122 results about "Matrix differential equation" patented technology

The invention discloses a shale gas well productivity evaluation and prediction method. The method comprises the following steps: an expression of a differential equation of a single-phase seepage mathematical model is obtained; the differential equation is solved and represented by a pressure form to obtain a seepage velocity and output formula; a deliverability equation is determined through fitting production data; the derived output formula is arranged to obtain a shale gas horizontal well staged fracturing output formula; boundary pressure (pe) required to be known can be known from the shale gas output formula; and as shale gas has the influences of absorption and desorption, a deviation factor is required to be corrected to obtain formation pressure of a shale gas reservoir. The prediction method deduces the deliverability equation for a shale vertical well and a horizontal well according to the desorption and dispersion characteristics of the shale gas, so that a shale gas output evaluation method is built, the precise output prediction is obtained, and the economic efficiency is improved.

The invention relates to a method for error suppression of inertial concretionary coarse alignment of a strapdown inertial navigation system and belongs to the technical field of inertial navigation. The method comprises the following steps of 1, according to current longitude and latitude of a carrier, carrying out transformation of an earth coordinate system into a navigation coordinate system, 2, driving two shafts of a rotation-type inertial navigation system to periodically rotate according to a certain rotating scheme, 3, according to angular velocity information output by a gyroscope in coarse alignment, updating a direction cosine matrix of a posture change of an inertial measurement unit (IMU) coordinate system relative to a p0 coordinate system through calculating a numerical solution of a matrix differential equation, and 4, orderly calculating solutions of matrixes to obtain a posture matrix of the carrier so that coarse alignment is finished. The method has the advantages that through an integral operation in coarse alignment, swinging and shaking-caused error components of outputs of an accelerometer of a ship in alignment of storm-caused swinging and shaking can be compensated; and through IMU double-shaft rotation modulation, an accelerometer zero-bias error accumulated over time is suppressed so that the precision of inertial concretionary coarse alignment is improved.

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.

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.

The invention discloses an evaluation method for the operation reliability of a milling cutter. According to the method, machining tool spindle and feed shaft three-phase current signals are acquired through a Hall sensor, time domain mean characteristics and tooth frequency energy characteristics are extracted through wavelet analysis, an observation vector output function: a mixed Gaussian distribution density function, is obtained through a mean algorithm aimed at characteristic vectors, a continuous 'hidden semi-Markov model' is trained through a Baum-Welch algorithm to obtain a parameter estimation result, and the operation reliability level of the middling cutting is calculated through a Chapman-Kolmogorov differential equation. According to the evaluation method, decision support is provided for preventive maintenance of milling cutters.

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 belongs to the technical field related to structure topological optimization design, and discloses an efficient structure frequency response topological optimization method. The method comprises the following steps that: (1) decoupling two coupling variables including time and space in a standard level set function in a dynamic model of which the structure is to be optimized, and meanwhile, expressing the level set function related to time as a matrix product form; (2) converting a partial differential equation of the time-related level set function into an ordinary differential equation so as to obtain a new linear system, and solving to obtain the time-related level set function; (3) carrying out finite element analysis on a macrostructure so as to calculate a target function and a constraint function of a structure optimization problem; and (4) calculating the sensitivity, which relates to a design variable of the target function and the constraint function obtained in the (3), and judging whether the target function is convergent or not after the design variable is updated. By use of the method, a discrete wavelet transform technology is adopted to carry out recompression on an interpolation matrix, efficiency is improved, and cost is lowered.

The invention discloses a space debris recovery control method based on a tethered technology. The space debris recovery control method is characterized by comprising the following steps that 1, the tether elasticity is considered, a space tethered debris system is researched by adopting an elastic rod module, and a system dynamics differential equation is built according to a class II Lagrange equation; 2, the system dynamics equation in the step 1 is rewrote into a non-dimensional system dynamics equation; 3, the in-surface outer pivot angle vibration abatement problem of nonlinear time-varying system dynamics equation in the recovery process is researched, and the tether length change analysis control law and the in-surface pitch angle value range in the expectation equilibrium position in the debris recovery process are inferred; and 4, the stability of the system and the value range, keeping stable asymptotically, of a pitch angle in an expectation surface are further analyzed through the Floquet theory. Through the space debris recovery control method, the effect that debris is stably recovered nearby an on-orbit spacecraft can be ensured, and meanwhile the safety in the recovery process especially the safety in the end time can be ensured.

