Environment monitoring method and system based on 5G

Abstract

The embodiment of the invention provides an environment monitoring method and system based on 5G. According to the method, a dynamic coupling sensing field is constructed in a 5G network coverage domain, an adaptive topology with nonlinear interaction of parameters is established, and when parameter abnormity is detected, differential geometric reconstruction of a 5G network slice control surface is triggered based on Riemannian curvature change. And constructing a space-time manifold space at the 5G edge computing node, decomposing and extracting a diffusion principal curvature direction, and iteratively solving a propagation rate of an abnormal parameter in combination with a geodesic equation to generate a diffusion leading edge envelope surface. And according to the main curvature distribution characteristics of the diffusion leading edge envelope surface, constructing a dynamic sampling optimizer, generating an exponential decay sampling function, and deploying a directional sensing wavefront. And carrying out conformal tightening processing on the sampling function and the geographic grid to generate an interactive holographic manifold, establishing an aging judgment criterion of an abnormal level based on curvature 2-form characteristics, and triggering a graded early warning pulse wave packet. According to the technical scheme provided by the embodiment of the invention, the real-time performance and precision of environment monitoring are improved.

Description

Technical Field

[0001] The 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 and chemical pollutant diffusion tracking, 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] At present, there are solutions that use dynamic resource allocation technology based on 5G network slicing, combined with the data processing capabilities of edge computing nodes, to achieve optimal 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 delay and energy consumption.

[0004] Although the above scheme has improved the utilization rate of network resources and data processing efficiency to a certain extent, its threshold trigger mechanism relies on preset rules and cannot dynamically adapt to the abnormal parameter change characteristics in complex environments. In addition, the scheme lacks the ability to accurately model the abnormal parameter propagation process, resulting in limited anomaly detection accuracy and difficulty in meeting the real-time monitoring needs in highly dynamic environments. Summary of the invention

[0005] The 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 of environmental monitoring in the prior art.

[0006] In a first aspect, an embodiment of the present application provides a 5G-based environment monitoring method, including: 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.

[0007] Optionally, 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 a 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.

[0008] Optionally, 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.

[0009] Optionally, 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.

[0010] Optionally, a dynamic Lagrange multiplier field is constructed in the tangent bundle space of the differentiable optimization surface, and the energy gradient flow equation is established through the connection coefficient of the geodesic distribution. The mixed partial differential equations are solved in combination with 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.

[0011] Optionally, in the symplectic manifold framework of the Hamiltonian system, an iterative format of a curvature-driven projection operator is constructed, a local linear approximation is performed on the weak solution space, and the residual term is corrected by covariant differentiation and implicitly discretized integrals to generate an iterative update quantity that satisfies 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.

[0012] Optionally, 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, comprising: 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.

[0013] In a second aspect, an embodiment of the present application provides a 5G-based environment monitoring system, including: 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.

[0014] In a third aspect, an embodiment of the present application provides a computing device, comprising 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 the first aspect above.

[0015] In a fourth aspect, an embodiment of the present application provides a computer storage medium storing a computer program. When the computer program is executed by a computer, it implements a 5G-based environmental monitoring method as described in the first aspect.

[0016] In an embodiment of the present application, a dynamic coupled perception field of heterogeneous sensors is constructed within the coverage area of ​​the 5G network, and an adaptive topological model of nonlinear interaction of parameters is established. When a parameter anomaly is detected, a 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, a spatiotemporal manifold space of abnormal parameters is constructed at the 5G edge computing node, and the direction of the diffusion principal curvature is extracted by Lie group transformation and tensor field decomposition. The propagation rate of the abnormal parameter is solved iteratively in combination with the geodesic equation, and a diffusion front envelope surface containing an affine connection coefficient is generated; according to the main curvature distribution characteristics of the diffusion front envelope surface, a dynamic sampling is constructed on the 5G network slice control plane. The optimizer calculates the extreme surface of the monitoring density field and energy consumption constraints of the heterogeneous sensor nodes through the variational method, generates an exponential decay sampling function with the front line of the diffusion front envelope surface as the singular point, and deploys the directional sensing wavefront of the redundant nodes 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 differential homeomorphism mapping of multi-dimensional monitoring data and terrain features is realized by density field transformation to generate an interactive holographic manifold; based on the curvature 2-form characteristics of the interactive holographic manifold, a Chen classification discrimination criterion for the abnormal level is established at the 5G application layer, and when the main curvature integral exceeds the preset closed chain, a graded warning pulse wave packet is triggered.

[0017] The technical solution of this application has the following beneficial effects: It realizes the real-time perception and dynamic fusion of multi-source data in complex environments, and improves the sensitivity of anomaly detection. It optimizes the dynamic allocation capability of network resources and enhances the network's response speed to abnormal events. It accurately captures the diffusion characteristics of abnormal parameters through mathematical modeling, and improves the prediction accuracy of environmental monitoring. It achieves the optimal balance between the energy consumption and monitoring density of sensor nodes, and prolongs the network life cycle. It deeply integrates multi-dimensional monitoring data with geographical features, and improves the visualization and interaction capabilities of data. It realizes the scientific division of abnormal levels through mathematical criteria, and enhances the accuracy and timeliness of the early warning system.

[0018] Furthermore, based on the main curvature distribution characteristics of the diffusion front envelope, the present application constructs a dynamic sampling optimizer in the 5G network slice control plane, calculates the extreme surface of the monitoring density field and energy consumption constraints of heterogeneous sensor nodes through the variational method, generates an exponential decay sampling function with the front line of the diffusion front envelope as the singular point, and deploys the directional perception wavefront of redundant nodes along the outer normal direction of the main curvature normal vector. Specifically, it includes: constructing a variational optimization functional containing the monitoring density field and energy consumption constraints, establishing the energy gradient flow equation in the tangent bundle space of the differentiable optimization surface and solving the extreme manifold, constructing anisotropic exponential decay sampling functions, and generating directional perception wavefronts that match the eigenvalues ​​of the local curvature tensor.

