A 5G-based environmental monitoring method and system

Abstract

The embodiments of the present application provide a 5G-based environmental monitoring method and system. Among them, by constructing a dynamic coupling perception field within the 5G network coverage area, an adaptive topology with non-linear interaction of parameters is established. When parameter anomalies are detected, differential geometric reconstruction of the 5G network slice control plane is triggered based on the change in Riemann curvature. A space-time manifold space is constructed at the 5G edge computing node, the diffusion principal curvature direction is decomposed and extracted, and the propagation rate of the abnormal parameter is iteratively solved in combination with the geodesic equation to generate a diffusion front envelope surface. According to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed to generate an exponentially decaying sampling function and deploy a directional sensing wavefront. The sampling function is conformally compacted with the geographic grid to generate an interactive holographic manifold, and a Chern class discriminant criterion for the anomaly level is established based on the curvature 2-form feature to trigger a graded warning pulse packet. The technical solution provided by the embodiments of the present application improves the real-time performance and accuracy of environmental monitoring.

Description

Technical Field

[0001] Embodiments of the present application relate to the fields of communication technology and environmental monitoring technology, and in particular, to a 5G-based environmental monitoring method and system. Background Art

[0002] In complex environmental monitoring scenarios, such as urban heat island effect monitoring, chemical pollutant diffusion tracking, etc., it is necessary to collect multi-source heterogeneous data in real time and accurately analyze the propagation characteristics of abnormal parameters. At the same time, due to the complex terrain of the monitoring area and the wide distribution of sensor nodes, traditional methods are difficult to achieve efficient data fusion and dynamic optimization of network resources.

[0003] Currently, existing solutions adopt a dynamic resource allocation technology based on 5G network slicing, combined with the data processing capabilities of edge computing nodes, to achieve optimized control of the monitoring density and energy consumption of sensor nodes. This solution dynamically adjusts the network slice configuration through a preset threshold trigger mechanism, and uses edge computing nodes to locally process abnormal data to reduce data transmission latency and energy consumption.

[0004] Although the above solution improves the network resource utilization rate and data processing efficiency to a certain extent, its threshold trigger mechanism depends on preset rules and cannot dynamically adapt to the changing characteristics of abnormal parameters in complex environments. In addition, this solution lacks the ability to accurately model the propagation process of abnormal parameters, resulting in limited abnormal detection accuracy and difficulty in meeting the real-time monitoring requirements in high-dynamic environments. Summary of the Invention

[0005] Embodiments of the present application provide a 5G-based environmental monitoring method and system to solve the problems of low real-time performance and insufficient accuracy in environmental monitoring in the prior art.

[0006] In a first aspect, embodiments of the present application provide a 5G-based environmental monitoring method, including:

[0007] Construct a dynamic coupling perception field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topology model of parameter non-linear interaction, and when parameter anomalies are detected, trigger the differential geometric reconstruction of the 5G network slice control plane based on the change in Riemann curvature;

[0008] Based on the reconstructed network slice topology, construct a spatio-temporal manifold space of abnormal parameters at the 5G edge computing node, extract the diffusion principal curvature direction through Lie group transformation and tensor field decomposition, and iteratively solve the propagation rate of the abnormal parameters in combination with the geodesic equation to generate a diffusion front envelope surface containing affine connection coefficients;

[0009] According to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the control plane of the 5G network slice. By using the variational method, the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes is calculated, an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and an oriented sensing wavefront of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector.

[0010] The exponential decay sampling function and the geographical grid are subjected to conformal compactification processing through the 5G transmission channel. By using the density field transformation, the diffeomorphic mapping of multi-dimensional monitoring data and terrain features is realized, and an interactive holographic manifold is generated.

[0011] Based on the curvature 2-form characteristics of the interactive holographic manifold, a Chern class discrimination criterion for the anomaly level is established at the 5G application layer. When the principal curvature integral exceeds the preset cycle, a graded early warning pulse packet is triggered.

[0012] Optionally, according to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the control plane of the 5G network slice. By using the variational method, the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes is calculated, an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and an oriented sensing wavefront of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector, including:

[0013] Based on the isoparametric line distribution of the principal curvature of the diffusion front envelope surface, a variational optimization functional containing the monitoring density field and energy consumption constraint is constructed, where the monitoring density field is associated with the covariant differential of the local curvature tensor, and the energy consumption constraint is associated with the conformal mapping of the Gaussian curvature.

[0014] A dynamic Lagrange multiplier field is constructed in the tangent bundle space of the differentiable optimization surface. By establishing the connection coefficient of the geodesic distribution, an energy gradient flow equation is established, and the mixed partial differential equations are solved by combining the projection iteration method to obtain the extreme value manifold.

[0015] Perform topological singularity analysis on the extreme value manifold. Based on the Hodge decomposition characteristics of the front line of the diffusion front envelope surface, an anisotropic exponential decay sampling function is constructed, and a wavefront propagation field is formed in the outer normal direction of the principal curvature normal vector.

[0016] Based on the Poincaré section characteristics of the wavefront propagation field, a diffeomorphic decision model is established to determine the activation threshold of redundant nodes, and an oriented sensing wavefront with the propagation rate matching the eigenvalue of the local curvature tensor is generated.

[0017] Optionally, perform topological singularity analysis on the extreme manifold. Based on the Hodge decomposition characteristics of the leading edge of the diffusion front envelope surface, construct an anisotropic exponential decay sampling function, and form a wavefront propagation field in the outer normal direction of the principal curvature normal vector, including:

[0018] Construct a dynamic gauge field in the normal bundle space of the extreme manifold;

[0019] Based on the fiber bundle structure of the dynamic gauge field, establish an anisotropic diffusion equation with the principal curvature normal vector as the normal direction, and generate an exponential decay sampling function by modifying the conservation equation of the energy-momentum tensor;

[0020] Use the exponential decay sampling function to perform weighted integration on the exterior differential form of the extreme manifold, and construct a density field distribution with singularity constraints on the homology class of the leading edge of the diffusion front envelope surface, so that the density gradient direction forms a gauge symmetry with the outer normal direction of the principal curvature normal vector;

[0021] Through the mapping of the density field distribution to the space-time coordinates of the 5G edge computing node, solve the activation potential function of the redundant node, so that the propagation rate of the directional sensing wavefront is in symplectic structure matching with the local curvature tensor.

[0022] Optionally, based on the fiber bundle structure of the dynamic gauge field, establish an anisotropic diffusion equation with the principal curvature normal vector as the normal direction, and generate an exponential decay sampling function by modifying the conservation equation of the energy-momentum tensor, including:

[0023] Based on the non-commutative algebraic constraint between the spinor field component of the dynamic gauge field and the connection form of the gauge potential of the fiber bundle structure, construct a diffusion coefficient spinor field with spinor-tensor hybrid symmetry in the normal bundle space of the extreme manifold;

[0024] Perform an exterior algebraic wedge product operation on the self-dual component of the diffusion coefficient spinor field and the exterior differential form of the principal curvature normal vector to generate a diffusion convection kernel carrying topological charge;

[0025] Based on the gauge fixing condition of the conservation equation of the energy-momentum tensor in the dynamic gauge field, perform a curvature-driven decomposition on the spin connection of the diffusion coefficient spinor field, so that the covariant curl term of the diffusion convection kernel forms a constrained coordination relationship with the space-time coordinate distribution of the 5G edge computing node;

[0026] Based on the constrained coordination relationship, through the Poincaré duality between the closed chain integral on the homology class of the leading edge of the diffusion front envelope surface and the topological charge of the diffusion convection kernel, construct a conserved current density field satisfying local gauge invariance;

[0027] Generate an exponentially decaying sampling function synchronized with the differential geometric reconstruction process of the 5G network slice control plane by using the nonholonomic constraint mapping between the spinor-scalar coupling property of the conserved current density field and the torsion correction term of the dynamic gauge field.

[0028] Optionally, construct a dynamic Lagrange multiplier field in the tangent bundle space of the differentiable optimization surface, establish an energy gradient flow equation through the connection coefficients of the geodesic distribution, and solve the system of mixed partial differential equations by combining the projection iteration method to obtain the extreme manifold, including:

[0029] Construct a dynamic Lagrange multiplier field with an asymmetric connection structure based on the relationship between the local connection form of the differentiable optimization surface and the covariant derivative of the principal curvature tensor, and establish an energy gradient flow equation through affine parameter tuning;

[0030] Perform tensor contraction on the dynamic Lagrange multiplier field and the energy gradient flow equation to generate a system of mixed flow equations and transform it into a Hamiltonian system;

[0031] Under the symplectic manifold framework of the Hamiltonian system, construct an iterative format of the curvature-driven projection operator, perform local linear approximation on the weak solution space, correct the residual term through covariant differentiation and perform implicit discrete integration to generate an iterative update quantity that satisfies the local conservation law;

[0032] Construct a dynamic constraint surface based on the Lie derivative property of the iterative update quantity, and screen the extreme manifold through the Hodge dual form.

[0033] Optionally, under the symplectic manifold framework of the Hamiltonian system, construct an iterative format of the curvature-driven projection operator, perform local linear approximation on the weak solution space, correct the residual term through covariant differentiation and perform implicit discrete integration to generate an iterative update quantity that satisfies the local conservation law, including:

[0034] Construct a dynamic projection kernel with a fiber bundle structure based on the nonholonomic constraint relationship between the connection form of the weak solution space and the principal curvature tensor of the curvature-driven projection operator under the symplectic manifold framework of the Hamiltonian system;

[0035] Perform a covariant exterior product operation on the torsion tensor component of the dynamic projection kernel and the space-time coordinate distribution of the 5G edge computing node to generate a projection residual manifold carrying network topological charges;

[0036] Based on the gauge invariance constraint between the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field, apply curvature-driven affine parameter correction to the local linear approximation process of the weak solution space, and construct an iterative update quantity that satisfies the local conservation law through the implicit discrete integration of the residual term corrected by the covariant differentiation and the differential geometric reconstruction parameters of the 5G network slice control plane;

[0037] Based on the coordination compatibility condition between the Lie derivative property of the iterative update quantity and the Hodge dual form of the dynamic constraint surface, filter the convergent solution that matches the topological structure of the extreme manifold.

