46 results about "Laplace's equation" patented technology

The invention relates to an asteroid gravitational field reconstruction method based on an embedded mathematical knowledge neural density field, and the method comprises the steps: completing the sampling of data points based on an asteroid mass point group model, and constructing a function solver from a spatial position to density; constructing a spatial sampling point function to obtain spatial densities of spatial points at different positions; aiming at the space points, utilizing an asteroid visual three-dimensional model to obtain star shell information, and screening the space points as prior information inside and outside a star shell; screening results of the density function solver according to prior information; further calculating a Laplace equation of the data points by using a partial differential equation solver, and calculating a gravitational acceleration equation of external space points of the star by using numerical integration; constructing a total loss function; error back propagation is carried out, and network parameters are optimized; recalculating the internal space point density of the star to obtain the internal density distribution of the asteroid; and further calculating the value of the gravitational acceleration of each position in the space to obtain asteroid external gravitational field distribution.

The invention provides a satellite magnetic measurement data downward continuation method, device and equipment and a medium, and the method comprises the steps: inputting observation data, and converting the observation data obtained during satellite in-orbit measurement from a spherical coordinate system to a rectangular coordinate system; determining a model calculation domain, and generating a series of configuration points in the model calculation domain; normalizing observation data position coordinates, configuration point position coordinates and magnetic field three-component data under the rectangular coordinate system to serve as training data; inputting observation data position coordinates and configuration point position coordinates under the rectangular coordinate system into a neural network model, constructing a loss function based on observation data fitting errors and Laplacian equation physical constraints, and training the neural network model; and according to application requirements, generating a target position coordinate on a target continuation plane or space, inputting the target position coordinate into the trained neural network model, obtaining magnetic field three-component data at the target position coordinate, and realizing high-precision downward continuation.

The invention discloses a three-dimensional anisotropic grid generation method based on a streamline tracking topological structure, and relates to the field of numerical simulation of fluid mechanics, and the method comprises the steps: S1, carrying out the tetrahedral subdivision processing of a computational domain of an aircraft through employing a triangulation algorithm Delaunay, and achieving the isotropic grid subdivision of the computational domain; s2, using isotropic grid point information generated in the isotropic topological structure to construct a corresponding sign distance SDF resolving model so as to obtain a scalar field satisfying a Laplace equation; s3, calculating the gradient of the scalar field by adopting an SDF gradient solving method based on local least square fitting to obtain a corresponding gradient field; s4, performing streamline tracking in the gradient field to obtain a corresponding grid topological structure; and S5, constructing a structured hexahedral mesh covering the whole computational domain according to the mesh topological structure and the corresponding surface mesh. According to the method, theoretical unification and engineering feasibility of two-dimensional to three-dimensional grid structure mapping are realized.

The invention relates to the technical field of cable detection, in particular to a method and system for detecting the thickness of an insulating layer of a cross-linked insulated cable. The method comprises the following steps: acquiring a cable cross section image, performing region segmentation to identify three topological connected domains, and extracting inner and outer boundaries; establishing a physical field model and applying a first type of boundary conditions; solving a Laplacian equation in the insulating layer region to generate a convergent scalar potential field; performing differential operation on the scalar potential field to obtain a gradient vector field, and searching gradient modulus length extreme points on the virtual equipotential line to mark thinnest and thickest feature points; and taking the thinnest feature point and the thickest feature point as starting points, respectively executing streamline tracking along positive and negative gradient directions, and calculating the sum of path lengths so as to respectively obtain the minimum thickness of the insulating layer and the maximum thickness of the insulating layer. Noise is eliminated by solving the Laplacian equation, rapid positioning is performed by using the gradient modulus length extreme value, and the detection precision is remarkably improved.

