241 results about "Algebraic equation" patented technology

A method is disclosed for estimating clutch engagement characteristics of a friction clutch system in a vehicle powertrain. A dynamic model of the system is used under conditions that cause clutch slipping. Algebraic equations defining a functional relationship between clutch torque and an engagement angle have characteristic parameters that are estimated using a non-linear least squares technique. A non-linear least squares technique iteratively minimizes the difference between a measured output clutch disk speed and an output clutch disk speed from the system dynamic model for the same inputs until a small insignificant error is reached. Parameter estimates are used to compile an estimated clutch engagement characteristic.

Methods and systems for computing algebraic equations are disclosed, with particular relevance to financial analytics. Analytic formulas may be represented as data, and the analytic system may be structured as a kind of an analytic interpretation engine in a database layer of a system. Because analytic formulas may be represented as data in some table or tables, analytics can be added, deleted or modified without having to make changes to the analytic engine's source code. The analytic engine may be implemented in some relational language, such as a dialect of SQL, to manipulate and compute the analytic formulas stored in the database.

The invention discloses a numerical integration method for electric power system full dynamic simulation, combining a fixed-step trapezoidal integration method and a variable-step Gear integration method organically in the full dynamic simulation. In the method, the fixed-step trapezoidal integration method, a differential equation of a dynamic element and an algebraic equation of power network are adopted to carry out iterative solution in a mechanical and electrical transient state process of the electric power system full simulation; in the method, the variable-step Gear integration method, the differential equation of the dynamic element and the algebraic equation of the power network are adopted to carry out simultaneous solution in a medium and long-term dynamic process. The fixed-step method and the variable-step method are switched automatically according to a certain strategy in the simulation. The method integrates the advantages of the two original numerical integration methods, thereby overcoming the defect of low calculational efficiency resulting from too small step in the simulation of mechanical and electrical transient state process of the electric power system of the existing full dynamic simulation program while ensuring numerical calculation stability and calculation accuracy.

The invention discloses a method for simulating energy flow based on a transient model of a power-gas interconnection comprehensive energy system. The method comprises the following steps of 1) by considering dynamic characteristics of a slow process of a natural gas pipe network, building a transient model of the natural gas pipe network; 2) by adopting an implicit finite difference method, dividing a time-space partial differential equation for describing dynamic characteristics of gas flow of a natural gas pipeline into algebraic equation expressions; 3) coupling a power network and the natural gas pipe network through a gas turbine and a power-to-gas technology, and building the transient model of the system; 4) solving multi-time-period transient energy flow of the power-gas interconnection comprehensive energy system; and 5) performing performance testing in the comprehensive energy system. According to the method provided by the invention, the calculation precision is effectively improved and a real-time running state of a natural gas system can be described more accurately.

The invention discloses an automatic elementary mathematic algebra type question answering method and system. The method comprises the following steps of: question input; question understanding: classifying each category of elementary mathematic algebra type questions and carrying out word segmentation and part-of-speech labelling on question texts; extracting a direct statement mathematic relationship by using a syntax-semantic hybrid model and adding an implicit type mathematic relationship according to question types so as to form an algebra relationship group; machine solution: distributing variables for entities in the formed algebra relationship group, converting the algebra relationship group into an algebra equation group, obtaining an entity-variable comparison table, and automatically solving the algebra equation group by a machine; and quasi-man answer generation: recovering semantic meanings of the variables in the algebra relationship group solution process according to solution sequences of the variables and the entity-variable comparison table, and combining the question texts to form a quasi-man answer process. According to the method and system, the automation degree of answering mathematic algebra type questions can be greatly improved.

The invention relates to a method of calculating AC impedance spectroscopy relaxation time distribution, so as to solve problems that the prior impedance spectroscopy analysis method has a low frequency resolution, the number of electrochemical reaction processes and actual impedance can not be effectively analyzed, and an analytical equation for relaxation time distribution can not be solved. The method is realized via the following technical scheme: 1, an AC impedance spectroscopy array including a frequency, an impedance real part and an impedance imaginary part are acquired; 2, KK test is carried out to enable the AC impedance spectroscopy array to be stable and analytical; 3, algebraic equations for relaxation time and a relaxation time distribution function are built; and 4, the relaxation time and a relaxation time distribution function array are obtained, a chart is drawn with logarithm of the relaxation time as transverse axis and with the relaxation time distribution function as longitudinal axis, each peak in the chart corresponds to a different electrochemical process, and the peak area represents the actual impedance of a different electrochemical process. The method of the invention is applied to the electrochemical field.

