11 results about "Eigenfunction" patented technology

The invention discloses a critical parameter prediction method for a vertical cantilever fluid conveying pipe comprising a water injection pump and a Y-shaped nozzle, and relates to the field of fluid conveying pipe critical parameter calculation. The prediction method is based on an Euler-Bernoulli beam model and a momentum theorem, bending force, centrifugal force, Coriolis force, inertia force, gravity and additional force generated by an elbow are comprehensively considered, and an oscillatory differential equation of the fluid conveying pipe is established. The method comprises the following steps: performing dimensionless processing on an oscillatory differential equation by introducing dimensionless parameters, deducing a characteristic equation, a characteristic function and a characteristic value under a cantilever boundary condition, converting a partial differential equation into an ordinary differential equation set, and performing matrix solution; and finally, accurate prediction values of the critical flow velocity and the critical frequency can be obtained. The method can effectively reflect the influence rule of the nozzle and the concentrated mass on the vibration characteristics of the fluid conveying pipe, and realizes the accurate prediction of the critical parameters of the vertical cantilever containing the concentrated mass belt Y-shaped nozzle fluid conveying pipe.

The invention discloses an integral transformation fracture phase field model implementation method of a random-order polynomial cohesion law, and belongs to the technical field of phase field model finite element analysis. The method comprises the following steps: inputting a parameter equation of a polynomial cohesion law of any order and a target order into a subprogram; deducing a cohesion eigenfunction of a random-order polynomial cohesion law by using a subprogram to determine an analytical expression of a random-order polynomial energy density eigenfunction, solving a target-order polynomial energy density eigenfunction expression and first two-order derivatives thereof, and determining an expansion expression at a zero point by using Maclaurin series; and inputting the target-order polynomial energy density eigenfunction expression, the first two-order derivatives thereof and the expansion expression at the zero point into a phase field model solver to obtain a calculation result of the target-order polynomial integral transformation fracture phase field model. According to the method, the simulation calculation of the integral transformation fracture phase field model of the target-order polynomial cohesion law can be realized under a universal finite element framework, and the accuracy and the efficiency are improved.

The invention discloses a three-phase current-based power transmission line ground fault phase identification method, system and device and a medium, and belongs to the technical field of ground fault identification, and the method comprises the steps: calculating a virtual space derivative of a zero-sequence current according to a time derivative of a three-phase current transient component and a line distributed capacitance parameter, and forming a space-time coupling tensor; performing spatial modal decomposition by adopting an intrinsic function of the zero-sequence traveling wave equation to obtain spatial modal coefficients of all orders; constructing a phase sequence leakage matrix by taking the spatial modal coefficient as a weight; performing singular value decomposition on the phase sequence leakage matrix, and extracting main singular vector feature parameters; transforming the composite mapping matrix to obtain an island vector; determining a suspected fault phase according to the projection coefficient energy ratio of the island vector; and reversely solving the distributed capacitance and calculating a theoretical value, and outputting a final fault phase when the deviation between the theoretical value and the measured value meets a condition. According to the method, accurate fault phase identification under high-resistance grounding and long-distance line working conditions is realized through virtual space derivative mapping and modal energy decomposition.

The invention discloses a multi-suspended-span elastic bearing fluid conveying pipe stability parameter prediction method, and relates to the technical field of fluid conveying pipe vibration characteristic analysis. A multi-suspended-span pipeline is divided into a plurality of independent pipe sections at the supporting position, vibration control equations for describing all the suspended-span pipelines are established respectively, and the vibration control equations only consider the coupling effect of bending force, centrifugal force, gravity, Coriolis force and inertia force of the pipeline and do not contain any middle supporting constraint term; the intermediate support constraint is completely written into the cross-coupling boundary condition, so that the defects that the traditional Dirac function method is fuzzy in significance and the numerical calculation is difficult to converge are avoided; carrying out dimensionless processing on an oscillatory differential equation by introducing a dimensionless parameter, deducing to obtain a characteristic equation, a characteristic function and a characteristic value under the complex boundary condition by combining the end elastic boundary and the cross coupling constraint, converting a partial differential equation into an ordinary differential equation set, and carrying out matrix solution, so as to obtain an oscillatory differential equation set; and finally, an accurate prediction value of the inherent frequency can be obtained.

The application discloses a kind of multi-span elastic supporting flow pipe stability parameter prediction method, it is related to flow pipeline vibration characteristic analysis technical field.By splitting the support position of multi-span pipeline into multiple independent pipe sections, vibration control equations describing each span pipeline are established respectively, the vibration control equations only consider the coupling effect of bending force, centrifugal force, gravity, coriolis force and inertia force of the pipeline, and do not contain any intermediate support constraint term;The intermediate support constraint is completely written into the inter-span coupling boundary condition, which avoids the defects of ambiguous meaning and difficult to converge in numerical calculation of traditional Dirac function method;By introducing dimensionless parameters to dimensionless the vibration differential equation, combined with the above elastic boundary and inter-span coupling constraint, the characteristic equation, characteristic function and eigenvalue under the complex boundary condition are derived, and the partial differential equation is converted into a system of ordinary differential equations after matrixization solution, and finally the accurate prediction value of natural frequency can be obtained.

