73 results about "Stochastic differential equation" patented technology

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.

The invention discloses a space debris recovery control method based on a tethered technology. The space debris recovery control method is characterized by comprising the following steps that 1, the tether elasticity is considered, a space tethered debris system is researched by adopting an elastic rod module, and a system dynamics differential equation is built according to a class II Lagrange equation; 2, the system dynamics equation in the step 1 is rewrote into a non-dimensional system dynamics equation; 3, the in-surface outer pivot angle vibration abatement problem of nonlinear time-varying system dynamics equation in the recovery process is researched, and the tether length change analysis control law and the in-surface pitch angle value range in the expectation equilibrium position in the debris recovery process are inferred; and 4, the stability of the system and the value range, keeping stable asymptotically, of a pitch angle in an expectation surface are further analyzed through the Floquet theory. Through the space debris recovery control method, the effect that debris is stably recovered nearby an on-orbit spacecraft can be ensured, and meanwhile the safety in the recovery process especially the safety in the end time can be ensured.

The invention provides a simulation generation method for wind speed data of multiple wind power farms. The method includes the steps that according to historical data of wind speeds of the multiple wind power farms, delay time among the wind speeds is determined; a model for the wind speeds of the multiple wind power farms is constructed through a Copula function theory, and the constructing step includes the substeps that marginal distribution of all the wind speeds is determined, the suitable Copula function model is selected, model parameters are estimated, and the model is evaluated; the wind speeds of the multiple wind power farms are generated according to the constructed Copula function model; the wind speeds generated in a simulation mode are reconstructed and adjusted in the aspect of the time sequence through a stochastic differential equation and a delay relation. The simulation generation method for the wind speed data of the multiple wind power farms can meet fluctuation characteristics of the respective wind speeds of the wind power farms and the cross correlation among the wind speeds of the multiple wind power farms.

The invention provides an under-actuated release control method based on a nonlinear space tether system. The method comprises the following steps: 1, a dumbbell model is adopted, system dynamics differential equations are built according to a second kind Lagrange equation, and a dimensionless form is introduced in the differential equations; 2, based on a normal form expression for the above dynamics differential equations, expected values for a system in-plane pitching angle and an out-plane rolling angle are set, and the balance position of the system in the release process is obtained; 3, starting from the balance position of the system, a tether length change control law for realizing tether release is deduced and obtained; and 4, the range for the expected in-plane pitching angle is determined to ensure the tether release process to be asymptotically stable under effects of the control law. Numerical simulations show that the space tether can be released asymptotically stably under effects of the release control method provided by the invention, and an attractor capable of covering the balance point and an attraction domain with enough thickness can be found out.

The invention provides a stochastic partial differential equation based wind speed fluctuation characteristic modeling method, comprising steps of: according to sample wind speed data, constructing a stochastic partial differential equation about wind speed variation, and obtaining a typical wind speed variation sequence by solving the stochastic partial differential equation; then, by fitting a probability distribution function of the sample wind speed, randomly generating a wind speed sequence, and using the solved typical wind speed variation sequence to reconstruct the random wind speed sequence according to the principle of least square method, thereby obtaining a final wind speed model; finally, verifying correctness of the modeling method through comparison with a measured wind speed sequence. The method provided by the invention can effectively depict the real wind speed fluctuation characteristics, and overcome the problem that the existing wind speed model can only consider the probability distribution of wind speed from one aspect; the wind speed model established by using the method provided by the invention can not only reflect the conditions of the probability distribution of wind speed, but also show the fluctuation characteristic of the wind speed within a required study period.

The invention belongs to the field of power systems, and particularly relates to a method for analyzing the stochastic stability of an electric power system containing wind electricity. The method includes the steps that a stochastic differential equation is used for conducting modeling on stochastic disturbance existing in the system, an applicable stochastic stability definition is provided, the stochastic differential equation theory, an Ito formula and a stochastic Lyapunov energy function method are used for finding out a practical stochastic asymptotically mean square stability criterion, and a stochastic stability criterion of a system with uncertain state matrix parameters is derived. According to the method, the essence of the stochastic stability can be revealed more accurately, the defect that a deterministic analysis method is not accurate enough can be overcome, a model can be made to be more accurate, and a new theory and a new method can be provided for improving system control; the stochastic stability definition suitable for a electric power time-varying parameter system is provided from the point of a stochastic system is provided; a practical stability criterion of a stochastic time-varying parameter system of the electric power system is provided; compared with other methods, the method has conciseness and practicability.

