186 results about "Coefficient matrix" patented technology

The invention discloses a current inversion method based on a magnetic sensor array, and the method comprises the steps: S1, setting a plurality of measurement points, uniformly dividing a conductor layout region in a to-be-measured part of a to-be-measured multi-conductor system into grids with M * N nodes, and numbering each grid node as (i, j); constructing a coordinate system and recording coordinates of all grid nodes; s2, establishing a finite element simulation calculation model, calculating a reference position coefficient matrix of all measurement points, and constructing a reference position coefficient matrix database; s3, calculating a conductor position coefficient matrix, and constructing a position coefficient matrix; s4, according to the magnetic field measurement value acquired by the magnetic sensor array, the conductor current is calculated through inversion; and S5, after resampling the magnetic field measurement value, substituting the updated measurement value and the position coefficient matrix stored in the step S4 into the linear equation set constructed in the step S4 to solve the current of each conductor. The method has the characteristics of rapid calculation and low operand while the accuracy is ensured, and the inversion calculation efficiency can be improved.

The invention discloses a nuclear reactor core channel analysis method based on two fluid models, which comprises the following steps of: 1, establishing a fluid domain computational grid according to the structure of a nuclear reactor core or an assembly; 2, respectively establishing a control equation set and a heat conduction model of the fuel rod for the continuous gas-liquid phase and the discrete liquid drop phase; 3, considering physical phenomena such as flow heat exchange, resistance pressure drop and turbulence mixing in a reactor core, and implanting a corresponding constitutive model; 4, discretizing the control equation based on a second-order discrete format to obtain a discrete equation set; 5, dividing parallel tasks and parallel regions through an MPI parallel strategy to form a large coefficient matrix of a pressure equation; and 6, solving a discrete equation set and a large coefficient matrix through a pressure coupling semi-implicit algorithm and a stable biconjugate gradient method. According to the method, the key physical parameter distribution of the pressurized water reactor can be more accurately and reasonably calculated, so that technical guidance is provided for safety analysis and engineering design of the reactor.

The invention discloses a current inversion method for a steel tape armored multi-core cable, and the method comprises the steps: S1, setting a plurality of measurement points at a to-be-measured part of a to-be-measured multi-core cable, building a polar coordinate system with the geometric center of the to-be-measured multi-core cable as an original point, and constructing a position coefficient matrix, a conductor current matrix, and an attenuation coefficient matrix; s2, assigning an initial value to the unknown variable, and calculating to obtain an initial conductor current matrix and an initial attenuation coefficient matrix; s3, searching a local optimal solution of the attenuation coefficient matrix through a random optimization method; s4, constructing a linear equation set taking the conductor current matrix as an unknown variable to solve the conductor current matrix; and S5, after the sampling value of the magnetic induction intensity component is updated, solving the linear equation set, and calculating to obtain the current value of each conductor of the current cable. According to the method, on the basis of the time-invariant characteristic of the magnetization curve, the undetermined coefficient of the approximation function is solved by using the stochastic optimization algorithm, the nonlinear attenuation coefficient of the steel tape armoring of the target cable is solved, the influence of the steel tape armoring on the current inversion result is corrected, and the measurement efficiency and precision can be improved.

The invention provides a real-time reconstruction method and system for an internal temperature field of a key section of a deformed ring forging. The real-time reconstruction method comprises the steps of detecting an edge contour, generating a temperature field reconstruction target section and measuring section edge temperature distribution; performing grid division on the target section according to a heat conduction forward problem to generate a stiffness matrix and a solution equation; a matrix C, a boundary temperature array Ts and a boundary thermal load array Fa are generated, an underdetermined equation set of the internal temperature field reconstruction problem is obtained, and a special solution is obtained; and bringing the special solution of the underdetermined equation set and the boundary thermal load array Fa back to the solving equation to obtain section temperature distribution. According to the method, a heat conduction inverse problem is converted into a heat conduction forward problem, the internal temperature field of the key section can be reconstructed in real time based on the measurable surface temperature for the forge piece in the deformation process, a large number of training samples are not needed, an underdetermined equation set coefficient matrix does not need to be processed, and all information is reserved; the method is simple, efficient, high in controllability, high in fidelity and wider in application range.

