processors, the memory being used to store program instructions that, when read and executed by the one or more processors, perform the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 6.

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