45 results about "Linear algebraic equation" patented technology

Disclosed is a method for calculating core neutron flux distribution of a small experimental reactor. The method includes steps of 1), determining geometrical and material parameters according to a core structure of the small experimental reactor, and establishing a neutron-transport equation describing movement rules of neutrons in each discrete direction inside a reactor core; 2), preparing corresponding quadrature sets for boundaries unparallel in normal surface vectors and each coordinate axis direction; 3), subjecting the neutron-transport equation to numerical discretion to acquire simultaneous linear algebraic equations of angular neutron flux density by a segment method of approximating unstructured geometry with unstructured grids to establish arbitrary triangular grids; 4), solving the simultaneous linear algebraic equations to acquire the discrete distribution of the angular neutron flux density in the reactor core, and acquiring the discrete distribution of neutron-flux density in the reactor core by the aid of relation of the angular neutron flux density and the neutron-flux density. By the method, the neutron-flux distribution of the small experimental reactor, especially that of an isotope production reactor, a pebble bed reactor and a high-flux reactor in the medical field can be accurately acquired.

The invention discloses a linear pseudo-spectrum GNEM guidance and control method. According to the linear pseudo-spectrum GNEM guidance and control method, an original nonlinear optimal control problem is converted into a group of problems for solving a system of linear algebraic equations based on the concept of GNEM through linearization and Gauss pseudo-spectrum dispersion by combining nonlinear approximation model predictive control, linear quadratic optimal control and a Gauss pseudo-spectrum method. The linear pseudo-spectrum GNEM guidance and control method has the advantages that the calculation efficiency of solving the optimal control problem is quite high, and high calculation precision can be obtained just through several nodes; in addition, a final solution can be presented through a smooth function relevant to control over disperse nodes, and the method is quite suitable for online calculation. It is indicated through a simulation result that by applying the method to tail-section attack guidance with terminal angle constraint, compared with an MPSP method, the linear pseudo-spectrum GNEM guidance and control method has higher calculation efficiency and high calculation precision and can be completely applicable to a guidance framework for terminal guidance, and a smaller required overload command is generated compared with self-adaptive tail-section proportion guidance.

The invention belongs to the field of oil-gas field development and provides a numerical simulation method for a large-scale fractured reservoir. The method includes: taking large-scale fractures in the reservoir as an inner boundary of the reservoir to perform reduction of dimensionality, setting up a geometric model of the reservoir, adopting triangular meshes for geometric subdivision of the geometric model of the reservoir to form discrete units, geometric information description files, geometric discrete information files and well information description files of the reservoir, setting up numerical computation units based on the discrete units, setting up a mathematical model representing fluid flow of such reservoirs, adopting an integral method for setting up a numerical computation format on each numerical computation unit to form a large-scale system of linear algebraic equations, and solving, so that numerical simulation of the large-scale fractured reservoir is realized. By adoption of the numerical simulation method for the large-scale fractured reservoir, the large-scale fractured reservoir can be represented accurately, and the method is definite in physical meaning and well adaptable to numerical simulation of the large-scale fractured reservoir.

The invention relates to a calculation method of proportion of each lode component in power grid comprehensive load model and belongs to the technical field of power grid stability control in power system. Bus voltage, initial phase of the bus voltage, active power, and reactive power of power grid load node are firstly measured when the power grid is in stable operation. The above parameters are remeasured when the power grid is in disturbance. When disturbance measurement data is accumulated to four times, eight unknowns linear algebraic equations of lode model parameters are listed according to the four measurements and motor power ratio is obtained through solving the equations and calculating. The calculation method of proportion of each lode component in power grid comprehensive load model has the advantages of being clear in physical meaning, easy to realize, accurate in results, and capable of being applied in power system lode modeling and parameter identification software system to realize rapid identification of lode dominant parameters. Analysis of security and stability and control of subsequent power system is provided with a base.

