50 results about "Z eigenvalue" patented technology

The invention discloses a multi-converter parameter collaborative optimization method for improving the small interference stability of an active power distribution network, and belongs to the technical field of power systems, and the method comprises the steps: building a differential algebraic equation model, and carrying out the linearization of a steady-state operation point, and obtaining a state space model; and a control parameter optimization problem taking the minimization of the spectrum intercept construction as a target is defined, and control parameters are a GFL converter phase-locked loop parameter and a GFM converter virtual damping parameter. First-order sensitivity and second-order sensitivity of eigenvalues to control parameters are calculated based on a matrix perturbation theory and are converted into local quadratic constraint sub-problems. And performing convexity solution by adopting a positive semidefinite relaxation method, adjusting the step length in combination with a line search mechanism, iteratively updating control parameters, and outputting an optimization result after a convergence condition is met. According to the method, the spectral intercept is reduced through multi-converter parameter collaborative optimization, and the weak stability characteristic is improved; the convergence and solvability are improved by utilizing matrix perturbation and positive semidefinite relaxation; and the stability is enhanced and optimized by adopting line search step length adjustment.

The invention provides a flow field evolution method and device based on quantum calculation and vortex characterization, and the method comprises the steps: defining a complex scalar field, constructing a Hermi matrix based on an initial velocity field, and converting a vortex thread positioning problem into a quantum ground state solving problem; solving the minimum characteristic value of the matrix through a quantum algorithm, and outputting an initial vortex quantum state; according to a fluid dynamic control equation, constructing Hamiltonian through discretization processing; constructing a Hamiltonian quantum circuit, and driving the initial vortex quantum state to evolve to a target quantum state; and measuring the evolved quantum state, obtaining a discrete numerical value of the complex scalar field on the central point of the grid unit, positioning a zero equivalence point through a discrete winding number and interpolation, and reconstructing a vortex thread structure after flow field evolution. According to the method, the parallel computing advantage of quantum computing in high-dimensional data processing is fully exerted, the computing efficiency of flow field simulation is remarkably improved, the data processing speed is increased, and meanwhile the high requirement for storage resources is effectively relieved.

The invention discloses a multi-modal practical dynamic security domain construction method and system based on the maximum Lyapunov exponent theory, and the method comprises the steps: obtaining the measurement information of the active power, the power angle, the angular velocity and the like of a generator node from an actual power system, and determining a fault line and a fault state corresponding to a required dynamic security domain; transient simulation of an initial operation point of the system is carried out to obtain a transient stability condition and a power angle leading cluster of the system; for generators in the leading cluster S, calculating to obtain a maximum Lyapunov exponent characteristic value and related characteristics of a control variable, and solving the maximum Lyapunov exponent sensitivity; and constructing a multi-modal practical dynamic security domain based on the maximum Lyapunov index by combining the upper limit and the lower limit of generator output and the output limit of a balancing machine. According to the method, accurate transient stability evaluation before a fault occurs is realized, the application range is expanded, and the limitation that the stability margin cannot be quantified by track stability judgment is changed.

The application discloses a silicon carbide grain size detection method based on image processing and relates to the technical field of semiconductor material quality detection. A first feature map is generated by calculating the phase consistency distribution of a silicon carbide metallographic image to suppress scratch interference. A topological anchor sequence is identified by using the eigenvalues of a Hessian matrix, and a balanced first gradient potential field matrix is generated by combining local entropy density to suppress polycrystalline contrast fluctuation. Under the constraint of the topological anchor, an optimization evolution is performed by using a path cost function with curvature penalty and energy saturation characteristics, physical inertia closure of a grain boundary signal fracture is realized, and a closed grid vector is generated. Twin grain boundaries are identified and logically merged based on geometric parameters, and grain size detection data consistent with the physical structure of the material is output.

The invention discloses a circuit fault diagnosis method based on a fractional order observer, and the method comprises the steps: constructing a fractional order circuit model based on the Kirchhoff's law, and describing a capacitor end voltage and an inductive current as a Caputo fractional order derivative form; a double-disturbance decoupling mechanism is designed, total disturbance is decomposed into a decoupling disturbance component and a non-decoupling disturbance component, physical isolation of the decoupling disturbance is achieved through a projection matrix, and the influence of the non-decoupling disturbance is eliminated through a dynamic suppression coefficient. Constructing a state observer to generate a state estimation error and a fault error vector, and dynamically compensating a fault estimation value in combination with an adaptive gain matrix; and ensuring the system stability through a Lyapunov function, and proving that an error state is converged to a preset boundary domain under the condition of satisfying a characteristic value correlation matrix inequality. Compared with the prior art, rapid and accurate diagnosis of faults such as inductance saturation and capacitance aging can be realized.