A method of tracking and inferring the underlying dynamics of a tagged molecule in a living cell may include receiving an ordered data set of time-valued location observations of the molecule, dividing the data set into time windows, and assigning a stochastic differential equation (SDE) model to each of the time windows with a set of parameters. The method may also include fitting the SDE models assigned to each of the plurality of time windows using likelihood-based techniques, and determining an initial value for each parameter. The method may further include fitting the set of parameters for each of the SDE models using a nonlinear maximum likelihood estimation search, applying an optimization routine to generate a set of computed parameters, determining whether the computed parameters are valid using goodness-of-fit tests, and determining whether each of the SDE models is valid based on the goodness-of-fit-tests.

The invention belongs to the technical field of spacecraft landing and returning, and relates to a method for analyzing the uncertainty of a drop point of planetary atmosphere entering into a lander. The method comprises the steps of: carrying out Askey orthogonal polynomial approximation on the system state based on the uncertainty distribution of an initial state of the system; then taking the state into the system dynamics; transforming a stochastic differential equation for representing the original system into an equivalent high dimensional certainty differential equation based on a Galerkin projection rule; and finally acquiring an orthogonal polynomial coefficient of each state for representing the system state by a Runge-Kutta equivalent numerical integration method so as to obtain a statistical property of the system state. In the whole process, an orthogonal polynomial basement is self-adaptively adjusted according to the statistical property of the lander state to overcome influences caused by truncation errors. According to the method, the statistical property of the system state can be accurately estimated and the calculating efficiency is effectively improved.

The invention discloses a simplified analysis method for an inherent frequency and the stability of a rotational symmetric structure. The method comprises the steps of establishing a complete dynamic differential equation of a system, a dynamic differential equation adopting a no-extension hypothesis, and a dynamic differential equation adopting an extension hypothesis: establishing the complete dynamic differential equation of the system; establishing the dynamic differential equation adopting the no-extension hypothesis; establishing the dynamic differential equation adopting the extension hypothesis; introducing coordinate conversion for converting the three dynamic differential equations to a support follow-up coordinate system so as to obtain corresponding three constant coefficient partial differential dynamic equations; performing discrete processing on the three constant coefficient partial differential dynamic equations in the support follow-up coordinate system to obtain three constant differential matrix equations; obtaining an eigenvalue of the complete dynamic differential equation and eigenvalues of two simplified dynamic differential equations; and analyzing a parametrically excited vibration mode characteristic and a dynamic stability change law of the rotational symmetric structure according to the three eigenvalues. According to the method, a specific analysis expression of system eigenvalues can be obtained more clearly.

The invention discloses an underground perforation test tool string optimization method based on packer stress analysis. The method comprises the steps that S1, a tubing string-shock absorber-perforating gun dynamic model is established; S2, an oscillatory differential equation of a perforated string is established; S3, an oscillatory differential equation of a shock absorber is established; S4, a tubing string-shock absorber-perforating gun coupled oscillation equation is established; and S5, a tubing string-shock absorber-perforating gun partial differential equation is solved. The method has the advantages that research about influences of the length of an oil tube and the explosive charging amount of a perforating bullet on underground tools is carried out, and the stress of a packer is increased along with increase of the length of the oil tube according to the research; the portion, prone to spiral buckling, of the oil tube is at a certain position at the bottom and in the middle of the oil tube; the tension and pressure borne by the oil tube are increased sharply along with increase of the explosive charging amount, so that the oil tube is prone to spiral buckling more easily, and theoretical guidance is provided for string design; the damage risk of a tubular column is lowered; and the underground tools are protected.

