62 results about "Hermite functions" patented technology

The invention provides a power distribution network voltage out-of-limit probability prediction method considering load fluctuation and photovoltaic output, and relates to the technical field of power distribution network safety. The method comprises the following steps: constructing a time-varying Gumbel-Copula joint distribution function according to a Spearman rank correlation coefficient, obtained by calculation, of a load and photovoltaic output; based on a time-varying Gumbel-Copula joint distribution function, probability distribution of the load and probability distribution of the photovoltaic output are reconstructed through a Hermite polynomial, and parallel probabilistic power flow solving is carried out; and calculating the voltage out-of-limit probability of each node according to the result of the parallelization probabilistic power flow solution. According to the method, dynamic coupling characteristics of different time periods are considered, a time-varying Gumbel-Copula joint distribution function is introduced, probability distribution of loads and probability distribution of photovoltaic output are reconstructed through a Hermite polynomial, the influence of intermittent superposition of load fluctuation and photovoltaic output can be overcome, and real-time prediction of the voltage out-of-limit probability can be accurately completed in extreme weather.

The invention discloses a Riemannian manifold-based space-time joint anti-interference direct positioning method. The method comprises the following steps of: acquiring signals emitted by an interference source and a radiation source by using a plurality of distributed antenna arrays; segmenting a received signal, constructing a sample covariance sequence, and establishing a model covariance matrix at each frequency; determining a Riemannian distance expression between the sample covariance sequences by constructing a Riemannian manifold on the basis of the characteristic that the sample covariance sequences are located on an Ermitt positive definite matrix manifold, and solving a Riemannian mean value of the sample covariance sequences; utilizing Riemannian geometric characteristics of a sample covariance matrix, and taking a Riemannian distance on an HPD matrix manifold as a judgment criterion of fitting accuracy; replacing an Euclidean distance with a Riemannian distance, performing approximate processing on the Riemannian distance by using a logarithm Euclidean distance, and constructing a direct positioning cost function based on the logarithm Euclidean distance; and two-step spectrum peak searching is carried out through the direct positioning power spectrum, and a direct positioning result of the direct positioning cost function is determined.

The invention relates to a universal two-phase flow phase field model mesoscopic design method, device and equipment and a storage medium. The method comprises the steps that a two-phase flow control equation based on a phase field model is established; presetting an equilibrium state of the Boltzmann distribution function, calculating a low-order moment, and associating the low-order moment to a macroscopic quantity; performing analysis by using Chapman-Enskog to obtain an integral constraint condition required by a source item; utilizing a Hermite expansion method to obtain an expression of a source item; and outputting a mesoscopic design result. According to the universal two-phase flow phase field model mesoscopic design method provided by the invention, when the phase field model is used for two-phase flow simulation in the future, a mesoscopic format can be quickly obtained even if a new phase field equation is encountered, so that the mesoscopic method can be directly used for simulating the two-phase flow, and mesoscopic design does not need to be carried out again.

The invention discloses a quantum state coding method of a polynomial function and a related device, and belongs to the technical field of quantum computing, and the method comprises the steps: determining the scale of a unitary matrix based on the highest order of the polynomial function, and constructing a target matrix based on a plurality of function values of the polynomial function; wherein the quantum logic gate corresponding to the unitary matrix is used for constructing a quantum circuit of a quantum state of a coding polynomial function, and the line number of the target matrix is the same as that of the unitary matrix; performing singular value decomposition on the target matrix to obtain a plurality of unitary matrixes; and determining a quantum logic gate corresponding to each unitary matrix, and acting each quantum logic gate on the corresponding quantum bit to obtain the quantum state of the polynomial function, thereby realizing coding from the classical data form to the quantum state of the polynomial function.

The invention provides a random point collocation method for solving global sensitivity of an augmented failure probability of a turbine blade structure, and belongs to the technical field of reliability design. Comprising the following steps: constructing an expected density function of an n-dimensional random input variable of a turbine blade structure to obtain an n-dimensional expected density function; calculating an unconditional augmentation failure probability of the turbine blade structure based on the n-dimensional expected density function and the performance function; a Gauss-Hermite integral quadrature node of the n-dimensional expected density function is determined; constructing an expected density function of (n-1)-dimensional random input variables except the i-th dimension of the turbine blade structure to obtain an (n-1)-dimensional expected density function except the i-th dimension; based on the (n-1)-dimensional expected density function and the conditional performance function, the conditional augmentation failure probability of the turbine blade structure corresponding to the Gauss-Hermite integral quadrature node is calculated; and determining the augmented failure probability global sensitivity of the turbine blade structure. According to the invention, the calculation efficiency of the global sensitivity of the augmentation failure probability of the turbine blade structure can be improved.

