51 results about "Legendre polynomials" patented technology

The invention relates to a method for testing the key performance of a drive shaft assembly of a constant velocity universal joint in the technical field of automobile part test. The method comprises: (1) automobile steering equivalent testing: using a Hermite interpolation method to locate a critical point, judging the boundary value of neighborhood of the critical point by a cubic interpolation polynomial, thereby realizing the testing on high precision swing moment and swing angle properties; (2) equivalent testing on integrated relationship of mobile terminal universal joint displacement, swing angle and sliding force: using an inflection point subdivision sampling method and an optimal square approximation method to carry out fitting on the boundary value of the neighborhood of an inflection point by a Legendre polynomial operator, thereby realizing the testing on the integrated relationship of the displacement, the swing angle and the sliding force; and (3) power transmission stability equivalent testing: using a LOG operator to carry out precise edge localization of the boundary position,and using an optimal uniform approximation method to carry out fitting on the boundary property value in the domain of the critical point, thereby realizing the testing on assembly clearance property. In the invention, high precision automatic detection technology and algorithm are used to test multiple key performance indexes, thereby effectively reflecting the performance property of tested products.

The invention discloses an improved method for calculating three-dimensional neutron flux density fine distribution of a reactor core. The method comprises the following steps that 1, modeling is conducted on the reactor core, needed parameters are calculated, and variables are initialized; 2, a radial leakage item is unfolded in the axial direction through a Legendre polynomial expansion, a one-dimensional discrete ordinate difference equation is calculated according to information obtained in the step 1, and an axial leakage item is acquired; 3, two-dimensional spatial distribution of the axial leakage item is obtained through calculation, two-dimensional transportation calculation is conducted according to the information obtained in the step 1, and neutron flux density distribution, a cell-homogenized cross section and the radial leakage item are acquired; 4, whether a characteristic value and the three-dimensional neutron flux density are convergent or not is judged, if not, iteration is continuously conducted from the step to the step 2 till the problems are convergent, and then three-dimensional neutron flux density fine distribution is obtained. According to the method, Legendre polynomial expansion unfolding is conducted on the radial leakage item in the axial direction, the calculation precision is improved, and two-dimensional spatial distribution of the axial leakage item is calculated, so that calculation is closer to true conditions.

The invention belongs to an imaging method for nonlinear frequency modulation label change in the synthetic aperture radar imaging technology, which comprises the steps of two-dimensional frequency domain unfolding, filtering processing, nonlinear frequency modulation label change, distance compression, distance migration correction, rest phase compensation and position compression. In the method of the invention, the characteristics of orthogonality and minimum square error of the Legendre polynomials are utilized for carrying out three-order unfolding on the two-dimensional frequency domain signals of the obtained echo signals according to the Legendre orthogonality polynomials, and then, the focusing imaging on targets is realized through carrying out filtering processing and the like on three-order phase items in echo signal two-dimensional frequency domain expression. When the method of the invention is adopted, the maximum phase error under the same condition is less than 0.2 percent of the maximum phase error in the prior art, so the assurance is provided for the high-precision imaging under the large-inclination view angle condition. Therefore, the method of the invention has the characteristics that the phase error in the imaging process can be effectively reduced, the imaging processing of the large-inclination view angle is realized, in addition, the imaging effect is good, the imaging processing efficiency and the precision are high, and the like.

The invention discloses an intelligent setting method for the on-line target strip shape of a cold rolling strip. The intelligent setting method comprises the following steps that a strip shape curve is divided into an original strip shape detection curve, a technology error strip shape compensation curve and a target strip shape curve, wherein the original strip shape detection curve and the technology error strip shape compensation curve are overlaid to form an effective actually-measured strip shape curve which is called the effective strip shape curve for short, and the target strip shape curve only needs to consider a strip shape control target for the follow-up process requirement; an on-line strip shape target curve is built on the basis of a quartic Legendre polynomial, the self-balanced constraint condition requirement (that is, the transverse integration in the width direction of the strip is zero) of the residual stress deviation of the rolled strip in the width direction of the strip is met, the target is clear, and the function is explicit; and a target strip shape standard curve library is built on the basis of an intelligent algorithm, the optimal parameter of the on-line target strip shape is obtained, and the control precision of the strip shape is ensured.