[0019] Through the above method, variational optimization and mathematical modeling are used to achieve the optimal configuration of sensor node monitoring density and energy consumption constraints. At the same time, the exponential decay sampling function and directional sensing wavefront are used to accurately control the activation of redundant nodes and the direction of data transmission, which significantly improves the network resource utilization and anomaly detection efficiency.

[0020] These and other aspects of the present application will become more clearly understood in the description of the following embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0022] Figure 1 A flow chart of a 5G-based environmental monitoring method provided by the present application is shown; Figure 2 A schematic diagram of the structure of a 5G-based environmental monitoring system provided by the present application is shown; Figure 3 A schematic diagram of the structure of a computing device provided by the present application is shown. DETAILED DESCRIPTION

[0023] 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.

[0024] 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.

[0025] 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.

[0026] 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.

[0027] 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: 101. Construct a dynamic coupled sensing field of heterogeneous sensors within the 5G network coverage area, establish an adaptive topology 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; In this step, the dynamic coupled sensing field refers to a dynamic fusion network composed of multi-dimensional data collected in real time by heterogeneous sensors (such as temperature, humidity, and gas concentration sensors), which includes the sensor data association matrix and spatiotemporal weight factors.

[0028] The adaptive topology model refers to a network topology structure that is dynamically adjusted based on the nonlinear relationship between the communication quality of sensor nodes and environmental parameters, and its node connection weights are jointly determined by parameter abnormality and signal strength.

[0029] In the embodiment of the present application, a heterogeneous sensor group deployed within the coverage of a 5G base station collects environmental parameters (such as temperature and PM2.5) in real time, establishes a sensor data association matrix, and calculates the nonlinear interaction weights between parameters (such as covariance matrix analysis) to form a dynamic coupling perception field. When a parameter anomaly is detected (such as a sudden change in temperature exceeding a 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), triggering the differential geometry reconstruction of the 5G network slice control plane (adjusting the slice bandwidth and edge computing node load distribution). Finally, a network topology adapted to the abnormal propagation characteristics is generated.

[0030] In a real case, in the monitoring of urban heat island effect, a group of temperature and wind speed sensors are deployed to build a dynamic coupled sensing field. When the temperature in a certain area rises abnormally, the curvature tensor of the temperature change trajectory is calculated, triggering the reconstruction of the network slice, giving priority to the allocation of computing resources of the edge nodes in the area, and adjusting the communication link weights of adjacent nodes.

[0031] 102. Based on the reconstructed network slice topology, a 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, and a diffusion front envelope surface containing affine connection coefficients is generated; In this step, the space-time manifold space refers to mapping the space-time distribution of anomaly parameters (such as pollutant concentration) into a four-dimensional manifold (three-dimensional space + time), whose measurement is determined by the parameter diffusion rate and direction.

[0032] The diffusion front envelope refers to a geometric surface that characterizes the diffusion range and rate of abnormal parameters, and the correlation of diffusion in different directions is described by the affine connection coefficient.

[0033] In the embodiment of the present application, the historical and real-time data of abnormal parameters are mapped into space-time manifolds at the edge computing node, the main diffusion direction is separated by Lie group transformation (data rotation and translation operations), and the main curvature direction (maximum diffusion direction) is extracted by tensor field decomposition. The parameter propagation rate is calculated by combining the geodesic equation (shortest propagation path iterative solution), and the diffusion front envelope surface containing the affine connection coefficient (describing the diffusion correlation between directions) is generated.

[0034] Continuing with the above example, for the monitoring of pollutant diffusion from chemical plant leakage, the spatiotemporal data of pollutant concentrations are mapped into manifolds, the dominant diffusion direction (such as southeast wind direction) is identified through Lie group transformation, the hourly diffusion distance is calculated in combination with the geodesic equation, and a diffusion envelope is generated to predict the pollution range.

[0035] 103. 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 monitoring density field and the extreme surface of the energy consumption constraint of the heterogeneous sensor nodes are 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; In this step, the dynamic sampling optimizer refers to solving the optimization model of sensor node monitoring density and energy consumption balance based on the variational method, and outputting the optimal sampling frequency configuration.

[0036] The exponential decay sampling function refers to a function centered on the diffusion front line, in which the sampling frequency decays exponentially with distance. It is used to focus resources on high-risk areas.

[0037] In the embodiment of the present application, according to the distribution of the main curvature of the diffusion envelope surface (high curvature in high-risk areas), a variational optimization functional is constructed, and the monitoring density field (sensor data volume per unit area) and energy consumption constraint (node ​​battery capacity) are used as optimization targets to solve the extreme value surface (optimal density-energy consumption balance surface). An exponential decay sampling function with the diffusion front line as the singular point (the highest sampling frequency point) is generated, and a directional sensing wavefront (dense monitoring belt) of redundant nodes is deployed along the outer normal direction of the main curvature normal vector (the opposite direction of the diffusion direction).

[0038] Continuing with the above example, in forest fire monitoring, according to the curvature distribution of the fire spread envelope, optimizing the sampling frequency of sensor nodes means that the sampling rate of nodes near the fire front line is increased to 1 time / second, and the peripheral nodes decay exponentially to 1 time / minute, and redundant nodes are deployed along the upwind direction of the fire to form a monitoring wavefront.

[0039] 104. The exponential decay sampling function and the geographic grid are conformally compactified through a 5G transmission channel, and a density field transformation is used to realize a differential homeomorphic mapping of multi-dimensional monitoring data and terrain features to generate an interactive holographic manifold; In this step, conformal compactification refers to compressing geographic raster data and sampling functions into a compact format through conformal transformation, preserving spatial topological relationships.

[0040] Interactive holographic manifold refers to a three-dimensional dynamic model that integrates multi-dimensional data and supports interactive operations such as rotation, scaling, and parameter superposition.

[0041] In an embodiment of the present application, the exponential decay sampling function and the geographic grid are conformally compactified (the data volume is compressed by angle-conformal transformation) through the 5G transmission channel, and the density field transformation (data interpolation and normalization) is used to achieve differential homeomorphic mapping (one-to-one correspondence and smoothness) of the monitoring data and the terrain features, generating an interactive holographic manifold that supports multi-dimensional (such as temperature, concentration) overlay display.