A system and method for spectral learning in persistent cognitive machines implements learning through controlled evolution of a spectral decomposition of a cognitive manifold. The spectral decomposition, comprising eigenvectors and eigenvalues, encodes long-term memory as global geometric structure rather than as stored data or network parameters. The system performs inference operations by projecting incoming data onto the cognitive manifold using a fixed spectral decomposition without modification. Geometric invariants including principal angles, spectral gap ratios, projection residuals, and curvature statistics are continuously monitored to detect structural inadequacy. When invariants exceed thresholds, a learning event modifies the spectral decomposition through eigen decomposition with warm-start initialization while enforcing mode-specific plasticity bounds that are tighter for low-frequency eigenvectors than high-frequency eigenvectors, thereby preventing catastrophic forgetting. The system operates continuously by alternating between inference using fixed spectral decompositions and learning events that modify spectral decompositions through controlled spectral evolution.

The application discloses a kind of graph data semantic analysis methods, this method will graph data semantic analysis process be disassembled into three parts of calculating N order inner eigenvalue, N order outer neighbor feature and feature combination, the calculation of neighbor feature most consumed resource is moved to offline stage, when receiving the data analysis request initiated by user, when certain node is as the N order neighbor node of target node, take out the X order historical neighbor feature pre-cached, the whole flow of deep neighbor modeling calculation can be recovered, can be guaranteed to analyze the depth as N+X order neighbor feature, while, the query order of online graph database is reduced to N order neighbor from N+X order neighbor, greatly reduce the query pressure of online graph database, guarantee the calculation of online stage, through the light degree of data to speed up the calculation speed, reduce the consumption of computing resources.The application also discloses a kind of graph data semantic analysis device, equipment and readable storage medium, with corresponding technical effects.

The application relates to a kind of computing method and device for improving the numerical shock stability of hypersonic speed, belonging to the technical field of computational fluid dynamics.The method comprises: obtaining the grid information of numerical simulation of hypersonic vehicle, and initializing flow field information; for each calculation grid unit, two calculation localities are constructed along the x direction and the y direction with two adjacent grids; two localities are respectively equipped with stability matrix, and the instability condition of grid in the calculation process is judged by the positive and negative of the eigenvalue thereof; according to the instability condition of the grid unit, a Riemann solver is selected: for the grid unit not prone to instability, a high-resolution HLLC Riemann solver is used for calculation; for the grid unit prone to shock instability, a high-robustness HLL Riemann solver is used for calculation. By using different Riemann solvers for calculation at different positions, the shock instability position in the flow field can be detected, identified and processed, and the stable capture of shock is realized.

The application provides a new energy unit clustering method based on a modified node admittance matrix, comprising the following steps: (1) reading power grid topology data and element parameters to obtain a branch table of the power grid; (2) constructing a modified node admittance matrix according to the branch table of the power grid; (3) calculating eigenvalues and eigenvectors of the modified node admittance matrix; (4) sorting n eigenvalues in ascending order to obtain new eigenvalues and corresponding eigenvector sequences; and (5) based on the new eigenvalues and corresponding eigenvector sequences obtained in step (4), using a mean value division method based on Laplacian spectrum to divide nodes in the power grid. The network topology is described by the constructed modified node admittance matrix, and the nodes are divided by the mean value division method based on the Laplacian spectrum, so that the new energy units can be accurately clustered. The application is suitable for grouping of various new energy stations.

The application discloses a kind of double box girder flow field dynamics modal and flow stability analysis method and system, belong to bridge engineering field.This method first establishes double box girder flow field model by computational fluid dynamics, solves the momentum equation and continuity equation of two-dimensional incompressible flow;Dynamic modal decomposition is carried out again, and eigenvalue, characteristic mode and other information are obtained;Finally, based on linear stability theory, the flow field component is expressed as the sum of steady-state solution and disturbance term, and the global linear flow stability equation is obtained by substituting into the equation, and the flow stability is analyzed by discrete.This method can accurately extract the modal characteristics of each order, providing a scientific basis for wind-induced vibration analysis of double box girder, and has important application value.The method of the application occupies less computing resources, has high numerical accuracy, and can be further expanded to higher precision calculation model according to computing resources, and is suitable for application in actual bridge engineering.

