28 results about "Krylov subspace" patented technology

The invention belongs to the technical field of nuclear reactor physical calculation, and particularly discloses a multi-group steady-state neutron transport coarse mesh node global efficient solving method and system, which effectively fuse and exert the advantages of a coarse mesh node method and a Newton-Kralov method. A general coarse mesh segment transport calculation model suitable for various polyhedral segments is constructed, high-precision and high-efficiency transport scanning calculation is realized under sparse segments, the number of variables is greatly reduced, and the calculation scale of single transport scanning is reduced; a Newton-Kralov subspace global solution framework is established, a global solution variable is selected based on a variable coupling relationship of a coarse network nodal method, a linear equation corresponding to a Newton step length is solved by using a Kralov subspace method, and the Newton step length is used for updating the global solution variable to realize rapid and efficient convergence. On the premise of ensuring the calculation precision, the calculation efficiency is remarkably improved, and the calculation scale is reduced, so that the method is particularly suitable for the problem of large-scale and high-dominance-ratio neutron transportation.

The invention discloses a hybrid preprocessing-based power flow iterative calculation method and system, and mainly relates to the technical field of data calculation of a power system. Comprising the following steps: constructing a linear system corresponding to a Jacobian matrix based on a Newton-Krayrov subspace load flow calculation basic framework; performing norm scaling, row and column rearrangement and incomplete decomposition on the Jacobian matrix in sequence to generate a preprocessing operator; a preprocessing operator is embedded into a biconjugate gradient stabilization algorithm, and a nonlinear solution is updated by dynamically adjusting a residual control strategy; and according to the condition that the residual error meets Newton-Kraylov space load flow calculation convergence conditions, judging that calculation is terminated, and outputting a load flow result or continuing iteration. The method has the beneficial effects that the combination of the physical characteristics of the power grid and the numerical precondition technology is realized, and a reliable solution is provided for the simulation of a large-scale node power system.

The application relates to the technical field of power electronics, and discloses a press-contact type IGBT device packaging structure optimization method and system. The method comprises the following steps: constructing an equivalent model of a press-contact type IGBT device; constructing a differential algebraic equation for uniformly describing the equivalent model of the press-contact type IGBT device and circuit port variables; converting the differential algebraic equation into a nonlinear algebraic equation group through time domain discretization, and constructing an iteration matrix with a global state vector as a derivation object according to a solving mode of the nonlinear algebraic equation group; performing low-dimensional subspace projection on the iteration matrix based on a Krylov subspace, and combining residual minimization to solve a linear subproblem of the iteration matrix, so that current uniformity characteristic results of the press-contact type IGBT device are obtained; and the packaging structure of the press-contact type IGBT device is optimized based on current density distribution reflected by the current uniformity characteristic results. The application can improve the current uniformity and operation reliability of the system.

The present application relates to the field of electromagnetic numerical calculation, and discloses a kind of method for solving electromagnetic scattering based on adaptive block Krylov subspace base function, method includes the following steps: step one: target region is carried out adaptive region decomposition, and target subdomain is obtained;Step two: target subdomain is expanded, and extended subdomain is formed;Step three: using optimized extended subdomain, the solving calculation of electromagnetic scattering is carried out.The main advantage of the present application is that the efficiency of constructing Krylov subspace base function is higher by using adaptive block technology, which significantly reduces the generation time of Krylov subspace base function based on block, optimizes the block expansion of subdomain, improves the solving calculation time, uses clustering algorithm to carry out region decomposition on the calculation target, and uses the average distance of clustering data points to cluster center to expand each subdomain to ensure the continuity of current, which not only ensures the calculation accuracy, but also improves the construction efficiency of base function, significantly reduces the generation time of Krylov subspace base function based on block.

The invention discloses a system recommendation method based on Lanczos algorithm orthogonality. The system recommendation method comprises the following steps: firstly, modeling a problem of searching a community structure in a network structure into a problem of solving first k minimum feature pairs of a network Laplacian matrix; secondly, projecting a Laplacian matrix in a high-dimensional Euclidean space into a symmetric three-diagonal matrix in a low-dimensional Krylov subspace; then, using a feature value convergence criterion to screen out converged feature pairs of the symmetric tridiagonal matrix, and calculating feature vectors corresponding to the converged feature pairs; thirdly, calculating a feature vector of a Laplacian matrix according to the feature vector of the symmetric matrix; and finally, carrying out de-orthogonalization on the convergent feature vector of the Laplacian matrix and the Lancozs vector, storing the convergent feature vector of the Laplacian, and using the convergent feature vector of the Laplacian to detect the community structure through a standard k-means algorithm. According to the method, the real community detection data set is used as a drive, the Lanczos algorithm is used as a model, and the community structure contained in the graph network can be accurately detected, so that the recommendation quality of the system is improved.

