Smoothing Spline Interpolation Research Articles

A Trainable Approach to Zero-Delay Smoothing Spline Interpolation

A Trainable Approach to Zero-Delay Smoothing Spline Interpolation

Comparative Study on Two Solutions of 3-RPS Parallel Mechanism Pose

In this paper, the performance of the different methods for solving the pose of parallel mechanism is different in the amount and precision of calculation. Taking typical 3-RPS parallel mechanism as the analysis object, kinematics models of the mechanism were established with quaternion and Rodriguez parameter method respectively, and the bar length of the maximum reachable space was solved by genetic algorithm, so as to compare the advantages and disadvantages of the solution of the model. Finally, numerical simulation is used to compare the amplitude and fluctuation degree of the curve according to the smooth spline interpolation in both calculation and precision. The results show that the Rodriguez parameter method is superior to the quaternion method in the accuracy of pose resolution of 3-RPS parallel mechanism, while the quaternion method is superior in the real-time performance of the solution. This result provides a theoretical basis for the pose control of parallel mechanism.

Experimental and statistical analysis of hybrid-fiber-reinforced recycled aggregate concrete

Although concrete is the most widely used construction material, its deficiency in shrinkage and low tensile resistance is undeniable. However, the aforementioned defects can be partially modified by addition of fibers. On the other hand, possibility of adding waste materials in concrete has provided a new ground for use of recycled concrete aggregates in the construction industry. In this study, a constant combination of recyclable coarse and fine concrete aggregates was used to replace the corresponding aggregates at 50% substitution percentage. Moreover, in order to investigate the effects of fibers on mechanical and durability properties of recycled aggregate concrete, the amounts of 0.5%, 1%, and 1.5% steel fibers (ST) and 0.05%, 0.1% and 0.15% polypropylene (PP) fibers by volumes were used individually and in hybrid forms. Compressive strength, tensile strength, flexural strength, ultrasonic pulse velocity (UPV), water absorption, toughness, elastic modulus and shrinkage of samples were investigated. The results of mechanical properties showed that PP fibers reduced the compressive strength while positive impact of steel fibers was evident both in single and hybrid forms. Tensile and flexural strength of samples were improved and the energy absorption of samples containing fibers increased substantially before and after crack presence. Growth in toughness especially in hybrid fiber-reinforced specimens retarded the propagation of cracks. Modulus of elasticity was decreased by the addition of PP fibers while the contrary trend was observed with the addition of steel fibers. PP fibers decreased the ultrasonic pulse velocity slightly and had undesirable effect on water absorption. However, steel fiber caused negligible decline in UPV and a small impact on water absorption. Steel fibers reduce the drying shrinkage by up to 35% when was applied solely. Using fibers also resulted in increasing the ductility of samples in failure. In addition, mechanical properties changes were also evaluated by statistical analysis of MATLAB software and smoothing spline interpolation on compressive, flexural, and indirect tensile strength. Using shell interpolation, the optimization process in areas without laboratory results led to determining optimal theoretical points in a two-parameter system including steel fibers and polypropylene.

Authors: Yunhui Zeng ; Wenjuan Hu ; Hongfei Guo ; Shiyue Shen ; Li Huang ; Yiying Lou

Focused on the lane occupancy phenomenon, this paper analyzes the roads during two different accidents to the evacuation period. Firstly, according to the statistical data, this paper calculated the correction coefficients under the road traffic condition, and then obtained the actual traffic capacity result at each moment of the road when combining the function model of the actual traffic capacity corrected by the running speed and the road traffic condition. Next the actual traffic capacity results are fitted to the Smooth spline interpolation, and then the actual traffic capacity is further verified by the traffic congestion situation. The actual traffic capacity of the road during the accident to evacuation is summarized as follows: the actual traffic capacity shows a nonlinear trend, that is, ascending-attenuating-recovering and gradually stabilizing. Finally, using Mann-Whitney U test to carry out the difference test on the actual traffic capacity, it is found that there is significant difference between the two groups of data, and the actual traffic capacity of the second case is stronger than that of the first one, and the reasons for the difference are analyzed as follows: the ratio of the steering traffic volume at the downstream intersection is different; this road section includes the community intersection and there are vehicles entering and leaving; meanwhile the speed of each lane is different and there are buildings near the lane. The above conclusions will provide theoretical basis for the traffic management department to correctly guide the vehicle driving, approve the road construction, design the road channelization plan, set the roadside parking space and the non-port-type bus stations.

