173 results about "Analytic expression" patented technology

A design method of a trust region satellite-borne dual-base interference SAR system is provided, relating to the field of radar measurement. Firstly, error sources of the interference SAR system are classified and analyzed, phase errors caused by image decoherence are calculated according to wave positions, and an analytical expression of baseline-related errors is reserved; a maximum phase error caused by imaging processing and an electronic device are estimated; and a baseline error is estimated. Then, the phase errors and the baseline errors are converted into elevation errors through an elevation fuzzy number, thereby obtaining an analytical expression of the elevation errors and the baseline parameters (length and dip angle). With a relative height measurement accuracy index of the system as an optimization object, a feasible solution interval between the baseline length and the baseline dip angle of the system is solved through a trust region algorithm. A minimum value of the baseline length is corrected according to a flying-around safety distance of a dual-satellite formation. According to the method of the present disclosure, the design of the satellite-borne dual-base interference SAR system can be guided, so that the satellite-borne dual-base interference SAR system is ensured to carry out terrain elevation surveying and mapping tasks with high accuracy and high reliability.

The invention provides a DCIM-based method for rapidly calculating a green function of a uniaxial anisotropic layered medium and an electromagnetic simulation system. The method comprises the following steps: modeling a uniaxial anisotropic layered medium to be simulated; determining a uniaxial anisotropic dielectric material of each layer, and assigning transverse parameters and longitudinal parameters; determining longitudinal coordinates of field point and source point distribution required to be solved, fitting a uniaxial anisotropic medium Green function spectral domain expression under the field source distribution by using a DCIM method, and solving an analytical expression in a spatial domain by using Somerfeld identical equation properties; solving the size of the electromagnetic field on the plane according to the fitted analytical expression; compared with a direct numerical integration method or a finite element method numerical solution using the Green function, the method has the advantages that the airspace analytical expression corresponding to the field source distributed on the plane is directly fitted, so that the solution of the airspace Green function is greatly accelerated, and the calculation efficiency and the calculation precision are both good in an actual example.

Provided are analytical expressions for multi-sample preference sampling distributions. A distillation training approach can be framed as a distribution matching problem with respect to one of these analytical expressions. The distribution matching problem can be solved using various algorithms. For example, a student model can be finetuned via policy distillation techniques. The resulting student model is therefore able to provide the benefits of the multi-sample preference sampling process, including its robustness and ability to align with human preferences, while significantly reducing the computational overhead at inference time.

The invention belongs to the technical field of aircraft structure design, and particularly relates to an aircraft arbitrary space four-bar mechanism parameter optimization method, which comprises the following steps: firstly, determining input conditions or preposed requirements of a four-bar mechanism, secondly, establishing a mathematical model of a four-bar mechanism optimization problem, and then, carrying out derivation and analysis to obtain a four-bar mechanism parameter optimization result. The method comprises the following steps: establishing an analytic expression of parameter variables of the four-bar mechanism and compiling a corresponding calculation program, then carrying out iterative optimization on the parameters of the four-bar mechanism by utilizing an optimization algorithm, and finally outputting an optimization result to obtain an optimal design parameter.

Disclosed are techniques for an AI system with a large language mode (LLM) with improved accuracy and reliability in solving mathematical problems. An initial query is transformed into a template query by replacing the original input values with variables. Multiple prompts are sent to the LLM, each being different from one another, and contextually related to the template query. Multiple results are responsively received from the LLM, each result including an analytical expression to solve the mathematical problem. Each of the expressions is evaluated using a numerical evaluation tool with variables of the expression being assigned a common set of randomly sampled values. A consensus is achieved when the evaluated expressions satisfy a consensus condition, such as when all outputs match consistently over N experiments or trials. After the consensus condition is reached, the original inputs are evaluated with one or more of the expressions, and the solution is output.

The invention discloses a geometric analytic expression three-dimensional reconstruction method, and relates to the technical field of computer vision and three-dimensional environment perception. According to the method, for an application scene with a target area located in a known space attitude plane, an accurate geometric mapping relation among a navigation coordinate system, a camera coordinate system and an imaging plane is constructed by fusing a visible light image, a single-point distance measurement value and attitude information output by an attitude sensor (such as an IMU); and pixel-level depth estimation is realized by adopting an analytic expression calculation strategy, so that high-precision and low-complexity three-dimensional reconstruction of a coplanar region is completed.

