12 results about "Hermite functions" patented technology

This invention discloses an efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model, belonging to the field of structural dynamics technology. This invention achieves rapid simulation of non-Gaussian processes through parameter estimation using Hermitian polynomial and Johnson transformation models based on machine learning, explicit transformation from non-Gaussian correlation functions to Gaussian correlation functions, and fast simulation of non-Gaussian processes based on linear filtering. While ensuring accuracy, this method effectively improves the efficiency of non-Gaussian process simulation and is applicable to non-Gaussian process simulation in various engineering fields.

This invention discloses a design method for a long-short split-flow impeller based on S-shaped short blades and a water pump. The long-short split-flow impeller includes a hub, several long blades, and several short blades. Each short blade includes an inlet section, a middle section, and an outlet section. The inlet section is identical to the original inlet section, while the outlet section rotates slightly relative to the original outlet section. The shape of the middle section is determined by a cubic Hermite basis function. One end of the middle section smoothly transitions to the inlet section, and the other end smoothly transitions to the outlet section. This invention achieves continuous, smooth, and controllable curvature geometry for the short blade profile throughout the entire design range, enabling controlled geometric adjustment of the short blade in the middle section. This allows for curvature control of the short blade in localized areas, thereby improving the pressure and velocity distribution in the flow field, enhancing the flow stability of the blade channel, and significantly optimizing the pump's hydrodynamic performance and operating efficiency.

This disclosure provides a motion optimization obstacle avoidance control method and system for vehicle-like robots, relating to the field of robot path planning and obstacle avoidance technology. The method includes: defining the state space of the vehicle-like robot; planning the global path of the vehicle-like robot; fitting the sparse state sequence using Hermite curves to obtain a time-space continuous trajectory; establishing a collision model between the vehicle-like robot and obstacles; transforming the geometric separation conditions between the robot and obstacles into a set of continuously differentiable nonlinear algebraic constraints based on duality theory; using the time-space continuous trajectory as a reference trajectory; and constructing a trajectory optimization objective function. This function can solve for the motion control quantities of the vehicle-like robot while satisfying its dynamic constraints, input constraints, and acceleration smoothing constraints, thus achieving obstacle avoidance planning and control of polygonal obstacles. This disclosure enables real-time, full-size robot planning and obstacle avoidance control.

This application relates to the field of earthquake engineering and discloses a method for quantifying the uncertainty of complex ground motions and a stochastic simulation system. The method first identifies non-stationary ground motions, mainshock and aftershock sequences, and near-fault pulse ground motions that meet the requirements in measured ground motion records, and uses an evolved power spectral density model to identify their parameters. Then, based on Copula theory, a high-dimensional nonlinear correlation joint probability distribution model of the parameters is constructed. Simultaneously, a high-order Hermite polynomial model is established to achieve non-Gaussian transformation, and the autocorrelation function mapping relationship is derived to reproduce the non-Gaussian properties. In the simulation stage, by combining representative point set selection, POD spectral representation, and non-Gaussian mapping, non-Gaussian ground motion time history samples consistent with the characteristics of measured records are efficiently synthesized. This invention can accurately quantify and simulate the stochastic uncertainty of complex ground motions, improving the realism of the simulation samples and computational efficiency.

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 application discloses a non-iterative design method of a non-uniform continuous distribution composite pupil function, solves the problem that the design method of an existing pupil function is relatively complex, including expansion of the pupil function, matrix calculation and a calculation process of solving a high-resolution gain expression, the non-uniform continuous distribution composite pupil function is composed of a Sonine polynomial, a Zernike polynomial and a Fourier-Bessel series, numerical mapping relationships between the Sonine polynomial, the Zernike polynomial, the Fourier-Bessel series and an imaging complex amplitude distribution at a radial focal plane are respectively constructed, coefficients of the Sonine polynomial, the Zernike polynomial and the Fourier-Bessel series are solved, a function formula of the composite pupil function is finally determined, and the mapping relationship is relatively simple and operable.

This invention discloses a method and system for simulating stationary non-Gaussian wind fields based on random waves, relating to the field of non-Gaussian wind field simulation in structural wind engineering. It includes: acquiring the autopower spectrum and coherence function of the target wind speed field to construct the target non-Gaussian wavenumber-frequency spectrum; discretizing the wavenumber and frequency, and generating a bottom-level stationary Gaussian random field by combining random wave spectrum representation and two-dimensional fast Fourier transform; reconstructing the target non-Gaussian marginal probability density function and cumulative distribution function based on finite-order statistical moments using the maximum entropy method; embedding a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian; inversely calculating the bottom-level Gaussian correlation structure and determining its spectral characteristics based on the correlation distortion relationship; and applying the piecewise translation mapping function to obtain stationary non-Gaussian wind field samples. This invention eliminates the need to decompose high-dimensional matrices, balancing computational efficiency and numerical stability, characterizing the high-order statistical properties and tail probabilities of strong non-Gaussian wind fields, and ensuring the spatiotemporal correlation of the wind field.

The application discloses a kind of complex equipment fault diagnosis methods based on polynomial improved graph convolution network.It includes the following steps: (1) the vibration signal of complex equipment operation is collected;(2) using cross-correlation coefficient, construct multi-objective fitness function, combine particle swarm optimization algorithm to optimize the selection of variational mode decomposition parameters;(3) according to the parameter obtained by optimization, the vibration signal is decomposed by variational mode, obtains several modal components and reconstructs to obtain denoising signal;(4) the signal after reconstruction is divided to construct graph;(5) the graph structure is input into the graph convolution model improved by Hermite polynomial to complete the diagnosis of fault.The application is used for the fault diagnosis of complex equipment, uses modal decomposition to denoise signal and improves the graph convolution model, improves the accuracy of diagnosis, and is suitable for the technical field of complex equipment fault diagnosis.

This invention discloses a non-iterative design method for composite pupil functions based on Zernike radial polynomials. It solves the problems of existing composite pupil function design methods having complex calculation processes and relying too heavily on model assumptions, which only consider a finite number of terms in the Zernike radial polynomial expansion. Starting from the imaging complex amplitude distribution at the radial focal plane, this invention establishes a numerical mapping relationship between the composite pupil function and the radial complex amplitude distribution at the imaging plane, and constructs a system of multivariate linear equations related to the coefficients of the composite pupil function, providing a new approach to pupil function design.

This invention discloses a method for calculating polarization parameters of radar array signals based on the vector MUSIC algorithm, relating to the field of radar array signal processing technology. First, this invention obtains the polarization signal steering vector matrix and noise subspace corresponding to the radar array signal, and performs matrix multiplication to obtain a 2×2 complex Hermitian matrix. By extracting the ratio of the imaginary to the real part of the second element in the first row of the complex Hermitian matrix, the arctangent function is directly applied to obtain the polarization phase difference, avoiding the process of solving for eigenvectors. Then, the minimum eigenvalue of the complex Hermitian matrix is ​​calculated, and combined with the trace of the complex Hermitian matrix, the arctangent value is calculated, and the polarization auxiliary angle is directly derived, eliminating the need for a complete eigenvalue decomposition process. Therefore, when calculating polarization parameters, the calculation starts from the definition of polarization parameters, i.e., directly from the definition of polarization phase difference and polarization auxiliary angle, directly avoiding the complex calculations brought about by eigenvalue decomposition, thereby reducing computational complexity and improving computational accuracy.