23 results about "Eigenvalues and eigenvectors" patented technology

The invention discloses a field programmable gate array (FPGA) implementation method for Hermite matrix eigenvalue decomposition, which comprises the following steps of: performing real number processing on a Hermite matrix according to a corresponding relationship between the Hermite matrix and eigenvalues and eigenvectors; grouping the dimension real matrix obtained by the real number processing; calculating rotation matrixes of diagonal units and non-diagonal units; performing Jacobi rotation operation on the diagonal units and the non-diagonal units, and updating the feature vector matrix according to a rotation matrix; after a group of Jacobi rotation is completed, data exchange is carried out according to grouping of a parallel Jacobi algorithm; and multi-stage cleaning can be carried out according to actual requirements. According to the method, a parallel Jacobi algorithm is selected, a series of matrix rotation is adopted, the matrix is converted into a diagonal matrix, and therefore the eigenvalue and the eigenvector of the matrix are calculated. According to the method, the parallel computing advantages of the FPGA and the Jacobi algorithm are fully utilized, and the real-time performance of the algorithm is effectively improved.

The application belongs to the technical field of power systems, and discloses an EIGD time-delay power system stability analysis method and device, wherein the method comprises the following steps: a linear model of the time-delay power system is established, and the differential equation in the model is converted into an abstract Cauchy problem by using an infinitesimal generator; a group of discrete points is selected for each time-delay interval of the time-delay power system, a discrete function space is established according to the discrete points, and the time-delay variable is discretized to generate a low-order partial infinitesimal generator discretization matrix; displacement and inverse transformation are performed on the discretization matrix to obtain an inverse matrix, and the characteristic value of the system is obtained according to the inverse matrix; the characteristic value is checked by using the Newton method to obtain the accurate characteristic value and the characteristic vector, and the stability of the time-delay power system is analyzed and judged. The method solves the problem of large matrix LU decomposition calculation amount in the existing EIGD time-delay power system characteristic value sparse calculation method based on the DDAE model.

The present application belongs to the technical field of image analysis and processing, and particularly relates to a rotary furnace combustion state prediction method and system based on flame images. The method comprises: collecting video image sequences of the flame in the rotary furnace, and converting each image to the YUV color space; calculating the combustion contribution degree based on the luminance component and the chrominance component, and screening out the core flame pixel set; taking the combustion contribution degree as the weight, calculating the weighted covariance matrix, determining the confidence ellipse according to the eigenvalue and eigenvector of the matrix, the center of the confidence ellipse being the weighted centroid, the rotation angle being determined by the eigenvector, and the long and short semi-axis lengths being proportional to the square root of the eigenvalue; extracting the area, eccentricity, rotation angle and center position of the confidence ellipse as the combustion state feature vector at the current time; inputting the time sequence sequence composed of the combustion state feature vectors at multiple times into the pre-trained hidden Markov model, and outputting the rotary furnace combustion state. The present application improves the accuracy and anti-interference ability of the combustion state prediction.

The invention belongs to the field of unit operation optimization control, and particularly relates to a bearing bush gap regulation and control method based on an LSTM-XGB integrated prediction model, and the method comprises the steps: collecting unit data affecting the temperature of a bearing bush, and carrying out the preprocessing; a principal component analysis method is used to calculate the eigenvalue and eigenvector of a covariance matrix, and a projection direction with the maximum data variance is found to carry out dimensionality reduction on unit data; constructing an LSTM prediction model and an XGB prediction model, and optimizing the LSTM prediction model and the XGB prediction model by using a sparrow search algorithm; finding an optimal combination strategy of the LSTM prediction model and the XGB prediction model through a stacking integration architecture; and obtaining a prediction result of the optimal LSTM-XGB integrated prediction model, and adjusting the bearing bush gap according to the prediction result of the optimal LSTM-XGB integrated prediction model. Through LSTM and XGBoost models, in combination with a sparrow search algorithm SSA optimization and Stacking integration strategy, the accuracy and stability of bearing bush gap prediction are improved, compared with a traditional method, errors are reduced, and millisecond-level prediction response is achieved.