The application discloses a kind of analytic expression probabilistic power flow calculation method, device and storage medium.The application is determined after the mapping relationship between the injection power of node and the operating state of power system by linear power flow model, using first-order polynomial fitting correction method to revise the operating state of power system, make the operating state of the power system after revision be closer to real operating state, according to the mapping relationship between the injection power of node and the operating state of power system after revision, update linear power flow model, carry out analytic expression probabilistic power flow calculation using updated linear power flow model, to effectively improve the accuracy of probabilistic power flow calculation.

The invention discloses a linear variation stiffness matrix method for suspension bridge space cable forming form finding, relates to the technical field of bridge numerical simulation, and solves the defects of a stiffness matrix in the process of solving the suspension bridge forming form finding through a segmented catenary method. The method comprises the steps that a suspension bridge is simplified into a space cable system composed of a main span, a side span and an anchor span, and the main span, the side span and the anchor span are sequentially subjected to a bridge forming and shape finding process; the linear change stiffness matrix solved in the bridge forming and shape finding process of the main span is used for representing the linear relation between the displacement change of the control point and the initial force change of the main cable; according to the method, an analytical expression of a linear change stiffness matrix is deduced, and an efficient iterative algorithm is established. According to the algorithm, the initial force correction is directly calculated according to the displacement error of the control point in each iteration.

The invention relates to an off-axis three-reflector system design method and system based on a vector aberration theory. The method comprises the following steps: determining the focal length of an off-axis three-reflector system; determining the distance between the mirrors and the distance between the three reflectors and the image surface; according to the design requirements of the coaxial three-reflector system, calculating the curvature radiuses and quadric surface coefficients of the three reflectors; calculating the pupil radius of the pupil off-axis front three-reflector system according to the relationship between the pupil radius before and after the pupil off-axis and the pupil eccentric vector, and determining a wave aberration expression of the pupil off-axis rear three-reflector system; based on a paraxial ray tracing method and a vector aberration theory, establishing analytic expressions of a visual axis error, an increased coma error and an increased astigmatic aberration on a primary imaging surface about an inclination amount and an eccentricity amount; by taking optical axis error, coma error minimization and astigmatic aberration minimization as constraint conditions, optimally solving inclination amounts and eccentricity amounts of the three reflectors; structural parameters of the three-mirror system are optimized through optical simulation software. The efficient and reliable design method and system are achieved.

The invention belongs to the technical field of rub-impact force calculation, and discloses a blade-coating casing normal rub-impact force calculation method considering a heat-wear effect. Based on a one-dimensional unsteady state heat conduction theory, analytic expressions of temperature rise and linear thermal expansion of the blade and the casing are respectively established, and instantaneous temperature change in each contact process is considered. Secondly, physical modeling of various abrasion mechanisms (such as cutting type abrasion, adhesive abrasion and microcrack abrasion) is introduced, and the influence of coating gap changes on the contact force is effectively captured; in addition, the composite stiffness characteristics of the casing coating and the supporting structure are further integrated, so that the rub-impact force calculation can cover the response characteristics under different structural stiffness conditions. Through finite element comparison and experimental verification, the calculation method disclosed by the invention shows relatively high precision in the aspects of predicting thermal deformation, contact force and wear trend, and provides powerful support for subsequent rub-impact fault diagnosis and structural design.

The invention provides a new energy grid-connected short-circuit current and peak value calculation method considering a voltage drop transient state, and belongs to the field of new energy grid-connected system short-circuit current calculation. According to the method, a topological structure and electrical parameters of the doubly-fed wind power generation system are imported, an electromagnetic differential equation is established, a fault voltage initial value expression is deduced, a matrix equation is constructed to solve a node voltage initial value and a loop current derivative initial value, an equivalent attenuation time constant after a fault is calculated, and an approximate analytical expression of a node voltage drop process is established. And calculating a fault point short-circuit current peak value and a double-fed fan short-circuit current peak value. According to the new energy grid-connected short-circuit current and peak value calculation method considering the voltage drop transient state, full-time-domain iterative calculation is avoided, calculation precision and convergence are both considered, the method is suitable for a doubly-fed wind power generation system, and important reference can be provided for equipment type selection and protection setting calculation.

