Local Smoothing Method Research Articles

Real-Time Trajectory Smoothing and Obstacle Avoidance: A Method Based on Virtual Force Guidance.

In dynamic environments, real-time trajectory planners are required to generate smooth trajectories. However, trajectory planners based on real-time sampling often produce jerky trajectories that necessitate post-processing steps for smoothing. Existing local smoothing methods may result in trajectories that collide with obstacles due to the lack of a direct connection between the smoothing process and trajectory optimization. To address this limitation, this paper proposes a novel trajectory-smoothing method that considers obstacle constraints in real time. By introducing virtual attractive forces from original trajectory points and virtual repulsive forces from obstacles, the resultant force guides the generation of smooth trajectories. This approach enables parallel execution with the trajectory-planning process and requires low computational overhead. Experimental validation in different scenarios demonstrates that the proposed method not only achieves real-time trajectory smoothing but also effectively avoids obstacles.

Enhancing five-axis CNC toolpath smoothing: Overlap elimination with asymmetrical B-splines

In the realm of five-axis Computer Numerical Control (CNC) machining, the challenge of minimizing velocity, acceleration, and jerk fluctuations has prompted the development of various local corner smoothing methods. However, existing techniques often rely on symmetrical spline curves or impose pre-set transition length constraints, limiting their effectiveness in reducing curvature and maintaining velocity at critical corners. To comprehensively address these limitations comprehensively, a novel approach for local smoothing of five-axis linear toolpaths is presented in this paper. The proposed method introduces two asymmetrical B-splines at corners, effectively smoothing both the tool-tip position in the workpiece coordinate system and the tool orientation in the machine coordinate system. To fine-tune transition curve scales and minimize velocity disparities between adjacent corners, an overlap elimination scheme is employed. Furthermore, the two-step strategy emphasizes the synchronization of tool-tip position and tool orientation while considering maximal approximation error. The outcome is a blended five-axis toolpath that significantly reduces curvature extremes in the smoothed path, achieving reductions ranging from 36.28 % to 45.51 %. Additionally, the proposed method streamlines the interpolation process, resulting in time savings ranging from 5.68 % to 8.78 %, all the while adhering to the same geometric and kinematic constraints.

Acceleration and age in soccer

This paper considers how player acceleration changes in soccer relative to age. A plot of average maximum acceleration versus age is produced. The construction of the plot is based on methods from functional data analysis and the availability of tracking data from the 2019 season of the Chinese Super League. For an individual player, we calculate his maximum acceleration for each single match of the 2019 season. Since the players’ maximum accelerations are observed only on a single season instead of their entire careers, we treat them as incomplete functional data, called functional snippets. The average maximum acceleration, i.e., the mean function of the functional snippets rather than full curves is estimated by a local linear smoothing method. The most important observation is that the shape of the acceleration curve closely resembles curves of soccer performance versus age. This observation has implications for predicting future performance since acceleration is more easily and more accurately measured than performance.

Comparison of Kernel Smoothing and Local Polynomial Smoothing Method in Overcoming Age Heaping

Age data plays an important role in every aspect yet there are found age misreporting. It involves digit preference that causes build up in a certain age. Digit preference in demography is called age heaping that often happens at age with 0 and 5 as the last digit. Age heaping induces poor data quality and data bias that could influence government policy making. Two indicators used to detect age heaping are Whipple Index (WI) and Myers Blended Index (MBI). Methods to cope with age heaping are nonparametric regression approaches which are Kernel Smoothing and Local Polynomial Smoothing. The objective of this research is to measure and elevate the quality of population age data and population mortality data in Sensus Penduduk (SP) 2020 as well as comparing methods between Kernel Smoothing and Local Polynomial Smoothing. The data being used in this paper is SP2020 which the research variables are age population, age of death, and total population. The result shows that the data quality of total population death is inaccurate compared to total population thus needs a smoothing process to improve age data to population data accuration. The method that has better accuracy is the Local Polynomial Smoothing method.

