Smooth cutting pattern generation technique for membrane structures using geodesic line on subplane and spline interpolation

Practical techniques for smooth geodesic patterning of membrane structures were investigated.For the geodesic search,adjustment of the subplane of the extracted elements series was proposed,and various spline approximation methods were used to flatten the strip for the generation of a smooth pattern.This search approach is very simple,and the geodesic line could be easily attained by the proposed method without the need for a difficult computation method.Smooth cutting patterning can also be generated by spline approximation without the noise in discrete nodal information.Additionally,the geodesic cutting pattern saved about 21%of the required area for the catenary model due to the reduction of the curvature of the planar pattern seam line.

Non-overshooting and Non-undershooting Cubic Spline Interpolation for Empirical Mode Decomposition

To suppress the overshoots and undershoots in the envelope fitting for empirical mode decomposition （EMD）, an alternative cubic spline interpolation method without overshooting and undershooting is proposed. On the basis of the derived slope constraints of knots of a non-overshooting and non-undershooting cubic interpolant, together with ＂not-a-knot＂ conditions the cubic spline interpolants are constructed by replacing the requirement for equal second order derivatives at every knot with Brodlie＇ s derivative formula. Analysis and simulation experiments show that this approach can effectively avoid generating new extrema, shifting or exaggerating the existing ones in a signal, and thus significantly improve the decomposition performance of EMD.

Improvement of Orbit Prediction Algorithm for Spacecraft Through Simplified Precession-Nutation Model Using Cubic Spline Interpolation Method

For the on-orbit flight missions,the model of orbit prediction is critical for the tasks with high accuracy requirement and limited computing resources of spacecraft.The precession-nutation model,as the main part of extended orbit prediction,affects the efficiency and accuracy of on-board operation.In this paper,the previous research about the conversion between the Geocentric Celestial Reference System and International Terrestrial Reference System is briefly summarized,and a practical concise precession-nutation model is proposed for coordinate transformation computation based on Celestial Intermediate Pole(CIP).The idea that simplifying the CIP-based model with interpolation method is driven by characteristics of precession-nutation parameters changing with time.A cubic spline interpolation algorithm is applied to obtain the required CIP coordinates and Celestial Intermediate Origin locator.The complete precession nutation model containing more than 4000 parameters is simplified to the calculation of a cubic polynomial,which greatly reduces the computational load.In addition,for evaluating the actual performance,an orbit propagator is built with the proposed simplified precession-nutationmodel.Compared with the orbit prediction results obtained by the truncated series of IAU2000/2006 precession-nutation model,the simplified precession-nutation model with cubic spline interpolation can significantly improve the accuracy of orbit prediction,which implicates great practical application value in further on-orbit missions of spacecraft.

Combining Cubic Spline Interpolation and Fast Fourier Transform to Extend Measuring Range of Reflectometry

The reflectometry is a common method used to measure the thickness of thin films. Using a conventional method,its measurable range is limited due to the low resolution of the current spectrometer embedded in the reflectometer.We present a simple method, using cubic spline interpolation to resample the spectrum with a high resolution,to extend the measurable transparent film thickness. A large measuring range up to 385 m in optical thickness is achieved with the commonly used system. The numerical calculation and experimental results demonstrate that using the FFT method combined with cubic spline interpolation resampling in reflectrometry, a simple,easy-to-operate, economic measuring system can be achieved with high measuring accuracy and replicability.

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

A polynomial smooth epsilon-support vector regression based on cubic spline interpolation

Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to support vector regression models, this study takes cubic spline interpolation to generate a new polynomial smooth function ｜×｜ε^ 2, in g-insensitive support vector regression. Theoretical analysis shows that Sε^2 -function is better than pε^2 -function in properties, and the approximation accuracy of the proposed smoothing function is two order higher than that of classical pε^2 -function. The experimental data shows the efficiency of the new approach.

ERROR BOUNDS IN PERIODIC QUARTIC SPLINE INTERPOLATION

In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).

Inverse Spline Interpolation for All-time Resistivity of Central-Loop TEM

A convenient numerical calculation method (inverse spline interpolation) for all-time apparent resistivity intransient electromagnetic method (TEM) is proposed in this paper. Characteristic of early and late normalized inductiveelectromotive force was investigated. According to the turning point, the transient process is divided into the earlyphase, the turning point, and the late phase. Afterwards, apparent resistivity is obtained through inverse spline interpo-lation in the early and the late phases, respectively. Finally, the resistivities of the early-time and the late-time wereconnected together by the turning point. The result shows that the inverse spline method is feasible and the method alsolays a foundation for initial model construction in the TEM automatic inversion.

