15 results about "Laplace's equation" patented technology

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.

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 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 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.

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.

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 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.

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.

The application discloses an asymmetric axial electromagnetic force wave calculation method of an axial magnetic field permanent magnet memory motor, which mainly comprises the following steps: determining a solving coordinate system, respectively establishing Poisson equations and Laplace equations for the motor according to different solving regions of air gaps and Halbach array permanent magnets, solving static axial air gap magnetic flux density and circumferential air gap magnetic flux density according to boundary conditions that should be met by an open-circuit magnetic field analytical model on the basis of obtaining a Laplace general solution, calculating a Halbach array permanent magnet magnetic motive force during motor operation, respectively calculating a single-phase winding generated magnetic motive force and a three-phase winding generated magnetic motive force when the motor is supplied with three-phase symmetrical sinusoidal currents, and deducing and calculating a motor axial air gap magnetic field distribution formula in the case of considering air gap permeability. In the case of ignoring air gap saturation, axial electromagnetic force acting on a unit area of the axial magnetic field permanent magnet memory motor is calculated according to Maxwell tensor equations.

The application relates to the technical field of cable detection, in particular to a method and system for detecting the thickness of the insulation layer of a cross-linked insulation cable. The method comprises the following steps: obtaining a cable cross-section image and performing region segmentation to identify three topologically connected domains and extract inner and outer boundaries; establishing a physical field model and applying a first type of boundary condition; solving a Laplace equation in the insulation layer region to generate a convergent scalar potential field; performing differential operation on the scalar potential field to obtain a gradient vector field, searching for gradient modulus extreme points on virtual equipotential lines to mark the thinnest and thickest feature points; taking the thinnest feature point and the thickest feature point as starting points, respectively performing streamline tracing along positive and negative gradient directions, and calculating the sum of path lengths to obtain the minimum thickness of the insulation layer and the maximum thickness of the insulation layer respectively. The application eliminates noise by solving the Laplace equation, quickly locates by using the gradient modulus extreme value, and significantly improves the detection accuracy.