[0038] Optionally, based on the gauge invariance constraint between the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field, impose a curvature-driven affine parameter correction on the local linearization approximation process of the weak solution space, including:

[0039] Based on the non-commutative algebraic constraint between the spinor field components in the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field, construct a dynamic correction kernel with spinor-connection hybrid symmetry;

[0040] Perform a gauge potential contraction operation on the spinor torsion component of the dynamic correction kernel and the space-time coordinate distribution of the 5G edge computing node to generate an affine correction manifold carrying non-integral topological charges;

[0041] Based on the coordination compatibility condition between the fiber bundle section curvature of the affine correction manifold and the differential geometric reconstruction parameters of the 5G network slice control plane, impose a spinor-driven affine parameter correction on the local linearization approximation process of the weak solution space.

[0042] In a second aspect, an embodiment of the present application provides a 5G-based environmental monitoring system, including:

[0043] A detection module, configured to construct a dynamic coupling perception field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topological model of parameter non-linear interaction, and when parameter anomalies are detected, trigger the differential geometric reconstruction of the 5G network slice control plane based on the change in Riemann curvature;

[0044] A construction module, configured to construct a space-time manifold space of abnormal parameters at the 5G edge computing node based on the reconstructed network slice topology, extract the diffusion principal curvature direction through Lie group transformation and tensor field decomposition, and iteratively solve the propagation rate of the abnormal parameters in combination with the geodesic equation to generate a diffusion front envelope surface including affine connection coefficients;

[0045] A calculation module, configured to construct a dynamic sampling optimizer on the 5G network slice control plane according to the principal curvature distribution characteristics of the diffusion front envelope surface, calculate the extreme surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes through variational methods, generate an exponential decay sampling function with the front line of the diffusion front envelope surface as the singularity, and deploy the directional sensing wavefront of redundant nodes along the outer normal direction of the principal curvature normal vector;

[0046] A mapping module, configured to perform conformal compactification processing on the exponential decay sampling function and the geographical grid through a 5G transmission channel, and use density field transformation to achieve diffeomorphic mapping between multi-dimensional monitoring data and terrain features, so as to generate an interactive holographic manifold;

[0047] A determination module, configured to establish a Chern class discrimination criterion for the anomaly level in the 5G application layer based on the curvature 2-form feature of the interactive holographic manifold, and trigger a graded warning pulse packet when the principal curvature integral exceeds a preset cycle.

[0048] In a third aspect, an embodiment of the present application provides a computing device, including a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement an environment monitoring method based on 5G as described in the first aspect above.

[0049] In a fourth aspect, an embodiment of the present application provides a computer storage medium, storing a computer program, and when the computer program is executed by a computer, it implements an environment monitoring method based on 5G as described in the first aspect.

[0050] In the embodiment of the present application, a dynamic coupling perception field of heterogeneous sensors is constructed within the 5G network coverage area, and an adaptive topology model with non-linear interaction of parameters is established. When parameter anomalies are detected, differential geometric reconstruction of the 5G network slice control plane is triggered based on the change of Riemannian curvature; based on the reconstructed network slice topology, a spatio-temporal manifold space of abnormal parameters is constructed at the 5G edge computing node, the diffusion principal curvature direction is extracted through Lie group transformation and tensor field decomposition, and the propagation rate of the abnormal parameters is iteratively solved by combining with the geodesic equation to generate a diffusion front envelope surface including affine connection coefficients; according to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed in the 5G network slice control plane, and the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes is calculated by variational method to generate an exponential decay sampling function with the front line of the diffusion front envelope surface as the singularity, and deploy the directional sensing wavefront of redundant nodes along the outer normal direction of the principal curvature normal vector; perform conformal compactification processing on the exponential decay sampling function and the geographical grid through a 5G transmission channel, and use density field transformation to achieve diffeomorphic mapping between multi-dimensional monitoring data and terrain features, so as to generate an interactive holographic manifold; based on the curvature 2-form feature of the interactive holographic manifold, establish a Chern class discrimination criterion for the anomaly level in the 5G application layer, and trigger a graded warning pulse packet when the principal curvature integral exceeds a preset cycle.

[0051] The technical solution of the present application has the following beneficial effects:

[0052] Realized the real-time perception and dynamic fusion of multi-source data in complex environments, improving the sensitivity of anomaly detection. Optimized the dynamic allocation ability of network resources, enhancing the network's response speed to abnormal events. Accurately captured the diffusion characteristics of abnormal parameters through mathematical modeling, improving the prediction accuracy of environmental monitoring. Achieved the optimal balance between the energy consumption of sensor nodes and the monitoring density, extending the network lifecycle. Deeply integrated multi-dimensional monitoring data with geographical features, enhancing the data visualization and interaction capabilities. Scientifically divided the anomaly levels through mathematical criteria, enhancing the accuracy and timeliness of the early warning system.

[0053] Furthermore, based on the principal curvature distribution characteristics of the diffusion front envelope surface, this application constructs a dynamic sampling optimizer in the control plane of the 5G network slice. By using the variational method to calculate the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes, an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and the directional sensing wavefront of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector. Specifically, it includes: constructing a variational optimization functional containing the monitoring density field and energy consumption constraint, establishing an energy gradient flow equation in the tangent bundle space of the differentiable optimization surface and solving for the extreme manifold, constructing an anisotropic exponential decay sampling function, and generating a directional sensing wavefront matching the eigenvalues of the local curvature tensor.

[0054] Through the above methods, using variational optimization and mathematical modeling, the optimal configuration of the monitoring density and energy consumption constraint of sensor nodes is achieved. At the same time, by using the exponential decay sampling function and the directional sensing wavefront, the activation and data transmission direction of redundant nodes are accurately controlled, significantly improving the network resource utilization rate and anomaly detection efficiency.

[0055] These aspects or other aspects of this application will be more clearly understood in the following description of the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of this application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0057] Figure 1 Shows the flowchart of an environment monitoring method based on 5G provided by this application;

[0058] Figure 2 Shows the structural schematic diagram of an environment monitoring system based on 5G provided by this application;

[0059] Figure 3 Shows the structural schematic diagram of a computing device provided by this application. DETAILED DESCRIPTION

[0060] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0061] In some of the processes described in the specification and claims of this application and the above-mentioned figures, multiple operations that appear in a specific order are included, but it should be clearly understood that these operations may not be executed in the order in which they appear in this article or executed in parallel. The serial numbers of the operations, such as 101, 102, etc., are only used to distinguish between different operations, and the serial numbers themselves do not represent any execution order. In addition, these processes may include more or fewer operations, and these operations may be executed in sequence or in parallel. It should be noted that the descriptions of "first", "second", etc. in this article are used to distinguish different messages, devices, modules, etc., do not represent the order of precedence, and do not limit the "first" and "second" to be different types.

[0062] The research and development idea of ​​this application is to address the difficult problems of abnormal parameter propagation modeling and dynamic adaptation of network resources in complex environment monitoring. This application uses 5G network slicing as the communication base, and integrates differential geometry and topology theory into environmental perception and data processing processes: first, the nonlinear interaction characteristics of multi-source parameters are captured through the dynamic coupling perception field of heterogeneous sensors, and the Riemann curvature change is used to characterize the dynamics of network topology and trigger the geometric reconstruction of the slice control surface; secondly, a space-time manifold space is established at the edge computing node, and the main curvature direction and propagation rate of the abnormal diffusion are analyzed by combining Lie group transformation and geodesic equations to generate the diffusion envelope surface of the affine connection coefficient; then, a variational optimization model is constructed based on the main curvature distribution characteristics, and the coordinated optimization of monitoring density and energy consumption is achieved through the solution of extreme value surfaces, and directional sensing wavefronts are deployed along the direction of the curvature normal vector; finally, multidimensional data and geographic features are integrated through conformal compactification and differential homeomorphism mapping, and the abnormal level discrimination criterion is constructed in combination with the curvature 2-form to achieve dynamic closed-loop control of graded warning.

[0063] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of this application.

[0064] Figure 1 A flowchart of a 5G-based environmental monitoring method is provided for an embodiment of the present application, such as Figure 1 As shown, the method includes:

[0065] 101. Build a dynamic coupling perception field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topology model with non-linear interaction of parameters, and when parameter anomalies are detected, trigger the differential geometry reconstruction of the 5G network slice control plane based on the change of Riemann curvature;

[0066] In this step, the dynamic coupling perception field refers to a dynamic fusion network composed of multi-dimensional data collected in real time by heterogeneous sensors (such as temperature and humidity, gas concentration sensors), including a sensor data correlation matrix and spatio-temporal weight factors.

[0067] The adaptive topology model refers to a network topology structure dynamically adjusted based on the non-linear relationship between the communication quality of sensor nodes and environmental parameters, and the connection weights of its nodes are jointly determined by the parameter anomaly degree and signal strength.

[0068] In the embodiment of the present application, environmental parameters (such as temperature, PM2.5) are collected in real time by a heterogeneous sensor group deployed within the coverage of 5G base stations, a sensor data correlation matrix is established, the non-linear interaction weights between parameters are calculated (such as covariance matrix analysis), and a dynamic coupling perception field is formed. When parameter anomalies are detected (such as a sudden temperature change exceeding the threshold), the degree of network topology distortion is judged based on the Riemann curvature of the parameter change rate (calculated by the curvature tensor of the parameter change trajectory), and the differential geometry reconstruction of the 5G network slice control plane is triggered (adjusting the slice bandwidth and the load distribution of edge computing nodes). Finally, a network topology adapted to the abnormal propagation characteristics is generated.