The invention relates to the technical field of computer vision, and discloses a road damage detection method based on vision assistance. The method comprises the following steps: firstly, collecting a pavement grayscale image, and establishing a pixel coordinate and a row-column index with the left upper corner as an original point; gaussian smoothing is carried out on the image, and first-order partial derivative is solved in row and column directions to obtain a gradient field; carrying out weighted accumulation on the gradient in a local window to form a symmetric structure tensor, and taking a characteristic value difference as structure energy; second-order and mixed partial derivatives are solved through second-order difference, and curvature tensor is constructed to obtain curvature energy; standardizing the two types of energy, and weighting the two types of energy into coupling energy according to a self-adaptive proportion; setting a threshold value according to the total graph statistics to generate candidate masks; and outputting structured results such as boundaries, geometric centers and the like through four neighborhood connected domain and area and shape ratio screening. The method gives consideration to cracks and pits, improves the accuracy and adaptability, reduces the manual dependence, and is convenient for large-scale batch application.

The invention relates to a large-scale power system discrete eigenvalue parallel computing method based on surrounding channel integration. Comprising the following steps: performing contour integral spectrum transformation on a system state matrix, and determining characteristic value dominance; differentiated integral curves are designed based on characteristic value dominance, the number of characteristic values in each integral curve is estimated, and the initial dimension of the corresponding characteristic subspace is determined; determining the number of initial integral points of each integral curve by adopting a self-adaptive method, and performing self-adaptive integral point configuration on each integral curve; determining an initial subspace dimension of each block based on the number of feature values and the number of parallel integral blocks; performing singular value decomposition on a block basis matrix to construct a standard orthogonal basis; combining the orthogonal basis of each block to form a global orthogonal subspace basis; performing Rayleigh-Ritz projection in a global space to solve a dimension-reduced generalized feature value; and outputting the discrete eigenvalue and the eigenvector. And accurate and efficient calculation of discrete characteristic values of a large-scale power system is realized.

The present application provides a kind of dumpling micro crack identification method, system, the identification method includes collecting the image of the region to be measured, fusion pixel main curvature tensor and multi-direction phase consistency feature, constructs multi-scale feature pyramid;Rely on the multi-scale micro crack membership degree feature map generated by convolution network containing channel attention, weighted fusion obtains main membership degree atlas, calculates threshold screening pixel average membership degree as main membership value, screening pixel constructs binary connected domain and skeleton, extracts topological node, constructs local topological atlas according to the difference of node quantity;Solve Laplace matrix eigenvalue to obtain algebraic connectivity, combined with the eigenvalue proportion of covariance matrix to calculate linear structure degree, fusion three core indexes input classification decision model, realize accurate identification of dumpling surface micro crack.

This application discloses a method and system for detecting the vulnerability of multi-sensor network topology, relating to the field of sensor technology. The method includes: calculating eigenvalues ​​of the state matrix. l i ( A Construct a weighted directed topological graph, establish the Laplace matrix, and obtain eigenvalues ​​through eigenvalue decomposition. m j ( L ); Calculate the state estimates of each sensor and stack them to obtain the overall system error; Establish the state matrix Φ of the unified consensus estimation error system and find the joint eigenvalues ​​of Φ; Construct the deviation system to form the reachability matrix. R If eigenvalues ​​exist m j ( L ) and eigenvalues l i ( A This allows for the simultaneous joint eigenvectors. v ij Belongs to reachable subspace span ( R If the current multi-sensor network topology and consensus gain configuration are vulnerable to Byzantine attacks, then the present application's method can determine the vulnerability of the topology without extensive time-domain simulations or physical attack experiments.

This invention discloses a method, system, and medium for determining the stability of a linear periodic time-varying system based on a harmonic state-space model, belonging to the field of linear system dynamics analysis. The method includes: constructing harmonic state-space models M with high truncation order H and low truncation order L for the system, respectively. H M L ; Calculate M L The first eigenvalue and the first eigenvector; for M H Arrange its state variables in the order of to transform them; calculate M under the first eigenvalue. L The system matrix relative to the transformed M H The deviation of the system matrix is ​​used to obtain the deviation matrix; the eigenvalue deviations are calculated based on the deviation matrix and the first eigenvector; the sum of the eigenvalue deviations and the first eigenvalue is calculated to obtain M. H The second eigenvalue is used to determine the stability of the linear periodic time-varying system. This approach ensures the accuracy of eigenvalue calculation while improving computational efficiency, thus enhancing the applicability of the harmonic state-space model to large-scale systems.

