25 results about "Legendre polynomials" patented technology

The invention discloses a vibration solving method for an elliptical perforated plate in any shape based on an elliptical energy element, and belongs to the technical field of thin-wall structures, and the method comprises the steps: carrying out the overall mapping of the elliptical perforated plate in any shape, building an elliptical equation in a dimensionless coordinate system, and carrying out the Boolean operation modeling of geometry; constructing a boundary condition function simulation constraint; simulating board deformation according to a first-order shear deformation theory, and constructing a global trial function in combination with a Legendre polynomial and a boundary condition function; establishing a total energy functional based on a minimum potential energy principle and a Ritz method, solving a total energy functional stationary value, and obtaining element calculation formulas in the stiffness matrix and the mass matrix; and constructing an elliptical energy element based on local mapping, and performing numerical integration on each element of the matrix based on the elliptical energy element and completing vibration problem solving. According to the method, an energy functional and a numerical integration formula are both constructed on a square solution domain in an overall mapping stage, so that the calculation solution process of the elliptical perforated plate in any shape is completely standard.

The invention discloses a modal modeling method for a tendon-driven continuum robot. The method comprises the following steps: carrying out differential modeling on a configuration under a SE (3) Lie group-se (3) Lie algebra framework; the strain field is subjected to spectrum parameterization and is decomposed into active / passive orthogonal subspaces, and an inner product adopts energy weighted Hilbert measurement containing material and section parameters. The active mode is constructed by a linear continuous Jacobian of a tendon path; legendre polynomial expansion is adopted under the collinear layout, and complex Fourier harmonic expansion is adopted under the non-collinear layout; the passive mode is selected according to a spectrum slot position mutual exclusion principle so as to ensure that the passive mode is orthogonal to the active mode in energy and suppress spectrum leakage. Lie group integration and spectral integration are adopted for numerical value realization; newton-Rafson iteration is used in the quasi-static state, and generalized-alpha time integration or Newmark-beta integration is used in the dynamics. The method has high precision and robustness under nonlinear large deformation and multi-tendon coupling conditions, and is suitable for scenes such as software operation, minimally invasive intervention and precise detection.

The invention discloses an intermediate-frequency surface shape white light interference splicing measurement method based on polynomial filtering. The method comprises the following steps: carrying out white light interference splicing measurement on an X-ray plane mirror to obtain a group of interference measurement surface shape results with overlapped adjacent sub-aperture space positions; fitting the surface shape result of each sub-aperture by using a Legendre polynomial to obtain a polynomial coefficient under a preset order; fitting according to a polynomial coefficient to generate a fitting surface shape of a corresponding order, and subtracting the fitting surface shapes of all orders from the measurement result to obtain a group of surface shape results subjected to Legendre polynomial filtering; and splicing the filtered shape results according to a least square algorithm to obtain a final measurement result. The method aims at meeting the splicing measurement of sub-nanometer PV precision required by the intermediate-frequency surface shape error detection of the X-ray plane mirror, the least square optimization splicing method is used, the method is not limited by the low-frequency characteristic of the measurement error of the white light interferometer, and the precision and flexibility of the splicing measurement are improved.

The present invention discloses a PolInSAR forest height inversion method with dual constraints of parameter association and scattering difference, which belongs to the field of remote sensing information processing technology. The method comprises the following steps: using forest height prior information to determine the Fourier-Legendre polynomial coefficient constraint interval; constructing inequality constraints based on the polarization scattering difference between the forest canopy and the bottom layer; combining the constraints, using a nonlinear least squares iterative algorithm to invert the forest height and vertical structure parameters. The polynomial coefficient constraint interval is determined by statistically analyzing the coefficient values ​​corresponding to different forest heights, and the scattering difference constraint is constructed based on the relationship between the top and bottom scattering powers of the polarization modes dominated by volume scattering and surface scattering. The objective function is the sum of squares of the measured value of the complex coherence coefficient and the estimated residual, and the iterative termination conditions include the number of times, function tolerance and parameter tolerance. Experiments show that compared with the conventional unconstrained nonlinear iterative method, the RMSE of forest height estimation is reduced by 12%, effectively improving the inversion accuracy and stability.