Provided is a simulation analysis method of the electromechanical transient process of an electrical power system. An electromechanical transient system model of the electrical power system is established, the electromechanical transient of the electrical power system is simulated through network dividing and solving of differential algebraic equations, simulating calculation is performed according to the simulation process, the electromechanical transient of the electrical power system is analyzed through simulation modeling, and therefore stability and safety of the electric power system are guaranteed.

A turbo coded communication system includes a gray scale mapper in a transmitter for generating a symbol constellation of modulated signals points that can be separated by boundary lines in the constellation space into bitwise groups of zero bits and one bits where the shortest distance from a boundary line to received value in the constellation space indicates the bitwise soft metrics that is computed using a set of bitwise soft metric equations are a function of the minimum distance using closed form algebraic equations in turbo decoding receiver. In the case of quadrature amplitude modulation (QAM), the bit boundary lines are predetermined by a minimum distance in the constellation space for a specified M-ary modulation, so that, the soft metric equations are only a function of the received signal value for providing efficient computation of the bitwise soft metric.

The present invention concerns a method of decoding a one-point algebraic geometric code defined on an algebraic curve represented by an equation in X and Z of degree 2μφ in Z, where φ is a strictly positive integer and μ an integer greater than 1, obtained by taking the fiber product of μ component algebraic equations, each of said component equations governing the unknown X and an unknown Yi, where i=0, . . . , μ−1, and being of degree 2φ in Yi. This method comprises the decoding of 2(μ−1)φ“clustered” codes, all defined on the same algebraic curve represented by one of said component equations. The invention also relates to devices and apparatuses adapted to implement this method.

The invention discloses a nuclear power unit steam generator mechanism model building method and a system thereof; the method comprises the following steps: building mechanism models for nuclear powerunit steam generator segments; integrally processing the built segment models; dynamic model structure processing; dynamic model verification, respectively step disturbance for three inputs includingfeed water flow, steam flow and coolant temperature, analyzing to obtain a response curve, determining whether the curve trends is consistent with theory or not, and verifying the model building rationality and accuracy. The method combines segment and lumped parameters to carry out mechanism modeling, uses a special solution aiming at a DAE differential equation in a MATLAB, redistributes ODE resolver quality matrix parameters, and converts the differential algebraic equation into a non-linear state space form, thus realizing differential algebraic equation accurate solving, and finally verifying the accuracy of the built models.

The invention provides a global optimization method for control parameters of a photovoltaic power generation system. The method comprises the following steps: firstly, an established differential-algebraic equation of a photovoltaic plant power generation system is linearized at a steady-state value to obtain a state matrix used for analyzing the small disturbance stability of the system; then the influence on the system small disturbance stability of the system caused by control parameters is analyzed by calculating the eigenvalue, the damping ratio and participation factors of the state matrix to further determine the reasonable variation range of the control parameters; and finally, a quantitative model is introduced to serve as a parameter optimization objective function and the optimization algorithm is utilized to achieve global optimization of the control parameters of the photovoltaic plant power generation system. According to the invention, as for the small disturbance stability of the system, a scientific and reasonable quantification standard is established, and the problem of difficult single optimization due to mutual coupling of the system control parameters is solved. By adopting the method for parameter optimization, global optimization of the control parameters can be realized, and the small disturbance stability of the photovoltaic plant power generation system is improved.

The invention provides a method for obtaining the static aeroelastic deformation influencing quantity of a wind tunnel model. According to the scheme, for solving the problem that different incoming flow velocity pressure test data extrapolation methods depend on the capability of total temperature and total pressure independently controlled test facilities, an independently-variable total pressure wind tunnel testing method which can be achieved by most wind tunnels is adopted to obtain wind tunnel test data of different Reynolds number and incoming flow velocity pressure combinations, the difficulty and cost of an air tunnel test is remarkably reduced, and a preparation period of the air tunnel test is remarkably shortened, the dependency of static aeroelastic deformation influence correction on wind tunnels is eliminated, and a technical support is provided for corresponding correction tests carried out for various conventional air tunnels. For solving the problem that the time and calculation costs of numerical simulation / model deformation measurement combined methods are high and the static aeroelastic deformation influence cannot be analyzed in real time, an algebraic equation solving method is adopted, rapid separation of a Reynolds number effect and a static aeroelastic deformation influencing effect can be achieved, and accordingly the influencing quantity of static aeroelastic deformation to aerodynamic force characteristics can be analyzed in real time.

