46 results about "Solution of equations" patented technology

The invention belongs to the field of machine vision, and discloses a fast optical flow field calculation method based on an error-distributed multilayer grid. The method comprises the following steps: step one, inputting an image, and constructing a linear equation, that is Ax is equal to f; step two, establishing a multilayer image pyramid; step three, performing prior optimization, and eliminating high-frequency components; step four, performing residual error transmission, and eliminating low-frequency components; step five, repeating steps three and four until residual errors are transmitted to the thickest layer; step six, solving equation sets on thick girds; step seven, performing error passing back from the thickest layer; step eight, performing error correction on thin grids; step nine, performing subsequent optimization iteration, and improving stability of solutions; and step ten, repeating steps seven, eight and nine until the residual errors are transmitted to the thinnest layer. The method provided by the invention is an effective method for accelerating optimization solution of equations, can quick converge high-frequency errors, and can remarkably improve computing speed of a visual optical flow field; and compared with a variational method, the convergence rate of the method can be improved above 3.5 times.

The invention relates to a time-varying feedback finite-time stabilization method of a control limited spacecraft rendezvous control system. The stabilization method comprises the steps of: (1), establishing an orbital dynamics model of the control limited spacecraft rendezvous control system, and obtaining a state-space equation; (2), establishing a parametric Lyapunov equation, analyzing the property thereof, according to the positive definite solution P(gamma) of the parametric Lyapunov equation, designing an explicit linear time-varying feedback control law in a control limited condition,namely, designing a state feedback controller of the control limited spacecraft rendezvous control system; and (3), designing controller parameters by constructing an explicit Lyapunov function and utilizing the property of the parametric Lyapunov equation solution, and ensuring that a tracking spacecraft and a target spacecraft complete a rendezvous task in limited time. By means of the time-varying feedback finite-time stabilization method of the control limited spacecraft rendezvous control system in the invention, limited time stabilization of the spacecraft rendezvous control system in the control limited condition can be realized.

This invention relates to a interim/high frequency viscoelastic material acoustic parameter measurement method, and the major content of the method is using Legendre function to expand the scattering field acoustic dies function of the viscoelastic ball, and compare the Legendre expansion coefficients of the experiment and the Legendre coefficient expression derived from the theoretical formulas, establishing the simultaneous equations, and using optimization algorithms for solving the solution of equations, which is the acoustic parameters of measured material. The method avoids the sound pressure phase measurement, and only need to know the scattering field sound pressure amplitude. The method can simultaneously get material latitudinal/longitudinal wave parameters, no need separately measuring each parameter. It gives more accurately error correction model, to improve the accuracy of parameters measurement, particularly applicable to interim/high frequency viscoelastic material acoustic parameter measurement that difficult to achieve in conventional methods, and with a broad frequencies range.

The invention relates to a calculation method of the first-order natural circular frequency of bending vibration of a stepped beam, which belongs to the calculation method of mechanical vibration. (1) Based on the bending free vibration theory of equal straight bars, the bending free vibration equations of each section of the stepped beam are listed; (2) The modal solution of the stepped beam is assumed by the method of separation of variables; (3) The boundary conditions and analysis of the whole beam are listed. (4) Substituting the hypothetical modal solution into the bending free vibration equation of each segment of the stepped beam to obtain the mode shape function of each segment; The state solution is brought into the boundary conditions and continuity conditions, and the corresponding boundary condition equations and continuity equations are obtained; (6) Solving the boundary condition equations and continuity equations, and solving the equations simultaneously, the elimination of elements only contains two undetermined coefficients and (7) Find the frequency equation of the stepped beam according to the condition that the equation system has a non-zero solution; (8) Use Matcad software to solve the frequency equation to obtain the first-order natural circular frequency value.

The present invention relates to a solution-finding method, which finds an approximate solution of an equation having difficulty in obtaining an actual solution and a complicated equation in numerical analysis. The method obtains an approximate solution of an equation having a solution in a predetermined interval. Initial values are calculated based on upper and lower limits of the interval. The initial values are applied to a solution-finding equation, including a sign function and the upper and lower limits, and the solution-finding equation is arranged so that a definite integral formula for the sign function is included in the equation. The definite integral formula in the solution-finding equation is calculated using numerical integration, and results of the definite integral formula are applied to the solution-finding equation, thus obtaining an approximate solution. This performance is iterated until the approximate solution satisfies an allowable error.