The application discloses a kind of single-area PI type load frequency control time-delay power system stability analysis method, comprising the following steps: 1) establish single-area PI type load frequency control power system mathematical model;2) considering the influence of time delay on power system, on the basis of power system mathematical model, establish time-delay power system mathematical model;3) construct Lyapunov functional;4) the derivation of Lyapunov functional;5) the integral term of the Lyapunov functional after derivation is estimated using the first lemma, and the stability of the time-delay power system mathematical model is analyzed using a two-parameter quadratic polynomial function and the Schur complement theorem, to obtain a less conservative stability criterion.The application has the advantages of less conservative, lower analysis process complexity, etc.

A method for optimizing a system that includes a set of degrees of freedom (DOF) and a set of constraints on the set of DOF is disclosed. Each constraint is associated with a subset of the set of DOF. The method includes determining a first polynomial function. A set of qubits of a quantum computing system (QCS) is prepared in a first quantum state Subsequent to preparing the set of qubits in the first quantum state, the QCS performs a set of unitary operations on the set of qubits. Subsequent to performing the set of unitary operations on the set of qubits, the QCS generates a first set of observables by performing a first measurement operation on each qubit of the set of qubits. A set of values is determined based on the first set of observables.

The invention discloses a Hermite windward interpolation-based five-order WCNS format construction method, which comprises the following steps of: setting a computational domain according to a hyperbolic conservation law equation to be solved; dividing a computational domain into solution points and flux points in each coordinate direction by adopting a uniform grid distribution mode; dividing a calculation interval into a plurality of units by utilizing flux points at equal intervals, and arranging solving points in the centers of the units; calculating left and right windward values of a flux point based on a Hermite three-point five-order windward interpolation format; calculating a numerical flux at a corresponding flux point by using a numerical flux function; according to the numerical flux, adopting a preset node and half node mixed implicit difference format to obtain an approximate derivative of the flux in each coordinate direction; and carrying out numerical simulation by adopting a time-marching mode to complete the solution of the partial differential equation. An implicit format is adopted, the calculation stability is guaranteed, high-order precision is kept in a smooth area, numerical errors are reduced, and the flow field calculation efficiency is effectively improved.

The purpose of this invention is to provide a method for DOA estimation of acoustic vector arrays based on quaternion matrix dimensionality reduction, comprising the following steps: constructing a CAACIS acoustic vector coprime array at the receiver; establishing a quaternion model of the received signal based on the array output; estimating the quaternion covariance matrix; performing dimensionality reduction on the quaternion covariance matrix to obtain a virtual array received signal model of the acoustic vector coprime array; reconstructing the Hermitian-Toeplitz matrix; performing eigenvalue decomposition on the Hermitian-Toeplitz matrix and constructing a spatial spectral function; and obtaining the DOA estimation result through spectral peak search. This invention addresses the problem of how to achieve multi-objective DOA estimation with both low complexity and good performance based on a quaternion framework under acoustic vector coprime arrays.

This invention relates to a method and system for simulating stationary non-Gaussian wind pressure based on a machine learning-enhanced Hermite multinomial model. First, a multi-input, single-output machine learning model is constructed to determine the statistical moments required in the transformation function of the proposed method. Then, based on this, a neural network transformation model is established from a non-Gaussian power spectrum to a potential Gaussian power spectrum using a multi-input, multi-output model. Finally, an ML-EHPM model constructed based on dual machine learning models predicts the statistical moments required for the transformation function and the potential Gaussian power spectrum predicted by the Gaussian PSD prediction model, respectively. This potential Gaussian power spectrum representation is then used to simulate non-Gaussian wind pressure. Under conditions of strong non-Gaussian wind pressure, wind pressure exceeding the monotonic region, and bimodal wind pressure distribution, the ML-EHPM method can more realistically reproduce the target probability density function and power spectral density, significantly outperforming the traditional HPM method in simulation accuracy, especially in strong non-Gaussian samples.

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.

