34 results about "Integro-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 discloses an engine suspension system optimization design method capable of considering the dynamic change of rigidity and damping due to excitation force. The method comprises the following steps: firstly, establishing a dynamics model of an engine suspension system; selecting a sample point in an interval formed by a suspension vertical static rigidity design range and an excitation frequency change range, calculating a dynamic rigidity and damping value corresponding to the sample point, carrying out data fitting, and establishing a prediction model; then, according to a multi-degree-of-freedom vibration theory, obtaining a vibration differential equation of the suspension system; solving the differential equation to obtain the inherent frequency of a six degrees of freedom of the suspension system and corresponding dynamic response, taking an integral sum of vibration transmissibility in a vertical direction on the centroid within a vibration frequency range as an optimization target, selecting four suspension vertical static rigidity values as optimization design variables, and taking the inherent frequency of the six degrees of freedom of the suspension system as a constraint condition; adopting a genetic algorithm to carry out optimization; and finally, verifying the feasibility of the method through a specific example. The engine suspension system optimization design method has integrity and practicality.

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 discloses a 3D TTI double-phase medium seismic wave field value simulation method based on a finite difference method. The 3D TTI double-phase medium seismic wave field value simulation method comprises steps of obtaining a solid and fluid stress tensor and a solid and flow strain tensor and transforming the tensors to a constitutive equation, obtaining a geometry equation according to the corresponding relation of stress and the displacement, obtaining a motion differential equation according to the constitutive equation, the geometry equation and the fluid motion relative to the solid and the corresponding relation between the stress and the displacement, taking the divergence on two ends of the motion differential equation to obtain a first longitudinal wave equation and a second longitudinal wave equation of the seismic wave, as for the first longitudinal wave equation and the second longitudinal equation, enabling a partial derivative to y to be zero and performing difference discrete on the space partial derivative and the time partial derivative by employing an 2N order precision expansion formula and a 2-order precision center difference form to obtain a first difference equation and a second difference equation, and performing boundary absorbing condition processing on the first difference equation and the second difference equation to obtain the corresponding seismic wave field value. The invention realizes the real-time transmission simulation of the physics seismic wave field.

A dynamic predictor usable for rapid and accurate calculation of joint commands of an articulated dynamical mechanism describes the relationship between the joints in the form of a differential equation. The predictor solves this differential equation for predicted joint states by fitting a polynomial equation having free parameters describing the predicted joint states to the differential equations by minimizing the differential equation residuals. This minimization employs a series expansion allowing algorithmic differentiation.

The invention discloses a method for estimating generated heat of a lithium ion battery under conditions of charge and discharge, and the method comprises the steps: firstly collecting temperature data of a to-be-detected lithium ion battery under the conditions of electric heating and charge and discharge; secondly inputting the temperature data of the battery under different electric heating power into data processing software, and determining the relation equation between the heat loss power and temperature of a lithium ion battery thermal runaway testing and analysis system through employing a thermal balance integro-differential equation (1) and a thermal balance integro-differential equation (2); thirdly inputting the temperature data of the battery under the conditions of charge and discharge into the data processing software, inputting heat, generated within a certain time period, of the lithium ion battery into the data processing software according to the heat of the lithium ion battery, which is obtained by a thermal balance integro-differential equation (3) and is generated within a certain time period, in a process of charge or discharge, and obtaining a relation curve between the charge / discharge heating rate and time and the total generated heat in the process of charge or discharge. The method takes the whole lithium ion battery as a research object, and can obtain the impact on the battery from the charge and discharge conditions.

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 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.

The invention discloses a decoupling design method for helicopter control, relating to the technical field of helicopters. The decoupling design method for a helicopter comprises the following steps: 1, establishing an aerodynamic force and moment model for a helicopter component, and substituting the obtained force and moment into a movement equation of six freedom degree to obtain a nonlinear differential equation set; 2, solving trim control amounts of control mechanisms in helicopter flight according to the nonlinear differential equation set; 3, determining a coupling relationship between the control mechanisms, and substituting the trim control amounts in the step 2 into the coupling relationship; 4, verifying that whether the design improves the driving quality or not via a flight simulation test; 5, carrying out flight testing. The decoupling design method disclosed by the invention has the advantage that in the flight process, the tail rotor tension and the horizontal trim can be automatically adjusted just by the total pulling moment. The control correction precision is improved, the workload of a pilot is reduced, and the requirements on driving skills of the helicopter are reduced.

