213 results about "Ordinary differential equation" patented technology

Simultaneous Dynamical Integration modeling techniques are applied to global placement of elements of integrated circuits as described by netlists specifying interconnection of morphable-devices. Solutions to a system of coupled ordinary differential equations in accordance with Newtonian mechanics are approximated by numerical integration. A resultant time-evolving system of nodes moves through a continuous location space in continuous time, and is used to derive placements of the morphable-devices having one-to-one correspondences with the nodes. Nodes under the influence of net attractive forces, computed based on the interconnections between the morphable devices, tend to coalesce into well-organized topologies. Nodes are also affected by spreading forces determined by density fields that are developed based on local spatial node populations.

A robot control system includes a force control unit configured to output a correction value of a target track of a robot on the basis of sensor information acquired from a force sensor, a target-value output unit configured to apply correction processing based on the correction value to the target track to calculate a target value and output the calculated target value, and a robot control unit configured to perform feedback control of the robot on the basis of the target value. The force control unit includes a digital filter unit. The force control unit applies digital filter processing by the digital filter unit to the sensor information to calculate a solution of an ordinary differential equation in force control and outputs the correction value on the basis of the calculated solution.

A boring tool moves having a pitch orientation, a yaw orientation and a roll orientation and is steerable underground using the roll orientation. A maximum drill string curvature is established for steering. The boring tool is advanced over a path segment. An averaged roll characteristic is determined for movement of the boring tool along the path segment. A path segment pitch orientation is established based on at least one measured pitch orientation along the path segment. Using the maximum drill string curvature in combination with the averaged roll characteristic and the path segment pitch orientation, the yaw orientation is determined. The averaged roll characteristic is determined based on a series of incremental roll measurements that are spaced across the path segment. A set of coupled ordinary differential equations is used to characterize movement of the boring tool.

A method and system for rendering the shape of a multi-core optical fiber or multi-fiber bundle in three-dimensional space in real time based on measured fiber strain data. Three optical fiber cores arc arranged in parallel at 120° intervals about a central axis. A series of longitudinally co-located strain sensor triplets, typically fiber Bragg gratings, are positioned along the length of each fiber at known intervals. A tunable laser interrogates the sensors to detect strain on the fiber cores. Software determines the strain magnitude (ΔL/L) for each fiber at a given triplet, but then applies beam theory to calculate curvature, beading angle and torsion of the fiber bundle, and from there it determines the shape of the fiber in s Cartesian coordinate system by solving a series of ordinary differential equations expanded from the Frenet-Serrat equations. This approach eliminates the need for computationally time-intensive curve-tilting and allows the three-dimensional shape of the optical fiber assembly to be displayed in real-time.

Methods for finite-difference-based inkjet simulation enable more precise control of ink droplet size and shape. A discrete transformation (mapping) is constructed so that a quadrilateral grid in physical space is transferred to the uniform square grid in a computational space. Since the grid in the computational space is square, numerical finite difference differentiation can be easily done. Governing partial differential equations, including a viscosity term, a surface tension term, and a level set convection equation for two-phase flows, are derived on the quadrilateral grid and then transformed to the computational space for application on the uniform square grid. A stable and powerful numerical algorithm is developed to solve the derived and transformed equations to enable finite-difference-based ink-jet simulation.

A system (10) is disclosed for eliminating sway of a load (30) in a crane or crane-like system subject to operator's command. The load is suspended by a cable (40) from a horizontally movable trolley (20) and can be hoisted vertically. The system uses the principle of cancellation to eliminate sway even when the crane has simultaneous trolley and hoisting motions. The system takes into account the full dynamical effect in computing cancellation signals. The use of a family of ordinary differential equations for the computation of the cancellation controls is a key component of the invention. In computing these controls, the differential equations are solved in real time using sensory measurement of the cable length and its time derivative. The cancellation controls handle the sway induced by the operator's command. Sway can also be induced by other factors, like wind load and external disturbances. This system also includes a feedback mechanism for eliminating sway due to such factors. The system ensures saturation limits, corresponding to the velocity and acceleration limits of the drive system of the trolley are not exceeded for proper functioning of the system.