A double-lane millimeter wave vehicle networking safety transmission method, system, device and medium based on STAR-RIS, the method comprising: constructing a STAR-RIS assisted double-lane millimeter wave vehicle networking communication scene; based on the propagation characteristics of millimeter wave signals, combining the channel fading characteristics under the conditions of line-of-sight and non-line-of-sight transmission and the transmission and reflection functions of STAR-RIS, calculating the channel gain of the cascaded channel of the STAR-RIS assisted link; based on the random geometry theory, respectively calculating the probability density functions of the associated distances of the direct link, the STAR-RIS reflection link and the STAR-RIS transmission link; constructing a dynamic link association strategy supporting ternary selection; establishing a signal-to-interference-and-noise ratio model under three association modes; combining the physical layer security performance index definition, calculating the closed-form analytical expressions of the connection interruption probability and the secrecy interruption probability, and verifying the security gain of STAR-RIS; the present application has the advantages of effectively overcoming the half-space coverage blind area of the traditional reflective RIS, and improving the link connection reliability and physical layer safety transmission performance under the double-lane complex shielding environment.

The invention relates to a rapid calculation method and system for a space magnetic field of a circular coil. The method comprises the following steps: converting an integral expression of a Biot-Savart law into a closed analytical solution containing first and second types of complete elliptic integrals; on the basis of an analytical expression of elliptic integration, the magnetic field intensity and direction generated by the coil at any point in the space can be efficiently and precisely calculated, and the defects that traditional finite element simulation calculation is complex, consumed time is too long, and efficiency and precision of a direct numerical integration method are difficult to consider at the same time are overcome. The method is particularly suitable for application scenes such as WPT system design, multi-transmitting-coil amplitude-phase control optimization and real-time simulation which need to carry out rapid and frequent calculation on the magnetic field. According to the method, full-automatic rapid calculation from physical parameter input to magnetic field result output is achieved, the core advantage of the method is that an analytical formula is utilized, the tedious process of numerical simulation and integration is avoided, and the calculation efficiency is remarkably improved while high precision is guaranteed.

The application relates to the technical field of estimation of maximum frequency deviation of power grid nodes and is used for solving the problem that the existing estimation method of maximum frequency deviation of power grid nodes cannot reflect the time-space difference characteristics of frequency response of an interconnected power system. First, a two-region frequency response model TAFR considering the time-space difference characteristics of frequency of power grid nodes is established, a time-domain analytical expression describing the node frequency difference mechanism is obtained by adopting the mode analysis and average system frequency model aggregation idea, and a maximum frequency deviation estimation method reflecting the time-space difference is proposed on the basis of the analytical expression. The established TAFR model considers the distribution of tie-line parameters, system inertia and damping, and equivalently processes the new energy frequency modulation parameters, compared with the existing frequency dynamic response model, the model has improved accuracy and applicability while ensuring the time-space difference.

The invention discloses a turbulence model construction method for aerodynamic simulation of a hybrid three-compartment vehicle, and relates to the field of model simulation, and the method comprises the steps: S1, employing a flow field inversion method, and obtaining the dense space distribution of a turbulence model correction term; s2, screening local flow field characteristics related to the correction distribution characteristics; s3, training by adopting a symbol regression method to obtain an analytical expression of a turbulence model correction term; s4, through mathematical derivation, an analytical expression of a correction term is migrated into the standard model, so that the correction term is added in front of a damage term of a transport equation of the dissipation rate of the standard model; s5, selecting an initial value of a to-be-calibrated coefficient in the correction item according to the smoothness degree of the chassis of the hybrid three-compartment vehicle; and S6, calibrating the to-be-calibrated coefficient in the expression in the step S4 on the basis of real vehicle experimental data of the hybrid three-compartment vehicle to obtain the turbulence model for aerodynamic simulation of the hybrid three-compartment vehicle.

