37 results about "Polynomial chaos" patented technology

The invention relates to the field of acoustics, in particular to a method for quickly calculating characterization and transfer of uncertainties of marine environment and sound fields. The invention aims to solve the problems of random spectrum characterization of uncertain environmental parameters and uncertain sound pressure fields and whether to transfer the uncertainties form the environmental parameters to the sound pressure fields. The method comprises the following steps of: establishing a domain space taking the known quantity as a center for the uncertain environmental parameters and the uncertain sound pressure fields respectively; performing the probability density function description on the uncertain quantity; and chaotically carrying out the random spectrum characterization according to a polynomial taking the probability density function as the uncertain quantity, and further combining the chaotic random spectrum characterization of the polynomial and a certain wave equation, educing the random wave equation embedded with uncertainty, acquiring the system of partial differential equation of uncertain coefficients, and finally acquiring the uncertain sound pressure fields formed by the linear superposition of the chaos based function of the uncertain coefficient weighting polynomial. The method has the advantages that: the acquired uncertain sound pressure fields are the same as the result acquired by MonteCarlo, and the calculating speed of the method is improved by more than 10 times.

The invention relates to a stochastic model modification method based on uncertainty of a stochastic response surface estimated parameter, which comprises the following steps: 1, representing an uncertain parameter of a structure system as a function of a standard stochastic variable and representing a response of the structure system as a polynomial chaos expansion which uses the standard stochastic variable as an independent variable and is based on a Hermite polynomial, and solving an undetermined coefficient of the polynomial chaos expansion so as to establish a stochastic response surface model of the response of the structure system and calculate a statistical characteristic value of the response of the structure system; 2, utilizing an error function of a statistical characteristic value of the stochastic response surface model and the statistical characteristic value of the actually measured response to establish a target function required by stochastic model modification; 3, utilizing the target function to construct optimization inverse problems and modifying a parameter statistical characteristic value step by step; and 4, on the basis of the parameter statistical characteristic value obtained by stochastic modification, utilizing a stochastic response surface to calculate and obtain the statistical characteristic value of the response of the structure system. The method ensures modification accuracy when improving modification efficiency.

The invention discloses an improved random perturbation method on the basis of a repetition frequency structure vibration characteristic value of an agent model. The method comprises the following steps: firstly, carrying out perturbation analysis on the characteristic value of a repetition frequency structure, and obtaining a matrix equation in regard to the first-order perturbation amount of the free vibration characteristic value of an original repetition frequency structure after parameters including the rigidity, the quality and the like of the repetition frequency structure are subjected to disturbance and change; and then, on the basis of a polynomial chaos expansion method, constructing an agent model in regard to the first-order perturbation amount of a repetition frequency characteristic value; and combining a perturbation method with an agent model technology on the basis of the polynomial chaos expansion, putting forward an improved approximate calculation method of the free vibration characteristic value of the repetition frequency structure, and further obtaining the expressions of a mean value and a variance under the parameter disturbance situation of the repetition frequency structure characteristic value on the basis of the approximate calculation method. The improved random perturbation method solves the problem in the traditional perturbation method that the statistical characteristics of the traditional perturbation method can not be further researched since the first-order perturbation amount of the repetition frequency structure characteristic value can not be expressed by an explicit expression.

The invention discloses a method for quickly predicting the crosstalk frequency domain dynamic characteristics of a vehicle harness. The method includes the steps that first, wires in the vehicle harness are considered to be weakly coupled in a loss-free mode; second, a primary function corresponding to a polynomial chaos expansion method is selected to be used as a Legendre orthogonal polynomial through the calculation method in the first step according to variables in a uniform distribution type; third, a random process Y (theta) can be expanded through the orthogonal polynomial; fourth, the Legendre orthogonal polynomial is used for expanding unit mutual reactance Lm and unit mutual capacitance Cm; fifth, after the mean value and variance of the unit mutual reactance Lm and the unit mutual capacitance Cm of vehicle harness wires are acquired, the crosstalk mean value and variance of the harness wires are calculated. The method for quickly predicting the crosstalk frequency domain dynamic characteristics of the vehicle harness has the advantages that the crosstalk frequency domain dynamic characteristics of the vehicle harness can be predicted rapidly, an important basis is provided for the early stage design of the electromagnetic compatibility of a vehicle, so that the determination method is more complete, simulation computing time is shortened, the requirement for a computer memory is lowered, and calculation results are more accurate.