The invention discloses a comprehensive regulation and control method of high-order local flatness defect of ultra-thin cold-rolled strip steel with a high width-to-thickness ratio. The comprehensive regulation and control method comprises the following steps of: establishing a flatness pattern recognition model based on super high-order Legendre orthogonal polynomials, to be specific, selecting appropriate Legendre polynomial degrees according to number of channels of a detecting roller and stated standard error requirements, which describes the measured high-order flatness state of the cold-rolled strip steel, avoids the error message of local high points or low points and reduces the calculated amount of an evaluation function; establishing an efficacy evaluation function grading regulation and control model based on high-order flatness pattern recognition: to be specific, adopting a first-grade regulation and control efficacy function based on Legendre polynomials according to typical regulation and control measures of a tilting roller, a bending roller and lateral movement; and establishing a second-grade regulation and control efficacy function based on local high-order flatness according to a segmented cooling regulation and control measure.

The invention discloses an intelligent and comprehensive evaluation method for cold-rolled strip steel plate shapes. The method is used for carrying out comprehensive evaluation on the macroscopic plate shapes and all plate shape components based on the fuzzy comprehensive evaluation theory and the fuzzy neural network theory and combined with the plate shape theory and a plate shape online detection method. The method includes the steps of carrying out online real-time pattern recognition on the plate shapes in a pattern recognition method based on the Legendre polynomial least square method, then building a plate shape comprehensive evaluation index model based on the fuzzy comprehensive evaluation theory, meanwhile, building a T-S type fuzzy neural network by using data of the macroscopic plate shapes and data of all the plate shape components, and carrying out comprehensive evaluation on an average value of the macroscopic plate shapes and an average value of all the plate shape components. According to the intelligent and comprehensive evaluation method for the cold-rolled strip steel plate shapes, the data of all the plate shapes are organically combined to build the comprehensive evaluation index model, and intelligent and comprehensive evaluation on plate shape quality is achieved.

A method for decoding data symbols modulated with a corresponding codeword from a constellation set of codewords expands the constellation set of codewords with a set of basis functions to produce a basis-expanded constellation set and projects projecting a received modulated data symbol onto orthogonal complements of the basis expanded constellation set to obtain a set of distance metric of a generalized likelihood ratio test (GLRT) for each codeword of the constellation set. The set of basis functions includes a Fourier exponential basis function in a frequency domain, a Legendre polynomial basis function in a time domain, and a Fourier-Legendre product basis function in the frequency domain. The method selects a codeword corresponding to a minimal distance metric or a maximal correlation metric and decodes the data symbol from the received modulated data symbol using the codeword.

The invention relates to a high-efficiency system for the dynamic optimization of an industrial process. The system comprises a field intelligent instrument, a DCS system and an upper computer, wherein the field intelligent instrument is connected with an industrial process target. The upper computer comprises an initialization module, a variant configuration module, a constraint enforcement module, a model transformation module and an NLP solution module, wherein initialization module is used to set initial parameters; the variant configuration module is used to conduct Lagrange interpolation conversion and to take the root of Legendre polynomials as a configuration point; the constraint enforcement module is used to enforce constrains on control vector u (t) and time division length hi; the model transformation module is used to discretize a dynamic optimization model, to increase state vector continuity conditions and the constraint conditions of the constraint enforcement module, and to convert an infinite dimensional dynamic optimization problem into a finite dimensional nonlinear programming problem; and the NLP solution module is used to solve the finite dimensional nonlinear programming problem obtained by the model transformation module. The invention additionally provides a method for the dynamic optimization of the industrial process. The invention hast the advantages that the optimum solution to the complex nonlinear dynamic optimization problem can be accurately found, the convergence rate is very high and the applicability is wide.

The invention discloses a PSWF (Prolate Spheroidal Wave Function) pulse generating method in a communication system, and relates to a pulse generating method based on a normalized Legendre polynomial, which comprises the following steps of: computing the coefficient of the normalized Legendre polynomial according to the duration T and the bandwidth B of a pulse to be designed, and establishing a coefficient lookup table on the basis; when the pulse is generated, obtaining the coefficient of the normalized Legendre polynomial from the coefficient lookup table according to a design parameter, and generating a required PSWF pulse through the mode of the weighted sum of the Legendre polynomial. The coefficient of the normalized Legendre polynomial is only stored in the coefficient lookup table, so that fewer storage spaces are needed, and the hardware complexity is reduced. The PSWF pulse can be generated in real time in the invention according to the requirements of system frequency spectra. The PSWF pulse generated by the invention can be dynamically adapted to the requirements of the system frequency spectra.