The invention discloses an implicit staggered-grid finite difference elastic wave numerical simulation method and device. The method comprises the steps that a dispersion relation expression is obtained based on an implicit staggered-grid finite difference scheme and a plane wave theoretical formula; (M+1) discrete points are evenly taken within the value range of beta in the dispersion relation expression, and the left and right sides of the dispersion relation expression are set to be equal on the discrete points so that a linear algebraic equation set is obtained; the linear algebraic equation set is solved so that the implicit staggered-grid finite difference coefficient am and constant b are obtained; an elastic wave equation is solved based on the implicit staggered-grid finite difference coefficient am, the constant b and the implicit staggered-grid finite difference format; and a wave field diagram is generated according to the solving result and wave field analysis is performed according to the wave field diagram. The solving error of the elastic wave equation can be reduced and the numerical solution accuracy can be enhanced so that a more accurate wave field stimulation record can be obtained. When the same calculation error is constrained, calculation time can be reduced and calculation efficiency can be enhanced.

A computer implemented method (200) is described for determining the equivalence of two sets of simultaneous linear algebraic equations. Each of said equations is of a form:

e_i1x₁+e_i2x₂+e_i3x₃+ . . . +e_iix_n=b_i

wherein x_j are unknowns, e_ij are coefficients and b_i are quantities, and defining the relationship between the unknowns within the set. The coefficients and quantities are known algebraic expressions. The unknowns are iteratively eliminated (250 to 280) from each of the sets of simultaneous linear algebraic equations until each of said equations are in the form:

(l_ii)_kx_i=(r_i)_k

wherein l_ii and r_i are algebraic expressions, and k={1;2} indicate one of said sets that said equation is derived from. The products (l_ii)₁*(r_i)₂ and (l_ii)₂*(r_i)₁ are compared (300) for each of the unknowns. Only if the products match (310) for all the unknowns are the two sets of simultaneous linear algebraic equations equivalent (312). An apparatus (100) for performing the above method (200) is also provided.

The invention relates to a short-circuit current attenuation calculating method with consideration of a dynamic load for a power system. Dynamic and static loads are distributed appropriately according to reactive power requirements of the dynamic load, the electric potential attenuation of a generator and an electromotor is calculated through non-mutation principle of a flux linkage (electric potential) of the generator and the electromotor, the instant flux linkage (electric potential) before the short circuit of the generator and the electromotor serves as an initial value of the flux linkage attenuation calculation, and the short-circuit current attenuation with consideration of dynamic feature of the load is solved according to the attenuation of the flux linkage (electric potential) through writing circuit equation ( linear algebraic equations). The method can be used in research on short-circuit current attenuation features with consideration of the dynamic load, and the calculating result with consideration of the dynamic load is more accorded with the actual short-circuit current condition than the calculating result without consideration of the dynamic load.

A method for reducing metal artifacts in computed tomography (CT) is disclosed. The method for reducing metal artifacts in CT includes: obtaining a sinogram reduced in size from an original sinogram; setting up a linear algebraic equation according to remaining data excluding data damaged by a metal based on the obtained sinogram; restoring a low-resolution image based on the set up linear algebraic equation; calculating a sinogram from the restored low-resolution image; restoring a sinogram by disposing the calculated sinogram data in the original sinogram and by utilizing the calculated sinogram data as pre-information; and restoring a final CT image from the restored sinogram. Through introduction of a novel metal artifact reduction (MAR) technique referred to as an algebraic correction technique (ACT) using an intermediate image of an attenuation coefficient of an outside of a metal area, an image closest to an original image can be obtained by minimizing metal artifacts in CT.