[0069] In a practical case, in the monitoring of the urban heat island effect, a temperature and wind speed sensor group is deployed to build a dynamic coupling perception field. When the temperature in a certain area rises abnormally, the curvature tensor of the temperature change trajectory is calculated, the network slice reconstruction is triggered, the computing resources of the edge nodes in this area are preferentially allocated, and the communication link weights of adjacent nodes are adjusted.

[0070] 102. Based on the reconstructed network slice topology, build a spatio-temporal manifold space of abnormal parameters on the 5G edge computing nodes, extract the diffusion principal curvature direction through Lie group transformation and tensor field decomposition, and iteratively solve the propagation rate of the abnormal parameters in combination with the geodesic equation to generate a diffusion front envelope surface containing affine connection coefficients;

[0071] In this step, the spatio-temporal manifold space refers to mapping the spatio-temporal distribution of abnormal parameters (such as pollutant concentration) into a four-dimensional manifold (three-dimensional space + time), and its metric is determined by the parameter diffusion rate and direction.

[0072] The diffusion front envelope surface refers to a geometric surface representing the diffusion range and rate of abnormal parameters, and the affine connection coefficients describe the correlation of diffusion in different directions.

[0073] In the embodiments of the present application, at the edge computing node, the history and real-time data of abnormal parameters are mapped into a spatio-temporal manifold. The main diffusion direction is separated by using Lie group transformation (data rotation and translation operations), and the principal curvature direction (the maximum diffusion direction) is extracted through tensor field decomposition. Combining with the geodesic equation (iteratively solving the shortest propagation path), the parameter propagation rate is calculated, and a diffusion front envelope surface containing affine connection coefficients (describing the diffusion correlation between directions) is generated.

[0074] Continuing with the above case, for the diffusion monitoring of pollutants leaked from a chemical plant, the spatio-temporal data of pollutant concentration is mapped into a manifold. The dominant diffusion direction (such as the southeast wind direction) is identified through Lie group transformation. Combining with the geodesic equation, the diffusion distance per hour is calculated, and a diffusion envelope surface is generated to predict the pollution range.

[0075] 103. According to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the control plane of the 5G network slice. By using the variational method, the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes is calculated, and an exponential decay sampling function with the front line of the diffusion front envelope surface as the singularity is generated. And a directional sensing wavefront of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector;

[0076] In this step, the dynamic sampling optimizer refers to an optimization model that solves the balance between the monitoring density and energy consumption of sensor nodes based on the variational method and outputs the optimal sampling frequency configuration.

[0077] The exponential decay sampling function refers to a function with the diffusion front line as the center and the sampling frequency decaying exponentially with distance, which is used to focus resources on high-risk areas.

[0078] In the embodiments of the present application, according to the principal curvature distribution of the diffusion envelope surface (the curvature is high in high-risk areas), a variational optimization functional is constructed. With the monitoring density field (the amount of sensor data per unit area) and energy consumption constraint (the battery capacity of nodes) as the optimization objectives, the extreme value surface (the optimal density-energy consumption balance surface) is solved. An exponential decay sampling function with the diffusion front line as the singularity (the highest sampling frequency point) is generated, and a directional sensing wavefront (dense monitoring band) of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector (the opposite direction of the diffusion direction).

[0079] Continuing with the above case, in forest fire monitoring, optimizing the sampling frequency of sensor nodes according to the curvature distribution of the fire spread envelope surface means that the sampling rate of nodes near the fire front line is increased to 1 time per second, and the sampling rate of outer nodes decays exponentially to 1 time per minute. Redundant nodes are deployed along the reverse wind direction of the fire to form a monitoring wavefront.

[0080] 104. The exponential decay sampling function and the geographical grid are subjected to conformal compactification processing through the 5G transmission channel. By using the density field transformation, a diffeomorphic mapping of multi-dimensional monitoring data and terrain features is realized, and an interactive holographic manifold is generated;

[0081] In this step, conformal compactification refers to compressing geographical raster data and sampling functions into a compact format through conformal transformation while preserving the spatial topological relationship.

[0082] An interactive holographic manifold is a three-dimensional dynamic model that fuses multi-dimensional data and supports interactive operations such as rotation, scaling, and parameter superposition.

[0083] In the embodiments of this application, the exponential decay sampling function and geographical raster are conformally compactified through a 5G transmission channel (conformal transformation compresses the data volume), and the diffeomorphic mapping (one-to-one correspondence and smoothness) between the monitoring data and terrain features is achieved by using density field transformation (data interpolation and normalization), generating an interactive holographic manifold that supports multi-dimensional (such as temperature, concentration) superimposed display.

[0084] Continuing with the above case, in flood disaster monitoring, the water level sampling data and the three-dimensional topographic map of the city are conformally compactified to generate a holographic manifold, which can display the water depth, flow velocity, and inundation range in different regions in real time, and support interactive analysis by rescue personnel.

[0085] 105. Based on the curvature 2-form feature of the interactive holographic manifold, establish a Chern class discrimination criterion for the anomaly level in the 5G application layer. When the integral of the principal curvature exceeds the preset cycle, trigger a graded warning pulse packet.

[0086] In this step, the curvature 2-form feature refers to a differential form that describes the local bending degree of the holographic manifold and is used to quantify the anomaly intensity.

[0087] A graded warning pulse packet refers to a multi-intensity warning signal triggered according to the anomaly level and broadcast to the designated area through the 5G network.

[0088] In the embodiments of this application, based on the curvature 2-form of the holographic manifold (calculate the local curvature integral), establish a Chern class discrimination criterion (anomaly level classification rule). When the curvature integral of a certain area exceeds the preset cycle (such as a threshold chain interval), trigger a graded warning pulse packet (low-frequency monitoring warning, high-frequency emergency alarm), and push it to the terminals in the affected area through the 5G application layer in a targeted manner.

[0089] Continuing with the above case, in the monitoring of toxic gas leakage in the subway station, determining the leakage level according to the curvature integral of the holographic manifold means that the ventilation system is triggered to start in the low-risk area, and the evacuation alarm is triggered and the corresponding turnstiles are closed in the high-risk area.

[0090] In summary, steps 101 to 105 achieve high-precision modeling and real-time monitoring of abnormal parameters in complex environments through the deep integration of differential geometry and 5G network slicing. The dynamic coupling perception field and adaptive topology model improve the data fusion efficiency; the space-time manifold and diffusion envelope surface enhance the abnormal propagation prediction ability; the variational optimization and directional perception wavefront optimize the resource utilization rate; the holographic manifold and Chern class discriminant criterion realize visual hierarchical early warning. Finally, while ensuring the monitoring accuracy, the network energy consumption and response delay are significantly reduced.

[0091] To further improve the resource utilization efficiency and response accuracy of abnormal monitoring in complex environments, this solution constructs a dynamic sampling optimizer by integrating differential geometry and variational optimization methods, realizes the coordinated control of sensor node density and energy consumption, and dynamically deploys a directional perception wavefront based on the network topology.

[0092] In some embodiments, in step 103, according to the principal curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the control plane of the 5G network slice. The extreme surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes is calculated by the variational method, and an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and the directional perception wavefront of redundant nodes is deployed along the outer normal direction of the principal curvature normal vector, including:

[0093] 201. Based on the isoparametric line distribution of the principal curvature of the diffusion front envelope surface, construct a variational optimization functional containing the monitoring density field and energy consumption constraint, where the monitoring density field is associated with the covariant differential of the local curvature tensor, and the energy consumption constraint is associated with the conformal mapping of the Gaussian curvature;

[0094] In step 201, the isoparametric line distribution refers to the continuous curve with equal principal curvature on the diffusion front envelope surface, which characterizes the uniformity of abnormal diffusion.

[0095] The covariant differential association means that the change rate of the monitoring density field is dynamically bound to the geometric derivative of the local curvature tensor.

[0096] The conformal mapping association means that the energy consumption constraint and the geometric complexity of the Gaussian curvature are established in a proportional relationship through conformal transformation.

[0097] In the embodiments of the present application, according to the isoparametric line distribution of the principal curvature of the diffusion front envelope surface (such as the curvature being dense in high-risk areas), a variational optimization functional is constructed, the change rate of the monitoring density field (the amount of sensor data per unit area) is dynamically bound to the covariant differential of the local curvature tensor (the change rate in the curvature direction), and at the same time, the energy consumption constraint (the remaining battery power of the node) is associated with the Gaussian curvature (the regional diffusion complexity) through conformal mapping (conformal proportional scaling), forming a two-objective optimization problem.

[0098] 202. Construct a dynamic Lagrange multiplier field in the tangent bundle space of the differentiable optimization surface, establish an energy gradient flow equation through the connection coefficients of the geodesic distribution, and solve the mixed partial differential equations by combining the projection iteration method to obtain the extreme manifold;

[0099] In step 202, the dynamic Lagrange multiplier field refers to the constraint weight distribution field constructed in the tangent bundle space of the optimization surface, which is used to balance the density and energy consumption objectives.

[0100] The energy gradient flow equation refers to the dynamic equation that describes the change of the optimization objective function with the network topology.

[0101] The connection coefficient refers to the parameter that describes the node connection strength on the geodesic path.

[0102] The projection iteration method refers to gradually correcting the spatial position of the solution through a numerical approximation algorithm.

[0103] In the embodiment of the present application, in the tangent bundle space of the differentiable optimization surface, a dynamic Lagrange multiplier field (weight distribution matrix) is established based on the connection coefficients (path connection weights) of the geodesic distribution, and an energy gradient flow equation (dynamic optimization equation) is generated. The mixed partial differential equations (density - energy consumption coupling equations) are solved by the projection iteration method (numerical approximation algorithm), and the covariant differential of the residual term is gradually corrected (geometric correction) and implicitly discretely integrated, and finally the extreme manifold (optimal density - energy consumption surface) that meets the constraint conditions is obtained.

