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48 results about "Solution of equations" patented technology
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Fast optical flow field calculation method based on error-distributed multilayer grid
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.
Owner:BEIJING UNIV OF TECH
Model unknown multi-agent consistency control method based on reinforcement learning
ActiveCN112947084ASolve the defect that information communication cannot be carried out in real timeSolve the problem of constructing Lyapunov functions in multiple stepsTotal factory controlAdaptive controlSolution of equationsControl engineering
The invention relates to a model unknown multi-agent consistency control method based on reinforcement learning, and belongs to the field of intellectualization. According to the method, the scheme adopted when an adaptive distributed observer is designed comprises three steps; firstly, the adaptive distributed observer is designed to estimate the states of a system matrix and a leader system; secondly, after the adaptive distributed observer is designed, a method for calculating the equation solution of the observer on line is provided; and thirdly, in order to eliminate extremely few extreme conditions, under the condition that each follower is assumed not to know a leader system matrix, adaptive state feedback and adaptive measurement output feedback control are integrated to solve the problem of distributed consistency output adjustment of the system. According to the estimated state, a method based on reinforcement learning is adopted to design a controller, an optimal solution is obtained through an iteration method, and optimal control over the multi-agent system is achieved.
Owner:CHONGQING UNIV
Time-varying feedback finite-time stabilization method of control limited spacecraft rendezvous control system
ActiveCN110727199AGuaranteed Rendezvous MissionFast convergenceAdaptive controlSolution of equationsFeedback controller
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.
Owner:HARBIN INST OF TECH
Method for measuring acoustics parameter of viscous-elastic material under medium-high frequency
InactiveCN1967238AAvoid sound pressure phase measurementsImprove measurement efficiencyAnalysing solids using sonic/ultrasonic/infrasonic wavesSpecial data processing applicationsSolution of equationsCauchy elastic material
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.
Owner:HARBIN ENG UNIV
Method for calculating first-order natural cyclic frequency of bending vibration of stepped beam
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.
Owner:XUZHOU NORMAL UNIVERSITY
Method of finding solution of equation and recording medium storing program for implementing the same
InactiveUS20100241678A1Reliably and accurately solutionFast convergenceDigital computer detailsProgram controlLower limitSolution of equations
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.
Owner:IND ACADEMIC COOPERATION FOUND KUNSAN NAT UNIV
Calibration device and method for carrying out calibration on transfer function in monitoring device
ActiveCN103092815ASmall absolute errorHigh precisionComplex mathematical operationsSolution of equationsSignal transfer function
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.
Owner:HISENSE BROADBAND MULTIMEDIA TECH
Multi-working-condition one-dimensional wave equation solving method based on neural network
ActiveCN113468466ASolve time-consuming and laborious problemsGuaranteed solution accuracyNeural architecturesSeismic signal processingHidden layerAlgorithm
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.
Owner:HARBIN INST OF TECH
Time-varying feedback finite time control method for controlling limited satellite formation flight system
ActiveCN112286058AGuaranteed escort missionArtificial satellitesSpacecraft guiding apparatusSolution of equationsOrbit (dynamics)
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.
Owner:HARBIN INST OF TECH
Finite-volume-method-based simulation method of cavitation flow in water pipe
ActiveCN106777770AAdaptableNo pulse peaksDesign optimisation/simulationSpecial data processing applicationsComputer scienceCavitation flow
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.
Owner:HOHAI UNIV
Existence inspection method for solution of equation set in automated design of integrated circuit
ActiveCN106650139ASimple Judgment StandardClear and unified processCAD circuit designSpecial data processing applicationsSolution of equationsDevice form
The invention discloses an existence inspection method for a solution of an equation set in the automated design of an integrated circuit. The method comprises the following steps that: according to the connection relationship of a device, constructing a container; according to the container, judging whether the device forms a special loop to cause an equation set to have no solutions; and according to the device, judging whether optimization forms the special loop to cause the equation set to have no solutions. By use of the method disclosed by the invention, in the automated product of the integrated circuit, the reasonability of circuit design is inspected, especially, the existence of the solution of the equation set due to the special loop is inspected so as to reduce an ergodic process and improve circuit design efficiency.
Owner:北京华大九天科技股份有限公司
System And Method For Finding Integer Solutions
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.
Owner:IBM CORP
Trajectory prediction method for wind tunnel multi-body separation test model
ActiveCN112964450AImprove timelinessEfficient screeningAerodynamic testingMeasurement testMathematical model
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.