Discloses is a method for calculating single rod power of an overall reactor core. The method includes steps of 1), determining geometrical and material parameters of a target nuclear reactor according a reactor core structure thereof; establishing an SP3 equation set of step 0 or step 2 neutron angular flux torque density according to a multigroup neutron transport theory; 2), adopting structural grids to subdivide structural geometry zones with corresponding shapes, and unstructured grids to subdivide unstructured geometry zones; 3), establishing a segment SP3 method, subjecting the SP3 equation set in the step 2) to numerical discretion by adopting approximate processing modes which are mutually compatible under a structural grid and the unstructured grid, and acquiring neutron-flux density on all grids of the nuclear reactor core by utilizing iterative algorithm to solve discrete algebraic equation set; 4), adopting the neutron-flux density acquired in the step 3) to calculate the single rod power of the overall reactor core. By reducing approximation from grid subdivision, approximation from the numerical discretion and iterative calculation process and approximation from component homogenization and component power reconstitution, the high-precision single rod power of the overall reactor core can be calculated.

A method use line-frequency disturb the zero-sequence impedance parameter of resource charge measure mutual inductance circuit, cuts the power of a certain circuit in the mutual inductance circuit in order, puts one three-phase of the power cut circuit to earth, measures the induction voltage of the other one after it is in short-circuit; at the same time measures the zero-sequence voltage pressure loss and zero-sequence current in the other run circuit; uses the GPS technology sample the zero-sequence voltage, zero-sequence current in the mutual inductance circuit in-phase, gets the zero-sequence voltage, zero-sequence current data in the mutual inductance circuit; collects the data of each measurement point to the center computer; gets the zero-sequence impedance parameter of the mutual inductance circuit by using the least square law solute the algebraic equations, differential equations or integral equations; this equipment is composed of GPS antenna, signal input connection interface, signal transducer, embedded DPS synchromesh data collection card, launch amount card, relay group, embed PC card, the electrical source card.

The invention discloses a 6R robot inverse kinematic geometry solving method based on a screw theory and belongs to the field of robot kinematic inverse solution research. A basal coordinate system and a tool coordinate system are established, kinematic parameters of a 6R robot are determined through the basal coordinate system and the tool coordinate system, and a forward kinematic model is established; inverse solution motion of first three joints of the 6R robot is descripted in a decomposed mode, and a six-variable quadratic equation set is established; and a target position qe1 corresponding to an initial position qs1 is solved based on a screw forward kinematic model. Through the method, geometric description is combined with the screw theory, the geometrical significance is more explicit, the algebraic equation set is solved through a simplified inverse kinematic algorithm, the calculation efficiency is effectively improved, and a new inverse kinematics processing method is provided for real-time control over robot movement.

The invention provides a design method of a light-emitting diode (LED) even-illumination light source based on a high-diffuse-reflection-rate free-form surface. A general mathematical model of a free-form surface diffuse reflection surface for secondary light distribution is built by utilizing a bidirectional reflection distribution function (BRDF) of a high-diffuse-reflection-rate surface according to light-emitting characteristics of the LED light source. The mathematical model is utilized to write a nonlinear algebraic equation set by combining specific requirements for target illumination areas and the irradiance distribution in an actual application occasion, and a numerical method is utilized to conduct calculation to obtain a surface type outline of the diffuse free-form surface. The LED indirect light source based on the high-diffuse-reflection-rate free-form surface is compact in system structure, high in illumination evenness and capable of being used in the fields of color vision measurement, indoor illumination, projector devices and the like requiring high-evenness illumination conditions and has good application prospects.

