15 results about "Approximation error" patented technology

The invention discloses a free-form surface three-axis ball-end cutter equal approximation error finish machining tool path generation method which comprises the following steps: firstly, importing a free-form surface model to be machined, and setting data such as the radius, the line spacing, the approximation error maximum allowable value and the precision of a ball-end cutter; secondly, a group of section planes are planned according to the row spacing to intersect with the curved surface, the intersecting line serves as a cutter contact curve, and an equal-bow-height-error cutter contact iterative search method for driving cutter contact adjustment through the geometric distance is provided for the cutter contact curve on the section planes; the maximum distance between a cutter cutting envelope surface and a cutter contact track line is used as an approximation error, and an adaptive discrete method is adopted to carry out approximation error calculation; and finally, the cutter location points of the equal-bow-height-error cutter contact points serve as initial values, an equal-error cutter location point calculation method of step length self-adaptive adjustment iteration is provided, approximation errors between the cutter location points are all within an allowable range, and therefore the free-form surface three-axis ball-end cutter equal approximation error finish machining cutter path is obtained.

This application belongs to the field of delay differential equation modeling, specifically disclosing a delay differential equation modeling method based on Bayesian optimization and neural networks. The method includes: generating multiple trajectory data of the system; searching for the optimal delay term using a Bayesian optimization algorithm, where the delay term to be solved is the optimization variable, and the error based on neural network simulation is the objective function, obtaining the optimal delay term through iterative optimization using a surrogate model; constructing a state matrix and a delay matrix from the trajectory data based on the optimal delay term, using the concatenated matrix as input to a neural network to construct a neural network for approximating a nonlinear function; integrating a linear multi-step method into the loss function of the neural network, training the neural network using the trajectory data to obtain a nonlinear function approximation model; and separating the numerical discretization error and the neural network approximation error based on this model to construct a total error bound. This application can achieve high-precision, high-efficiency delay differential equation modeling with quantization error guarantee.

This invention discloses a track smoothness adjustment method based on 3D coordinates and multi-wavelength technology, aiming to solve the problems of accumulated adjustment errors caused by reliance on approximate models in existing technologies, and low efficiency due to the inability to simultaneously handle long and short wave irregularities caused by the single wavelength. The method includes: acquiring the designed and measured three-dimensional coordinates of the track; directly calculating the lateral and vertical versine deviations for each wavelength based on the three-dimensional coordinates using the moving string method according to a preset wavelength list; directly correcting the three-dimensional coordinates using a predetermined proportion of these deviations as a correction amount; completing a single-round adjustment by traversing the wavelength list, and performing multiple rounds of iterative optimization based on the updated coordinates to achieve multi-wavelength gradient smoothness of the track's three-dimensional curve. This invention eliminates approximation errors at their source, significantly improving adjustment accuracy and linear continuity; it can simultaneously correct long and short wave irregularities in one go, greatly improving operational efficiency; and through iteration, it converges the deviations, meeting millimeter-level high smoothness standards, and has strong versatility.

This invention discloses a method and system for stabilizing a robotic arm based on fractional-order sliding mode adaptive compensation. The method includes: constructing a unified dynamic model incorporating time-varying delays, nonlinear disturbances, and neural network approximation errors; defining the sliding mode function using Caputo fractional derivatives, establishing an improved trend law based on the improved Fal function and hyperbolic tangent function, and obtaining a control law based on the error-driven dynamic model and the improved approach law; constructing a dynamic adaptive compensator linked to time-delay gradient information to address the residual errors of the radial basis function and the unknown nonlinear terms in the neural network approximation, and dynamically adjusting the compensation gain based on the dynamic adaptive compensator; constructing a Lyapunov functional adapted to the fractional-order system, deriving the exponential stability criterion for the closed-loop system using Young's inequality and Halany's inequality, and determining the quantitative correlation between the fractional-order order and the convergence rate. This invention solves the problems of imbalance between robustness and smoothness and weak time-delay adaptability in existing technologies, significantly improving control accuracy and reliability.

This application belongs to the field of light field display technology, specifically disclosing a rigorous scalar light field calculation and solution method and system. It includes: obtaining the complex amplitude distribution on the source plane; and calculating the rigorous scalar light field distribution on the observation plane based on rigorous scalar diffraction theory and the complex amplitude distribution on the source plane. Based on scalar diffraction theory, this application constructs a light field propagation model for arbitrary propagation distances, avoids approximation errors in geometric correction methods through a rigorous scalar light field propagation method, overcomes the propagation distance constraints of the scalable angular spectrum propagation model, and achieves Abbe diffraction-limited resolution through a phase retrieval algorithm.