The invention discloses a neutron transport constitutive relation and low-dimensional control equation modeling method based on sparse regression, and the method comprises the steps: enabling a state parameter of each state and a physical parameter calculated through a neutron transport program to form a neutron current matrix under a plurality of state parameters, and filling a sparse regression physical parameter matrix with the built fitting physical parameter, calculating an inverse matrix by using a least square method to obtain a coefficient matrix, and assembling to obtain a neutron transport constitutive relationship under the plurality of state parameters; according to the method, the characteristic that the calculation result of the neutron transport equation is accurate is utilized, the reason that the calculation result of the neutron diffusion equation is large in deviation in a small-scale range is grasped, the neutron transport constitutive relation is obtained in combination with sparse regression fitting, then the low-dimensional macroscopic neutron transport control equation is obtained, the theoretical derivation difficulty is small, the research progress is easier, and the method has good application prospects. And the effect of improving the calculation precision is obvious, the applicability is better, the difference from the situation under the actual reactor core working condition is small, and certain practicability is achieved.

The invention discloses an all-pure embedded power system security checking method based on a compensation method, and the method comprises the steps: firstly constructing an all-pure embedded power flow equation according to different node types based on an all-pure embedded theory; secondly, a compensation method is introduced to correct a coefficient matrix of the full-pure embedded power flow equation; and finally, a high-efficiency power system security checking algorithm is provided in combination with a full-pure embedded power flow equation and a compensation method, inversion of a high-dimensional matrix is avoided, and the calculation amount is greatly reduced. According to the method, the advantages of a full-pure embedding algorithm and a compensation method are combined, and the accuracy, the robustness and the high efficiency of safety checking of the power system can be considered.

The invention discloses a deep and far sea wind power time-varying impedance model grid connection analysis method based on a time domain residual error method, relates to the technical field of power system modeling simulation, and can efficiently and accurately analyze deep and far sea wind power grid connection. The method comprises the following steps: establishing a differential algebraic equation set containing high-capacity submarine cable impedance and a plurality of nonlinear links, and constructing a recursive coefficient matrix; dividing a preset global time domain into a plurality of time domain subintervals, and solving the recursion coefficient matrix in each time domain subinterval by referring to a universal analytic solution represented by a power series explicit operator to generate a global time domain explicit solution corresponding to the preset global time domain; performing discrete Fourier transform on the global time domain explicit solution to obtain a time-frequency domain spectrum result; and constructing a time-varying impedance model according to the differential algebraic equation, setting the time-varying impedance model by adopting a time-frequency domain spectrum result, and analyzing the deep and far sea wind power grid-connected control system by utilizing the set time-varying impedance model.

This classical computer transmits, to a quantum computer, a quantum circuit that is for performing quantum phase estimation, and that is generated on the basis of a quantum state |ψ> corresponding to the eigenstate of a target system, and information on a coefficient matrix when the equation of motion of the target system is expressed by a matrix format. The quantum computer acquires a measurement result of the eigenvalue of the coefficient matrix by executing the quantum circuit, and transmits the measurement result of the eigenvalue to the classical computer. The classical computer calculates the eigenfrequency of the target system on the basis of the measurement result of the eigenvalue.

