52 results about "Differential of a function" patented technology

The invention discloses an orbital uncertainty analysis method based on differential algebra technology. Based on Taylor expansion of multivariate functions and polynomial operation framework, and based on the dynamic model of geosynchronous satellite orbit element description, solar pressure to the kinetic model, the third gravitational perturbation and the three perturbation terms of the Earth'soblateness are added in the dynamic model , the right term of the dynamic model is expanded along the nominal orbit by Taylor expansion, the expansion polynomial with initial deviation as variable isobtained, Under the frame of differential algebra, the orbital state expressed by the polynomial with the initial deviation as variable at any time is obtained, and the concrete value of the initialdeviation is brought into the polynomial result to obtain the state of the final spacecraft. The invention analyzes the optimal expansion order, the balance calculation time and the calculation precision according to different perturbation forces. The method can be used to analyze the orbit evolution of geostationary satellites with initial state deviation and parameter uncertainty, and can also be used in other spacecraft orbit evolution and attitude evolution missions.

A method of on-track detection for MTF (modulation transfer function) of an interference hyperspectral imager includes: firstly, reading an interference data graph of the hyperspectral imager and subjecting interference data of the hyperspectral imager to discrete inverse discrete Fourier transformation to obtain a spectral data graph of the interference hyperspectral imager; secondly, selecting a 'knife-edge' image module from the spectral data graph of the hyperspectral imager and calculating proper effective wavebands of the MTF of the interference hyperspectral imager according to SNR (signal to noise ratio) of the image module; thirdly, extracting knife-edge points from the knife-edge image module in the effective waveband, and fitting the knife-edge points to form ESF (edge spread function); fourthly, subjecting the ESF to differential computing, fitting results of differential computing to obtain LSF (linear spread function), and subjecting the LSF to discrete Fourier transformation to obtain the effective wavebands of the MTF of the interference hyperspectral imager; and fifthly, averaging the effective wavebands of the MTF to finally obtain overall MTF of the interference hyperspectral imager.

The invention provides a fractional differential-based multi-feature combined sparse representation tracking method. The method includes the following steps: in a frame of particle filtering, first, performing partitioning processing on a target image region, dividing the target region into 9 related and unequal subblocks according to the features of the target region, extracting the gray scale feature and HOG feature of each subblock, combining the two features to perform sparse representation on a target subblock, and also performing the same feature extraction and sparse representation on 8 adjacent regions around the target; then, adopting a nucleating accelerated neighbor gradient algorithm to jointly solve sparse coefficients of 9 candidate particles; and finally, regarding target blocks in different positions as different categories, utilizing a block of the same category as a candidate particle block and a representation coefficient in a dictionary to reconstruct the block, and building a likelihood function according to a reconstruction error to determine an optimal candidate particle, thereby realizing accurate tracking of a main target and 8 auxiliary targets.

The invention discloses a three-step three-order pre-estimation correcting method for wind wheel vortex line control equation discretion. According to the method, when a vortex convection control equation is solved according to a free vortex back track method, a linear display three-step method is adopted for a time step differential for pre-estimation, an implicit linear three-step method is used as a corrector step, a three-step pre-estimation correcting differential format for solving a vortex line control equation is formed, and three-order precision is obtained. By the adoption of the method, iteration stability and iteration speed are improved when the non-constant aerodynamic characteristic of a wind turbine is calculated according to the free vortex back trace method, the calculation time is greatly shortened, and the calculation accuracy can be improved.

The polyase chain-reaction biochip temperature control method includes: Set up integrating factor, when the error is greater, make the controller reach output saturation in a short time, the temperature rises or drops at full speed, relatively weaker controller saturation degree has guaranteed very fast speed of desaturation. When the error is less, uses ordinary integrating function to dispel the stable state error after the desaturation. Set up suitable factor of proportionality, enter the false integrating saturated condition fast with the auxiliary controller when the error is greater. Use the integrating function to resist the exceed adjusting when the error is less, uses ordinary proportion function to output steadily after the desaturation.

This invention is based on a new class of mathematical transforms named Rao Transforms invented recently by the author of the present invention. Different types of Rao Transforms are used for solving different types of linear/non-linear, uni-variable/multi-variable integral/integro-differential equations/systems of equations. Methods and apparatus that are unified and computationally efficient are disclosed for solving such equations. These methods and apparatus are also useful in solving ordinary and partial differential equations as they can be converted to integral/integro-differential equations. The methods and apparatus of the present invention have applications in many fields including engineering, science, medicine, and economics.

