23 results about "Analytical expressions" patented technology

This invention provides an adaptive admittance method and system based on the optimal control LQR theory, including constructing an environmental dynamics model and a robotic arm admittance control model, and deriving their interactive dynamics model; defining state variables and control inputs, and establishing a standard form state-space equation; constructing a quadratic performance index function, transforming admittance parameter optimization into an LQR problem; substituting the linear quadratic regulator framework into the quadratic performance index function, transforming the LQR problem into solving the Riccati matrix differential equation, and deriving analytical expressions for virtual optimal stiffness and virtual optimal damping; within the robotic arm control sampling frequency, inputting real-time collected environmental contact forces and the actual pose of the robotic arm end effector, along with set weighting coefficients, into the analytical expressions to calculate optimal virtual stiffness and damping; and then calculating pose corrections based on the admittance control model to correct the robotic arm's motion trajectory.

This invention discloses a design method for a Type I ternary coprime array based on coprime sparse arrangement, relating to the field of array structure design. Two coprime positive integers M and N are selected to construct the basic structure of a prototype coprime array. A subarray with n elements and n spacing is added in reverse to the prototype coprime array to form a Type I ternary coprime array. Based on the distribution law of holes in the prototype coprime array, the lower bound expression of the optimal parameters of the subarray can be obtained, ensuring that the holes in the prototype coprime array are completely filled. Analytical expressions for the distinct and continuous degrees of freedom of the Type I ternary coprime array are derived. The method is scalable, allowing for the expansion of array degrees of freedom without destroying the prototype coprime array structure by adding array elements in reverse. The Type I ternary coprime array designed using this method exhibits weak mutual coupling, scalability, and high distinct degrees of freedom.

This invention discloses a rapid voltage calculation method for a radial virtual power plant based on the branch U-S theorem, belonging to the field of power system analysis and calculation technology. The method includes: acquiring the power network topology of the radial virtual power plant; numbering each node in the network layer by layer; collecting the voltage and power of each node and the impedance data of each branch; calculating the voltage of each node layer by layer based on the branch U-S theorem, according to the known head-end voltage and the power flowing into the tail end; and outputting the voltage calculation results for each node. The branch U-S theorem provides an analytical expression for the tail voltage of a single power branch. This invention avoids the complex iterative process required by traditional voltage calculation methods, enabling rapid and accurate calculation of the voltage of each node in a radial virtual power plant, significantly improving computational efficiency, and is suitable for scenarios such as real-time monitoring, rapid dispatching, and market response of virtual power plants.

This invention belongs to the field of rotating machinery condition monitoring and fault diagnosis technology. It proposes a bearing failure assessment method and system. The method involves acquiring bearing vibration signals and performing mean and absolute value removal processing to obtain the signal to be processed. Next, a lower threshold for the tail is determined, and a set of tail samples with amplitudes greater than this threshold is selected. Then, a soft-truncated power-law distribution model is constructed based on the tail sample set, and the distribution parameters, including the power-law tail exponent, truncation scale parameter, and truncation smoothing exponent, are solved using maximum likelihood estimation. Furthermore, an analytical expression for the improved Gini index is constructed based on the distribution parameters, and the bearing degradation degree index is calculated. Finally, a bearing degradation curve is constructed based on the degradation degree index for different time periods. This invention accurately characterizes the tail impact features of vibration signals using a soft-truncated power-law model and quantifies the degradation degree using an improved Gini index, effectively assessing the health status and failure trend of rolling bearings.

This invention belongs to the field of seismic design technology for railway bridges, and relates to a seismic analysis method for railway bridges using a variable friction coefficient friction pendulum bearing for seismic isolation and vibration reduction. This method is used to determine the design displacement D of the variable friction coefficient friction pendulum bearing; specifically, it includes the following steps: establishing an equivalent period T based on the design parameters of the variable friction coefficient friction pendulum bearing. eff The relationship between the coefficient of friction and the variable friction coefficient; based on the bridge design conditions, the relationship between the equivalent period and the acceleration response spectrum value is established, and S(T) is obtained. eff Determine the damping adjustment coefficient η; equivalent damping ratio ξ; establish support displacement and equivalent period T. eff S(T) eff By considering the relationship between η and η, and combining it with Newton's iteration process, the final support displacement D is determined. This invention saves time by using analytical expressions for calculation, avoiding tedious modeling, long computation times, and convergence issues compared to the finite element model nonlinear time history analysis method. This allows for rapid evaluation of the seismic performance of different support parameters and structural configurations during the scheme design, parameter optimization, and preliminary design stages.