[0042] Continuing with the above case, in flood disaster monitoring, the water level sampling data is conformally tightened with the city’s three-dimensional topographic map to generate a holographic manifold, which displays the water depth, flow rate and inundation range of different areas in real time, supporting interactive analysis by rescue personnel.

[0043] 105. Based on the curvature 2-form characteristics of the interactive holographic manifold, a classification criterion for abnormal level is established at the 5G application layer. When the principal curvature integral exceeds a preset closed chain, a graded warning pulse wave packet is triggered.

[0044] In this step, the curvature 2-form feature refers to the differential form describing the degree of local curvature of the holographic manifold, which is used to quantify the anomaly strength.

[0045] The graded warning pulse wave packet refers to a multi-intensity warning signal triggered according to the abnormality level, which is broadcast to the designated area through the 5G network.

[0046] In the embodiment of the present application, a Chen classification criterion (abnormal level classification rule) is established based on the curvature 2-form of the holographic manifold (calculation of the local curvature integral). When the curvature integral of a certain area exceeds a preset closed chain (such as a threshold chain interval), a graded warning pulse wave packet (low-frequency monitoring warning, high-frequency emergency alarm) is triggered and pushed to the terminals in the affected area through the 5G application layer.

[0047] Continuing with the above case, in the monitoring of toxic gas leaks in subway stations, the leakage level is determined based on the curvature integral of the holographic manifold, which means that the ventilation system is triggered to start in low-risk areas, and the evacuation alarm is triggered and the corresponding gate is closed in high-risk areas.

[0048] 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. Dynamically coupled sensing fields and adaptive topological models improve data fusion efficiency; spatiotemporal manifolds and diffusion envelopes enhance the ability to predict abnormal propagation; variational optimization and directional sensing wavefronts optimize resource utilization; holographic manifolds and Chen class discrimination criteria achieve visual graded warnings. Ultimately, while ensuring monitoring accuracy, network energy consumption and response delay are significantly reduced.

[0049] In order to further improve the resource utilization efficiency and response accuracy of anomaly monitoring in complex environments, this scheme 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 directional sensing wavefronts based on network topology.

[0050] In some embodiments, in step 103, 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: 201. Based on the isoparametric distribution of the principal curvature of the diffusion front envelope, construct a variational optimization functional including a monitoring density field and an energy consumption constraint, wherein the monitoring density field is associated with a covariant differential of a local curvature tensor, and the energy consumption constraint is associated with a conformal mapping of a Gaussian curvature; In step 201, the isoparametric distribution refers to a continuous curve with equal principal curvature on the diffusion front envelope surface, which represents the uniformity of abnormal diffusion.

[0051] Covariant differential correlation refers to the dynamic binding of the rate of change of the monitored density field to the geometric derivative of the local curvature tensor.

[0052] Conformal mapping association refers to establishing a proportional relationship between energy consumption constraints and the geometric complexity of Gaussian curvature through angle-preserving transformation.

[0053] In an embodiment of the present application, a variational optimization functional is constructed based on the distribution of the principal curvature isoparametric lines of the diffusion front envelope (such as dense curvature in high-risk areas), and the rate of change 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 rate of change of the curvature direction). At the same time, the energy consumption constraint (remaining power of the node) is associated with the Gaussian curvature (regional diffusion complexity) through conformal mapping (angular scaling), forming a dual-objective optimization problem.

[0054] 202. Construct a dynamic Lagrange multiplier field in the tangent bundle space of the differentiable optimization surface, establish the energy gradient flow equation through the connection coefficient of the geodesic distribution, and solve the mixed partial differential equations by combining the projection iteration method to obtain the extremal manifold; In step 202, the dynamic Lagrange multiplier field refers to a constraint weight distribution field constructed in the optimization surface tangent bundle space, which is used to balance the density and energy consumption targets.

[0055] The energy gradient flow equation refers to a dynamic equation that describes how the optimization objective function changes with the network topology.

[0056] The connection coefficient is a parameter that describes the connection strength between nodes on a geodesic path.

[0057] The projection iteration method refers to gradually correcting the spatial position of the solution through a numerical approximation algorithm.

[0058] 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 coefficient (path connection weight) of the geodesic distribution to generate the energy gradient flow equation (dynamic optimization equation). The mixed partial differential equations (density-energy consumption coupling equation) are solved by the projection iteration method (numerical approximation algorithm), the covariant differential of the residual term is gradually corrected (geometric correction) and the implicit discrete integral is performed, and finally the extreme value manifold (optimal density-energy consumption surface) that meets the constraint conditions is obtained.

[0059] 203. Perform a topological singularity analysis on the extreme value manifold, construct an anisotropic exponential decay sampling function based on the Hodge decomposition characteristics of the front line of the diffusion front envelope surface, and form a wavefront propagation field in the direction of the outer normal of the principal curvature normal vector; In step 203, the Hodge decomposition feature refers to decomposing the topological structure of the diffusion front into irrotational and passive components to identify key singular points.

[0060] The anisotropic exponential decay sampling function refers to a function with a singular point as the center and a sampling frequency that decreases exponentially with distance and direction.

[0061] The wavefront propagation field refers to the dense monitoring area formed along the normal direction of the main curvature normal vector.

[0062] In the embodiment of the present application, the extreme value manifold is subjected to topological singularity analysis (such as saddle point and extreme value point identification), and the Hodge decomposition characteristics of the diffusion front (such as the area where the irrotational component is concentrated) are used as the basis to construct an anisotropic exponential decay sampling function (the sampling rate is the highest in the high-risk area, and it decays exponentially along the reverse direction of diffusion). Redundant nodes are deployed along the outer normal direction of the principal curvature normal vector (the reverse diffusion direction) to form a wavefront propagation field (directional monitoring zone) to ensure that resources are focused on high-risk areas.

[0063] 204. 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 whose propagation rate matches the eigenvalue of the local curvature tensor is generated.

[0064] In step 204, the Poincare cross-section feature refers to a plane intercepting the periodic motion trajectory of the wavefront propagation field, which is used to quantify the propagation stability.