The invention provides a parasitic resistance calculation method and system applied to VLSI design, and the method comprises the following steps: S1, selecting a target physical layer in a VLSI layout, and obtaining a parasitic resistance geometric shape in the target physical layer based on the position of a current inlet terminal, the position of a current outlet terminal and the position of a conductive element through frame selection; s2, performing similarity comparison on the geometrical shape of the parasitic resistor and cached data in a comparison database, if the cached data matched with the geometrical shape of the parasitic resistor exists in the comparison database, outputting a resistance matrix corresponding to the cached data, and if the cached data matched with the geometrical shape of the parasitic resistor does not exist in the comparison database, outputting a resistance matrix corresponding to the cached data; if yes, resistance matrix calculation is carried out on the parasitic resistance geometrical shape through a Laplacian equation field solver, and the parasitic resistance geometrical shape and a corresponding resistance matrix are cached into a comparison database. According to the invention, the calculation precision and speed of the resistance value of the parasitic resistor in the VLSI design can be effectively improved.

The invention discloses a method for designing a mixed type boundary contour line of a progressive multi-focus ophthalmic lens, and belongs to the field of design of progressive multi-focus ophthalmic lenses. The method comprises the following steps: constructing a Laplacian equation, and selecting a mixed rectangular boundary as a boundary of the Laplacian equation; two nodes with adjustable positions are arranged on the right side edge of the second rectangular boundary; solving a Laplacian equation for the second rectangle by adopting a finite element method, and carrying out interpolation to obtain a contour line numerical matrix solution of the second rectangle; and combining the contour line numerical solutions of the first rectangle, the second rectangle and the third rectangle to obtain a contour line function numerical matrix solution of the hybrid rectangular region. According to the invention, the contour line mixed type boundary design method is utilized to greatly improve the use range of the far vision area and the near vision area of the ophthalmic lens again, reduce the astigmatism area and improve the optical performance of the lens; the contour line mixed type boundary design method provided by the invention can also be applied to the personalized design aspect of progressive multi-focus spectacle lenses.

This invention discloses a high-precision density reversal method and system for gravity anomalies based on regular, stable, and high-speed solution. [Solution] Based on the above-mentioned field source regularization solution, we propose using data with false anomalies at the field source imaging depth as boundary value conditions. Again, by solving the upper space of the first class boundary value problem of Laplace's equation, we calculate gravity anomalies on the ground and perform least-squares optimization iterative solution with the actual ground anomalies to obtain high-precision anomaly imaging data at the field source depth that does not contain false anomalies due to the Gibbs effect. This depth is used as the top interface of the field source, and the top interface is divided into grid prisms to construct the field source morphology. Density inversion is performed on each prism top surface in the frequency domain to obtain the density distribution of the field source morphology. Since this algorithm is implemented in the frequency domain and the inversion is performed at a known field source depth, the present invention is a gravity density inversion method with high speed, high precision, and high resolution characteristics, and provides a new concept for realizing the solution of gravity field source density parameters.

The present invention discloses a method for solving three-dimensional water wave energy band structure based on high-order boundary elements, which belongs to the field of water wave control and includes the following steps: S1. Based on the linear potential flow theory, a model of an infinite periodic array of three-dimensional fixed structures is established, the fluid is divided into a number of identical units, and the control equations and boundary conditions satisfied by the velocity potential of the fluid domain are obtained; S2. The high-order boundary element method is used to solve the three-dimensional Laplace equation, the boundary conditions are substituted into the boundary integral equation and a simple Green's function is selected. By numerically discretizing into high-order grid units, a linear homogeneous system of equations is established; S3. By arranging the system of equations, the solvable problem of the system of equations is converted into an eigenvalue problem to solve the real Bloch wave number and obtain a water wave energy band structure diagram. The present invention adopts the above-mentioned method for solving three-dimensional water wave energy band structure based on high-order boundary elements to achieve a rapid and accurate solution of the water wave energy band structure of three-dimensional fixed structures of arbitrary shape and underwater terrain.