The invention discloses a station weighting-based micro-seismic event plane positioning confidence ellipse calculation method, which comprises the following steps of: screening P-wave arrival time data simultaneously received by a plurality of stations, and calculating an initial seismic source position coordinate and an arrival time residual error of each station; the arrival time equation is linearized, and a design matrix and an initial weight matrix are constructed; constructing a normal equation based on the design matrix and the station weight matrix, solving a parameter correction amount, and updating a seismic source position coordinate and a seismic moment; calculating a covariance matrix and extracting a sub-matrix, performing eigenvalue decomposition to obtain eigenvalues and eigenvectors, and calculating an ellipse area under a preset confidence level; respectively resetting the weight of each station to zero, recalculating the area of the confidence ellipse, constructing an influence index of the station on the area of the ellipse, and adjusting the weight of the station according to the influence to obtain an updated weight matrix; and judging a convergence state based on the relative change rate of the confidence ellipse area, and outputting a final seismic source plane position and confidence ellipse parameters during convergence. According to the invention, rapid and accurate positioning operation of a micro-seismic monitoring scene can be realized.

The invention relates to a petrochemical engineering emergency early warning method and device based on large model data distillation. The method comprises the steps of obtaining original data, preprocessing and standardizing the original data, and constructing a data set. The method comprises the following steps: mapping a data set from a high-dimensional space to a low-dimensional space through linear transformation, and performing eigenvalue decomposition on a covariance matrix of data in the data set to obtain eigenvalues and eigenvectors; and sorting the feature vectors according to the feature values from large to small, selecting the feature vectors of which the feature value ranking is not lower than a first threshold value to form a new feature space, and extracting important features from the feature space through LASSO regression. And calling a CNN deep learning model to extract key features from the important features, distilling representative features in the original data, and outputting a feature set after distillation. And performing anomaly detection on the petrochemical engineering system through a clustering algorithm according to the feature set after distillation, and triggering early warning when a detection result does not meet a preset condition.

The invention discloses a power distribution network communication fault diagnosis method, and relates to the technical field of power distribution network communication, and the method comprises the steps: dividing a multi-dimensional data variable into a plurality of data groups, forming a neighborhood graph, and constructing a similarity matrix; obtaining a low-dimensional data variable based on the feature value and the feature vector of the similarity matrix; calculating a corresponding influence weight and correlation between any two variables based on the low-dimensional data variables; performing preliminary grouping on the low-dimensional data variables according to the correlation, and dividing manifold groups according to the total group weight ratio of each group; acquiring a real-time data group, calculating a manifold coordinate and determining a manifold group, calculating a final credibility according to the manifold group, and determining fault data according to the final credibility; the influence degree of dominant paths of different factors is accurately measured; according to the manifold group condition to which the real-time data group belongs, different methods are adopted to calculate the final trust degree so as to determine the fault data, and the problems of high calculation complexity and limitation and accuracy which are difficult to understand in a traditional analysis method are solved.

A structural damage identification method based on random sparse regularization comprises the following steps: S1, establishing a finite element model of a to-be-identified damage structure, dispersing the structure into a finite number of units, setting a damage working condition, and simulating the damage working condition; s2, performing modal analysis, calculating a stiffness matrix and a mass matrix of the structure, adding boundary conditions, and solving feature values and feature vectors; s3, constructing an objective function of damage identification; s4, introducing an l1 / 2 regularization optimization method, and establishing a structural damage identification equation; s5, introducing a random class algorithm, optimizing and solving the structural damage identification target equation, and obtaining a solution vector; and S6, determining the damage position and the damage degree in the structure according to the solution vector of the damage identification equation. According to the method, the damage position can be quickly positioned, the damage degree can be accurately quantified, the accuracy of a damage identification result is improved, and the identification time of damage identification is shortened.

The present application relates to the field of information technology, and more particularly to a data principal component acquisition method based on transverse federated learning, comprising: respectively obtaining features and vectors of local sample data; participating parties negotiate to generate a random number vector; adding the features and the vectors and sending to a trusted coordinator; the trusted coordinator calculates the mean; the participating parties calculate the difference and the covariance matrix; again generating a random number vector, adding the covariance matrix and sending to the trusted coordinator; calculating the global covariance matrix; obtaining m eigenvalues and eigenvectors of the covariance matrix; selecting d eigenvalues and corresponding eigenvectors from the m eigenvalues in descending order and sending to each participating party; the participating party projects the local sample data into a d-dimensional space formed by the eigenvalues to obtain a projection, which is the principal component of the local sample data. The beneficial technical effects of the present application include: while protecting data privacy, allowing more sources of data to be used, and improving the accuracy of model analysis.