Toolpath smoothing with reduced curvature and synchronized motion for hybrid robots

G01 commands are the most commonly used toolpath format in Computer Numerical Control (CNC) machining. Due to the discontinuity between adjacent linear segments, toolpath smoothing is necessary to improve machining efficiency and machined surface quality. This paper proposes an analytical C3 continuous local toolpath smoothing and synchronization method for a five-axis hybrid robot. Position and orientation smoothing are decoupled, with quintic B-spline segments replacing the original linear segments. The curvatures of the toolpath are reduced under constrained smoothing errors by weaving transition splines along the linear segments instead of confining them within the corners. A synchronization method based on arc length parameterization tailored to the smoothing method is also proposed. Tool tip position and tool axis orientation are synchronized using another monotonic, C3 continuous spline, which achieves smoother joint motion along the toolpath. For the hybrid robot with highly nonlinear kinematics, improved results in feedrate scheduling considering joint constraints can be realized. Simulations and experiments validate the effectiveness of the proposed method.

Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure

This article considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogeneous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalization rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from U.K. local authority districts, which reveals different homogeneity structures at different quantile levels.

Wavelets in the analysis of local time series of the Earth's surface air

The practical application of local smoothing and wavelet analysis methods for studying the spectral composition and coherent relationships of local average annual surface air temperatures with solar activity and the displacement of the Earth's North Pole is presented. A preliminary analysis of local time series of surface temperatures revealed the presence of emissions and their localization. It is shown that to eliminate the influence of outliers (short-term events) on the reliability of identifying a long-term nonlinear trend, the wavelet decomposition method, which filters high frequencies, is most suitable. Functional approximation models are constructed and compared at different levels of wavelet decomposition of the data. Time or scale smoothing is used to improve the reliability of the wavelet spectrum. Based on data on average annual surface air temperatures in Yalta (44.48⁰, 34.17⁰, = 72.0 m) for the time interval from 1869 to 2022, functional models of long-term trends were built and used to obtain short-term forecasts. Information about the linear relationship of events in the compared time series is obtained and discussed in the analysis of wavelet cross-correlation, wavelet coherence and phase coherence. Local similarities were discovered between data on surface air temperature and solar activity data (Wolf numbers) for a period of ∼(30–70) years, as well as oscillations with period of 11 years, manifested in the constancy of the phase difference and an increase in the modulus of wavelet coherence power over time. Localized similarities were also found in data on surface air temperature in Yalta and in data on displacements of the Earth's mean pole relative to the conventional beginning of EOP (IERS) CO1 in the interval of periods ∼ (30–70) years.

Identifying Multi-Scale Gravity and Magnetic Anomalies Using Statistical Empirical Mode Decomposition: A Case Study from the Eastern Tianshan Orogenic Belt

Identifying multi-scale anomalies that have simple forms and geological significance is critical for enhancing the interpretability of gravity and magnetic survey data. In recent years, empirical mode decomposition (EMD), which was developed as a significant data-driven approach for analyzing complex signals, has been widely used in identifying gravity and magnetic anomalies due to its advantages of adaptability to nonlinear and nonstationary data. Nevertheless, the traditional EMD method is usually sensitive to outliers and irregularly spaced data because of the interpolation process in the construction of envelopes. In this regard, an extended algorithm called statistical EMD (SEMD) has been proposed based on the smoothing technique. In this study, for validation purposes, the novel SEMD method has been employed to identify multi-scale gravity and magnetic anomalies. The sensitivities of local polynomial and cubic spline smoothing methods in SEMD to combination and arrangement patterns of field sources including the size, depth, and distance in gravity and magnetic anomaly identification were investigated and compared by forward modeling under the same conditions. The results demonstrated that the local polynomial smoothing method performed better than the cubic spline smoothing method. Thus, in the case study, the SEMD method using the local polynomial smoothing technique was employed for identifying multi-scale gravity and magnetic anomalies in the eastern Tianshan orogenic belt, northwestern China. It has illustrated that the SEMD method provides a novel and useful data-driven method for extracting gravity and magnetic anomalies.