A method is disclosed for reflection time shift matching a first and a second set of seismic reflection data (10,30) comprising first and second seismic reflection traces (1,3) with series of generally corresponding seismic reflections (11,31). The second set of seismic data (30) comprises at least one laterally extending series (40) of new seismic events (4) not present in the first set of seismic data (10). Reflection time shifts (22) are calculated as required for matching seismic reflections (31) of the second reflection traces (3) of the second seismic reflection data (30) with corresponding seismic reflections (11) of the first reflection traces (1). The calculation of the time shifts (22) are made by calculating coefficients of basis function estimates such as Legendre polynomials in order to save calculation effort.

The invention discloses a construction and inversion method for a vegetation height inversion model based on a second-order Fourier-Legendre polynomial. According to the construction method, first, anSAR image of a vegetation coverage vertical structure is acquired, polarization interference processing is performed, and a polarization multiple correlation coefficient gamma(omega) is generated; second, the vegetation coverage vertical structure corresponding to the SAR image is expressed into the second-order Fourier-Legendre polynomial; and last, the polarization multiple correlation coefficient gamma(omega) is used as an observation value to establish the vegetation height inversion model based on the second-order Fourier-Legendre polynomial on the basis of Fourier-Legendre coefficientsa<00>, a<10> and a<20>, vegetation height h<v> and surface elevation h<g>. According to the vegetation height inversion model in the scheme, vegetation height, surface elevation and the Fourier-Legendre coefficients used for expressing the vegetation coverage vertical structure are organically combined into the same function equation to serve as model parameters, and the vegetation height inversion model is established, so that the modeling process is simple and clear, and implementation is easy.

The present invention provides systems and methods for modeling the impact of a medium on the appearances of encompassed light sources using a Legendre polynomial series solution to a Radiative Transfer Equation for Spherical Media (RTE-SM) called an Atmospheric Point Spread Function (APSF). Using this APSF, it is possible to determine characteristics of the medium causing the multiple scattering of the light from the encompassed light source. For example, by observing a street light in bad weather at night, using the APSF, it is possible to determine whether the bad weather is haze, mist, fog, or rain. Similarly, the APSF may be used to estimate the size of particles in a liquid. It is also possible using the APSF to remove and / or add an effect of the medium on a light source captured in an image.

The invention discloses an illumination method based on picture level images. The method mainly includes the steps that an illumination equation is resolved through a particular solution Legendre polynomial in a Legendre equation; spherical harmonic coefficients are utilized, a resolved function is projected through a spherical harmonic function, and then the restored illumination equation is obtained; the illumination value of an environment map and the color value of a map are multiplied, and the obtained result is the final pixel color value. According to the illumination method based on the picture level images, the defects that in the prior art, the image processing difficulty is large, the image quality is poor, and the simulation effect is not good can be overcome, and the advantages that the image processing difficulty is small, the image quality is good, and the simulation effect is good are achieved.

The invention discloses a method for calculating a coefficient of any order in a neutron transport discrete nodal method. The method mainly comprises the steps of 1, performing form simplification: performing form simplification on complex source coefficient, flux coefficient and coupling coefficient by introducing an intermediate coefficient; 2, performing integral transformation: transforming an integral, appearing in the source coefficient, the flux coefficient and the coupling coefficient, of an exponential function and Legendre polynomial product into an integral of the exponential function and general polynomial product according to properties of a Legendre polynomial; and 3, performing analytic solving: analytically deriving accurate expressions and recursive relations of an intermediate integral through a mathematic method, substituting an intermediate integral value accurately solved by a computer into expressions of the source coefficient, the flux coefficient and the coupling coefficient after integral transformation, and obtaining accurate values of the source coefficient, the flux coefficient and the coupling coefficient of any order in combination with an intermediate coefficient value as a known condition, wherein the accurate expressions and the recursive relations do not contain complex integral operations and are easily realized by computer programming.