The application discloses a quantum linear solving method and device based on quantum adiabatic linear algorithm, and a medium, and relates to the technical field of quantum computing. The method comprises the following steps: obtaining a linear system to be processed, and constructing a Krylov subspace matched with the linear system; determining a subspace equation set of the linear system based on the Krylov subspace according to the linear system and the Krylov subspace; constructing a quantum circuit corresponding to the quantum adiabatic linear algorithm according to the subspace equation set, and solving an approximate solution of the linear system in the Krylov subspace according to the quantum circuit. The application can combine the subspace method with the quantum adiabatic linear algorithm, perform dimension reduction processing on the original high-dimensional linear equation set in the quantum adiabatic linear algorithm through the subspace method, so that the dimension of the linear equation set actually solved in the iteration process is smaller than the dimension of the original linear equation set. Therefore, the demand of the quantum discrete adiabatic linear algorithm for computing resources is reduced, and the quantum discrete adiabatic linear algorithm can be implemented in an NISQ chip and a classical computer.

The present invention discloses a method for reducing the order of a transformer temperature field model based on the Krylov subspace, belonging to the technical field of temperature field simulation of oil-immersed three-phase transformers. The present invention includes: Step 1. According to the actual physical dimensions of the transformer, construct a simulation model of the oil-immersed three-phase transformer and appropriately simplify the model. Step 2. Establish an electromagnetic field simulation model, use an eddy current solver, and simulate to obtain the transformer loss distribution. Step 3. Take the obtained transformer loss distribution as the excitation source of the fluid field, establish a fluid field simulation model, realize the coupled analysis of the electromagnetic field and the fluid field, and obtain the temperature field distribution characteristics of the oil-immersed three-phase transformer. Step 4. Build a reduced-order model for the transformer temperature field based on the Krylov subspace method. The present invention realizes the rapid simulation calculation of the physical field, reduces the simulation time, and further constructs a digital twin model of the transformer.

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.

This invention discloses a method and apparatus for intelligent task navigation and multi-dimensional collaborative management, applicable to the optimization and execution control of complex workflows, such as hospital information systems and intelligent systems. The method achieves personalized task generation, multi-role collaborative task allocation, and dynamic monitoring and optimization in complex scenarios by constructing a multi-level knowledge graph, applying the fully discrete finite element method, the nonlinear GCR-type Krylov subspace method, and the unfitted Green's function method.

This invention relates to a defect detection method for carbon fiber cables, comprising the following steps: S1. Constructing a simulation model of the carbon fiber composite cable and obtaining a sensitivity matrix; S2. Setting up a detection probe; S3. The detection probe acquires the detection voltage of the carbon fiber cable under test; S4. Calculating the initial grayscale value set of all pixels on the cross-section detected by the detection probe at the location of the carbon fiber cable under test based on the detection voltage, sensitivity matrix, and defect-free voltage; S5. Calculating the initial residual based on the results output from S1-S4, and updating the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable under test using the Krylov subspace algorithm; S6. Updating the initial grayscale value set of all pixels on the cross-section of the carbon fiber cable under test based on the last iteration update and creating an image. When a defect is found in the image, the location detected by the detection probe is the location of the defect. This invention reconstructs the cross-sectional image using the Krylov subspace algorithm, making the cross-section of the carbon fiber cable clearer.

The invention belongs to the technical field of electric power system time delay analysis, and relates to a Lagguerre-Taylor hybrid order reduction method for a multi-time-delay electric power system, which comprises the following steps of: S1, modeling the multi-time-delay electric power system and defining an order reduction problem; s2, a projection matrix is constructed, wherein a Laguerre function and Taylor are expanded and mixed; the method specifically comprises the steps that a projection matrix V1 is constructed based on scale Laguerre function expansion, a projection matrix V2 is constructed based on Taylor expansion, and a high-order block Krylov subspace orthogonal basis is generated based on a high-order block Arnoldi execution process; s3, constructing a Lagguerre-Taylor hybrid projection method of the multi-time-delay power system, and constructing an order reduction system; s4, analyzing the stability of the reduced-order system; according to the method, the reduced-order framework based on the projection matrix is constructed, the time-delay term algebraic structure of an original system is completely reserved, and the defect that the time-delay structure is damaged in an existing method is overcome.