An analytical local tool path smoothing method with curvature control

In traditional multi-axis machining, the linear tool path generated by computer-aided manufacturing systems is still in a broad tool path format, resulting in discontinuities at the corners, which slow down tool motion, and also trigger tool vibration, reducing machining accuracy and surface quality. In order to ensure the C3 continuity of the tool during the multi-axis machining process, this paper proposes an analytical B-spline local smoothing method with curvature control. The tool position trajectory and tool orientation are both smoothed by a 5th spline curve with 9 control points. Optimal control points are determined for position and orientation splines to achieve C3 continuity at the junctions between the spline and linear segment while preserving the predefined geometric tolerance limits and minimizing the maximum curvature of the inserted B-spline curve. The smoothed tool path is expected to have less curvature fluctuation, which can significantly improve both the kinematic performance of the machine tool and the machining efficiency. Both computer simulations and physical printing experiments are carried out to demonstrate the improvements of our proposed method in motion smoothness and tracking accuracy in multi-axis machining tasks.

Using Optimal Transport to Improve Spherical Harmonic Quantification of Complex Biological Shapes.

The knowledge of the anatomical shape of both gross and microscopic structures is the key to understanding the effects of disease processes on cellular structure. Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology. Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface. It starts from initial mapping and performs local and global smoothing methods alternately to control the area and length distortions simultaneously. However, this parameterization may not be sufficient in complex morphological cases. To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization. First, the genus 0 3D objects are conformally mapped onto a sphere. Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. This new algorithm can effectively reduce the area distortion and lead to a better reconstruction result. We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.

Simultaneous confidence bands and global inferences for extended partially linear single-index models

Substantial efforts have been made for the popular semiparametric single-index models in the last two decades. Extended partially linear single-index models as generalized single-index semiparametric models effectively reduce the problem of model misspecification by allowing the data to automatically choose the principal linear component and the principal nonlinear component. In this paper, we construct an oracle-efficient simultaneous confidence band as a global inference tool for the extended partially linear single-index models. Specifically, we apply a LASSO penalized local linear smoothing method to estimate the coefficient parameters and conduct variable selection to avoid model overfitting caused by the two appearances of covariates. It is shown that the local linear estimator for the nonparametric link function by employing the penalized coefficient estimates is oracle-efficient in the sense that it is uniformly as efficient as the ideal one obtained by utilizing the true coefficient parameters. Then by applying the oracle efficiency and the extreme value distribution theory of the local linear regression, an asymptotically accurate simultaneous confidence band for the nonparametric link function in the extended partially linear single-index models is established. Simulation experiments with commonly encountered sample sizes corroborate our theoretical findings. The proposed method is applied to analyze two engineering datasets: motor trend car road tests dataset and concrete slump tests dataset.

Asymmetrical Pythagorean-hodograph spline-based $${{\mathrm{C}}}^{4}$$ continuous local corner smoothing method with jerk-continuous feedrate scheduling along linear toolpath

Asymmetrical Pythagorean-hodograph spline-based $${{\mathrm{C}}}^{4}$$ continuous local corner smoothing method with jerk-continuous feedrate scheduling along linear toolpath

Local least product relative error estimation for single-index varying-coefficient multiplicative model with positive responses

In this paper, we study the single-index varying-coefficient multiplicative model (SIVCMM) for analyzing data with positive response. Based on the least product relative error (LPRE) and local kernel smoothing methods, an efficient approach is proposed for estimating the unknown parameter vector and nonparametric functions arising in SIVCMM. Furthermore, the convergence properties of the proposed estimators are established. Finally, numerical studies are conducted to test the performance of the proposed approach, and a real data analysis is presented to illustrate the new estimator’s efficiency in practical computation.

Dynamic Learning Framework for Smooth-Aided Machine-Learning-Based Backbone Traffic Forecasts.

Recently, there has been an increasing need for new applications and services such as big data, blockchains, vehicle-to-everything (V2X), the Internet of things, 5G, and beyond. Therefore, to maintain quality of service (QoS), accurate network resource planning and forecasting are essential steps for resource allocation. This study proposes a reliable hybrid dynamic bandwidth slice forecasting framework that combines the long short-term memory (LSTM) neural network and local smoothing methods to improve the network forecasting model. Moreover, the proposed framework can dynamically react to all the changes occurring in the data series. Backbone traffic was used to validate the proposed method. As a result, the forecasting accuracy improved significantly with the proposed framework and with minimal data loss from the smoothing process. The results showed that the hybrid moving average LSTM (MLSTM) achieved the most remarkable improvement in the training and testing forecasts, with 28% and 24% for long-term evolution (LTE) time series and with 35% and 32% for the multiprotocol label switching (MPLS) time series, respectively, while robust locally weighted scatter plot smoothing and LSTM (RLWLSTM) achieved the most significant improvement for upstream traffic with 45%; moreover, the dynamic learning framework achieved improvement percentages that can reach up to 100%.

