213 results about "Analytic expression" patented technology

The invention discloses a single-epoch GNSS-oriented PAR ambiguity precision factor determination method, and relates to the technical field of satellite navigation and positioning. Comprising the following steps: dividing pseudo-range and carrier wave observed quantities in a GNSS double-difference mathematical model into two groups, and constructing a function relationship between a floating point solution # imgabs1 # and a floating point solution # imgabs2 # variance-covariance matrix of an ambiguity vector # imgabs0 #; constructing a single-frequency single-epoch single-system P-ADOP expression and establishing a shrinkage factor k de-inversion transformation analytic expression, and simultaneously obtaining a single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximation formula; and performing analogy derivation on the single-frequency single-epoch single-system non-inverse transformation P-ADOP approximate formula to obtain a single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula. The method has important theoretical value and practical guiding significance for GNSS optimal ambiguity subset rapid selection and positioning and partial ambiguity fixing success rate influence mechanism analysis.

The invention relates to the field of heat supply network analogue simulation, and particularly discloses a regional heat supply network dynamic simulation method and system, a terminal and a medium, the method comprises the following steps: constructing a hydraulic model semi-analytical expression and a thermal model semi-analytical expression of a pipeline in a regional heat supply network, and according to the pipeline momentum conservation and the node mass conservation, calculating the thermal model semi-analytical expression of the pipeline in the regional heat supply network; constructing semi-analytic coefficient recursive relation linear equations, and respectively calculating semi-analytic coefficients of a hydraulic model semi-analytic expression and a thermal model semi-analytic expression through the two semi-analytic coefficient recursive relation linear equations according to initial conditions and boundary conditions of the pipe section; the calculated semi-analytic coefficient meets the condition that the truncation error is not greater than a truncation error threshold value; and substituting the semi-analytic coefficient into the semi-analytic expression to obtain a semi-analytic calculation result of each pipe section of each pipeline under all time steps. According to the method, non-iterative calculation of the PDAEs is realized, the calculation complexity is reduced, the simulation efficiency is improved, and the solution continuity can be ensured.

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.

The invention discloses a human body posture intelligent identification method based on a multi-modal micro-motion feature and a Transform network, and the method comprises the steps: deducing micro-Doppler signal mathematical analysis expressions corresponding to different parts of a human body from human body target radar echo modeling; the method comprises the following steps: performing data preprocessing on target echo data acquired by a millimeter wave radar by adopting two-dimensional fast Fourier transform to obtain a one-dimensional spectrum sequence and a two-dimensional Doppler image corresponding to different postures, and respectively sending the one-dimensional spectrum sequence and the two-dimensional Doppler image into a one-dimensional Transform network and a two-dimensional Transform network for feature extraction; and carrying out feature splicing by adopting a multi-modal feature fusion model and outputting a classification result. According to the method, the problems of low recognition rate, poor robustness and the like in the existing human body posture intelligent recognition means can be solved.

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 belongs to the technical field of resource planning, and particularly relates to a power distribution network distributed resource robust planning method and device based on cluster division, and the method comprises the steps: building a source-storage robust locating and sizing model as an upper model based on cluster division, and setting a target function and constraint conditions thereof; based on cluster planning, constructing an intra-cluster reliability index calculation model as a lower-layer model, and setting a target function; combining the upper-layer model and the lower-layer model to obtain a double-layer joint planning model; aiming at an island operation scene under a cluster division condition, designing a reliability merging optimization method integrated with island operation characteristics, and optimizing the double-layer joint planning model to obtain an analytical expression of a reliability index; and obtaining a joint planning scheme of the distributed resources of the power distribution network by solving the optimized double-layer joint planning model. According to the method, the source load uncertainty and the reliability index are effectively considered, and the economical efficiency, the flexibility and the reliability of power distribution network planning are remarkably improved.