This invention belongs to the field of numerical simulation in computational electromagnetics, specifically a non-uniform conformal FDTD method based on submesh technology. This invention introduces non-uniform conformal geometric corrections within the submesh to achieve high-precision fitting of curved surface boundaries, reducing step approximation errors and improving the accuracy of field calculations near the boundaries. At the master-submesh interface, a bidirectional coupling transfer is established that simultaneously satisfies line integral conservation and flux conservation, avoiding disruption of the conservation relationships required by the non-uniform conformal FDTD method. This effectively suppresses numerical reflections at the interface, reduces energy non-physical errors, and improves long-term stability. Furthermore, by using fine meshes only in the neighborhood of local microstructures and coordinating with time sub-cycle progression, global mesh refinement and the global time step being limited by the smallest unit are avoided, significantly reducing storage and computation time overhead while maintaining accuracy. This invention balances geometric modeling accuracy, interface stability, and computational efficiency, and has high engineering application value.

This invention provides a control method and system for a multi-input robot system based on intelligent game theory learning. The method includes: modeling each control input of the multi-input robot system as a player to obtain a continuous-time nonlinear multi-input robot system and applying permissible control inputs; collecting local state information acquired by each player and control information from neighboring players via a directed communication network; using a polynomial function to perform a structured approximation of the unknown coupling terms formed by non-adjacent players, and constructing an observer to estimate the polynomial weights online; modeling the polynomial approximation error as a bounded uncertainty term, constructing a cost function and introducing a robust compensation term; employing a reinforcement learning framework, using a neural network to approximate the unknown optimal cost function as an evaluation network, and iteratively obtaining an approximate solution to the cost function; when the weight error of the evaluation network in two adjacent iterations meets a preset threshold, obtaining the robust optimal control strategy corresponding to each player. This invention can control a multi-input robot system.

This invention discloses a method for global smoothing and curvature optimization of linear paths based on PH curves, relating to the field of CNC machining technology. The method includes: obtaining an original toolpath containing three consecutive straight line segments; constructing an 11th-order PH curve to replace the local polyline path containing the middle second straight line segment and its two end corners; determining an offset distance satisfying a preset upper limit of approximate error based on the angle bisectors of the two corners, and determining entry and exit points on adjacent straight line segments; calculating four initial complex coefficients based on the continuity constraints of the first and second derivatives; establishing tangential parallel constraints and distance constraints at intermediate parameter points; and solving for two complex coefficients based on displacement continuity constraints, tangential parallel constraints, and distance constraints to generate a complete curve. This method can eliminate interference between adjacent transition curves, reduce curvature peaks, and improve machine tool transition speed and cutting efficiency.

The application discloses a ruled surface and plane approximation method of NURBS surface, comprising: carrying out equal parameter line discretization and surface slicing pretreatment on a target NURBS surface; adopting a straight line cluster search technology based on principal component analysis method to obtain an initial straight line cluster approximating the NURBS surface; utilizing the initial straight line cluster to construct an initial ruled surface, and carrying out overall optimization on the initial ruled surface based on a least square method to obtain one or a group of ruled surfaces meeting the approximation error requirement. The application converts a complex NURBS surface into one or a group of ruled surfaces through three steps of pretreatment, straight line cluster search and overall optimization, and is suitable for efficient rough machining and tool path planning.

The application discloses a kind of based on conformal technology's core particle through silicon via interconnection structure signal integrity simulation excitation method, using time domain finite difference method analysis core particle interconnection structure application scene, to through silicon via structure model using conformal technology is analyzed;Overall calculation region is divided into excitation region and structure calculation region two sub-regions;Using total field / scattering field boundary technology, the result of excitation region is introduced as incident wave into structure calculation region, as excitation source to through silicon via structure is excited;The surface power integration at port in total field and scattering field is calculated, and by Fourier transform is converted into frequency domain calculation each port S parameter.The present application reduces the step approximation error of time domain finite difference method using conformal technology, by dividing the calculation region into two sub-regions solve the high-order mode crosstalk problem existing in typical coaxial structure such as through silicon via, and greatly improve the calculation precision of through silicon via structure signal integrity.