A new cartoon–texture image decomposition approach with smoothing spline interpolation

In this paper, we present an effective approach to decompose an image into its cartoon part and texture part without losing edge information. The cartoon and texture parts of an image have their own importance in various applications like medical imaging and image segmentation, etc. Although image decomposition is a widely explored area and a number of approaches are available in the literature, but most of these methods are unable to preserve the edge information effectively. The proposed method is able to deal with this drawback. The proposed method involves two simple steps texture detection followed by smoothing. We demonstrate the experimental results with some state-of-the-art methods to show the efficiency of the proposed approach.

Methods of approximation influence aquatic ecosystem metabolism estimates

Aquatic ecologists have recently employed dynamic models to estimate aquatic ecosystem metabolism. All approaches involve numerically solving a differential equation describing dissolved oxygen (DO) dynamics. Although the DO differential equation can be solved accurately with linear multistep or Runge–Kutta methods, less accurate methods, such as the Euler method, have been applied. The methods also differ in how discrete temperature and light measurements are used to drive DO dynamics. Here, we used a representative stream DO data set to compare the metabolism estimates generated by multiple Euler based methods and an accurate numerical method. We also compared metabolism estimates using linear, piecewise constant and smoothing spline interpolation of light and temperature. Using observed DO to calculate DO saturation deficit in the Euler method results in a substantial difference in metabolism estimates compared to all other methods. If modeled DO is used to calculate DO saturation deficit, the Euler method introduces smaller error in metabolism estimates, which diminishes as logging interval decreases. Linear and smoothing spline interpolation result in similar metabolism estimates, but differ from estimates based on piecewise constant interpolation. We demonstrate how different computational methods imply distinct assumptions about process and observation error, and conclude that under the assumption of observation error, the best practice is to use the accurate numerical method of solving differential equation with a continuous interpolation of light and temperature. The Euler method will introduce minimal error if it is paired with frequently logged data and DO saturation deficit is computed using modeled DO.

Sensor-Free Stress Estimation Model for Steel Beam Structures Using a Motion Capture System

As a new paradigm for safety assessment of beam structures, this paper proposes a sensor-free monitoring model to estimate the stress distribution of steel beam structures with uncertain loads. The model consists of three steps: 1) the use of a sensor- and wire-free measurement step using a motion capture system; 2) a deformed shape estimation step employing cubic smoothing spline interpolation; and 3) a stress distribution and maximum stress estimation step using the radius of curvature of the estimated deformed shape or a finite-element method. Therefore, unlike the conventional sensor-based structural health monitoring with lengthy cables, the model can determine the maximum stress in a non-contact manner without the deterioration of the measurement accuracy. The sensor-free stress estimation method was applied to estimate the stress distribution of a steel beam structure subjected to static loads applied at the mid-span of the beam by a hydraulic jack. The validity of the proposed method was confirmed by comparing the estimated stresses with stresses measured in static loading tests.

Observations and analysis with the spline-based Rydberg–Klein–Rees approach for the 31Σg+ state of Rb2

Ro-vibrational term values of the 3(1)Σg (+) state of (85,85)Rb2 and (85,87)Rb2 and resolved fluorescence spectra to the A(1)Σu (+) state are recorded following optical-optical double resonance excitation. The experimental data are heavily perturbed, and as a result, the standard analysis based on Dunham series representation of the energy levels fails. The analysis is done via modeling the adiabatic potential function with the Rydberg-Klein-Rees potential constructed from the generalized smoothing spline interpolation of the vibrational energies Gv and rotational constants Bv.