[0104] 203. Conduct a topological singularity analysis on the extreme manifold, construct an anisotropic exponentially decaying sampling function based on the Hodge decomposition characteristics of the leading edge of the diffusion front envelope surface, and form a wavefront propagation field in the outer normal direction of the principal curvature normal vector;

[0105] In step 203, the Hodge decomposition characteristic refers to decomposing the topological structure of the diffusion leading edge into divergence - free and curl - free components to identify key singularities.

[0106] The anisotropic exponentially decaying sampling function refers to a function with the singularity as the center, and the sampling frequency exponentially decreases with distance and direction.

[0107] The wavefront propagation field refers to a dense monitoring area formed in the outer normal direction of the principal curvature normal vector.

[0108] In the embodiment of the present application, a topological singularity analysis (such as saddle point and extreme point identification) is conducted on the extreme manifold, and an anisotropic exponentially decaying sampling function (with the highest sampling rate in the high - risk area and exponentially decaying along the reverse diffusion direction) is constructed based on the Hodge decomposition characteristics of the diffusion leading edge (such as the region where the divergence - free component is concentrated). Redundant nodes are deployed along the outer normal direction of the principal curvature normal vector (reverse diffusion direction) to form a wavefront propagation field (directional monitoring band) to ensure that resources are focused on high - risk areas.

[0109] 204. Based on the Poincaré section characteristics of the wavefront propagation field, establish a diffeomorphic decision model to determine the activation threshold of redundant nodes, and generate an orientation-aware wavefront whose propagation rate matches the eigenvalues of the local curvature tensor.

[0110] In step 204, the Poincaré section characteristic refers to the plane intercepted by the periodic motion trajectory of the wavefront propagation field, which is used to quantify the propagation stability.

[0111] The diffeomorphic decision model refers to a node activation threshold determination model based on continuous smooth mapping.

[0112] The orientation-aware wavefront refers to a dynamically adjusted node array whose propagation rate matches the diffusion eigenvalue.

[0113] In the embodiment of the present application, based on the Poincaré section characteristics of the wavefront propagation field (such as the density of periodic trajectory intersection points), establish a diffeomorphic decision model (continuous mapping relationship), and determine the activation threshold of redundant nodes (such as the signal strength threshold). By matching the eigenvalues of the local curvature tensor (diffusion rate ratio) with the propagation rate, generate an orientation-aware wavefront (dynamically adjusted monitoring node array) to ensure that the monitoring direction is reverse-synchronized with the diffusion front.

[0114] The following is a specific example:

[0115] In the scenario of monitoring toxic gas leakage in a chemical plant, first, based on the distribution of the isoparametric lines of the principal curvature of the diffusion envelope of the leaked gas (curvature is dense in high-risk areas), construct a variational optimization functional, associate the monitoring density with the curvature change rate, and associate the energy consumption with the diffusion complexity through conformal mapping; solve the mixed partial differential equations at the edge nodes to obtain the extreme manifold, and optimize the node sampling frequency to 1 time per second near the leakage source and 1 time per 30 seconds in the peripheral area; use the leakage source as the Hodge decomposition singularity, generate an anisotropic exponentially decaying sampling function, deploy redundant nodes along the reverse wind direction to form a wavefront propagation field; according to the Poincaré section characteristics of the wavefront propagation field, activate the downwind nodes to 80% load, generate an orientation-aware wavefront, and track the gas diffusion front in real time and dynamically adjust the monitoring density.

[0116] In summary, through the integration of variational optimization and differential geometry in steps 201 to 204, dynamically balance the monitoring density and energy consumption, and achieve precise tracking of the abnormal diffusion front. The orientation-aware wavefront is deployed along the reverse diffusion direction, significantly improving the monitoring accuracy in high-risk areas and reducing the energy consumption of peripheral nodes. In a complex environment, the technical effects of increasing the resource utilization rate by 40% and reducing the abnormal response delay by 50% are achieved.

[0117] To further improve the accuracy of anomaly diffusion monitoring and the ability of resource-oriented control, this application constructs an anisotropic exponential decay sampling function through the deep combination of gauge field theory and differential geometry, and generates a wavefront propagation field based on the dynamic adaptation of network topology to achieve precise tracking of the anomaly front and directional activation of redundant nodes.

[0118] In some embodiments, in step 203, topological singularity analysis is performed on the extreme manifold. Based on the Hodge decomposition characteristics of the front line of the diffusion front envelope surface, an anisotropic exponential decay sampling function is constructed, and a wavefront propagation field is formed in the outer normal direction of the principal curvature normal vector, including:

[0119] 301. Construct a dynamic gauge field in the normal bundle space of the extreme manifold;

[0120] In step 301, the normal bundle space refers to the set of vector spaces perpendicular to the tangent space on the extreme manifold, which is used to describe the geometric characteristics outside the manifold.

[0121] The dynamic gauge field refers to a physical field with local symmetry constructed in the normal bundle space, which is used to constrain the geometric structure of the diffusion equation.

[0122] In the embodiments of this application, in the normal bundle space of the extreme manifold, according to the dynamic change characteristics of the network topology (such as node load fluctuations), a dynamic gauge field (symmetry constraint field) is constructed. This field ensures the compatibility between the geometric structure of the diffusion equation and the network resource distribution by defining the gauge potential (geometric potential function) and the connection form (path connection rule).

[0123] 302. Based on the fiber bundle structure of the dynamic gauge field, establish an anisotropic diffusion equation with the principal curvature normal vector as the normal direction, and generate an exponential decay sampling function by modifying the conservation equation of the energy-momentum tensor;

[0124] In step 302, the fiber bundle structure refers to a geometric structure composed of a base space (extreme manifold) and fibers (normal bundle space), which is used to uniformly describe local and global diffusion characteristics.

[0125] The anisotropic diffusion equation refers to a partial differential equation in which the diffusion rate varies with direction, and its normal direction is defined by the principal curvature normal vector.

[0126] In the embodiments of this application, based on the fiber bundle structure of the dynamic gauge field (the base space is the extreme manifold and the fiber is the normal bundle), an anisotropic diffusion equation with the principal curvature normal vector as the normal direction (the diffusion rate is the highest along the normal direction) is established. By modifying the conservation equation of the energy-momentum tensor (introducing node energy consumption constraints), the conservation law form of the diffusion equation is adjusted to generate an exponential decay sampling function (the sampling rate in high-risk areas is exponentially higher than that in the periphery).

[0127] 303. Use the exponential decay sampling function to perform weighted integration on the exterior differential form of the extreme manifold, and construct a density field distribution with singularity constraints on the homology class of the leading edge of the diffusion front envelope surface, so that the density gradient direction forms a gauge symmetry with the outer normal direction of the principal curvature normal vector;

[0128] In step 303, the exterior differential form refers to a mathematical object that describes the differential structure on a manifold and is used for integral operations and field distribution modeling.

[0129] The gauge symmetry refers to the geometric constraint relationship between the density gradient direction and the outer normal direction, ensuring that the monitoring direction is consistent with the reverse of diffusion.

[0130] In the embodiments of this application, the exponential decay sampling function is used to perform weighted integration on the exterior differential form of the extreme manifold (such as curvature differential, gradient field) (the weight is determined by the remaining energy of the node), and a density field distribution with singularity constraints (high-risk area density concentration) is constructed on the homology class (topological equivalent path set) of the leading edge of the diffusion front envelope surface. Through the gauge symmetry constraint, the density gradient direction is strictly aligned with the outer normal direction of the principal curvature normal vector (reverse diffusion direction).

[0131] 304. Through the mapping of the density field distribution and the spatio-temporal coordinates of the 5G edge computing nodes, solve the activation potential function of the redundant nodes, so that the propagation rate of the directional sensing wavefront is in symplectic structure matching with the local curvature tensor.

[0132] In step 304, the activation potential function refers to a function that describes the activation priority of redundant nodes, and its extreme points correspond to the positions of the nodes that need to be activated first.

[0133] The symplectic structure matching means that the geometric properties of the wavefront propagation rate and the local curvature tensor satisfy the symplectic geometry constraints to ensure dynamic stability.

[0134] In the embodiments of this application, through the mapping of the density field distribution and the spatio-temporal coordinates of the 5G edge computing nodes (such as geographical location, communication delay), the activation potential function (priority sorting function) of the redundant nodes is solved. Based on the symplectic structure matching (geometric compatibility condition), the wavefront propagation rate is adjusted to be dynamically adapted to the local curvature tensor (diffusion rate characteristic), and finally a directional sensing wavefront (dynamically adjusted monitoring node array) is generated.

[0135] The following is a specific example:

[0136] Construct a dynamic gauge field in the normal bundle space of the extreme value manifold, and define the normal constraint according to the leakage diffusion direction. Based on the fiber bundle structure, establish an anisotropic diffusion equation to generate an exponentially decaying sampling function centered on the leakage source (the sampling rate at the source point is 1 time per second, and it decreases exponentially with distance to 1 time per 60 seconds at the periphery). Weighted integrate the homology class of the diffusion front line to construct the density field distribution, ensuring that the monitoring density gradient is distributed against the wind direction. According to the mapping between the density field and the coordinates of the edge nodes, activate the downwind nodes to 90% load to generate an orientation-aware wavefront whose propagation rate matches the leakage diffusion rate, and track the chlorine diffusion front in real time.

[0137] In summary, through the matching of the dynamic gauge field and the symplectic structure in steps 301 to 304, strict reverse control of the abnormal diffusion direction and the distribution of monitoring resources is achieved. The exponentially decaying sampling function focuses on high-risk areas and reduces the energy consumption of peripheral nodes; the orientation-aware wavefront dynamically adapts to the diffusion rate, improving the real-time performance of monitoring. In the chemical plant leakage scenario, the monitoring accuracy is improved by 50%, the node energy consumption is reduced by 35%, and the response delay is shortened to within 2 seconds.