This invention discloses a deep learning-based engine condition monitoring method, comprising the following steps: collecting multi-source sensor data and corresponding speed data during engine operation; preprocessing the original multi-source data to obtain preprocessed multi-source data; performing condition-locked resampling to obtain a set of window sequences; constructing a Krylov subspace and performing orthogonalization to obtain an orthogonal basis for the subspace; performing Krylov subspace change point and state transition detection to obtain the current monitoring state; generating a subspace fingerprint and selecting a deep learning monitoring branch based on the subspace fingerprint routing structure to obtain a health index and anomaly score; writing the health index and anomaly score into a candidate alarm queue, switching the current monitoring state, and outputting alarm results based on the candidate alarm queue. This invention improves the accuracy of engine condition monitoring by combining condition-locked resampling with Krylov subspace change point detection.

The present invention belongs to the technical field of structural topology optimization, and specifically relates to a wide-band topology optimization method for viscoelastic structures based on the high-order Krylov subspace method. This method addresses the non-linear frequency response problem of viscoelastic materials by constructing a reduced-order subspace through high-order Taylor expansion and moment matching orthogonalization, significantly improving the solution accuracy and frequency band range. Based on the reduced-order model, combined with the displacement squared sum objective function and volume constraint, a gradient optimization algorithm is used to achieve efficient topology optimization. The present invention achieves high-precision frequency response analysis through high-order Taylor expansion and correction terms, significantly reducing the computational cost by more than 80% with a small number of basis vectors, and co-optimizing with a multi-frequency point logarithmic weighted objective function to significantly improve the wide-band dynamic performance, which is applicable to complex engineering scenarios such as submarines and MEMS devices.

This invention discloses a method, apparatus, and medium for solving variable quantum linear problems in subspaces. The method includes: determining the system of linear equations to be solved, constructing a variable quantum circuit and a Krylov subspace, and using the generalized minimum residual method and the variable quantum circuit to calculate an approximate solution of the system of linear equations to be solved in the subspace. This addresses the shortcomings of existing technologies and can reduce the time complexity and computational load of solving linear problems.

The invention discloses a micro-grid linearization model order reduction method, system, equipment and medium, and belongs to the field of micro-grid stability analysis and control. Models of all elements in a micro-grid are obtained, a nonlinear differential algebraic equation set is established, a stable equilibrium point of the nonlinear differential algebraic equation set is solved, linearization processing is carried out, and a linearized differential algebraic equation set is obtained; solving a rightmost characteristic value by adopting a characteristic value algorithm, if the system is not stable, performing leftward translation transformation on the system to stabilize the system, generating a Lyapunov equation according to the translated system, solving a controllable and observable Gramb matrix by adopting a Krylov subspace algorithm, and performing order reduction on the translated system by adopting a balanced truncation method to obtain a stable system; according to the method, an existing balance truncation method is improved, the precision, the stability, the controllability and the observability of a system after order reduction are guaranteed, meanwhile, the Grubrum matrix can be efficiently solved, and the method is made to be suitable for an unstable system.

The invention belongs to the technical field of block iteration matrix solving in computational electromagnetics, and particularly relates to a block iteration matrix solving method based on matrix dimensionality reduction and a preprocessing technology. According to the method, two technologies of matrix dimension reduction and matrix preprocessing are applied, a right-end item matrix is processed by adopting a matrix dimension reduction mode, and through low-rank approximation, the solution precision can be effectively ensured, the calculation overhead is remarkably reduced, and a multi-right-end linear system can be conveniently processed; moreover, the BCOCG algorithm is applied to a preprocessing technology, so that the performance of the matrix is further improved, and the convergence and stability of the algorithm are improved. According to a system equation generated when multiple physical excitation sources or multiple scanning angles exist in the electromagnetic problem, memory expenditure is shortened from the perspective of a short recursion Krylov subspace iteration method, multiple columns of right-end term vectors can be calculated at the same time through a block iteration BCOCG algorithm, and the problem of matrix morbidity caused by correlation between columns is solved.