A local gradient smoothing method for solving the free vibration model of functionally graded coupled structures

In this paper, a meshless method for analyzing the free vibration of four-parameter functionally graded composite shells is presented, which is based on moving least square (MLS) approximation and local gradient smoothing method (LGSM). Firstly, the displacement field model of the substructure is established by using the first order shear deformation theory (FSDT), and the governing equation of the substructure is obtained by using Hamilton principle. Starting from the MLS approximation the displacement field of substructure, the derivative of the shape function is approximated by the LGSM, and the vibration analysis models of each substructure are established respectively. Then, the vibration model of the whole coupling structure is established by coupling each substructure with the displacement coordination relation of the substructure, and the vibration model of the whole coupling structure is established. For the vibration problems considering different boundary conditions, the results obtained from the meshless vibration model are compared with the FEM results to verify the accuracy and applicability of the established analysis model. At the same time, in order to improve the accuracy of the solution, the convergence analysis is also carried out. Finally, in order to enrich the research content, the influence of geometric parameters and material parameters of the structure on the vibration characteristics of the whole structure is studied. The results show that this method can effectively analyze the free vibration of the coupled structure.

An Analytical Corner Rounding Algorithm With G01 Shape Preserving for Five-Axis Computer Numerical Controlled Machining

Abstract G01 blocks are the widespread format of toolpath in computer numerical controlled (CNC) machining. For achieving smooth motion and eliminating the geometrical discontinuity at the block transitions, various local corner smoothing methods have been developed. However, in these methods, the loss of featured information of parts is inevitable. Focused on this topic, this article proposes a new analytical G2 continuous corner smoothing method with G01 shape preserving for five-axis linear toolpath by locally inserting specially designed B-splines into the corners of consecutive segments. First, by analyzing the condition of G01 shape preserving, the configuration expression of control points for B-splines is yielded for passing through G01 point. On this basis, the tool tip position is smoothed by symmetrical B-splines with minimum curvature in the workpiece coordinate system (WCS). Then, another asymmetrical B-splines is used to smooth tool orientation in the machine coordinate system (MCS). After that, the satisfaction conditions of parametric synchronization between tool tip position and tool orientation are mathematically derived at junctions, while the corresponding maximum smoothing errors are also constrained in WCS. Compared with the existing methods, not only the tool tip points and orientation vectors specified in original G01 blocks are preserved but also the optimal control points considering the curvature of smooth splines can be obtained analytically. Finally, simulations and experiments are performed to validate the effectiveness of the developed method.

An Analytical Method for Decoupled Local Smoothing of Linear Paths in Industrial Robots

The linear-format path is widely adopted to approximate the continuous contour in robot controllers. The tangential discontinuity of the linear paths usually causes the discontinuity of the joint velocity. To comply with the joint kinematics limits, the robots have to stop at each corner point, resulting in a great loss of efficiency. To achieve a smooth motion, this paper presents an analytical decoupled C3 continuous local path smoothing method for industrial robots. The tool position path is smoothed in the reference frame while the tool orientation is smoothed in the rotation parametric space based on the exponential coordinates of rotations. The quintic B-splines are inserted at the corners of the linear segments to achieve the G3 continuity of the tool position path and tool orientation path. The orientation smoothing error is constrained analytically. By reparameterization of the remaining linear segments using specially constructed B-splines, the C3 continuity of the tool position path and tool orientation path is achieved. Then, the synchronization of the tool orientation path and tool position path can be guaranteed by sharing the same curve parameter. Besides, to improve the smoothness of the angular motion on the remaining linear segments during parameter synchronization, the transition lengths of the inserted B-splines are optimized. The proposed local smoothing method guarantees that the generated smooth orientation path in the rotation space is invariant with the selection of the reference frame and the orientation of the tool frame, and ensures the jerk-continuous motion with a smoother angular motion on the remaining linear segments, which could improve the motion smoothness of the tool path and tracking accuracy. The effectiveness of the proposed method is validated through simulation and experiments.