The invention discloses a traveling-wave differential protection method suitable for a series capacitor compensation circuit. The method comprises the steps: 1) current calculation under a mold domain, calculating mold currents im<x> and in<x> flowing into a series capacitor device from onside and offside; 2) establishment of differential equation; 3) resolution of differential currents, utilizingthe reverse transformation of phase molds to solve vectors icd<phi> of the differential currents of each fault phase and each non-fault phase; 4) action judgment of a differential relay: utilizing the fault-phase action amount as braking, and adding an appropriate fixing threshold. The invention can effectively solve the effect of capacitor current on differential protection of long-distance transmission lines, can be well suitable for the series capacitor compensation circuit, and enhances the sensitivity of differential protection.

A method comprising a computational procedure for obtaining reduced-order models of partial element equivalent circuit (PEEC) models of very large scale integrated (VLSI) interconnects. The methodology is not limited to PEEC applications, and can be used for generating reduced-order models of other systems which can be modeled with linear, time-invariant systems of ordinary differential equations with time delays.

The invention relates to a method for de-noising a dual-tree complex wavelet image on the basis of partial differential equation. The method comprises the following steps: inputting a noised digital image; carrying out the dual-tree complex wavelet transform decomposition on the inputted noised digital image to obtain two low-frequency sub-band images and six high-frequency detailed sub-band images; carrying out the isotropic diffusion on the two decomposed low-frequency sub-band images; designing an improved adaptive model; calculating the dual-tree complex wavelet transform modulus and gradient modulus of the high-frequency detain sub-band images on each direction, and designing an adaptive diffusion coefficient function to improve the P-M (Perona-Malik) model (i.e., the isotropic diffusion model) by using the weighted average of the dual-tree complex wavelet transform modulus and gradient modulus; carrying out the diffusion processing on the improved adaptive model; carrying out the isotropic diffusion on the six high-frequency sub-band images; and carrying out the dual-tree complex wavelet transform, and outputting the de-noised digital image. The invention has the beneficial effect that more detailed information of the image can be preserved on the premise that the higher rate of image de-noising is maintained.

The invention discloses a TBM hobbing cutter stress online real-time monitoring apparatus and monitoring method. The apparatus comprises a support cushion block, an upper compaction block, a strain gauge, a strain instrument, a wireless emission module, a wireless receiving module and a monitoring computer. According to the monitoring method, by use of strain data of the support cushion block, obtained by the apparatus, through the monitoring computer, by use of a hobbing cutter system vibration differential equation established through a hobbing cutter vertical and swing-direction coupling vibration mechanical model, stress of a hobbing cutter during work is calculated, such that work personnel can monitor the stress condition of the hobbing cutter in real time and adjust driving parameters based thereon, damage is reduced, vibration is mitigated, and the driving efficiency is improved.

A system and method for designing a progressive lens. Mean power is specified at points distributed over the entire surface of the lens and lens height is specified around the edge of the lens. Lens height is determined at the points consistent with the specified mean power and the lens edge height in part by solving a partial differential equation of the elliptic type subject to the lens edge height as a boundary condition. A successive over-relaxation technique may be employed to converge on the solution to the partial differential equation, and an over-relaxation factor may be determined to most efficiently relax the equation.

Simultaneous Dynamical Integration modeling techniques are applied to global placement of elements of integrated circuits as described by netlists specifying interconnection of morphable-devices. Solutions to a system of coupled ordinary differential equations in accordance with Newtonian mechanics are approximated by numerical integration. A resultant time-evolving system of nodes moves through a continuous location space in continuous time, and is used to derive placements of the morphable-devices having one-to-one correspondences with the nodes. Nodes under the influence of net attractive forces, computed based on the interconnections between the morphable devices, tend to coalesce into well-organized topologies. Nodes are also affected by spreading forces determined by density fields that are developed based on local spatial node populations.

The invention discloses an acquisition method of inclination biased quantity for sun synchronous orbit. The method comprises the following steps: 1, correcting an initial value i0 of an orbit inclination by virtue of a correction value delta I of the initial value of the orbit inclination; 2, establishing an ordinary differential equation to acquire an orbit inclination at moment t and orbit right ascension of ascending node, and variation delta LTDN of local time of descending node at moment t; 3, judging the orbit drifting direction, wherein the biased quantity of the orbit inclination is negative if the direction is toward east, while the biased quantity of the orbit inclination is positive if the direction is toward west; and 4, traversing inclination biased quantities with step length of 0.0001 degree in a range from 0.0 to 0.1 degree, and respectively adding the corrected initial value of the sun synchronous orbit inclination in the step 1 to serve as an orbit initial value with inclination biased quantity, and carrying out the step 2 to obtain the variation of the local time of descending node at the moment t, arranging the maximum values of absolute values of variations into vectors according to a sequence, and the minimum value in the vectors is the inclination biased quantity. According to the method, the defect of low calculation accuracy of inclination biased quantity of the conventional sun synchronous orbit inclination biased quantity is overcome, and the orbit control capability is effectively improved.

