13 results about "Series expansion" patented technology

The invention relates to an orbit identification method based on earth-moon collinear translation point orbit parameter characterization. The method comprises the following steps: describing a circular restrictive three-body problem as a chaotic Hamiltonian power system, converting a motion equation into a new coordinate system for series expansion, and taking a quadratic term of a Hamiltonian function in a polynomial form as a linear model of a translation point in the circular restrictive three-body problem; and carrying out complex transformation and regular transformation on the linearized model transformation to realize the decoupling of the hyperbolic unstable direction and the central direction of the central manifold, and constructing a mapping relation between CRTBP coordinates and characterization parameters to carry out parameter characterization. Selecting spacecraft coordinates from parameter characterization to calculate characterization parameters of a reference orbit and integral initial values of the coordinates, and then calculating mean square errors of a real orbit and the reference orbit; and by taking the mean square error as a target function and a preset constraint condition, constructing an orbit identification solving model and solving to obtain an orbit identification result. By adopting the method, the track identification accuracy can be improved.

The application provides a training method and device of a current density distribution identification model, the method comprising: inputting a plurality of sampling source points into the current density distribution identification model, and obtaining a loss function in the current density distribution identification model, which is constructed based on a current density distribution function and an electric field integral equation; wherein the loss function comprises a hyperbolic tangent function, a derivative of the hyperbolic tangent function and a product of the Green function; performing series expansion on the hyperbolic tangent function in the loss function, and extracting singular terms from the electric field integral equation in the series expanded loss function to obtain a plurality of singular integrals; performing inner integral calculation and outer integral calculation on each high-order singular integral in the singular integrals to determine the current density distribution function corresponding to the minimum value of the loss function on all sampling source points. The application can quickly solve the singular integrals comprising the hyperbolic tangent function, the derivative of the hyperbolic tangent function and the product of the Green function to obtain the current density distribution function.

The invention discloses a safe three-party computing method and system supporting a complex nonlinear function, and relates to the field of safe multi-party computing. According to the method, part of data is calculated in advance in the offline stage, so that the online operation speed in multi-party copy secret sharing is increased, the online communication traffic is reduced, and the query response time of a user is optimized. Moreover, the sigmoid function is approximately expressed by adopting a Fourier series expansion technology, so that a gradient explosion phenomenon caused in an approximate interval boundary region is avoided, and better communication efficiency is realized at the same time. Secondly, based on linear conversion characteristics of sigmoid and a tanh function, obtaining a safe three-party calculation method capable of being reused to the tanh function; finally, an ordinary differential equation is constructed to replace a conventional approximation algorithm, a softmax safe three-party calculation method is provided, and higher accuracy and lower communication complexity are achieved.

The invention relates to a characterization parameter analysis method for an earth-moon collinear translation point orbit. The method comprises the following steps: describing a circular restrictive three-body problem as a chaotic Hamiltonian power system, converting a motion equation into a new coordinate system for series expansion, and taking a quadratic term of a Hamiltonian function in a polynomial form as a linear model of a translation point in the circular restrictive three-body problem; carrying out complex transformation and regular transformation on the linearized model transformation to realize decoupling of a hyperbolic unstable direction and a central direction of the central manifold, and constructing a mapping relation between CRTBP coordinates and characterization parameters to carry out parameter characterization; analyzing the two motion characteristics in the hyperbolic unstable direction and the central direction and the corresponding characterization parameters, determining the orbit of the target spacecraft through the phase difference of the angular variables in the characterization parameters, and obtaining the orbit transfer information of the target spacecraft through the change condition of the hyperbolic motion components in the characterization parameters. By adopting the method, characterization parameter analysis can be realized.