The invention belongs to the field of system simulation, and particularly discloses a power electronic system simulation method and system based on an event triggering update state space model and a medium, and the method comprises the steps: respectively constructing an incidence matrix corresponding to each coefficient matrix in the system state space model, whether the corresponding coefficient matrix needs to be updated is determined; simulating the system according to a preset integral step size, and in the simulation process, updating the current integral step size according to the moment of an event discrete point whenever the system passes through the event discrete point, and determining whether each coefficient matrix needs to be updated or not according to the incidence matrix; and for the coefficient matrix needing to be updated, according to the system mathematical model described by the state equation, a new value of the coefficient matrix is calculated through a perturbation method, and updating is achieved. According to the invention, timely and efficient online model conversion can be realized, and the simulation speed of the power electronic system is improved.

The invention relates to the technical field of ion beam physical calculation, in particular to an ion beam optical property evaluation method based on a CPU-GPU hybrid parallel stable double-gradient conjugate algorithm. According to the technical scheme, the method comprises the following steps that a CPU-GPU hybrid parallel architecture is initialized, and CPU end and GPU end memory allocation, CUDA related object creation and GPU equipment initialization and parameter setting are completed; constructing a linear equation set, a sparse coefficient matrix A and a right-end vector b, and setting an initial solution vector, convergence precision epsilon and related parameters of the number of iterations; and analyzing the sparseness of the coefficient matrix A. Through combination of three core mechanisms of CPU-GPU cooperative calculation, dynamic load balancing and intelligent preprocessor selection, efficient, stable and universal evaluation of the ion beam optical characteristics is successfully realized, and an excellent solution is provided for solving the solving problem of a large-scale sparse linear equation set in the field of high-performance calculation.

The invention relates to the technical field of geometric error evaluation of hole and shaft parts in the field of machinery, and discloses a hole and shaft part action boundary discrimination method, which comprises the following steps of: deriving a motion coefficient vector for describing radius change of each measuring point based on a tiny rigid body motion model of a surface measuring point set of a measured part; and the motion coefficients are combined into a motion coefficient matrix. Furthermore, the method establishes a discriminant inequality group based on a mutual exclusion proposition. The judgment process is realized by analyzing the rank of the motion coefficient matrix and iteratively solving an equation set formed by the maximum linear independent matrix of the motion coefficient matrix, and finally, whether the fitting cylinder is the action boundary or not is determined by judging whether the inequality set has a feasible solution or not. According to the method, the problems of complicated geometric discrimination conditions, lack of universality and the like in the existing evaluation method can be solved, and a reliable basis which is easy to realize in a stylization manner is provided for determining the action boundary of the hole-shaft part.

The invention discloses a method for calculating the lateral deformation of a ground-connected wall using a third-order shear deformation plate theory, comprising the following steps: combining actual working conditions to obtain parameters of a calculation object, the parameters including geometric and physical mechanical parameters of a soil layer, a ground-connected wall and a support system; determining a deformation function of the underground continuous wall according to the third-order shear deformation plate theory; determining a coefficient matrix according to the Ritz method, the minimum potential energy principle and the earth pressure theory; obtaining a matrix equation according to the minimum potential energy principle; bringing the coefficient matrix into the matrix equation to solve the lateral deformation function of the underground continuous wall; the invention has the advantages of high precision of the calculation result and fast calculation speed, and providing optimized design guidance for the internal support arrangement mode, excavation step, ground-connected wall thickness and insertion ratio in actual construction.

A method of non-destructive testing (NDT) using prompt gamma neutron activation analysis (PGAA) and a suite of algorithms based on various mathematical algorithms, includes: analyzing stored spectra for net peak areas; determining aggregate type from the analyzed stored spectra; calculating dominant element ratios; solving for dominant element mass fractions; calculating elemental mass fractions; solving a linear equations system including a coefficient matrix; and determining material components.