The invention provides a coupling uncertainty acquisition method for a high-altitude electromagnetic pulse field line based on polynomial chaos expansion. The method comprises the following steps that(1) a coupling model of a field line of a transmission line under a high-altitude electromagnetic pulse is established, and related input parameters are determined; (2) according to uncertainty variables set by a user and a submissive statistic characteristic distribution type of the uncertainty variables, unified conversion is conducted according to demands, corresponding polynomial bases are used, and a coupling random response is subjected to polynomial chaos expansion; (3) according to types of different polynomials, coefficients of all the polynomials are obtained through corresponding-form Gaussian integral, and an analytic expression of a coupling response of the high-altitude electromagnetic pulse field line is obtained; (4) according to the coefficients of all the polynomials anddistribution types of the uncertainty variables, statistic characteristic parameters of the coupling response of the high-altitude electromagnetic pulse field line are obtained, a fluctuation range,a probability density distribution function and a cumulative probability distribution function are obtained by using a Monte-Carlo method.

The invention provides a time-variant reliability sensitivity analysis method and device. The method comprises the following steps: step 101, n-order PCE (Polynomial chaos expansions) operation is performed on a motion mechanism, and the MRF (maximum resistance force) of the nth order of the motion mechanism and an nth-order PCE functional expression are obtained, wherein n is a positive integer larger than 1; step 102, estimated MRF obtained on the basis of simulation model estimation is acquired; step 103, whether the absolute value of the difference between the nth-order MRF and the estimated MRF is smaller than a preset threshold is judged; step 104, when the absolute value of the difference between the nth-order MRF and the estimated MRF is smaller than the preset threshold, a time-variant limit state function is constructed according to the nth-order PCE functional expression, time-variant reliability sensitivity of the motion mechanism is obtained, so that time-variant reliability sensitivity analysis based on the long-period degeneration motion mechanism is realized, and support is provided for reliability-based design optimization of the long-period degeneration motion mechanism.

The invention discloses an in-car random vibration noise prediction method based on a sparse grid point collocation theory. The method comprises the following steps: firstly, according to the practical requirements of an engineering field, establishing a finite element model for in-car random vibration noise prediction, and determining a target spatial position and a target frequency range; secondly, after a random model realizes the quantification of relevant uncertainty, sampling random parameters on the basis of the sparse grid point collocation theory, and utilizing the finite element model for the in-car random vibration noise prediction to calculate a response value on each random parameter sample point; and finally, according to a discrete scheme response value, calculating to obtain the coefficient matrix of a polynomial chaos expansion agent model responded by the in-car random vibration noise, and furthermore, calculating to obtain the mean value frequency response distribution and the variance frequency response distribution of the in-car random vibration noise on the basis of the coefficient matrix. The method simultaneously considers the random effect on the in-car random vibration noise by external load and structure material parameters and air dielectric characteristic parameters, and provides a basis for formulating noise reduction measures including in-car noise optimization and control and the like.

The invention discloses a polynomial chaos-based turbine blade tip gas thermal performance uncertainty quantification system. The system comprises a parameterized geometric modeling module, a sampling point generation module, a polynomial chaos expansion model construction module, a sample point initial field distribution module, a turbine blade tip gas heat performance full-automatic pretreatment module, a multi-core remote asynchronous distributed calculation module, a calculation progress real-time feedback module, a polynomial chaos expansion coefficient solving module, a sensitivity analysis module, a result file sampling and analysis module and the like. According to the turbine blade tip gas thermal performance uncertainty detection system, the number of samples needed for obtaining the turbine blade tip gas thermal performance uncertainty can be greatly reduced, the time needed for calculating the numerical value of a single sample can be shortened, and the system is further suitable for turbine blade tips of any size and form; and the requirements of designers of the turbine cooling system are better met.