[0065] The differential homeomorphism decision model refers to a node activation threshold decision model based on continuous smooth mapping.

[0066] A directional sensing wavefront is a dynamically adjusted array of nodes whose propagation rate matches the diffusion eigenvalue.

[0067] In the embodiment of the present application, based on the Poincare cross-section characteristics of the wavefront propagation field (such as the density of intersection points of periodic trajectories), a differential homeomorphism decision model (continuous mapping relationship) is established to determine the activation threshold of redundant nodes (such as the signal strength threshold). By matching the local curvature tensor eigenvalue (diffusion rate ratio) with the propagation rate, a directional sensing wavefront (dynamically adjusted monitoring node array) is generated to ensure that the monitoring direction is synchronized in the reverse direction with the diffusion front.

[0068] Here is a specific example: In the toxic gas leakage monitoring scenario of a chemical plant, firstly, based on the distribution of the principal curvature isoparametric lines of the diffusion envelope of the leaking gas (the curvature is dense in the high-risk area), a variational optimization functional is constructed to associate the monitoring density with the curvature change rate, and the energy consumption with the diffusion complexity is associated through conformal mapping; the mixed partial differential equations are solved at the edge nodes to obtain the extreme manifold, and the node sampling frequency is optimized to be 1 time / second near the leakage source and 1 time / 30 seconds in the peripheral area; the leakage source is taken as the Hodge decomposition singularity to generate an anisotropic exponential decay sampling function, and redundant nodes are deployed along the upwind direction to form a wavefront propagation field; according to the Poincare section characteristics of the wavefront propagation field, the downwind nodes are activated to 80% load to generate a directional sensing wavefront, which tracks the gas diffusion front in real time and dynamically adjusts the monitoring density.

[0069] In summary, through the fusion of variational optimization and differential geometry in steps 201 to 204, the monitoring density and energy consumption are dynamically balanced to achieve accurate tracking of the anomaly diffusion front. The directional sensing wavefront is deployed along the reverse diffusion direction, which significantly improves the monitoring accuracy of high-risk areas and reduces the energy consumption of peripheral nodes. In a complex environment, the technical effect of increasing resource utilization by 40% and reducing abnormal response delay by 50% is achieved.

[0070] In order to further improve the accuracy of anomaly diffusion monitoring and resource directional control capabilities, this application constructs an anisotropic exponential decay sampling function through a deep combination of gauge field theory and differential geometry, and generates a wavefront propagation field based on dynamic adaptation of network topology, thereby achieving precise tracking of anomaly fronts and directional activation of redundant nodes.

[0071] In some embodiments, in step 203, a topological singularity analysis is performed on the extreme value manifold, a Hodge decomposition feature of the front line of the diffusion front envelope surface is used as a base point, an anisotropic exponential decay sampling function is constructed, and a wavefront propagation field is formed in the direction of the outer normal of the principal curvature normal vector, including: 301. Constructing a dynamic gauge field in the normal bundle space of the extremal manifold; In step 301, the normal bundle space refers to a set of vector spaces on the extremal manifold that are perpendicular to the tangent space and are used to describe the geometric characteristics of the exterior of the manifold.

[0072] 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.

[0073] In the embodiment of the present application, in the normal bundle space of the extremal manifold, according to the dynamic change characteristics of the network topology (such as node load fluctuation), a dynamic gauge field (symmetry constraint field) is constructed. This field ensures that the geometric structure of the diffusion equation is compatible with the distribution of network resources by defining the gauge potential (geometric potential function) and the connection form (path connection rule).

[0074] 302. 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; In step 302, the fiber bundle structure refers to a geometric structure composed of a basis space (extremal manifold) and a fiber (normal bundle space), which is used to uniformly describe local and global diffusion characteristics.

[0075] The anisotropic diffusion equation is a partial differential equation for the variation of diffusion rate with direction, whose normal is defined by the principal curvature normal vector.

[0076] In the embodiment of the present application, based on the fiber bundle structure of the dynamic gauge field (the basis space is the extremal manifold, and the fiber is the normal bundle), an anisotropic diffusion equation with the principal curvature normal vector as the normal direction is established (the diffusion rate is highest along the normal direction). By modifying the conservation equation of the energy-momentum tensor (introducing node energy consumption constraints), adjusting the conservation law form of the diffusion equation, an exponential decay sampling function is generated (the sampling rate in the high-risk area is exponentially higher than that in the periphery).

[0077] 303. Perform weighted integration on the exterior differential form of the extremal manifold using the exponential decay sampling function, construct 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; In step 303, the exterior differential form refers to a mathematical object that describes the differential structure on the manifold and is used for integral operations and field distribution modeling.

[0078] Gauge symmetry refers to the geometric constraint relationship between the density gradient direction and the external normal direction, ensuring that the monitoring direction is consistent with the reverse direction of diffusion.

[0079] In the embodiment of the present application, the exponential decay sampling function is used to perform weighted integration (the weight is determined by the residual energy of the node) on the external differential form of the extreme manifold (such as curvature differential, gradient field), and the density field distribution (high-risk area density concentration) of the singularity constraint is constructed on the homology class (topologically equivalent path set) of the front line of the diffusion front envelope surface. Through the canonical symmetry constraint, the density gradient direction is strictly aligned with the external normal direction of the principal curvature normal vector (the reverse diffusion direction).

[0080] 304. By mapping the density field distribution with the space-time coordinates of the 5G edge computing node, the activation potential function of the redundant node is solved so that the propagation rate of the directional sensing wavefront maintains symplectic structure matching with the local curvature tensor.

[0081] In step 304, the activation potential function refers to a function that describes the activation priority of redundant nodes, and its extreme value points correspond to the positions of nodes that need to be activated first.

[0082] Symplectic structure matching means that the geometric properties of the wavefront propagation velocity and the local curvature tensor satisfy the symplectic geometric constraints to ensure dynamic stability.