The application relates to the technical field of bridge engineering and provides a method for determining the spatial dynamic response of a four-corner elastic support bridge, which comprises the following steps: introducing a virtual rigid arm, converting a complex four-corner elastic support bridge system into a simplified mechanical model with clear physical meaning, and obtaining a parameter-adjustable analytical simplified theoretical model; based on the parameter-adjustable analytical simplified theoretical model, solving bridge vertical and torsional dynamic response equations by using Duhamel integral, and outputting dynamic response analytical solutions. The application converts the traditional bridge dynamic response problem depending on high-dimensional finite element simulation into an analytical expression which can be obtained by using Duhamel integral, greatly improving the solution efficiency; the application can be used for bridge design, evaluation and health monitoring: the dynamic response analytical solution of the simplified theoretical model can be embedded into a bridge structure response analysis tool chain, realizing bridge performance prediction and diagnosis under the working conditions of extreme load action, support degradation and the like, and having good engineering popularization value.

This invention relates to the field of thread turning technology, and discloses a thread turning cutting simulation method and system based on the analytical formula of a helical surface. The method includes: acquiring helical surface data during thread turning and constructing a geometric space model of the helical surface that can represent the tool sweep body; acquiring blank data and constructing a blank model using a tri-dexel model; for dexel segments parallel to the rotation axis, calculating the corresponding rotation angle and axial intersection point using the helical surface geometric space model, and calculating the axial cutting result of the tool based on the axial intersection point; for dexel segments perpendicular to the rotation axis, solving multiple solutions for the rotation angle and multiple intersection points using the helical surface geometric space model, selecting the effective intersection points as non-axial intersection points, and calculating the non-axial cutting result of the tool based on the non-axial intersection points. This invention can improve the efficiency and accuracy of thread turning cutting simulation.

The application relates to a time-optimal three-axis reorientation method and device for an inertia-symmetrical rigid spacecraft, which determines an angular velocity analytical expression according to inertia symmetry of the spacecraft and a time-optimal control switch structure set in advance; through introduction of a new inertia axis coordinate system, the symmetry characteristic of a reorientation track is explicitly derived; a Radau pseudo-spectrum discrete method is used to discretize a quaternion dynamic equation, so that the time-optimal reorientation problem is converted into a nonlinear programming problem; through given two parameter values, the discretized quaternion dynamic equation is converted into a linear equation set and is solved, a discrete quaternion value sequence obtained through decomposition is used, a gradient method or a Newton method is used to optimize the two parameters, and a time-optimal reorientation track is determined according to an optimization result. The method does not need to perform numerical integration or solve a large-scale nonlinear programming problem, and the calculation efficiency is significantly improved, so that fast and accurate track generation of an inertial rigid spacecraft is realized.

The application discloses a voltage fast correction method and device for wide-area new energy fluctuation, relates to the field of power system optimization control, and comprises the following steps: S1, centralized reactive power optimization is carried out by using an opportunity constraint programming reactive power optimization model, and an optimal operation point of a power system in a time period is solved; S2, at the optimal operation point, analytical expressions of voltage sensitivity coefficients and network loss micro-increment rates are derived; S3, when power fluctuation of a new energy node occurs, the amplitude and phase angle states of the node voltage are corrected according to a power fluctuation interval, and the corrected voltage sensitivity coefficients and network loss micro-increment rates are obtained by substituting the analytical expressions; and S4, at each time of the time period, the optimal reactive power regulation amount of each new energy node is solved by using a segmented calculation mode, and voltage fast correction is completed. The application can effectively suppress system voltage disturbance caused by active power fluctuation of new energy, reduce system active power loss, and simultaneously improve voltage safety level and system operation economy under wide-area new energy fluctuation.