For the control problem of a non-affine nonlinear uncertain system, the invention relates to a two-speed adaptive proportional-derivative (2SAPD) control method independent of a controlled object model. According to the control method in the invention, system dynamics and internal and external uncertainty are defined as total disturbance; therefore, the non-affine nonlinear uncertain system is converted into a linear uncertain system, so that an error dynamics system under total disturbance excitation is constructed; thereby, a two-speed adaptive proportional-derivative control model by takingthe central speed factor as the core is designed; the facts that a closed-loop control system composed of a 2SAPD controller has the global asymptotic stability robustness and the 2SAPD controller also has good anti-disturbance robustness are theoretically analyzed; and the two-speed adaptive proportional-derivative control method in the invention has wide application value in the fields of power, mechanisms, chemical engineering, traffic, aviation, spaceflight and the like.

The invention discloses an inductance current interrupted mode fractional order switch converter symbol analysis method combining a harmonic wave balance principle; the method converts differential operation relating to status variable fractional order in a converter into differential operators, and combines all differential operators into an opposite angle symbol matrix, thus converting a non-integer order calculus operation solving process into a matrix operation and linear equation (group) solving process. Compared with a conventional normal analysis method, aiming at the fractional order switch converter, of building an Oustaloup filter approximation model in a Matlab/Simulink, the novel method can parse and analyze converter status variable ripple peak-to-peak value size and influences on converter work status by energy storage element order changes, can fast obtain a status variable stable state periodic analytic solution, and can parse status variable harmonic wave components.

The invention discloses a single-speed adaptive proportional-derivative control method which does not rely on a controlled object model for the control difficulty of the non-affine nonlinear uncertainsystem. According to the control method, the system dynamic and internal and external uncertainty are defined as sum disturbance, so that the non-affine nonlinear uncertainty system is transformed into a linear uncertainty system, and then an error dynamic system under the sum disturbance excitation is constructed, and the single-speed adaptive proportional-derivative controller model with the speed factor as the kernel is designed accordingly. Theoretical analysis shows that the closed-loop control system composed of SAPD controller not only has global asymptotic stability and robustness, but also has good anti-disturbance robustness. The invention has wide application value in the fields of electric power, machinery, chemical industry, transportation, aviation and aerospace.

The invention discloses a nonlinear system state deviation evolution method based on differential algebra and Gaussian sum. The method includes forecasting the terminal state of a nonlinear system according to a differential algebra method, and representing it as a high-order Taylor expansion polynomial related to original-state deviation; determining a sub Gaussian distribution covariance matrix, and fitting a Gaussian sum model for each sub Gaussian distribution through shooting; calculating the high-order central moment of the sub Gaussian distributions; determining the mean value and the covariance matrix of each sub Gaussian distribution at the terminal moment, and providing a terminal-state deviation distribution probability density function in the form of the Gaussian sum. The method can be extended to any designated-order deviation evolution accuracy automatically, manual derivation of high-order partial derivatives of kinetic equations is not needed, the method is applicable to long-term forecasted nonlinear system deviation evolution analysis problems with high nonlinearity, the remarkable efficiency advantages of the method can be still maintained as compared to the Monte Carlo simulation method while deviation distribution and non-Gaussianity thereof are described accurately, and accordingly, the method has the advantages of convenience in use and high calculation accuracy.

The invention provides an adaptive weight activity contour model construction method based on the fractional order differential information and a system. The system comprises an input module, an initiation module, a first calculation module, a second calculation module, a determination module and an output module. The system is advantaged in that fractional order differential is introduced, a new difference image is constructed, a local term is constructed by utilizing the difference image, and a new activity contour model is proposed; by utilizing the fractional order gradient mode information, one adaptive weight is proposed, so local and global terms of the model can be dynamically adjusted; by utilizing change of an inner area of an evolution curve, a new evolution stop standard is proposed, and the evolution curve can automatically stop at a correct boundary.

An image processing apparatus, including a filtering unit that performs filtering on an image using a second order partial differential and calculates a Hessian matrix and an evaluation unit that discriminates a structure included in the image using eigenvalues and eigenvectors of the Hessian matrix, in which the filtering unit includes a correction unit that performs filtering on the image using a first order partial differential of a function representing a hollow sphere having the same radius as the radius of the solid sphere and obtains first order partial differential vectors, and carries out correction to cancel out one of response waveforms of the function representing the solid sphere in each direction, the response waveforms appearing at two positions symmetrically separated with respect to the center of the solid sphere, using values obtained by projecting the first order partial differential vectors onto directions of the eigenvectors.