The present application relates to the field of data processing technology, and provides a method and system for spatial simulation of temperature data based on quantum computing. The method includes: generating a grid in a study area according to a target resolution; dividing the grid in the study area into a sliding window to obtain a plurality of sub-windows; for each sub-window, generating a HASM master equation corresponding to each sub-window; inputting the coefficient matrix A and the right-hand side term b of the HASM master equation corresponding to each sub-window into a quantum computer, and using the Harrow‑Hassidim‑Lloyd algorithm (HHL for short) to solve the equation group consisting of the coefficient matrix A and the right-hand side term b of the equation, and obtaining the solution results of the HASM master equation corresponding to each sub-window; combining the solution results of the HASM master equation corresponding to each sub-window to obtain the final spatial simulation results of the temperature data in the study area, and realizing exponential acceleration of the traditional HASM method through the above steps, which is expected to fundamentally solve the problem of slow computing speed.

The present application discloses a method for solving mechanical problems based on a hybrid finite element method. It includes: analyzing each unit of a force-bearing body, constructing a coefficient matrix and a load vector; processing the boundary conditions on the boundary units, adjusting the load vector and obtaining a set of constraint equations; analyzing each unit interface of a Lagrangian unit and an intrinsic hybrid finite element unit, obtaining a local coefficient matrix of each unit interface, and assembling the local coefficient matrix of each unit interface into a coefficient matrix; processing the load vector and the coefficient matrix based on the set of constraint equations to obtain a set of linear algebraic equations and solving them to obtain stress and displacement results. The present application combines the Lagrangian unit method and the intrinsic hybrid finite element method to solve the linear elastic mechanics problem of a force-bearing body, and solves the problem of low accuracy of the results obtained by using the traditional finite element method to solve the linear elastic mechanics problem in the related technology while ensuring the solution efficiency.

The invention provides a balance calibration modeling method and system based on sample errors and space optimization. The method comprises the steps of obtaining a calibration data set and dividing the calibration data set into a sample set and a verification set; calculating a load space weight and a load complexity weight of the sample set, and obtaining a comprehensive weight based on the load space weight and the load complexity weight; and constructing a polynomial model of the sample set, and solving a coefficient matrix in the polynomial model based on the comprehensive weight to obtain a final balance calibration model. The method further comprises the following steps: verifying and evaluating the balance calibration model by using the sample set and the verification set, and optimizing the balance calibration model according to an evaluation result. According to the balance calibration modeling method cooperating with the sample space distance and the load complexity weight provided by the invention, nonlinear system errors introduced by calibration load complexity are fully considered, so that the influence of error distribution of calibration samples under various load combinations on modeling is more uniform and reasonable; and meanwhile, the problem of sample space occupation ratio is also solved.

The embodiment of the invention discloses a fluid steady-state characteristic determination method and a related device. The method comprises the steps that physical attributes and state parameters of fluid in a target system are acquired; according to the physical attributes and the state parameters, a fluid dynamic equation is constructed and discretized into a linear equation set, and the linear equation set is expressed as that the product of a coefficient matrix and a vector corresponding to an unknown quantity is equal to a constant vector; a quantum circuit is constructed according to the target unitary operator to solve the linear equation set, the steady-state characteristic of the fluid is obtained, the target unitary operator acts on the two registers, when the quantum state of one register represents any line of the coefficient matrix, the target unitary operator executes NOT gate operation on the other register, and when the quantum state of the other register represents any line of the coefficient matrix, the steady-state characteristic of the fluid is obtained. When the quantum state of one register represents the orthogonal complement space of any row of the coefficient matrix, the target unitary operator does not execute any operation on the other register. By adopting the embodiment of the invention, the steady-state characteristics of the fluid can be quickly determined.

