34 results about "Systems of partial differential equations" patented technology

The invention relates to the field of acoustics, in particular to a method for quickly calculating characterization and transfer of uncertainties of marine environment and sound fields. The invention aims to solve the problems of random spectrum characterization of uncertain environmental parameters and uncertain sound pressure fields and whether to transfer the uncertainties form the environmental parameters to the sound pressure fields. The method comprises the following steps of: establishing a domain space taking the known quantity as a center for the uncertain environmental parameters and the uncertain sound pressure fields respectively; performing the probability density function description on the uncertain quantity; and chaotically carrying out the random spectrum characterizationaccording to a polynomial taking the probability density function as the uncertain quantity, and further combining the chaotic random spectrum characterization of the polynomial and a certain wave equation, educing the random wave equation embedded with uncertainty, acquiring the system of partial differential equation of uncertain coefficients, and finally acquiring the uncertain sound pressure fields formed by the linear superposition of the chaos based function of the uncertain coefficient weighting polynomial. The method has the advantages that: the acquired uncertain sound pressure fields are the same as the result acquired by MonteCarlo, and the calculating speed of the method is improved by more than 10 times.

An online measurement method and measurement apparatus for a residual stress of a conductive thin-film material (1). The method comprises: using an electrostatic driving pull-in principle to design a measurement structure; using synchronous processing to control relevance between parameters of two measurement members (104-1, 104-2); by means of limiting relevant parameters of total strain energy of the two measurement members (104-1, 104-2), constraining a partial differential equation set of the total strain energy thereof; and by means of solving the partial differential equation set, obtaining unknown numerical values of residual stress σ0 and Young's modulus E of the two measurement members (104-1, 104-2).

The invention relates to a divisional application of an invention with the application number being 202010752659.8. The invention discloses an online monitoring method for key process parameters of a drying cylinder of a paper machine, which comprises the steps of establishing a quaternary partial differential equation set process model which takes the temperature (Tp) and the humidity (u) of paper at a monitoring part of a drying part and the temperature (Ta) and the humidity (AHa) of air in a bag area at the monitoring part as unknown quantities through conservation of materials and energy in the drying process, then taking process data which is easily acquired in real time in the actual papermaking drying production process as a known quantity, an initial value and a boundary condition, and solving the quaternary partial differential equation set process model established in the invention to obtain real-time data of key process parameters of a papermaking drying part, thereby achieving online monitoring of the paper drying process, avoiding black box operation, being capable of accurately mastering the operation condition of the drying part of the paper machine, and providing possibility for evaluation of the drying capacity and the energy efficiency level of the drying part of the paper machine.

The invention relates to a high accuracy surface modeling method based on big data. The method comprises the following steps: creating geographic coordinate information and to-be-tested variable sampling values of all sampling points; turning a to-be-tested regional space into a grid point form through discretization, and establishing a sampling equation; conducting high order difference discretization on a partial differential equation set of a surface, obtaining a corresponding algebraic system, combining the algebraic system and the sampling equation to form an equality constrain least squares problem, converting the problem into a solve cross cutting object function minimum value problem, and then converting the minimum value problem into a solve symmetry indeterminate equation set; randomly selecting iteration initial values; blocking a coefficient matrix, and storing the block matrixes after decomposition; solving an HASM equation set through a block line projection iterative method, and determining whether a solving result is convergent; determining whether a solution meets demands of a Gauss and C.odazzi equation set; and outputting a high accuracy simulation surface model. Large-scale problems can be solved, the needed storage space is small, and defects of HASM for solving large-scale problems are prevented.