The invention relates to a control method of a magnetofluid system based on PDE model learning. The method comprises the following steps that a topological structure of a magnetofluid system in a channel is constructed, wherein the magnetofluid system comprises a channel with the two ends closed, magnetofluid in the channel and an external electromagnetic field perpendicular to the flowing direction of the magnetofluid; upper and lower boundaries of a magnetofluid Reynolds number are set; the control parameters are used for approximating an external adjustable induced magnetic field; the magnetofluid speed at the initial moment is obtained, and the magnetofluid induction intensity at the initial moment is obtained; and with the control parameters and the Reynolds number of the fluid as input and the magnetofluid flow velocity value at the moment T as output, a polynomial chaos expansion model for approximating the speed of the magnetofluid is constructed. The method has the following advantages: the magnetofluid system with the parameter uncertainty is considered; and since the model uncertainty parameters and the control parameters are uniformly distributed, the approximation of polynomial chaos expansion is ensured.

The invention discloses a stochastic perturbation method oriented to a dense frequency structural vibration characteristic value. The method firstly caries out spectral factorization on a rigidity matrix and a mass matrix, then carries out displacement on the characteristic value and converts a dense frequency system into a repetition frequency system. Then, the revised characteristic value is subjected to perturbation analysis, and a matrix equation about the first order perturbation item of the dense frequency structural vibration characteristic value after a structure parameter is subjected to disturbance is obtained. Then, through a polynomial chaos expansion method, an agent model of the first order perturbation item of the dense frequency structural characteristic value is constructed. The perturbation method is combined with an agent model technology are combined to put forward an approximate calculation method oriented to the dense frequency structural vibration characteristic value, and the expression of a mean value and a variance of the dense frequency structural characteristic value under a parameter disturbance situation is further obtained on the basis of the approximate calculation method. The stochastic perturbation method solves the problem that the statistical characteristics of the dense frequency structural characteristic value can not be directly researched since the dense frequency structural characteristic value can not be expressed by the structure parameter in a traditional perturbation method.

The invention provides an antenna high-altitude electromagnetic pulse (HEMP) coupling response performance statistic method based on polynomial chaos expansion, which has high precision of statistic result, excellent computation efficiency and meets requirements on related profession evaluation work well. The method includes the steps of (1), according to the antenna structure, building an antennaHEMP coupling response model through a corresponding electromagnetic field scattering algorithm; (2), performing uniform conversion as needed according to uncertainty variable set by users and its statistical property distribution pattern, and subjecting coupled random response to the polynomial chaos expansion by using the corresponding polynomial basis; (3), according to types of different polynomials, acquiring coefficients of the different polynomials through Gauss integral in corresponding manners so as to obtain the analytical expression of the antenna HEMP coupling response; (4), deducing to obtain statistical characteristic parameter of the antenna HEMP coupling response and performing the Monte Carlo method to obtain a probability density function and a cumulative probability distribution function.

The invention discloses and protects a near-threshold circuit delay estimation method based on a polynomial chaos Kriging element model, which considers the influence of process parameter fluctuation increase under a near-threshold voltage, constructs a model from process parameters to circuit delay through the polynomial chaos Kriging element model, and further performs yield evaluation on circuit path delay. The accurate and effective time sequence analysis method under the near-threshold voltage is realized, and guidance is provided for circuit design. Firstly, a key path of a circuit is extracted through a tool PrimeTime, efficient sampling is carried out on the circuit through Latin hypercube, then delay of the key path is obtained through SPICE simulation under different technological parameter conditions, delay data of non-Gaussian distribution are converted into data conforming to Gaussian distribution through generalized power transformation and maximum likelihood estimation, and a path delay model under low voltage is built by using a polynomial chaos Kriging element model; and finally the time sequence yield evaluation of the circuit is finished.

The invention discloses a Mars entering flight state uncertainty quantification method. Random Mars entering dynamics is converted into an equivalent deterministic dynamics differential equation set through a polynomial chaos theory. The updating of the orthogonal basis in the polynomial chaos is realized by utilizing the spectral decomposition theory when the statistical characteristics of the Mars entering the flight state uncertainty change drastically, so that the uncertainty quantization accuracy is ensured under the condition that the polynomial order is not increased. And violent increase of the equation dimension under the condition of uncertainty of the initial state is inhibited by adopting a random space decomposition theory, so that the calculation efficiency is improved. The method is suitable for instantaneous state uncertainty quantification and state evolution uncertainty quantification of Mars entering flight.