Vibration analysis of closed laminate conical, cylindrical shells and annular plates using meshfree method

A local gradient smoothing method(LGSM) in the framework of meshless theory is developed for implementing vibration analysis of closed laminate conical, cylindrical shells and annular plates. Based on the theoretical assumptions of the first-order laminated structure, the governing equations and boundary condition equations of the structure elements of revolution are derived and numerically discretized for the discrete vibration characteristic equations of the studied structures. Then, the meshless method is used to solve the vibration characteristic of the composite laminated shell, in which the derivatives of the displacement variables are approximated by employing LGSM. On this basis, the effects of the number of the involved discrete nodes and the dimensional coefficient related to the local smooth domain on the solution convergence are examined in detail. Meanwhile, for sake of checking the applicability of LGSM, several numerical results simulated by the presented method are compared with those from some published literature as well as FEM models. Moreover, some parametric studies with regard to the influence of structural boundary conditions, geometric dimensions, and fiber angle on the vibration behaviors of composite laminated shells are analyze. The results reveal that the developed LGSM meshless method has a good application potential in clarifying vibration phenomena of such laminated structure.

Simultaneous variable selection and structural identification for time‐varying coefficient models

Time‐varying coefficient models are important tools in time series analysis due to their flexibility to fit non‐stationary data. To improve the accuracy of these models, it is important to identify covariates with null, constant and time‐varying effects and to estimate their coefficients. This article proposes a combination of the local linear smoothing method and the adaptive group lasso penalty approach to achieve covariate identification and coefficient estimation. The penalty term consists of two parts. The first term penalizes the norm of the coefficient function, which is used to select relevant variables. The second term penalizes the norm of the derivative function, which assesses the constancy of the coefficient functions. The asymptotic properties of the proposed methodology are established. Performance of the proposed method is demonstrated using simulated data along with an application to the analysis of the air quality and health data in Hong Kong.

Asymmetrical pythagorean-hodograph (PH) spline-based C3 continuous corner smoothing algorithm for five-axis tool paths with short segments

• A real-time C 3 continuous corner smoothing algorithm is proposed for five-axis short linear segments. • The proposed method can achieve lower curvature based on asymmetrical PH splines. • Smoothing errors around the corners are bounded under given constraints. • The arc-length can be analytically calculated to achieve real-time interpolation. • Experiments verify that much lower curvature and higher machining efficiency can be realized. Local corner smoothing is widely used for the G01 motion commands to achieve the motion continuity of transition corners. Most splines constructed by the existing local corner smoothing methods oriented for five-axis machining mainly must be connected by linear segments. However, with respect to the five axis machining of the corners with short line segments, these kinds of methods need that both ends of the constructed splines usually must be shrunk with the same proportion to avoid the overlapping of adjacent splines. This will lead to relatively large curvatures of the obtained trajectories together with relatively low machining efficiency. This article proposes a new real-time corner smoothing algorithm for five-axis machine tools by constructing the C 3 continuous asymmetrical PH splines. The typical characteristic lies in that the control points related to the two ends of the PH spline can be independently adjusted through reasonably introducing two more adjustable variables, which are realized by analytically calculating and then adding two additional control points into the corresponding control polygon. As a result, the PH spline poses the property of the asymmetry about the angular bisector. Based on this, the short linear commands of tool tip and tool orientation can be smoothed only through inserting different lengths of asymmetrical PH splines that can be connected directly. The motion variance of the smoothed tool orientation related to the tool tip displacement is analytically proved to be C 3 continuous, and thus, the synchronization between tool tip and tool orientation is guaranteed. The outstanding advantage of the algorithm for short line segments is twofold. The first is that the performance of the drives can be more fully utilized to reduce cycle time since the curvature around corners are reduced by adopting the asymmetrical profile, and the second is that the synchronization procedure is greatly simplified since the algorithm eliminates the requirement to convert the intermediate line segments into a spline between the adjacent connected PH splines. Both simulation and the experimental results demonstrate that the proposed algorithm can realize a higher machining efficiency.