The application relates to the field of water conservancy and hydropower engineering, and particularly discloses a soil-rock dam foundation three-dimensional space variability simulation method based on an intermittent Galerkin method, which comprises the following steps: establishing a geometric model of a soil-rock dam foundation; determining probability distribution information of a three-dimensional random field of soil parameters; dividing the three-dimensional random field domain of the soil parameters into three-dimensional random field subdomains; creating base functions in the three-dimensional random field subdomains and assembling a generalized stiffness matrix; calculating eigenvalues and eigenfunctions of an autocorrelation function; extracting standard normal distribution samples and simulating the three-dimensional random field of the soil parameters. The three-dimensional random field domain is divided into a plurality of subdomains, and independent base functions are constructed in each subdomain, so that the independence between the base functions in the subdomains is ensured. The numerical instability of high-order polynomials is eliminated, the assembly format of the generalized stiffness matrix is simplified, and the three-dimensional random field with large scale and high resolution can be generated.

The invention discloses a calculation method of an integral transformation fracture phase field model of an exponential cohesion law, and belongs to the technical field of finite element analysis of phase field models. The method comprises the following steps: deducing a cohesion eigenfunction of an index cohesion law by using a subprogram, deducing an analytical expression of an index energy density eigenfunction, and solving the expression of the index energy density eigenfunction and first two-order derivatives thereof by adopting multiple integral transformations, the Maclaurin series is adopted to determine an index energy density eigenfunction expression and an expansion expression of the first two-order derivatives at the zero point of the index energy density eigenfunction expression; and inputting the index energy density eigenfunction expression, the first two-order derivatives of the index energy density eigenfunction expression, and the expansion expression of the index energy density eigenfunction expression and the first two-order derivatives of the index energy density eigenfunction expression at the zero point into a solver for performing an integral transformation fracture phase field model to perform phase field model simulation calculation. According to the method, the simulation calculation of the exponential integral transformation fracture phase field model can be realized under a universal finite element framework, and the accuracy and the calculation efficiency are greatly improved.

The invention discloses a calculation method of an integral transformation fracture phase field model of a PPR cohesion law, and belongs to the technical field of finite element analysis of phase field models. The method comprises the following steps: inputting a PPR potential into a subprogram; deriving a cohesion eigenfunction of the PPR cohesion law by using a subprogram, and after obtaining an analytical expression of a PPR energy density eigenfunction conjugated with the cohesion eigenfunction based on integral transformation, solving an expression of the PPR energy density eigenfunction and first two-order derivatives thereof by using a complex Simpson integral; determining an expansion expression of first two-order derivatives of the PPR energy density eigenfunction by adopting Maclaurin series; inputting the PPR energy density eigenfunction expression, the first two-order derivatives of the PPR energy density eigenfunction expression and the corresponding expansion expression into a solver to obtain a simulation calculation result. According to the method, the simulation calculation of the integral transformation fracture phase field model of the PPR cohesion law can be realized under a universal finite element framework, and the accuracy and the efficiency are improved.

The application discloses a kind of vertical cantilever flow pipe critical parameter prediction methods containing water injection pump and Y type nozzle, it is related to flow pipe critical parameter calculation field.Prediction method is based on Euler-Bernoulli beam model and momentum theorem, the additional force generated by bending force, centrifugal force, coriolis force, inertia force, gravity and bend is considered comprehensively to establish the vibration differential equation of flow pipe.By introducing dimensionless parameter to vibration differential equation, the characteristic equation, characteristic function and eigenvalue under cantilever boundary condition are deduced, and after partial differential equation is converted into ordinary differential equation group, it is solved by matrixization.Finally, the accurate prediction value of critical flow velocity and critical frequency can be obtained.The method can effectively reflect the influence law of nozzle and concentrated mass on the vibration characteristics of flow pipe, and realize the accurate prediction of the critical parameters of vertical cantilever flow pipe with Y type nozzle and concentrated mass.

This invention discloses a method, system, device, and medium for characterizing the intrinsic features of spatial field strength distribution. It verifies the existence of intrinsic features by constructing characteristic basis functions of the field strength distribution, then establishes an eigenvalue set through eigenmode decomposition, and iteratively solves the corresponding constraint functions. The final eigenvalue dataset is used to characterize the intrinsic features of the spatial field strength distribution, improving the feature analysis capability of electromagnetic information in the spatial domain. Based on a reasonable characterization of the intrinsic features of the field strength distribution, it uses sparse space construction as a breakthrough to reduce the sampling rate and the non-correlation of the sampling matrix and sparse basis as constraints to construct sparse basis and sampling methods. This combines basic electromagnetic field theory, signal processing methods, and mathematical theory, filling the gap in the theoretical research on the construction of characteristic functions in the spatial domain for electromagnetic signal time-frequency analysis.

Embodiments of the present disclosure relate to a method for determining relationship between molecules and an electronic device. The method comprises: determining a first chemical feature of a first molecule based on eigenfunctions of a Laplacian operator on a surface Riemannian manifold of the first molecule; determining a second chemical feature of a second molecule based on eigenfunctions of the Laplacian operator on a surface Riemannian manifold of the second molecule; determining a functional mapping matrix between the first chemical feature and the second chemical feature by a functional mapping; and determining a similarity between the first molecule and the second molecule based on the functional mapping matrix. In this way, embodiments of the present disclosure can determine a functional mapping matrix based on chemical features determined based on eigenfunctions of a Laplacian operator on a Riemannian manifold, so that the similarity between different molecules can be compared in a manifold space. This avoids comparing the three-dimensional geometric structure of molecules by alignment and the like, reduces the amount of calculation, and improves the efficiency of processing.