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.

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 present invention provides a viscous-acoustic undulating surface forward modeling system and method based on a viscous-acoustic quasi-differential equation, belonging to the field of oil exploration. The method comprises the following steps of: performing irregular mesh generation of speed and quality factors, mapping the speed and quality factors in a mesh coordinate system, mapping a traditional first-order viscous-acoustic-stress equation to a curved mesh coordinate system, and applying the first-order viscous-acoustic-stress equation in the curved mesh coordinate system to deduce a second-order viscous-acoustic quasi-differential equation without memory variables in the same coordinate system. The new viscous-acoustic equation can better control the amplitude loss and phase dispersion caused by the viscous-acoustic medium to more accurately simulate the propagating precision of the viscous-acoustic medium of the undulating surface in a seismic wave, and when the equation is solved, a mixed space partial derivative difference method is provided to perform solution, and a new boundary condition suitable for an undulating surface curved mesh coordinate system is provided to absorb artificial boundary reflection.

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.

The invention aims to provide an image denoising method based on Tetrolet transform. In the method, a partial differential equation (PDE) and generalized cross validation (PDE) are combined, thereby achieving a better noise denoising effect. The method comprises the following steps: performing Tetrolet transform on a noise-including image; determining an optimal denoising threshold by using a GCV theory in a transform domain and performing threshold processing; performing Tetrolet inverse transform to obtain an initial denoised image; smoothening the image by using a PDE denoising model under the consideration that a square block effect is generated by the Tetrolet transform in order to keep the edge information of the image. The PDE comprises three denoising models, namely, PM1, PM2 and TV. Meanwhile, compared with other five kinds of denoising results based on a multi-scale transform method, the method has the advantages of high PSNR (Peak Signal Noise Ratio) value of the denoising result, good image vision effect, outstanding details, further improvement on the subjective and objective quality of the denoised image and great promotion of subsequent work of the denoised image.

The invention discloses an electric power system transient stability simulation method based on a fine integral algorithm. Compared to an existing electric power system transient stability value integral method, in the method of the invention, non-linear differential equations describing an electric power system transient process are expressed as a linear part and a nonlinear part. Through reasonably selecting a system matrix of the linear part and using an integrable function to approximate a nonlinear term function, an implicit fine single step integral formula is derived. Through finely solving a state transition matrix corresponding to a linear part system matrix, the integral formula with high precision can be obtained so as to reduce a calculated amount of the transient stability simulation.

The invention provides a method for inhibiting an infrared image background based on a PDE (Partial Differential Equation), concretely comprising the following steps of: (1) carrying out noise filtering background estimation on an initial image by using a PDE theory based filtering model to obtain a background image; and (2) carrying out neighboring difference on the initial image and a background image to obtain a result image of which the background is inhibited. Test data show that the method can be used for remaining the target property, lowering the target segmenting difficulty, facilitating later target detection and identification, increasing the target detection rate and realizing good adaptability of a filtering method while effectively inhibiting strong clutter backgrounds in the images.

The invention discloses a simplified analysis method for an inherent frequency and the stability of a rotational symmetric structure. The method comprises the steps of establishing a complete dynamic differential equation of a system, a dynamic differential equation adopting a no-extension hypothesis, and a dynamic differential equation adopting an extension hypothesis: establishing the complete dynamic differential equation of the system; establishing the dynamic differential equation adopting the no-extension hypothesis; establishing the dynamic differential equation adopting the extension hypothesis; introducing coordinate conversion for converting the three dynamic differential equations to a support follow-up coordinate system so as to obtain corresponding three constant coefficient partial differential dynamic equations; performing discrete processing on the three constant coefficient partial differential dynamic equations in the support follow-up coordinate system to obtain three constant differential matrix equations; obtaining an eigenvalue of the complete dynamic differential equation and eigenvalues of two simplified dynamic differential equations; and analyzing a parametrically excited vibration mode characteristic and a dynamic stability change law of the rotational symmetric structure according to the three eigenvalues. According to the method, a specific analysis expression of system eigenvalues can be obtained more clearly.