The invention relates to a POD secondary manifold lower chamber flow field nonlinear model order reduction method based on anchor point optimization, and the method comprises the steps: obtaining a two-dimensional lower chamber computational fluid mechanics model as a full-order model, and building a snapshot matrix according to the full-order model; carrying out POD order reduction on the snapshot matrix, and calculating a POD reconstruction error matrix and a secondary manifold coefficient matrix of the snapshot matrix; determining an anchor point, and calculating a quadratic manifold modal matrix at the anchor point according to the POD reconstruction error matrix and the quadratic manifold coefficient matrix; according to the secondary manifold modal matrix at each anchor point, obtaining a secondary manifold modal matrix at the test point; and according to the quadratic manifold modal matrix at the test point, calculating an approximate snapshot of the POD quadratic manifold nonlinear reduced-order model at the test point. According to the method, the representative anchor points are introduced into the parameter sampling space, so that self-adaptive calculation of the secondary manifold modal matrix is realized, and the approximation precision of the reduced-order model is improved.

In order to overcome the problem that the current technology is difficult to estimate and continuously correct the bridge twin model by obtaining a series of test and test data, the application provides a bridge twin dynamic model Fourier modeling method based on test data, which is only related to the parameters of the bridge according to the system matrix related to all nodes of the bridge and the observation coefficient matrix related to all nodes, and the first continuous test process of the bridge does not change greatly, and the first comprehensive detection of the bridge twin dynamic mathematical model and the subsequent each time of the bridge twin dynamic mathematical model comprehensive correction process is relatively short, according to the characteristics of the fast and slow change matrix, the slow change matrix is set as a constant matrix in the first continuous test, and the system matrix related to all nodes of the bridge and the observation coefficient matrix related to all nodes in the bridge twin model are established through a series of effective tests and optimal indexes, and the bridge twin model is continuously corrected in the whole life cycle of the bridge, so that the technical problem of estimating and improving the bridge vibration model by obtaining a series of test and test data is solved.

The present invention discloses a method for quickly calculating the frequency response characteristics of a hollow winding coil of arbitrary shape, belonging to the technical field of electrical and electronic equipment components and sensors. The method comprises: establishing a three-dimensional rectangular reference coordinate system with a certain point in space as the origin; calculating the geometric center spatial coordinates of each turn based on the geometric centerline parameter equation of the skeleton, thereby obtaining the spatial parameter equation of each turn; combining the Newman formula to calculate the mutual inductance of any two turns and the self-inductance coefficient of the turns, the capacitance, resistance and skin depth between the turns, and the electrical relationship equation between any turn and other turns; writing the electrical relationship equation in matrix form, converting the coefficient matrix of the equation into an upper triangular matrix, and then converting the matrix into a coil port voltage and current relationship equation to obtain the coil port frequency response characteristics. The present invention has strong versatility, convenient calculation, and is easy to program for calculation, saving design time. No empirical formula is required during the calculation process, and the calculation accuracy is high.

Embodiments of the present disclosure disclose an implicit geological modeling method based on adaptive grid and an electronic device. A specific implementation of the method comprises: performing initial grid division on a calculation region according to geological modeling parameters and geological source data to obtain a first grid set; determining a grid to be refined in the first grid set according to a preset judgment rule; dividing the grid to be refined into a set of sub-elements according to a preset refinement rule to obtain a second grid set of the calculation region; storing grid data of the second grid set; performing difference on a second grid in the second grid set and determining a coefficient matrix A according to a difference coefficient; constructing a linear equation set Ax=b based on the Lagrange multiplier method, wherein the vector b is used to represent point constraints and directional constraints; solving the linear equation set to obtain a second grid value, and outputting a modeling result according to the second grid value. Thus, a new implicit geological modeling method based on adaptive grid is provided.

The application discloses a neutron transport constitutive relation and low-dimensional control equation modeling method based on sparse regression, which comprises the following steps: a neutron flow matrix under multiple state parameters is formed by state parameters of each state and physical quantity parameters calculated through a neutron transport program; fitting physical quantity parameters are filled into a sparse regression physical quantity matrix; a coefficient matrix is obtained by using a least square method to calculate an inverse matrix; and a neutron transport constitutive relation under multiple state parameters is obtained by assembling. The application utilizes the accurate characteristics of the calculation result of the neutron transport equation, grasps the cause of the larger deviation of the calculation result of the neutron diffusion equation in a small scale range, combines sparse regression fitting to obtain the neutron transport constitutive relation, and further obtains a low-dimensional macroscopic neutron transport control equation. The theoretical derivation is less difficult, the research progress is easier, the effect of improving the calculation precision is more obvious, the applicability is better, the gap with the situation under the actual reactor core working condition is not large, and the application has certain practicality.

