LINEAR SYSTEMS AND LINEAR INTERPOLATION I

The linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.

Decomposing InSAR LOS displacement into co-seismic dislocation with a linear in-terpolation model: A case study of the Kunlun Mountain M_s=8.1 earthquake

It has always been a difficult problem to extract horizontal and vertical displacement components from the InSAR LOS （Line of Sight） displacement since the advent of monitoring ground surface deformation with InSAR technique. Having tried to fit the firsthand field investigation data with a least squares model and obtained a preliminary result, this paper, based on the previous field data and the InSAR data, presents a linear cubic interpolation model which well fits the feature of earthquake fracture zone. This model inherits the precision of investigation data; moreover make use of some advantages of the InSAR technique, such as quasi-real time observation, continuous recording and all-weather measurement. Accordingly, by means of the model this paper presents a method to decompose the InSAR slant range co-seismic displacement （i.e. LOS change） into horizontal and vertical displacement components. Approaching the real motion step by step, finally a serial of curves representing the co-seismic horizontal and vertical displacement component along the main earthquake fracture zone are approximately obtained.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

A Virtual Walk along Street Based on View Interpolation

Image morphing is a powerful tool for visual effect. In this paper, a view interpolation algorithm is proposed to simulate a virtual walk along a street from start position to end position. To simulate a virtual walking view needs to create new appearing scene in the vision-vanishing point and disappearing scene beyond the scope of view. To attain these two aims we use two enhanced position parameters to match pixels of source images and target images. One enhanced position parameter is the angular coordinates of pixels. Another enhanced position parameter is the distances from pixels to the vision-vanishing point. According to the parameter values, pixels beyond the scope of view can be ＂moved＂ out in linear interpolation. Result demonstrates the validity of the algorithm. Another advantage of this algorithm is that the enhanced position parameters are based on real locations and walking distances, so it is also an approach to online virtual tour by satellite maps of virtual globe applications such as Google Earth.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY

Algebraic reflexivity introduced by Hadwin is related to linear interpolation.In this paper,the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced.Some properties of them are obtained and some relations between them revealed

Dependence of the AGCM Climatology on the Method of Prescribing Surface Boundary Conditions and Its Climatological Implication

By using IAP 9L AGCM, two sets of long-term climatological integration have been performed with the two different interpolation procedures for generating the daily surface boundary conditions. One interpolation procedure is the so-called “traditional” scheme, for which the daily surface boundary conditions are obtained by linearly interpolating between the observed monthly mean values, however the observed monthly means cannot be preserved after interpolation. The other one is the “new” scheme, for which the daily surface boundary conditions are obtained by linearly interpolating between the “artificial” monthly mean values which are based on, but are different from the observed ones, after interpolating with this new scheme, not only the observed monthly mean values are preserved, the time series of the new generated daily values is also more consistent with the observation. Comparison of the model results shows that the differences of the globally or zonally averaged fields between these two integrations are quite small, and this is due to the compensating effect between the different regions. However, the differences of the two patterns (the global or regional geographical distributions), are quite significant, for example, the magnitude of the difference in the JJA mean rainfall between these two integrations can exceed 2 mm/ day over Asian monsoon regions, and the difference in DJF mean surface air temperature can also exceed 2?C over this region. The fact that the model climatology depends quite strongly on the method of prescribing the daily surface boundary conditions suggests that in order to validate the climate model or to predict the short-term climate anomalies, either the “new? interpolation scheme or the high frequency surface boundary conditions (e.g., daily or weekly data instead of the monthly data) should be introduced. Meanwhile, as for the coupled model, the daily coupling scheme between the different component climate models ( e.g., atmospheric and oceanic general circulation models) is preferred in order to partly eliminate the “climate drift” problem which may appear during the course of direct coupling.

Simultaneous inversion of velocity distribution and interface positions

This paper deals with the simultaneous inversion of velocity distribution and interface positions in a laterally heterogeneous medium using seismic travel time data. Due to the application of variable step length and linear interpolation techniques (for both theoretical travel times and the partial derivative matrix), the computing speed is increased greatly. As compared with other domestic computing programs of this kind, it is five times or more faster than others. Besides reflected waves, the transmitted waves can also be used to form the partial derivative matrix of travel times with respect to interface positions. So this method can make full use of the information about interface positions contained in various transmitted waves and speed up the convergence rate. Digital tests and processing results of real data indicate the feasibility and effectiveness of the method and its program.

Evolutionary GAN–Based Data Augmentation for Cardiac Magnetic Resonance Image

Generative adversarial networks(GANs)have considerable potential to alleviate challenges linked to data scarcity.Recent research has demonstrated the good performance of this method for data augmentation because GANs synthesize semantically meaningful data from standard signal distribution.The goal of this study was to solve the overfitting problem that is caused by the training process of convolution networks with a small dataset.In this context,we propose a data augmentation method based on an evolutionary generative adversarial network for cardiac magnetic resonance images to extend the training data.In our structure of the evolutionary GAN,the most optimal generator is chosen that considers the quality and diversity of generated images simultaneously from many generator mutations.Also,to expand the distribution of the whole training set,we combine the linear interpolation of eigenvectors to synthesize new training samples and synthesize related linear interpolation labels.This approach makes the discrete sample space become continuous and improves the smoothness between domains.The visual quality of the augmented cardiac magnetic resonance images is improved by our proposed method as shown by the data-augmented experiments.In addition,the effectiveness of our proposed method is verified by the classification experiments.The influence of the proportion of synthesized samples on the classification results of cardiac magnetic resonance images is also explored.