The application discloses a method for impedance mismatch design of a multi-flame tube combined flame system of a gas turbine combustion chamber, comprising the following steps: based on graph theory, 12 flame tubes in a gas turbine are combined through a combined flame pipe to form a combustion chamber, modeling is performed as a cycle graph, and an adjacency matrix and a Laplace matrix are constructed; based on the angular frequency of the flame tube and the coupling strength of the combined flame pipe, a system matrix is constructed; eigenvalues and eigenvectors of the system matrix are calculated, oscillation frequency and vibration mode are determined, and degenerate modes are identified; by modifying the coupling strength of at least one combined flame pipe, the eigenvalues and eigenvectors of the system matrix are recalculated, degenerate frequency splitting is performed, and symmetry is broken; according to the split frequency and mode, the parameters of the combustion chamber are adjusted to optimize the combustion stability. The application simplifies the modeling of a complex system based on a graph theory method, reduces the calculation cost, breaks the symmetry of the system by modifying the coupling strength of the combined flame pipe, splits the degenerate frequency, and relieves the combustion instability.

Provided in the present application is a data processing method for improving the efficiency of solving for an eigenvalue and an eigenvector of a matrix. The data processing method comprises: acquiring a target matrix; on the basis of a plurality of characteristic parameters of the target matrix, searching a first database to determine at least one target reference eigenvector, wherein the first database stores a plurality of groups of first reference data, each group of first reference data corresponds to one first reference matrix, each group of first reference data comprises a plurality of characteristic parameters and eigenvectors of the first reference matrix, a plurality of target reference eigenvectors are eigenvectors of a target first reference matrix, and a plurality of characteristic parameters of the target first reference matrix match the plurality of characteristic parameters of the target matrix; and on the basis of the at least one target reference eigenvector, determining an initial reference vector, wherein the initial reference vector is used for solving for eigenvalues and eigenvectors of the target matrix. In addition, further provided in the present application are a corresponding apparatus, a computing device cluster, a computer-readable storage medium and a computer program product.

This invention discloses a method, apparatus, equipment, and storage medium for non-stop wind turbine inspection, relating to the field of wind turbine inspection technology. The method includes: acquiring point cloud data of the wind turbine to be inspected and determining the covariance matrix of the blade point cloud in the point cloud data; determining the eigenvalues ​​and corresponding eigenvectors of the covariance matrix, and determining the rotation axis direction of the wind turbine to be inspected based on the eigenvalues ​​and eigenvectors; determining the yaw angle of the wind turbine to be inspected based on the rotation axis direction, and determining the blade azimuth angle of the wind turbine to be inspected based on the point cloud data; and determining the UAV inspection route of the wind turbine to be inspected based on the yaw angle and blade azimuth angle at different times. The technical solution of this invention achieves non-stop, adaptive, and highly secure intelligent wind turbine inspection.

The invention discloses a customer credit rating method and device in the financial field, a medium and a product, and relates to the technical field of credit rating, and the method comprises the steps: obtaining basic economic data and basic rating data; standardizing the basic economic data to obtain a standardized matrix; calculating a covariance matrix according to the standardized matrix, and calculating a characteristic value and a characteristic vector of the covariance matrix; determining an eigenvector matrix based on the eigenvalues and the eigenvectors, and performing principal component analysis data dimension reduction on the standardized matrix according to the eigenvector matrix to obtain a dimension-reduced data matrix; establishing a multiple linear regression model based on the data matrix after dimension reduction and the basic rating data, and fitting to obtain a regression coefficient; and determining a principal component weight matrix based on the regression coefficient and the feature vector matrix, and calculating a credit score according to the principal component weight matrix and the standardized matrix. According to the invention, the time and cost required by evaluation can be reduced, and the reliability of the evaluation result is improved.

The invention discloses a radar-oriented order constraint Jacobi eigenvalue self-sorting method and system, solves the problem of resource consumption caused by an additional sorting module in a Jacobi iteration eigenvalue decomposition post-processing flow in the prior art, realizes direct output of ordered eigenvalues and eigenvectors, and omits an independent sorting module. The method comprises the steps that a real symmetric matrix A obtained through radar baseband signal sampling and covariance estimation is processed to obtain a compressed array, and a feature vector matrix V is initialized; in the parallel iteration process, index pairs are generated according to a scheduling sequence, sub-matrixes are extracted, two types of asymmetric rotation operators are generated through a condition driving mechanism, and a feature vector matrix is synchronously updated to track feature vectors; global data replacement is carried out, and non-diagonal element energy judgment convergence is calculated; after iteration is ended, feature values arranged in a descending order can be directly extracted from the main diagonal of the final compressed array, and corresponding feature vectors are output and used for direction of arrival estimation.

