108 results about "Shape function" patented technology

The invention discloses a rapid calculation method based on a non-coordination and reanalysis theory and a computer device. The invention relates to the technical field of structural design optimization, and solves the problem that it is difficult to realize efficient structural response analysis while ensuring the calculation precision in the prior art. The method comprises the following steps: selecting a structural member of a to-be-calculated structural response and discretizing the structural member; preprocessing the data, and determining a coarse and fine grid index set corresponding to interface fine grid nodes; solving a unit shape function, and embedding the shape function into a body stiffness matrix according to a degree-of-freedom position to serve as an interface constraint condition; calculating a variable element stiffness matrix, and completing the construction of a modified model stiffness matrix; carrying out iterative calculation to obtain a basis vector; and calculating and solving the structural response of the modified model. According to the method, the efficient response analysis of the non-coordinated variable structure is realized on the premise of ensuring the calculation precision.

The invention discloses an interpretable load prediction method based on knowledge distillation and a time self-attention additive neural network, and the method comprises the steps: collecting the historical load and meteorological data of a power grid as the input characteristics of a model, carrying out the detection of a data quartile abnormal value, dividing the data quartile abnormal value into a training set, a test set and a verification set, and carrying out the detection of the data quartile abnormal value; standardization and abnormal value filling are carried out through Z-shaped orthogonalization and linear filling, and finally, a tensor form meeting the model input requirement is converted through a sliding window; designing a knowledge distillation'teacher-student 'framework based on multiple scales and multiple cycles; constructing a time self-attention additive neural network TSA-NAM as a student model; calculating a shape function representing the contribution degree and the characteristic value in the sub-network to obtain the interpretability of the characteristic dimension; exporting the attention weight of the time self-attention module to obtain the interpretability of the time dimension; performing simulation verification; according to the method, high reliability and high precision are guaranteed, and meanwhile, multi-dimensional interpretability is brought to power load prediction.

The invention provides a shape function KL expansion random field discretization method considering a slope soil body irregular domain, and belongs to the technical field of soil body parameter random field analysis. Comprising the following steps: establishing a slope numerical model and dividing a discrete grid and a form function grid; establishing a probability distribution model of a soil parameter random field; calculating an element stiffness submatrix ke and an element mass matrix Ee; calculating an autocorrelation matrix rho and a global stiffness matrix B; assembling a global matrix; calculating a characteristic value lambda k, a characteristic function phi k and an expansion term number M; and random field discretization of the slope numerical model is realized. The random field discrete technology provided by the invention is used for efficiently and accurately analyzing the random distribution characteristics of the soil parameters in the rock-soil structure. The discrete random field model can be efficiently constructed in a complex geological structure, the calculation cost is remarkably reduced, the method can be conveniently combined with numerical simulation tools such as a finite element method, and the requirement of actual engineering for efficiency is met while the precision is improved.

The invention relates to an MVP formula-based edge element magnetostatic high-precision calculation method for smooth edges, and the method comprises the steps: dividing grid data into a plurality of polyhedral smooth regions with corresponding edges as centers according to the edges in the grid data; the polyhedral smooth domain is formed by surrounding corresponding edges by nodes, body centers and face centers of tetrahedron units in the grid data; calculating the vector shape function gradient of the corresponding edge based on the vector shape function of each tetrahedron unit in the polyhedral smooth domain corresponding to the edge; constructing a static magnetic field equation based on an MVP formula and coulomb specifications, and rewriting the static magnetic field equation according to the vector shape function gradient of each edge and a Galerkin method to obtain a system equation of a static magnetic field; further rewriting the system equation of the static magnetic field into a Newton iteration linear equation; and iteratively solving the Newton iteration linear equation by adopting a Newton iteration method until convergence to obtain the magnetic vector position in the static magnetic field. According to the method, the requirements of high calculation precision and stability of the engineering static magnetic field problem are met.