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 relates to the technical field of broadband radar signals, and provides a radar target robust intelligent detection and interference adaptive suppression method and system, and the method comprises the steps: carrying out the decorrelation transformation of received data and a parameter matrix through employing the skew symmetry characteristic of a clutter covariance matrix, and completing the preprocessing of initial data; carrying out correlation calculation estimation under the condition of no target hypothesis and under the condition of target hypothesis, and constructing distance extension target Gradient detection statistics under the condition of a known clutter skew symmetry covariance matrix; constructing a detection statistic lambda of the radar target robust intelligent detection and interference adaptive suppression method; and determining a detection threshold T through theoretical calculation or Monte Carlo simulation according to a preset false alarm probability, comparing the detection statistic lambda with the detection threshold T, and judging whether a distance expansion target exists in the current distance unit to be detected or not according to a comparison result. According to the method, an analytical expression design is adopted, a complex iterative calculation process is avoided, and the operation efficiency is improved.

The invention discloses a method for calculating the diffusion coefficient of an electrode material, which comprises the following steps: establishing a Fick diffusion law-based constant current gap titration (GITT) theoretical model, and describing the concentration distribution of ions in the electrode material; solving a partial differential equation in the GITT theoretical model through Laplace transformation to obtain an analytical expression of ion concentration; obtaining a diffusion coefficient calculation formula suitable for a full time range; verifying the accuracy of the diffusion coefficient calculation formula through numerical simulation; and a concentration-based diffusion coefficient expression is converted into a voltage-based diffusion coefficient expression, so that processing and analysis of experimental data are facilitated. The method for calculating the diffusion coefficient of the electrode material, provided by the invention, is based on a constant current gap titration technology, is suitable for full-range data, extracts experimental data, calculates a voltage difference, selects an optimal formula and generates a visual image through an automatic program, and remarkably improves the calculation precision of the diffusion coefficient and the processing efficiency of the experimental data.

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.

The invention discloses a full-power type wind turbine generator fault occurrence moment current analysis method and related equipment, and the method comprises the steps: obtaining control parameters and operation parameters of a full-power type wind turbine generator, and when low-voltage fault ride-through is detected, substituting the control parameters and the operation parameters into a fault ride-through controller model, fault current partition logic is combined to obtain fault current analytic expressions corresponding to different fault state intervals, and then the current instruction data are substituted into the fault current analytic expressions under the corresponding fault state intervals, so that current analysis is carried out through the fault current analytic expressions and a closed-loop transfer function, and fault current analysis is carried out through the fault current analytic expressions and the closed-loop transfer function. And obtaining the fault current at the fault occurrence moment of the full-power wind turbine generator. According to the scheme, the control strategy of the active and reactive current during low voltage ride through is analyzed, and the current analysis formula of the fault occurrence moment corresponding to each fault current partition is obtained by combining different fault current partitions, so that the fault current of the unit fault occurrence moment is obtained based on the current analysis formula.

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 provides a performance analysis method of a multi-RIS-assisted underwater wireless optical communication system under an RIS selection scheme. The performance analysis method comprises the following steps: establishing a multi-RIS-assisted underwater wireless optical communication system model under the RIS selection scheme; the method comprises the following steps: deriving a cumulative distribution function expression of an instantaneous signal-to-noise ratio between a source node and a destination node based on a multi-RIS-assisted underwater wireless optical communication system model under an RIS selection scheme; deriving a probability density function expression of an instantaneous signal-to-noise ratio between a source node and a destination node; based on the cumulative distribution function and the probability density function expression of the instantaneous signal-to-noise ratio, deriving to obtain an analytical expression of the outage probability and the M-PAM average bit error rate, and based on the obtained analytical expression, analyzing the performance of the outage probability and the M-PAM average bit error rate of the multi-RIS-assisted underwater wireless optical communication system under the RIS selection scheme. The invention shows the potential advantage of integrating multiple RISs into an underwater wireless optical communication system.

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.