The invention provides a method for controlling edge flatness defects of cold-rolling strip steel. The method includes the following steps that 1, the flatness deviation is calculated; 2, a flatness deviation compensation scheme is as followings: the flatness deviation value of each section is compensated directly, and meanwhile, different compensation coefficients are applied to the flatness deviations of the first section, the second section and other sections of the edge of the strip steel; 3, the flatness deviation compensation condition is as followings: only when the two sides of the edge of the strip steel have flatness defects at the same time, can they be compensated; 4, the compensation coefficients for the flatness deviations of the strip steel of different specifications are calculated; 5, calculation is performed after compensation, wherein least square fitting is performed on the flatness deviation after compensation, then mode decomposition is conducted through the legendre polynomial expansion to obtain the quadratic flatness deviation coefficient and the quadratic flatness deviation coefficient, and finally a flatness control system adjusts the flatness deviation according to the obtained flatness deviation coefficient. Effective and fast control over strip steel edge flatness defects is achieved by changing the strip steel edge flatness defect adjustment rateof the flatness control system.

The invention discloses a high-precision numerical value method for solving an interval heat convection diffusion problem. The high-precision numerical value method comprises the following steps: establishing a heat transfer control equation of the heat convection diffusion problem; introducing an interval variable to represent the uncertainty of an input parameter in a heat transfer model, and establishing an interval control equation of the heat convection diffusion problem; utilizing a Legendre polynomial expansion to carry out approximate representation on temperature response in the interval control equation; according to tensor product operation, determining a collocation point set in a high-dimension space; utilizing a finite element program to calculate the temperature response of all collocation points, establishing a linear equation set in regard to an expansion coefficient in a temperature response approximate expression, and adopting a least square method to solve; and on the basis of the smoothness of a polynomial function, determining an extreme point of the temperature response approximate expression, and obtaining the upper bound and the lower bound of interval temperature response. The high-precision numerical value method can systematically solve the heat convection diffusion problem with interval uncertainty parameters and effectively improves the calculation precision of the interval numerical value method.

Provided is a guided wave and fuzzy algorithm-based functional gradient structural material characteristic inversion method. The guided wave group velocity is obtained through forward calculation by applying a Legendre polynomial method, and a volume distribution function of FGM structural material parameters is subjected to inversion identification by means of a fuzzy algorithm. The method comprises the specific steps that 1, a given FGM structure volume distribution function is selected, and the guided wave group velocity in the FGM structure is obtained through a Legendre polynomial method; 2, a fuzzy controller is designed through a genetic algorithm; 3, a fuzzy controller parameter optimization program based on the genetic algorithm is written; 4, a fuzzy controller program is written; 5, multiple guided wave group velocities at the FGM structure low order mode low frequency are input into the designed fuzzy controller, and the FGM material characteristics are output through inversion. Accordingly, an error between a parameter value in the FGM structure volume distribution function obtained through inversion and a set value is very small, and an effective method is provided for FGM material characteristic detection.

A method is disclosed for reflection time shift matching a first and a second set of seismic reflection data (10,30) comprising first and second seismic reflection traces (1,3) with series of generally corresponding seismic reflections (11,31). The second set of seismic data (30) comprises at least one laterally extending series (40) of new seismic events (4) not present in the first set of seismic data (10). Reflection time shifts (22) are calculated as required for matching seismic reflections (31) of the second reflection traces (3) of the second seismic reflection data (30) with corresponding seismic reflections (11) of the first reflection traces (1). The calculation of the time shifts (22) are made by calculating coefficients of basis function estimates such as Legendre polynomials in order to save calculation effort.

The invention relates to the advanced manufacturing field, particularly to a method for forecasting milling stability based on Legendre polynomial expansion. According to the method, the Legendre polynomial expansion is adopted to approximate a state item, a time-lag term and a periodic coefficient item in a kinetic equation, and a plurality of known time points and responses thereof are used for fitting the items required, so that the partial error of the calculation method is reduced, thus the precision of the forecast method is improved. Meanwhile, in the process of obtaining a stable lobe graph, an H matrix is introduced rather than being directly put into an F matrix to calculate, so that iterative times in the calculation process of the F matrix are reduced, thus the time of the calculation method is saved, and the calculation efficiency is improved.

