37 results about "Polynomial chaos" patented technology

System, method and device for reducing the time required for solution of problems in the NP complexity class to polynomial time. Within satisfaction problems or problems reducible to a satisfaction problem, the invention tracks the sources of implications and identifies proximal parameterizations of conditional contradictions and subsequently avoids those contradictory conditions. The action is completed in less time than is incurred by existing methods and thus provides a performance improvement to the devices, software, or processes which address such problems.

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 characterizationaccording 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 present invention provides a PCE_BO-based fast inversion method for structural performance parameters, comprising the following steps: Step 1: establish a high-fidelity numerical model that can characterize the characteristics of the physical model of the structure; Step 2: select the structural performance parameters to be inverted as input Variables, randomly sample a finite set of input variables through the Latin hypercube method, and substitute them into the structural numerical model to solve the corresponding output variable set, and construct a polynomial chaotic expansion surrogate model that can characterize the structural characteristics; Step 3: By incorporating the corresponding engineering requirements parameters The measured data is used as the input set in the Bayesian optimizer, and then based on the polynomial chaos expansion surrogate model combined with the Bayesian optimization algorithm to quickly update the structural performance parameters to be inverted. The invention makes up for the deficiencies of traditional deterministic inverse analysis, liberates the inversion efficiency in the field of classical inversion analysis from the limitation of computational cost of complex numerical models, improves inversion efficiency and robustness to noise, and realizes fast inversion of structural performance parameters. The goal.

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 a data collection and regression analysis method providing privacy protection, adopts differential privacy to protect the privacy of data providers, and encourages providers to provide real data through a compensation mechanism. First, in the analysis module of the regression model, this method adopts the ridge regression model, expands the loss function into a form of polynomial chaos, and adds Laplace noise to the coefficients in front of each polynomial, so as to ensure that the regression model obtained by training is both The privacy of the data provider is protected, and the accuracy of the model is guaranteed; then, in the remuneration payment module, the regression model obtained by removing the data provided by the data provider is calculated, compared with the overall regression model, and the above two The error is used as a measure of the remuneration of each data provider, in other words, the smaller the error, that is, the more accurate the data, the more the corresponding reward. In short, through privacy protection and appropriate rewards, this method can incentivize more realistic reporting data and train more accurate models.