The invention discloses a calibration device and a method for carrying out calibration on a transfer function in a monitoring device. The method comprises the steps: setting m parameters of the transfer function as parameter values of first iteration; carrying out at least one iterative process; in a jth iterative process, if a calculated error evaluation value s is smaller than an evaluation target value according to AD1-ADn, Rxp1-Rxpn, and a parameter value of jth iteration, confirming the parameter value of the jth iteration as a calibration result; if not, adjusting the parameter value of the jth iteration according to a shrinkage algorithm, obtaining a parameter value of j+1th iteration, and continuing the next iterative process, wherein the Rxp1-Rxpn are n index values of a monitored object, and the AD1-ADn are n sampling values. Due to the fact that the shrinkage algorithm is adopted to carry out iterative calculation on the parameters of the transfer function, the process of missing solution of equations is avoided, the method can be applied to situations of a non-linear transfer function and a non-least-square error evaluation function, and accordingly the calibration method has wide application situations.

The invention discloses a multi-working-condition one-dimensional wave equation solving method based on a neural network, belongs to the field of seismic engineering, and aims to solve the problem that time and labor are consumed when the neural network is used for solving one-dimensional wave equations under different working conditions. The one-dimensional wave equation solving method comprises the following steps: 1, selecting a one-dimensional wave equation as an equation to be solved; 2, determining a solution domain and the number of residues of an input variable; 3, establishing a full connection layer neural network comprising six hidden layers; 4, designing a specific loss function; and 5, performing pre-training and fine training of the neural network. The invention provides the one-dimensional wave equation solving method based on the neural network by taking the wave velocity as input, so that the model can learn the influence of different working conditions on an equation solution, and the interpretability of the solving method is also improved by adding a generic equation and a stress condition on the premise of keeping high solving precision.

A time-varying feedback finite time control method for controlling a limited satellite formation flight system comprises the steps: step 1, establishing an orbital dynamics model for controlling the limited satellite formation flight system and obtaining a state-space equation, establishing a to-be-tracked signal model and obtaining the state-space equation; step 2, establishing a parameter Lyapunov equation and analyzing the property of the parameter Lyapunov equation, designing an explicit linear time-varying feedback control law through a positive definite solution of the parameter Lyapunovequation, establishing an output adjustment equation, and designing an explicit linear time-varying feedforward control law through a solution of the output adjustment equation; and designing a time-varying state controller for controlling the limited satellite formation flight system through a linear time-varying feedback control law and a linear time-varying feedforward control law; and step 3,constructing an explicit Lyapunov function, and designing controller parameters by utilizing the properties of a parameter Lyapunov equation and an adjustment equation solution to ensure that the accompanying satellite completes a tracking task within finite time. The invention aims to realize finite time control of the satellite formation flight system under the condition of limited control.

The invention discloses a finite-volume-method-based simulation method of cavitation flow in a water pipe. The method includes: building a transient flow basic control equation containing free gas; building a grid system containing free gas according to a finite volume method (FVM), and performing control equation discrete; using a Godunov format with space-time second order accuracy to calculate the flux of a control unit interface during pure convection; introducing a source item into the solution to obtain the second order explicit FVM-Godunov format of the discrete equation solution; using two methods to correct pressure according to pressure obtained by calculation, and calculating cavitation volume. The finite-volume-method-based simulation method has the advantages that false numerical oscillation is inhibited by introducing a slope limiter; the influence of the free gas and cavitation on the pressure is considered successfully by introducing the pressure correction coefficient C-ap, unreal pulses near the pressure peak of the cavitation flow are eliminated, and the cavitation in a water pipe system is simulated accurately.

A system and a method for finding integer solutions of equations whose graphs are conic sections. The system provides a physical implementation of a geometric formulation of integer solutions of conic sections. The system includes a first source of waves and an arrangement of a plurality of reflectors to provide a lattice of interference patterns of standing waves in a plane, the lattice representing intersections at integer values. The system also includes a second source of waves and a detector provided along a curve that, with the second source, defines a cone of waves, which intersects with the plane of the lattice to provide a conic section. The detector finds points of intersection of the lattice and the conic section to determine integer solutions of the conic section. The conic section may be y=N/x, in which case the integer solutions provide a factorization into integers of N.

The invention discloses a trajectory prediction method for a wind tunnel multi-body separation test model. According to the prediction method, a Kriging mathematical model of six-component aerodynamic coefficients under different relative positions and postures of a multi-body separation test model is established by using multi-body separation wind tunnel grid force measurement test data, and a motion track is calculated by using a rigid body six-degree-of-freedom motion equation. The separation track is divided into a plurality of moments according to time, the aerodynamic force at the initial moment is predicted according to the mathematical model, the model posture at the next moment is calculated according to the model posture at the initial moment in combination with the motion equation, and the aerodynamic force under the model posture at the next moment continues to be predicted according to the model posture. The process is cyclically executed to obtain a separation track of the multi-body separation test model. The prediction method is simple and efficient, is not limited by the CTS mechanism, solves the problem of trajectory prediction of the multi-body model of the CTS mechanism equipment, avoids the problems and risks of travel, time, collision and the like of the CTS mechanism, and reduces the test cost.