The invention provides a convex polygon roadway surrounding rock stress calculation method, belongs to the technical field of underground engineering technologies, and solves the problems that an existing calculation method is low in efficiency, single in applicable scene and incapable of accurately reflecting the actual stress state. According to the convex polygon roadway surrounding rock stress calculation method, roadway surrounding rocks are numbered as a plurality of planes, the equivalent concentrated force borne by each plane is calculated through the Gaussian integral of the w-order Legendre polynomial, and the stress of any point in the roadway surrounding rocks is obtained based on force balance calculation. According to the method, the calculation process is not limited by the shape of the roadway, the method is suitable for stress calculation of various polygon-shaped roadways, the actual load borne by the roadway can be fully simulated, the effect of concentrated force on the roadway and the effect of distributed force are considered, the roadway construction load influence is truly reflected, and the stress around the roadway and the roadway corner points can be calculated; the calculation precision is high, and the singularity characteristics of the roadway corner stress can be accurately reflected.

The invention discloses an invisible shipboard aircraft re-flight trajectory optimization method and device based on a pseudo-spectral method, a medium and a product, and relates to the technical field of automatic control, and the method comprises the steps: constructing a re-flight dynamics model according to dynamics and kinematics equations of an invisible shipboard aircraft, and determining a target function and constraint conditions; determining a plurality of collocation points through a zero point of a Legendre polynomial, respectively converting a state variable and a control variable into discrete variables at each collocation point, and then converting a target function and a constraint condition into algebraic constraints to obtain a nonlinear programming equation set; solving an optimal solution of the nonlinear programming equation set at each collocation point by using a sequential quadratic programming algorithm; and finally, carrying out serialization by utilizing a Lagrange interpolation polynomial to obtain a camouflage shipboard aircraft re-flight trajectory optimization result. According to the method, the capacity of an execution mechanism of the stealth shipboard aircraft is fully considered, the optimal re-flight track of the stealth shipboard aircraft is obtained, and the problem that the flight capacity in a traditional re-flight strategy is not fully utilized is solved.

The present invention discloses an image defogging transformer based on Legendre polynomial approximation and error compensation modules, comprising a multi-scale feature extraction and embedding module, a Legendre polynomial self-attention module, a calculation error compensation module, and a sampling error compensation module. The multi-scale feature extraction and embedding module is used to perform multi-scale feature extraction; the Legendre polynomial self-attention module approximates the exponential function in the softmax function by using Legendre polynomials to reduce computational complexity; and the calculation error compensation module and the sampling error compensation module are used to reduce errors introduced in the calculation and sampling processes, thereby enhancing the image defogging effect.

This invention provides an integrated monitoring method for fatigue type differentiation and dynamic state tracking, belonging to the field of biometric recognition and fatigue monitoring technology. It includes continuously acquiring pupil time-series data through a sliding window, sequentially performing time-delay embedding, Legendre polynomial decomposition, and incremental VAE dimensionality reduction to obtain a dynamic manifold; then, incremental unsupervised clustering is used to differentiate between active and passive fatigue in real time, and the continuous window trajectory is analyzed to predict state trends, ultimately outputting a dynamic early warning. This integrated approach of differentiation, monitoring, and prediction overcomes the shortcomings of existing technologies, such as delayed early warnings and insufficient long-term accuracy, and can be widely applied to safety management scenarios such as driving.

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.

The application provides an online self-adaptive calibration method and system for low power factor error of an electric energy meter, comprising the following steps: measuring initial phase error at multiple preset low power factor calibration points to establish a data set of power factor and error; constructing an initial error function based on the data set; calculating a second derivative sign change point of the function as a boundary point to divide multiple calibration subintervals; adopting a weighted sum model of Legendre polynomial and hyperbolic tangent function to fit a phase error compensation formula in each subinterval; calculating a compensation value according to a real-time power factor position and a corresponding subinterval compensation formula during actual operation of the electric energy meter; and if the power factor is near the boundary point, then smoothing and fusing adjacent interval results through a Gaussian weighting function to realize online correction of the phase error.

The application discloses a kind of based on module component homomorphism's Legendre-KAN encryption reasoning method, it is related to information security technical field, including: step 1: based on Legendre polynomial's KAN structure constructs Legendre-KAN network;Step 2: image sample set is collected to the Legendre-KAN network training obtains Legendre-KAN model;Step 3: to be predicted image is encrypted, obtains ciphertext data;Step 4: in GPU, utilizes Legendre-KAN model and uses module component homomorphism algorithm to ciphertext data and carries out parallel reasoning, obtains encryption result;Step 5: to encryption result is decrypted and obtains image prediction result.The application can make the data in entire reasoning process always in encrypted state, effectively avoid privacy leakage, and can improve model reasoning efficiency, accelerates data reasoning process.