AN ALGORITHM OF LOCAL PREDICTION FOR CHAOTIC SEQUENCES WITH VARIABLE FRAME LENGTH

According to the issues that the predict errors of chaotic sequences rapidly accumulated in multi-step forecasting which affects the predict accuracy, we proposed a new predict algorithm based on local modeling with variable frame length and interpolation points. The core idea is that, using interpolation method to increase the available sample data, then modeling the chaos dynamics system with least square algorithm which based on the Bernstein polynomial to realize the forecasting. We use the local modeling method, looking for the optimum frame length and interpolation points in every frame to improve the predict peformance. The experimental results show that the proposed algorithm can improve the predictive ability effectively, decreasing the accumulation of iterative errors in multi-step prediction.

An efficient technique for recovering responses of parameterized structural dynamic problems

In this article,an effective technique is developed to efficiently obtain the output responses of parameterized structural dynamic problems.This technique is based on the conception of reduced basis method and the usage of linear interpolation principle.The original problem is projected onto the reduced basis space by linear interpolation projection,and subsequently an associated interpolation matrix is generated.To ensure the largest nonsingularity,the interpolation matrix needs to go through a timenode choosing process,which is developed by applying the angle of vector spaces.As a part of this technique,error estimation is recommended for achieving the computational error bound.To ensure the successful performance of this technique,the offline-online computational procedures are conducted in practical engineering.Two numerical examples demonstrate the accuracy and efficiency of the presented method.

An Improved 3-D Ray Tracing Method Using Linear Traveltime Interpolation

An approach of three-dimensional seismic ray tracing is presented,which is derived from adopting two-dimensional linear traveltime interpolation（LTI）.By adjusting the forward process using the partition of grid interface,and backward step by considering more directions,the new approach is suitable for the application of three-dimensional models.The calculation results show that,with the same accuracy,the improved 3-D method is much faster than the method of traditional LTI directly applied in the three-dimensional case.

A Finite-Difference Approximation for the Oneand Two-Dimensional Tempered Fractional Laplacian

This paper provides a finite-difference discretization for the one-and two-dimensional tempered fractional Laplacian and solves the tempered fractional Poisson equation with homogeneous Dirichlet boundary conditions.The main ideas are to,respectively,use linear and quadratic interpolations to approximate the singularity and non-singularity of the one-dimensional tempered fractional Laplacian and bilinear and biquadratic interpolations to the two-dimensional tempered fractional Laplacian.Then,we give the truncation errors and prove the convergence.Numerical experiments verify the convergence rates of the order O(h^2−2s).

Sub-pixel motion estimation using phase correlation: comparisons and evaluations

Purpose-Effective and robust motion estimation with sub-pixel accuracy is essential in many image processing and computer vision applications.Due to its computational efficiency and robustness in the presence of intensity changes as well as geometric distortions,phase correlation in the Fourier domain provides an attractive solution for global motion estimation and image registration.The paper aims to discuss these issues.Design/methodology/approach-In this paper,relevant sub-pixel strategies are categorized into three classes,namely,single-side peak interpolation,dual-side peak interpolation and curve fitting.The well-known images“Barbara”and“Pentagon”were used to evaluate the performance of eight typical methods,in which Gaussian noise was attached in the synthetic data.Findings-For eight such typical methods,the tests using synthetic data have suggested that considering dual-side peaks in interpolation or fitting helps to produce better results.In addition,dual-side interpolation outperforms curve fitting methods in dealing with noisy samples.Overall,Gaussian-based dual-side interpolation seems the best in the experiments.Originality/value-Based on the comparisons of eight typical methods,the authors can have a better understanding of the phase correlation for motion estimation.The evaluation can provide useful guidance in this context.

Validation and correction of auto-logged position measurements

Accurate position measurements are extremely valuable in the shipping industry for various reasons such as safety(collision avoidance),security(situational awareness),fuel-saving(weather identification),punctuality(route prediction),etc.Although GNSS(Global Navigation Satellite System)receivers installed on-board the ships are proven to be highly accurate,the data logging process may occasionally be problematic,mainly due to the complexity of the measurements and the decimal precision that is required.Data were collected from 3 years of operations of 228 Maersk Line container vessels and an analysis reveals that there is a substantial amount (≈20%) of historical position measurements sent to shore that does not reflect reality.In the study,the sources of the faulty logged position measurements are categorized and an interpolation methodology is proposed to validate and correct them by using AIS(Automatic Identification System)data.

LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

In recent years,the Active Flutter Suppression(AFS)employing Linear ParameterVarying(LPV)framework has become a hot spot in the research field.Nevertheless,the flutter suppression technique is facing two severe challenges.On the one hand,due to the fatal risk of flight test near critical airspeed,it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data.On the other hand,saturation of the actuator may degrade the closed-loop performance,which was often neglected in the past work.To tackle these two problems,a new active controller design procedure is proposed to suppress flutter in this paper.Firstly,with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates(SMILE)technique,a set of high-fidelity Linear Time-Invariant(LTI)models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system.And then,the unstable aeroelastic dynamics beyond critical airspeed are‘predicted’by extrapolating the resulting LPV model.Secondly,based on the control-oriented LPV model,an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation.Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored,the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter(BFF)when encountering the actuator saturation.However,the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system whenencountering serious actuator saturation.