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.

The invention discloses a delayed power system stability analysis method based on low-order EIGD (Explicitly Infinitesimal Generator Discretization). The method comprises the steps of establishing a delayed power system model for a power system, and linearizing the delayed power system model, that is, expressing the delayed power system model through a delayed differential equation; re-ranking state variables of the delayed power system in the delayed differential equation, and dividing the state variables into delay-independent state variables and delay-dependent state variables; transformingthe delayed differential equation into an ordinary differential equation by use of an infinitesimal generator, thereby equivalently transforming a characteristic equation of the delayed power systeminto an ordinary characteristic equation, and further transforming calculation for characteristic values of the delayed power system into calculation for characteristic values of the infinitesimal generator. According to the delayed power system stability analysis method based on the low-order EIGD, through re-ranking of the state variable of the system, discretization of the delay-independent state variables is removed, the number of dimensions of a discretization matrix is reduced, and therefore, the calculated amount for calculation of key characteristic values of a DCPPS (Delayed Cyber-Physical Power System) is reduced.

The invention discloses a method for realizing a perfectly matched layer through an auxiliary differential equation in plasma. The method comprises the following specific steps: 1, inputting a model file; 2, performing initialization and setting a parameter of the model file in the step 1; 3, calculating an electric field component coefficient E<y><q> by using the parameter in the step 2; 4, calculating an electric field component coefficient E<x><q> by using the parameter in the step 2; 5, calculating a magnetic field component coefficient H<z><q> by using the electric field component coefficients obtained in the step 3 and the step 4; 6, calculating intermediate variable coefficients psi<x><q> and psi<y><q> by using the electric field component coefficients in the step 3 and the step 4; 7, updating and calculating an auxiliary variable of an electromagnetic field component coefficient in a whole computational domain; 8, updating and calculating an electromagnetic field component of an observation point; and 9, assigning q+1 to q, judging whether q is up to a preset value or not, returning the step 3 if q is not up to the preset value, and ending if q is up to the preset value. The method has the advantages of low calculation speed, low memory consumption, and very good absorption effects on low-frequency and evanescent waves.

The invention discloses an analysis method of similar frequency-dependent delay electro-optic phase chaotic dynamics. The method is executed according to the following steps: step 1, building a dynamic mathematical model in a chaotic communication system; step 2, determining a relation between delay and frequency; step 3, dividing time interval and determining an equation initial value; step 4, solving a delay signal of each moment in one period of time after delay through Fourier time-frequency transformation; step 5, converting a delay differential equation into an ordinary differential equation; step 6, performing numerical solution for the ordinary differential equation of the step 5 through a Runge-Kutta method. The method provided by the invention can accurately solve a differential-integral equation having frequency-dependent delay, and can accurately analyze chaotic dynamics and chaotic communication having frequency-dependent delay feedback.

The invention relates to a one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm based on an auxiliary differential equation, and belongs to the technical field of numerical simulation. The method aims at reducing the left-handed material FDTD (Finite-Different Time-Domain) computational domain, and simulating a computer finite memory space into an infinite space. The one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm has the technical characteristics that in a process of converting a plurality of stretched coordinate variables from the frequency domain to the time domain, the second-order differential in the stretched variables is eliminated by an improved auxiliary differential equation method, so that the number of the introduced auxiliary variables is obviously lowered, and a memory is optimized; then, a time domain Maxwell equation is subjected to discretization by a Crank-Nicolson time domain finite differential method; an explicit iteration equation of an electric field is deduced out; and finally, a value of an electromagnetic field component is obtained. The one-dimension left-handed material Crank-Nicolson perfectly matched layer realizing algorithm has the advantages that the unconditional stability is realized; the electromagnetic calculation is accelerated; and the memory is saved.

The invention provides a seepage solving method based on conditions of seepage boundaries and a differential equation of motion. The method is characterized by comprising the following steps: step 1, accurately measuring macroscopic geometric features of a study object, and establishing a corresponding geometric feature description equation; step 2, studying seepage coefficient distribution features of the study object, and establishing seepage coefficient distribution equations of the study object in a study area; step 3, studying boundary condition flow and water head features of the study object, and establishing a corresponding boundary condition flow and water head expression equation; and step 4, selecting the water head expression equation to enable the same to meet the corresponding differential equation of motion and the flow and water head boundary condition equations, and carrying out solving for each corresponding constant coefficient. The provision of the method has a promoting action on seepage movement study and application of various built structures and natural bodies such as dams, slopes, subgrades, tunnels, roadways and culverts.