The invention discloses a geomagnetic model online approximation method based on a Legendre polynomial and a BP neural network. The method includes the following steps that: 1, position information and aircraft navigation error which are indicated by a current integrated navigation system, and the measured value of a geomagnetic sensor are read; 2, a Legendre polynomial model is established according to a priori geomagnetic map; 3, a BP neural network is constructed, with the position information and aircraft navigation error adopted as input, the difference value of the measured value of thegeomagnetic sensor and the read value of the Legendre polynomial adopted as output, the constructed BP neural network is trained, so that the expression of input and output can be obtained, and geomagnetic model error at the current moment is obtained according to the read position information and aircraft navigation error; and 4, the geomagnetic value of the geomagnetic model at the current position at the current moment is corrected. The method is applicable to the measurement modeling of a regional geomagnetic assisted inertial navigation system and can realize the online approximationof the geomagnetic model, improve the accuracy of the geomagnetic model, and improve the positioning accuracy of the integrated navigation system.

The present invention realizes a Doppler velocity detecting technique capable of performing velocity detection and analysis with a suppressed error while excellently distinguishing a clutter signal, and provides an ultrasonographic device using the technique. In a Doppler velocity detection device comprising means for transmitting / receiving pulse waves to / from a subject a plurality of times, and velocity analyzing means for analyzing a velocity of a moving reflector in the subject on the basis of a reception echo signal, the velocity analyzing means obtains a complex expansion coefficient by linearly connecting an expansion coefficient of an even-numbered degree term and an expansion coefficient of an odd-numbered degree term which is different from the even-numbered degree term by one degree, derived when reception echo time-series signals obtained by arranging reception echo signals of equal lapse time from pulse transmission times in order of the transmission times are expanded as components of a Legendre polynomial starting from the 0th degree, by using an imaginary unit as a coefficient, and obtains a signed velocity signal of a moving reflector in the subject on the basis of-the ratio between the magnitude of each complex expansion coefficient and the magnitude of an interval between the complex expansion coefficients.

The invention provides a synchronous phasor measurement method, and the method comprises the steps: carrying out the fitting of a signal through employing a synchronous phasor dynamic model and a Legendre polynomial; calculating a fitting coefficient, and obtaining an instant synchronous phasor. The method provided by the invention reduces the matrix condition number, can carry out the accurate and quick measurement of the phasor, and improves the measurement precision of the phasor.

The invention discloses a low peak-to-average ratio orthogonal pulse modulation method based on a Legendre polynomial. The method comprises: orthogonal pulses used for modulating data adopting elliptic spherical wave function pulses with the same channel bandwidth, mutually aliasing frequency spectrums and orthogonal time domains; wherein the elliptic spherical wave function pulse is generated byadopting a Legendre polynomial weighted combination; discretizing the orthogonal pulses to form an orthogonal basis matrix; constructing a dimension reduction matrix of the orthogonal basis matrix, wherein the row number of the dimension reduction matrix is smaller than the column number; carrying out left multiplication operation on the orthogonal basis matrix and the dimension reduction matrix to realize dimension reduction processing; data information to be transmitted being subjected to serial-parallel conversion to form a multi-path parallel data group, the multi-path parallel data groupand the orthogonal basis matrix subjected to dimension reduction processing being subjected to left multiplication operation, completing data modulation, and forming a path of modulation signal through time domain signal superposition. According to the method, the practicability of the ellipsoidal wave function in the quadrature modulation technology is improved, and meanwhile, the peak-to-averageratio of multiple paths of quadrature modulation signals is inhibited.

The invention discloses a blank initial residual stress high-precision reverse calculation method based on a deformation test, and the method comprises the steps: determining a deformation measurementpoint of a to-be-measured part according to the thickness of an aluminum alloy blank plate, and obtaining a flexibility matrix of the measurement point through employing a finite element method; Measuring the actual deformation value of the part measuring point by using a three-coordinate measuring machine; processing the to-be-detected part to meet the size requirement by using high-speed processing, and solving equivalent residual stress in the rolling direction and the transverse direction; residual stress in the rolling direction and the transverse direction of the part is obtained. In the method for testing the initial residual stress of the blank, the determination of the Legendre polynomial order is determined according to the principle that the stress uncertainty is minimum, and the method can specifically refer to a calculation method of the stress uncertainty of a crack flexibility method. The method provided by the invention is simple, high in measurement precision and easyto realize on site.