Owner:中国空气动力研究与发展中心超高速空气动力研究所
Method of finding solution of equation and recording medium storing program for implementing the same
InactiveUS8577947B2Reliably and accurately solutionFast convergenceDigital computer detailsProgram controlLower limitSolution of equations
Owner:IND ACADEMIC COOPERATION FOUND KUNSAN NAT UNIV
Multi-gyroscope fault diagnosis and reconstruction method based on non-homogeneous equation solution
ActiveCN111637901ARealize fault locationWeak versatilityMeasurement devicesGyroscopeSolution of equations
The invention relates to a multi-gyroscope fault diagnosis and reconstruction method based on a non-homogeneous equation solution, which is suitable for a spacecraft for measuring a plurality of gyroscopes. According to the method, a general non-homogeneous equation set described by m gyroscopes is solved, the equation set contains three unknown quantities and m equations, and through equivalent transformation, the satellite three-axis angular velocity described by m gyroscope measurement values and m-3 groups of gyroscope associated equations are obtained. By processing the associated equations of the gyroscopes, not only can the fault location of a plurality of gyroscopes be quickly realized, but also a plurality of problem gyroscopes can be avoided at the same time to realize the quickself-reconfiguration design of the gyroscope group. The invention provides a universal design method for multi-gyroscope anomaly positioning and reconstruction, is wide in application range, and is suitable for gyroscope autonomous anomaly positioning and reconstruction design of satellites of various models.
Owner:BEIJING INST OF CONTROL ENG
Method for computing spherical conformal and riemann mapping
InactiveUS20170212867A1Fast convergenceImprove performanceComplex mathematical operationsPresent methodEulerian method
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.
Owner:GEOMETRIC INFORMATICS TECH INC
A variable mass simulation device and method for motion operation
ActiveCN109165419AAccurate methodRealize Force Closed Loop ControlPhysical therapies and activitiesDesign optimisation/simulationLoop controlGeneralized inverse
The invention provides a variable mass simulation device for motion operation and a simulation method based on the device, belonging to the technical field of mass simulation, the device comprising asupport system frame, a traction system, a simulation particle and an operation end. At work, a trainer can feel the corresponding load at the operate end by inputting the simulation quality through the upper computer. The basic method is to solve the cable tension based on the particle motion state of the manipulator by using the space sink force system and the generalized inverse solution of equations, and to control each cable element by force closed-loop control. The support system frame is constructed from profiles. The variable mass point to be simulated in the device is pulled by four rope units at the same point. Each rope unit is connected to the winch on the motor through the tension sensor and the acceleration sensor through the passing wheel fixed on the frame. The invention can be used for simulating a variable mass of a particle in a space, so as to realize some simulation training which ignores the volume but requires the working condition of the mass change.
Owner:HARBIN ENG UNIV
Rapid and flexible full-pure embedded economic strategy adjustment method and device
PendingCN113487196AIncrease profitEfficient solutionResourcesForecastingSolution of equationsBusiness enterprise
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.
Owner:SUN YAT SEN UNIV
Modelica-based flight simulator motion system modeling method
PendingCN114488850ACosmonautic condition simulationsSimulator controlSolution of equationsMotion system
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.
Owner:中航航空模拟系统有限公司
Surface intersection method
InactiveCN101980231AImprove iteration efficiencyImprove accuracySpecial data processing applicationsComputer scienceAlgorithm
Owner:GLODON CO LTD
Method for predicating GDP (Gross Domestic Product) by applying electric power big data based on backward regression equation
The invention discloses a method for predicating GDP (Gross Domestic Product) by applying electric power big data based on a backward regression equation. The method comprises the following steps: step 1, acquiring historical data; step 2, carrying out variable setting; step 3, carrying out logarithmic differential processing on variables on power utilization amount and the GDP of industrial enterprises; step 4, setting a forward regression equation and carrying out parameter estimation; and step 5, deducing a backward regression equation model by utilizing estimated parameter, wherein a calculation formula of a predicated value GDPt+1 of the GDP of the next period is as follows: GDPt+1= GDPt.exp(gdpt+1). The backward regression equation is deduced by utilizing a parameter estimated value of the forward regression equation, electric power data is deconstructed and an economic development condition of a region is predicated; and an effective modeling method and decision-making reference are provided for electric power and economy competent departments.
Owner:NANJING UNIV +1
System for convergence evaluation for stationary method iterative linear solvers
InactiveUS9176928B2Computation using non-contact making devicesCode conversionReconfigurable computingEvaluation system
A system for evaluating the convergence to a solution for a matrix equation comprises at least one reconfigurable computing device such as a field programmable gate array (FPGA), an update storage element, a conversion element, a summation unit, and a comparator. The FPGA includes a plurality of configurable logic elements and a plurality of configurable storage elements, which are utilized to form the update storage element, the conversion element, the summation unit, and the comparator. The update storage element is configured to store a plurality of updates. The conversion element determines the absolute value of the updates. The summation unit accumulates the absolute values of the updates to produce a total sum, which is compared to a convergence factor by the comparator. Convergence is signaled when the total sum is less than the convergence factor.
Owner:L 3 COMM INTEGRATED SYST
Substance evolution simulation method based on exponential time difference format solution
ActiveCN110717271ASimplify complexityQuick solveDesign optimisation/simulationComplex mathematical operationsFast Fourier transformConcurrent computation
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.
Owner:CHINA INSTITUTE OF ATOMIC ENERGY +1
Method for calculating change of vertical displacement in beam bridge span along with temperature
ActiveCN112016143AEasy to analyzeAvoid mockingGeometric CADDesign optimisation/simulationStructure analysisSolution of equations
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.