The invention relates to the technical field of bridge engineering, and particularly discloses a method for predicting earthquake-induced high-low geometric irregularity of a high-speed railway target under a longitudinal earthquake, which comprises the following steps of: establishing an earthquake-induced high-low geometric irregularity random sample library on a high-speed railway bridge; the earthquake-induced high-low geometric irregularity is considered as the product of the shape and the amplitude variable; establishing a shape function expression of the target earthquake-induced high-low geometric irregularity; combining uncertainty analysis to fit a high-speed railway pier top displacement peak value upper bound spectrum; solving an amplitude variable through a structure period and a pier top displacement peak value upper bound spectrum; and constructing a time domain sample of the seismic-induced high-low geometric irregularity of the target based on the shape function and the amplitude variable. According to the method, the high-low geometric irregularity under the action of the longitudinal earthquake can be quickly predicted, the post-earthquake traffic capacity of the high-speed railway bridge can be quickly evaluated, and a basis is provided for the post-earthquake running speed limiting and emergency processing scheme optimization of the high-speed railway.

The invention discloses a current deposition calculation method and device in particle grid simulation and a storage medium, and relates to the technical field of particle flow simulation, and the method comprises the steps that a VPU determines the shape function value of each dimension of a particle and the current weight of each dimension based on the particle data of the particle corresponding to a target grid unit; taking two particles with adjacent index positions as a particle pair, and constructing a first operand vector and a second operand vector corresponding to the particle pair by the VPU based on the shape function value and the current weight of each dimension; the MPU executes matrix outer product operation on the first operand vector and the second operand vector, matrix outer product operation results in the target grid unit are accumulated until a total contribution matrix corresponding to the target grid unit is obtained, the VPU merges the total contribution matrix to a global current array, and the global current array is obtained. The technical problem that the performance of the particle grid simulation algorithm is limited due to the multi-thread writing conflict in the global merging stage is solved, and the expandability and the calculation efficiency of the particle grid simulation algorithm are improved.

The invention discloses a meshless analysis method considering background grid partition refinement and truncation optimization, and belongs to the technical field of meshless method numerical simulation. The method comprises the following steps: S1, sequentially reading boundary node information, internal node information, material information and load information of a meshless model; s2, positioning a background grid near the boundary of the meshless model, and carrying out local quartering on the background grid; s3, generating a plurality of Gaussian points in the background grid after local quartering, and calculating the integral area of each Gaussian point for subsequent numerical integration; and S4, calculating a shape function of each Gaussian point, and discretizing and solving the meshless balance equation based on the integral area of each Gaussian point in the S3 to complete meshless analysis considering background grid partition refinement and truncation optimization. Through background grid local quartering and truncation optimization, the characterization capability of the meshless method for a complex boundary is improved, the problem that the simulation precision of the meshless method at the boundary is reduced is solved, and the application range of the meshless method is expanded.

The invention provides a bridge steel box girder linetype control method based on multistage monitoring and dynamic adjustment. The method comprises the steps that S1, inclination angle data, mileage data and section temperature difference of a bridge steel box girder and coordinate data of all control point positions continuously collected by a sensor network are obtained; s2, constructing a theoretical linear reference curve according to the inclination angle data, the mileage data and the section temperature difference, and generating a deformation vector according to the inclination angle data and the coordinate data; s3, generating an elevation variation vector according to the theoretical linear reference curve and the deformation vector, and introducing a shape function to solve the elevation variation vector so as to obtain a hydraulic adjustment amount; and S4, the hydraulic adjustment amount is input into a PID controller, and synchronous lifting control is conducted on the hydraulic jacks so that the supporting height can be adjusted. The method has the beneficial effects that dynamic lifting control over the hydraulic jack cluster can be achieved, and the control precision is improved.

This invention provides a method and system for three-dimensional high-frequency controllable source electromagnetic numerical simulation with dual-source excitation. The method constructs a single-source electromagnetic field grid model and a three-dimensional spatial domain total field equation, converting it into a quadratic field control equation by separating the primary and secondary fields. Fourier transform is used to transform the equations to the wavenumber domain, and shape function interpolation is performed iteratively to obtain the wavenumber domain numerical solution. A single-source forward excitation solution is obtained through inverse Fourier transform. A single-source reverse excitation solution is obtained by reversing the current direction. Finally, the forward and reverse solutions are vector-superimposed to obtain the dual-source excitation simulation result. This invention solves the technical problems of existing technologies, such as simulation distortion caused by neglecting displacement current in the 100kHz-10MHz frequency band, numerical calculation interference from field source singularities, and low spatial resolution of complex underground anomalies under single-source excitation. By simulating gradient field response characteristics through dual-source reverse superposition, the sensitivity and exploration resolution of underground target boundaries are significantly improved.