The invention relates to a charging method of a battery. The method comprises the steps of acquiring a battery parameter, wherein the battery parameter comprises an electrode parameter of the battery;inputting a battery model expressed by ordinary differential equation according to the battery parameter; acquiring a safety charging boundary value of the battery under circulation for n times, wherein the parameter also comprises one or more of a structure parameter of the battery, a manufacturing process parameter, an electrical parameter, an electrolyte parameter, a separator parameter and athermo-physical property parameter, the safety boundary value is maximum charging current which the battery does not generate lithium separation under different states of charge (SOC) and different temperatures, n is larger than or equal to 2 but smaller than or equal to N, N is cycle lifetime of the battery, and circulation for n times is n(th) circulation selected from 0(th) circulation to N(th)circulation; and finally, acquiring maximum safety charging current value of the battery under current circulation frequency and current SOC according to the current circulation frequency, a currenttemperature, current SOC and the safety charging boundary value of the battery.

The invention relates to a spherical motor rotor position detection method based on an MEMS (Micro Electron Mechanical Systems) sensor. The method comprises steps: the original data of the MEMS sensorare acquired; zero bias error compensation is carried out on an angular velocity, and ellipsoid fitting compensation is carried out on an acceleration and a magnetic induction intensity; the angularvelocity, the acceleration and the magnetic induction intensity data after compensation are subjected to complementary filter-based data fusion and are substituted to a quaternion differential equation to obtain an attitude updating quaternion; the attitude updating quaternion is converted to an Euler angle, the change characteristics of the Euler angle in different intervals are combined, accurate interval transfer judgment is made, and conversion of the Euler angle in a full angle range change condition can be realized.

The invention discloses a denoising method of a strong noise pollution image on the basis of partial differential equation, mainly solving the problem of poor traditional denoising effect of the strong noise pollution image. The realization process comprises: (1) pretreating an input noise image u0, and recording the result as u; (2) calculating the partial derivative sum of the image u; (3) calculating the gradient module value of the image u; (4) according to the gradient and the gradient module value, building the partial differential equation; (5) calculating diffusion coefficients and psi in the partial differential equation; (6) utilizing the coefficients and psi, solving the partial differential equation to obtain a filter image; (7) calculating the peak signal to noise ratio PSNR of the filter image; and (8) repeating steps 2 to 7, when the PSNR value of the filter image output iteratively one time is smaller than that output iteratively in the previous time, stopping iteration, and outputting the previously iterated filter image. The invention has simple calculation and high operation speed, can better keep image texture details while smoothening strong noise and can be used for denoising a natural image with strong noise pollution.

A parametric elastic vibration analysis method of a rotating annular periodic structure comprises the steps of building a rigid-elastic coupling dynamic model of the rotating annular periodic structure according to a Hamilton principle under a global stationary coordinate system; introducing coordinate conversion, and converting the dynamic model to a support follow-up coordinate system so that a parametric item in an original equation is eliminated; performing discrete processing on a partial differential constant coefficient dynamic equation under the rotating support follow-up coordinate system by a Galerkin method to obtain an ordinary differential matrix equation; analyzing a characteristic value of the ordinary differential matrix equation by using a classical vibration theory; and respectively analyzing mode characteristic of the rotating annular periodic structure and a dynamic stability rule of parametric elastic vibration by employing an imaginary part and a real part of the characteristic value of the ordinary differential matrix equation. The parametric elastic vibration analysis method can be used for dynamic analysis of rotating machinery, calculation and solution of the mode characteristic of a system, and analysis on the dynamic stability and the dynamic response of the system.