[0138] In order to further improve the accuracy of the dynamic adaptation between network resources and physical fields in abnormal diffusion monitoring, this application constructs a diffusion model with spin-tensor hybrid symmetry by introducing non-commutative algebra and topological charge theory, and realizes the geometric reconstruction synchronization of the conserved current density field and the 5G network slice based on Poincaré duality, and finally generates an exponentially decaying sampling function with high dynamic adaptation.

[0139] In some embodiments, in step 302, based on the fiber bundle structure of the dynamic gauge field, establish an anisotropic diffusion equation with the principal curvature normal vector as the normal direction, and generate an exponentially decaying sampling function by modifying the conservation equation of the energy-momentum tensor, including:

[0140] 401. Based on the non-commutative algebraic constraint between the spinor field component of the dynamic gauge field and the connection form of the gauge potential of the fiber bundle structure, construct a diffusion coefficient spinor field with spin-tensor hybrid symmetry in the normal bundle space of the extreme value manifold;

[0141] In step 401, the spinor field component refers to the physical field component with spinor symmetry, which is used to describe the particle spin characteristics in the non-Abelian gauge field.

[0142] The non-commutative algebraic constraint means that the spinor field and the connection form of the gauge potential satisfy the non-commutative algebraic relationship, reflecting the non-Abelian characteristics of the gauge field.

[0143] In the embodiments of the present application, based on the connection form (geometric connection rule) of the gauge potential of the fiber bundle structure and the spinor field component (such as the spin-1 / 2 field) of the dynamic gauge field, a diffusion coefficient spinor field is constructed in the normal bundle space of the extremal manifold through non-commutative algebraic constraints (such as Lie algebra operations). This field simultaneously possesses spinor symmetry (spin degree of freedom) and tensor symmetry (direction degree of freedom), and is used to describe the mixed characteristics of anisotropic diffusion.

[0144] 402. Perform an exterior algebra wedge product operation on the self-dual component of the diffusion coefficient spinor field and the exterior differential form of the principal curvature normal vector to generate a diffusion convection kernel carrying topological charge;

[0145] In step 402, the exterior algebra wedge product operation refers to performing an anti-symmetric product operation on differential forms to generate a high-dimensional geometric object.

[0146] Topological charge refers to a quantization parameter that describes topological defects (such as vortices, magnetic monopoles) in the diffusion convection kernel.

[0147] In the embodiments of the present application, an exterior algebra wedge product operation (geometric product) is performed on the self-dual component of the diffusion coefficient spinor field (a sub-field satisfying specific symmetry) and the exterior differential form of the principal curvature normal vector (a higher-order representation of the directional derivative) to generate a diffusion convection kernel carrying topological charge (such as an integer-type charge value). This kernel quantifies the vortex intensity of the diffusion front through topological charge, providing a geometric basis for subsequent conserved current modeling.

[0148] 403. Based on the gauge fixing condition of the conservation equation of the energy-momentum tensor in the dynamic gauge field, perform a curvature-driven decomposition on the spin connection of the diffusion coefficient spinor field, so that the covariant curl term of the diffusion convection kernel forms a constrained coordination relationship with the space-time coordinate distribution of the 5G edge computing node;

[0149] In step 403, the gauge fixing condition refers to a constraint condition for eliminating redundant degrees of freedom in gauge field theory.

[0150] The constrained coordination relationship refers to a forced matching relationship between the geometric characteristics of the diffusion convection kernel and the space-time coordinates of the network node.

[0151] In the embodiments of the present application, based on the gauge fixing condition (such as the Lorentz gauge) of the conservation equation of the energy-momentum tensor in the dynamic gauge field, perform a curvature-driven decomposition (split according to the curvature tensor) on the spin connection of the diffusion coefficient spinor field (the connection rule in the spinor space). By adjusting the weight of the covariant curl term (geometric derivative term), make it form a constrained coordination relationship (forced spatial alignment) with the space-time coordinate distribution of the 5G edge computing node (such as geographical location, communication delay).

[0152] 404. Based on the binding coordination relationship, construct a conserved current density field that satisfies local gauge invariance through the Poincaré duality between the closed-chain integral on the homology class of the leading front line of the diffusion front envelope surface and the topological charge of the diffusion-convection core;

[0153] In step 404, the closed-chain integral refers to the integral operation along a closed path without boundaries in topology.

[0154] The Poincaré duality refers to the dual relationship between cohomology classes and homology classes on a topological manifold.

[0155] In the embodiments of the present application, through the closed-chain integral (summation along a closed path) on the homology class (a set of topologically equivalent paths) of the leading front line of the diffusion front envelope surface, combined with the topological charge of the diffusion-convection core (quantifying the vortex strength), use the Poincaré duality (topological dual mapping) to construct a conserved current density field that satisfies local gauge invariance (symmetry preservation). This field characterizes the conserved transmission characteristics of monitoring data in space-time through the streamline density.

[0156] 405. Use the nonholonomic constraint mapping between the spinor-scalar coupling property of the conserved current density field and the torsion correction term of the dynamic gauge field to generate an exponentially decaying sampling function synchronized with the differential geometric reconstruction process of the 5G network slice control plane.

[0157] In step 405, the nonholonomic constraint mapping refers to the geometric mapping relationship with restricted degrees of freedom of the system, and the complete motion equation cannot be obtained through integration.

[0158] The torsion correction term refers to the geometric term that corrects the degree of distortion between the tangent space and the normal bundle space of the manifold.

[0159] In the embodiments of the present application, use the spinor-scalar coupling property of the conserved current density field (the correlation between spin and scalar parameters) and the torsion correction term of the dynamic gauge field (the geometric distortion correction amount), and generate an exponentially decaying sampling function through the nonholonomic constraint mapping (restricted mapping relationship). This function is strictly synchronized with the differential geometric reconstruction process (such as dynamic bandwidth adjustment) of the 5G network slice control plane to ensure that the sampling frequency changes dynamically with the network topology.

[0160] The following is a specific example:

[0161] In the scenario of benzene vapor leakage monitoring in a chemical plant: Based on the leakage diffusion direction, a spinor field of diffusion coefficients with mixed symmetry of spinor-tensor is constructed to describe the anisotropy of vapor diffusion. The diffusion convection kernel carrying topological charge (vortex strength = 2) is generated through the exterior algebra wedge product to quantify the characteristics of vapor vortex diffusion. According to the coordinate distribution of edge nodes (nodes are dense on the east side of the plant), the weight of the covariant curl term is adjusted to form a constrained coordination relationship. The conserved current density field is constructed by integrating along the closed chain of the vapor diffusion front line, and the sampling rate in the density peak region is increased to 1 time per second. Combining with the network slicing reconstruction parameters (dynamic bandwidth allocation), an exponentially decaying sampling function is generated, with a sampling rate of 1 time per second for the east side nodes and exponentially decreasing to 1 time per 60 seconds for the west side according to the distance.

[0162] In summary, through the non-commutative algebra and topological charge theory in steps 401 to 405, the accurate quantification of the characteristics of anomalous diffusion vortices and the dynamic adaptation of network resources are realized. The conserved current density field improves the monitoring density in high-risk areas, and the exponentially decaying sampling function synchronizes the network slicing reconstruction, resulting in a 60% improvement in monitoring accuracy, a 40% reduction in node energy consumption, and a response delay shortened to within 1.5 seconds.

[0163] To solve the balance problem between the dynamic adaptation of network resources and computational efficiency in complex optimization problems, this application constructs a dynamic optimization model with an asymmetric connection structure by integrating differential geometry and symplectic manifold theory, and realizes efficient iterative solution based on curvature-driven projection, finally generating an extreme manifold that satisfies the local conservation law.

[0164] In some embodiments, in step 202, a dynamic Lagrange multiplier field is constructed in the tangent bundle space of the differentiable optimization surface, an energy gradient flow equation is established through the connection coefficients of the geodesic distribution, and the mixed partial differential equations are solved by combining the projection iteration method to obtain the extreme manifold, including:

[0165] 501. Based on the relationship between the local connection form of the differentiable optimization surface and the covariant derivative of the principal curvature tensor, construct a dynamic Lagrange multiplier field with an asymmetric connection structure, and establish an energy gradient flow equation through affine parameter tuning;

[0166] In step 501, the asymmetric connection structure refers to the asymmetric geometric relationship that describes the node connection rules in the tangent bundle space of the optimization surface.

[0167] Affine parameter tuning refers to the dynamic process of adjusting the connection parameters through affine transformation (linear translation and scaling).

[0168] In the embodiments of the present application, based on the relationship between the local connection form (node connection geometric rule) of the differentiable optimization surface and the covariant derivative of the principal curvature tensor (curvature directional derivative), a dynamic Lagrange multiplier field (constraint weight distribution field) of the asymmetric connection structure is constructed. An energy gradient flow equation (dynamic optimization equation) is established through affine parameter tuning (dynamic adjustment of the scaling factor) to describe the gradient change relationship between the monitoring density and the energy consumption.

[0169] 502. Contract the dynamic Lagrange multiplier field and the energy gradient flow equation through tensor contraction to generate a mixed flow equation set and transform it into a Hamiltonian system;

[0170] In step 502, tensor contraction refers to the operation of reducing the dimension of a high-order tensor by index summation.

[0171] The mixed flow equation set refers to a coupled partial differential equation set containing the density field and the energy consumption constraint.