The present invention provides an imaging method for the singular mode vibration mode of FBAR based on the semi - analytical finite element theory, including the following steps: Step S1, constructing a semi - analytical finite element formulation of a FBAR with a complex electrode configuration; Step S2, using triangular elements to mesh the upper surface of the FBAR to obtain the coordinates of three nodes in each mesh element; Step S3, determining the interpolation shape function, stiffness matrix and mass matrix of each mesh element according to the node coordinates; Based on the semi - analytical finite element theory, the present invention characterizes the vibration mode of a three - dimensional FBAR at ultra - high frequencies, reduces the three - dimensional modal vibration imaging of a three - dimensional FBAR device to two - dimensional planar imaging. The simplification of the element type and the substantial reduction in the number of elements make the imaging technology provided by the present invention have a lower time cost. At the same time, it does not require various parameter settings and post - processing in commercial finite element software, realizing fast and quantitative imaging of the FBAR vibration mode.

The invention provides a method and a device for predicting the plane shape of a rolled medium plate. The method comprises the following steps: acquiring related process parameters and intermediate parameters in the rolling process of the medium plate; obtaining non-uniform deformation node coordinates of the head part and the tail part of the rolled medium-thickness plate based on the related process parameters and the intermediate parameters; on the basis of the related process parameters and the intermediate parameters, obtaining non-uniform deformation node coordinates of the rolled edge part of the medium-thickness plate; performing data fitting on the non-uniform deformation node coordinates of the head part, the tail part and the edge part to obtain a plurality of shape functions of a plane shape profile curve; and connecting the plurality of shape functions to obtain a complete plane shape profile curve of the rolled medium-thickness plate. According to the method, the complete profile curve of the plane shape of the rolled medium-thickness plate can be obtained by inputting the technological parameters, the rolled piece size and the equipment parameters in the rolling process of the medium-thickness plate, and therefore the change rule of the plane shape of the rolled piece in the rolling deformation process can be described more accurately.

The invention discloses a method and a system for designing a variable cross-section ultrahigh pressure plunger structure, comprising the following steps: firstly setting load and boundary conditions of a plunger, then determining an inner cavity structure of the variable cross-section plunger by constructing a shape function of the variable cross-section plunger, and then obtaining deformation distribution of the surface of the current plunger based on finite element simulation calculation, and finally, iteratively optimizing parameters of the shape function of the inner cavity of the plunger by adopting a gradient descent method until a termination condition is met, and obtaining an optimal variable cross-section ultrahigh-pressure plunger structure. According to the variable-cross-section ultrahigh-pressure plunger structure and the design method thereof, the inner and outer pressure difference of the plunger is matched with the cross section rigidity by changing the cross section structure of the inner cavity of the plunger, so that the surface deformation of the plunger is remarkably reduced, the deformation resistance and the lightweight requirement are both considered, machining is convenient, and large-scale engineering application prospects are achieved.

The invention discloses a structural response analysis and robustness topological optimization design method based on a convolutional neural network, and belongs to the technical field of structural response analysis and topological design. Comprising the steps that sensitivity analysis and substructure unit modulus clustering of a substructure numerical value shape function about substructure unit moduli are carried out, and substructure sampling and sample transformation under a level set method framework are carried out; constructing a convolutional neural network between the substructure numerical value shape function and the substructure unit modulus and a continuum structure topological optimization model, and defining input of the continuum structure topological optimization model; based on the structure statics response analysis of the extended multi-scale finite element, the displacement response solution of the whole structure is realized; and carrying out topological optimization model sensitivity calculation, level set function updating and convergence determination. According to the method, a network structure with fewer layers and lighter weight is adopted, the neural network model is simplified, and the difficulty of neural network training is reduced.

A model representing a physical object in a shape optimization according to a design objective, and a control point for altering a shape of the physical object are received. The shape is defined by a set of nodes in the model. Sibling models are generated from the model according to a perturbation scheme. The control point is perturbed with respective perturbed values for the sibling models. Each sibling model contains nodal location changes for the nodes. The nodal location changes are determined based on a respective shape function formulated according to a respective perturbed value at the control point and one or more simulated physical behaviors of the model. The model is updated to have an optimal value for the control point. The optimal value is identified from a relationship according to the design objective. The relationship correlates a physical characteristic of the sibling models to the respective perturbed values.