The invention relates to a fractional order differential compensation type VSG control method, which comprises the following steps: S1. In a closed-loop control loop of VSG grid-connected output active power Pout, a fractional-order differential compensation forward channel is added, wherein the fractional-order differential order is u, so that a closed-loop zero point is added on a closed-loop transfer function G1(s) of the VSG grid-connected output active power Pout, and the position of a closed-loop pole is changed, so as to obtain a closed-loop transfer function G3(s) of the fractional order differential compensation type VSG grid-connected output active power Pout, wherein u is more than or equal to 0 but less than or equal to 1;S2,.An improved biogeography optimization algorithm (IBBO) is used to solve the optimal u, and then an optimal closed-loop transfer function G3(s) is obtained. According to the invention, by adding the closed-loop zero point and introducing the adjustableparameter u at the same time, the contradiction between the dynamic performance and the steady-state performance adjustment of the VSG is decoupled, namely the steady-state performance of the system is ensured to be unchanged, and meanwhile, the degree of freedom of the dynamic performance of the system is increased by changing the position of the zero pole, and the dynamic performance of the active power is improved.

The invention discloses a transfer function model identification method with a differential characteristic process. According to the method, first, step response dynamic characteristic test data of the process is acquired through a field test; second, three characteristic parameters of a step response curve of the process are calculated according to the test data, wherein the three characteristicparameters include time T<0> corresponding to an extreme point of the curve, a corresponding extreme value K<m> and time T<q> corresponding to an inflection point of the curve before the moment T<0>;and last, according to the characteristic parameters T<q>, T<0> and K<m>, parameters of a process transfer function model (shown in the description) are calculated, wherein the parameters include a transfer coefficient K, a time constant T<c> and an order n. The method is simple and easy to implement and brings convenience to engineering application.

The invention provides a method capable of accurately acquiring a precision annealing temperature. The acquisition method for the precision annealing temperature comprises the following steps: (1) heating a material, and obtaining a heat expansion curve; (2) carrying out first-order differential on the heat expansion curve to obtain a heat expansion first-order differential curve; (3) when a beginning conversion temperature Tg0* of the heat expansion first-order differential curve is a lowest annealing temperature, the first-order differential curve displays that length variation occurs per unit time; when the conversion temperature Tg1* of the heat expansion first-order differential curve is a best annealing temperature, determining the relaxation state of the material to be optimal, wherein the relaxation state of a glass micro structure is an optimum value eliminating the stress. By utilizing the first-order differential curve of the heat expansion curve, the lowest and optimum annealing temperatures needed in a glass or ceramic annealing process can be rapidly and accurately obtained.

The present invention discloses a differential algorithm based on an FIR (finite impulse response) filter. The differential algorithm based on the FIR filter is a novel differential computation method designed according to features of an actual transformer vibration signal and an idea of a minimum mean square error; a filter length self-adjusting strategy is adopted; the length of the filter is gradually changed and finally, a differential result is optimized (as shown in figures) by a linear adjusting method; the problem of a large result error span, which is obtained in different frequency ranges, of differential computing results obtained by conventional FIR filtering is solved; and the differential algorithm is applicable to research on the power transformer vibration signal.

A method for stably solving an electric field integral equation in a time domain is disclosed. Another form of a thin-line time-domain electric field integral equation suitable for a finite differencesolution is deduced, and in the fine wire structure, symbols shown in the description are considered to be the line current and charge density respectively. The invention does not need to introduce an expansion function, directly discretizes the temporal and spatial differentials of the unknown current, and further advances the solution in time.

The invention discloses a multi-mode Lamb wave signal separation method based on a fractional differential. The method comprises the following steps that: (1) calculating the Fourier transform of a multi-mode signal; (2) calculating the fractional differential of an amplitude spectrum; (3) calculating the multinomial coefficient of the fractional order and the fractional differential maximum valueof the amplitude spectrum of a Gaussian model; (4) calculating an amplitude spectrum parameter; (5) on the basis of the Gaussian model, calculating the amplitude spectrum; (6) calculating a phase spectrum; (7) extracting a single-mode Lamb wave signal by the amplitude spectrum and the phase spectrum; and (8) removing a mixed signal of which the signal is extracted, and repeating the above steps to realize the separation of each mode. Compared with the prior art, the method can extract the single-mode characteristic parameter of a multi-mode mixed signal through the fractional differential soas to more favorably keep the detail characteristic of each mode signal, each-mode characteristic parameter can be effectively extracted, and each-mode amplitude spectrum reconstruction is realized soas to realize the separation of the multi-mode mixing signals.