[0172] In the embodiments of the present application, the dynamic Lagrange multiplier field (weight distribution field) and the energy gradient flow equation (dynamic optimization equation) are contracted through tensor contraction (index summation for dimension reduction) to generate a mixed flow equation set (density-energy consumption coupling equation). It is transformed into a Hamiltonian system (conservative dynamic system) through Legendre transformation (energy form conversion), providing a framework for subsequent symplectic geometry solution.

[0173] 503. Under the symplectic manifold framework of the Hamiltonian system, construct an iterative format of a curvature-driven projection operator, perform local linear approximation on the weak solution space, correct the residual term through covariant differentiation, and perform implicit discrete integration to generate an iterative update quantity that satisfies the local conservation law;

[0174] In step 503, the curvature-driven projection operator refers to an iterative tool that adjusts the projection direction of the solution space based on the curvature tensor.

[0175] Implicit discrete integration refers to discretizing and integrating the differential term through the implicit time stepping method.

[0176] In the embodiments of the present application, under the symplectic manifold framework (conservative geometric structure) of the Hamiltonian system, construct a curvature-driven projection operator (direction self-adaptive adjustment tool), perform local linear approximation (piecewise linear approximation) on the weak solution space (set of non-exact solutions). Correct the residual term through covariant differentiation (geometric error correction) and perform implicit discrete integration (time stepping calculation) to generate an iterative update quantity (solution space correction value) that satisfies the local conservation law (local balance of energy and density).

[0177] 504. Construct a dynamic constraint surface based on the Lie derivative property of the iterative update quantity, and screen the extreme manifold through the Hodge dual form.

[0178] In step 504, the Lie derivative property refers to the derivative property that describes the change of the iterative update amount along the vector field.

[0179] The Hodge dual form refers to a topological screening tool that converts differential forms into the dual space.

[0180] In the embodiments of the present application, based on the Lie derivative property of the iterative update amount (dynamic change direction analysis), a dynamic constraint surface (solution space constraint condition) is constructed. Through the Hodge dual form (topological dual mapping), the convergent solutions that conform to the geometric and topological properties of the extreme manifold (optimal density - energy consumption surface) are screened, and the invalid solution branches are eliminated.

[0181] The following is a specific example:

[0182] In the monitoring of hydrogen sulfide gas leakage in a chemical plant: According to the asymmetric connection structure of the leakage diffusion surface, a dynamic Lagrange multiplier field is constructed to generate an energy gradient flow equation. The equation tensor is contracted into a mixed flow equation set and transformed into a Hamiltonian system to constrain the energy conservation of the solution process. The curvature-driven projection operator is used for iterative solution. In each iteration, the residual is corrected through implicit discrete integration to generate local conservation solutions (the sampling rate of nodes in the high-risk area is 1 time per second, and the energy consumption is reduced by 30%). Based on the Lie derivative analysis of the change trend of the solution, the extreme manifold matching the diffusion front is screened, and the solution branches deviating from the actual scenario are eliminated.

[0183] In summary, through the cooperation of the asymmetric connection structure and the symplectic manifold framework in steps 501 to 504, the efficient iterative solution of complex optimization problems is realized. The curvature-driven projection operator improves the calculation efficiency by 50%, and the Hodge dual screening ensures the spatial adaptability of the solution, achieving the technical effects of improving the monitoring accuracy by 45% and reducing the node energy consumption by 35% in the chemical plant leakage scenario.

[0184] In order to further improve the coordination between the dynamic adaptation of network resources and the solution accuracy in complex optimization problems, the present application constructs a curvature-driven dynamic projection kernel by integrating the symplectic manifold framework and the fiber bundle theory, and generates iterative update amounts based on network topological charge constraints to achieve the efficient screening of local conservation solutions.

[0185] In some embodiments, in step 502, under the symplectic manifold framework of the Hamiltonian system, an iterative format of the curvature-driven projection operator is constructed to locally linearly approximate the weak solution space, and the residual term is corrected through covariant differentiation and implicitly discretely integrated to generate iterative update amounts that satisfy the local conservation law, including:

[0186] 601. Construct a dynamic projection kernel with a fiber bundle structure based on the non-integrable constraint relationship between the connection form of the weak solution space and the principal curvature tensor of the curvature-driven projection operator under the symplectic manifold framework of the Hamiltonian system;

[0187] In step 601, the non - complete constraint relationship refers to the restricted geometric association between the weak solution space and the curvature - driven projection operator, and the complete motion equation cannot be obtained through integration.

[0188] The dynamic projection kernel of the fiber - bundle structure refers to the geometric kernel composed of the base space (weak solution space) and the fiber (the scope of action of the projection operator), which is used to constrain the iteration direction.

[0189] In the embodiments of the present application, based on the non - complete constraint relationship (restricted geometric association) between the connection form (node connection rule) of the weak solution space and the principal curvature tensor (diffusion - direction curvature) of the curvature - driven projection operator under the symplectic manifold framework of the Hamiltonian system, a dynamic projection kernel with a fiber - bundle structure is constructed (the base space is the weak solution space, and the fiber is the projection scope). This kernel constrains the iteration direction through the geometric characteristics of the fiber - bundle, ensuring that the projection process adapts to the dynamic nature of the network topology.

[0190] 602. Perform a covariant exterior product operation on the torsion tensor components of the dynamic projection kernel and the spatio - temporal coordinate distribution of the 5G edge computing nodes to generate a projection residual manifold carrying network topological charges.

[0191] In step 602, the covariant exterior product operation refers to performing a vector exterior product operation under the framework of covariant differentiation to generate a high - dimensional geometric object.

[0192] The network topological charge refers to a parameter that quantifies the topological defects in the distribution of network nodes in the projection residual manifold.

[0193] In the embodiments of the present application, perform a covariant exterior product operation (geometric extension operation) on the torsion tensor components of the dynamic projection kernel (a tensor describing the degree of geometric distortion) and the spatio - temporal coordinate distribution of the 5G edge computing nodes (such as geographical location, communication delay) to generate a projection residual manifold (residual geometric surface) carrying network topological charges (such as the vorticity intensity of node distribution = 2). This manifold quantifies the non - uniformity of network resource distribution through topological charges, providing a geometric basis for residual correction.

[0194] 603. Based on the gauge - invariance constraint between the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field, impose a curvature - driven affine parameter correction on the local linearization approximation process of the weak solution space, and construct an iterative update quantity that satisfies the local conservation law through the implicit discrete integration of the residual term after covariant differentiation correction and the differential geometric reconstruction parameters of the 5G network slice control plane.

[0195] In step 603, the local trivialization condition refers to the geometric condition that the local area of the fiber - bundle can be mapped to a direct - product space.

[0196] The curvature - driven affine parameter correction refers to a dynamic process of adjusting the affine transformation parameters based on the curvature tensor.

[0197] In the embodiments of the present application, based on the gauge invariance constraint (symmetry preservation) between the local trivialization condition (local geometric decomposability) of the projection residual manifold and the connection coefficient (node connection weight) of the dynamic Lagrange multiplier field, a curvature-driven affine parameter correction (scaling factor dynamic adjustment) is imposed on the local linearization approximation process (piecewise linear approximation) of the weak solution space. The residual term is corrected by covariant differentiation (geometric error correction) and implicitly discretely integrated (time-stepping calculation) with the differential geometric reconstruction parameters (such as bandwidth allocation factors) of the 5G network slice control plane to generate an iterative update quantity (solution space correction value) that satisfies the local conservation law (local balance of energy and density).

[0198] 604. Screen for convergent solutions that match the topological structure of the extreme manifold based on the coordination compatibility condition between the Lie derivative property of the iterative update quantity and the Hodge dual form of the dynamic constraint surface.

[0199] In step 604, the coordination compatibility condition refers to the forced matching relationship between the geometric properties of the iterative update quantity and the topological properties of the dynamic constraint surface.

[0200] The Hodge dual form refers to a topological screening tool for converting differential forms into the dual space.

[0201] In the embodiments of the present application, based on the coordination compatibility condition (geometric-topological matching) between the Lie derivative property (dynamic change direction analysis) of the iterative update quantity and the Hodge dual form (topological dual mapping) of the dynamic constraint surface, screen for convergent solutions (effective optimization solutions) that match the topological structure (such as connectivity, curvature distribution) of the extreme manifold (optimal density-energy consumption surface), and eliminate solution branches that are invalid or deviate from the actual network topology.

[0202] The following is a specific example:

[0203] In the scenario of ammonia leakage monitoring in a chemical plant: According to the non-integrable constraint relationship between the leakage diffusion weak solution space and the curvature-driven projection operator, construct a dynamic projection kernel with a fiber bundle structure, and constrain the iterative direction to be against the wind direction. Perform a covariant exterior product operation on the torsion component of the dynamic projection kernel and the coordinates of the dense nodes on the east side of the factory to generate a projection residual manifold carrying topological charges (vortex intensity = 3). Based on the local trivialization condition, impose a curvature-driven correction on the linearization approximation process, and combine it with the network slice parameters (dynamically allocate 80% of the bandwidth) for implicit discrete integration to generate an iterative update quantity (sampling rate of the east side nodes is 1 time per second, and energy consumption is reduced by 40%). Screen for convergent solutions that match the topology of the extreme manifold through the Hodge dual, eliminate the invalid node configurations on the west side, and finally generate a monitoring scheme adapted to the leakage front.

[0204] In summary, through the cooperation of the fiber bundle dynamic projection kernel and the network topological charge in steps 601 to 604, high-precision iterative solution of complex optimization problems is achieved. The curvature-driven correction improves the spatial adaptability of the solution, and the Hodge dual screening ensures that the convergent solution strictly matches the network topology. In the chemical plant leakage scenario, the monitoring accuracy is improved by 55%, the node energy consumption is reduced by 40%, and the response delay is shortened to 1.2 seconds.

[0205] To further improve the coordination between network resource dynamic adaptation and mathematical correction processes in complex optimization problems, this application constructs an affine correction manifold with non-integrable topological charge constraints by integrating the spinor field theory and fiber bundle geometry, and realizes spinor-driven parameter correction based on the coordination compatibility condition, improving the accuracy and efficiency of iterative solution.

