14 results about "Legendre polynomials" patented technology

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 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.

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 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.

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.

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 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.