The application provides a random phase shift measurement method based on dynamic mode decomposition, comprising: obtaining three frames of random phase shift interferograms of an object to be measured, performing difference and normalization processing to obtain a first interferogram sequence without background; performing difference and algebraic operation on the first interferogram sequence to generate an equal-step second interferogram sequence; expanding the second interferogram sequence into a column vector form and constructing a data matrix X and a data matrix in time sequence; performing singular value decomposition on the data matrix to calculate an approximate matrix; performing characteristic analysis on the approximate matrix to extract eigenvalues and eigenvectors, and mapping the eigenvectors back to the space of the second interferogram sequence to reconstruct the dynamic mode of the second interferogram sequence; and recovering the phase distribution of the object to be measured according to the amplitude angle information of the main mode in the dynamic mode. The application breaks through the limitation of the existing algorithm that at least four frames of interferograms are required, and can realize stable phase demodulation under any unknown phase shift condition.

The invention discloses a fault identification method and device based on weighted gradient structure entropy. The method comprises the steps of 1, partitioning three-dimensional seismic data; 2, adaptive Gaussian smoothing filtering is carried out; step 3, constructing a gradient vector body; 4, constructing a gradient structure tensor matrix according to the gradient vector body; 5, performing characteristic decomposition by using the gradient structure tensor matrix, and calculating three characteristic values and characteristic vectors corresponding to each piece of hour window seismic data; step 6, introducing a feature vector direction constraint; 7, calculating a gradient structure tensor attribute value; calculating a weighted gradient structure tensor attribute value; 8, calculating a local structure entropy attribute value; step 9, calculating a weighted gradient structure entropy attribute value; and step 10, calculating data in each window, completing calculation of the whole three-dimensional seismic data volume, and obtaining a weighted gradient structure entropy attribute value. According to the method, the fault identification precision and the boundary depiction definition are effectively improved, and the calculation complexity is low.

The application discloses a low-rank seismic data denoising processing method of adaptive symplectic geometric decomposition, comprising the following steps: converting three-dimensional seismic data into a frequency domain by using Fourier transform; forming a Hankel matrix by frequency slicing of the frequency domain seismic data; forming a Hamilton matrix form by the Hankel matrix; using symplectic QR decomposition to obtain eigenvalues and eigenvectors of the Hamilton matrix; obtaining symplectic geometric entropy of the eigenvalues, and adaptively selecting the number of ranks through the symplectic geometric entropy; reconstructing the block Hankel matrix through low-rank approximation; and converting the processed frequency domain into a time domain through inverse Fourier transform. The application extracts eigenvalues and eigenvectors of the Hankel matrix by constructing the Hankel matrix and applying symplectic QR decomposition, and adaptively determines the number of ranks by using symplectic geometric entropy, so that low-rank approximation reconstruction is realized, effective denoising is achieved, and effective signals in the seismic data are preserved.

The application discloses a live teaching analysis method based on portrait point mode matching and belongs to the technical field of live teaching analysis, which comprises the following steps: obtaining the portraits of students when live teaching starts; extracting the triplet portrait graph G of each student according to the characteristics of each student portrait; constructing a point set to be matched for each student's triplet portrait graph G; constructing a Laplace matrix for the point set to be matched respectively; and performing singular decomposition on the student portrait graph to obtain the eigenvalue and eigenvector of the student portrait graph. The application evaluates the performance of students during live teaching by displaying the change of the head posture of students during live teaching, and provides a basis for scoring for teachers when scoring the usual scores of the final teaching by setting the distraction index, and solves the problem that the existing Internet live platform cannot analyze the concentration degree of students in real time in combination with the student portraits during live teaching.

