scholarly journals Nonuniform Rational Basis Spline Interpolation for Off-Axis Aspheric Mirror Grinding Based on Wheel Path Planning

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jianpu Xi ◽  
Laibang Zhang ◽  
Qing Yang ◽  
Bin Li ◽  
Zexiang Zhao ◽  
...  
Keyword(s):  
Path Planning ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Large Diameter ◽  
Grinding Wheel ◽  
Normal Vector ◽  
Control Points ◽  
Rational Basis ◽  
Nurbs Interpolation ◽  
Aspheric Mirror

Large-diameter aspheric mirrors made of hard and brittle materials suffer from low efficiency in the grinding stage, making them difficult to process. In this study, a nonuniform rational basis spline (NURBS) interpolation method is proposed and developed based on the grinding wheel path planning. The characteristic parameters of NURBS machining program are calculated to ensure the accuracy of curve interpolation path planning, and a series of control points are selected according to the normal vector points of the grinding wheel path. The control points were determined by the distance between the aspheric tangent and the next type value point at a fixed distance d. We then established a mathematical model for the knot point and simulated the relationship between the knot point and d. This indicated that d must be optimized according to the number of points to reduce the number of control points. According to this established model, a comparison experiment was conducted using an off-axis aspheric mirror, with a 280 mm diameter. Straight line and NURBS grinding were compared, and the NURBS interpolation method was shown to effectively improve grinding accuracy and efficiency by about 30%.

scholarly journals Cubic Spline Interpolation-Based Robot Path Planning Using a Chaotic Adaptive Particle Swarm Optimization Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Jianfang Lian ◽  
Wentao Yu ◽  
Kui Xiao ◽  
Weirong Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Path Planning ◽  
Spline Interpolation ◽  
Particle Swarm ◽  
Cubic Spline ◽  
Control Points ◽  
Swarm Optimization ◽  
Cubic Spline Interpolation ◽  
Adaptive Particle Swarm Optimization ◽  
Starting Point

This paper proposed a cubic spline interpolation-based path planning method to maintain the smoothness of moving the robot’s path. Several path nodes were selected as control points for cubic spline interpolation. A full path was formed by interpolating on the path of the starting point, control points, and target point. In this paper, a novel chaotic adaptive particle swarm optimization (CAPSO) algorithm has been proposed to optimize the control points in cubic spline interpolation. In order to improve the global search ability of the algorithm, the position updating equation of the particle swarm optimization (PSO) is modified by the beetle foraging strategy. Then, the trigonometric function is adopted for the adaptive adjustment of the control parameters for CAPSO to weigh global and local search capabilities. At the beginning of the algorithm, particles can explore better regions in the global scope with a larger speed step to improve the searchability of the algorithm. At the later stage of the search, particles do fine search around the extremum points to accelerate the convergence speed of the algorithm. The chaotic map is also used to replace the random parameter of the PSO to improve the diversity of particle swarm and maintain the original random characteristics. Since all chaotic maps are different, the performance of six benchmark functions was tested to choose the most suitable one. The CAPSO algorithm was tested for different number of control points and various obstacles. The simulation results verified the effectiveness of the proposed algorithm compared with other algorithms. And experiments proved the feasibility of the proposed model in different dynamic environments.

scholarly journals UAV Path Planning of Combining Ant Colony and Beetle Antennae Algorithm Using Intelligent Wireless Communication

2021 ◽  
Vol 2083 (2) ◽  
pp. 022058
Author(s):  
Le Xu ◽  
Wenlong Zhao
Keyword(s):  
Path Planning ◽  
Ant Colony Algorithm ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Three Dimensional ◽  
Ant Colony ◽  
Fusion Algorithm ◽  
Third Order ◽  
Environment Model ◽  
Speed Up

Abstract In order to settle the problem of UAV path planning under mountain, an algorithm which based on the combination of ant colony algorithm and beetle antennae algorithm is proposed. Three dimensional environment model is established and objective function is constructed. It used ant colony algorithm to initialize the search path and the particle coordinates of all the next steps are updated by the beetle antennae algorithm. The improved algorithm adopted a new step update rule to speed up the convergence of the algorithm and used third-order B-spline interpolation method to smooth the path. Simulation results show that improved fusion algorithm has faster convergence speed and high stability by comparing with other algorithms under the same conditions, which verifies its effectiveness.

Optimal path generation in scala tympani and path planning for robotic cochlear implant of perimodiolar electrode

2020 ◽  
Vol 234 (6) ◽  
pp. 578-589
Author(s):  
Zuo Wang ◽  
Jianjun Li ◽  
Yongzhen Wu ◽  
Ruifeng Zhu ◽  
Binrui Wang ◽  
...  
Keyword(s):  
Path Planning ◽  
Cochlear Implant ◽  
Cross Sections ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Optimal Path ◽  
Path Generation ◽  
Scala Tympani ◽  
Micro Computed Tomography ◽  
Computed Tomography Images