This invention discloses a fast method for generating broadband null patterns, belonging to the field of array signal processing. First, the invention constructs an objective function and its constraints based on the pointing of the main lobe and nulls of the pattern. After converting this function into a Lagrangian function, its extreme points are solved to obtain the analytical expression of the array excitation vector at each sampling frequency. Next, the FIR filter coefficients are solved based on the element excitations corresponding to each frequency sampling point. Finally, a filter is constructed based on the FIR filter coefficients to obtain the desired broadband array pattern synthesis result. This invention provides a fully analytical expression for generating null pattern element excitations, solving the problem of large computational load and long processing time caused by multiple iterations of optimization algorithms in existing methods. It possesses real-time synthesis capabilities and has engineering application significance.

This invention provides a method and system for reconstructing the outer contour function of a projectile's head shape based on machine vision, belonging to the field of machine vision image processing and automatic parameter calculation technology. First, the invention performs semantic segmentation on the frontal view image of the projectile's head shape to obtain a binary mask of the projectile target, and extracts and crops the outer contour of the head shape segment. Second, through coordinate axis self-calibration and attitude alignment, the standard attitude coordinates of the projectile's head shape outer contour are obtained. Then, in the local coordinate system, geometric constraint feature points are extracted to obtain the endpoints, pixel areas, and single-point coordinates of the projectile's head shape outer contour. Third, a two-parameter head shape outer contour shape function satisfying endpoint constraints is constructed, and the shape parameters are solved using area constraints and single-point constraints to obtain the analytical expression of the head shape outer contour. Finally, the outer contour function and its derivative are substituted into the head shape factor integral formula to achieve automatic calculation of the head shape factor.

The application discloses a power and electricity balance sensitivity calculation method and device containing parameter programming and data driving fusion, relates to the field of power system dispatching operation, and comprises the following steps: constructing a power and electricity balance analysis model; obtaining a segmented analytical expression of a balance evaluation index about boundary conditions based on a parameter programming theory; identifying a turning point and adaptively sampling based on the segmented analytical expression to generate a training sample set; training a neural network model based on the training sample set; and calculating the power and electricity balance sensitivity by using the trained neural network model. The application overcomes the shortcomings of low sampling efficiency and large modeling error of traditional sensitivity calculation based on random sampling, and provides technical support for dynamic updating of power and electricity balance.

This invention relates to the field of multi-axis CNC machining and industrial robot machining technology, specifically disclosing an asymmetric five-axis toolpath smoothing method based on path weighted synthesis. The method includes: constructing a universal corner smoothing model based on path weighting; constructing an analytical expression for a high-order continuous weighted function; Cartesian space smoothing of the tool tip position path; unit spherical space smoothing of the tool axis direction path; synchronous adjustment of C3 continuous parameters for position and direction paths; interference verification and asymmetric adjustment of adjacent corner transition intervals; continuous speed planning and real-time interpolation; and motion control of the machining equipment. This invention overcomes the shortcomings of existing five-axis path transition smoothing technologies, such as poor geometric versatility, incoordination between tool tip and tool axis movements, easy interference in short path segments, and inconsistent bidirectional machining trajectories. It improves geometric versatility and processing efficiency, achieves high-order continuity and consistent machining surfaces, and can be ported across platforms and extended to higher orders.

This invention discloses a method for calculating the virtual inertia of a photovoltaic-storage system based on a virtual synchronous machine, belonging to the field of new energy power generation technology. Addressing the complex frequency response characteristics of photovoltaic-storage systems based on virtual synchronous machines, this invention first constructs per-unit power balance equations for both grid-connected and off-grid modes. Based on this, it constructs frequency response transfer function models for both grid-connected and off-grid modes. Then, it derives analytical expressions for system frequency changes and calculates key frequency response indicators. This invention can quantitatively reveal the virtual inertia J. vsg and virtual damping coefficient D vsg The quantitative relationship between control parameters and these key performance indicators helps guide the optimal design of VSG controller parameters and the precise and rational scheduling of power in photovoltaic energy storage systems.