A safety design method for water tank used in airtightness test of aeroengine casing is disclosed. Based on the relevant technical parameters of the water tank and the machine case with specific requirements, By using the equations of motion and gas state, combining with dimensionless time and pressure and initial conditions, the second order differential equations of dimensionless pressure and flight angle of plug fracture are established, the differential equations can be used to calculate different internal pressures, the initial and angular velocities of the plug fragment as it exits at the debris size, and then the mechanics equation is established by using the fluid mechanics principle, a method for calculating the impact velocity of plug considering the resistance coefficient of medium is established, the theorem of kinetic energy and the law of conservation of energy are used to model and estimate the wall thickness of water tank, the impact force of plug fragment and the impact strength of fragment. In order to meet the needs of engineering calculation, a conservative formula for calculating the initial velocity of plug separation is established. Finally, the safety designscheme of water tank for aero-engine casing airtightness test which meets the technical requirements can be obtained.

Each ordinary differential equation of simultaneous ordinary differential equations is solved with an embedded Runge-Kutta method. A difference Δ between an N-th order approximation and an (N+1)th order approximation is computed, and it is determined whether the difference is smaller than a predetermined threshold Δ0. If Δ≦Δ0, then a step size is determined using a predetermined computation formula containing Δ0 / Δ, and then the process proceeds to next computation. A strand having an error of Δ>Δ0 is directed to execute recomputation using a step size calculated based on Δ0 / Δ. Then the strand having the error executes recomputation by using a computed interpolated value. When the strand's error becomes smaller than the threshold Δ0 the strand reaches the same time step as the strands computing the other ordinary differential equations having no error. The process thereby proceeds to next computation of the whole simultaneous ordinary differential equations.

The invention disclosed herein employs an algorithm, the Gas Formation Model (“GFM”), to calculate the formation of free gas in a human body. The GFM is based on a novel theory of the formation of free gas relative to the physiology of the human cardiovascular system. Additionally, the GFM utilizes a novel means for the solution of integro-differential equations, the type of equations that derive from the introduction of physiological parameters. GFM-based dive computers utilize novel inputs, including a measure of exercise at depth to reflect the state of an individual's cardiovascular system. GFM-based dive computers also produce novel outputs, including the actual volume of free gas present in a diver's cardiovascular system. The GFM is implemented as a practical computational tool by means of a incorporating the algorithm into a dive computer.

The invention provides a modeling method for an aircraft longitudinal phase plane directly based on a three-dimensional model. The built model performs equivalent transformation directly based on an aircraft three-dimensional motion model, and avoids incorrect direct approximate cuased by the aerodynamical moment effect, the lateral-directional influence and the like ignored in an aerodynamic force equation; an equivalent second-order differential equation set is obtained through a three-dimensional aircraft motion equation and aerodynamic force and aerodynamical moment models obtained through experiments; the equation set expresses a system stability model, can directly adopt a phase plane analytical method to perform theoretical analysis, or adopts an Ode45 module and the like in MATLAB (matrix laboratory) to dreictly perform numerical analysis; more non-linear phenomena and unstable factors and unsafe factors of the system can be found out; and problems of unstable and unsafe flight and the like are reduced or even avoided.

The invention discloses an analysis method of signal transmission and switching characteristics of a fiber bragg grating or a similar fiber bragg grating. The analysis method includes steps: 1 constructing a fiber bragg grating coupled mode equation, 2 determining the border and the starting condition of the fiber bragg grating, 3 performing mesh dividing, 4 discretizing a partial differential equation to an ordinary differential equation, 5 performing numerical solution for the ordinary differential equation obtained in the step 4 in a Runge-Kutta method, and 6 obtaining a transmission coefficient for representing the switching characteristics. The analysis method can accurately analyze the switching characteristics and the signal transmission characteristics, and the analyzed signal transmission characteristics can accurately reflect walk-off, amplitude and width change conditions of signals in the fiber bragg grating.

The invention relates to an electric quantity track sensitivity determination method. The electric quantity track sensitivity determination method comprises the following steps: establishing a differential equation or a differential equation set of a model of electric system equipment; converting the differential equation or the differential equation set into an integral equation; multiplying a state variable of equipment in the differential equation or the differential equation set by an integral equation coefficient to obtain an equation U X=Y; converting the equation into an equivalent equation through a least square method; and solving total differential of two sides of the equivalent equation to obtain track sensitivity to state variable parameters X by the integral equation coefficients U and Y. According to the technical scheme provided by the invention, the track sensitivity to power grid parameters or set parameters of each electric quantity is calculated in real time by using various electric energy tracks which are actually measured by a wide area measuring system (WAMS) of an electric system.