The invention discloses an anti-quantum function commitment method based on a chain function commitment, and the method specifically comprises the steps: carrying out the system initialization, generating a system public key parameter through a trusted third party according to a function scale parameter and a safety parameter, and distributing the system public key parameter to a commitment end and a receiving end; the commitment end generates a commitment value for the function input value based on the public key parameter and sends the commitment value to the receiving end; the commitment end represents an objective function as a directed acyclic graph and splits the directed acyclic graph into a plurality of multivariate quadratic polynomials, and the objective function comprises a function capable of being represented as a finite-scale arithmetic circuit; on the basis of the function input value and the split multivariate quadratic polynomial, the commitment end generates an output proof that the target function takes the input value as the input; and the receiving end verifies the validity of the function value and the corresponding commitment information by using the public key parameter and the proof, if the verification is passed, the commitment value and the function value are valid, otherwise, the commitment value and the function value are invalid. According to the scheme of the invention, the quantum collapse attack can be effectively prevented, and the node storage and synchronization overhead can be greatly reduced.

The application provides a CHF prediction model determination method, a medium and an electronic device, and relates to the technical field of data processing. The method comprises the following steps: introducing a first norm penalty term and a second norm penalty term into a composite loss function simultaneously, the first norm penalty term being associated with the sum of the absolute values of each coefficient included in a coefficient set in a CHF initial prediction model, and the second norm penalty term being associated with the sum of squares of each coefficient in the coefficient set. In the process of optimizing the CHF initial prediction model with the optimization target of minimizing the composite loss function, the first norm penalty term is used to induce the sparsity of the corresponding polynomial function of the model, and tends to accurately compress the coefficients corresponding to the working condition parameters with weak contribution to the predicted CHF to zero, which is equivalent to automatically removing the redundant terms in the polynomial function. The second norm penalty is used to control the complexity of the model, prevent the value of a certain coefficient in the coefficient set from becoming too large, and effectively improve the stability and anti-overfitting ability of the model.

The invention discloses a priori knowledge-guided universal inverter power supply model non-mechanism analysis method, which can realize accurate prediction of impedance in a relatively large frequency band range by only needing a small amount of data and working condition points, meets the generalization of network tracking and network construction, and has strong generalization ability. The method is characterized in that 1-1000 Hz coarse frequency sweeping is carried out on an unknown inverter-based power supply (IBPS), frequency bands are divided according to the impedance change slope, actual measurement points are reserved in the rapid change frequency bands, data are enhanced by segmented cubic Hermite interpolation in the smooth frequency bands, and the test points are greatly reduced while the accuracy of the key frequency bands is guaranteed; and a Bayesian optimization neural network structure, L2 regularization, an EI sampling function and Z-score standardization are further introduced, so that the robustness and generalization ability of the model are improved. The method is suitable for limited working conditions and small sample conditions, and is good in applicability and strong in generalization ability under the control of a network tracking type and a network constructing type.

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.

The invention relates to the technical field of thin-wall reinforced structure design, and discloses a main stress trace-driven porous rigidity-variable composite material curved rib structure design method, which comprises the following steps: carrying out finite element analysis on an initial porous structure, extracting a stress field, and processing to generate a smooth and continuous main stress direction field; carrying out principal stress trace tracking on the basis of the principal stress direction field, carrying out clustering analysis on a principal stress trace family obtained through tracking so as to determine a representative equivalent principal stress trace from the principal stress trace family, and setting the equivalent principal stress trace as a non-uniform path of the curved rib structure; describing the thickness distribution of the curved rib section based on a piecewise cubic Hermite interpolation polynomial function; describing a curve fiber track based on a linear function; and fusing the non-uniform curved rib path, the curved rib section thickness distribution function and the curve fiber trajectory function to generate the pore-containing variable stiffness composite material curved rib structure driven by the main stress trace. And the bearing potential of the hole-containing variable-stiffness composite material structure is fully excavated.

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.

A method of performing a cryptographic operation is described, the method comprising performing masking inversion on a ring element f belonging to Rq, where Rq is an exchange ring, and the ring element f is represented by a plurality of shares. A masking inversion is calculated by performing a number-theoretical transformation on a plurality of shares to generate a corresponding plurality of shares of a polynomial function a, with each coefficient; i belongs to [n]; determining a set of coefficients, the set of coefficients corresponding to a product of the n coefficients of the plurality of shares; determining inverse elements of a set of coefficients corresponding to a product of the n coefficients of the plurality of shares; generating a set of coefficients ci of a plurality of shares corresponding to inverse elements of the polynomial function a; wherein an i-th coefficient of the plurality of shares is calculated by multiplying a value derived from an inverse of a product of n coefficients of the plurality of shares by values derived from other coefficients of the plurality of shares; and performing an inverse number theory transform on the plurality of shares corresponding to the inverse element of the polynomial function a to generate a plurality of shares corresponding to the inverse element of the ring element f. By applying the NTT transform to the masked ring elements and then determining inverse elements of a set of coefficients corresponding to the product of the masked transform coefficients, the processing cost of inversion of the masked ring elements can be reduced.

