Polynom- und Spline-Interpolation ein Farbfilm

This chapter deals with two related problems occurring frequently in the physical sciences: first, the problem of estimating the value of a function from a limited number of data points; and second, the problem of calculating its value from a series approximation. Numerical methods for interpolating and extrapolating data are presented. The famous Lagrange interpolating polynomial is introduced and applied to one-dimensional and multidimensional problems. Cubic spline interpolation is introduced and an implementation in terms of Eigen classes is given. Several techniques for improving the convergence of Taylor series are discussed, including Shank’s transformation, Richardson extrapolation, and the use of Padé approximants. Conversion between representations with the quotient-difference algorithm is discussed. The exercises explore public transportation, human vision, the wine market, and SU(2) lattice gauge theory, among other topics.

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Spline interpolation and deep neural networks as feature extractors for signature verification purposes

IEEE Internet of Things Journal ◽

10.1109/jiot.2021.3086034 ◽

2021 ◽

pp. 1-1

Author(s):

Wei Wei ◽

Qiao Ke ◽

Dawid Polap ◽

Marcin Wozniak

Keyword(s):

Neural Networks ◽

Deep Neural Networks ◽

Spline Interpolation ◽

Signature Verification

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Subway Gearbox Fault Diagnosis Algorithm Based on Adaptive Spline Impact Suppression

Entropy ◽

10.3390/e23060660 ◽

2021 ◽

Vol 23 (6) ◽

pp. 660

Author(s):

Zhongshuo Hu ◽

Jianwei Yang ◽

Dechen Yao ◽

Jinhai Wang ◽

Yongliang Bai

Keyword(s):

Fault Diagnosis ◽

Spline Interpolation ◽

Reference Value ◽

High Amplitude ◽

Engineering Practice ◽

Negative Effects ◽

Short Term ◽

Time Domain Signal ◽

Gearbox Vibration ◽

Long Time

In the signal processing of real subway vehicles, impacts between wheelsets and rail joint gaps have significant negative effects on the spectrum. This introduces great difficulties for the fault diagnosis of gearboxes. To solve this problem, this paper proposes an adaptive time-domain signal segmentation method that envelopes the original signal using a cubic spline interpolation. The peak values of the rail joint gap impacts are extracted to realize the adaptive segmentation of gearbox fault signals when the vehicle was moving at a uniform speed. A long-time and unsteady signal affected by wheel–rail impacts is segmented into multiple short-term, steady-state signals, which can suppress the high amplitude of the shock response signal. Finally, on this basis, multiple short-term sample signals are analyzed by time- and frequency-domain analyses and compared with the nonfaulty results. The results showed that the method can efficiently suppress the high-amplitude components of subway gearbox vibration signals and effectively extract the characteristics of weak faults due to uniform wear of the gearbox in the time and frequency domains. This provides reference value for the gearbox fault diagnosis in engineering practice.

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Improving the Speed of Volumetric Density Map Generation via Cubic Spline Interpolation

Journal of Molecular Graphics and Modelling ◽

10.1016/j.jmgm.2021.107832 ◽

2021 ◽

pp. 107832

Author(s):

Daniel R. Roe ◽

Bernard R. Brooks

Keyword(s):

Spline Interpolation ◽

Cubic Spline ◽

Cubic Spline Interpolation ◽

Volumetric Density ◽

Map Generation ◽

Density Map

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A novel GNSS deformation feature extraction method based on ensemble improved LMD threshold denoising

Journal of Applied Geodesy ◽

10.1515/jag-2020-0039 ◽

2020 ◽

Vol 14 (4) ◽

pp. 445-453

Author(s):

Qian Fan ◽

Yiqun Zhu

Keyword(s):

Feature Extraction ◽

Spline Interpolation ◽

Simulated Data ◽

Mining Area ◽

Deformation Monitoring ◽

Denoising Method ◽

Feature Extraction Method ◽

Deformation Feature ◽

Mode Decomposition ◽

Better Than

AbstractIn order to solve the problem that the moving span of basic local mean decomposition (LMD) method is difficult to choose reasonably, an improved LMD method (ILMD), which uses three cubic spline interpolation to replace the sliding average, is proposed. On this basis, with the help of noise aided calculation, an ensemble improved LMD method (EILMD) is proposed to effectively solve the modal aliasing problem in original LMD. On the basis of using EILMD to effectively decompose the data of GNSS deformation monitoring series, GNSS deformation feature extraction model based on EILMD threshold denoising is given by means of wavelet soft threshold processing mode and threshold setting method in empirical mode decomposition denoising. Through the analysis of simulated data and the actual GNSS monitoring data in the mining area, the results show that denoising effect of the proposed method is better than EILMD, ILMD and LMD direct coercive denoising methods. It is also better than wavelet analysis denoising method, and has good adaptability. This fully demonstrates the feasibility and effectiveness of the proposed method in GNSS feature extraction.

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