Seasonal mortality variations of cardiovascular, respiratory and malignant diseases in the City of Belgrade

The main purpose of this paper is to examine seasonal variations in mortality resulting from cardiovascular diseases, respiratory diseases and cancer, as well as to provide a review of environmental factors underlying such phenomenon. The herein presented study was conducted on the territory of Belgrade based on the data on daily mortality rates obtained from the Institute of Public Health in Belgrade for the period 2009-2014, as well as the data on annual mortality rates provided by the Statistical Office of the Republic of Serbia for the period 2000-2014. The analysis of mortality variations was performed by the use of Theil-Sen method, smooth trend method and cubic spline interpolation, whereas desriptive tools, such as winter/summer ratio and dissimilarity index, were used to examine the seasonal pattern. According to the Institute of Public Health, over 113430 deaths were registered in Belgrade area for the period 2009-2014, out of which 53.25% is attributed to cardiovascular diseases, 4.01% to respiratory diseases and 27.50% to cancer. The annual mortality rates caused by cardiovascular diseases and cancer on the territory of Belgrade are among the highest ranking in Europe. The leading causes of death in the observed period included: cardiomyopathy, heart attack and stroke with accompanying complications, breast cancer in women, prostate and colorectal cancer in men, lung and bronchus cancer for both genders, and chronic obstructive pulmonary disease. Cardiovascular and respiratory mortality rates are significantly higher among people aged 65 and over, whereas more than one third of deaths caused by cancer is observed among younger people aged between 45 and 64 years. Research results show that seasonal variations were most pronounced in mortality resulting from cardiovascular and respiratory diseases, with highest mortality rates recorded in February and March and lowest during the summer season. Also, the number of deaths due to cardiovascular diseases increased twice, namely at the end of June and October, which is assumed to be the result of sudden temperature changes. Nonetheless, no such seasonal variations were observed in mortality caused by cancer. Seasonal variations in mortality resulting from cardiovascular diseases also indicate gender differences, which is why sudden temperature changes in interim periods affect more women than men. As regards deseasonalized trend, mortality caused by cardiovascular diseases stagnates, while mortality caused by cancer and mortality caused by respiratory diseases records moderate to severe increase. This is a uniform trend in almost all municipalities in Belgrade, with average mortality rates being higher in central zones than in suburbs over the last 15 years, particularly mortality caused by cancer. A slight increase in the overall mortality can also be attributed to aging of the population, which cannot be verified due to lack of available accurate data on the average age structure of Belgrade population for the observed period. A better understanding of seasonal variations in mortality caused by chronic non-communicable diseases can contribute to improving the population health care and rising awareness of the population concerning greater health care in changeable weather conditions due to global warming and climate change. These findings can also enhance preventive action on environmental risk factors that are not limited exclusively to weather conditions, such as air pollution.

The Estimation Method of Stress Distribution for Beam Structures Using the Terrestrial Laser Scanning

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed. Keywords—Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

Continuous phase estimation from noisy fringe patterns based on the implicit smoothing splines.

We introduce the algorithm for the direct phase estimation from the single noisy interferometric pattern. The method, named implicit smoothing spline (ISS), can be regarded as a formal generalization of the smoothing spline interpolation for the case when the interpolated data is given implicitly. We derive the necessary equations, discuss the properties of the method and address its application for the direct estimation of the continuous phase in both classical interferometry and digital speckle pattern interferometry (DSPI). The numerical illustrations of the algorithm performance are provided to corroborate the high quality of the results.

An update of high‐resolution monthly climate surfaces for Mexico

ABSTRACTClimate surfaces are digital representations of climatic variables from a region in the planet estimated via geographical interpolation techniques. Climate surfaces have multiple applications in research planning, experimental design, and technology transfer. Although high‐resolution climatologies have been developed worldwide, Mexico is one of the few countries that have developed several climatic surfaces. Here, we present an updated high‐resolution (30 arc sec) climatic surfaces for Mexico for the average monthly climate period 1910–2009, corresponding to monthly values of precipitation, daily maximum, and minimum temperature, as well as 19 bioclimatic variables derived from the monthly precipitation and temperature values. To produce these surfaces we applied the thin‐plate smoothing spline interpolation algorithm implemented in the ANUSPLIN software to nearly 5000 climate weather stations countrywide. As an additional product and unlike the previous efforts, we generated monthly standard error surfaces for the three climate parameters, which can be used for error assessment when using these climate surfaces. Our climate surface predicted slightly drier and cooler conditions than the previous ones. ANUSPLIN diagnostic statistics indicated that model fit was adequate. We implemented a more recent error assessment, a set of withheld stations to perform an independent evaluation of the model surfaces. We estimate the mean absolute error and mean error, with the withheld data and all the available data. Average RTGCV for monthly temperatures was of 1.26–1.12 °C and 24.67% for monthly precipitation, and a RTMSE of 0.48–0.56 °C and 11.11%. The main advantage of the surfaces presented here regarding the other three developed for the country is that ours cover practically the entire 20th century and almost the entire first decade of the 21st century. It is the most up to date high‐resolution climatology for the country.