The invention discloses a positioning method based on adaptive carrier phase smoothing pseudo-range, which belongs to the technical field of satellite navigation system signal processing, and comprises the following steps: establishing a frequency-point-crossing adaptive carrier phase smoothing model to realize smooth continuity maintenance in a carrier lock loss state; constructing a sectional ionosphere delay compensation model, dividing a space region into a core modeling region, a boundary fusion region and a global approximation region, and respectively adopting Legendre polynomial, progressive weight fusion and spherical harmonic function modeling; a regularization constraint parameter estimation method is adopted, and the numerical stability of parameter estimation is ensured by introducing regularization items and multiple constraint conditions; a predictive model switching protocol is implemented, and seamless switching of modeling strategies is realized based on real-time performance monitoring. The technical problems that a traditional carrier phase smoothing method is poor in smoothing continuity, the ionosphere compensation precision and efficiency are contradictory, and parameter estimation numerical values are unstable in a complex environment are solved, and the precision, continuity and reliability of GNSS positioning are improved.

The present application discloses a vibration solution method for an elliptical perforated plate of arbitrary shape based on an elliptical energy element, which belongs to the field of thin-walled structure technology and includes: overall mapping of the elliptical perforated plate of arbitrary shape, establishing the elliptical equation in a dimensionless coordinate system, and implementing Boolean operation modeling on the geometry; constructing a boundary condition function to simulate the constraint; simulating the plate deformation according to the first-order shear deformation theory, and constructing a global test function in combination with Legendre polynomials and boundary condition functions; establishing a total energy functional based on the minimum potential energy principle and the Ritz method, solving the stationary value of the total energy functional, and obtaining the calculation formula of each element in the stiffness matrix and the mass matrix; constructing an elliptical energy element based on local mapping, and numerically integrating each element of the matrix based on the elliptical energy element and completing the solution to the vibration problem. In this method, the energy functional and the numerical integration formula are both constructed on the square solution domain in the overall mapping stage, so that the calculation and solution process for the elliptical perforated plate of arbitrary shape is completely standard.

The present invention belongs to the technical field of seismic data processing for oil and gas exploration, and specifically discloses a method and system for estimating formation Q value by two-dimensional Legendre polynomial decomposition in the time-frequency domain. The method of the present invention first calculates the time-varying logarithmic amplitude spectrum of seismic data based on the short-time Fourier transform, and then maps the time-varying logarithmic amplitude spectrum of seismic data into a two-dimensional square-integrable function space spanned by Legendre polynomials. In this space, the time-varying logarithmic amplitude spectrum of seismic data is decomposed by two-dimensional Legendre polynomials to estimate the time-varying wavelet amplitude spectrum, and finally the equivalent formation Q value is calculated using the time-varying wavelet amplitude spectrum. The method of the present invention uses Legendre polynomial decomposition to estimate the time-varying wavelet amplitude spectrum. Compared with the methods of decomposing into Fourier series and traditional polynomials, this method has the advantages of fast convergence, strong approximation ability, and reduction of matrix ill-conditioning. It can also eliminate the influence of factors such as local strong reflections and waveform coupling, and improve the stability and accuracy of Q value estimation.

The invention relates to the technical field of hydrological simulation, and particularly discloses an extra-small watershed layered three-dimensional hydrological-hydrodynamic full-coupling simulation method, which comprises the following steps: collecting multi-source data to construct a three-dimensional space discrete grid and dividing initial time units; the control equation set is converted into an algebraic system based on a Legendre polynomial and a Gaussian-Loabar node; adaptively adjusting a time unit length and a spectral basis function order according to the local time gradient change rate; a convergence spectral coefficient is obtained through spectral delay correction iteration solution; and finally, forcibly executing mass conservation constraint, controlling step recalculation according to a local time error, and gradually outputting a flow hydrograph and water depth and infiltration rate distribution according to time unit endpoints. According to the method, the dual self-adaption of the time step length and the polynomial order is realized, the numerical oscillation of the infiltration rate caused by the sudden change of the ponding depth can be effectively inhibited, the mass conservation is ensured, and the stability and the efficiency of the rainstorm flood simulation of the extra-small watershed are improved.