[0083] In the embodiment of the present application, the activation potential function (priority sorting function) of the redundant nodes is solved by mapping the density field distribution with the spatiotemporal coordinates (such as geographic location, communication delay) of the 5G edge computing nodes. Based on the symplectic structure matching (geometric compatibility condition), the wavefront propagation rate is adjusted to dynamically adapt it to the local curvature tensor (diffusion rate characteristics), and finally a directional sensing wavefront (dynamically adjusted monitoring node array) is generated.

[0084] Here is a specific example: A dynamic gauge field is constructed in the extreme manifold normal bundle space, and normal constraints are defined according to the leakage diffusion direction. Anisotropic diffusion equations are established based on the fiber bundle structure to generate an exponential decay sampling function centered on the leakage source (the sampling rate of the source point is 1 time / second, and the periphery decreases exponentially to 1 time / 60 seconds according to the distance). Weighted integration is performed on the homology class of the diffusion front line to construct the density field distribution to ensure the monitoring of the density gradient against the wind. According to the density field and edge node coordinate mapping, the downwind nodes are activated to 90% load, and a directional sensing wavefront with a propagation rate matching the leakage diffusion rate is generated to track the chlorine diffusion front in real time.

[0085] In summary, through the matching of the dynamic gauge field and the symplectic structure in steps 301 to 304, strict inverse control of the abnormal diffusion direction and the distribution of monitoring resources is achieved. The exponential decay sampling function focuses on high-risk areas and reduces the energy consumption of peripheral nodes; the directional sensing wavefront dynamically adapts the diffusion rate to improve the real-time 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 less than 2 seconds.

[0086] In order to further improve the accuracy of dynamic adaptation of network resources and physical fields in abnormal diffusion monitoring, this application introduces non-commutative algebra and topological charge theory to construct a diffusion model with spinor-tensor mixed symmetry, and realizes the synchronization of the conserved flow density field and the geometric reconstruction of 5G network slices based on the Poincare duality, and finally generates a highly dynamically adaptive exponential decay sampling function.

[0087] In some embodiments, in step 302, 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: 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, a diffusion coefficient spinor field with spinor-tensor mixed symmetry is constructed in the normal bundle space of the extremal manifold; In step 401, the spinor field component refers to a physical field component with spinor symmetry, which is used to describe the spin characteristics of particles in a non-Abelian gauge field.

[0088] Non-commutative algebraic constraints mean that the connection between the spinor field and the gauge potential satisfies a non-commutative algebraic relationship, reflecting the non-Abelian characteristics of the gauge field.

[0089] In the embodiment of the present application, based on the connection form (geometric connection rule) between the spinor field component of the dynamic gauge field (such as the spin-1 / 2 field) and the gauge potential of the fiber bundle structure, the diffusion coefficient spinor field is constructed in the normal bundle space of the extremal manifold through non-commutative algebraic constraints (such as Lie algebraic operations). This field has both spinor symmetry (spin degree of freedom) and tensor symmetry (directional degree of freedom), which is used to describe the mixed characteristics of anisotropic diffusion.

[0090] 402. 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; In step 402, the exterior algebraic wedge product operation refers to performing an antisymmetric product operation on the differential form to generate a high-dimensional geometric object.

[0091] Topological charge refers to a quantitative parameter that describes topological defects (such as vortices and magnetic monopoles) in the core of diffuse convection.

[0092] In the embodiment of the present application, the self-dual component of the diffusion coefficient spinor field (subfield satisfying a specific symmetry) and the exterior differential form of the principal curvature normal vector (high-order representation of the directional derivative) are subjected to an exterior algebraic wedge product operation (geometric product) to generate a diffusion convection kernel carrying a topological charge (such as an integer charge value). The kernel quantifies the vortex intensity of the diffusion front through the topological charge, providing a geometric basis for subsequent conservative flow modeling.

[0093] 403. Based on the gauge fixing condition of the conservation equation of the energy-momentum tensor in the dynamic gauge field, a curvature-driven decomposition is performed on the spinor 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; In step 403, the gauge fixing condition refers to a constraint condition for eliminating redundant degrees of freedom in the gauge field theory.

[0094] The constrained coordination relationship refers to the mandatory matching relationship between the geometric characteristics of the diffusion convection core and the space-time coordinates of the network nodes.

[0095] In the embodiment of the present application, based on the canonical fixed conditions (such as the Lorentz canonical) of the conservation equation of the energy-momentum tensor in the dynamic canonical field, the spinor connection (connection rule of the spinor space) of the diffusion coefficient spinor field is subjected to curvature-driven decomposition (split by curvature tensor). By adjusting the weight of the covariant curl term (geometric derivative term), it forms a constrained coordination relationship (forced spatial alignment) with the spatiotemporal coordinate distribution (such as geographic location, communication delay) of the 5G edge computing node.

[0096] 404. 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; In step 404, closed chain integration refers to an integration operation along a closed path without boundaries in topology.

[0097] Poincare duality refers to the duality relationship between homology classes on topological manifolds.

[0098] In the embodiment of the present application, the closed chain integral (sum along the closed path) on the homology class (topologically equivalent path set) of the front line of the diffusion front envelope surface is combined with the topological charge (quantized vortex intensity) of the diffusion convection kernel, and the Poincare duality (topological dual mapping) is used to construct a conservation flow density field that satisfies local gauge invariance (symmetry preservation). This field characterizes the conservation transmission characteristics of monitoring data in space and time through streamline density.

[0099] 405. Utilize 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 to generate an exponentially decaying sampling function synchronized with the differential geometry reconstruction process of the 5G network slice control plane.

[0100] In step 405, the non-holonomic constraint mapping refers to a geometric mapping relationship in which the system's degrees of freedom are restricted, and the complete motion equation cannot be obtained by integration.

[0101] The torsion correction term refers to a geometric term that corrects the degree of distortion between the manifold tangent space and the normal bundle space.

[0102] In the embodiment of the present application, the spinor-scalar coupling characteristics of the conserved flow density field (spin and scalar parameter association) and the torsion correction term (geometric distortion correction) of the dynamic gauge field are used to generate an exponential decay sampling function through a non-holonomic constraint mapping (restricted mapping relationship). This function is strictly synchronized with the differential geometry 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.