The present application relates to the field of information technology, and more particularly to a data principal component acquisition method based on transverse federated learning, comprising: respectively obtaining features and vectors of local sample data; participating parties negotiate to generate a random number vector; adding the features and the vectors and sending to a trusted coordinator; the trusted coordinator calculates the mean; the participating parties calculate the difference and the covariance matrix; again generating a random number vector, adding the covariance matrix and sending to the trusted coordinator; calculating the global covariance matrix; obtaining m eigenvalues and eigenvectors of the covariance matrix; selecting d eigenvalues and corresponding eigenvectors from the m eigenvalues in descending order and sending to each participating party; the participating party projects the local sample data into a d-dimensional space formed by the eigenvalues to obtain a projection, which is the principal component of the local sample data. The beneficial technical effects of the present application include: while protecting data privacy, allowing more sources of data to be used, and improving the accuracy of model analysis.

The application provides a new energy unit grouping method based on an admittance Laplacian matrix and a multi-dimensional binary coding quadrant division, and comprises the following steps: reading power grid topology data and element parameters to obtain a branch table of the power grid; constructing an admittance Laplacian matrix according to the branch table of the power grid; calculating eigenvalues and eigenvectors of the admittance Laplacian matrix; sorting n eigenvalues in ascending order to obtain new eigenvalues and a corresponding eigenvector sequence; and dividing nodes in the power grid by using a Laplacian spectrum multi-dimensional binary coding quadrant division method. The network topology is described by the constructed Laplacian matrix, the nodes in the power grid are divided by using the Laplacian spectrum multi-dimensional binary coding quadrant division method, and the new energy unit can be accurately grouped. The application is suitable for grouping and clustering of various new energy stations.

The application discloses a pruning optimization method for a large language model, comprising: an inter-layer feature spectrum acquisition step, based on PCA or eigenvalue decomposition, estimating the amount of information that can be preserved in each layer under different reserved dimensions; a gradient sensitivity acquisition and logarithmic mapping calibration step, using gradient to describe the influence of parameter change, and weakening resource allocation imbalance through logarithmic mapping; and a global non-uniform sparsity allocation step, allocating the reserved dimensions according to the principle of maximum marginal benefit. The application solves the problem that the traditional pruning method ignores the inter-layer heterogeneity and the long-tail distribution of gradients, leading to resource allocation imbalance, realizes a sparse configuration that is more in line with the inter-layer heterogeneity of the model, is suitable for edge computing devices and low-memory server deployment, and effectively reduces resource consumption under the premise of ensuring the performance of the model.

The invention discloses a mechanical arm heterogeneous task cooperative control method based on a graph neural network, and the method comprises the following steps: obtaining a plurality of heterogeneous tasks, and constructing a task relation graph; carrying out feature decomposition to obtain a Laplacian feature value set and a Laplacian feature vector set; coding is carried out, graph structure propagation processing is executed, and spatial domain task embedding representation is generated; projecting the spatial domain task embedded representation to a spectral domain to generate a spectral domain task representation; executing improved neural Laplacian operator processing, and performing weighting and adjustment to obtain spectral domain response representation; performing frequency domain energy modulation to obtain spectral domain control representation; inverse spectral domain transformation is executed, and time domain cooperative control representation is generated; the time domain cooperative control is converted and expressed as a mechanical arm action control quantity, and a control instruction is output; and executing feedback to construct a frequency domain error, and executing adaptive updating. According to the invention, the graph neural network and spectral domain regulation are adopted to realize the cooperative control of the heterogeneous task of the mechanical arm, and the control stability is high.

This specification discloses a method, apparatus, and device for generating attention maps based on weight decay. By determining the feature matrix corresponding to the knowledge point sequence, the feature matrix includes a key matrix K, a query matrix Q, and a value matrix V; the feature value Q of the i-th knowledge point in the query matrix Q is obtained. i And, obtain the eigenvalue K of the j-th knowledge point in the key matrix K. j Determine the time difference Δ(t) between the i-th knowledge point and the j-th knowledge point. i ,t j ), determine the decay function γ(t) that includes the time difference and the decay parameter θ. i ,t j ,θ), where θ is a learnable decay parameter; based on the eigenvalue Q i eigenvalue K j The attenuation function γ(t) i ,t j The attention map is generated using the value matrix V, which in turn reinforces performance information of recently relevant questions and other questions by taking into account the time interval factor of learner forgetting behavior.