A first representation of an electrical network includes a first set of simultaneous linear algebraic equations (SLAE's). A second representation of an electrical network includes a second set of SLAE's. The equations of the SLAE's include a number of unknowns and have coefficients for the respective unknowns. A number of the coefficients are expressed in algebraic form. The coefficients of one such equation from one of the sets of SLAE's are for respective elements of the set's respective electrical network and the unknowns are for respective operating properties of the set's respective electrical network. Results are derived in pairs for each unknown of each respective one of the SLAE's. The pairs of results are compared in a specified manner to determine a network equivalence. The results are derived from the SLAE's and expressed in algebraic form, so that the comparing of the pairs of results includes comparing algebraic expressions.

The invention provides a method for accurately calculating the electric field intensity on the conductor surface based on a simulated charge method, which comprises the following steps of setting simulated charge inside each sub-conductor of a split conductor; at the given boundary of each sub-conductor of each pole, setting the matching points with the same number as the simulated charges, and obtaining the simulated charges in each sub-conductor by the linear algebraic equations established by the position and potential information of the matching points and the simulated charges; then by setting the same number of check points as the matching points, checking the potential of each check point by the simulated charge inside each sub-conductor, and obtaining the simulated charge quantitysatisfying the precision requirement; and finally calculating the electric field strength of each sub-conductor surface by using the formula. The method of the invention fully considers the influenceof the line splitting conductor, effectively overcomes the problem that the electric field on the surface of the conductor cannot be accurately calculated due to the equivalence of the splitting conductor, and greatly improves the accuracy of the calculation of the electric field strength on the surface of the conductor.

An educational kit for teaching mathematics includes easily manipulated elements, which serve as cognitive reinforcement during the learning process. These physical elements are used in conjunction with a set of grouping rules. The educational kit and corresponding grouping rules determine a model and process to represent both an algebraic linear equation and its algebraic solution. A simple element, such as an item/figure including a variable “X”, is used to denote the unknown quantity. An item/figure including a number is used to represent a numerical value. These items/figures contain the exact elements used to form the expressions of the linear equation and are not items/figures that simulate the elements that form the expressions of the equation. By the use of this educational kit and associated grouping, students learn to simplify a given linear algebraic equation to the point where the solution is obvious.

The invention discloses a method for calculating zero sequence mutual inductive impedance in multiple transmission lines on a common tower. The method comprises steps of acquiring basic data related to each loop, a base tower, a power transmission conductor, and a ground wire; equating the soil along the line to the soil resistivity [Rho]t in the same tower section and the soil resistivity [Rho]f in the different tower section; equating the soil of the entire line with a uniform soil resistivity having the same soil resistivity and constructing initial values of [Rho]t and [Rho]f with the uniform soil resistivity; writing a linear algebraic equation group of [Rho]t and [Rho]f for each loop and using an iterative method and the initial values of the iteration to solve [Rho]t and [Rho]f; and according to the basic data, [Rho]t and [Rho]f, obtaining the zero sequence mutual inductive impedance of each type of tower in each loop line and the entire line. The zero sequence mutual inductive impedance and the soil resistivity calculated by the method of the invention can be applied to the research of protection setting calculation, short-circuit calculation, power flow calculation and computer simulation and can greatly improve the accuracy of the analysis and calculation and reduce the error caused by the empirical estimation.

The invention discloses a method for measuring stress intensity factors of a multi-round-hole multi-crack anisotropic material. The method comprises the following steps of: constructing a plane unit model containing a plurality of round holes and a plurality of cracks by taking a to-be-measured material as a prototype, and defining boundary conditions; constructing a plane unit model containing a single round hole, and solving a stress basic solution of a concentrated force on the surface of the hole of the model according to a complex variable function Cauchy integral theory; constructing a plane unit model containing a single crack, and solving a stress basic solution of a concentrated force on the surface of the crack of the model according to a complex variable function Cauchy integral theory; according to the obtained stress basic solution and stress boundary conditions, obtaining an integral equation about the interaction surface stress of each round hole and each crack; discretizing the obtained integral equation into a linear algebraic equation; and deriving a stress intensity factor calculation formula of the plane unit model containing the single crack, and calculating a stress intensity factor of the plane unit model under the interaction of multiple round holes and multiple cracks by combining the solved crack surface interaction surface stress.