The present invention discloses a T-type Halbach plug-in axial flux motor and an analytical method thereof. The motor structure is a double-stator single rotor, and a plug-in T-type Halbach magnetic pole array is provided between the rotor and each stator, and the magnetic pole array includes a plurality of magnetic poles. In the method, a subdomain model method is first used to divide the motor into three subdomains, and the magnetization intensity components of different subdomains are respectively given to establish a double Fourier decomposition expression of the total magnetization intensity. Secondly, according to the Poisson equation and the Laplace equation in a three-dimensional coordinate system, the separation of variables method is used to calculate the general solution expression of the scalar magnetic potential of each subdomain. Then, according to the interface connection condition of the Ampere circuit law and the flux continuity principle, the unknown coefficients in the scalar magnetic potential are solved, and based on the relationship between the magnetic field intensity and the magnetic flux density and the scalar magnetic potential, the general expressions of the magnetic field intensity and the magnetic flux density are calculated. Then, the Carter coefficient is introduced to correct the magnetic flux density to obtain the corrected magnetic flux density expression.

The invention discloses a particle earth and rockfill dam large deformation calculation method based on node integration, and relates to the technical field of geotechnical engineering large deformation. The method comprises the following steps: establishing a generalized shape function and a strain displacement matrix of a proportion boundary finite element SBFEM under a Laplacian equation; under an updated Lagrange framework, state variables at Gaussian integral points of the triangular SBFEM unit are projected to nodes through a strain smoothing technology, a momentum equation is converted into a balance equation based on node integration through a virtual work principle and a Green divergence theorem, and the dynamic equation is solved through a central difference method; and when the grid distortion degree reaches a significant level, discarding the current grid and performing re-grid division. All state variables such as stress, displacement, speed and the like are concentrated on nodes of abandoned grids, so that the subsequent grid generation and calculation process can be seamlessly continued. According to the invention, continuous simulation of the whole large deformation process based on the proportional boundary finite element method is realized.

The application discloses a kind of equivalent thermal conductivity calculation method and system of electric propulsion motor winding, it is related to electric propulsion motor temperature field calculation field, wherein the equivalent thermal conductivity calculation method of electric propulsion motor winding includes the following steps: according to the arrangement state of entire winding in electric propulsion motor in slot, winding is divided into multiple unit circular structure;Establish the Laplace equation of the temperature of insulating layer subdomain in multiple unit circular structure, and the Poisson equation of the temperature of winding layer subdomain;According to the boundary condition in multiple unit circular structure, the temperature rise of each subdomain is solved, and the total temperature rise of multiple unit circular structure is solved, the entire winding is equivalent to circular heating body, and the total temperature rise of multiple unit circular structure is taken as the temperature rise of circular heating body;Equivalent thermal conductivity of entire winding is calculated.The winding equivalent model based on the analytical method proposed in the application obtains more accurate winding temperature;The method also provides a reference for temperature solution of other types of motor.

The present invention discloses a method and system for high-precision density inversion of gravity anomalies based on regular stable fast solution. [Solution] Based on the above source regularization solution, we propose using data containing spurious anomalies at the source imaging depth as boundary value conditions. Then, through the upper half-space solution of the first-class boundary value problem of Laplace's equation, we calculate the gravity anomaly on the ground, and perform a least-squares optimization iteration with the actual ground anomaly to obtain high-precision anomaly imaging data at the source depth without spurious anomalies caused by the Gibbs effect. This depth is used as the top interface of the source, and the top interface is divided into grid prisms to construct a source configuration. Density inversion is performed on each prism top surface in the frequency domain to obtain the density distribution of the source configuration. Because this algorithm is implemented in the frequency domain and the inversion is performed at a known source depth, the present invention provides a gravity density inversion method with high speed, high precision, and high resolution, and provides a new concept for solving gravity source density parameters.

The invention relates to the technical field of finite element grids, and particularly discloses a block structure method-based hexahedral grid parallel generation method for a fast reactor core component, which comprises the following steps of: performing Delay inner triangulation in an area on the same side of a winding wire, solving a Laplace equation to generate an isoline, and generating an orthogonal grid according to the isoline; obtaining a triangular surface grid template on the same side of the winding wire; dividing the fuel rod assembly into six sections, dividing each section into a plurality of layers, taking the first section as a basic section, dividing block grids in each layer on the basis of the triangular surface grid template on the same side of the winding wire, generating quadrilateral surface grids in the block grids, rotating the grids on each layer at a set angle once to obtain grids on each layer of other sections, and forming the quadrilateral surface grids on the same side of the winding wire; the grids of all the layers are connected to form a hexahedral grid model; the hexahedral mesh model is expanded; and carrying out parallel optimization on the loop call function. According to the method, the problems that the hexahedral mesh of the fast reactor core assembly cannot be correctly generated and the mesh division efficiency is low are solved.