The application discloses a multi-unmanned aerial vehicle control method based on reinforcement learning and belongs to the technical field of unmanned aerial vehicle cooperative control. The application designs a control algorithm for a double-time-scale multi-agent, effectively avoids possible calculation errors in the process of solving a matrix equation by introducing a novel coefficient matrix, and proposes a hybrid iteration algorithm which is independent of initial stable controller gain and has a fast convergence speed and is used for solving an approximate solution of a game algebraic Riccati equation based on a communication topology between agents. The application can realize consistency between unmanned aerial vehicles, enables the unmanned aerial vehicles to work cooperatively, and completes a task.

Embodiments of the invention disclose a constraint equation determination method and apparatus, a medium, a device and a product. The method comprises the steps of obtaining a constraint equation of an augmented matrix group; the constraint equation is represented as follows: the sum of the first product and the second product is zero, a subordinate degree-of-freedom vector in the constraint equation is determined by an independent degree-of-freedom vector, a weight coefficient matrix, a displacement matrix and a distribution matrix, and the distribution matrix is determined by the weight coefficient matrix and the displacement matrix; and determining a target weight coefficient matrix and a target displacement matrix, and substituting the target weight coefficient matrix and the target displacement matrix into the constraint equation to obtain a target constraint equation of the augmented matrix group. According to the method, the weight coefficient matrix capable of accurately reflecting the physical coupling strength between the nodes and the displacement matrix capable of representing the real deformation state can be automatically calculated, the constraint equation is generated, the defect of insufficient calculation precision caused by simple hypothesis of the constraint relation is effectively overcome, and therefore the construction effectiveness of the constraint equation can be improved.

The invention discloses a parallel solving method and system for a system of linear equations of an electric power system based on a Woodbury theory, and belongs to the technical field of large-scale electric power system computation.The method comprises the steps that a coefficient matrix of a network equation of the electric power system is obtained and subjected to block representation; performing truncated singular value decomposition on the non-diagonal block coupling matrix, and realizing low-rank decomposition through an Arnoldi iterative algorithm; carrying out inversion on the coefficient matrix based on a Woodbury matrix identical equation, and carrying out parallel calculation on each block sub-matrix and an intermediate variable; and solving the system of linear equations by using the inversed matrix. According to the method, the low-rank characteristic and parallel computing advantages of the inter-region coupling matrix of the power system are fully utilized, the solving efficiency of the large-scale linear equation set is remarkably improved, and the method is suitable for transient analysis, real-time simulation and other high-performance computing scenes of the power system.

The invention relates to a wide-range concentration detection system and method for a gas analyzer, and the system comprises a light source, a collimator, a measuring cell, a spectrometer, a temperature controller, a signal converter, a data collection module and a data analysis module. The method comprises the following steps: acquiring a reference zero spectrum and concentration sequence spectrums of n gases as a reference original spectrum sequence, carrying out difference, normalization and polynomial fitting treatment on the reference original spectrum sequence to obtain n fitting coefficient matrixes of the n gases, and forming a nonlinear equation set together with a real-time difference spectrum of a gas to be detected, and solving the nonlinear equation set by adopting a least square method to obtain an initial normalized concentration solution of each gas, further optimizing the initial normalized concentration solution, and carrying out reverse normalization to obtain a final concentration value of each gas. The problem of gas concentration detection when the absorption cross section of the gas to be detected and the concentration are in a non-linear relationship is solved, the detection efficiency and the detection precision are high, and the concentration detection range is wide.