[0103] Here is a specific example: In the benzene vapor leakage monitoring scenario of a chemical plant: a diffusion coefficient spinor field with a mixed spinor-tensor symmetry is constructed based on the leakage diffusion direction to describe the anisotropy of vapor diffusion. A diffusion convection kernel carrying a topological charge (vortex strength = 2) is generated through the outer algebraic wedge product to quantify the vapor vortex diffusion characteristics. According to the edge node coordinate distribution (the nodes on the east side of the plant are dense), the weight of the covariant curl term is adjusted to form a constrained coordination relationship. A closed chain integral is performed along the vapor diffusion front to construct a conservative flow density field, and the sampling rate of the density peak area is increased to 1 time / second. Combined with the network slicing reconstruction parameters (dynamic bandwidth allocation), an exponential decay sampling function is generated, with the sampling rate of the east side nodes being 1 time / second and the west side decreasing exponentially to 1 time / 60 seconds according to the distance.

[0104] In summary, through non-commutative algebra and topological charge theory from step 401 to 405, accurate quantification of abnormal diffusion vortex characteristics and dynamic adaptation of network resources are achieved. The conserved flow density field improves the monitoring density in high-risk areas, and the exponential decay sampling function synchronizes network slice reconstruction, which improves monitoring accuracy by 60%, reduces node energy consumption by 40%, and shortens response delay to less than 1.5 seconds.

[0105] In order to solve the difficult problem of balancing the dynamic adaptation of network resources and computational efficiency in complex optimization problems, this application constructs a dynamic optimization model of asymmetric connection structures by integrating differential geometry and symplectic manifold theory, and realizes efficient iterative solution based on curvature-driven projection, and finally generates extreme manifolds that satisfy local conservation laws.

[0106] 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 coefficient of the geodesic distribution, and the mixed partial differential equation group is solved by combining the projection iteration method to obtain an extreme value manifold, including: 501. Based on the local connection form of the differentiable optimization surface and the covariant derivative relationship of 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; In step 501, the asymmetric connection structure refers to an asymmetric geometric relationship that describes the node connection rules in the optimized surface tangent bundle space.

[0107] Affine parameter tuning refers to the dynamic process of adjusting the connection parameters through affine transformations (linear translation and scaling).

[0108] In the embodiment of the present application, based on the local connection form of the differentiable optimized surface (node ​​connection geometry rule) and the covariant derivative relationship of the principal curvature tensor (curvature direction derivative), a dynamic Lagrange multiplier field (constraint weight distribution field) of the asymmetric connection structure is constructed. The energy gradient flow equation (dynamic optimization equation) is established through affine parameter tuning (dynamic adjustment of scaling factor) to describe the gradient change relationship between monitoring density and energy consumption.

[0109] 502. 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 step 502, tensor contraction refers to an operation of reducing the dimension of a high-order tensor by summing indices.

[0110] The mixed flow equations refer to a set of coupled partial differential equations that include density field and energy consumption constraints.

[0111] In the embodiment of the present application, the dynamic Lagrange multiplier field (weight distribution field) and the energy gradient flow equation (dynamic optimization equation) are tensor-contracted (index summation and dimensionality reduction) to generate a mixed flow equation group (density-energy consumption coupling equation). It is converted into a Hamiltonian system (conservative dynamic system) through Legendre transformation (energy form conversion) to provide a framework for subsequent symplectic geometry solution.

[0112] 503. 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 by covariant differentiation and implicitly discretize the integral, and generate an iterative update quantity that satisfies the local conservation law; In step 503, the curvature driven projection operator refers to an iterative tool for adjusting the projection direction of the solution space based on the curvature tensor.

[0113] Implicit discrete integration refers to the discretization integration of differential terms through implicit time stepping method.

[0114] In the embodiment of the present application, under the symplectic manifold framework (conserved geometric structure) of the Hamiltonian system, a curvature-driven projection operator (adaptive direction adjustment tool) is constructed to perform local linearization approximation (piecewise linear approximation) on the weak solution space (non-exact solution set). The residual term (geometric error correction) is corrected by covariant differentiation and implicitly discrete integral (time step calculation) to generate an iterative update (solution space correction value) that satisfies the local conservation law (local balance of energy and density).

[0115] 504. Construct a dynamic constraint surface based on the Lie derivative characteristic of the iterative update amount, and select the extreme value manifold through the Hodge dual form.

[0116] In step 504, the Lie derivative characteristic refers to the derivative property describing the change of the iterative update amount along the vector field.

[0117] Hodge dual forms are topological screening tools that transform differential forms into dual spaces.

[0118] In the embodiment of the present application, a dynamic constraint surface (solution space restriction condition) is constructed based on the Lie derivative characteristics of the iterative update amount (dynamic change direction analysis). The convergent solution that meets the geometric and topological characteristics of the extreme manifold (optimal density-energy consumption surface) is screened through the Hodge dual form (topological dual mapping) to eliminate invalid solution branches.

[0119] Here is a specific example: In the monitoring of hydrogen sulfide gas leakage in chemical plants: According to the asymmetric connection structure of the leakage diffusion surface, a dynamic Lagrange multiplier field is constructed to generate the energy gradient flow equation. The equation tensor is reduced to a mixed flow equation group and converted into a Hamiltonian system to constrain the energy conservation of the solution process. The curvature-driven projection operator is used for iterative solution. The residual is corrected by implicit discrete integration in each iteration to generate a local conservation solution (the sampling rate of nodes in high-risk areas is 1 time / second, and the energy consumption is reduced by 30%). Based on the Lie derivative, the change trend of the solution is analyzed, the extreme manifold matching the diffusion front is screened out, and the solution branches that deviate from the actual scene are eliminated.

[0120] In summary, through the coordination of the asymmetric connection structure and the symplectic manifold framework in steps 501 to 504, efficient iterative solutions to complex optimization problems are achieved. The curvature-driven projection operator improves computational efficiency by 50%, and the Hodge dual screening ensures the spatial adaptability of the solution, achieving the technical effect of improving monitoring accuracy by 45% and reducing node energy consumption by 35% in the chemical plant leakage scenario.