The present invention discloses a real-time joint filtering method for gravity and gravity gradient data, belonging to the field of geophysics technology. The method comprises: combining gravity and gravity gradient data using gravity potential, incorporating the relationship between gravity and gravity gradient into the system equation and measurement equation of a standard Kalman filter using the Taylor formula; utilizing the difference between the predicted state and the actual state in the Kalman filter to adaptively update the filter parameters, thereby obtaining an adaptive update process equation for Kalman filter measurement noise; utilizing the system equation and the measurement equation to combine gravity and gravity gradient data, combined with the adaptive update process equation for Kalman filter measurement noise, to remove noise from the data in real time, thereby achieving real-time joint filtering of gravity and gravity gradient data. The present invention not only filters out noise but also ensures that the filtered data satisfies the constraints of the Laplace equation and meets the real-time data processing requirements, thereby achieving real-time joint filtering of gravity and gravity gradient data.

The present invention presents a computer-implemented method for automatically identifying and sealing gaps in geometrical or three-dimensional models for simulation. The method involves creating a multi-volume mesh of the model, defining boundaries to distinguish inside and outside regions, and solving the Laplace equation to identify gaps. By adjusting the iso-surface of the equation's primary variable, the gaps are sealed at desired locations. The model is then divided into distinct inner and outer volumes. The process reduces manual intervention, ensures accurate simulation preparation, and allows user interaction for boundary definition and visualization. The invention streamlines model preparation for simulations, enhancing the efficiency and accuracy of design validation across various industries and allowing much more efficient analysis.

A kind of high-precision outer rotor permanent magnet motor stray field analytical method, it is related to outer rotor permanent magnet motor magnetic field calculation field, including the following steps: S1 in two-dimensional polar coordinate system, according to the structure equivalence principle, outer rotor permanent magnet motor is divided into 5+n sub-domain;S2 the Laplace equation or Poisson equation of each sub-domain is established, the boundary condition of the interface of ferromagnetic material and non-ferromagnetic material is solved by separation of variables method, the vector magnetic potential of each sub-domain;S3 according to boundary condition column write constraint equation, solve the harmonic coefficient of each vector magnetic potential;S4 sub-domain model and iterative convergence algorithm are integrated, and the rotor unsaturated permeability of motor at different radiuses of core under various operating conditions is automatically iterated and updated;S5 the partial derivative of the vector magnetic potential of outer air domain is solved, and the radial component and tangential component of stray magnetic field are obtained.The present application can accurately predict the core unsaturated permeability of motor at different radiuses of core under different operating conditions, and improve the calculation accuracy of stray magnetic field.

The application discloses a kind of based on high-order boundary element's three-dimensional water wave band gap attenuation coefficient solving method, belong to water wave regulation field, including the following steps: S1, based on linear potential flow theory establishes three-dimensional fixed structure infinite periodic array model, fluid is divided into several identical units, and the control equation and boundary condition that fluid domain velocity potential satisfies are obtained;S2, high-order boundary element method is selected to solve three-dimensional Laplace equation, boundary condition is substituted into boundary integral equation and simple Green function is selected, by numerical dispersion into high-order grid unit, and linear homogeneous equation set is established;S3, by organizing equation set, equation set has solution problem is converted into local minimum value problem to solve complex Bloch wave number, and the attenuation coefficient of water wave band in band gap is obtained.The application adopts the above solving method, realizes the fast and accurate solution of three-dimensional fixed structure band gap structure and attenuation coefficient in band gap.