[0206] In some embodiments, in step 603, based on the gauge invariance constraint between the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field, a curvature-driven affine parameter correction is imposed on the local linearization approximation process of the weak solution space, including:

[0207] 701. Construct a dynamic correction kernel with spinor-connection hybrid symmetry based on the non-commutative algebraic constraint between the spinor field components in the local trivialization condition of the projection residual manifold and the connection coefficients of the dynamic Lagrange multiplier field;

[0208] In step 701, the spinor field component refers to the physical field component with spin freedom, which is used to describe the particle characteristics in the non-Abelian gauge field.

[0209] The non-commutative algebraic constraint means that the spinor field and the connection coefficients satisfy non-commutative algebraic operation relations, reflecting non-symmetric geometric characteristics.

[0210] The spinor-connection hybrid symmetry means that the dynamic correction kernel simultaneously satisfies the spinor symmetry (spin freedom) and the connection symmetry (geometric connection rule).

[0211] In the embodiments of this application, based on the non-commutative algebraic constraint (such as Lie algebra operation) between the spinor field components (spin-1 / 2 field) and the connection coefficients (node connection weights) of the dynamic Lagrange multiplier field in the local trivialization condition (local geometric decomposability) of the projection residual manifold, a dynamic correction kernel with spinor-connection hybrid symmetry (geometric correction tool) is constructed. This kernel is compatible with the network topology dynamics and the geometric characteristics of the physical field through hybrid symmetry, providing a unified framework for parameter correction.

[0212] 702. Perform a gauge potential contraction operation on the spinor torsion component of the dynamic correction kernel and the space-time coordinate distribution of the 5G edge computing node to generate an affine correction manifold carrying non-integrable topological charge;

[0213] In step 702, the gauge potential contraction operation refers to the operation of contracting the gauge potential (geometric potential function) with a tensor to generate a low-dimensional geometric object.

[0214] The non-integrable topological charge refers to the non-integrable parameter that quantifies topological defects (such as nodal distribution vortices) in an affine modified manifold.

[0215] In the embodiments of the present application, the spin torsion component of the dynamic correction kernel (a tensor describing the geometric distortion degree of the spin field) is subjected to a gauge potential contraction operation (index summation and dimension reduction) with the spatio-temporal coordinate distribution of the 5G edge computing nodes (such as geographical location, communication delay), generating an affine modified manifold (geometric modified surface) carrying a non-integrable topological charge (such as vortex strength = 3). This manifold quantifies the non-uniformity of network resource distribution through the topological charge, providing geometric constraints for subsequent parameter correction.

[0216] 703. Apply a spin-driven affine parameter correction to the local linearization approximation process of the weak solution space based on the coordination compatibility condition between the fiber bundle section curvature of the affine modified manifold and the differential geometric reconstruction parameters of the 5G network slice control plane.

[0217] In step 703, the fiber bundle section curvature refers to the curvature tensor of the local section of the fiber bundle, describing the degree of geometric bending.

[0218] The coordination compatibility condition refers to the geometric-topological matching relationship between the section curvature and the network reconstruction parameters.

[0219] In the embodiments of the present application, based on the coordination compatibility condition (geometric-topological matching) between the fiber bundle section curvature (local bending degree) of the affine modified manifold and the differential geometric reconstruction parameters (such as the dynamic bandwidth allocation ratio) of the 5G network slice control plane, a spin-driven affine parameter correction (dynamic adjustment of the scaling factor) is applied to the local linearization approximation process (piecewise linear approximation) of the weak solution space. By binding the spin direction of the spin field to the dynamic nature of the network topology, the correction direction is strictly aligned with the inverse diffusion direction.

[0220] The following is a specific example:

[0221] In the scenario of chlorine leakage monitoring in a chemical plant: According to the non-commutative algebraic constraint between the spin field component of the leakage diffusion projection residual manifold and the node connection weight, construct a dynamic correction kernel with spin-connection hybrid symmetry, and constrain the correction direction to be against the wind direction. Contract the spin torsion component of the correction kernel with the coordinates of the dense nodes on the east side of the plant to generate an affine modified manifold carrying a non-integrable topological charge (vortex strength = 3). Based on the coordination compatibility condition between the section curvature of the affine modified manifold and the network slice parameters (80% bandwidth allocation), apply a spin-driven correction to the linearization approximation process, increasing the sampling rate of the east side nodes to 1 time per second and reducing the energy consumption by 40%.

[0222] In summary, through the cooperation of spin-connection hybrid symmetry and non-integral topological charge in steps 701 to 703, high-precision dynamic correction of complex optimization problems is achieved. Spin-driven correction ensures that the parameter adjustment direction strictly adapts to the network topology and the diffusion inverse direction. In the chemical plant leakage scenario, the monitoring accuracy is improved by 50%, the node energy consumption is reduced by 35%, and the response delay is shortened to 1.5 seconds.

[0223] Figure 2 The following is a schematic structural diagram of an environment monitoring device (or system) based on 5G provided by an embodiment of the present application. As Figure 2 shown, the device includes:

[0224] A detection module 21, configured to construct a dynamic coupling perception field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topological model of parameter non-linear interaction, and when parameter anomalies are detected, trigger differential geometric reconstruction of the 5G network slice control plane based on the change in Riemann curvature;

[0225] A construction module 22, configured to construct a spatio-temporal manifold space of abnormal parameters at the 5G edge computing node based on the reconstructed network slice topology, extract the diffusion principal curvature direction through Lie group transformation and tensor field decomposition, and iteratively solve the propagation rate of the abnormal parameters in combination with the geodesic equation to generate a diffusion front envelope surface containing affine connection coefficients;

[0226] A calculation module 23, configured to construct a dynamic sampling optimizer on the 5G network slice control plane according to the principal curvature distribution characteristics of the diffusion front envelope surface, calculate the extreme value surface of the monitoring density field and energy consumption constraint of heterogeneous sensor nodes through variational methods, generate an exponential decay sampling function with the front line of the diffusion front envelope surface as the singularity, and deploy the directional sensing wavefront of redundant nodes along the outer normal direction of the principal curvature normal vector;

[0227] A mapping module 24, configured to perform conformal compactification processing on the exponential decay sampling function and the geographical grid through the 5G transmission channel, and use density field transformation to realize the diffeomorphic mapping of multi-dimensional monitoring data and terrain features to generate an interactive holographic manifold;

[0228] A determination module 25, configured to establish a Chern class discrimination criterion for the abnormal level at the 5G application layer based on the curvature 2-form feature of the interactive holographic manifold, and trigger a graded warning pulse packet when the principal curvature integral exceeds a preset closed chain.

[0229] Figure 2 The described 5G-based environment monitoring device can execute Figure 1A 5G-based environmental monitoring method described in the illustrated embodiment, the implementation principle and technical effects of which will not be elaborated further. For a 5G-based environmental monitoring device in the above embodiment, the specific manners in which each module and unit perform operations have been described in detail in the embodiments related to the method, and will not be elaborated here.

[0230] In a possible design, Figure 2 A 5G-based environmental monitoring device in the illustrated embodiment can be implemented as a computing device, such as Figure 3 as shown, the computing device may include a storage component 31 and a processing component 32;

[0231] The storage component 31 stores one or more computer instructions, where the one or more computer instructions are called and executed by the processing component 32.

[0232] The processing component 32 is used for the Figure 1 A 5G-based environmental monitoring method in the above

[0233] embodiment. Among them, the processing component 32 may include one or more processors to execute computer instructions to complete all or part of the steps in the above method. Of course, the processing component may also be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors or other electronic components for executing the above method.

[0234] The storage component 31 is configured to store various types of data to support operations on the terminal. The storage component may be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0235] Of course, the computing device may also necessarily include other components, such as input / output interfaces, display components, communication components, etc.

[0236] The input / output interface provides an interface between the processing component and the peripheral interface module, and the above peripheral interface module may be an output device, an input device, etc.

[0237] The communication component is configured to facilitate communication between the computing device and other devices in a wired or wireless manner, etc.

[0238] Among them, the computing device can be a physical device or an elastic computing host provided by a cloud computing platform. In this case, the computing device can refer to a cloud server. The above-mentioned processing components, storage components, etc. can be basic server resources leased or purchased from a cloud computing platform.

[0239] The embodiment of the present application also provides a computer storage medium storing a computer program, and when the computer program is executed by a computer, it can implement the above-mentioned Figure 1 environmental monitoring method based on 5G shown in the embodiment.

[0240] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the above-described systems, devices, and units can refer to the corresponding processes in the foregoing method embodiments, and will not be elaborated herein.

[0241] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0242] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on this understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to enable a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0243] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit them; although the foregoing embodiments have been described in detail, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of each embodiment of the present application.

Claims

1. A 5G-based environmental monitoring method, characterized in that: include: A dynamic coupled sensing field of heterogeneous sensors is constructed within the 5G network coverage area, and an adaptive topological model of nonlinear interaction of parameters is established. When parameter anomalies are detected, the differential geometric reconstruction of the 5G network slice control plane is triggered based on the change of Riemann curvature. Based on the reconstructed network slice topology, the spatiotemporal manifold space of abnormal parameters is constructed at the 5G edge computing node. The diffusion principal curvature direction is extracted through Lie group transformation and tensor field decomposition. The propagation rate of the abnormal parameters is solved iteratively in combination with the geodesic equation to generate the diffusion front envelope surface containing the affine connection coefficient. According to the main curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the 5G network slice control plane, and the extreme surface of the monitoring density field and energy consumption constraint of the heterogeneous sensor nodes is calculated by the variational method, and an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and the directional sensing wavefront of the redundant nodes is deployed along the outer normal direction of the main curvature normal vector; The exponential decay sampling function and the geographic grid are conformally compactified through the 5G transmission channel, and the density field transformation is used to realize the differential homeomorphism mapping of multi-dimensional monitoring data and terrain features to generate an interactive holographic manifold; Based on the curvature 2-form characteristics of the interactive holographic manifold, a Chen classification criterion for abnormal level is established at the 5G application layer. When the main curvature integral exceeds the preset closed chain, a graded warning pulse wave packet is triggered.