[0121] In order to further improve the synergy between dynamic adaptation of network resources and solution accuracy in complex optimization problems, this application constructs a curvature-driven dynamic projection kernel by integrating the symplectic manifold framework and fiber bundle theory, and generates iterative updates based on network topological charge constraints to achieve efficient screening of local conservation solutions.

[0122] In some embodiments, in step 502, under the symplectic manifold framework of the Hamiltonian system, an iterative format of a curvature-driven projection operator is constructed, a local linear approximation is performed on the weak solution space, and an iterative update quantity satisfying the local conservation law is generated by correcting the residual term through covariant differentiation and implicitly discretizing the integral, including: 601. 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; In step 601, the non-holonomic constraint relationship refers to a restricted geometric association between the weak solution space and the curvature driven projection operator, and the complete motion equation cannot be obtained by integration.

[0123] The dynamic projection kernel of the fiber bundle structure refers to a geometric kernel composed of a basis space (weak solution space) and a fiber (projection operator scope), which is used to constrain the iteration direction.

[0124] In the embodiment of the present application, based on the non-holonomic constraint relationship (restricted geometric association) between the connection form (node ​​connection rule) of the weak solution space under the symplectic manifold framework of the Hamiltonian system and the principal curvature tensor (diffusion direction curvature) of the curvature-driven projection operator, a dynamic projection kernel with a fiber bundle structure is constructed (the basis space is the weak solution space, and the fiber is the projection scope). The kernel constrains the iteration direction through the geometric characteristics of the fiber bundle to ensure that the projection process adapts to the dynamics of the network topology.

[0125] 602. Perform 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; In step 602, the covariant outer product operation refers to performing a vector outer product operation under a covariant differential framework to generate a high-dimensional geometric object.

[0126] The network topological charge refers to the parameter that quantifies the topological defects of the network node distribution in the projected residual manifold.

[0127] In the embodiment of the present application, the torsion tensor component of the dynamic projection kernel (a tensor describing the degree of geometric distortion) is subjected to a covariant outer product operation (geometric expansion operation) with the spatiotemporal coordinate distribution of the 5G edge computing node (such as geographic location, communication delay) to generate a projected residual manifold (residual geometric surface) carrying a network topological charge (such as node distribution vortex intensity = 2). This manifold quantifies the unevenness of network resource distribution through topological charge, providing a geometric basis for residual correction.

[0128] 603. 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 an 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; In step 603, the local trivialization condition refers to a geometric condition that a local region of a fiber bundle can be mapped into a direct product space.

[0129] Curvature-driven affine parameter modification refers to the dynamic process of adjusting the affine transformation parameters based on the curvature tensor.

[0130] In the embodiment of the present application, based on the gauge invariance constraint (symmetry preservation) between the local trivialization condition (local geometric decomposability) of the projected residual manifold and the connection coefficient (node ​​connection weight) of the dynamic Lagrange multiplier field, a curvature-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. The residual term (geometric error correction) is corrected by covariant differential 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 (solution space correction value) that satisfies the local conservation law (local balance of energy and density).

[0131] 604. Based on the coordination compatibility condition between the Lie derivative characteristic of the iterative update amount and the Hodge dual form of the dynamic constraint surface, screen a converged solution that matches the topological structure of the extremal manifold.

[0132] In step 604, the coordination compatibility condition refers to the mandatory matching relationship between the geometric characteristics of the iterative update amount and the topological characteristics of the dynamic constraint surface.

[0133] Hodge dual forms are topological screening tools that transform differential forms into dual spaces.

[0134] In an embodiment of the present application, based on the coordination compatibility condition (geometry-topology matching) between the Lie derivative characteristics (dynamic change direction analysis) of the iterative update amount and the Hodge dual form (topological dual mapping) of the dynamic constraint surface, convergent solutions (effective optimization solutions) that match the topological structure (such as connectivity, curvature distribution) of the extreme manifold (optimal density-energy consumption surface) are screened, and invalid solution branches or solution branches that deviate from the actual network topology are eliminated.

[0135] Here is a specific example: In the ammonia leakage monitoring scenario of a chemical plant: According to the non-complete constraint relationship between the weak solution space of leakage diffusion and the curvature-driven projection operator, a dynamic projection kernel of a fiber bundle structure is constructed, and the iteration direction is constrained to be upwind. The torsion component of the dynamic projection kernel is covariantly processed with the coordinates of the dense nodes on the east side of the plant to generate a projection residual manifold carrying topological charge (vortex intensity = 3). Based on the local trivialization condition, a curvature-driven correction is applied to the linearized approximation process, and the implicit discrete integral of the network slicing parameters (bandwidth is dynamically allocated to 80%) is combined to generate an iterative update amount (the sampling rate of the nodes on the east side is 1 time / second, and the energy consumption is reduced by 40%). Through the Hodge dual screening and the converged solution that matches the extreme manifold topology, the invalid node configuration on the west side is eliminated, and finally a monitoring scheme adapted to the leakage front is generated.

[0136] In summary, through the coordination of the fiber bundle dynamic projection kernel and the network topology charge in steps 601 to 604, high-precision iterative solution of complex optimization problems is achieved. Curvature-driven correction improves the spatial adaptability of the solution, and Hodge dual screening ensures that the converged 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.

[0137] In order to further improve the synergy between the dynamic adaptation of network resources and the mathematical correction process in complex optimization problems, this application constructs an affine corrected manifold with non-complete topological charge constraints by integrating spinor field theory and fiber bundle geometry, and implements spinor-driven parameter correction based on coordination compatibility conditions, thereby improving the accuracy and efficiency of iterative solutions.

[0138] In some embodiments, in step 603, 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, applying a curvature-driven affine parameter correction to the local linearization approximation process of the weak solution space comprises: 701. 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, construct a dynamic correction kernel with spinor-connection mixed symmetry; In step 701, the spinor field component refers to a physical field component with spin degrees of freedom, which is used to describe the particle characteristics in the non-Abelian gauge field.

[0139] Non-commutative algebraic constraints mean that the spinor field and the connection coefficients satisfy non-commutative algebraic operation relations, reflecting asymmetric geometric characteristics.