The invention provides an under-actuated release control method based on a nonlinear space tether system. The method comprises the following steps: 1, a dumbbell model is adopted, system dynamics differential equations are built according to a second kind Lagrange equation, and a dimensionless form is introduced in the differential equations; 2, based on a normal form expression for the above dynamics differential equations, expected values for a system in-plane pitching angle and an out-plane rolling angle are set, and the balance position of the system in the release process is obtained; 3, starting from the balance position of the system, a tether length change control law for realizing tether release is deduced and obtained; and 4, the range for the expected in-plane pitching angle is determined to ensure the tether release process to be asymptotically stable under effects of the control law. Numerical simulations show that the space tether can be released asymptotically stably under effects of the release control method provided by the invention, and an attractor capable of covering the balance point and an attraction domain with enough thickness can be found out.

The invention discloses an electronic power switch interpolation real-time simulation method based on backward euler-trapezoidal weighted integral method. The electronic power switch interpolation real-time simulation method comprises the steps that at the turn-off time of an electronic power switch, linear interpolation is adopted for determining the accurate switch action time point and relevant state variables; according to the position of the switch action time point in the single-step simulation step size, an ordinary differential equation backward euler-trapezoidal weighted integral method is utilized for building a piecewise function, and the numerical solution of the system whole-step stimulation time point is obtained through integration, wherein in the process, all amounts of the system are reinitialized, and therefore the accurate network topology and system initial value at the time moment are obtained. A traditional problem that the electromagnetic transient stimulation efficiency is affected due to the fact that system topology high frequency changes are caused when the electronic power switch frequently acts during power system electromagnetic transient simulation is effectively solved.

The invention discloses a short-term climate forecast method based on Kalman filtering and evolution modeling. The method comprises the following steps of: establishing a linear model about a forecast factor by the Kalman filtering at first; and simulating an error sequence approaching the Kalman filtering by using a non-linear ordinary differential equation math model on the basis of the linear model a, and performing error forecast. An evolution algorithm is an evolution process for simulating the nature by using a computer, in particular a calculation method for solving complicated problems by simulating biological evolution processes, and has the intelligent characteristics of self-adaptation, self-organization, self-learning, internal parallelism and the like. The two algorithms are combined with each other, so the natural characteristic of the climate can be simulated better than being simulated by a pure linear model, so the climate forecast precision is enhanced. By the method, short-term sunshine duration, temperature and rainfall can be forecast, so future knowledge of the short-term climate can be provided.

The invention provides an industrial process dynamic optimization system based on a nonlinear conjugate gradient method, which comprises an in-site intelligent meter, a DCS system and a host machine, wherein the in-site intelligent meter is connected with an industrial process object, the host machine comprises a restriction processing module, an initialization processing module, an ODE solving module, an iteration optimization module and a convergence judgment module, the restriction processing module is used for processing the control variable boundary restriction in the optimization process, the initialization processing module is used for setting initialization parameters, the OED solving module is used for solving ordinary differential equation groups of a dynamic optimization question, the iteration optimization module is used for searching a decision vector w which makes a target function J optimum, the convergence judgment module is used for judging whether the error absolute value of the target value obtained by the current convergence and the target value obtained by the former convergence is smaller than or equal to the set convergence precision omicron, and the current optimum vector w*, the current optimum target value J* and the current convergence time number k are stored if the error absolute value of the target value obtained by the current convergence and the target value obtained by the former convergence is smaller than or equal to the set convergence precision omicron. The invention also provides an industrial process dynamic optimization method based on the nonlinear conjugate gradient method. The invention can simultaneously meet the requirements of high efficiency and high precision of the on-line dynamic optimization solving.

A modeling method of reusable parameterized component for space continuous deformation MEMS includes confirming each dynamic control equation and boundary condition equation of MEMS device, carrying out space discretization on dynamic control equation and converting said control equation to be constant-differential equation set, utilizing hardware description language of analog and mixed signal to carry out coding for realizing function description, plotting schematic diagram of MEMS device and connecting said diagram with code to form MEMS device being called in system modeling and in simulation analysis.

A method and apparatus for executing high performance computation to solve PDEs and for outputting three-dimensional interactive images in collaboration with a GPU is disclosed. The method includes: (A) executing a coordinate transformation to a three-dimensional image by the CPU, setting a boundary condition required by a simulation according to a coordinate transformation result, and inputting the boundary condition to the GPU; (B) executing a numerical simulation of the PDEs and the boundary condition in the step (A); (C) processing and rendering each drawn element by the GPU according to a numerical simulation result to draw a visual image featured with physical quantity variation and overlapping the visual image on the three-dimensional image to form the three-dimensional interactive images.