The invention provides a concrete chloride ion diffusion coefficient analysis method and system in a natural exposure environment, and relates to the technical field of material durability evaluation and testing. The method comprises the following steps: acquiring chloride ion content data and initial chloride ion content at different depths; constructing a nonlinear mathematical model containing an error function based on a chloride ion diffusion theory; carrying out linear approximation on the model by utilizing a series expansion of an error function, and generating a linear expression taking the to-be-optimized parameter as a coefficient; calculating residual sum of squares under different parameter values by changing to-be-optimized parameter values and solving corresponding linear equations, and determining an optimal parameter value by using a minimum residual sum of squares; and carrying out back calculation to obtain the chloride ion diffusion coefficient and the surface chloride ion content. According to the method, a traditional nonlinear fitting problem is converted into single-parameter global optimization under a linear framework, the calculation complexity is reduced while the precision is ensured, and engineering practical application is facilitated.

This invention belongs to the field of shield tunneling technology, specifically a method and system for calculating the three-dimensional steady-state seepage field at the excavation face of a shield tunnel under isolated rock conditions. It includes: S1 establishing a three-dimensional geometric model of the seepage field around the tunnel excavation face as a cuboid, with the vertical direction as the z-axis, the direction perpendicular to the tunnel excavation as the x-axis, and the direction along the tunnel excavation as the y-axis; S2, combining the boundary conditions of each region of the seepage field, establishing two-dimensional hydraulic head expressions for the six face regions of the three-dimensional geometric model based on the cuboid three-dimensional geometric model; S3 using the continuity conditions between regions to construct linear partial differential equations and Fourier series expansion equations, solving for the three-dimensional hydraulic head expressions for the six regions; and S4 obtaining the analytical solution for the hydraulic head at any position in the three-dimensional seepage field in front of the excavation face based on the superposition of Fourier series. This invention can accurately calculate the water pressure borne by the excavation face, which also has significant engineering significance for ensuring the safe construction of shield tunnels.

According to the hot-rolled coil post-cooling temperature distribution calculation method, a heat conduction differential equation is obtained through the Fourier law, the heat conduction differential equation is solved through a variable separation method and an intrinsic function method, a temperature field analytic expression of series expansion is obtained, then boundary conditions are substituted, and under the condition that temperature distribution at any initial moment is drawn up, the temperature distribution of the hot-rolled coil is calculated. And solving an undetermined coefficient in the temperature field expression according to the initial condition and the boundary condition to obtain a complete solution. Compared with traditional finite element modeling, the method based on a mathematical physical method has remarkable advantages. According to the method, the temperature distribution result in the post-cooling process of the hot-rolled coil can be obtained at a higher speed, the result precision is relatively accurate, and an efficient and reliable technical means is provided for temperature control and process optimization in the post-cooling process of the hot-rolled coil.

The invention discloses an approximate critical eccentricity rate Kepler equation solving method, and belongs to the technical field of aerospace dynamics. Aiming at an elliptical or hyperbolic orbit of which the eccentricity is close to 1, the method adopts a mixed strategy of combining series expansion and Newton iteration, and comprises the following steps: acquiring orbit eccentricity and mean anomaly parameters; constructing an iteration initial value by using Lagrange series expansion; setting a tolerance error condition and the maximum number of iterations; and carrying out iterative solution by adopting a Newton iteration method. According to the method, when the eccentricity is close to the critical value 1, rapid convergence and high-precision calculation can still be achieved, the problems that a traditional method is slow in convergence and prone to divergence in a critical region are effectively solved, and reliable orbit position calculation support is provided for tasks such as earth spacecraft orbit design and deep space exploration.

The embodiment of the invention discloses a Helmholtz equation quantum solving method and an electromagnetic wave characteristic determination method and device, and the method comprises the steps: carrying out the series expansion of a solution and a source item of a Helmholtz equation according to a selected primary function, and discretizing a computational domain of the Helmholtz equation into grid points; substituting the solution and the series form of the source item into a margin function corresponding to the Helmholtz equation, and applying a weighted margin method at each network point to obtain a large linear equation set of which the dimension is consistent with the number of grid points; solving a linear equation set through a quantum linear solver to obtain a solution coefficient of the primary function, wherein the linear equation set is obtained by applying a weighted margin method to all grid points; and substituting the solution coefficient of the primary function into the series form of the solution to obtain the solution. By adopting the embodiment of the invention, the hardware resources of the computer can be saved, and the solving speed of the Helmholtz equation can be improved.