The present disclosure relates to a method of driving a quantum computing network for determining an extremum of a cost function of a solution to a quadratic unconstrained binary optimization problem, the method comprising: initializing qubits; sequentially applying quantum gate layers to the qubits, wherein each layer comprises a multi-qubit quantum gate acting on a plurality of qubits and a plurality of variational quantum gates having two eigenvalues and a variable action on the qubits, wherein the variable actions of the variational quantum gates of the quantum gate layers form a set of variational parameters; and determining an output state of the quantum computing network to obtain a solution associated with the set of variational parameters, wherein each binary variable of the quadratic unconstrained binary optimization problem is associated with a computational ground state of the register qubits and the solution is obtained by evaluating probabilities of measuring the computational ground states corresponding to the binary variables, and wherein the solution is iteratively improved by determining an output state of altered variational parameters to evaluate partial derivatives with respect to a subset of the variational parameters, thereby determining a gradient of the cost function based on the output state of the altered variational parameters; and updating the variational parameters based on an update function of a moving average over the gradient of the cost function and a moving average over the square gradient of the cost function.

The invention discloses an Internet of Things multi-view feature selection method and system based on similar matrix fusion, and relates to the technical field of machine learning, and the method comprises the steps: firstly splicing incomplete data of each view into a wide table according to columns, and constructing a complete matrix of each view through sampling and filling; secondly, clustering each view data for multiple times, and constructing a corresponding similar matrix; stacking all similar matrixes into tensors along a third dimension, introducing adaptive weight fusion under low-rank constraint, learning a unified common similar matrix to perform eigenvalue decomposition, and extracting eigenvectors corresponding to positive eigenvalues to form pseudo tags; in combination with a pace learning strategy, high-confidence samples are screened, and feature selection coefficients and self-paced weights of all views are jointly optimized; and calculating an importance score based on each view feature to obtain an optimal subset. Through similar matrix tensor fusion, adaptive low-rank constraint and pace learning joint optimization, feature selection of incomplete multi-view data of the industrial Internet of Things is realized.

The application provides a flow field evolution method and device based on quantum computing and vortex characterization, which comprises the following steps: defining a complex scalar field, constructing an Hermite matrix based on an initial velocity field, and converting a vortex filament positioning problem into a quantum ground state solving problem; solving the minimum eigenvalue of the matrix through a quantum algorithm, and outputting an initial vortex quantum state; constructing a Hamiltonian through discretization processing according to a fluid dynamics control equation; constructing a quantum circuit of the Hamiltonian, and driving the initial vortex quantum state to evolve into a target quantum state; measuring the evolved quantum state, obtaining discrete numerical values of the complex scalar field at the center points of grid cells, positioning zero contour points through discrete winding numbers and interpolation, and reconstructing the vortex filament structure of the evolved flow field. The application fully utilizes the parallel computing advantage of quantum computing in high-dimensional data processing, significantly improves the computing efficiency of flow field simulation, speeds up the data processing speed, and effectively relieves the high demand for storage resources.

The application discloses a kind of seismic data adaptive denoising method and system based on quantum mechanics, belong to seismic data denoising field, this method includes the following steps: based on the predictability of seismic signal in frequency-space domain, seismic data is mapped into quantum potential energy field, and the eigenvalue problem of solving Schrodinger equation is used to construct adaptive quantum base function;Quantum base function is used to carry out sparse representation to seismic data, and the expansion coefficient of signal on quantum base is obtained;Using energy-based threshold processing mechanism, the expansion coefficient is suppressed to noise, and the coefficient after denoising is obtained;The seismic data after denoising is reconstructed by linear combination of quantum base function using the coefficient after denoising.The application can be seamlessly connected with existing seismic data processing procedure, facilitate the use of seismic data processing personnel, improve the analysis precision of seismic data.

The application discloses a dynamic stability analysis control method, device and system of a linear periodic time-varying system, and belongs to the technical field of system stability analysis. i The partial derivative of the concerned parameter alpha with respect to the dominant eigenvalue lambda i The sensitivity of the concerned variable alpha to the dominant eigenvalue of the linear periodic time-varying system is analyzed, the influence size and direction of the system control concerned parameter on the dominant eigenvalue can be accurately described, the technical defects that the classical dominant eigenvalue sensitivity analysis method is only applicable to linear time-invariant systems are made up, and theoretical support is provided for the dominant eigenvalue sensitivity analysis of the linear periodic time-varying system. In addition, the system matrix with complex time-varying characteristics does not need to be time-invariant, and the operation is simpler.