The invention relates to the technical field of oil exploration and development reservoir evaluation, and discloses a method and system for fitting a capillary pressure curve and reservoir evaluation based on a Sigmoid function, and a medium, and the method comprises the following steps: obtaining rock core sample mercury injection experiment test data; carrying out outlier elimination and logarithm transformation on the rock core sample test data curve; fitting a capillary pressure curve by using a Sigmoid function to obtain parameters, namely, a formula, a formula and a formula; performing inversion according to a capillary pressure curve fitted by a Laplace equation and a Sigmoid function to obtain mercury injection characteristic parameters; s5, constructing a reservoir evaluation grading rule according to the Sigmoid fitting parameter and the inversion parameter; outputting a rock core sample fitting capillary pressure curve, mercury injection characteristic parameters and a reservoir evaluation result; and according to the mercury injection experiment test data of the rock core sample, outputting an actual fitting capillary pressure curve, mercury injection characteristic parameters and reservoir classification of the rock core sample. According to the method, the Sigmoid function can adapt to the capillary pressure curve formed by the heterogeneous reservoir complex and diversified pore structures, fitting parameters have clear physical significance, and based on fitting and inversion parameters, high-precision and repeatable evaluation of multiple types of complex reservoir samples can be achieved.

The invention relates to a high-voltage distribution room robot path planning method and device based on a physical information neural network. The method comprises the steps that internal environment information of a high-voltage power distribution room is acquired, a semantic map is constructed based on the internal environment information, and the semantic map comprises an obstacle geometric information channel and a radiation source field intensity priori information channel; inputting the semantic map into a pre-trained physical information neural network model to obtain an electric field intensity distribution diagram of the high-voltage power distribution room; wherein the training loss function of the physical information neural network model comprises a data fitting loss function and a physical constraint loss function based on a Laplacian equation; and based on the electric field intensity distribution diagram, a motion path of the robot is generated by adopting a heuristic path planning algorithm, and a cost function of the heuristic path planning algorithm is used for optimizing the weighted sum of the path length and the accumulated electromagnetic exposure risk. By adopting the method, autonomous and intelligent management and control of the strong electromagnetic risk environment can be realized.

The invention discloses a grounding grid electrical impedance imaging method based on an adaptive smooth Newton method. The method comprises the following steps: S1, constructing a mathematical model of grounding grid electrical impedance imaging; s2, solving a correction problem: S21, dispersing a grounding grid field domain into triangular unit grids; s22, converting the Laplacian equation into a weak form by adopting a Galerkin method; s23, potential distribution is solved; s3, solving the inverse problem; S31, constructing a target function; s32, constructing a smooth functional, and performing continuous differentiable smooth approximation on a total variation regularization item in the target function; s33, dynamically adjusting the smoothing parameter by adopting a homotopy continuation strategy, and performing iterative solution based on the smoothed target function to obtain reconstructed conductivity distribution; and S4, generating an electrical impedance image of the grounding grid. The grounding grid electrical impedance imaging method effectively improves the accuracy and stability of grounding grid electrical impedance imaging, and is suitable for solving inverse problems such as grounding grid electrical impedance imaging.

The invention provides a sea surface sparse gravity anomaly data interpolation method, device, equipment and medium, and the method comprises the steps: obtaining a sea surface sparse gravity observation point and a corresponding real sea surface sparse gravity anomaly value; determining a configuration area range and generating a series of configuration points according to the area range of the three-dimensional position coordinates of the sea surface sparse gravity observation points; normalizing the sea surface sparse gravity observation points, the three-dimensional position coordinates of the configuration points and real sea surface sparse gravity abnormal values corresponding to the sea surface sparse gravity observation points, and taking the normalized data as training data; according to a fitting error of a sea surface sparse gravity abnormal value, introducing a Laplacian equation as a physical constraint, constructing a loss function, and training a neural network model by using training data; and setting position coordinates of a to-be-interpolated region, and predicting sea surface sparse gravity abnormal values at the position coordinates of the to-be-interpolated region by using the trained neural network model to ensure high precision and high resolution of an interpolation result.