Owner:UNIV OF SCI & TECH BEIJING
A method for analyzing the aerodynamic nonlinear lower-angle motion characteristics of double-rotating bombs
ActiveCN112325713BAngle of attack does not decayAmmunition testingSolution of equationsAngular velocity
The invention discloses a method for analyzing the aerodynamic nonlinear lower-angle motion characteristics of a double-rotating projectile, which includes the following steps: Step 1: establishing a double-rotating projectile with respect to the angle of attack α, the sideslip angle β, and the pitch angular velocity ω z , Yaw angular velocity ω y The nonlinear angular motion equation; Step 2: Determine the nonlinear complex angle of attack equation of the double-rotating bomb according to the nonlinear angular motion equation established in step 1; Step 3: Transform the stability analysis of the solution of the nonlinear complex angle of attack equation into Analysis of its corresponding homogeneous equation solution; Step 4: Determine the amplitude plane equation of the double-rotating bomb under the action of the cubic static moment; Step 5: Determine the necessity for the double-rotating bomb to produce stable conical motion under the action of the cubic static moment Conditions; Starting from the aerodynamic nonlinearity, the necessary conditions for the stable conical oscillation of the double-rotating bomb under the action of the cubic static moment are obtained, thus pointing out that the angle of attack produced by it under the action of the nonlinear static moment does not attenuate, and even Causes of flight instability.
Owner:BEIJING INSTITUTE OF TECHNOLOGYGY
Method for calibrating transfer function in monitoring device
ActiveCN103092815BSmall absolute errorHigh precisionComplex mathematical operationsSolution of equationsSignal transfer function
Owner:HISENSE BROADBAND MULTIMEDIA TECH
Algebraic calculator based on identical deformation
InactiveCN106502954AImprove efficiencyReduce errorsDigital computer detailsComplex mathematical operationsAlgebraic equationSolution of equations
The invention discloses an algebraic calculator based on identical deformation. The algebraic calculator is electronic equipment capable of assisting in algebraic operation. According to the equipment, elements in an algebraic expression are selected and operated according to a hierarchical permeation method based on touch screen equipment or computers so as to perform identical deformation of the algebraic expression, wherein the hierarchy is to perform hierarchical division on the algebraic expression by an application program according to the priority of arithmetic and define the element selection and operation in the same hierarchy; permeation refers to switch among the levels and is performed by a user through a touch screen or a mouse, so that the element selection and operation can spread all over the whole algebraic expression. The equipment can help teachers, students and engineering technicians to perform paperless algebraic operations such as algebraic expression reduction, factorization, and solution of equations (equation sets). In addition, the tool has excellent teaching and demonstration functions.
Owner:邵良
One-Dimensional Wave Equation Solving Method Based on Neural Network
ActiveCN113468466BSolve time-consuming and laborious problemsGuaranteed solution accuracySeismic signal processingNeural architecturesHidden layerAlgorithm
The invention relates to a method for solving one-dimensional wave equations under different working conditions based on a neural network. The invention belongs to the field of earthquake engineering. One-dimensional wave equation solution method: 1. Select the 1-dimensional wave equation as the equation to be solved; 2. Determine the solution domain of input variables and the number of residual points; 3. Establish a fully connected layer neural network including 6 hidden layers; 4. Design a specific loss function; 5. Pre-training and refined training of the neural network. The present invention takes the wave velocity as an input, and proposes a neural network-based one-dimensional wave equation solution method, so that the model can learn the influence of different working conditions on the equation solution. On the premise of maintaining high solution accuracy, the general equation and stress condition The addition of also increases the interpretability of the solution method.
Owner:HARBIN INST OF TECH
Data enhancement method based on automatic derivation and Taylor series expansion
InactiveCN112926019AReduce usageReduce data pointsNeural architecturesNeural learning methodsAlgorithmSolution of equations
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.
Owner:JILIN UNIV
A Trajectory Prediction Method for Multi-Body Separation Test Models in Wind Tunnels
ActiveCN112964450BImprove timelinessEfficient screeningAerodynamic testingMeasurement testMathematical model
The invention discloses a trajectory prediction method for a multi-body separation test model in a wind tunnel. The prediction method uses the multi-body separation wind tunnel grid force measurement test data to establish the Kriging mathematical model of the six-component aerodynamic coefficient under different relative positions and attitudes of the multi-body separation test model, and combines the rigid body six-degree-of-freedom motion equation to solve the motion trajectory. Divide the separation trajectory into multiple moments according to time, predict the aerodynamic force at the initial moment according to the mathematical model, solve the model attitude at the next moment according to the model pose at the initial moment combined with the equation of motion, and continue to predict the aerodynamic force at the next moment according to the model attitude The aerodynamic forces in the model attitude. The loop is executed to obtain the separation trajectory of the multi-body separation test model. The prediction method is simple and efficient, and is not limited by the CTS mechanism. It solves the trajectory prediction problem of the multi-body model of the CTS mechanism equipment, avoids the problems and risks of the CTS mechanism travel, time, collision, etc., and reduces the test cost.
Owner:中国空气动力研究与发展中心超高速空气动力研究所
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