The invention discloses an electric power system transient stability calculation method based on a semi-implicit Runge-Kutta method. The method includes: establishing a dynamic element model for transient stability simulation calculation of the power system; forming a whole system differential algebraic equation set; inputting raw data and information, carrying out tide calculation, obtaining an operation parameter initial value before system disturbance; calculating an initial value of the state variable; generating a Jacobian matrix and a network admittance matrix of each dynamic element; performing system disturbance judgment; generating a Jacobian matrix of the differential equation set of the whole system; solving and obtaining the value of each state variable at the next moment; carrying out machine network alternate iterative computation, obtaining an operation parameter value at the next moment until a convergence condition is met, and taking the operation parameter value as aninitial value to calculate the next step length. The calculation is simple and stable, the larger step length can be used, the problem that the numerical stability and the calculation efficiency of the algorithm are difficult to consider at the same time in the transient stability simulation calculation is solved, and the method is more efficient, accurate and stable.

A method is disclosed for computing clutch engagement characteristics of a friction clutch system in a vehicle powertrain. A dynamic model of the system is used under conditions that cause clutch slipping. Algebraic equations defining a functional relationship between clutch torque and an engagement angle have characteristic parameters that are estimated using a non-linear least squares technique. The non-linear least squares technique repetitively minimizes the difference between a measured clutch output speed and a clutch output speed from the system dynamic model for the same inputs until a small insignificant error is reached. Parameter estimates are used to update each engagement characteristic.

The present invention discloses an convergence RLC circuit model-based method for analyzing subsynchronous resonance in a power system. The method comprises the following steps of: establishing a power plant model and a series compensated transmission line system model so as to acquire a non-linear differential equation model of each subsystem; generating a state equation model according to a parameter under a particular working condition and the non-linear differential equation model; generating an algebraic equation model according to the Laplace transform and the state equation model; acquiring a final equivalent resistance model so as to acquire a series resonance point; aggregating the final equivalent resistance model into an equivalent second order RLC electric circuit model according to the series resonance point; and quantifying SSR analysis. According to the analysis method provided by an embodiment of the present invention, the final equivalent resistance model is aggregated into the equivalent second order RLC electric circuit model, so that the SSR analysis is quantified, thus implementing the accurate quantification evaluation of SSR, reducing analysis errors and improving analysis accuracy.

The invention discloses an electromechanical transient method based relay protection fixed value online check method. The method comprises the following steps of (1) obtaining real-time measurement data of a power grid from an EMS, and establishing a power grid network algebraic model; (2) obtaining zero-sequence parameters and a protection fixed value of the power grid from a relay protection setting software database; (3) combining with a self electromechanical transient model parameter database, and solving a simultaneous algebraic equation and nonlinear equation through an electromechanical transient simulation method to obtain dynamic process data of each state variable of the system in a fault process and after the fault disappears respectively; and (4) performing check on the protection fixed value according to the dynamic process information of each state variable obtained in the step (3). According to the method, the accuracy of the short-circuit calculation result can be improved; online check and real-time early warning for the relay protection fixed value can be realized; and the automatic degree of the protection fixed value operation is improved.

The invention discloses a doubly-fed wind power generation virtual synchronous generator modeling method based on Thevenin-Norton equivalence. The doubly-fed wind power generation virtual synchronousgenerator modeling method comprises the steps of sampling; changing a traditional doubly-fed fan modeling method, establishing a doubly-fed motor model based on Thevenin and Norton equivalence by utilizing the Thevenin-Norton equivalence theorem, mainly establishing a Thevenin equivalent mathematical model on the stator side of the doubly-fed motor and a Norton equivalent mathematical model on the rotor side of the doubly-fed motor. The modeling method greatly simplifies the algebraic equation calculation of the common connection part of the power grid, the doubly-fed motor stator and the grid-side converter, so that the algebraic equation calculation is more matched with a system mathematical model, and the physical significance is clearer.

Provided is a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The invention relates to a control-limited minisatellite three-axis magnetic moment attitude control method based on an algebraic Lyapunov equation. The method is used to realize global stability of a minisatellite three-axis magnetic moment attitude control under control-limited conditions. The method comprises: step 1, establishing attitude kinematics and attitude kinetic models of control-limited minisatellite three-axis magnetic moment attitude control, to obtain a state-space equation; step 2, solving explicit solution P0 of the algebraic Lyapunov equation A<T>P0+P0A=-D<T>D, wherein A is a system matrix, D is a matrix in arbitrary dimensions, the system matrix A being critical stable or Lyapunov stable, ensuring the algebraic Lyapunov equation have a positive definite solution P0; step 3, and through the positive definite solution P0 of the algebraic Lyapunov equation, designing linear feedback control law under explicit control-limited conditions. The method is applied in the field of satellite control.