The invention discloses a robustness topology optimization method of a thin-shell structure considering thickness uncertainty. The method comprises the following steps of firstly, determining the random field probability distribution of a thickness t; establishing a robustness topology optimization mathematical model of the structure; discretizing the random field by adopting an EOLE method to reduce the number of random variables; determining the sample points of the polynomial chaos expansion (PCE); calculating the structure response and the sensitivity information at the sample point based on a finite element method; calculating a mean value and a variance of the structure response; calculating an objective function value and the sensitivity information of the objective function; inputting the sensitivity and target function information into an MMA, and updating a design variable; and judging the result convergence, if the result is convergent, outputting an optimization result, and if the judgment result is not convergent, continuing iteration.

The invention discloses a characteristic curve parameter identification method and system for operating an impact lower voltage limiter. The method comprises: measuring a current signal of the operation impact lower voltage limiter, and determining parameters of equivalent resistance, inductance and capacitance of an operation impact discharge loop; obtaining a voltage limiter operation impact loop equivalent model according to the equivalent resistance, inductance and capacitance parameters, and constructing an impact circuit differential equation containing nonlinear curve parameters; calculating a polynomial chaotic configuration point coefficient matrix X according to the constructed impact circuit differential equation; calculating operation matrixes Dyy and DXy by utilizing the polynomial chaotic configuration point coefficient matrix, and constructing a maximum likelihood estimation objective function according to the formula shown in the specification; calculating based on an L-M optimization method, to obtain an identification value of a random variable [epsilon] related to a nonlinear curve parameter [theta] and identification of the nonlinear curve parameter. The identification value of the random variable related to the nonlinear curve parameter is shown in the specification. According to the identification result (shown in the specification), the identification reliability is ensured, and the implementability of the identification method is improved at the same time.

A turbine gas thermal performance uncertainty quantification method based on a universal Kriging model comprises the following steps: generating a to-be-solved polynomial chaos expansion through a polynomial chaos theory, and generating to-be-calculated sparse/dense sample point data based on a low-order/high-order Symolak sparse grid technology; using a genetic algorithm to automatically plan the calculation sequence of all sparse samples, and obtaining gas heat parameters of all the samples through multi-machine different-place asynchronous distributed calculation; solving the coefficient of the polynomial chaos expansion, using the obtained explicit expression as a regression function of a generic Kriging model building module to construct a generic Kriging model, and solving the expression of the generic Kriging model; calculating gas heat parameters of each dense sample point through an expression of the universal Kriging model; and solving the coefficient of the polynomial chaos expansion by using a Galerkin projection method, the uncertainty mean value and deviation of the turbine gas heat parameters can be obtained, and the sample size of the polynomial chaos method in turbine gas heat performance uncertainty quantitative calculation can be reduced.

The invention discloses a turbine gas thermal performance uncertainty visualization analysis method and system. The method comprises the following steps: carrying out mathematical modeling through a polynomial chaos theory, generating a to-be-solved polynomial chaos expansion, generating to-be-calculated sample point distribution data based on a Symolak sparse grid technology, mapping the uncertainty characteristics of a system to a polynomial chaos expansion coefficient, acquiring an initial field of a to-be-solved sample, carrying out turbine gas-heat performance numerical calculation, carrying out Hill sorting preprocessing on calculation result data, carrying out clustering analysis to gather grid nodes representing the same spatial position in all samples into one class, then solving class center coordinates, calculating turbine gas-heat parameters on the class center coordinates, and finally, calculating to obtain the mean value and deviation of the turbine gas-heat parameters on each class core and the sensitivity of the turbine gas-heat performance on each class core to each input variable. The uncertainty quantification of the turbine blade tip gas thermal performance can be carried out, and the research work of turbine designers is guided.