The invention discloses a finite element calculation method for a nonlinear gas-solid coupling heat exchange problem, and relates to the technical field of heat transfer science, finite element methods and aero-engine design. The method comprises the following steps of reading an axisymmetric part three-dimensional geometric model file established by a CAD system, and carrying out detail feature processing; selecting and intercepting an axisymmetric meridian plane to obtain a two-dimensional geometric model; dividing the meridian plane into the triangular unit grids; establishing a finite element model of the internal triangular unit and the boundary unit; superposing and synthesizing an integral finite element model of the axisymmetric region to obtain a linear algebraic equation set about all node temperatures; and solving the linear algebraic equation set, obtaining a numerical value of the node temperature, and carrying out computer graphic visualization display. According to the method, the defects of a classic heat transfer analysis method are overcome, the coupling effect of the gas-solid heat exchange is fully considered, compared with a linear gas-solid heat coupling algorithm, the temperature field distribution of an aero-engine part structure can be more accurately calculated, and the design level is improved.

The invention provides a power system transient stability digital simulation computation model and an algorithm thereof, and belongs to the field of power system digital simulation. In the traditional machine-network interface algorithm, the conversion computation of a dq axis of each generator is solved in grid node voltage algebraic equations, so that the power system simulation model becomes time variant nonlinear algebraic equations. In the invention, the conversion computation of the dq axis of each generator is solved in a simulation model of each generator set, so that the power system simulation model becomes time invariant linear algebraic equations, and a calculated amount of the power system simulation model during alternate solving is largely reduced. The power system transient stability digital simulation computation employing alternate solving is simplified, a physical significance of the model is clearer, and the programming difficulty is remarkably reduced; and the computation of the simulation model of each generator set during alternate solving is decoupling, so the practical power system transient stability digital simulation parallel computation model can be formed.

Provided is a universal right-angle geometric scalar field reconstruction method. The method comprises the steps that 1, an orthogonal basis function is determined according to the primary function type and order needed by a user; 2, a to-be-solved continuous cylindrical geometric scalar field is approximatively expanded according to the orthogonal basis function obtained in the step 1; 3, an underdetermined linear algebraic equation system about an underdetermined coefficient is set up through all known information; 4, on the basis of variable substitution, a least square method is used for solving the underdetermined linear algebraic equation system, the least square solution of the underdetermined linear algebraic equation system is obtained to serve as a scalar field expansion coefficient, the scalar field expansion coefficient is substituted into a scalar field expansion equation, and a continuous scalar field can be obtained; 5, according to the obtained continuous scalar field, designated discrete information of the scalar field is obtained through further discretizing; the undetermined scalar field is expanded through the orthogonal basis function, an expansion function is constructed through variants and orders, the least square method is used for solving, the influence of selection of an expansion basis function on reconstruction precision is effectively reduced, the requirement for the reconstruction condition number is reduced, meanwhile multiple kinds of discrete information can be processed, and the adaptability of the method to different problems is effectively improved.

The invention discloses a method for calculating electromagnetic interference of a power grid to a buried pipe network, which comprises the following steps of: dividing a conductor into conductor micro-sections, enabling a potential difference between two ends of the outer surface of each conductor micro-section to be equal to a potential difference between two ends in each conductor micro-section, and establishing an equation set according to the characteristics of continuity, calculating the potential difference between two ends of the outer surface of the conductor micro-segment according to the leakage current, and calculating the potential difference between two ends in the conductor micro-segment according to the product of the impedance of the conductor micro-segment and the axial current; and according to the Kirchhoff's law, obtaining a relational expression between axial current and leakage current on each conductor micro-segment, comprehensively establishing a group of linear algebraic equations, and solving the linear algebraic equations to obtain leakage current distribution on the conductor. The result is used for evaluating the influence of electromagnetic interference on the buried pipe network, so that the risk is controlled in advance, and harmonious co-existence of the power grid and the oil-gas pipe network is realized.