The invention relates to the technical field of five axes of numerical control machine tools, and discloses a five-axis linear path local fairing and parameter synchronization method based on a spiral curve, which comprises the following steps: determining the transition length of a tool nose transition curve according to a tool nose point approximation error and a segment length constraint condition; determining the transition length of the cutter shaft transition curve according to the cutter shaft point approximation error and the segment length constraint condition; the tool nose actual track displacement serves as a shared parameter to achieve parameter synchronization between the tool nose actual track and the tool shaft actual track; the control vertex distribution of the displacement B splines in the three adjacent segments is optimized through a least square method, and only the control vertex distribution of the displacement B splines in the first segment is reserved, so that the optimal control vertex distribution of the displacement B splines in the segments is obtained; according to the method, analytic calculation of the arc length of the fairing curve can be realized, and the calculation efficiency is relatively high.

This invention relates to the fields of artificial intelligence and machine learning, proposing a training data selection method for supervised instruction fine-tuning of large language models. The steps include: decomposing the training loss of the large language model during supervised instruction fine-tuning into a knowledge-related capability loss component and an instruction-following capability loss component; constructing a selection target for a representative subset based on the sum of the gradient approximation errors of the knowledge-related capability loss component and the instruction-following capability loss component; and selecting a representative subset and its corresponding weights from the full training data that satisfy the selection target to replace the full data for instruction fine-tuning training. This invention decomposes the instruction fine-tuning loss into two components—knowledge-related capability and instruction-following capability—and constrains the gradient approximation errors of each, significantly reducing training costs while effectively avoiding the unbalanced degradation of the two types of capabilities in subset selection, thus improving the accuracy of the model's factual output and execution stability in cross-domain scenarios.

The application discloses a robust low-approximation-error Cage generation method, relates to the technical field of shape design and generation, and effectively guarantees the robustness of Cage generation and saves a large amount of time overhead through a shape-preserving tetrahedralization algorithm, a tetrahedral mesh subdivision algorithm, a constrained optimization algorithm, an accurate algorithm, a floating-point filtering technology and a space hierarchical structure, a hash structure and the like, and improves the performance of Cage in several important indexes. The algorithm of the application is suitable for general mesh models, for a triangular mesh meeting the requirements, the method can automatically generate a Cage meeting two hard constraint requirements, and the quality of the generated result is better than that of the result generated by the previous method in the indexes of complexity and approximation error.

The application provides an improved type II multiplication distribution frequency analysis method suitable for zero value hydrological sequence, constructs a mixed distribution model combining zero value discrete probability function and improved continuous type II multiplication distribution, introduces an exponential smooth connection coefficient, eliminates zero point singular point and segmented jump; a joint global optimization algorithm is used to synchronously estimate zero value probability, head and tail density parameters and the smooth connection coefficient, and an experience calculation mode of traditional mean trial, multi-stage recursion and linear wiring is abandoned; a design value is directly inverted through the mixed distribution, a conversion link of variation coefficient and skewness coefficient is skipped, and artificial approximation error and recursion error are eliminated from the root. The application can directly adapt to zero value, near zero value, dry drought type hydrological sequence, is continuous and derivable in the whole region, is stable in calculation, is high in fitting precision, does not need artificial minimum value correction, and is suitable for frequency analysis and engineering design value deduction of non-negative hydrological sequence such as annual runoff, dry flow, rainfall and drought index.

The application discloses a Lagrange polynomial interpolation approximation error analysis method based on a sine wave, which comprises the following steps: taking a one-dimensional sine wave as an original function, calculating one-dimensional Lagrange polynomial interpolation under different interpolation node distribution conditions; analyzing the approximation error between the Lagrange polynomial interpolation under different interpolation node distribution conditions and the original function; establishing a two-dimensional sine wave original function according to the approximation error; establishing a two-dimensional irregular grid with different interpolation node distributions, and mapping the two-dimensional sine wave original function into the two-dimensional irregular grid to obtain a two-dimensional sine wave original wave field; calculating two-dimensional Lagrange polynomial interpolation approximation wave fields in different irregular grids according to the interpolation nodes with different distributions in the two-dimensional irregular grid; comparing the two-dimensional Lagrange polynomial interpolation approximation wave fields in the different irregular grids with the two-dimensional sine wave original wave field in the two-dimensional irregular grid to determine the Lagrange polynomial interpolation approximation error quantitative relationship. The method can effectively evaluate the relationship between the grid quality and the forward simulation precision without performing wave field forward simulation calculation.