In this study, a new idea of the optimal path generation method was proposed and a path planning strategy for robotic cochlear implant of perimodiolar electrode was designed. The centerline of scala tympani channel was taken as the optimal implant path of the perimodiolar electrode, which aimed to reduce the damage of the electrode to the cochlea during implantation. First, the three-dimensional cochlear model was reconstructed based on the micro-computed tomography images of cochlea, and it was re-segmented to obtain the cross sections of the scala tympani at different angles. Then, the image processing method was used to determine the central point of the scala tympani cross sections. The cubic B-spline interpolation method was used to fit these discrete central points to generate the optimal path. Finally, the coordinate information of the optimal path was combined with the stylet extraction state of perimodiolar electrode to conduct the path planning for robotic cochlear implant, and the result was sent to the robot for kinematic inverse solution to obtain the robot motion trajectory. The robotic cochlear implant experiment was performed with the model of scala tympani. The results showed that the maximum implant force based on path planning was 0.084 N, and the maximum implant force without path planning was 0.134 N. The optimal path generation and the path planning method effectively help to reduce the damage of the electrode to the cochlea.

scholarly journals Study on Fault Diagnosis Method of Planetary Gearbox Based on Turn Domain Resampling and Variable Multi-Scale Morphological Filtering

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 52
Author(s):  
Tongtong Liu ◽  
Lingli Cui ◽  
Chao Zhang
Keyword(s):  
Frequency Conversion ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Operating Efficiency ◽  
Planetary Gearbox ◽  
Noise Interference ◽  
Multi Scale ◽  
Morphological Filtering ◽  
Diagnosis Method ◽  
Simulation Signal

The turn domain resampling (TDR) method is proposed in the paper on the basis of the existing angle domain resampling for solving the problem of non-fixed fault frequency under variable working conditions. TDR can select the appropriate sampling order according to the influence of frequency conversion, which avoided the error caused by the spline interpolation method. It can provide accurate parameters for the subsequent calculation of the equivalent frequency order. Variable multi-scale morphological filtering (VMSMF) method is proposed for the purpose of further reducing the interference of noise in resampling signal to feature extraction. VMSMF adaptively selects structural elements according to the parameter change of impact signal to make its scale more targeted. It only needs to calculate once using the optimal structural unit for a particular impact, and the filtering accuracy and operating efficiency have been greatly improved. The main steps of this article are as follows. First, the TDR is used to resample the original signal as to get the resampling signal which is still submerged by the strong noise. In the second step, VMSMF is used to filter the resampling signal to obtain the signal with less noise interference. Finally, the fault characteristics of the filtering signal was extracted and compared with the possible fault frequency calculated by the sampling parameters provided by resampling, so as to determine the fault type of the planetary gearbox. By analyzing the simulation signal and the experimental signal respectively, this method can find out the corresponding fault characteristics effectively.

scholarly journals Analysis on the Synergy Evolutionary Development of the Collecting, Distributing, and Transporting System of Railway Heavy Haul Transportation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Fenling Feng ◽  
Dan Lan ◽  
Liuwen Yang
Keyword(s):  
Fourth Order ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Research Result ◽  
Evolutionary Model ◽  
Evolutionary Development ◽  
Heavy Load ◽  
Heavy Haul ◽  
Load Transportation ◽  
The Empirical Analysis

A synergy evolutionary model of the collecting, distributing, and transporting system of railway heavy haul transportation is built by introducing synergy-related concepts and applying synergy evolutionary theory. Then spline interpolation method, numerical differential five-point formula, and method of least squares are used to solve synergistic coefficient, while fourth-order Rugge-kutta method and fourth-order Adams linear implicit formula method are used to solve coevolutionary curve of the system. Finally, the heavy load transportation of Daqin Railway is an example of the empirical analysis. The research result shows that the degree of order of the system and its three subsystems—collecting, transporting, and distributing—increases as the synergetic coefficient of the subsystems increases; otherwise, the degree of the order will decrease. It also shows that this model can better analyze the coevolutionary process of the heavy load collecting, distributing, and transporting system of Daqin Railway, with its rationality and applicability verified.

scholarly journals Error Analysis for a Noisy Lacunary Cubic Spline Interpolation and a Simple Noisy Cubic Spline Quasi Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Feng-Gong Lang ◽  
Xiao-Ping Xu
Keyword(s):  
Error Analysis ◽  
Error Bounds ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
The Other ◽  
Cubic Spline Interpolation ◽  
Numerical Tests ◽  
New Methods ◽  
Noisy Function

We mainly present the error analysis for two new cubic spline based methods; one is a lacunary interpolation method and the other is a very simple quasi interpolation method. The new methods are able to reconstruct a function and its first two derivatives from noisy function data. The explicit error bounds for the methods are given and proved. Numerical tests and comparisons are performed. Numerical results verify the efficiency of our methods.

scholarly journals A Nonlinear Calibration Method Based on Sinusoidal Excitation and DFT Transformation for High-Precision Power Analyzers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Wenjian Zhou ◽  
Sheng Yang ◽  
Li Wang ◽  
Hanmin Sheng ◽  
Yang Deng
Keyword(s):  
High Precision ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Calibration Method ◽  
Calibration Error ◽  
Initial Moment ◽  
Calibration Process ◽  
Calibration Methods ◽  
Nonlinear Calibration ◽  
Sinusoidal Excitation

