16 results about "Orthogonal basis" patented technology

The application discloses a material deformation displacement calculation method and a calculation system. The method comprises the following steps: in response to obtained design parameters, a corresponding structure and a geometric model are constructed, and a stiffness matrix K and a load matrix F are generated; the stiffness matrix K is stored in a sparse form by row compression, the load matrix F is input, and a Krylov subspace dimension m, an initial value U0 and an allowable error ε are selected; a set of standard orthogonal bases of the Krylov subspace is constructed; the best approximation U of the displacement in the Krylov subspace is calculated m ; the residual ||F-KU m || is calculated, and if the residual is less than the allowable error ε, the best approximation U m is output as the material deformation displacement; if the residual is greater than the allowable error ε, the best approximation U m is taken as a new initial value, the Krylov subspace is updated, and the material deformation displacement is recalculated. The application provides a stiffness calculation method which can be flexibly deployed and efficiently parallel, and realizes acceleration of finite element analysis.

The invention discloses a thermal-mechanical coupling field state inversion method and device for a compressor hot charging process, and relates to the technical field of intelligent manufacturing and digital twinning, and the method comprises the steps: carrying out the offline modeling based on historical temperature data and historical displacement data of a key node of a compressor impeller, obtaining a reduced-order model and a physical and data hybrid evolution model which meet preset conditions; performing order reduction processing on the observation state of the previous moment by adopting an order reduction model to obtain an order reduction state and an order reduction orthogonal basis matrix; calculating by adopting a physical and data hybrid evolution model based on the reduced-order state to obtain an estimated state at the current moment; based on the estimation state and current observation data obtained in real time, an extended Kalman filtering method is adopted for calculation, and a target estimation state is obtained; and performing inversion by using a preset projection function based on the target estimation state and the reduced-order orthogonal basis matrix to obtain an inversion result. According to the method, the accuracy of an inversion result is improved, and the assembly quality of high-end equipment can be improved.

The invention discloses an AUV (Autonomous Underwater Vehicle) velocity field reduction method based on intrinsic orthogonal decomposition and neural network fusion, which comprises the following steps: constructing a velocity field snapshot matrix of an AUV, each velocity field snapshot being a multi-dimensional velocity field obtained by training sample simulation; preprocessing the speed field snapshot matrix, and then performing matrix decomposition by using a POD method to obtain a standard orthogonal basis matrix and a diagonal matrix; setting a truncation coefficient, determining the number of singular values needing to be reserved from the diagonal matrix by using the truncation coefficient, performing dimensionality reduction on the standard orthogonal basis matrix by taking the number as a dimensionality reduction order, and determining an order reduction coefficient matrix based on the standard orthogonal basis matrix after dimensionality reduction; constructing a working condition matrix, wherein the working condition matrix comprises working conditions of different dimensions; and fitting a mapping relation between the working condition matrix and the reduced-order coefficient transpose matrix by using a neural network so as to predict the velocity field under the to-be-predicted working condition.

The invention relates to a large-scale power system discrete eigenvalue parallel computing method based on surrounding channel integration. Comprising the following steps: performing contour integral spectrum transformation on a system state matrix, and determining characteristic value dominance; differentiated integral curves are designed based on characteristic value dominance, the number of characteristic values in each integral curve is estimated, and the initial dimension of the corresponding characteristic subspace is determined; determining the number of initial integral points of each integral curve by adopting a self-adaptive method, and performing self-adaptive integral point configuration on each integral curve; determining an initial subspace dimension of each block based on the number of feature values and the number of parallel integral blocks; performing singular value decomposition on a block basis matrix to construct a standard orthogonal basis; combining the orthogonal basis of each block to form a global orthogonal subspace basis; performing Rayleigh-Ritz projection in a global space to solve a dimension-reduced generalized feature value; and outputting the discrete eigenvalue and the eigenvector. And accurate and efficient calculation of discrete characteristic values of a large-scale power system is realized.

The invention discloses a concrete penetration depth prediction method, device, equipment and medium, and relates to the technical field of concrete anti-penetration performance analysis, and the technical scheme is as follows: constructing a state vector according to a physical variable set generated in a rigid elastic body penetration concrete process; constructing a dimension matrix according to the state vector, and performing singular value decomposition on the dimension matrix to obtain a null space orthogonal base; performing linear mapping on the null space orthogonal base through a pre-trained learnable parameter matrix to obtain a feature index matrix; inputting the logarithm mapping result of the state vector and the feature index matrix into a neural network for forward propagation calculation, and outputting dimensionless features; inputting the dimensionless features into a multi-objective optimization algorithm, searching in an operator space of the multi-objective optimization algorithm, and outputting an analytic formula of the dimensionless penetration depth when the Pareto front of formula complexity and fitting loss reaches an optimal solution; and predicting the penetration depth of the concrete based on the analytical formula.