The application belongs to the field of computational mechanics, and discloses a scale order reduction near-field finite element calculation acceleration method and implementation method for structure fracture analysis.The acceleration method comprises the following steps: firstly, geometric modeling is performed on a target structure; secondly, the split finite element is recorded as a fine scale element and constitutes a fine scale grid; thirdly, based on a spatial neighborhood relationship, the fine scale element is collected into a coarse scale element and constitutes a coarse scale grid; fourthly, an equivalent shape function of the coarse scale element is obtained; fifthly, the overall stiffness matrix and the load vector of the coarse scale grid are calculated; sixthly, the overall node displacement of the coarse scale and fine scale grid is solved; seventhly, it is judged whether the current loading step or time step reaches the maximum loading step or time step; if yes, the displacement nephogram and equivalent damage nephogram of the target structure are output; if not, the key state of all fine scale near-field elements is updated; and finally, the implementation method is that the acceleration method is taken as a core calculation module to be implemented in different scenes.The application significantly improves the calculation efficiency of near-field dynamics in large-scale simulation analysis.

The present invention relates to the technical field of computer-aided design, and further relates to a method for analyzing the stress of spherical reticulated shell structure nodes based on refined simulation optimization. The method includes: Step 1: Uniformly select a plurality of observation points in the target spherical reticulated shell area, correct the displacement field corresponding to each observation point with spherical harmonic functions in spherical coordinates, and construct a total potential energy functional; Step 2: Discretize the target spherical reticulated shell area into finite element meshes, approximate the displacement field using high-order finite element shape functions, construct a discrete residual equation, and solve to obtain the overall degree-of-freedom vector; Step 3: Calculate the absolute value of the difference between the local error index of each grid element and the modulus of the overall degree-of-freedom vector of the observation point closest to it, and then determine that the grid element has abnormal stress. The present invention significantly improves the calculation accuracy, numerical stability and local anomaly detection ability.

This invention discloses a lithography simulation method and system based on circular sampling function decomposition and superimposed pupil shift matrix. The method includes: sampling the shape function and pupil function of the extended light source to obtain the corresponding superimposed pupil shift matrix; processing the superimposed pupil shift matrix, the frequency domain circular sampling function matrix of the extended light source and the pupil plane to obtain the frequency domain cross-transmission coefficient matrix and the projection matrix; performing singular value decomposition on the projection matrix to obtain the singular value decomposition result; processing the spatial domain circular sampling function matrix based on the singular vectors to obtain the convolution kernel matrix; constructing a spatial domain image simulation model based on the singular value decomposition result, the convolution kernel matrix and the initial Hopkins model; and obtaining the spatial domain image simulation result based on the spatial domain image simulation model. This invention utilizes the superimposed pupil shift matrix method and analytical circular sampling function decomposition, which can reduce the direct calculation and storage of the TCC matrix and significantly reduce the computational cost required to obtain the kernel.

A method for calculating a band gap of a built-in harmonic oscillator periodic structure of a hollow pipe pile comprises the steps that a hollow pipe pile body, a soil body and a harmonic oscillator coordinate system are divided through regional decomposition, and a unit cell structure total constraint condition matrix composed of a periodic boundary constraint condition matrix and a pile-soil contact interface constraint condition matrix is established; processing the unit cell structure total constraint condition matrix through a linear expression method to obtain a basic solution set; establishing a unit cell structure total energy functional and a motion equation of the unit cell structure according to the basic solution system set, and scanning the wave number of the first Brillouin region to obtain a vibration frequency dispersion curve of a built-in harmonic oscillator periodic structure of the hollow pipe pile; and analyzing the corresponding relationship between the wave vector and the frequency of the periodic pile-in-row structure to obtain the band gap characteristics of the periodic structure of the built-in harmonic oscillator of the hollow pipe pile. According to the method, the pile-soil parameter distortion problem and the boundary dependence problem in shape function construction are avoided, so that the method for calculating the band gap of the built-in harmonic oscillator periodic structure of the hollow pipe pile is provided, the calculation implementation complexity is low, and the calculation result is accurate.

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 invention relates to a concrete skewback segment crack simulation analysis method, and belongs to the field of concrete construction. According to the technical scheme, the concrete skewback segment crack simulation analysis method comprises the following steps that S1, simulation analysis basic conditions are determined, specifically, concrete damage parameters are set, and finite element software is selected; s2, constructing a concrete skewback segment simulation model by adopting an extended finite element method, defining a level set function to characterize a crack interface through a level set method, and constructing a displacement function by adopting a discontinuous shape function; s3, setting a concrete crack initiation criterion and a concrete crack propagation direction criterion; and S4, anti-cracking simulation analysis is conducted on the construction stage and the operation stage of the skewback section, and the cracking state and stress field distribution of skewback section concrete are obtained. According to the method, the anti-cracking performance under the load effect in the operation stage is evaluated, the whole-stage cracking state and the stress field distribution rule are output, a whole-cycle data support is provided for engineering practice, and the problem that single-stage analysis and evaluation are one-sided in the traditional technology is solved.