The invention discloses a radar array signal polarization parameter resolving method based on a vector MUSIC algorithm, and relates to the technical field of radar array signal processing.The radar array signal polarization parameter resolving method comprises the steps that firstly, a polarization signal steering vector matrix and a noise subspace corresponding to a radar array signal are obtained, matrix multiplication is conducted, and a 2 * 2 complex ermitt matrix is obtained; by extracting the ratio of the imaginary part to the real part of the second element in the first row in the complex Ermit matrix, the polarization phase difference is obtained by directly applying the arc tangent function, and the solving process of the feature vector is avoided; then the minimum eigenvalue of the complex Ermit matrix is calculated, an arc tangent value is calculated in combination with the trace of the complex Ermit matrix, and the polarization auxiliary angle is directly derived, so that a complete eigendecomposition process is omitted, and therefore, when the polarization parameters are calculated, the polarization auxiliary angle is calculated from the angle of definition of the polarization parameters; in other words, resolving is directly carried out from the angles defined by the polarization phase difference and the polarization auxiliary angle, and complex operation caused by characteristic decomposition is directly avoided, so that the calculation complexity is reduced, and the calculation precision is improved.

The application provides a structure probability risk assessment method and system based on SRSMBRA and Copula-MCM, and the method comprises the following steps: improving the probability matching point of a classical random response surface method, obtaining undetermined coefficients of a Hermite expansion by a random response surface method SRSMBRA based on regression analysis, taking the probability matching point method as a breakthrough point, and constructing a limit state equation of a structure; based on the limit state equation of the structure, constructing a joint probability density function of multi-dimensional random variables of the structure by means of a Copula function and a Vine model, obtaining a failure probability when there is a correlation between the multi-dimensional random variables of the structure based on a structure probability risk assessment method of Copula-MCM; and integrating the structure probability risk assessment of SRSMBRA and Copula-MCM by means of Rosenblatt transformation, obtaining the failure probability by a Copula-SRSMBRA risk assessment method by using a moment method or a Monte Carlo method, and performing efficient and feasible structure probability risk assessment of an engine life-limited part by the above method.

The application discloses a method for equal geometric robust topology optimization of a composite material structure considering band constraints, and comprises the following steps: firstly, constructing an equal geometric robust topology optimization model of the composite material structure considering material attribute correlation uncertainty and band constraints, calculating the mean value and standard deviation of the structural dynamic flexibility under the correlation uncertainty through Nataf transformation and Gauss-Hermite integral; then, solving the worst limit state approximation function corresponding to each limit state function and the uncertainty parameter point vector through a gradient search algorithm; finally, calculating the sensitivity of the objective function, the worst limit state approximation function and the volume constraint function, and obtaining the robust optimal topology structure satisfying the dynamic performance requirement by combining the moving asymptote method. The equal geometric robust topology optimization model of the composite material structure established by the application can truly reflect the correlation of material attribute uncertainty and the dynamic performance requirement, can efficiently obtain the optimization result, and has good engineering application value.

The present application belongs to the field of transcendental function operation technology, and discloses a resource reuse type transcendental function operation implementation method, which comprises a preprocessing step, a table lookup step, a calculation step and a post-processing step; the preprocessing step performs corresponding data processing according to the type of the operation function and sends the obtained multiple data to the other three steps for operation; the table lookup step looks up the corresponding table according to the type of the operation function, obtains the polynomial coefficient and sends it to the calculation step; the calculation step performs finite multiplication and addition on the preprocessed data and the coefficient obtained after the table lookup, and sends the result to the post-processing step; the post-processing step performs corresponding data post-processing according to the type of the operation function, obtains the result and outputs it. The present application can realize the operation of sine function, cosine function, inverse tangent function, exponential function, logarithmic function and hyperbolic function. The error of each function realized by the present application is less than 2ulp, which meets the accuracy requirement of the design.