For most high-precision power analyzers, the measurement accuracy may be affected due to the nonlinear relationship between the input and output signal. Therefore, calibration before measurement is important to ensure accuracy. However, the traditional calibration methods usually have complicated structures, cumbersome calibration process, and difficult selection of calibration points, which is not suitable for situations with many measurement points. To solve these issues, a nonlinear calibration method based on sinusoidal excitation and DFT transformation is proposed in this paper. By obtaining the effective value data of the current sinusoidal excitation from the calibration source, the accurate calibration process can be done, and the calibration efficiency can be improved effectively. Firstly, through Fourier transform, the phase value at the initial moment of the fundamental frequency is calculated. Then, the mapping relationship between the sampling value and the theoretical calculation value is established according to the obtained theoretical discrete expression, and a cubic spline interpolation method is used to further reduce the calibration error. Simulations and experiments show that the calibration method presented in this paper achieves high calibration accuracy, and the results are compensation value after calibration with a deviation of ± 3 × 10 − 4 .

scholarly journals Seismic tomography of the Gulf of Corinth: a comparison of methods

1997 ◽  
Vol 40 (1) ◽  
Author(s):  
E. Le Meur ◽  
J. Virieux ◽  
P. Podvin
Keyword(s):  
Linear System ◽  
Travel Time ◽  
Velocity Structure ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Linear Interpolation ◽  
Regular Grid ◽  
Partial Derivatives ◽  
Simultaneous Inversion ◽  
Gulf Of Corinth

At a local scale, travel-time tomography requires a simultaneous inversion of earthquake positions and velocity structure. We applied a joint iterative inversion scheme where medium parameters and hypocenter parameters were inverted simultaneously. At each step of the inversion, rays between hypocenters and stations were traced, new partial derivatives of travel-time were estimated and scaling between parameters was performed as well. The large sparse linear system modified by the scaling was solved by the LSQR method at each iteration. We compared performances of two different forward techniques. Our first approach was a fast ray tracing based on a paraxial method to solve the two-point boundary value problem. The rays connect sources and stations in a velocity structure described by a 3D B-spline interpolation over a regular grid. The second approach is the finite-difference solution of the eikonal equation with a 3D linear interpolation over a regular grid. The partial derivatives are estimated differently depending on the interpolation method. The reconstructed images are sensitive to the spatial variation of the partial derivatives shown by synthetic examples. We aldo found that a scaling between velocity and hypocenter parameters involved in the linear system to be solved is important in recovering accurate amplitudes of anomalies. This scaling was estimated to be five through synthetic examples with the real configuration of stations and sources. We also found it necessary to scale Pand S velocities in order to recover better amplitudes of S velocity anomaly. The crustal velocity structure of a 50X50X20 km domain near Patras in the Gulf of Corinth (Greece) was recovered using microearthquake data. These data were recorded during a field experiment in 1991 where a dense network of 60 digital stations was deployed. These microearthquakes were widely distributed under the Gulf of Corinth and enabled us to perform a reliable tomography of first arrival P and S travel-times. The obtained images of this seismically active zone show a south/north asymmetry in agreement with the tectonic context. The transition to high velocity lies between 6 km and 9 km indicating a very thin crust related to the active extension regime.At a local scale, travel-time tomography requires a simultaneous inversion of earthquake positions and velocity structure. We applied a joint iterative inversion scheme where medium parameters and hypocenter parameters were inverted simultaneously. At each step of the inversion, rays between hypocenters and stations were traced, new partial derivatives of travel-time were estimated and scaling between parameters was performed as well. The large sparse linear system modified by the scaling was solved by the LSQR method at each iteration. We compared performances of two different forward techniques. Our first approach was a fast ray tracing based on a paraxial method to solve the two-point boundary value problem. The rays connect sources and stations in a velocity structure described by a 3D B-spline interpolation over a regular grid. The second approach is the finite-difference solution of the eikonal equation with a 3D linear interpolation over a regular grid. The partial derivatives are estimated differently depending on the interpolation method. The reconstructed images are sensitive to the spatial variation of the partial derivatives shown by synthetic examples. We aldo found that a scaling between velocity and hypocenter parameters involved in the linear system to be solved is important in recovering accurate amplitudes of anomalies. This scaling was estimated to be five through synthetic examples with the real configuration of stations and sources. We also found it necessary to scale Pand S velocities in order to recover better amplitudes of S velocity anomaly. The crustal velocity structure of a 50X50X20 km domain near Patras in the Gulf of Corinth (Greece) was recovered using microearthquake data. These data were recorded during a field experiment in 1991 where a dense network of 60 digital stations was deployed. These microearthquakes were widely distributed under the Gulf of Corinth and enabled us to perform a reliable tomography of first arrival P and S travel-times. The obtained images of this seismically active zone show a south/north asymmetry in agreement with the tectonic context. The transition to high velocity lies between 6 km and 9 km indicating a very thin crust related to the active extension regime.

Sign in / Sign up

Export Citation Format

Share Document