The invention relates to a three-dimensional volume data generation method and system based on angular deformation and secondary peak constraint. The three-dimensional volume data generation method comprises the following steps: constructing a three-dimensional equidistant grid and calculating a radial distance and a spherical coordinate angle of grid points; designing a controllable random coefficient, acquiring an angular deformation factor based on a Legendre polynomial, and acquiring a coordinate point of the original coordinate point after angular deformation by combining the original radius; constructing a main peak point, designing a secondary peak point center constraint to generate a secondary peak point, calculating intensity contribution and accumulating the intensity contribution to a total intensity field; carrying out NaN value replacement and total intensity field normalization; carrying out volume data storage and metadata file output; shared variables are pre-calculated through outer-layer control circulation, inner-layer samples generate circulation sampling, variable parameters are updated, and the volume data generation efficiency is improved; the system supports a parallel generation mode and GPU acceleration. According to the method, the problems that in traditional volume data synthesis, secondary peak merging and angular asymmetric expression are limited, and controllability and reproducibility are poor are solved.

The invention discloses a Legendre-KAN encryption inference method based on module component homomorphism, and relates to the technical field of information security, and the method comprises the steps: 1, constructing a Legendre-KAN network based on a KAN structure of a Legendre polynomial; step 2, acquiring an image sample set to train the Legendre-KAN network to obtain a Legendre-KAN model; 3, encrypting the to-be-predicted image to obtain ciphertext data; 4, performing parallel reasoning on the ciphertext data in the GPU by using a Legendre-KAN model and a modular component homomorphic algorithm to obtain an encryption result; and 5, decrypting the encryption result to obtain an image prediction result. According to the method, the data can be always in an encrypted state in the whole reasoning process, privacy leakage is effectively avoided, the model reasoning efficiency can be improved, and the data reasoning process is accelerated.

This invention discloses a high-security ranging code design method based on a pseudosatellite system. It utilizes a Legendre polynomial sequence based on quadratic residue theory, incorporating truncation point parameters and phase difference parameters. A Weil code is generated through a shift-and-XOR operation. The generated Weil code sequence is then used to generate the primary ranging code sequence through cyclic truncation and splitting operations. A periodic code-changing scheme is introduced to further enhance the security of this code sequence. This invention improves the security performance of the ranging code without significantly affecting its correlation, making it more suitable for scenarios with high confidentiality and correlation requirements.

The invention discloses a parameter correlation and scattering difference double-constrained PolInSAR forest high inversion method, and belongs to the technical field of remote sensing information processing. Comprising the following steps: determining a Fourier-Legendre polynomial coefficient constraint interval by using forest height prior information; an inequality constraint condition is constructed based on the forest canopy and bottom layer polarization scattering difference; and in combination with the constraint conditions, inversion of forest height and vertical structure parameters is carried out by using a nonlinear least square iterative algorithm. Wherein the polynomial coefficient constraint interval is determined by counting coefficient values corresponding to different forest heights, and the scattering difference constraint condition is constructed according to a top and bottom scattering power relationship of volume scattering and surface scattering dominant polarization modes. The target function is the residual sum of squares of the measured value and the estimated value of the complex coherence coefficient, and the iteration termination condition comprises the number of times, the function tolerance and the parameter tolerance. Experiments show that compared with a conventional unconstrained nonlinear iteration method, the method has the advantages that the forest overestimation value RMSE is reduced by 12%, and the inversion precision and stability are effectively improved.

This invention discloses a method for predicting the dynamic response and reliability of a hybrid uncertain system, belonging to the field of uncertain system dynamics and reliability prediction. The implementation method of this invention is as follows: A polynomial surrogate model of the hybrid uncertain system is represented based on the PCLM method. An orthogonal polynomial basis corresponding to the random variables is established based on data-driven methods: a one-dimensional orthogonal polynomial basis is represented based on the origin moments of the random variables; a tensor product operation is performed to obtain a multi-dimensional orthogonal polynomial basis corresponding to the random variables; and Legendre polynomials are used as the orthogonal polynomial basis corresponding to the interval parameters. The coefficient matrix γ in the polynomial surrogate model of the hybrid uncertain system is solved using a double-weighted least squares method. Based on the established polynomial surrogate model, the dynamics and reliability of the hybrid uncertain system are predicted respectively. This invention can improve the accuracy and efficiency of predicting the dynamic response and reliability of hybrid uncertain systems.