This invention relates to a method for reconstructing the gravitational field of an asteroid based on a physical information neural network, comprising the following steps: sampling data points and generating auxiliary points based on an asteroid mass swarm model, and constructing a gravitational potential function solver; preprocessing the data points and generated auxiliary points, and calculating the gravitational potential of each sampling point; calculating the Laplace equation and gravitational curl equation of the auxiliary points and the gravitational acceleration equation of the data points using a partial differential equation solver for the gravitational potential of the sampling points; constructing a total loss function based on the equation calculation results and the mean square error of the gravitational potential; performing backpropagation of the error for the loss function, and simultaneously optimizing the network parameters and the weights of each loss; evaluating the model prediction results for the optimized model, focusing on sampling in key areas with large prediction errors, and finally adding the sampling results to the auxiliary point dataset for further training.

This invention discloses a method for patching holes in the trimmed surface of a mechanical part with N-sided holes. The method includes: parametrically mapping the hole boundary of the surface; establishing a Laplace equation on the parameter region enclosed by the boundary, transforming the hole patching problem into a partial differential equation solution problem on a two-dimensional plane with given first-kind boundary conditions; arbitrarily triangulating the parameter region; using linear trigonometric elements to discretize and solve the Laplace equation to obtain the initial discrete mesh vertex position information of the hole-patch region; fitting Hermite information to the initial discrete mesh using bicubic B-spline surfaces; and adjusting the Hermite information near the boundary to ensure a smooth connection between the hole-patch surface and the original surface at the boundary, ultimately outputting a complete, hole-free surface model of the mechanical part. This invention only requires the input of a trimmed surface model and can automatically process and output the hole-patch surface model.

The application provides a finite element grid deformation electromagnetic simulation method based on harmonic field gradient lines, which comprises the following steps: step 1, taking the grid of an electromagnetic structure before deformation as an initial grid; step 2, defining three types of boundaries according to the deformation of the electromagnetic device geometric boundary and the movement of the grid nodes on the geometric boundary; step 3, establishing a boundary value problem of a harmonic field described by a Laplace equation; step 4, drawing gradient lines passing through each grid node by using the distribution of the obtained scalar field u; step 5, obtaining a new position P2' of a P2 point after deformation according to the property that the relative position of the P2 point is unchanged, performing linear mapping on the gradient lines, and obtaining the gradient lines after deformation with P2' and P3 as end points; step 6, weighting the displacement of the end points of the gradient lines according to the linear mapping relationship and the proportion of the P1 point in dividing the gradient lines, so as to obtain the displacement of the grid node P1; and step 7, moving the grid nodes on the slip boundary Γ d . s ​

The application discloses a kind of flat wire winding alternating current copper consumption's fast calculation method, first by complex Fourier series decomposition method, establish the Poisson equation and Laplace equation that stator tooth slot area and air gap area satisfy, carry out analytical modeling to slot leakage magnetic field of flat wire motor, the distribution of leakage magnetic field in slot in an electric period is calculated, then alternating current copper consumption calculation model is established to each flat wire conductor in slot, the above-mentioned leakage magnetic field is brought into each conductor alternating current copper consumption calculation model in slot, then the alternating current copper consumption of flat wire winding in slot in an electric period is calculated.The alternating current copper consumption calculation method of flat wire winding winding in slot of the application does not need the auxiliary calculation of electromagnetic field finite element software, while guaranteeing the accuracy of alternating current copper consumption calculation, provides a new method for the calculation of alternating current copper consumption of flat wire motor slot winding.

The invention belongs to the field of composite material liquid forming simulation and prediction, and relates to a composite material vacuum-assisted resin infusion simulation method based on a dynamic mesh, which comprises the following steps: establishing a two-phase flow control equation set in a VARI mold filling process; tracking to obtain the thickness of the preform in the mold filling process of the vacuum-assisted resin infusion process, and predicting the permeability of the preform by using an exponential function fitting model; updating the grids in each time step, iteratively solving the flow field in the corresponding new grids in each time step, dispersing and solving the Laplacian equation to obtain the new grids, and updating the physical property parameters of the preform; the grid surface speed is added for the two-phase flow control equation set, and the unit volume change is corrected; and circularly updating the grid form and iteratively solving the flow field, continuously advancing the time step, and stopping calculation until a preset cycle index is reached and a preset filling threshold value is reached. According to the invention, the dynamic change of the component shape can be visually presented geometrically, and the integrated simulation of the filling process and the component shape evolution is realized.

