33 results about "Nonlinear differential equations" patented technology

A method for the estimation of the state variables of nonlinear systems with exogenous inputs is based on improved extended Kalman filtering (EKF) type techniques. The method uses a discrete-time model, based on a set of nonlinear differential equations describing the system, that is linearized about the current operating point. The time update for the state estimates is performed using integration methods. Integration, which is accomplished through the use of matrix exponential techniques, avoids the inaccuracies of approximate numerical integration techniques. The updated state estimates and corresponding covariance estimates use a common time-varying system model for ensuring stability of both estimates. Other improvements include the use of QR factorization for both time and measurement updating of square-root covariance and Kalman gain matrices and the use of simulated annealing for ensuring that globally optimal estimates are produced.

The invention discloses a power system transient stability simulating method based on implicit numerical integration. Compared with an existing power system transient stability numerical simulation implicit trapezoidal integration method, the power system transient stability simulating method employs a power-angle integration formula with a smaller local truncation error, namely, enables a non-linear differential equation set for describing a power system transient process to be expressed as a linear portion and a non-linear portion. An accurate analysis expression of a state transition matrix is obtained by reasonably selecting a system matrix of the linear portion as a singular matrix, and a group of implicit integration formulas is obtained by leading linear integrable functions to be approximate to the non-linear portion of the differential equation set. The local truncation error of the power-angle implicit integration formulas of the generator refers to O (h5) which is larger than a local truncation error O (h3) of implicit trapezoidal integration, the calculated quantity of integration each time is equivalent to that of the implicit trapezoidal integration. By means of the high-precision implicit integration formulas, iteration times of each integration step under the same iteration precision condition are decreased, so that the simulated calculated quantity is remarkably decreased.

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.

The invention provides a simulating analog device of a transmission line secondary arc and a method thereof, which adopt the following technical proposal: the arcing situation of an arc channel is simulated by adopting a nonlinear time-varying resistance, and the arc channel resistance satisfies a dynamic equation which is established according to arc conservation of energy; a real-time secondary arc length is obtained according to arc movement characteristics by analyzing electrodynamic power, wind load and air resistance of an arc in movement and is used for modifying an arc length in the arc resistance equation; and by combining the characteristics of secondary arc current, whether self-extinguishing of the arc can be achieved is judged according to a change rate of the arc channel resistance when the arc current runs through a zero zone. A nonlinear differential equation which applies mathematical methods to solve the arc resistance occurs the electromagnetic transient process of the secondary arc with a computing system connected with an external circuit, and an the self-extinguishing time of the secondary arc is obtained by the arc channel resistance criterion during the zero-rest period of the arc current.

The invention discloses a tilt-rotor helicopter control decoupling design method which comprises the following steps: making an initial longitudinal control strategy of a tilt-rotor helicopter, establishing an aerodynamic force and moment model and a gravity model of a tilt-rotor helicopter component, and obtaining a nonlinear differential equation set based on a six-degree-of-freedom motion equation; according to the nonlinear differential equation set, selecting a rotor wing deflection angle under an interval value, solving the flight trim control quantity of the maximum speed of the tilt rotor wing helicopter and the required engine power, establishing a maximum level flight speed trim result table under different rotor wing deflection angles, and determining a new longitudinal controlstrategy; determining a new level flight speed balancing result table based on the new longitudinal control strategy; selecting a rotor total propeller pitch corresponding to the same steering columnlongitudinal control quantity under different rotor deflection angles in the table, and determining a decoupling coefficient between the rotor deflection angles and the rotor total propeller pitch based on the rotor total propeller pitch; calculating the change of the total pitch along with the inclination angle of the rotor according to the decoupling coefficient so as to solve the total pitch ofthe rotor.

The invention provides a dish type solar energy concentrator. The bottom of a dish surface is provided with a circular opening, the dish surface is a rotation curved surface, and the bus of the rotation curved surface is a curve based on a specific first-order nonlinear differential equation. Disclosed is also a design method of the dish type solar energy concentrator. According to a light uniform reflection principle and related optical geometry knowledge, the specific first-order nonlinear differential equation bus equation of the rotation curved surface of the dish surface is derived through calculating. According to the dish type solar energy concentrator and the design method thereof, the dish type solar energy concentrator is provided with the dish bottom opening, and the rotation curved surface bus of the dish surface is a specific first-order nonlinear differential equation curve, so that the dish type solar energy concentrator can form quite uniform hot-fluid distribution on a receiver, and the energy conversion efficiency and other integration performance of the concentrator are substantially improved. Therefore, the dish type solar energy concentrator and the design method thereof are especially suitable for an optically focused photovoltaic solar device of a large-dimension receiver.