This invention proposes a novel high-latitude navigation method based on the ECEF system, belonging to the field of high-precision navigation technology. This invention addresses the problems of low positioning accuracy and large error fluctuations in traditional grid coordinate system and transverse coordinate system navigation algorithms in high-latitude environments, as well as the navigation interference caused by meridian convergence and high-latitude dynamic effects. The steps of this invention include: establishing a transformation matrix between the geographic coordinate system and the geocentric-fixed coordinate system; establishing discrete navigation solution equations for attitude direction cosine matrix, velocity, and position in the geocentric-fixed coordinate system; establishing error equations for attitude error, velocity error, and position error in the geocentric-fixed coordinate system; performing an S-domain transformation based on the error equations and converting to the time domain to obtain an analytical expression for inertial navigation error in the geocentric-fixed coordinate system; and obtaining optimized high-latitude navigation results based on the oscillation and divergence characteristics of attitude and velocity errors presented by the analytical expression for inertial navigation error.

The application discloses a target motion parameter estimation method and system based on a bistatic Doppler time-frequency curve; a plane rectangular coordinate system is established with a receiver position as an origin, a transmitter position is a known fixed coordinate, and a target is assumed to be a uniform linear motion; according to analytical expressions of distances between the transmitter and the target and between the receiver and the target, a bistatic equivalent path length is constructed, and an analytical expression of Doppler variation with time is derived based on a Doppler physical model; a target Doppler time-frequency curve is sampled at multiple time points to obtain a Doppler measurement vector, and outputs of the analytical model at corresponding time points are combined to form a model vector, so that an observation equation with target motion parameters as unknown quantities is formed; and a nonlinear least square algorithm is used to estimate the target motion parameters. The application has the advantages of not needing distance measurement, complete theoretical basis, high estimation precision and easy engineering implementation, and can be used for multi-station radar target trajectory matching and information fusion.

This application discloses a method for solving damage evolution parameters in a damage constitutive model, belonging to structural mechanics and fracture mechanics. The method includes: establishing a mathematical relationship between damage variables and associated variables based on thermodynamic principles, and obtaining an integral expression for the energy dissipation potential per unit volume by combining damage evolution criteria; simplifying the integral expression for the energy dissipation potential per unit volume based on the principle of equivalent strain, obtaining a scalar analytical expression; numerically integrating the scalar analytical expression using the three-point Newton-Cotes integration algorithm, and iteratively solving for the damage evolution parameters using the secant method. This method transforms complex tensor operations into simple scalar analysis, reducing the computational burden. Furthermore, the use of the Newton-Cotes integration method and the secant method iterative solution strategy ensures accurate calculation of damage parameters, enhances computational stability and reliability, and significantly improves the efficiency and accuracy of the solution.

The application discloses a power communication network precise timing optimization method and device based on asynchronous traffic shaping, and relates to the technical field of power communication. The method comprises the following steps: constructing a power communication network system model, classifying heterogeneous service flows into PTP flows, key background flows and low-priority flows according to priorities; quantifying the interference relationship between aggregated bursts and non-preemptive congestion to the queuing delay jitter of PTP flows based on network calculus, constructing a single-hop delay and deducing a jitter analytical expression; constructing a planning model with the minimum PTP flow jitter square sum as an objective and containing hard real-time constraints based on the single-hop delay and the jitter analytical expression, and determining an objective function; adopting a two-stage heuristic algorithm based on gradients to optimize the objective function and solve optimal ATS configuration parameters meeting power deterministic service requirements; and performing power communication network traffic scheduling according to the optimal ATS configuration parameters. The application can improve timing accuracy in an asynchronous environment.