The application relates to a wave direction angle analysis method and device, belonging to the field of wave test simulation. The specific process comprises the following steps: 1) generating a wave height data array of a target area; 2) performing forward and backward smoothing on the wave height data array of the target area to obtain a doubled data array; 3) calculating a covariance matrix of the doubled data array; 4) calculating an optimized covariance matrix by using a spatial smoothing method; 5) calculating all eigenvalues and eigenvectors of the optimized covariance matrix; 6) arranging the eigenvalues according to the size, distinguishing a signal subspace / noise subspace, and constructing a noise matrix; 7) performing translation and reciprocal weighting processing on the eigenvalues of the noise subspace to obtain a weighted noise matrix; 8) utilizing the orthogonal relationship between a wave guide vector and the weighted noise matrix to construct a spectral function; and 9) calculating the spectral function corresponding to all angles, and the angle corresponding to the peak value of the spectral function is the oblique wave direction estimation angle. The method can quickly and accurately calculate the wave field direction angle in real time.

The invention discloses a stress-containing kp energy band first-order derivative and second-order derivative calculation method, and belongs to the technical field of semiconductor device simulation. The method comprises the following steps: constructing a kp matrix containing stress based on a material parameter and a stress parameter of a target semiconductor material, and representing the kp matrix through four types of matrix elements; calculating a first-order derivative matrix and a second-order derivative matrix of the kp matrix about k space coordinates through analysis and derivation; the eigenvalue and the eigenvector of the kp matrix are solved, and the first-order derivative and the second-order derivative of the eigenvalue are obtained based on the Hellmann-Feynman theory and analysis inverse matrix calculation. According to the method, through matrix split expression and analytic derivative calculation, the derivative of each order can be obtained only by solving the eigenvalue and the eigenvector for one time, the problems that an existing finite difference method needs a large number of discrete points, the calculation speed is low, and the precision is influenced by the step length are solved, and the simulation efficiency and precision of the stress-containing semiconductor device are improved.

This invention proposes a method for analyzing the unsteady flow characteristics of a pump-turbine based on modal decomposition, belonging to the field of pump-turbine flow field simulation analysis technology. First, the three-dimensional or two-dimensional flow field data obtained from large eddy simulation (LES) calculations of the pump and turbine operating conditions are sorted according to the time dimension of the runner operation to form a data matrix. Then, the order reduction method is used to restore and replace the data with lower-dimensional data. The data matrix is ​​constructed based on the energy of each mode, and the POD modes and time coefficients are calculated. The approximate matrix is ​​found using the DMD method, and its eigenvalues ​​and eigenvectors are calculated to determine the DMD modes. Modal energy analysis is performed to identify the main modes. The flow field structure is reconstructed using the main modes, and transient error analysis of the reconstructed flow field is conducted to determine the characteristics of the unsteady modes, providing guidance for optimization design and flow field control while reducing the computational burden.

The application provides a multi-source heterogeneous data source fusion processing method, and belongs to the field of data fusion; solves the problem of low multi-source heterogeneous data fusion efficiency; specifically as follows: acquiring and saving numerical data and non-numerical data; dividing the numerical data into mixed data, one-dimensional data and multi-dimensional data; integrating the mixed data, unifying the dimension, and obtaining explicit fusion data; normalizing the one-dimensional data, obtaining primary fusion data, and constructing a correlation function; extracting eigenvalues and eigenvectors of the multi-dimensional data, and obtaining explicit fusion data of the multi-dimensional data; performing secondary fusion on the multi-dimensional data with correlation; in the non-numerical data, screening and fusing the non-numerical data corresponding to the extraction target, and obtaining non-numerical fusion data; the application improves the interpretability of data by analyzing, extracting and integrating various different structural data or non-structural data.

The invention provides a photoetching mask imaging method considering a vector TCC implicit operator of polarization aberration and Lanczos decomposition. The method comprises the following steps: determining a photoetching imaging model based on a mask frequency spectrum and an effective source point set; constructing a complex value Jones pupil matrix according to the polarization aberration, the defocus phase and the aperture constraint, and sampling and splicing the pupil matrix by using the polarization intensity component of the effective source point to form a center frequency domain shift pupil column vector library; in the solving process, based on the vector library, an implicit vector cross transfer function operator is realized in an operator multiplied vector mode, and the characteristic value and the characteristic vector of the implicit operator are solved by using a Lanczos algorithm so as to obtain a central frequency domain block of a coherent component decomposition (SOCS) kernel function; and in combination with the mask frequency spectrum and each kernel function, weighting and accumulating according to characteristic values to obtain a space image of the mask. According to the method, explicit construction of a high-dimensional TCC matrix is avoided, physical consistency is guaranteed, meanwhile, memory overhead is remarkably reduced, and the simulation efficiency of a photoetching imaging system is improved.