The invention belongs to the technical field of ship intelligent digital optimization design, and particularly relates to a ship global deformation and optimization method, program and equipment considering drainage volume precision control and deformation rationality and a storage medium. The analytical expression of the drainage volume variation about the global deformation parameter is obtained based on the numerical integration and the recursion formula, the reasonable deformation parameter range of the ship body is determined based on the global deformation modification function and the regular design space, the ship body does not need to be actually deformed, the corresponding volume variation can be directly predicted according to the design parameter, and the calculation accuracy is improved. Accurate feedforward control of volume constraint and direct judgment of rationality of the deformed ship are realized. On the basis, rapid optimization of any ship type structure under the constraint of reasonable deformation and accurate volume control is realized in combination with an agent model. According to the method, a traditional'design-verification-adjustment 'experience iteration process is converted into deterministic one-step calculation, and subsequent optimization can be directly carried out in a pre-verified reasonable design space.

The invention discloses a two-point grounding fault model analysis method in a neutral point non-effective grounding mode, and aims to solve the problem that a unified accurate mathematical model suitable for a neutral point non-grounding and arc suppression coil grounding system under an in-phase two-point grounding fault is lacked in the prior art. According to the method, a fault network topology is reconstructed, a multivariate function equation set containing a fault position, ground capacitance, arc suppression coil parameters and a power supply initial phase angle is established, explicit analytical expressions of zero-sequence voltage current and phase voltage current are deduced, and a transient process is modeled in combination with a state space method. And accurate description of a fault characteristic quantity spatio-temporal evolution rule is realized. By adopting the above technical scheme, the method can provide a modeling basis which can be directly called for high-fidelity simulation platforms such as RTDS, and supports intelligent protection algorithm development and fault diagnosis system optimization.

The application relates to the technical field of wind power generation, and discloses a wind turbine design method adopting a frictional tuned mass damper, which adds a frictional tuned mass damper to a man platform in a tower drum of a wind turbine, establishes a motion equation of the wind turbine after adding the frictional tuned mass damper based on a structural dynamics principle, deduces a mathematical analytic expression of a system dynamic coefficient, and obtains parameters of the frictional tuned mass damper through a system optimization theory. The application solves the problems that the prior art is difficult to realize damping through the tuned mass damper in the narrow space in the cabin or the tower drum, and the damping control effect is poor.

The invention discloses a rapid calculation method and device for the sensitivity of a linear periodic time-varying system based on a matrix sparse technology, and belongs to the technical field of modeling analysis of the linear periodic time-varying system.The rapid calculation method comprises the steps that an LTP system is converted into an equivalent LTI system, and the eigenvalue, the left eigenvector and the right eigenvector of the LTP system are obtained; based on a functional derivative method, obtaining a sensitivity analytical expression of the LTP system characteristic value to the parameter; according to the influence mechanism of the parameters on the system matrix, obtaining an analysis form of the influence of the parameters on the LTP system matrix in the sensitivity analysis expression; and converting a partial derivative of a system matrix to a steady-state trajectory into sparse calculation of a vector field Hessian matrix by using a matrix sparse technology, thereby obtaining a calculation result of the characteristic value sensitivity of the LTP system. According to the method, the sparse characteristic of the system matrix in the PEPS is utilized, the calculated amount and the storage requirement of the system matrix on trajectory partial derivative solving are reduced, and therefore calculation of the LTP characteristic value sensitivity is accelerated.

The application discloses a control method for primary frequency modulation in a power dead zone range of a hydroelectric generating set, and belongs to the technical field of hydroelectric generating set regulation. The method comprises the following steps: S1, calculating H1 and H2 of a water diversion system according to the water flow inertia time constant of the water diversion system and the mechanical inertia time constant of the generating set; S2, calculating a dynamic analytical expression of the generating set power when a frequency unit step disturbance occurs; S3, calculating a first-order differential link coefficient decomposed by a second-order correction link based on the dynamic analytical expression of the generating set power; and S4, calculating the output of a PID speed regulator in a current sampling period. The scheme calculates the oscillation link transfer function parameters in a dynamic process, and a second-order system correction transfer function of a frequency given value is designed on the basis, so that the oscillation phenomenon of the generating set power does not occur when the frequency given value of the generating set changes, the problem that the power exceeds the power dead zone in the dynamic process is prevented, and a limiting link is arranged at the frequency deviation value to ensure that the power steady-state value exceeds the power dead zone range.