The invention belongs to the technical field of open source software reliability models, and particularly relates to an open source software reliability modeling method based on random fault introduction. According to the invention, the method comprises the steps: employing a stochastic differential equation for simulating a fault introduction process in an open source software development process, establishing a corresponding open source software reliability model, estimating model parameters by adopting a least square estimation (LSE) method, and employing three fault data sets from an Apache open source software project for comparing model performance. Comparison is carried out by using a closed source software reliability model and an open source software reliability model which are completely debugged and incompletely debugged, and the proposed model has optimal fitting and prediction performance. Therefore, the random change of the fault introduced by the open source software isconsidered, and the actual change of the introduced fault in the open source software development process is met. The model can be used as a tool for evaluating the reliability of the open source software, and helps developers or managers to manage and evaluate the software quality in the development process of the open source software.

The invention provides a rapid cable temperature calculation method based on parameter fitting.The method includes the steps that firstly, according to cable laying characteristics, a heat circuit method is adopted, a transient cable temperature heat circuit model for parameter fitting is established, and a cable temperature differential equation is listed and written; aiming at a certain specific working condition of a cable, the cable gets into a zero initial state, rated currents are applied to the cable, and the cable core and surface temperatures of the cable generated when the cable temperature reaches a stable state are measured; according to the actually-measured cable core and surface temperatures of the cable, heat capacity and heat resistance heat parameters in the cable differential equation are fit through a trust region algorithm; finally according to the fit heat parameters, a cable temperature transient heat circuit is solved, the cable temperature is obtained, and a calculation equation is simplified.According to the rapid cable temperature calculation method based on parameter fitting, transient heat parameters of a conversion model can be rapidly acquired in combination with the actually-measured temperatures under the rated transmission capacity of the cable, the simplified calculation equation of the cable core and surface temperatures of the cable is obtained, and the purpose of rapidly calculating the cable temperature is achieved.

The invention provides a control method of an automobile active suspension system. The control method includes the following steps that an active suspension system model of automobile wheels is established, according to the model, a dynamic differential equation of the vehicle active suspension system is established, and a state space equation of the vehicle active suspension system is obtained, in consideration of the uncertainty of the system, a controller of the active suspension system under the disturbance condition is designed, and substituted into a simulation system to be subjected toa simulation test, and thus the performance of the designed controller is verified. According to the control method of the automobile active suspension system, the output feedback H<infinite> controller considers the condition of total four factors including the system parameter uncertainty, the actuator delay, the road surface unevenness disturbance and the sensor measurement output disturbance,the active suspension system is controlled, and the controller has the wider adaptability.

The invention discloses an optimal linear quadratic Gaussian control method for a discrete system and particularly relates to a linear quadratic Gaussian control technology. The method is based on a discrete time optimal linear quadratic Gaussian (LQG) control problem of multi-time-lag and state/control related noise. The method comprises the following steps of deriving a maximum principle of a linear quadratic Gaussian system with multi-time-lag and state/control related noise by using a variational method, obtaining a solution of forward-backward reverse stochastic differential equations (FBSDEs) composed of an adjoint equation and a balance condition through a mathematical induction method, based on the solution of the FBSDEs, sufficient necessary conditions for THE existence of an optimal linear quadratic Gaussian controller are given, and an explicit solution and a minimum quadratic performance index of the optimal controller are obtained.

The invention provides a backward stochastic differential equation (BSDE)-based option pricing method and a BSDE-based option pricing device. The option pricing method comprises the following steps of: acquiring a spatial discrete grid and an isosceles triangle model which are constructed by a central processing unit (CPU) terminal by a many integrated core (MIC) processor and acquiring a terminal condition according to the spatial discrete grid; and performing Monte Carlo simulation on each spatial grid point on each time layer between adjacent time layers according to the terminal condition by the MIC processor, performing backward induction on all time layers one by one by using the isosceles triangle model, and finally calculating to obtain the mathematical expectation of the option price. According to the BSDE-based option pricing method and the BSDE-based option pricing device, the operation of the option pricing can be accelerated easily and greatly in a short cycle by a BSDE mode and concurrent computation capacity of the MIC processor.