Smooth trajectory generation for five-axis machine tools

This paper presents a smooth spline interpolation technique for five-axis machining of sculptured surfaces. The tool tip and orientation locations generated by the CAM system are first fitted to quintic splines independently to achieve geometric jerk continuity while decoupling the relative changes in position and orientation of the cutter along the curved path. The non-linear relationship between spline parameters and displacements along the path is approximated with ninth order and seventh order feed correction splines for position and orientation, respectively. The high order feed correction splines allow minimum deviation from the reference axis commands while preserving continuous jerk on three translational and two rotary drives. The proposed method has been experimentally demonstrated to show improvements in reducing the excitation of inertial vibrations while improving tracking accuracy in five-axis machining of curved paths found in dies, molds and aerospace parts.

Measurement of intervertebral cervical motion by means of dynamic x-ray image processing and data interpolation.

Accurate measurement of intervertebral kinematics of the cervical spine can support the diagnosis of widespread diseases related to neck pain, such as chronic whiplash dysfunction, arthritis, and segmental degeneration. The natural inaccessibility of the spine, its complex anatomy, and the small range of motion only permit concise measurement in vivo. Low dose X-ray fluoroscopy allows time-continuous screening of cervical spine during patient's spontaneous motion. To obtain accurate motion measurements, each vertebra was tracked by means of image processing along a sequence of radiographic images. To obtain a time-continuous representation of motion and to reduce noise in the experimental data, smoothing spline interpolation was used. Estimation of intervertebral motion for cervical segments was obtained by processing patient's fluoroscopic sequence; intervertebral angle and displacement and the instantaneous centre of rotation were computed. The RMS value of fitting errors resulted in about 0.2 degree for rotation and 0.2 mm for displacements.

Trajectory Learning for Robot Programming by Demonstration Using Hidden Markov Model and Dynamic Time Warping

The main objective of this paper is to develop an efficient method for learning and reproduction of complex trajectories for robot programming by demonstration. Encoding of the demonstrated trajectories is performed with hidden Markov model, and generation of a generalized trajectory is achieved by using the concept of key points. Identification of the key points is based on significant changes in position and velocity in the demonstrated trajectories. The resulting sequences of trajectory key points are temporally aligned using the multidimensional dynamic time warping algorithm, and a generalized trajectory is obtained by smoothing spline interpolation of the clustered key points. The principal advantage of our proposed approach is utilization of the trajectory key points from all demonstrations for generation of a generalized trajectory. In addition, variability of the key points' clusters across the demonstrated set is employed for assigning weighting coefficients, resulting in a generalization procedure which accounts for the relevance of reproduction of different parts of the trajectories. The approach is verified experimentally for trajectories with two different levels of complexity.

A continuous description of intervertebral motion by means of spline interpolation of kinematic data extracted by videofluoroscopy