The invention relates to a radio energy transmission tuning control technology, in particular to a radio energy transmission system tuning feedback control method considering dynamic performance. Themethod includes the steps of obtaining the phase nonlinear differential equation model of the transmitting end and the receiving end of a system through analysis by utilizing a coupling mode theory and a circuit theory; utilizing a small signal linearization method to linearize a phase nonlinear differential equation model nearby a system resonance point, and analyzing the closed-loop dynamic performance of the system; taking the linear model as a controlled object and the phase value of the output voltage of an inverter circuit of the system as a reference phase, and forming a system tuning closed-loop feedback control loop by using the phase value of the transmitting end and the phase difference value of the transmitting end and the receiving end as the given values of the system transmitting end and the receiving end control loops when the system works in a resonance state. The control method can quickly and accurately control a magnetic coupling wireless energy transmission systemto work under the working states of high transmission efficiency and power, and has good robustness for detuning disturbance.

The invention discloses a nonlinear analysis method for steering stability of an electric automobile. A nonlinear dynamics model capable of describing steering of the electric automobile is established, a nonlinear differential equation is constructed, then on the basis of an adiabatic elimination principle, order reduction processing is performed on the constructed nonlinear differential equation for steering of the electric automobile, in this way, fast relaxation parameters in a system are eliminated, and a simplified nonlinear differential equation is obtained; finally, on the basis of an isoclinic line principle, a multi-step recurrence method is adopted for drawing the phase trajectory of the nonlinear dynamics system for steering of the electric automobile, the balance state, stability precision and stability of the system are visually reflected, and the stability of the electric automobile in the steering process at different speeds and turning angles is analyzed.

The embodiment of the present invention relates to the field of automotive electronic test technology, and discloses an adjustable two-stage supercharged engine model building method and a simulationplatform. In the invention, the method comprises the following steps of: obtaining multivariate nonlinear differential equations of an adjustable two-stage turbo supercharged engine; and decoupling and simplifying the multivariate nonlinear differential equations to obtain a real-time simulation model of the adjustable two-stage turbo supercharged engine. An embodiment of the invention also discloses an adjustable two-stage supercharged engine simulation platform. The embodiments of the present invention achieves semi-physical real-time simulation of the adjustable two-stage turbo superchargedengine and provides a basis for the development of control strategies for the engine and the two-stage turbo supercharged system.

The invention relates to a generalized state space average modeling method based on aircraft electric power system dynamic characteristics. The method includes the steps that time-variant nonlinear differential equations of all links of an aircraft electric power system are built according to an aircraft electric power system structure; state variables are determined according to the differential equations in the above step, Fourier decomposition is conducted on the state variables, and the state variables described by the Fourier coefficients are obtained; the obtained Fourier coefficient state variables are substituted into the differential equations, and a generalized state space average model of the aircraft electric power system is obtained; the dynamic characteristics of different time scales of the aircraft electric power system are analyzed according to different flying working conditions of an aircraft; the generalized state space average model of the aircraft electric power system is simplified according to the dynamic characteristics. The generalized state space average modeling method has the advantages that by means of the method, the operating working conditions and dynamic characteristics of the aircraft electric power system can be discriminated, a time domain model can be replaced in system analysis and design, the time domain model can be simplified into the state space average model in the steady state, good engineering accuracy is achieved, fast analysis ability is achieved as well, and the generalized state space average modeling method is suitable for the field of steady state and transient state analysis of different aircraft models.

The invention discloses an MLP method for strong nonlinear vibration of a hyperelastic cylindrical thin shell, and belongs to the field of material analysis. The invention aims to solve the problem ofstrong nonlinear vibration when the inner surface of a thin-wall cylindrical shell made of incompressible hyperelastic materials is subjected to radial simple harmonic excitation. Technical point comprises: obtaining a nonlinear differential equation set describing large-deflection vibration of the cylindrical shell on the basis of a Donnell nonlinear shallow shell theory, a Lagrange equation anda small strain hypothesis; simplifying the nonlinear equation set into a strong nonlinear Duffing equation containing large parameters based on a degree-of-freedom condensation method; obtaining a corresponding amplitude-frequency and phase-frequency response curve by utilizing proper parameter transformation and an improved MLP method. The effect is that the material has a hardening behavior dueto geometrical nonlinear characteristics caused by large-deflection vibration, and the nonlinearity of the hyperelastic material can cause a softening effect.