The invention discloses a multilayer tablet drug controlled release system optimization method and system. The method comprises the following steps: acquiring a multilayer tablet drug controlled release system; establishing a mathematical model according to the multilayer tablet drug controlled release system; transforming an optimization problem of a drug release behavior into inverse problem solving on the basis of a mathematical physics inverse problem framework according to the mathematical model so as to obtain a first type of Fredholm integral equations; performing discrete processing onthe integral equations so as to obtain a system of linear algebraic equations; solving by a regularization method to obtain a solution according to the system of linear algebraic equations; determining the multilayer tablet drug controlled release system optimization scheme according to the solution. According to the method or system disclosed by the invention, parameters can be accurately predicted.

An educational kit for teaching mathematics includes easily manipulated elements, which serve as cognitive reinforcement during the learning process. These physical elements are used in conjunction with a set of grouping rules. The educational kit and corresponding grouping rules determine a model and process to represent both an algebraic linear equation and its algebraic solution. A simple element, such as an item/figure including a variable “X”, is used to denote the unknown quantity. An item/figure including a number is used to represent a numerical value. These items/figures contain the exact elements used to form the expressions of the linear equation and are not items/figures that simulate the elements that form the expressions of the equation. By the use of this educational kit and associated grouping, students learn to simplify a given linear algebraic equation to the point where the solution is obvious.

The invention provides a load flow calculation method based on an active power distribution network. The method comprises the steps of: obtaining topological information including nodes, loops and branches based on a network topological structure of the active power distribution network, and collecting power data corresponding to the topological information; establishing a loop-branch matrix based on a feature vector group; and calculating voltage distribution according to the established loop-branch matrix and an obtained power value, and according to obtained power distribution and the voltage distribution, calculating a load flow calculation result. According to the method, an existing nonlinear load flow calculation equation is simplified into a linear algebraic equation, the load flow calculation difficulty is reduced, the iteration process is reduced, the operation time is shortened, and a calculation result can be quickly obtained when the load flow of a power distribution network which contains a plurality of distributed power supplies and is large in scale is calculated.

The invention discloses a directivity identification method for noise sources of an engine and parts thereof, and belongs to the technical field of noise source separation of aero-engines and parts thereof. The sound source noise is experimented through a microphone array, and if the spectral characteristics of the noise of each part of the sound source are obtained, the sound power spectrum matrix about the intensity, namely directivity, of each sound source can be constructed only by using a sufficient number of microphones; by applying an SODIX-Bes inversion algorithm, the sound source intensity and directivity can be obtained by solving from a benign linear algebraic equation set. The sound source directivity simulation technology (SODIX) based on a cross-spectrum matrix developed by the DLR of German is improved. According to the invention, the noise directivity and sound intensity of the engine and each part thereof can be separated from the experimental data of the whole engine noise or the part noise thereof.

The invention discloses a state space model extraction method based on a linear circuit network. The method comprises the steps: 1, converting a time-domain circuit network into an S-domain operational circuit network according to a circuit complex frequency domain analysis principle; 2, processing the S-domain operational circuit network by using an improved node method to generate a linear algebraic equation set; 3, solving the linear algebraic equation set by using a symbolic operation tool to obtain a Laplace transformation expression of each circuit variable; 4, selecting a circuit variable as excitation and response, and solving a transfer function of the circuit network; 5, comparing the transfer function molecule with the denominator polynomial coefficient vector dimension; if so,ending all the steps, otherwise, executing the step 6; and 6, converting the transfer function into a true situation, and constructing a state space model by using molecules and denominator polynomialcoefficients of the true situation. The method does not involve a network graph theory, and has the advantages of convenience, quickness, high applicability and the like.