The invention provides a PCEBO-based structure performance parameter rapid inversion method. The method comprises the following steps of 1, establishing a high-fidelity numerical model capable of representing structure physical model characteristics; 2, selecting structural performance parameters to be inverted as input variables, randomly sampling a finite group of input variable sets through a Latin super-cubic method, substituting the input variable sets into the structural numerical model to solve a corresponding output variable set, and constructing a polynomial chaos expansion agent model capable of representing structural characteristics; and step 3, taking actual measurement data corresponding to engineering demand parameters as an input set in a Bayesian optimizer, and rapidly updating structural performance parameters to be inverted based on a polynomial chaos expansion agent model in combination with a Bayesian optimization algorithm. According to the method, the defects of traditional deterministic back analysis are made up, the limitation that the inversion efficiency is limited by the calculation cost of a complex numerical model in the field of classical back analysis is liberated, the inversion efficiency and the robustness to noise are improved, and the purpose of quick inversion of structural performance parameters is achieved.

The invention discloses a spatio-temporal variation reliability analysis method based on polynomial chaos expansion, which comprises the following steps of: firstly, generating a sample of a random variable by adopting Latin hypercube sampling, then dispersing the time variable into a series of discrete time moments, and obtaining a spatial response extreme value sample of the discrete time moments by utilizing sequential quadratic programming; then, on the basis of the samples, a substitution model of a spatial response extreme value is constructed by using PCE, so that a response hypersurface of a structure in a time domain and a spatial domain is converted into a trajectory of the spatial response extreme value in time, and finally, Monte Carlo simulation is performed on the constructed polynomial chaos expansion agent model to calculate a failure probability so as to realize reliability analysis.

The invention discloses a random noise analysis method and system based on a sequence planning sampling point technology. The method comprises the following steps: establishing a random finite elementmodel of a structure-acoustic cavity coupling system; establishing random polynomial chaotic expansion of noise response of the random finite element model; generating Gaussian integral points corresponding to the polynomial basis, and taking the Gaussian integral points as candidate sample points; performing sparse sampling on the candidate sample points based on a sequence planning sampling point technology to obtain sparse sampling points; calculating an undetermined coefficient of any polynomial chaotic response surface by utilizing the sparse sampling points; and solving the probabilitystatistical characteristics of the system noise response. According to the method, the noise response of the random structure-acoustic cavity coupling system can be effectively predicted, and theoretical guidance is provided for reliability analysis and optimization design of the subsequent structure-acoustic cavity coupling system.

The invention provides a structure dynamic parameter identification method assisted by an rPCK proxy model, and belongs to the field of structure engineering. Comprising the following steps: establishing a finite element model capable of roughly reflecting a to-be-analyzed structural system; establishing a dynamic parameter space sample set; establishing a structural system response space sample set driven by the dynamic parameter space sample set by adopting probabilistic finite element analysis; establishing a robust polynomial chaos-Kriging (rPCK) proxy model capable of mapping the dynamic parameter space sample set to a structural system response space sample set; and driving the rPCK proxy model according to the actually measured structure system response, performing structure dynamic parameter identification by adopting Bayesian inference, and taking a Bayesian posteriori estimation mean value as a structure dynamic parameter estimation value. The method provided by the invention breaks through the limitation that an existing deterministic parameter identification method is difficult to accurately identify the dynamic parameters of the structure, and creates conditions for establishing a high-fidelity finite element model of an engineering actual structure system.

The invention discloses a worm gear mother machine key error term identification method, which comprises the following steps of 1, analyzing geometric errors of motion shafts of a worm gear mother machine, and establishing a position error model of a worm gear hob-worm gear workpiece based on a worm gear mother machine kinematic chain, an actual pose transformation matrix Twt and an ideal pose transformation matrix Twti of the worm gear hob relative to the worm gear workpiece being obtained, so that a machining error model of the worm gear machine is obtained; 2, regarding the machining error model of the worm gear machine as a multi-input multi-output nonlinear system, and analyzing the pose error model by using the global sensitivity of a polynomial chaos expansion method, 3, the single-effect sensitive index estimator and the full-effect sensitive index estimator being used for solving to obtain a sensitive index corresponding to each geometric error, wherein the larger the sensitive index is, the more critical the geometric error is, and the larger the sensitive index is, the more critical the geometric error is. And the influence on the machining precision of the worm gear machine is greater.