The invention belongs to the technical field of geophysical exploration, and provides a boundary identification and fracture feature determination method, device, equipment and medium, and the method comprises the steps: obtaining the analysis signal vertical guide number of a gravity and magnetic anomalous body; a tilt angle technology and a Laplacian equation are used for analyzing a vertical guide number of the analytic signal, and a boundary position is determined by calculating a difference perpendicular to a signal gradient direction; identifying the position and shape features of the gravity and magnetic anomalous body boundary to obtain fracture features; calculating analytic signals and curvatures of a gravity and magnetic anomaly field and an upward extension field of the gravity and magnetic anomaly body, and quantitatively extracting the top surface depth and the structure index of the boundary of the gravity and magnetic anomaly body to obtain the property of the fracture feature; according to the method, the Laplacian equation is introduced to deeply analyze the vertical guide number of the analysis signal, and only the first-order vertical guide number of the potential field needs to be calculated, so that the influence of high-frequency noise is reduced to a certain extent, and a basis is provided for subsequently determining the boundary position of the gravity and magnetic anomalous body.

The invention discloses an isoplane paving digital art pattern generation method and device based on a partial differential equation. The method comprises the following steps: taking an isoplane body shape after interactive curve editing as a paving unit basic domain; a Laplacian equation is introduced into a basic domain, geometric constraints of paving units are converted into Dirichlet boundary conditions of a Laplacian operator, then smooth invariant mapping meeting isohedron symmetric constraints is constructed, and seamless transition of textures at joints of the paving units is guaranteed; and finally, finishing texture coloring in combination with the power system model and the quasi-regular pattern model. The method has the core advantages that the method can adapt to any isohedron type, the symmetry, the texture details and the visual effect of the pattern can be flexibly regulated and controlled by adjusting the constraint vertex, the power system function and the quasi-regular pattern function, a brand new solution is provided for dynamic real-time generation and personalized design of the digital art pattern, and the method can be applied to the field of digital art design. And abundant material sources are provided for the fields of costume design, textile design and the like.

This invention provides a real-time magnetic anomaly target identification method and system based on a physically constrained neural network (PCNN). The method includes: acquiring spatial geomagnetic total field data; preprocessing the total field data to generate input samples and labeling them with category tags; designing a lightweight convolutional neural network (HNN) as the backbone network, introducing physical constraint terms, and constructing a PCNN model. The physical constraint terms specifically include: the magnetic field in the passive region should satisfy the Laplace equation and the magnetic anomaly signal should conform to the dipole field decay law; training and optimizing the PCNN model based on the labeled input sample data and simulated target data; receiving the magnetic signal stream in real time, inputting it into the trained PCNN model according to time windows, and completing the target identification and output. This invention addresses the technical problems of low identification accuracy, poor interpretability, and weak generalization ability in existing magnetic anomaly target identification methods under conditions of small samples and low signal-to-noise ratio.

The present application relates to the technical field of underground engineering surveying, and particularly relates to a tunnel azimuth angle determination method based on a gyro and a gravity plumb line, which comprises the following steps: continuously outputting an absolute azimuth reference by switching a star-based and optical gyro dual reference of a ground multi-source data reference station; generating a differential compensation sequence with a microsecond-level time stamp by differentiating a homologous gyroscope; combining a gravity plumb line deviation and a Laplace equation to complete real-time reduction of astronomical azimuth to geodetic true azimuth; and completing error compensation by time alignment and dynamic extended Kalman filtering, and outputting a high-precision geodetic true azimuth. The present application eliminates MEMS gyro zero bias, random walk and temperature drift error by differential processing of a ground reference station and a homologous reference gyro underground. Astronomical azimuth is converted to a geodetic coordinate system by combining gravity plumb line deviation correction and Laplace equation reduction, and underground equipment is accurately and real-timely oriented by star-based gyro redundancy and time alignment compensation.