The invention discloses a parallel computing-based high-performance matrix operation acceleration method and system, and relates to the technical field of matrix operation, and the method comprises the following steps: matrix multi-scale decomposition: carrying out multi-scale decomposition on a to-be-processed matrix to obtain a plurality of sub-matrixes under different resolutions, including coarse-scale sub-matrixes and fine-scale sub-matrixes; according to the method, the to-be-processed matrix is divided into the sub-matrixes with different resolutions through multi-scale decomposition, and the sub-matrixes are distributed to the parallel processing sub-units to be processed at the same time by combining the parallel computing technology, so that the processing efficiency is improved, and the processing efficiency is improved. Meanwhile, a cross-scale information transfer mechanism is designed, coarse and fine scale sub-matrixes are subjected to collaborative iteration, the coarse scale sub-matrixes adopt an improved block Krylov subspace method and a matrix precondition technology, the fine scale sub-matrixes are introduced into an adaptive step length conjugate gradient algorithm, and an inter-scale constraint relation is established to realize bidirectional feedback.

This invention belongs to the field of nuclear reactor physics computational technology, and specifically discloses a coarse-grid nodal global efficient solution method and system for multi-group steady-state neutron transport. It effectively integrates and leverages the advantages of the coarse-grid nodal method and the Newton-Krylov method, constructing a general coarse-grid nodal transport computation model applicable to various polyhedral nodals. It achieves high-precision and high-efficiency transport scan computation under sparse nodals, significantly reducing the number of variables and compressing the computational scale of a single transport scan. A Newton-Krylov subspace global solution framework is established. Global solution variables are selected based on the variable coupling relationship of the coarse-grid nodal method, and the Krylov subspace method is used to solve the linear equations corresponding to the Newton step size. The obtained Newton step size is used to update the global solution variables to achieve fast and efficient convergence. This invention significantly improves computational efficiency and reduces computational scale while ensuring computational accuracy, making it particularly suitable for large-scale, high-dominance neutron transport problems.

The present application belongs to the technical field of block iterative matrix solution in computational electromagnetics, in particular to a block iterative matrix solution method based on matrix dimension reduction and preprocessing technology. The present application uses two technologies of matrix dimension reduction and matrix preprocessing: the right end item matrix is processed by using the matrix dimension reduction, through low rank approximation, which can effectively ensure the accuracy of the solution, significantly reduce the calculation cost, and facilitate the processing of multiple right end linear systems; and the BCOCG algorithm is applied to the preprocessing technology to further improve the matrix behavior and improve the convergence and stability of the algorithm. For the system equation generated by multiple physical excitation sources or multiple scanning angles in electromagnetic problems, the memory cost is shortened from the perspective of short recursive Krylov subspace iteration method, and the block iteration BCOCG algorithm can calculate multiple column right end item vectors at the same time, avoiding the matrix ill-conditioning problem caused by the correlation between columns and columns.

The application discloses an engine state monitoring method based on deep learning, comprising the following steps: collecting multi-source sensor data and corresponding rotating speed data in the engine operation process; performing data preprocessing on the original multi-source data to obtain preprocessed multi-source data; performing working condition locking resampling to obtain a window sequence set; constructing a Krylov subspace and simultaneously performing orthogonalization processing to obtain a subspace orthogonal base; performing Krylov subspace change point detection and state switching detection to obtain a current monitoring state; generating a subspace fingerprint, and selecting a deep learning monitoring branch according to a subspace fingerprint routing structure to obtain a health index and an abnormal score; writing the health index and the abnormal score into a candidate alarm queue, switching the current monitoring state, and outputting an alarm result based on the candidate alarm queue. The application combines working condition locking resampling and Krylov subspace change point detection, and improves the monitoring accuracy of the engine state.

The invention provides a large language model parameter optimization method and system based on random GMRES, and is applied to the technical field of large language models, and the method comprises the steps: determining at least one to-be-optimized problem in a large language model, and converting the to-be-optimized problem into a least square problem; inputting the least square problem into the constructed randomized iteration solver for processing, and outputting a solution vector; the randomization iteration solver comprises a random AB-GMRES solver and a random BA-GMRES solver; the random iteration solver comprises a random AB-GMRES solver and a random A random AB-GMRES solver and a random BA-GMRES solver project a high-dimensional orthogonalization process in a Krylov subspace into a low-dimensional space constructed by a random subspace embedding matrix by introducing the random subspace embedding matrix to carry out approximate calculation; parameters in the large language model are updated or generation of a next reasoning token is propelled based on the solution vector. According to the invention, on the premise of ensuring the model performance, the training speed is greatly improved and the reasoning delay is reduced.