The invention discloses a light unmanned aerial vehicle electrodynamic system identification method and apparatus, and the method includes setting up Hammerstein-type nonlinear differential equation structure of mathematical model in time domain of electrodynamic system of light unmanned aerial vehicle, including first-order linear differential element and second-order power nonlinear element, identifying linear link parameters: a photoelectric encoder disk with equal moment of inertia is used to replace the air propeller to simulate the inertia force of accelerating rotation; obtaining the time constant and amplification coefficient of the first order linear differential link from the output speed response by giving a step signal; identifying nonlinear link parameters: the nonlinear linkdoes not involve differential terms, and the nonlinear link parameters can be fitted by multiple sets of steady-state input-output relations. As that method relate to by the invention is more objective and accurate than the traditional technology, the disadvantageous influence caused by the nonlinear term generate by the aerodynamic force of the propeller can be well avoided when the differentialterm is dynamically identified; the invention uses the ground testing device, and can collect the rotational speed response on line and accurately.

The invention discloses an energy internet communication security system and method based on a chaotic system array. The method comprises the following steps: 1) construction of the chaotic system array: constructing the chaotic system array with a chaotic system as a basic unit; 2) generation of a chaotic signal: solving a nonlinear differential equation of the basic unit in the chaotic system array to generate the chaotic signal required for secure communication; 3) processing of the chaotic signal: performing signal processing on the multi-channel chaotic signal generated by the chaotic array system to construct a new high-dimensional hyperchaotic signal as a key signal; and 4) encryption / decryption of information: performing encryption / decryption processing on the original / encrypted signal by using an output signal of the processed chaotic system array according to a given data encryption / decryption principle. The communication security method designed by the method provided by theinvention can be used for processing different kinds of information such as texts, waveforms, voice, images and the like, has the advantages of high data processing capability and wide type; and theenergy internet communication security system and method are flexible to expand, safe and reliable and are easy to implement.

A method is described for ascertaining a computational model for a position encoder system, in particular for a position encoder for controlling a gas mass flow rate for an internal combustion engine, having the following steps: providing a differential equation system with at least one nonlinear term; dividing the differential equation system to obtain a linear part which is describable by a linear differential equation and a nonlinear part which is describable by a nonlinear differential equation; discretizing the linear part of the differential equation system with the aid of a first discretization method to obtain a computational model for the discretized linear part; discretizing the nonlinear part of the differential equation system with the aid of a second discretization method to obtain a computational model for the discretized nonlinear part; combining the computational models of the discretized linear part and the discretized nonlinear part of the differential equation system to obtain the computational model for the position encoder system.

The invention provides a pool-type sodium-cooled fast reactor main coolant system heat transfer and flow rapid simulation method, which comprises the following steps: carrying out decoupling modeling on a flow and heat transfer process of a pool-type sodium-cooled fast reactor main coolant system to realize parallelization on a simulation modeling level; removing a control body in the modeling of the flow process of the pool-type sodium-cooled fast reactor main coolant system; carrying out nonlinear equation set analytic processing on a first-order nonlinear differential equation set for describing the flow process of the pool-type sodium-cooled fast reactor main coolant system; separately solving the heat transfer process and the flow process by applying different computing resources in parallel; updating the physical parameters of each control body through the calculated pressure and enthalpy value by utilizing a physical property calculation formula; and determining whether the simulation calculation within the required time duration is completed or not. According to the method, the heat transfer and flow simulation calculation efficiency of the pool-type sodium-cooled fast reactor main coolant system is improved through decoupling modeling, control body removal in modeling, nonlinear equation set analytic processing in solving and the like.

The invention discloses a method for analyzing the strength and rigidity of a geologic structure. The method comprises the following steps of: (a) establishing a solution domain, and discretizing the solution domain into a finite element; (b) supposing a shape function representative of an element physical behavior; (c) establishing an element equation; (d) constructing an element global stiffness matrix; (e) applying boundary conditions, initial conditions and loads; (f) solving linear or nonlinear differential equations, and thus obtaining a node solution result such as the displacement of different nodes, strain variables or temperature values in a thermodynamics issue; and (g) acquiring other important information. The strength and rigidity of the geologic structure can be quickly analyzed, the method is accurate in analysis result and simple in analysis step, and analysis cost is greatly reduced.