This invention relates to a hybrid path planning method for spiral machining of optical freeform surfaces with global constraint optimization, comprising: establishing a continuous trajectory equation in the projection plane to obtain a sampling point sequence; establishing the polar coordinate equation of the optical freeform surface and determining the local maximum allowable planar projection step size limit equation; dividing the machining area into an inner isoangular region and an outer isoar length region, with the switching radius as the boundary, and defining an actual programming step size function; according to the local maximum allowable planar projection step size limit equation, performing actual programming step size verification on the inner isoangular region and the outer isoar length region respectively, and combining machine tool dynamic constraints to determine whether the switching radius should be retained, obtaining a candidate set of switching radii; constructing an analytical expression with the goal of minimizing the total number of control points and solving it to obtain the optimal parameter combination, and using the obtained optimal parameter combination as the input parameters for the hybrid discrete operation of CAM software. This invention achieves synergistic optimization of machining accuracy and efficiency.

This invention provides a method for angle calibration and error analysis of a wide-angle arc detector, comprising: determining at least three diffraction peak data of a standard sample and calibrating a first parameter, a second parameter, and a third parameter based on the diffraction peak data; establishing analytical expressions for the first parameter, the second parameter, and the third parameter; solving for the first parameter, the second parameter, and the third parameter based on the analytical expressions for the first parameter, the second parameter, and the third parameter; obtaining the angle corresponding to the point on the detector of the arbitrary scattered signal of the sample under test based on the first parameter, the second parameter, and the third parameter; and using matrix formulas to solve for the error of the angle corresponding to the point on the detector of the arbitrary scattered signal of the sample under test. This invention solves the problems of limited descriptions of arc detector calibration in existing technologies and the large errors in measuring samples with arc detectors.

This specification relates to the field of hydraulic fracturing technology for oil and gas reservoirs, and more particularly to a method and apparatus for simulating fracture propagation. The method includes: discretizing a fracture domain containing fractures; determining the fracture width of discrete elements in the fracture domain using Newton's method iteratively based on an analytical expression of a fracture width function and a Jacobian matrix, wherein the fracture width function is obtained by embedding the fracture pressure equation into the fluid flow equation; calculating the tip stress intensity based on the fracture width of the discrete elements at the leading edge of the fracture domain; activating adjacent discrete elements in the fracture tip extension direction if the tip stress intensity satisfies the fracture propagation condition; and updating the fracture geometry in the fracture domain based on the activated adjacent discrete elements. The embodiments in this specification can improve the simulation accuracy and computational efficiency of fracture propagation simulation.

The application discloses an analytical method for a full frequency response model of an equivalent three-area interconnected power system, and belongs to the field of power system frequency stability analysis and control. First, a single-machine frequency full response model is established, and dynamic equations and parameter expressions of the single-machine frequency full response model are obtained. Second, considering the frequency space-time distribution characteristics and the influence of power exchange of a tie line, the network structure of an interconnected system is simplified based on DC power flow, and equivalent aggregation and order reduction are performed based on three-area division of a disturbance area and a non-disturbance area, so as to establish an equivalent frequency response model of a three-area system. Finally, a three-area system frequency full response model is constructed, and analytical expressions of frequency differences of each area are obtained. The application can accurately depict the full frequency response process of the system, and simultaneously reflect the frequency space-time distribution characteristics and the influence of power exchange of the tie line between areas, and is suitable for large-disturbance frequency safety analysis of a three-area interconnected power system, and has the advantages of fast calculation speed, clear physical meaning and convenience for online fast evaluation.

The present invention discloses an intelligent virtual synchronous machine control system and method for a high-temperature solid particle thermal energy storage device, comprising: a physical information graph neural network situational awareness architecture integrating constraints from partial differential equations of heat conduction; a causal reinforcement learning parameter generator based on an analytical expression architecture, replacing the traditional MLP black box with B-spline explicit polynomials; a thermoelectric coupled physical symbolic knowledge base and a neural symbolic inference engine to achieve rigid and safe truncation of rotor motion equations and thermal balance equations, and dynamically compensating for the SCR firing angle based on resistance temperature drift; cloud-based offline parameter optimization based on a pre-trained language model and parameter coordination with the edge analytical expression architecture; and a federated learning co-evolutionary framework for causal knowledge transfer. This invention utilizes generative AI, causal reasoning, and federated learning technologies to construct an intelligent control architecture with grid situational awareness, autonomous decision-making, and co-evolutionary capabilities.