The present invention discloses an arbitrary order output method for a rigid body space motion state. According to the method, three velocity components of a machine shaft system and a three-ary number form a linear differential equation by defining the three-ary number; a state transition matrix can be solved according to a manner of an arbitrary order keeper so as to acquire an expression of a rigid body motion discrete state equation, such that the singularity problem of the attitude equation is avoided so as to acquire the main motion state of the rigid body. According to the present invention, the three-ary number is introduced, such that the state transition matrix is the block upper triangular manner, and can be solved by reducing the order so as to substantially simplify the calculation complexity, and be easily used by the engineering.

The invention disclosed herein employs an algorithm, the Gas Formation Model (“GFM”), to calculate the formation of free gas in a human body. The GFM is based on a novel theory of the formation of free gas relative to the physiology of the human cardiovascular system. Additionally, the GFM utilizes a novel means for the solution of integro-differential equations, the type of equations that derive from the introduction of physiological parameters. GFM-based dive computers utilize novel inputs, including a measure of exercise at depth to reflect the state of an individual's cardiovascular system. GFM-based dive computers also produce novel outputs, including the actual volume of free gas present in a diver's cardiovascular system. The GFM is implemented as a practical computational tool by means of a incorporating the algorithm into a dive computer.

The invention relates to a wind power plant output power short-term prediction method, which is used to solve a problem of a conventional prediction method of low precision. The wind power plant output power short-term prediction method comprises steps that step 1, an original sequence of historical data is used as input data for input; step 2, a primary accumulative array and a neighborhood value generating array are generated according to the step 1; step 3, a grey differential equation is acquired by adopting the data generated according to the step 2; step 4, the parameter value of the grey differential equation is calculated by adopting a least square method; step 5, the parameter value acquired by the step 4 is introduced in the grey differential equation to acquire a white differential equation, and a prediction data value is acquired by solving the white differential equation; step 6, whether the prediction value meets a requirement is determined, and when the prediction value meets the requirement, a prediction power value is output; when the prediction value does not meet the requirement, repeated superposition calculation is carried out, until the prediction value meets the requirement, and then the value is output. The wind power plant output power short-term prediction method is suitable for the wind power generation field.

The invention discloses a Chebyshev output method for the space motion state of a rigid body. The method comprises the steps of: defining a ternary number so that three speed components of the set of axes of the body and the ternary number form a system of linear differential equations; and performing approximation description on rolling, pitching and yawing angular speeds p, q and r by using Shifted Chebyshev orthogonal polynomials, wherein the state transfer matrix of the system can be solved in the manner of any order holder, thus obtaining the expression of the discrete state equation of the motion of the rigid body; and the problem of singularity of the attitude equation is avoided; therefore, the main motion state of the rigid body is obtained. The Chebyshev output method is characterized in that the ternary number is introduced so that the state transfer matrix is in the form of portioned upper triangles and thereby can be solved through deflation; therefore, the complexity of calculation is greatly simplified; and the Chebyshev output method is convenient for engineering use.

The present invention provides a method which is used for calculating Thevenin equivalent parameters of power system. The active power and reactive power of a tidal current equation are respectively used for differentiating the Thevenin equivalent parameters so as to form a total differential equation system; the total differential equation system is solved with the Thevenin equivalent parametersas variables, so as to acquire the Thevenin equivalent parameters. The method overcomes the serious error in the existing calculating which assumes the invariable Thevenin equivalent parameters between two time steps, has the characteristics of strong adaptability, simple use and small amount of calculation, and can be used for analysis, calculation and on-site installation of the power system which requires a Thevenin equivalent system.

The invention relates to a production method of grid multiple butterfly wing chaotic attractors. The production method comprises the following steps of scaling a three-dimensional Lorenz chaotic system according to ratio, increasing two first order differential equations, respectively adding a non-linear coupling controller containing a sectional linear function on the two added first order differential equations, and producing the grid multiple butterfly wing chaotic attractors; controlling the number of grid multiple butterfly wing chaotic attractors by parameters. The production method has the advantages that the more complicated chaotic signals can be provided, and more selections are provided for chaotic confidential communication.