The invention discloses a multi-factor model optimization method for a gene regulatory network, which comprises the following steps: inferring the gene regulatory network by utilizing a nonlinear differential equation model and a differential operation method of a gene and combining a machine learning algorithm, and optimizing a key parameter attenuation rate based on a multi-objective optimization idea and a genetic algorithm. According to the invention, the effects of noise, attenuation rate and time delay are introduced on the basis of a traditional differential equation model, a nonlinear regulation and control function is trained based on a machine learning algorithm, and the nonlinear dynamic process of gene expression can be better simulated; the algorithm is used for optimizing the attenuation rate and time delay of important parameters influencing gene expression, and then a more accurate and efficient mathematical model is constructed to deduce the gene regulation network from gene expression data.

The invention discloses a method for describing large-deflection vibration of a rubber cylindrical shell, belongs to the field of mechanics, aims to solve the problem of establishing a mathematical model to research nonlinear vibration, and is characterized in that a nonlinear differential equation set for describing movement of the cylindrical shell is given by utilizing an energy principle, andthe effect is that based on a Donnell nonlinear thin shell theory, a Lagrange equation and a small strain hypothesis, the nonlinear differential equation for describing the large-deflection vibrationof the rubber cylindrical shell is obtained. According to the method, a mathematical model is established and solved, so that the basis of nonlinear vibration research of the thin-wall rubber cylindrical shell is provided, and the motion behavior of the thin-wall rubber cylindrical shell is analyzed through the mathematical model.

The invention discloses a prediction method of mine water inflow based on an NGBM-PSO model. By constructing time series data of actual measured value of mine water inflow, the time series data is converted into monotonically increasing series, then the discrete sequence data are continually transformed by nonlinear differential equation, parameters a, b, r are introduced, based on Particle SwarmOptimization (POS) to optimize the parameters, establish the prediction model, solve the prediction formula: (shown in the description) used for mine water inflow prediction calculation. The inventionhas the advantages of definite prediction result, strong applicability and high accuracy.

The invention provides a mathematical model of a four-order complex-valued hyperchaotic system and an implementation circuit, the mathematical model is composed of four nonlinear differential equations, and each differential equation comprises one nonlinear product term; the complex-valued hyper-chaotic system constructed by the mathematical model has three positive Lyapunov indexes and has very rich chaotic dynamics behaviors. The implementation circuit is characterized in that 23 operational amplifiers, 6 multipliers, 54 resistors and 7 capacitors form seven channel circuits, and 6 analog multipliers are used for achieving four quadratic product terms in a complex valued system; 23 operational amplifiers, 54 resistors and 7 capacitors are respectively used for completing addition, subtraction, voltage inversion and integration functions. The implementation circuit is simple to implement and convenient to integrate, and lays a foundation for application of the complex-valued hyper-chaotic system in the fields of information science, secret communication and the like.

The invention provides a simulating analog device of a transmission line secondary arc and a method thereof, which adopt the following technical proposal: the arcing situation of an arc channel is simulated by adopting a nonlinear time-varying resistance, and the arc channel resistance satisfies a dynamic equation which is established according to arc conservation of energy; a real-time secondaryarc length is obtained according to arc movement characteristics by analyzing electrodynamic power, wind load and air resistance of an arc in movement and is used for modifying an arc length in the arc resistance equation; and by combining the characteristics of secondary arc current, whether self-extinguishing of the arc can be achieved is judged according to a change rate of the arc channel resistance when the arc current runs through a zero zone. A nonlinear differential equation which applies mathematical methods to solve the arc resistance occurs the electromagnetic transient process of the secondary arc with a computing system connected with an external circuit, and an the self-extinguishing time of the secondary arc is obtained by the arc channel resistance criterion during the zero-rest period of the arc current.

The invention provides a method for calculate transient pressure of retained air mass in pipeline impinge by water flow. The equations of motion of water column and the instantaneous equations of gaspressure are established by taking the horizontal pressurized transmission / drainage pipeline with retained air mass as the center. The second-order nonlinear differential equations are obtained by simultaneous equations with the transient flow pressure of pipeline as the strain value and the instantaneous displacement of water column as the independent variable. The equation is subjected to linearization so as to obtain the calculation formula of air-water transient pressure of retained air mass in pipeline impinge by water flow, which takes into account the effects of time, local atmosphericpressure, gas state index, water flow density, inlet pressure, pipe length, and retained air mass length. The invention provides a tool for calculation of the peak value of air-water hammer pressure and oscillation period produced by the transient flow phenomenon that the water flow impinges on a retained air mass in a pressurized pipe, and provides theoretical basis for optimizing the engineeringdesign of the pressurized transmission / drainage pipeline, reducing the engineering cost and ensuring the safe operation of the engineering calculation.