The invention discloses a reservoir real-time flood control dispatching risk analytic calculating method considering error correlation. The method comprises the following steps of 1, putting forward amathematical expression of an indeterminate factor; 2, building a reservoir flood routing stochastic differential equation, and analyzing the mea value and variance of reservoir errors at each moment; 3, building a reservoir real-time flood control dispatching risk model, and analyzing the real-time flood control dispatching risk of the reservoir at each moment; 4, calculating the real-time floodcontrol dispatching risk of the reservoir. The influence of the reservoir inflow prediction error correlation coefficient on the reservoir real-time flood control dispatching risk is considered, thereservoir real-time flood control dispatching risk and whole flood process total risk analysis calculation formula can be obtained, and the method is high in calculation efficiency and easy to implement, and has the high universality.

The invention provides an option pricing method based on a backward stochastic differential equation (BSDE). The method comprises the following steps that: a central processing unit (CPU) is used for dispersing the BSDE on time layers, constructing space-time discrete grids, and calculating a terminal condition which is used for pricing option according to the space-time discrete grids; and performing Monte Carlo simulation on each space point of each time layer between neighboring time layers at a many integrated core (MIC) end according to the terminal condition, and solving a final option pricing mathematical expectation value by performing backward calculation on each time layer one by one. By the method, the powerful parallel computing capabilities of the BSDE algorithm and the MIC are utilized, and option pricing calculation can be accelerated by dozens of times; and meanwhile, because of simple, short-period and good-performance code transplantation on an MIC architecture, the method is low in cost and has high parallelism degree and high-speed operational performance.

The invention relates to a large unmanned aerial vehicle collision probability calculation method based on an STP model, and the method achieves the higher precision of a flight conflict detection model through the morphological optimization of the STP model and the introduction of a three-dimensional correlation stochastic differential equation and an elliptical STP model.

The invention belongs to the technical field of a modeling method, and discloses a wind speed fluctuation characteristic modeling method based on stochastic partial differential equations (SPDE). A wind farm modeling method is proposed to establish a wind farm stochastic model, the wind farm operating characteristics are simulated, in order to achieve predictable and controllable goal services of large scale wind power generation, through simulation comparison between a wind farm equivalent model and a detailed model, the rationality of the modeling method is verified, and a wind farm model considering random fluctuations in the wind speed and direction in the study of wind farm dynamic characteristics and the influence thereof on a power grid. The invention can adjust the predictable angles of fluctuation wind speed and direction randomly, and improves the wind speed fluctuation modeling method.

The invention discloses a control processing method and apparatus with minimum microgrid operation cost. The minimum operation cost of the whole controlled microgrid system is realized, and the main embodiment is that the service life of energy storage equipment can be prolonged to the maximum. The method comprises the steps of S1, modeling a microgrid scene in an offline state into a control system which is represented by a stochastic differential equation, and a target function, wherein a controller is arranged on a microcomputer; and the target function refers to the overall operation cost of the microgrid, comprising loss of the energy storage equipment and energy consumption caused by the controller; S2, solving the optimal controller according to the stochastic differential equation, wherein the target function value can be minimized by virtue of the optimal controller; and S3, inputting the optimal controller into the microgrid in a signal way.

The invention relates to a multi-breather realization method of an optical fiber system harmonic crystal lattice potential function, and belongs to the technical field of optical fiber communications. The method comprises the following steps: researching a non-linear BEC crystal lattice equation through a Riccati differential equation and linear variables separation method, constructing a plurality of exact solutions in variables separation modes of the system; properly setting any function in the solution to obtain multi-breather in different numbers. The problem that the multi-breather is hard to produce in the optical fiber communication technology is solved, the method provided by the invention is simple and easy to understand, convenient for realization, and strong in practicability; related parameters can be adjusted according to actual conditions so as to provide powerful support for the deep research on the field of optical fiber communication system and promote the development of the subject.