The invention discloses a dual quaternion solution of six degrees of freedom parallel robot forward kinetics. According to the method, dual quaternions are taken as generalized coordinates of a parallel robot system, a forward kinetic equation set is a quadratic algebraic equation about the dual quaternions, a high-efficiency value algorithm is brought forward for the equation set, and least square solutions of the position and attitude of such a six degrees of freedom parallel robot motion platform can be rapidly calculated. For a parallel robot not including redundancy driving, a least square solution is also an exact solution.

Methods, computer systems, and computer readable media are provided for simulation of a model of a system by detecting a violation of a cross condition while iteratively refining a first solution of a system of nonlinear algebraic equations at a current time point, and responsive to the detecting, predicting a crossing time step, projecting an initial guess for a second solution of the system of nonlinear algebraic equations at the crossing time point, and iteratively refining the second solution and the crossing time step by jointly solving an equation for the cross condition with the system of nonlinear algebraic equations as a coupled nonlinear system in which the crossing time step is treated as an unknown to compute changes to the second solution and the crossing time step in each iteration.

The invention discloses a multi-body-dynamics-equation solving method based on a Bathe integration strategy. The method includes: establishing a corresponding coordinate system in a multi-body dynamics system, and using a relative-coordinate method and a Lagrangian-multiplier method to obtain dynamics equations according to a virtual-power principle; seeking a second derivative of a constraint equation with respect to time to obtain differential-algebraic equations of an index -1, and adding constraint stability terms to form a general form of the dynamics equations with complete constraints;carrying out integration iteration solving on the general form of the dynamics equations with the complete constraints on a time step [t, t+h / 2] to obtain motion parameters of a moment t+h / 2; carryingout integration iteration solving on a time step [t+h / 2, t+h] to obtain the motion parameters of a moment t+h; and carrying out repeated iteration calculation, outputting values of generalized displacement, velocity and acceleration, which are of a system and are changed over time, when calculation time reaches set total simulation time, and thus analyzing motion status of the multi-body process-closed-loop dynamics system in certain time. The method can also achieve better precision in a case of larger integration step length.

The invention relates to the technical field of bridge engineering, in particular to a concrete creep effect analysis method. The method comprises the following steps that 1, a time-dependent concrete stress value sigma (t) is measured; 2, according to the time-dependent concrete stress value sigma (t) measured in the step 1, a time(t)-dependent variation curve graph is obtained; 3, a recurrence method is adopted for obtaining a creep strain increment; 4, according to a stress relaxation coefficient R(t, tau)=sigma(t) / sigma0, the curve graph obtained in the step 2 and the step 3, a stress value sigma 0 of the moment tau 0 of concrete is set to be equal to 1, and a computational formula of a stress relaxation coefficient R(t, tau) at the time t is obtained, wherein the equation of the computational formula is shown in the description; 5, according to the stress relaxation coefficient R(t, tau), a concrete time-dependent elasticity modulus E(t, t0) is obtained; 6, according to the computational formula of the stress relaxation coefficient R(t, tau) and the elasticity modulus E(t, t0), concrete creep effect analysis is completed. According to the analysis method, the stress-strain algebraic equation is adopted, computation is greatly simplified, and programming computational analysis is promoted.

The invention relates to a method for calculating the inherent frequency of a Euler-Bernoulli beam through an improved differential transformation method. The method comprises the steps that the improved differential transformation method is deduced on the basis of a differential transformation method; a corresponding oscillatory differential equation is built, the improved differential transformation method is used for solving the free vibration problem of the homogeneous Euler-Bernoulli beam with two freely-supported ends, a control differential equation is converted into an algebraic equation, and boundary conditions are changed to an algebraic frequency equation convenient to calculate; corresponding algebraic operation is carried out to obtain the inherent frequency and the modal shape of any order of the differential equation. According to the method for calculating the inherent frequency of the Euler-Bernoulli beam through the improved differential transformation method, the improved differential transformation method is used for solving the free vibration problem of the homogeneous Euler-Bernoulli beam, an approximate solution of a nonlinear problem is obtained in the mode that iteration is carried out to converge the series, closed-form solutions such as the four-order inherent frequency and the modal shape are obtained, the solution of a Taylor expansion power series can be converged at a larger time interval, and the calculation process is rapider and more accurate.