The invention discloses a dynamic modeling and stability evaluation method for a data-driven load frequency control system, and the method comprises the steps: constructing a Koopman operator neural network model with characteristic value penalty, and enabling a nonlinear state measurement value of a time-delay LFC system under a specific working condition to be mapped to a high-dimensional linear space through the Koopman operator neural network model with characteristic value penalty, obtaining a high-dimensional linear feature vector sequence; constructing a mixed regularized elastic network regression model, and constructing a system state transition matrix K and an eigenvalue spectrum thereof under corresponding working conditions by inputting the high-dimensional linear eigenvector sequence into the elastic network regression model; and based on the obtained characteristic value spectrum, the stability of the LFC system is judged by using a robust stability criterion considering an error, and quantitative evaluation of the stability of the time-delay LFC system is realized.

This invention belongs to the field of digital twin technology, specifically relating to a collaborative air defense combat method and system based on digital twins, including the following steps: S1, acquiring battlefield situation data; constructing a three-dimensional state gradient tensor field based on the battlefield situation data; when the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, asymmetricly splitting the spatial hexahedron along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles; S2, constructing a combat digital twin based on the heterogeneous combat tiles, and mapping the battlefield situation data into the combat digital twin; obtaining the spatiotemporal effectiveness of each heterogeneous combat tile based on the kinematic parameters of the target within the heterogeneous combat tiles and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle. This invention can improve the scientific nature and practical effectiveness of collaborative air defense combat schemes.

The invention relates to methods and systems for operating a quantum computing device to sample from an approximate stationary distribution of a Markov chain P having n states, through the construction and execution of a quantum circuit, said method comprising the step of: Initialize an ancilla qubit to the ∣0> state and at least one qubit register in its initial state; Prepare an unitary matrix U, which encodes a discriminant D in block form, allowing polynomial transformations of its singular values or eigenvalues; Apply successively a single qubit gate on the ancilla qubit and the ancilla controlled unitary matrix U on the qubit registers creating a reflection about an approximation of the stationary distribution of the Markov Chain P; and Prepare an approximation of the sought coherent quantum state associated with the stationary distribution, preferably using quantum amplitude amplification

The application provides a kind of commercial building energy consumption anomaly detection method based on graph method, it is related to intelligent building technical field, the method includes: based on the similarity graph structure is constructed, wherein node mapping is subentry partition subtable, and edge weight represents the time series similarity between corresponding nodes;By calculating the eigenvalue set of the Laplacian matrix of the graph structure, the spectral distribution representing the topological characteristics of the graph structure is generated, and the hierarchical clustering of multiple graph structures is performed based on the Battacharya distance between the spectral distributions, to obtain the energy consumption pattern clustering results of different time periods;The clustering results are analyzed by profile coefficient, and the number of class clusters corresponding to the maximum profile coefficient is selected as the corresponding division, and the class cluster set containing historical normal data is defined as the baseline class cluster.The application can improve the accuracy of building energy consumption anomaly detection.

The invention particularly relates to a B spline curve offset-selfing elimination method based on Legendre polynomial expansion. The method comprises the following steps of: obtaining a Legendre coefficient auxiliary matrix on the basis of a Legendre polynomial value and a Gauss-Legendre quadrature node weight; the method comprises the following steps: mapping a Gauss-Legendre quadrature node to a non-zero length node interval to obtain a corresponding normal direction; acquiring a corresponding offset point according to the normal direction and the specified distance; based on the Legendre coefficient auxiliary matrix and the offset point, obtaining a Legendre coefficient; compared with a Taylor expansion method, the Legendre orthogonal basis expansion method has the advantages that the approximation convergence rate is better; and the error can be further controlled through calculation of the truncation error of the Legendre coefficient and subsequent judgment and processing. The Legendre coefficient auxiliary matrix and the Legendre-Bezier transformation matrix are pre-calculated static data, so that global repeated calling for multiple times can be realized, and the approximation efficiency is improved. And when the tangent intersection detection triggered by the adjoint matrix eigenvalue method fails, returning is executed, and real intersection and tangent intersection are distinguished based on a GCD decomposition method, so that the selfing detection efficiency is further improved.