The invention relates to a Lagrange large-deformation finite element analysis interpolation method for geotechnical engineering, which comprises the following steps of: mapping state variables in an old grid into a new grid by adopting a super-convergence recovery technology and a unique element method, and aiming at the problem of interpolation error caused by a boundary effect, adopting a method of combining nearest neighbor and element shape function extrapolation to obtain an interpolation result. The mapping precision of model state variables is effectively improved, the convergence of large deformation finite element calculation is improved, and stable and reliable technical support is provided for geotechnical engineering large deformation finite element analysis.

The invention discloses a direct-current gas-solid insulation interface electric field calculation accuracy experimental verification method, which comprises the following steps of: firstly, designing a surface potential online measurement system, and accurately measuring potential distribution of an insulation material gas-solid interface under an electrified condition; then, on the basis of actually measured potential data, a Lagrange interpolation method is reconstructed under a polar coordinate system, a shape function describing insulator surface potential space distribution characteristics is constructed, and the electric field intensity of the gas-solid interface of the insulating material is solved; the surface potential online measurement system designed by the invention provides actually measured data support for simulating a simulation potential result of an actual operation condition, and the proposed shape function method based on Lagrange interpolation can realize continuous expression of discrete potential data and reflect spatial distribution characteristics of electric field intensity; consistency of experimental calculation results and simulation results in spatial distribution forms and numerical values is compared, and accuracy of the simulation model is effectively verified.

This invention relates to a method, device, and medium for displaying mechanical information for risk warning during impacted tooth extraction. The method includes: Step S1: Obtaining the three-dimensional modeling results of each tissue unit; Step S2: Obtaining the modeling results of each tooth segment unit; Step S3: Constructing the tooth segment and its contact constraints with surrounding tissues; Step S4: Based on the constructed contact constraints, combined with the overall finite element stiffness matrix and operational load, solving for the displacement response of each finite element mesh; Step S5: Based on the displacement response of each finite element mesh and the shape function, obtaining the displacement matrix of each element, and further obtaining the strain tensor of each element; Step S6: Based on the constitutive matrix of the tissue material corresponding to each element and the strain tensor, obtaining the stress tensor of each element; Step S7: Comparing the stress tensor of each element with its pre-configured threshold and assigning color values ​​to the finite element mesh of each element. Compared with the prior art, this invention has the advantages of real-time performance and high accuracy.

The invention discloses a novel modal shape function construction method suitable for a variable cross-section flexible structure, and the method comprises the following steps: firstly, building a linear kinetic equation of a flexible wing based on an Euler-Bernoulli beam theory and a Lagrange principle; secondly, geometric and physical parameters in the equation are normalized through dimensionless variable substitution, and the coupling relation between different variables is simplified; secondly, formalizing the solution into a linear combination of a first type of Bessel function and a second type of Bessel function by adopting a special function expansion method so as to ensure that boundary conditions are met and effectively reflect the influence of section change on modal characteristics; and finally, solving the inherent frequency and a modal shape function by constructing a novel modal shape function. According to the method, iteration and approximate truncation are not needed, the inherent frequency and the modal shape can be rapidly and accurately calculated, the calculation efficiency is remarkably improved, high calculation precision is guaranteed, and the method is suitable for efficient dynamic analysis of a complex structure.

The invention discloses a finite element calculation method of a nearly incompressible material and computer equipment, and the finite element calculation method comprises the following steps: constructing a geometric model, endowing parameters of the nearly incompressible material to the geometric model, endowing boundary conditions and loads to the geometric model, and obtaining a finite element parameter model of the nearly incompressible material; performing mesh generation on the finite element parameter model according to a pre-selected unit type to obtain a finite element model; establishing a unit stiffness matrix of the units; assembling the unit stiffness matrix to form a global stiffness matrix; discretizing the load to generate a global node force vector, and calculating to obtain a node displacement vector; and performing post-processing by utilizing the node displacement vector to obtain displacement, stress and strain of the finite element model. According to the method, the volume self-locking characteristic of the unit is eliminated by correcting the part, related to the volume, in the shape function derivative matrix B, so that the volume self-locking problem of the nearly incompressible material in the finite element calculation process can be well solved.