The invention belongs to the technical field of line resistance network analysis, and discloses a fast line resistance network analysis method for a nonvolatile memory array, which comprises the following steps of: establishing electrode KCL equations of all rows and columns in a line resistance network of the nonvolatile memory array; a voltage line and a coefficient matrix in the KCL equation are transformed and decomposed, a fixed point iterative algorithm is introduced, and voltage distribution of nodes at the top and the bottom of the array is iteratively calculated. An original complex large-scale linear equation set problem is converted into two small-scale sub-problems. And solving is carried out through mutual iteration of the two sub-problems, so that the calculation complexity and the calculation memory are reduced. According to the method, the influence of IR-drop on neural network calculation acceleration can be predicted and evaluated in the design stage. The method has the advantages that the accuracy is high, and the influence of IR-drop can be simulated with the accuracy exceeding 95%; the calculation complexity is low, and the calculation complexity is reduced from O ((2mn) 2) to O (mn); the memory load is small, and the use of the memory is minimized while high accuracy is kept.

The present invention provides a trajectory polynomial generation device, comprising a trajectory floating-point calculation circuit and a trajectory sequence controller. The trajectory sequence controller is coupled to the trajectory floating-point calculation circuit. The trajectory sequence controller performs a cubic spline interpolation algorithm to convert the coordinates of a plurality of path points into coefficients of a curve. The trajectory sequence controller schedules the trajectory floating-point calculation circuit to calculate the x-axis step length between any two adjacent path points among the plurality of path points, uses the x-axis step length to obtain multiple elements of a coefficient matrix in a linear equation system of the cubic spline interpolation algorithm, uses the x-axis step length and the coordinates of the plurality of path points to obtain multiple elements of a constant vector in the linear equation system, uses the coefficient matrix and the constant vector to obtain a quadratic difference value vector in the linear equation system, and uses the quadratic difference value vector to calculate the coefficients of the curve.

The present invention discloses a method for fast mode decomposition of anti-noise fiber laser, including: obtaining a spot to be decomposed with noise, rearranging the eigenmodes into vectors in sequence, and then multiplying the N eigenmode vectors pairwise to obtain a coefficient matrix A; obtaining a mode information vector X based on the coefficient matrix A; determining the errors of the elements in the mode information vector X based on the L2 norm of the pseudo-inverse matrix A<supgt;‑1< / supgt>, and deleting the elements with larger errors until at least 2N‑1 elements remain in the mode information vector X; establishing a nonlinear equation system based on the remaining elements in the mode information vector X, obtaining the mode coefficients and mode phases of each eigenmode restored, and generating a first reconstructed spot therefrom to obtain the mode decomposition result. The present invention is applied to the field of fiber laser mode decomposition. Based on the matrix analysis method, redundant feature information is screened and removed, so as to improve the measurement accuracy of mode coefficients and mode phases in a noise environment.

The invention discloses an efficient numerical solution method for a steady-state water head field of a dam containing a complex foundation, and relates to the technical field of geotechnical engineering. The method comprises the following steps: establishing a seepage mathematical model in a Cartesian coordinate system by acquiring foundation parameters and boundary conditions, introducing similar lines parallel to a far-field boundary to construct an improved proportional boundary finite element coordinate system mapping relation, and discretizing and deducing a variable coefficient control equation by adopting a one-dimensional high-order spectrum unit; an equation is simplified into a Riccati equation by analyzing the characteristics of a coefficient matrix, an infinite seepage matrix is solved in combination with Schur decomposition, a seepage matrix at a boundary is obtained through iteration of a fourth-order Runge-Kutta method with the infinite seepage matrix as an initial value, and finally steady-state water head field distribution is obtained. According to the method, the continuity of the interface water head and the flowing boundary condition is guaranteed, the precision and efficiency of complex foundation seepage solving are greatly improved, and reliable technical support is provided for engineering seepage-proofing design and stability evaluation.