The invention discloses a modeling method of a power electronic device. The modeling method comprises the following steps: establishing a nonlinear differential equation for a parallel part of each single module; fourier simplification is carried out on the nonlinear differential equation of the parallel connection part; establishing a mathematical model of the cascade part of each phase of each single module, and using the mathematical model to simplify the nonlinear differential equation after the parallel part is simplified again; the equivalent average value model of the power electronic device is obtained based on a nonlinear differential equation obtained after the parallel part of each single module is simplified again, a mathematical model of the cascade part and an external circuit, so that the simulation speed of the model is remarkably improved under the condition that the precision is stable, and the simulation efficiency is improved. Moreover, the average value model can effectively simulate the external characteristics of the power electronic device, neglects the internal dynamic characteristics, and has important theoretical significance and application value.

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.

A nonlinear analysis method for electric vehicle steering stability, by establishing a nonlinear dynamic model that can describe the electric vehicle steering, constructing a nonlinear differential equation, and then using the principle of adiabatic elimination to reduce the constructed electric vehicle steering nonlinear differential equation First-order processing, eliminate the fast relaxation parameters in the system, and obtain the simplified nonlinear differential equation. Finally, according to the principle of isoclines, use the multi-step recursion method to draw the phase trajectory of the electric vehicle steering nonlinear dynamic system. The balance state, stability accuracy and stability are intuitively reflected, and the stability of the electric vehicle steering process under different speeds and corners is analyzed.

The invention discloses a power system subsynchronous resonance analysis method based on an aggregated RLC circuit model, which includes the following steps: establishing a power plant model and a series compensation transmission system model to obtain nonlinear differential equation models of each subsystem; according to special working conditions The following parameters and nonlinear differential equation model generate state equation model; generate algebraic equation model according to Laplace transform and state equation model; obtain the final equivalent impedance model to obtain the series resonance point; according to the series resonance point, the final equivalent Impedance models aggregated into equivalent second-order RLC circuit models; quantitative SSR analysis. The analysis method of the embodiment of the present invention performs quantitative SSR analysis by aggregating equivalent impedance models into an equivalent second-order RLC circuit model, realizes accurate quantitative evaluation of SSR, reduces analysis errors, and improves analysis accuracy.

The invention relates to a small-disturbance stability analysis method for an aircraft power system based on generalized state space averaging. Based on the equivalent circuit of the generalized state space average modeling of the aircraft power system, the nonlinear differential equation of the aircraft power system is obtained; the state variables of the nonlinear differential equation are determined, and the generalized state space described by Fourier coefficients is obtained through Fourier decomposition Average model; according to the model, it is calculated and processed to judge the small disturbance stability of the aircraft power system. The effect of the invention is that the method realizes the small disturbance stability analysis under different dynamics of the aircraft power system, can realize the sensitivity analysis of the small disturbance stability, provides valuable suggestions for the design and improvement of the power system in the manufacture of large aircraft, and can be used by the crew at the same time Provide reliable aircraft electrical system operating information.

The invention provides a dish type solar energy concentrator. The bottom of a dish surface is provided with a circular opening, the dish surface is a rotation curved surface, and the bus of the rotation curved surface is a curve based on a specific first-order nonlinear differential equation. Disclosed is also a design method of the dish type solar energy concentrator. According to a light uniform reflection principle and related optical geometry knowledge, the specific first-order nonlinear differential equation bus equation of the rotation curved surface of the dish surface is derived through calculating. According to the dish type solar energy concentrator and the design method thereof, the dish type solar energy concentrator is provided with the dish bottom opening, and the rotation curved surface bus of the dish surface is a specific first-order nonlinear differential equation curve, so that the dish type solar energy concentrator can form quite uniform hot-fluid distribution on a receiver, and the energy conversion efficiency and other integration performance of the concentrator are substantially improved. Therefore, the dish type solar energy concentrator and the design method thereof are especially suitable for an optically focused photovoltaic solar device of a large-dimension receiver.

A method is described for ascertaining a computational model for a position encoder system (1), in particular for a position encoder for controlling a gas mass flow rate for an internal combustion engine, having the following steps: providing a differential equation system with at least one nonlinear term; dividing (S1) the differential equation system to obtain a linear part which is describable by a linear differential equation and a nonlinear part which is describable by a nonlinear differential equation; discretizing (S2) the linear part of the differential equation system with the aid of a first discretization method to obtain a computational model for the discretized linear part; discretizing (S3) the nonlinear part of the differential equation system with the aid of a second discretization method to obtain a computational model for the discretized nonlinear part; combining (S5) the computational models of the discretized linear part and the discretized nonlinear part of the differential equation system to obtain the computational model for the position encoder system (1).