The invention discloses a single-stage bidirectional DC-AC converter minimum current stress optimization method, system and device and a medium, and belongs to the technical field of power electronic converter control, and the method comprises the steps: building an operation mechanism comprising four effective working modes based on the single-stage bidirectional DC-AC converter through a frequency conversion phase shift control strategy and aiming at bidirectional energy transmission demands, the inverter and the rectifier respectively correspond to inversion and rectification modes under different relations of input and output voltages. Taking the minimum current stress as a target function, solving the optimal shift ratio by combining the transmission power constraint and the soft switching condition, and calculating the real-time switching frequency by adopting equal power modulation. Frequency conversion control is introduced on the basis of phase shift control, power factor correction and soft switching constraint can be achieved at the same time, the optimal phase shift ratio and the switching frequency are directly solved through an analytical expression, and the calculation complexity of a traditional iterative algorithm is avoided.

The present application relates to a kind of close approach trajectory robust control method in multi-target tracking, it is related to optimal control problem analytical objective function, constraint establishment and robust approach trajectory control scheme, belong to spacecraft situation awareness and control field.The present application first establishes optimal trajectory control problem, considers information gain and security constraint comprehensively, to establish the model basis of robust control instruction.Second, by establishing the analytical expression of Hellinger distance in optimal control problem under the theory of Outer Probability Measures (OPMs), the difference between the prior estimate and the posterior estimate of the target state is effectively evaluated, and then the information gain value under different control instructions is calculated to select the optimal control instruction.At the same time, by establishing the analytical upper and lower bound expression of the void probability in the constraint condition of optimal control problem under the theory of OPMs, the void probability of the approach trajectory at any time under different control instructions can be efficiently calculated, so as to evaluate the safety of the approach trajectory and select the control instruction that meets the constraint condition.Finally, a robust trajectory control and a possibility label multiple Bernoulli filter module are designed to form a close approach trajectory robust control scheme, which realizes the goal of generating optimal control instructions in real time during the approach and tracking process, and achieves the effect of maximizing information gain and ensuring the safety of the approach trajectory.

The invention discloses an integral transformation fracture phase field model implementation method of a random-order polynomial cohesion law, and belongs to the technical field of phase field model finite element analysis. The method comprises the following steps: inputting a parameter equation of a polynomial cohesion law of any order and a target order into a subprogram; deducing a cohesion eigenfunction of a random-order polynomial cohesion law by using a subprogram to determine an analytical expression of a random-order polynomial energy density eigenfunction, solving a target-order polynomial energy density eigenfunction expression and first two-order derivatives thereof, and determining an expansion expression at a zero point by using Maclaurin series; and inputting the target-order polynomial energy density eigenfunction expression, the first two-order derivatives thereof and the expansion expression at the zero point into a phase field model solver to obtain a calculation result of the target-order polynomial integral transformation fracture phase field model. According to the method, the simulation calculation of the integral transformation fracture phase field model of the target-order polynomial cohesion law can be realized under a universal finite element framework, and the accuracy and the efficiency are improved.

The invention discloses a low-frequency oscillation optimization method of an electric power system containing an SDC and a DFIG based on balanced truncation and series control compensation. The low-frequency oscillation optimization method comprises the following steps: 1, establishing a linear analysis model of a wind power grid-connected electric power system containing a synchronous generator SG, the DFIG and an additional damping controller SDC; 2, truncation processing is carried out on a state matrix in the state matrix equation of the main system after balance transformation, and a main system state matrix equation after order reduction is obtained; 3, constructing a time domain matrix of the system containing the series feedback controller to obtain a system state matrix equation containing the series feedback controller; 4, solving a characteristic value and a damping ratio of the system state matrix equation containing the series feedback controller, and constructing a control parameter analytic expression of the characteristic value and the damping ratio to the SDC in a low-frequency oscillation mode; and 5, solving by using the low-frequency oscillation optimization model of the SDC to obtain the optimal adjustment amount of the control parameters of the SDC. According to the invention, the control compensator is added to optimize the characteristic value under low-frequency oscillation and the control parameters of the SDC, so that the stability of the system is optimized.