The invention relates to a same-tower double-circuit alternating-current transmission line zero-sequence parameter estimation method based on internal faults. The method comprises the following steps: establishing different mathematical models according to line length differences, adopting a single-section pi lumped parameter model for medium-short distance transmission lines to approximate a distributed parameter model, and adopting a distributed parameter model for medium-long distance transmission lines, therefore, the electromagnetic characteristics during the single-phase earth fault can be accurately represented. Based on voltage and current measurement data at two ends of the line, establishing a parameter equation set in a fault state by combining a Kirchhoff's law, and performing linear approximate processing on a nonlinear equation by using Taylor series expansion; through algebraic operation and matrix solution, an explicit analytical expression of a zero-sequence parameter is deduced, and precise calculation without iteration is realized. According to the method, zero-sequence parameters such as zero-sequence self-impedance and mutual impedance are estimated based on the single-phase earth fault of the same-tower double-circuit line, and the method is suitable for online identification of the zero-sequence parameters of transmission lines with different lengths and has the characteristics of high calculation efficiency, clear physical significance and high engineering applicability.

The invention relates to an earth-moon collinear translation point orbit parameter characterization method. The method comprises the following steps: describing a circular restrictive three-body problem as a chaotic Hamiltonian power system, and converting a motion equation into a new coordinate system to obtain a Hamiltonian function of a corresponding system after coordinate system transformation; performing series expansion on nonlinear terms in the Hamiltonian function by utilizing a Legendre expansion method, and taking quadratic terms of the Hamiltonian function in a polynomial form as a linear model of a translation point in the circular restrictive three-body problem; transforming the linearization model into a real standard shape according to a real linear symplectic transformation matrix, and performing complex transformation on the central part of the real standard shape to obtain a linear complex standard shape; and carrying out regular transformation on a nonlinear term of the linear complex standard shape, and defining a local action-angle variable according to a motion mode of a translation point by referring to a linear integrable part of a final Hamiltonian function to describe the motion of the spacecraft on the central manifold so as to realize parameter representation. By adopting the method, track parameter characterization can be realized.

The invention provides a training method and device for a current density distribution identification model, and the method comprises the steps: inputting a plurality of sampling source points into the current density distribution identification model, and obtaining a loss function which is constructed based on a current density distribution function and an electric field integral equation in the current density distribution identification model; wherein the loss function comprises a hyperbolic tangent function and a product of a derivative of the hyperbolic tangent function and a Green function; performing series expansion on a hyperbolic tangent function in the loss function, and extracting singular terms from an electric field integral equation in the loss function after series expansion to obtain a plurality of singular integrals; and performing inner-layer integral calculation and outer-layer integral calculation on each high-order singular integral in the singular integral to determine a corresponding current density distribution function when the loss function takes a minimum value on all sampling source points. According to the method, the current density distribution function can be obtained by quickly solving the singular integral which contains the hyperbolic tangent function and is formed by the product of the derivative of the hyperbolic tangent function and the Green function.

The invention discloses an aircraft trajectory analysis planning method meeting multiple physical constraints, which comprises the following steps: in a three-dimensional space, according to a position relationship between an aircraft and a fixed target, constructing a kinematics equation for describing a motion state of the aircraft relative to the target; the relative kinematics equation is converted into a differential equation with the relative distance as an independent variable through equation transformation; respectively constructing polynomial functions of a front angle component relative to a relative distance in a pitch plane and a yaw plane, obtaining a front angle profile with only one to-be-set parameter based on a boundary condition, and exporting a control law that a terminal instruction is not divergent; and based on the proximity angle constraint and in combination with a kinematics equation, performing approximate solution and real-time updating on unknown parameters through a series expansion method, and finally obtaining a control law with an analysis form. According to the method, dependence on model linearization, constant speed hypothesis and a parameter numerical optimization method is avoided, and the trajectory planning requirement with the approach angle constraint is met.