A classical way of finding the harmonic map is to minimize the harmonic energy by the time evolution of the solution of a nonlinear heat diffusion equation. To arrive at the desired harmonic map, which is a steady state of this equation, an efficient quasi-implicit Euler method (QIEM) is revealed and its convergence under some simplifications is analyzed. It is difficult to find the stability region of the time steps if the initial map is not close to the steady state solution. A two-phase approach for the quasi-implicit Euler method (QIEM) is disclosed to overcome this drawback. In order to accelerate the convergence, a variant time step scheme and a heuristic method used to determine an initial time step have been developed. Numerical results clearly demonstrate that the present method far computing the spherical conformal and Riemnann mappings achieves high performance.

The invention discloses a rapid and flexible full-pure embedded economic strategy adjustment method and device. The method comprises the following steps: obtaining product data and establishing an equilibrium state polynomial equation set based on a Burtlander model; describing the equilibrium state polynomial equation set as a polynomial system and constructing a polynomial homotopy function; solving the equilibrium state polynomial equation set to obtain an equation solution; and analyzing the equilibrium state based on the equation solution and performing economic strategy selection. The device comprises a memory and a processor used for executing the rapid and flexible full-pure embedded economic strategy adjustment method. By using the method, the equilibrium state polynomial equation set can be efficiently solved, the economic strategy is adjusted accordingly, and the enterprise benefit is improved. The rapid and flexible full-pure embedded economic strategy adjustment method and device can be widely applied to the field of strategy adjustment.

The invention discloses a Modelica-based flight simulator motion system modeling method. The method comprises the following steps: 1) demand analysis; 2) system decomposition; 3) designing a connector; 4) modeling a component layer; 5) modeling a part layer; (6) subsystem modeling; 7) system modeling; 8) modeling a control system; and 9) performing system simulation analysis and optimization design. According to the invention, modeling is carried out through a multi-field modeling language Modelica, so that a flight simulator motion system is prevented from using multiple pieces of software to carry out joint simulation during modeling simulation; the non-causal modeling mode can save the time of equation decoupling and programming when an engineer models, improves the simulation analysis efficiency of the flight simulator motion system, and provides an efficient design analysis method for the engineer.

The embodiment of the invention provides a substance evolution simulation method based on exponential time difference format solution. A substance evolution model is established based on a phase fieldmodel, the phase field model does not need to carry out prior assumption on a crystal grain structure evolution path, the position of a crystal grain interface does not need to be tracked explicitly,and the complexity of simulation calculation is greatly simplified. The equation of the substance evolution model is solved by using an exponential time difference format, namely, in the solving process, a frequency domain equation of the equation is obtained through fast Fourier transform, the frequency equation is solved by using the exponential time difference format, and Fourier inverse processing is performed on a solving result to finally obtain an equation solution. When the method is used for solving the phase field model, the method is rapid, stable and accurate, parallel computing can be carried out, and the method is suitable for solving a large-scale equation set by utilizing a computer.

The invention provides a method for calculating the change of vertical displacement in a beam bridge span along with temperature, and belongs to the technical field of bridge structure analysis and monitoring. The method comprises the following steps of: setting a node corner of a main beam at each support as an unknown quantity; balancing conditions according to the bending moment of the node; the method comprises the following steps of: establishing an equation, introducing a sequence, establishing a quantitative relation among unknown quantities, substituting the relational expression intothe equation, solving a corner analytical formula of each node, solving a bending moment analytical formula of each node through a superposition principle, and finally solving an analytical formula ofmidspan vertical displacement of each span girder through a virtual work principle. The method is used for a uniform-section beam bridge with equal side span length and any span number. A given analytical formula belongs to an accurate solution, calculation is convenient, universality is high, the behavior rule of the beam bridge under the temperature change is disclosed from the mechanism level,the method can be used for guiding measurement point arrangement of a bridge monitoring system, and priori knowledge is provided for establishment of a temperature deformation reference model.

The invention provides a data enhancement method based on automatic derivation and Taylor series expansion. The method comprises the following steps: S1, firstly determining a primary function for a given differential (product) equation; s2, determining data points of a direct numerical solution given differential (product) equation; s4, on the premise of S1, S2 and S3, determining data enhancement hyper-parameters: the highest expansion order, the value of the displacement amplitude delta x and the distribution and parameters of the displacement coefficients, and determining the number of new data points generated for each data point obtained through expensive calculation; and distribution of random reckoning parameters of omission order contribution and determination of the number of the random reckoning parameters. According to the technology, training data required by fitting a complex differential (product) equation solution function by the neural network can be greatly reduced, computing resources are remarkably saved under the condition that the given fitting precision requirement is met, or the fitting precision is greatly improved by increasing training data supply under the given computing resources.