In vivo analysis of intervertebral kinematics provides useful information about spinal disorders and performance of disk prostheses. Diagnosis of intervertebral instability is based on measurement of abnormal range of segmental motion in sagittal plane through functional flexion–extension radiography; however, this concise measure does not take into account the progression of segmental motion in between flexion and extension extremes. Fluoroscopy can support analysis of intervertebral kinematics during patient's motion with an acceptable X-ray dose. A spline-based method designed for a continuous-time description of intervertebral motion extracted by videofluoroscopy is proposed. Fluoroscopic sagittal sequences of lumbar spine were processed by an automated method based on template matching to track vertebrae. A smoothing spline interpolation of the estimated intervertebral kinematic data was performed and a continuous-time description of segmental rotation and translation was obtained; the smoothing parameter was chosen both to preserve motion and to reduce noise. Concise measurements were extracted by the continuous-time kinematics and compared with standard clinical measurements of intervertebral sagittal rotation and translation. The trajectory of instantaneous center of rotation, never presented before for in vivo spinal segments, was provided and compared with standard measurements of the finite center of rotation. Results showed a good agreement with standard clinical measurements: on average, absolute differences resulted 0.74degree for sagittal rotation, 0.59mm for translation and 1.02mm for the x- and y-position of center of rotation. The proposed method offers an effective technique for the continuous-time description of intervertebral motion, maintaining standard clinical measurements for diagnosis of lumbar instability.

Mapping vegetation suitability in coarse sandy hill catchment areas of the Loess Plateau

Vegetation suitability mapping is important for the selection of species for implementing the re-vegeta- tion program in the coarse sandy hill catchment areas of the Loess Plateau, China. We introduce a Boolean model, which uses a thin plate smoothing spline interpolation method to model the distribution of precipitation and temperature and analyze the suitability of 38 species using GIS techniques considering the requirement of these spe- cies for environmental conditions. Then we overlay a sin- gle suitability map of these 38 species to obtain a species frequency map for a specific site. In our study, we mean with 'high frequency' a high suitability of a site for re- vegetation. The results show that we can model the spatial changes of vegetation suitability with a combination of topographic analyses based on DEM and GIS functions. We also demonstrate these spatial changes on the screen using Visual Basic language and GIS functions, which will help decision makers to have a clear view of species and site suitability changes over large areas. Although more powerful models, such as GLM and GAM, were not used due to data limitation, our methods can still provide some relevant insights for similar studies.

Thin plate smoothing spline interpolation of daily rainfall for New Zealand using a climatological rainfall surface

AbstractThis study presents a method for estimating daily rainfall on a 0.05° latitude/longitude grid covering all of New Zealand for the period 1960–2004 using a second order derivative trivariate thin plate smoothing spline spatial interpolation model. Use of a hand‐drawn (and subsequently digitised) mean annual rainfall surface as an independent variable in the interpolation is shown to reduce the interpolation error compared with using an elevation surface. This result is confirmed when long‐term average annual rainfall data, derived from the daily interpolations, are validated using long‐term river flow data. Copyright © 2006 Royal Meteorological Society

Estimation of Long-Term Climate Information at Locations with Short-Term Data Records

Abstract The accurate mapping of climate has widespread interest and benefit and depends on the availability of long-term data. Accuracy increases with the amount of data, but, often, insufficient data exist for the desired accuracy. To produce accurate maps within a short time frame, a scheme for estimating long-term climate statistics at locations with only short records is required. A general method is described that involves thin-plate smoothing-spline interpolation. Using data from the long-term stations, two independent interpolations are made to the short-term sites: first, the climate element's distribution and, second, the percentile for the period of observation at the short-term sites. Together these imply a value for the period of observation, but actual values are, of course, available for this period. The difference between the actual and implied values at the short-term sites provides an adjustment to the estimated distribution. It is also demonstrated that for short-term station deployment...

Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on the notion of autoregressive Hilbert processes that represent a generalization of the classical autoregressive processes to random variables with values in a Hilbert space. A careful analysis reveals, in particular, that this approach is related to the theory of function estimation in linear ill-posed inverse problems. In the deterministic literature, such problems are usually solved by suitable regularization techniques. We describe some recent approaches from the deterministic literature that can be adapted to obtain fast and feasible predictions. For large sample sizes, however, these approaches are not computationally efficient. With this in mind, we propose three linear wavelet methods to efficiently address the aforementioned prediction problem. We present regularization techniques for the sample paths of the stochastic process and obtain consistency results of the resulting prediction estimators. We illustrate the performance of the proposed methods in finite sample situations by means of a real-life data example which concerns with the prediction of the entire annual cycle of climatological El Niño-Southern Oscillation time series 1 year ahead. We also compare the resulting predictions with those obtained by other methods available in the literature, in particular with a smoothing spline interpolation method and with a SARIMA model.