The invention relates to a stationary non-Gaussian wind pressure simulation method and system based on a machine learning enhanced Hermite polynomial model, and the method comprises the steps: firstly constructing a multi-input single-output machine learning model to determine a statistical moment needed in a conversion function of a proposed method; then, on this basis, a neural network conversion model from a multi-input multi-output non-Gaussian power spectrum to a potential Gaussian power spectrum is established, and finally, a statistical moment required by a conversion function and the potential Gaussian power spectrum predicted by a Gaussian PSD prediction model are obtained through prediction respectively based on an ML-EHPM model constructed by a dual-machine learning model. Adopting the potential Gaussian power spectrum representation method to simulate non-Gaussian wind pressure; under the conditions of strong non-Gaussian wind pressure, wind pressure exceeding a monotonic region and bimodal wind pressure distribution, the ML-EHPM method can reproduce a target probability density function and power spectral density more truly, the simulation precision is significantly superior to that of a traditional HPM method, and the method has particularly outstanding advantages in strong non-Gaussian samples.

The invention discloses an MEMS resonant structure parameter identification and drift compensation method, which comprises the following steps: constructing a multi-error coupling model, establishing bias output and orthogonal output expressions, and dividing known, calibratable and to-be-identified parameters; the parameters to be identified are constructed into polynomial functions which are related to the temperature and have different orders, and the total number of coefficients is N; measuring calibratable parameters at different temperature points of which the number is greater than or equal to N / 2; constructing an equation set composed of bias output and orthogonal output expressions under different temperature points; solving a polynomial function coefficient by adopting a global-local hybrid optimization strategy and taking a minimum fitting residual error as a target function, and completing parameter identification; and taking a residual signal obtained by subtracting the fitting value output by the bias from the measured value as a compensated output signal to finish drift compensation. The method is applied to the field of silicon microsensors, and simplification and generalization of MEMS resonant structure parameter identification and high-precision compensation of drift under temperature change are realized by combining physical priori knowledge and an optimization algorithm.

A method for optimizing a system that includes a set of degrees of freedom (DOF) and a set of constraints on the set of DOF is disclosed. Each constraint is associated with a subset of the set of DOF. The method includes determining a first polynomial function. A set of qubits of a quantum computing system (QCS) is prepared in a first quantum state Subsequent to preparing the set of qubits in the first quantum state, the QCS performs a set of unitary operations on the set of qubits. Subsequent to performing the set of unitary operations on the set of qubits, the QCS generates a first set of observables by performing a first measurement operation on each qubit of the set of qubits. A set of values is determined based on the first set of observables.

An aspect includes an apparatus for evaluating a mathematical function at an input value. The apparatus includes a selector for selecting a mathematical function, an input for a value at which to evaluate the function, an identifier for identifying an interval containing the input value. The interval is described by at least one polynomial function. At least one control point representing the polynomial function is retrieved from at least one look up table, and the polynomial function can be derived from the control points. The function is evaluated at the input value and an output of the evaluation is used as a value of the function at that input value.

The application provides a device and method for calculating hyperbolic function in BP decoding of a polar code, comprising a first interval calculation unit, a second interval calculation unit and a third interval calculation unit; the positive definition domain of the hyperbolic function is divided into a first interval segment, a second interval segment and a third interval segment; the first interval calculation unit is used for obtaining the function value of the hyperbolic function in the first interval segment according to a first preset function; the second interval calculation unit is used for generating a corresponding Taylor polynomial function according to an input x and a pre-prepared parameter table of the second interval segment, and obtaining the function value of the hyperbolic function at the input x according to the Taylor polynomial function; and the third interval calculation unit is used for obtaining the function value of the hyperbolic function in the third interval segment according to a second preset function. The application reduces the implementation complexity of the calculation device, guarantees the fitting accuracy, improves the decoding performance, and realizes the 5G decoding requirement at low cost.

The invention discloses a space-based target visible window calculation and detection performance analysis method considering multiple constraints, and the method comprises the steps: analyzing the visibility of a space-based detection satellite to a space target, and determining a plurality of visibility constraint conditions; fitting a visible judgment function by adopting a piecewise cubic Hermite interpolation polynomial, and calculating a visible window corresponding to each visibility constraint condition; combining the visible windows corresponding to the visibility constraint conditions by adopting a set screening method to obtain a multi-constraint visible window of the space-based detection satellite to the space target; and establishing a coverage performance index and an observation performance index of space-based target detection based on the performance index of satellite ground coverage, and evaluating the detection performance based on the coverage performance index and the observation performance index. The method is applied to the field of space-based detection, the performance index of a space-based target detection scheme can be established while the multi-constraint visible window is rapidly calculated, and the influence of a satellite orbit and constellation configuration on the detection performance is effectively analyzed.