The application discloses a fast calculation method and device for scattered electromagnetic field based on random matrix approximation, and belongs to the field of fast modeling of scattered field. The method comprises the following steps: precalculating an incident field vector and a reciprocal incident field vector; generating a Gaussian random matrix matched with the column number of a to-be-determined scattered response matrix; performing linear superposition on the incident field vector to obtain a synthetic incident field vector, and constructing a random projection matrix according to the scattered field vector of an equivalent current vector at a receiving point; performing linear superposition on the reciprocal incident field vector to obtain a reciprocal synthetic incident field vector, and constructing a projection coefficient matrix according to the response of a reciprocal equivalent current vector at a transmitting source; and calculating a complete scattered response matrix based on the product of an orthogonal basis matrix and the projection coefficient matrix. In the application, a large-scale geophysical electromagnetic complex scene can be adapted, higher calculation precision and stable convergence are achieved, and the reconstruction of the complete scattered response matrix can be completed at a lower relative error level.

This application discloses a method and apparatus for thermo-coupling field state inversion in compressor hot-assembly processes, relating to the fields of intelligent manufacturing and digital twin technology. The method includes: offline modeling based on historical temperature and displacement data of key nodes of the compressor impeller to obtain a reduced-order model and a physics-data hybrid evolution model that meet preset conditions; using the reduced-order model to reduce the order of the observed state at the previous moment, obtaining a reduced-order state and a reduced-order orthogonal basis matrix; calculating the estimated state at the current moment using the physics-data hybrid evolution model based on the reduced-order state; calculating the target estimated state using the extended Kalman filter method based on the estimated state and the real-time acquired current observation data; and performing inversion using a preset projection function based on the target estimated state and the reduced-order orthogonal basis matrix to obtain the inversion result. This method improves the accuracy of the inversion results and can improve the assembly quality of high-end equipment.

The present application relates to data analysis and processing technical field, and further relates to natural resource asset big data analysis and accounting method, the method comprises the following steps: step 1: obtaining the physical inventory of different resource types in each period, obtaining the loss amount of different resource loss types in each period;Step 2: the normalized matrix of each period is calculated according to the half-life weight resource side covariance matrix and loss side covariance matrix, and the resource side covariance matrix and loss side covariance matrix are respectively decomposed, and the orthogonal basis vector with the largest contribution to the overall variation is extracted;Step 3: according to the orthogonal basis vector and the smoothed singular spectrum, the resource contribution and liability cost are linearly combined to obtain the principal component difference after removing the stray noise.The present application can effectively suppress data jump, improve the continuity, accuracy and interpretability of the accounting result.

The application relates to the technical field of electric propulsion digital twin simulation, and discloses an electric propulsion digital twin simulation data reduction method, which comprises the following steps: acquiring simulation data of electric propulsion plasma; based on the simulation data, snapshot data is extracted in a grid unit of a calculation domain; singular value decomposition is performed on the snapshot data, a reduced orthogonal basis is established, and reduced data representation is obtained through projection; based on a plasma fluid control equation, a semi-discrete ordinary differential algebraic equation group is constructed, and a coefficient matrix of a reduced model is determined through least square fitting; real-time simulation of an electric propulsion digital twin system is performed by using the reduced model, and field data is output. According to the application, the calculation precision and the simulation result obtained by PIC / MCC simulation are in the same order of magnitude, the calculation time reaches the level of seconds, and the real-time simulation demand can be met.

The invention discloses a forest fire detection incremental learning method and system based on geometric path regularization, and the method comprises the steps: building a forest fire data set, and constructing a forest fire detection reference model; in the incremental training stage, aiming at newly-collected fire missing report or false report data, while standard task loss is calculated, a geometric path regularization loss item is introduced, and the regularization loss is specifically as follows: a subspace orthogonal basis of a reference model and a current model weight matrix is extracted by adopting QR decomposition, a transformation matrix connecting a new orthogonal basis and an old orthogonal basis is constructed, and a geometric path regularization loss item is introduced; the rotation amount of the subspace is approximately calculated through efficient Lie algebra projection operation, and the Floribenius norm of the rotation amount is used as regularization loss. According to the method, unnecessary geometric rotation of the model weight subspace in the updating process is directly constrained, new knowledge can be effectively learned, and meanwhile, the recognition capability on an old scene is stably kept, so that model performance degradation is prevented, and continuous and stable performance improvement of a detection model is realized.