A predictor usable for rapid and accurate calculation of joint commands of an articulated mechanism describes relationship between the joints in the form of a differential equation. The predictor solves this differential equation by direct substitution of a power series for each of its variables and the combining of selected sets of coefficients of these power series into linear systems of equations which may be solved to determine power series coefficients to arbitrary order.

Disclosed is an imaging apparatus for generating data of a phase image based on an interference pattern acquired by a shearing interferometer, including: a differential phase data calculating unit that calculates first differential phase data expressing a change of a phase in a first direction and second differential phase data expressing a change of a phase in a second direction, based on interference pattern data generated by an electromagnetic wave transmitted through a subject; a second-order differential phase data calculating unit that calculates first second-order differential phase data by differentiating the first differential phase data in the first direction, and calculates second second-order differential phase data by differentiating the second differential phase data in the second direction; and a phase data calculating unit that calculates the phase image by solving a second-order differential equation including the first and second second-order differential phase data as functions.

The invention provides a hydrostatic guideway bearing capacity analyzing method considering guideway surface deformation and belongs to the field of supporting and lubricating. The analyzing method is provided for solving the problem that the bearing capacity of a hydrostatic guideway is affected due to the fact that the upper bearing surface and the lower bearing surface of the hydrostatic guideway deform under the effect of oil pressure. According to the hydrostatic guideway bearing capacity analyzing method considering guideway surface deformation, based on the Reynolds equation, pressure intensity distribution inside an oil cushion is obtained after the Reynolds equation is simplified, and deformation distribution of the guideway is obtained by introducing a one-dimensional elastic body balance differential equation. In the obtaining process, the differential equation is converted into a difference equation according to the finite difference method, and obtaining is accelerated through Gauss-Seidel iteration and primary and secondary super-relaxation iteration. Firstly, the Reynolds equation is solved, so that the pressure intensity distribution of oil is obtained, and the pressure intensity is taken as the external force condition to be substituted into the elastic body balance differential equation, so that deformation of the guideway below the oil cushion is obtained. The deformation is taken as the oil film thickness change condition to be substituted into the Reynolds equation, so that more accurate pressure intensity distribution is obtained. Loop iteration is conducted till a calculation result meets the precision requirement, and the change of the bearing capacity is analyzed according to the calculation result.

A guidance, navigation and control (GNC) system guides an aircraft based on a special partial differential equation (PDE). The system does not depend on a predetermined desired flight path. To overcome effects of unpredictable wind speed and direction, systems and methods effectively repeatedly determine the worst landing the wind can cause and issue flight control commands that minimize among these worst outcomes. A function C that satisfies the PDE calculates smallest miss distance a guidance system can bring about by appropriately steering an aircraft, given the aircraft's current heading, current location relative to a target and current remaining amount of time to fly. The system repeatedly determines at least a component of a current gradient of the function C. A value of the gradient component is used to select an appropriate flight control command, such as turn left or turn right.

The invention provides a method for designing a flexible mechanical arm disturbance observer based on a partial differential equation. The method includes the four steps that firstly, dynamic modeling of a flexible mechanical arm is conducted; secondly, the disturbance observer is designed; thirdly, stability of the disturbance observer is verified; fourthly, design is finished. According to the method, firstly the Hamilton principle is used, so that a PDE model of a whole system is obtained; then, based on the model, the reasonable disturbance observer is designed so that external unknown disturbance can be estimated; finally, a proper Lyapunov function is designed, so that the designed observer is analyzed and the stability of the observer is verified.