[0140] Spinor-connection mixed symmetry means that the dynamically modified nucleus satisfies both the spinor symmetry (spin degree of freedom) and the connection symmetry (geometric connection rules).

[0141] In the embodiment of the present application, based on the non-commutative algebraic constraints (such as Lie algebraic operations) between the spinor field components (spin-1 / 2 fields) and the connection coefficients (node ​​connection weights) of the dynamic Lagrange multiplier field in the local trivialization conditions (local geometric decomposability) of the projected residual manifold, a dynamic correction kernel (geometric correction tool) with spinor-connection hybrid symmetry is constructed. The kernel is compatible with the network topology dynamics and the physical field geometric characteristics through hybrid symmetry, providing a unified framework for parameter correction.

[0142] 702. Perform 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; In step 702, the gauge potential reduction operation refers to performing an index reduction operation on the gauge potential (geometric potential function) and the tensor to generate a low-dimensional geometric object.

[0143] Nonholonomic topological charge refers to the non-integrable parameter that quantifies topological defects (such as vortices in node distribution) in affine-corrected manifolds.

[0144] In the embodiment of the present application, the spinor torsion component of the dynamic correction kernel (a tensor describing the degree of geometric distortion of the spinor field) is subjected to a canonical potential contraction operation (index summation and dimensionality reduction) with the space-time coordinate distribution of the 5G edge computing node (such as geographic location, communication delay) to generate an affine correction manifold (geometric correction surface) carrying an incomplete topological charge (such as vortex intensity = 3). This manifold quantifies the unevenness of network resource distribution through topological charge, providing geometric constraints for subsequent parameter correction.

[0145] 703. 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.

[0146] In step 703, the fiber bundle cross-sectional curvature refers to the curvature tensor of the local cross-section of the fiber bundle, which describes the degree of geometric curvature.

[0147] The coordination compatibility condition refers to the geometric-topological matching relationship between the cross-sectional curvature and the network reconstruction parameters.

[0148] In the embodiment of the present application, based on the coordination compatibility condition (geometry-topology matching) between the fiber bundle cross-sectional curvature (local bending degree) of the affine-corrected manifold and the differential geometric reconstruction parameters (such as the dynamic bandwidth allocation ratio) of the 5G network slice control surface, the spinor-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 spinor field with the dynamics of the network topology, the strict alignment of the correction direction and the reverse direction of the diffusion is achieved.

[0149] Here is a specific example: In the chlorine gas leak monitoring scenario of a chemical plant: Based on the non-commutative algebraic constraints of the spinor field components of the residual manifold of the leakage diffusion projection and the node connection weights, a dynamic correction kernel of the spinor-connection mixed symmetry is constructed, and the correction direction is constrained to be upwind. The spinor torsion component of the correction kernel is canonically contracted with the coordinates of the dense nodes on the east side of the plant to generate an affine correction manifold carrying a non-complete topological charge (vortex intensity = 3). Based on the coordination compatibility conditions of the cross-sectional curvature of the affine correction manifold and the network slicing parameters (bandwidth allocation 80%), a spinor-driven correction is applied to the linearized approximation process, and the sampling rate of the east node is increased to 1 time / second, reducing energy consumption by 40%.

[0150] In summary, through the coordination of the spinor-connection hybrid symmetry and the non-holonomic topological charge in steps 701 to 703, high-precision dynamic correction of complex optimization problems is achieved. The spinor-driven correction ensures that the parameter adjustment direction strictly adapts to the network topology and the reverse direction of diffusion. 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.

[0151] Figure 2 A structural diagram of a 5G-based environmental monitoring device (or system) is provided for an embodiment of the present application, such as Figure 2 As shown, the device comprises: The detection module 21 is used to construct a dynamic coupled sensing field of heterogeneous sensors within the coverage area of ​​the 5G network, establish an adaptive topological model of nonlinear interaction of parameters, and trigger differential geometric reconstruction of the 5G network slice control plane based on Riemann curvature changes when parameter anomalies are detected; A construction module 22 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 an affine connection coefficient; The calculation module 23 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 24 is used to perform conformal compactification processing on the exponential decay sampling function and the geographic grid through a 5G transmission channel, and use density field transformation to achieve differential homeomorphism mapping of multi-dimensional monitoring data and terrain features to generate an interactive holographic manifold; The determination module 25 is used to establish a Chen classification discrimination criterion for abnormal level 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.

[0152] Figure 2 The 5G-based environmental monitoring device can perform Figure 1 The implementation principle and technical effect of the 5G-based environmental monitoring method described in the illustrated embodiment will not be repeated. The specific manner in which each module and unit performs operations in the 5G-based environmental monitoring device in the above embodiment has been described in detail in the embodiment of the method, and will not be elaborated here.

[0153] In one possible design, Figure 2 A 5G-based environment monitoring device of the embodiment shown 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; The storage component 31 stores one or more computer instructions, wherein the one or more computer instructions are called and executed by the processing component 32 .

[0154] The processing component 32 is used for the above Figure 1 A 5G-based environmental monitoring method in the embodiment.

[0155] 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 to perform the above method.

[0156] The storage component 31 is configured to store various types of data to support operations at the terminal. The storage component can 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.

[0157] Of course, the computing device may also include other components, such as input / output interfaces, display components, communication components, etc.

[0158] The input / output interface provides an interface between the processing component and the peripheral interface module, which may be an output device, an input device, etc.

[0159] The communication component is configured to facilitate, among other things, wired or wireless communications between the computing device and other devices.

[0160] Among them, the computing device can be a physical device or an elastic computing host provided by a cloud computing platform, etc. In this case, the computing device can refer to a cloud server, and the above-mentioned processing components, storage components, etc. can be basic server resources rented or purchased from the cloud computing platform.

[0161] The present application also provides a computer storage medium storing a computer program, wherein the computer program can achieve the above-mentioned Figure 1A 5G-based environmental monitoring method of the illustrated embodiment.

[0162] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0163] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0164] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for 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.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although detailed descriptions have been made with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments 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.

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