The invention discloses a Legendre cross section extreme value-based data-driven uncertainty modal parameter identification method, and belongs to the field of structural health monitoring, system identification and artificial intelligence. According to the method, uncertainty parameter boundaries of a structure model are quantified in an interval form, Legendre polynomial zero points are efficiently calculated by using a multi-layer perceptron neural network, and the Legendre polynomial zero points are mapped to an interval parameter space to generate sample points. Structural response data are obtained in combination with finite element analysis, modal parameter identification is performed by adopting a long-short-term memory neural network, an approximate model is fitted through a Legendre polynomial, an extreme value point is determined through derivation, and finally, the extreme value point is projected back to an interval parameter space to obtain an interval range of modal parameters. According to the method, deep learning and interval uncertainty quantification technologies are fused, the identification precision and the calculation efficiency are remarkably improved, and an efficient solution is provided for intelligent health monitoring of a complex structure in an uncertainty environment.

The invention provides a modeling method for an inertial lumped parameter model of a multi-layer frame structure for interaction of soil and structural power. The modeling method comprises the following steps: standardizing and describing foundation impedance of the multi-layer frame structure of an SSI effect; fitting the impedance of the multi-layer frame structure by utilizing a Legendre polynomial, decomposing the multi-layer frame structure into a partial fractional expansion form, comparing a decomposed first-order term and a decomposed second-order term with a first-order discrete element model and a second-order discrete element model respectively, and identifying undetermined coefficients of each spring, each inerter and each damper in the inerter type lumped parameter model. And finally, establishing a time domain kinetic equation of the multi-layer frame structure under the interaction of the soil and the structural power according to the Alembert principle, and solving a motion control equation by using a Wilson-theta method to obtain the time domain response of the multi-layer frame structure.

A parallel neutron transport calculation method and computing device for optimizing lateral leakage term processing belongs to the field of nuclear power. The parallel neutron transport calculation method for optimizing lateral leakage term processing introduces a second-order Legendre polynomial weighted boundary flow in the calculation process of a single node, and updates adjacent nodes in combination with the boundary neutron flow. The updated node neutron flux and eigenvalue k are obtained by traversing all nodes through parallel calculation. eff The updated data is substituted into the calculation model for iteration to obtain the final calculation result. This method obtains the high-order expansion coefficients of the nodal lateral leakage term based on a single nodal model, improving the calculation stability while ensuring the calculation accuracy.

The invention belongs to the technical field of optical communication, and particularly relates to a CPOV light beam atmospheric turbulence prediction method based on deep learning. The method comprises the following steps: constructing an atmospheric turbulence prediction model by using a Legendre polynomial which is orthogonal in a square domain; and inputting an intensity distribution diagram of the CPOV light beam after free transmission in the atmospheric turbulence into the atmospheric turbulence prediction model, and respectively predicting Legendre polynomial coefficients of the low-frequency part of the turbulence screen and the high-frequency part of the sub-region so as to obtain the turbulence screen equivalent to the atmospheric turbulence. According to the method, the prediction precision of the turbulence screen is higher by simultaneously predicting the Legendre polynomial coefficients of the low frequency of the turbulence screen and the high frequency of the sub-region. Meanwhile, for CPOV light beams with different turbulence intensities and different OAM modes, the generalization of the atmospheric turbulence prediction model is higher.

The application discloses a robust optimization method and device for pollutant emission. The robust optimization method comprises the following steps: obtaining sampling data of uncertain input variables of a cracking furnace; performing numerical simulation on the sampling data via a turbulent combustion coupling model to obtain a training data set; constructing a sparse chaotic polynomial model according to the uncertain input variables, and training the sparse chaotic polynomial model via the training data set to obtain a first uncertain quantification model; introducing deterministic optimization variables of the cracking furnace into the first uncertain quantification model, and obtaining a second uncertain quantification model dependent on the deterministic optimization variables based on a Legendre polynomial; and performing robust optimization on the deterministic optimization variables of the pollutant emission via the second uncertain quantification model. The application can solve the uncertain quantification precision and efficiency problem of a large-scale numerical model, establish a continuous robust optimization model, and greatly improve the optimization efficiency.