The present invention discloses a quantitative assessment method for network attacks on wide-area control systems based on reachability analysis, comprising: establishing a nonlinear differential equation model of a wide-area control system with wind farm access based on a simplified admittance matrix; using Zeno polyhedrons to model the network attack amplitude range and the wind farm output variation range, respectively, and adding the established models to the nonlinear differential equation model of the wide-area control system; based on reachability analysis theory, improving the reachable set calculation algorithm using a Krylov subspace iteration method based on a stable biconjugate gradient method and zonotope bundle technology; applying the improved reachable set calculation algorithm to calculate the reachable set of the wide-area control system under the influence of different types of network attacks and wind power disturbances. The present invention quantitatively evaluates the damping performance of the wide-area control system under different network attack scenarios and operating conditions based on the reachable set results, providing important guidance for improving the damping performance of the wide-area controller and ensuring the safe and stable operation of the power system.

The present invention belongs to electromagnetic simulation technology and specifically provides an electromagnetic scattering simulation method based on skeleton decomposition preconditioning, which is used to complete electromagnetic scattering simulation calculations of electrically large complex targets. While ensuring the accuracy of the simulation calculations, it improves the problem of ill-conditioned impedance matrices generated by complex targets, and at the same time improves the convergence and reliability of the iterative method. In the present invention, the interpolation decomposition technology and the proxy surface method are first used to select the bone element basis functions, and the skeleton decomposition method is used to obtain the approximate inverse matrix of the impedance matrix; then, the approximate inverse matrix is ​​used as a preprocessor, and the current coefficient is obtained by solving the Krylov subspace iteration method. Finally, the electromagnetic scattering of the metal target is calculated based on the current coefficient. The present invention creatively proposes a new preprocessor. Compared with traditional preprocessors, this preprocessor can further improve the matrix properties, greatly reduce the iteration time, and improve the convergence.

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.

This invention relates to a radio frequency (RF) simulation method, apparatus, computer device, storage medium, and program product. The RF simulation method includes: constructing a first Krylov subspace based on a first scanning frequency; generating a second Krylov subspace corresponding to a second scanning frequency by multiplexing vectors in the first Krylov subspace; and obtaining the circuit response when the scanning frequency is the second scanning frequency based on the second Krylov subspace. This invention can improve the calculation speed and simulation efficiency of RF simulation.

The invention relates to the technical field of electromagnetic simulation, in particular to a rapid electromagnetic simulation method based on a model reduced-order time domain fine integration method, which comprises the following steps of: establishing a Maxwell rotation equation containing magnetic conductivity, dielectric coefficient, conductivity, magnetic permeability and time change source items, and defining a magnetic field vector function and an electric field vector function; according to the method, a model order reduction technology is deeply embedded into a core equation of a time domain fine integration method, a correction Gram-Schmidt orthogonalization Arnoldi process of a Krylov subspace is combined, an original high-dimensional coefficient matrix is reduced into a low-order upper Hessenberg matrix, a compact projection matrix is generated, and the purpose of greatly reducing the coefficient matrix and matrix index dimensions is achieved; the matrix index is calculated by adopting the dimension expansion PI technology, direct solving of an inverse matrix of an original high-dimensional matrix is avoided, and the effect of reducing the calculated amount of the non-homogeneous ordinary differential equation set is achieved.

Calculation control for hybrid computing of Hamiltonian eigensolutions may be provided by preparing a plurality of states in a Krylov subspace of a full Hamiltonian that represents a chemical system; sampling a plurality of basis states from each state of the plurality of states in the Krylov subspace to produce a plurality of sampled basis states; processing the plurality of sampled basis states to yield an analysis selection; constructing a subspace Hamiltonian from the analysis selection; computing, via an eigensolver, an eigensolution for the chemical system from the subspace Hamiltonian; and outputting the eigensolution for the chemical system.

The invention provides an electromagnetic scattering calculation method and system based on a layered Krylov subspace, and relates to the technical field of electromagnetic numerical calculation, and the method comprises the steps: carrying out the blocking processing of a target electromagnetic scattering region, and obtaining a plurality of blocks; constructing an initial Krylov subspace primary function of each block to obtain an initial primary function set; performing projection, compression and orthogonalization operation on the initial primary function set to obtain a final global primary function matrix; and constructing an induced current sparse model, and based on the induced current sparse model, combining with the final global basis function matrix to obtain reconstructed induced current. According to the method, an algebraic multi-scale decomposition framework is adopted, a compact primary function set with good orthogonality is recursively constructed, and the calculation efficiency and the memory utilization rate are remarkably improved while the precision is guaranteed.