The invention discloses a deflection calculation method of a steel-concrete composite beam under uniformly distributed loads, and relates to the technical field of high-speed railway bridge construction. The method comprises the following steps: establishing a differential equation of the continuous steel-concrete composite beam and carrying out Laplace transformation to obtain an expression of a non-zero real solution; inverse transformation is carried out on the equation obtained after Laplace transformation, an analytical expression of the deflection of the composite beam is obtained, and the expression comprises a plurality of unknown quantities. Substituting the structure parameters and the material parameters of the composite beam into the non-zero real number solution expression to solve Laplace transformation parameters; the parameters and the boundary conditions are substituted into the deflection analytical expression, and matrix elements used for solving unknown quantities are obtained; and constructing a linear equation set, solving an unknown quantity, substituting the unknown quantity into a deflection analytical expression, and finally obtaining a complete expression for solving the deflection of the continuous composite beam. The complete expression of the deflection of the continuous composite beam provided by the invention is suitable for analyzing the deflection of a single-span or continuous steel-concrete composite beam, and has relatively high calculation precision.

The invention discloses a turbulence model construction method and device, electronic equipment, a storage medium and a vehicle, and relates to the field of sound production control, and the method comprises the steps: obtaining the experiment data of a target vehicle type separation flow, and determining the dense space distribution characteristics of a turbulence model correction term according to the experiment data; determining a first flow field feature related to the dense spatial distribution feature in the flow field features of the separation flow; according to the first flow field feature and the dense space distribution feature, determining an analytical expression of a turbulence model correction term; and constructing a turbulence model for calculating the air resistance of the target vehicle model based on the analytical expression. The precision of the turbulence model for calculating the air resistance of the target vehicle model can be improved, so that the research and development efficiency is improved and the research and development cost is reduced.

The application belongs to the technical field of communication system, and particularly relates to a method and system for deriving optimal degree distribution of regular LDPC code based on AWGN channel. The method comprises the following steps: S1, taking the maximization of code rate of the regular LDPC code as a criterion and taking the decoding success as a prerequisite, a target function with a constraint condition is constructed; S2, fixing the degree d v of the variable node, based on the fixed point analysis theory, a theoretical analytic expression of the degree d c of the check node in the LDPC code is derived, and an inverse function of the target function in the non-convex optimization problem is solved; S3, based on the mathematical set theory, the uncertainty in the inverse function solving problem in the step S2 is solved, and the optimal degree distribution of the LDPC code under the AWGN channel is obtained. The application has the characteristics of improving the channel coding performance in the communication system.

The invention provides a new energy networking flexible direct current system fault current sequence component characteristic characterization method, which comprises the following steps of: considering a fault ride-through control strategy of alternating current transmission line side equipment in a new energy networking flexible direct current system, and establishing an equivalent sequence network diagram of the system; solving analytic expressions of fault current sequence components on two sides of the line under different fault types based on the equivalent sequence network diagram; quantizing a fault current sequence component corresponding to each fault type through an analytical expression; and extracting influence parameters of the fault current sequence component, and representing the characteristics of the fault current sequence component in combination with the analytical expression. According to the method, the fault current sequence components under different fault types are systematically quantified, the association rule of the influence parameters and the fault current sequence components is represented, a theoretical basis is provided for formulation, optimization and parameter adjustment of a conventional control strategy, the adaptability and the operation reliability of the control strategy to different fault scenes are remarkably improved, and the method is suitable for large-scale popularization and application. And technical support can be directly provided for safe and stable operation of the new energy network construction flexible direct current system.

The present invention discloses a method for calculating the grid-connected power flow of a doubly-fed pumped-storage unit based on optimal speed, comprising: 1. fitting the efficiency curve of the doubly-fed pumped-storage unit to a polynomial function of flow rate and speed using a recursive least squares method with a discount factor; 2. establishing an analytical expression for the relationship between mechanical power and flow rate when the unit is operating at optimal speed; 3. introducing the unit's internal constraint equations into the grid power flow equation to establish a grid-connected power flow model; 4. converting the grid-connected power flow model into a least squares model; 5. introducing two approximate iteration steps and proposing a fourth-order Levenberg-Marquardt method for solution, thereby addressing the problem of non-convergence of power flow caused by the positive and negative switching of the rotor voltage phase angle. The present invention considers the impact of variable-speed operation of the doubly-fed pumped-storage unit on internal losses, establishes a grid-connected power flow model that combines its internal constraint equations with the grid power flow equation, and employs the fourth-order Levenberg-Marquardt method for solution, thereby improving the accuracy of grid-connected power flow calculation for the doubly-fed pumped-storage unit.