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 invention discloses a device thermal management-oriented simulation model order reduction method and system, and belongs to the technical field of numerical calculation and simulation analysis. The method aims at solving the problems that an existing finite element thermal simulation full-order system is large in calculation amount and difficult to process multiple heat sources efficiently, and a projection method is high in memory consumption. The method comprises the following steps: constructing a full-order heat conduction first state equation containing an input matrix representing multiple heat sources or multiple boundary conditions; performing iteration processing on the input matrix by applying a block second-order Arnoldi algorithm to generate an orthogonal basis matrix; reducing the order of the first state equation by using the orthogonal basis matrix and adopting a Galerkin projection method, and constructing a second state equation; and finally, carrying out time domain iteration solution and reduction on the reduced-order equation to obtain a full-order temperature field response result. According to the method, the dynamic characteristics under multiple heat sources are effectively captured by adopting the block second-order Arnoldi algorithm, the memory occupation is remarkably reduced by adopting Galerkin projection, and the simulation time is greatly shortened while high precision is ensured.

The invention discloses a self-adaptive model order reduction method and device, computer equipment and a storage medium. The method comprises the steps that initialization parameters are acquired; performing loop iteration until the actual moment matching order reaches the maximum total moment matching order; calculating residual errors of all moment matching points, identifying the moment matching point with the maximum residual error and recording the maximum residual error; residual errors of all the test points are calculated, the test point with the maximum residual error is recognized, and the maximum residual error is recorded; carrying out convergence check on the maximum value between the maximum residual error of the moment matching point and the maximum residual error of the test point, and if the maximum value is smaller than the tolerance, jumping out of circulation; and dynamically selecting to execute an order-increasing or point-increasing strategy based on the balance parameter: constructing an order-reducing model based on the finally obtained standard orthogonal basis matrix. The method aims at automatically solving the problem of balance between precision and speed in broadband simulation, the high-precision electromagnetic system reduced-order model can be obtained at the calculation cost as small as possible, the calculation efficiency is remarkably improved, and resource consumption is reduced.

The embodiment of the invention provides a matrix decomposition method and device based on a mercuric chloride chip, equipment and a storage medium. The method comprises the following steps: acquiring a to-be-decomposed original matrix; aiming at each column vector of the original matrix, performing projection processing on each column vector to obtain a middle orthogonal basis vector; performing iterative projection processing on the intermediate orthogonal basis vector to obtain a next intermediate orthogonal basis vector until the number of iterative projection times reaches a preset number of projection iterations, taking the next intermediate orthogonal basis vector obtained by the last iteration as an orthogonal basis vector of the corresponding column vector, and generating a corresponding coefficient vector according to the orthogonal basis vector; sequentially constructing an orthogonal matrix based on a plurality of orthogonal basis vectors corresponding to a plurality of column vectors contained in the original matrix, and constructing a coefficient matrix based on a plurality of corresponding coefficient vectors; and decomposing the original matrix based on the orthogonal matrix and the coefficient matrix to obtain a decomposition result corresponding to the original matrix. Therefore, the accuracy of matrix decomposition based on the mercuric chloride chip can be improved.

The application discloses a hybrid algorithm based on a classical discontinuous finite element and a variational quantum linear solver, relates to the technical field of quantum-classical hybrid computing crossover, and comprises the following steps: adopting a discontinuous finite element method to perform spatial dispersion on fluid control equations, using a high-order basis function to describe internal solution of a unit and exchanging unit interface information through numerical flux to form a semi-discrete form of a common differential equation group; adopting an implicit time advancing format on the semi-discrete common differential equation group to convert the physical quantity updating problem of the current time step into a solving task of a high-dimensional sparse linear equation group; applying a generalized minimum residual method on the high-dimensional sparse linear equation group on a classical computing platform, constructing a set of orthogonal basis vectors of a Krylov subspace through an Arnoldi process, and projecting the original equation group to the low-dimensional subspace to obtain a dense linear system with reduced dimension; and constructing a variational quantum solving process of an adaptive noise-containing medium-scale quantum processor based on the low-dimensional dense linear system.