The present invention discloses a method and system for mechanical-thermal coupling simulation and structural optimization of ultra-complex structures. The method comprises: generating parameters and data structures required for subsequent simulation and optimization for a given model and design domain; constructing a background coarse grid, seed points and radii, modeling a porous structure based on a Voronoi structure, and precalculating its stress field; calculating a density field, performing thermodynamic simulation on the generated porous structure based on the density field, the background coarse grid, and a shape function; querying the stress matrix corresponding to each seed point based on the obtained stress field, performing eigendecomposition and extraction on the stress matrix, and obtaining a weight matrix corresponding to the seed point; using a topology optimization method, updating control parameters through a GCMMA method based on sensitivity, thereby updating the porous structure and optimizing material distribution, and continuously optimizing until the change in control parameters is less than a threshold. The method can quickly and effectively solve the topology optimization problem of anisotropic porous structures under multi-physics field conditions.

The invention belongs to the related technical field of concrete bridges, and discloses a rigidity prediction method and system based on an order spectrum unit and an isoparametric unit in a concrete bridge. The method comprises the following steps: identifying key areas for creep analysis in a finite element model of a concrete bridge, setting order spectrum nodes in each key area according to creep characteristics of each key area, and determining an order spectrum shape function of each key area according to the number of the order spectrum nodes in each key area; connecting the order spectrum nodes in each key area to form a grid unit; each grid unit is regarded as an eight-node shape unit, and the rigidity of each key area is calculated through the shape function of the shape unit and the order spectrum shape function of each key area. According to the method, the problems of direction anisotropy self-adaption, low calculation precision and low numerical stability are solved.

The application relates to the technical field of structural simulation interaction, in particular to a building structure simulation result visual interaction system, which comprises the following modules: a data analysis module, which is used for acquiring a geometric model and a finite element analysis result file in parallel and extracting a coordinate sequence; a grid mapping module, which is used for calling a shape function interpolation algorithm based on physical field data flow to calculate local coordinate weights and projecting data to rendering grid vertices; an interactive detection module, which is used for capturing virtual probe tip world coordinates in real time and logically searching for surrounding elements based on voxel indexes; and a dynamic rendering module, which is used for rendering an over-limit area in a highlighted flickering mode in an enhanced three-dimensional rendering model in response to a judgment signal. In the application, local grid subdivision is performed on a high stress area according to a stress gradient change rate, an enhanced three-dimensional rendering model is constructed, a Boolean operation cutting is performed along a principal stress direction, and a dynamic section view and a local contour map are generated.

The invention provides an aircraft optimal recovery trajectory design method based on a Bezier shape function, and relates to the technical field of aircraft automatic control. The method comprises the following steps: S1, acquiring state parameters of an aircraft in real time and setting the state parameters as initial state constraints; s2, defining an end point state and setting an end point state constraint; s3, constructing a composite constraint function; s4, based on the initial state constraint and the end point state constraint, adopting a Bezier curve to calculate initial Bezier curve parameters, and generating an initial trajectory; and S5, iteratively optimizing the Bezier curve parameters by taking the initial Bezier curve parameters as an optimization initial value and taking the flight time minimization as an optimization index, and verifying the feasibility of the recovery trajectory by using a kinetic model, and finally generating an optimal recovery trajectory. According to the method, the calculation efficiency and the trajectory optimality are balanced, the real-time performance and reliability of boundary protection control are improved, and it is ensured that the aircraft can rapidly recover stable flight within the safe envelope boundary.

The present disclosure provides systems and methods for determining an anomaly score for defect detection in connection with a kinematic implementation, such as a vehicle implementation. The method includes receiving one or more design parameters relating to the vehicle implementation (104). Furthermore, one or more shape-function parameters relating to the implementation are received. A machine learning engine (ML engine) (316) is also employed, based on the one or more design parameters and the one or more shape-function parameters, to create an environment such that a learning agent associated with the environment is configured to analyze the design parameters and the shape-function parameters to identify anomalous patterns associated with the vehicle implementation (104).The anomaly score for error detection related to vehicle operation is then calculated based on the identified anomalous patterns.