The invention belongs to the technical field of detection, and discloses a mass distribution identification method, device and equipment of a composite material beam and a storage medium, and the method comprises the steps: obtaining a front-order modal function of a composite material cantilever beam; wherein the positive integer is a preset positive integer and is greater than 1; according to the front-order modal function, solving a Legendre orthogonal polynomial-based main mass orthogonal equation to obtain a front-order Legendre polynomial coefficient; based on a Legendre orthogonal polynomial, calculating the linear density of the composite cantilever beam according to the Legendre polynomial coefficient of the front order; therefore, the mass distribution condition of the composite cantilever beam can be accurately identified.

The invention discloses an SFO and CFO combined estimation method based on maximum likelihood estimation, and aims to solve the problems that the computational complexity is high due to two-dimensional global search, and the high-SNR (Signal Noise Ratio) error floor estimation accuracy cannot continue to converge in the existing SFO and CFO combined estimation method. The technical solution is that the method comprises the following steps: determining a range of SFO, transforming the range of SFO into a range of variable t, using first-order Legendre polynomial to approximate a formula I shown in the description to obtain first-order Legendre polynomial approximant, substituting the approximant into a formula II shown in the description to obtain t; transforming a final estimation value eta' of SFO by t; obtaining an estimation value epsilon' of CFO by the eta'. The SFO and CFO combined estimation method based on maximum likelihood estimation does not require the two-dimensional global search, so that the computational complexity is reduced greatly, meanwhile, the problem of error floor in high SNR in the existing estimation method is eliminated, and the estimation accuracy is improved.

The invention relates to a global ionosphere TEC model forecasting method and system, wherein the method comprises the steps: extracting a periodic term of a global ionosphere TEC model spherical harmonic function coefficient time sequence through employing fast Fourier transform, carrying out the fitting estimation of a spherical harmonic coefficient through employing a trigonometric series function, and forecasting a short-term spherical harmonic function coefficient; and generating a global forecast ionosphere TEC model according to the forecast spherical harmonic coefficient. According to the invention, the spherical harmonic function is adopted to describe the spatial-temporal change characteristics of the ionized layer TEC, the model is simple, and the operability is high; wherein the spherical harmonic function takes an orthogonal Legendre polynomial as a primary function and can represent physical meanings of the ionized layer TEC related to geographic latitude and geographic longitude; thus, not only is the trend term of the ionized layer TEC considered, but also the random change characteristic of the ionized layer TEC is considered.

The invention discloses a vegetation height inversion method and device based on two SAR images, wherein the method includes: when there are only two SAR images covering the same area, performing polarization interference processing on them to obtain a single baseline omnipolar Calculate the complex coherence coefficient; determine the spatial domain range; construct the Fourier-Legendre polynomial vegetation height inversion model based on two SAR images; determine the unknown The initial value of the parameter; according to the above-mentioned initial value of the parameter and the inversion model of the vegetation height, combined with the spatial domain, the vegetation height is obtained by using a nonlinear iterative algorithm. The invention solves the problem of limited expansion order of the existing single-baseline Fourier-Legendre polynomial model, and increases the expansion order of the Fourier-Legendre polynomial model when there are only two SAR images. Applicability and flexibility.

The invention discloses an LED nonlinear compensation method, system and device based on a Legendre polynomial and a medium, and belongs to the technical field of optical communication. The LED nonlinear compensation method comprises the following steps: acquiring a distortion signal; using a Legendre polynomial for carrying out feature broadening processing on the distorted signals, and obtaining an orthogonal function set; performing nonlinear compensation on the orthogonal function set to obtain an output signal; and updating the structure coefficient of the nonlinear compensator according to the output signal and the reference signal, and feeding back the updated structure coefficient to the nonlinear compensator. According to the LED nonlinear compensation method based on the Legendre polynomial, nonlinear compensation can be carried out on LED distortion signals of different modulation formats in different application scenes, and the applicability is high.