The invention discloses a design method for a large-view non-distortion rearview mirror. The method includes the steps that initial design parameters are input and set; based on a light ray reflection basic principle, a system of partial differential equations is established; according to the initial design parameters, image points and coordinate algebraic expressions of object point coordinates, the system of partial differential equations is solved through a step-by-step integration method and according to an appointed integral path, and height values of all discrete points on a mirror face of the designed rearview mirror are obtained; after deviation of the height values of all the discrete points on an xy plane is eliminated, rotary and symmetric polynomial fitting is conducted; and an equation of the face shape of the smooth and continuous large-view rearview mirror is obtained, and data required for machining of a numerical control machine tool are generated. The requirements for image non-distortion, the large view and the distance reality sense can be met at the same time, the rearview mirror which has the reasonable view amplification multiplying power and accords with the habits of a driver can be designed, and the rearview mirror can be used as any of outer rearview mirrors and inner rearview mirrors on the left side and the right side of various types of vehicles and can adapt to various appearances and sizes.

The invention relates to a flight icing numerical value simulation method of a helicopter rotor wing. The flight icing numerical value simulation method is mainly characterized by comprising the following steps that: a vorticity compensation force algorithm is added into a momentum equation and an energy equation in a single fluid model used for vortex movement used for simulating air-super cold water drop two-phase flows under a rotating coordinate system in rotor wing trail traces, and a centrifugal force and geostrophic force algorithm is added into a super cold water drop sliding velocity equation; a water film movement and icing model of the centrifugal force and the geostrophic force is considered; and the algorithms and the models are used for carrying out the flight icing numerical value simulation flow process of the helicopter rotor wing, wherein the model of single fluid two-phase flowing used for simulating the simulating air-super cold water drop movement is realized by a partial differential equation group for describing the movement of air and air-super cold water drop binary mixtures in a rotor wing tail trace flow field, and a two-phase flow slipping speed model. The condition that the quality and energy changes are generated in water films and ice layers because of the rotary movement of the rotor wing is considered in the model of the water film movement and icing process on the rotor wing surface, and the icing shape of the rotor wing surface is obtained.

The invention discloses a distribution type multi-sensing cooperation testing method and a system thereof; the method includes the following steps that: a multi-sensing cooperation testing model is established; area vectors of the area are obtained, and the area vectors of the area are automatically converted to the adjoint vectors; a plurality of systems of partial differential equations are converted to one or a plurality of sequence parameter equations, by the self organization evolution of sequence parameters, a macrostructure is created and a general calculation formula of the uncertain problem decision-making is obtained, wherein a 'cooperation-competition-coordination' process based multi-sensing cooperation testing mechanism model is established, which forms a three-layer reaction type cooperation testing method. The system includes that the data communication is made in the mode of the IPv4 / IPv6 based Ethernet, wherein the whole network testing platform comprises a filed test control layer, an enterprise-level monitoring layer and a remote test control layer.

The invention relates to a high-precision curve modeling intelligent method and a high-precision curve modeling intelligent device. The high-precision curve modeling intelligent method comprises the following steps of: building geographical coordinate information of sampling points and variable sampling values to be detected; dispersing regional spaces to be detected into grid points, and building sampling equations; carrying out high-order difference dispersion on systems of partial differential equations represented by a first fundamental quantity and a second fundamental quantity, and obtaining dispersion equation sets; randomly selecting iterative initial value of high-precision curve modeling equation sets; adopting a preset conjugate gradient method to solve the high-precision curve modeling equation sets, and judging whether solving results are constricted or not; and further judging whether the solution of the high-precision curve modeling equation sets meets a Gauss-Codazzi equation set or not, and outputting a high-precision stimulated curve model relative to a variable to be detected. The high-precision curve modeling intelligent method and the high-precision curve modeling intelligent device perfect and develop the existing model, improve the model precision, give a model stopping criteria, solve a sensitive problem to an initial value, solve a boundary shaking problem generated in the former interpolation, and improve the interpolation precision in the boundary.

Systems and methods are provided for use in predicting sand production in a geomechanical reservoir system. Computation of the sand production predictions can include solving a system of partial differential equations that model the geomechanical reservoir system. Systems and methods also are provided for use in operating a geomechanical reservoir system based on the sand production prediction for controlling sand production in the geomechanical reservoir system.