Downhole microseismic data reconstruction and imaging based on combination of spline interpolation and curveletsparse constrained interpolation

When cause of the aliasing lack probl using borehole sensors and microseimic events to image, spatial aliasing often occurred be- of sensors underground and the distance between the sensors which were too large. To solve em, data reconstruction is often needed. Curvelet transform sparsity constrained inversion was widely used in the seismic data reconstruction field for its anisotropic, muhiscale and local basis. However, for the downhole ease, because the number of sampling point is mueh larger than the number of the sensors, the advantage of the cnrvelet basis can＇t perform very well. To mitigate the problem, the method that joints spline and curvlet-based compressive sensing was proposed. First, we applied the spline interpolation to the first arri- vals that to be interpolated. And the events are moved to a certain direction, such as horizontal, which can be represented by the curvelet basis sparsely. Under the spasity condition, curvelet-based compressive sensing was applied for the data, and directional filter was also used to mute the near vertical noises. After that, the events were shifted to the spline line to finish the interpolation workflow. The method was applied to a synthetic mod- el, and better result was presented than using curvelet transform interpolation directly. We applied the method to a real dataset, a mieroseismic downhole observation field data in Nanyang, using Kirchhoff migration method to image the microseimic event. Compared with the origin data, artifacts were suppressed on a certain degree.

Modeling the Dynamic Gravity Variations of Northeastern Margin of Qinghai-Xizang (Tibet) Plateau by Using Bicubic Spline Interpolation Function

In this paper, the spatial-temporal gravity variation patterns of the northeastern margin of Qinghal-Xizang （Tibet） Plateau in 1992 - 2001 are modeled using bicubic spline interpolation functions and the relations of gravity change with seismicity and tectonic movement are discussed preliminarily. The results show as follows： ① Regional gravitational field changes regularly and the gravity abnormity zone or gravity concentration zone appears in the earthquake preparation process; ②In the significant time period, the gravity variation shows different features in the northwest, southeast and northeast parts of the surveyed region respectively, with Lanzhou as its boundary;③The gravity variation distribution is basically identical to the strike of tectonic fault zone of the region, and the contour of gravity variation is closely related to the fault distribution.

On the Cardinal Spline Interpolation Corresponding to Infinite Order Differential Operators

This paper discusses some problems on the cardinal spline interpolation correspond- ing to infinite order differential operators.The remainder formulas and a dual theorem are es- tablished for some convolution classes,where the kernels are PF densities.Moreover,the exact error of approximation of a convolution class with interpolation cardinal splines is determined. The exact values of average n-Kolmogorov widths are obtained for the convolution class.

MULTIPOINT BOUNDARY VALUE PROBLEM (MPBVP) AND SPLINE INTERPOLATION

The connection between spline interplation and MPBVP is dealt with and the research has been carried out with emphasis on the latter in this paper. With the aid of adjoint MPBVP, the sufficient and necessary conditions of the resolvability of the MPBVP have been provided and the solution is expressed by means of Green’s function. In absence of uniqueness of the solution, the minimum norm generalized solution is defined, its existence and uniqueness have been confirmed, and the generalized Green’s function has been constructed. Finally, the applications of the above theory to spline interpolation are given.

Curve length estimation based on cubic spline interpolation in gray-scale images

This paper deals with a novel local arc length estimator for curves in gray-scale images.The method first estimates a cubic spline curve fit for the boundary points using the gray-level information of the nearby pixels,and then computes the sum of the spline segments’lengths.In this model,the second derivatives and y coordinates at the knots are required in the computation;the spline polynomial coefficients need not be computed explicitly.We provide the algorithm pseudo code for estimation and preprocessing,both taking linear time.Implementation shows that the proposed model gains a smaller relative error than other state-of-the-art methods.

MEMS gyro temperature compensation identification algorithm based on thin plate spline interpolation method

MEMS gyroscopes are widely used in the underwater vehicles owing to their excellent performance and affordable costs.However,the temperature sensitivity of the sensor seriously affects measurement accuracy.Therefore,it is significantly to accurately identify the temperature compensation model in this paper,the calibration parameters were first extracted by using the fast calibration algorithm based on the Persistent Excitation Signal Criterion,and then,MEMS gyro temperature compensation model was established by utilizing the thin plate spline interpolation method,and the corresponding identification results were compared with the results from the polynomial fitting method.The effectiveness of the proposed algorithm has been validated through the comparative experiment.

A family of quasi-cubic blended splines and applications

A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.

Construction of n-sided polygonal spline element using area coordinates and B-net method

In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

Study of trajectory optimization using terminal-node adaptive-altered spline algorithm

The advantage of using a spline function to evaluate the trajectory parameters optimization is discussed. A new method that using adaptive varied terminal-node spline interpolation for solving trajectory optimization is proposed. And it is validated in optimizing the trajectory of guided bombs and extended range guided munitions （ERGM）. The solutions are approximate to the real optimization results. The advantage of this arithmetic is that it can be used to solve the trajectory optimization with complex models. Thus, it is helpful for solving the practical engineering optimization problem.

Two 8-node quadrilateral spline elements by B-net method

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

A 17-node quadrilateral spline finite element using the triangular area coordinates

Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.

Spline Solution for the Nonlinear Schrödinger Equation

We develop an exponential spline interpolation method to solve the nonlinear Schr&oumldinger equation. The truncation error and stability analysis of the method are investigated and the method is shown to be unconditionally stable. The conservation quantities are computed to determine the conservation properties of the problem. We will describe the method and present numerical tests by two problems. The numerical simulations results demonstrate the well performance of the proposed method.