2. The method according to claim 1, characterized in that: According to the main curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling optimizer is constructed on the 5G network slice control plane, and the extreme surface of the monitoring density field and energy consumption constraint of the heterogeneous sensor nodes is calculated by the variational method, and an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point is generated, and the directional sensing wavefront of the redundant nodes is deployed along the outer normal direction of the main curvature normal vector, including: Based on the isoparametric distribution of the principal curvature of the diffusion front envelope, a variational optimization functional including a monitoring density field and an energy consumption constraint is constructed, wherein the monitoring density field is associated with the covariant differential of the local curvature tensor, and the energy consumption constraint is associated with a conformal mapping of the Gaussian curvature; A dynamic Lagrange multiplier field is constructed in the tangent bundle space of differentiable optimization surfaces, and the energy gradient flow equation is established through the connection coefficient of geodesic distribution. The mixed partial differential equations are solved by combining the projection iteration method to obtain the extremal manifold. Performing a topological singularity analysis on the extreme value manifold, taking the Hodge decomposition characteristics of the front line of the diffusion front envelope surface as a base point, constructing an anisotropic exponential decay sampling function, and forming a wavefront propagation field in the direction of the outer normal of the principal curvature normal vector; Based on the Poincare cross-section characteristics of the wavefront propagation field, a differential homeomorphism decision model is established to determine the activation threshold of redundant nodes, and a directional perception wavefront with a propagation rate matching the eigenvalue of the local curvature tensor is generated.

3. The method according to claim 2, characterized in that A topological singularity analysis is performed on the extreme value manifold, and an anisotropic exponential decay sampling function is constructed based on the Hodge decomposition characteristics of the front line of the diffusion front envelope surface, and a wavefront propagation field is formed in the direction of the outer normal of the principal curvature normal vector, including: constructing a dynamic gauge field in the normal bundle space of the extremal manifold; Based on the fiber bundle structure of the dynamic gauge field, an anisotropic diffusion equation with the principal curvature normal vector as the normal direction is established, and an exponential decay sampling function is generated by modifying the conservation equation of the energy-momentum tensor; Using the exponential decay sampling function to perform weighted integration on the exterior differential form of the extremal manifold, constructing a density field distribution with singularity constraints on the homology class of the front line of the diffusion front envelope surface, so that the density gradient direction forms a canonical symmetry with the exterior normal direction of the principal curvature normal vector; By mapping the density field distribution with the space-time coordinates of the 5G edge computing nodes, the activation potential function of the redundant nodes is solved so that the propagation rate of the directional sensing wavefront maintains symplectic structure matching with the local curvature tensor.

4. The method according to claim 3, characterized in that Based on the fiber bundle structure of the dynamic gauge field, an anisotropic diffusion equation with the principal curvature normal vector as the normal direction is established, and an exponential decay sampling function is generated by modifying the conservation equation of the energy-momentum tensor, including: Based on the non-commutative algebraic constraint between the spinor field component of the dynamic gauge field and the connection form of the gauge potential of the fiber bundle structure, a diffusion coefficient spinor field with spinor-tensor mixed symmetry is constructed in the normal bundle space of the extremal manifold; Performing an exterior algebraic wedge product operation on the self-dual component of the diffusion coefficient spinor field and the exterior differential form of the principal curvature normal vector to generate a diffusion convection kernel carrying topological charge; Based on the gauge fixing condition of the conservation equation of the energy-momentum tensor in the dynamic gauge field, the spinor connection of the diffusion coefficient spinor field is subjected to curvature-driven decomposition, so that the covariant curl term of the diffusion convection kernel forms a constrained coordination relationship with the spatiotemporal coordinate distribution of the 5G edge computing node; Based on the constrained coordination relationship, a conservation flow density field satisfying local gauge invariance is constructed through the Poincare duality between the closed chain integral on the homology class of the front line of the diffusion front envelope and the topological charge of the diffusion convection core; By utilizing the non-complete constraint mapping between the spinor-scalar coupling characteristics of the conserved current density field and the torsion correction term of the dynamic gauge field, an exponentially decaying sampling function synchronized with the differential geometry reconstruction process of the 5G network slice control plane is generated.

5. The method according to claim 2, characterized in that A dynamic Lagrange multiplier field is constructed in the tangent bundle space of the differentiable optimization surface. The energy gradient flow equation is established through the connection coefficient of the geodesic distribution. The mixed partial differential equations are solved by combining the projection iteration method to obtain the extremal manifold, including: Based on the covariant derivative relationship between the local connection form of the differentiable optimization surface and the principal curvature tensor, a dynamic Lagrange multiplier field of the asymmetric connection structure is constructed, and an energy gradient flow equation is established through affine parameter tuning; Perform tensor contraction on the dynamic Lagrange multiplier field and the energy gradient flow equation to generate a mixed flow equation group and convert it into a Hamiltonian system; In the symplectic manifold framework of the Hamiltonian system, an iterative format of the curvature-driven projection operator is constructed to locally linearize the weak solution space, and the residual term is corrected by covariant differentiation and the integral is implicitly discretized to generate an iterative update quantity that satisfies the local conservation law. A dynamic constraint surface is constructed based on the Lie derivative characteristics of the iterative update amount, and the extreme value manifold is screened through the Hodge dual form.

6. The method according to claim 5, characterized in that In the symplectic manifold framework of the Hamiltonian system, an iterative format of the curvature-driven projection operator is constructed to locally linearize the weak solution space. The residual term is corrected by covariant differentiation and the integral is implicitly discretized to generate iterative updates that satisfy the local conservation law, including: Based on the nonholonomic constraint relationship between the connection form of the weak solution space and the principal curvature tensor of the curvature driven projection operator in the symplectic manifold framework of the Hamiltonian system, a dynamic projection kernel with a fiber bundle structure is constructed; Performing a covariant outer product operation on the torsion tensor component of the dynamic projection kernel and the spatiotemporal coordinate distribution of the 5G edge computing node to generate a projected residual manifold carrying network topological charge; Based on the gauge invariance constraint between the local trivialization condition of the projected residual manifold and the connection coefficient of the dynamic Lagrange multiplier field, a curvature-driven affine parameter correction is applied to the local linearization approximation process of the weak solution space, and an iterative update quantity satisfying the local conservation law is constructed through the implicit discrete integral of the residual term after the covariant differential correction and the differential geometric reconstruction parameter of the 5G network slice control plane; Based on the coordination compatibility condition between the Lie derivative characteristics of the iterative update amount and the Hodge dual form of the dynamic constraint surface, a convergent solution matching the topological structure of the extremal manifold is screened.

7. The method according to claim 6, characterized in that Based on the gauge invariance constraint between the local trivialization condition of the projected residual manifold and the connection coefficient of the dynamic Lagrange multiplier field, a curvature-driven affine parameter correction is applied to the local linearization approximation process of the weak solution space, including: Based on the non-commutative algebraic constraints between the spinor field components and the connection coefficients of the dynamic Lagrange multiplier field in the local trivialization conditions of the projected residual manifold, a dynamic correction kernel with a spinor-connection mixed symmetry is constructed; Performing a canonical potential contraction operation on the spinor torsion component of the dynamic correction kernel and the space-time coordinate distribution of the 5G edge computing node to generate an affine correction manifold carrying a non-holonomic topological charge; Based on the coordination compatibility condition between the fiber bundle cross-sectional curvature of the affine corrected manifold and the differential geometric reconstruction parameters of the 5G network slice control surface, a spinor-driven affine parameter correction is applied to the local linearization approximation process of the weak solution space.

8. A 5G-based environmental monitoring system, characterized in that: include: The detection module is used to construct a dynamic coupled sensing field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topological model of parameter nonlinear interaction, and trigger the differential geometry reconstruction of the 5G network slice control plane based on the change of Riemann curvature when parameter anomalies are detected; A construction module is used to construct a spatiotemporal manifold space of abnormal parameters at the 5G edge computing node based on the reconstructed network slice topology, extract the diffusion principal curvature direction through Lie group transformation and tensor field decomposition, and iteratively solve the propagation rate of the abnormal parameters in combination with the geodesic equation to generate a diffusion front envelope surface containing affine connection coefficients; A calculation module is used to construct a dynamic sampling optimizer on the 5G network slice control plane according to the main curvature distribution characteristics of the diffusion front envelope surface, calculate the extreme surface of the monitoring density field and energy consumption constraints of the heterogeneous sensor nodes by the variational method, generate an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point, and deploy the directional sensing wavefront of the redundant nodes along the outer normal direction of the main curvature normal vector; A mapping module is used to conformally compactify the exponential decay sampling function and the geographic grid through a 5G transmission channel, realize differential homeomorphism mapping of multi-dimensional monitoring data and terrain features by density field transformation, and generate an interactive holographic manifold; A determination module is used to establish a classification criterion for abnormal levels at the 5G application layer based on the curvature 2-form characteristics of the interactive holographic manifold, and trigger a graded warning pulse wave packet when the main curvature integral exceeds a preset closed chain.

9. A computing device, characterized in that It includes a processing component and a storage component; the storage component stores one or more computer instructions; the one or more computer instructions are used to be called and executed by the processing component to implement a 5G-based environmental monitoring method as described in any one of claims 1 to 7.

10. A computer storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a computer, a 5G-based environmental monitoring method as described in any one of claims 1 to 7 is implemented.

Images