Approximation by shape preserving interpolation splines

Kouibia, A.; Pasadas, M.

doi:10.1016/s0168-9274(00)00029-5

Cited by 13 publications

(4 citation statements)

References 20 publications

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“…The method of CS approximation [10] also belongs to the «classical» methods for identifying mathematical models. The analysis of these methods shows that, as applied to the solution of this problem, compared with the LSM, the CS provide an accurate approximation of the engine characteristics, but require large amounts of memory to store the coefficients.…”

Section: Input Layermentioning

confidence: 99%

The Problem of the Identification of Tv3-117 Aircraft Engine Dynamic Multi-Mode Model in Flight Envelope

Shmelоv¹,

Vladov²,

Derevyanko³

et al. 2019

Visnyk KrNU

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Purpose. Construction of a mathematical model of the aircraft engine TV3-117 based on the results of observations of its reaction to environmental disturbances. The solution of the problem of identifying a dynamic model of TV3-117 engine in onboard conditions by classical methods, including the method of least squares and approximation by cubic splines, and neural network, by building a neural network according to source data. Methodology. The work is based on the methods of probability theory and mathematical statistics, neuroinformatics, information systems theory and data processing. In this paper, the Elman recurrent network with one hidden layer with a sigmoid neuron activation function with feedback was applied. Results. A method was developed for determining the optimal structure of a neural network, which consists in determining the neural network architecture, choosing the optimal algorithm for finding weights of neurons and teaching a neural network, analyzing the effectiveness of various neural network training algorithms, determining the structure of a neural network, which consists in finding the minimum error of neural network training depending on the number of neurons in the hidden layer, as well as in the analysis of the effectiveness of the results. The ability of the developed neural network to smooth out white noise was proved by determining the identification error of the rotational speed of the turbocharger's rotor, which was 0,005 % and did not exceed the limit-permissible value of 0,5 %. Originality. The scientific novelty of the results obtained is as follows: For the first time, a method was developed for determining the optimal structure of a neural network, which made it possible to solve the problem of identifying a dynamic model of an aircraft engine, the TV3-117, in onboard conditions with minimal errors. The method of identifying the technical condition of the TV3-117 aircraft engine in onboard conditions, which differs from the existing ones due to the use of neural network technologies, makes it possible to increase the reliability of monitoring and diagnostics of the technical condition of the TV3-117 aircraft engine under its flight conditions. Practical value.The developed neural network can be one of the units of the expert system that can automatically make decisions regarding the technical condition of the aviation engine TV3-117 in flight modes and provide information to the crew about the possibility of further safe movement of the aircraft. The task of developing an expert system can be effectively solved using the mathematical apparatus of neural networks, since its use increases the reliability and accuracy of classification of modes, identification, control, diagnostics, time series analysis (forecasting), debugging of engine parameters, etc., which will increase reliability of obtaining the necessary results. References 10, table 1, figure 4.

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Section: Input Layermentioning

confidence: 99%

The Problem of the Identification of Tv3-117 Aircraft Engine Dynamic Multi-Mode Model in Flight Envelope

Shmelоv¹,

Vladov²,

Derevyanko³

et al. 2019

Visnyk KrNU

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“…Lastly, the envelope IF 1 [n] is interpolated using a shape-preserving method 35 to look for the IF in those points where no maxima have been found, and the signal is smoothed to eliminate small discontinuities. Another method to estimate the IF contour is proposed by Djurovic and Stankovic, 18 which is based on the calculation of the TFR maxima minimizing the IF variations between consecutive points.…”

Section: Moments Of the Conditional Densitymentioning

confidence: 99%

Selection of Dynamic Features Based on Time–Frequency Representations for Heart Murmur Detection from Phonocardiographic Signals

et al. 2009

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This work discusses a method for the selection of dynamic features, based on the calculation of the spectral power through time applied to the detection of systolic murmurs from phonocardiographic recordings. To investigate the dynamic properties of the spectral power during murmurs, several quadratic energy distributions have been studied, namely Wigner-Ville, Choi-Williams, smoothed pseudo Wigner-Ville, exponential, and hyperbolic T-distribution. The classification performance has been compared with that using a Short Time Fourier Transform and Continuous Wavelet Transform representations. Furthermore, this work discusses a variety of nonparametric techniques to estimate the spectral power contours as dynamic features that characterize the heart sounds (HS): instantaneous energy, eigenvectors, instantaneous frequency, equivalent bandwidth, subband spectral centroids, and Mel cepstral coefficients. In this way, the aforementioned time-frequency representations and their dynamic features were evaluated by means of their ability to detect the presence of murmurs using a simple k-Nearest Neighbors classifier. Moreover, the relevancies of the proposed dynamic features have been evaluated using a time-varying principal component analysis. The work presented is carried out using a database containing 22 phonocardiographic recordings (16 normal and 6 records with murmurs), segmented to extract 402 representative individual beats (201 per class). The results suggest that the smoothing given by the quadratic energy distribution significantly improves the classification performance for the detection of murmurs in HS. Moreover, it is shown that the power dynamic features which give the best overall classification performance are the MFCC contours. As a result, the proposed method can be implemented as a simple diagnostic tool for primary health-care purposes with high accuracy (up to 98%) discriminating between normal and pathologic beats.

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“…To demonstrate the usefulness of the method, some examples are studied to approximate the shape of the function inside the hole by using some given data of the function outside the hole only. Please note that the Abstract of this manuscript has been published in the ICRAMCS 2023 Proceedings, ISSN 2605-7700; for more details, please consult [22].…”

Section: Introductionmentioning

confidence: 99%

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

Kouibia,

Pasadas,

Omri

2024

Mathematics

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In the study of some real cases, it is possible to encounter well-defined geometric conditions, of an industrial or design type—for example, the case of a specific volume within each of several holes. In most of these cases, it is recommended to fulfil a function defined in a domain in which information is missing in one or more sub-domains (holes) of the global set, where the function data are not known. The problem of filling holes or completing a surface in three dimensions appears in many fields of computing, such as computer-aided geometric design (CAGD). A method to solve the shape-preserving variational spline approximation problem for hole filling in generalized offset surfaces is presented. The existence and uniqueness of the solution of the studied method are established, as well as the computation, and certain convergence results are analyzed. A graphic and numerical example complete this study to demonstrate the effectiveness of the presented method. This manuscript presents the resolution of a complicated problem due to the study of some criteria that can be traduced via an approximation problem related to generalized offset surfaces with holes and also the preservation of the shape of such surfaces.

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Approximation by shape preserving interpolation splines

Cited by 13 publications

References 20 publications

The Problem of the Identification of Tv3-117 Aircraft Engine Dynamic Multi-Mode Model in Flight Envelope

The Problem of the Identification of Tv3-117 Aircraft Engine Dynamic Multi-Mode Model in Flight Envelope

Selection of Dynamic Features Based on Time–Frequency Representations for Heart Murmur Detection from Phonocardiographic Signals

A Shape-Preserving Variational Spline Approximation Problem for Hole Filling in Generalized Offset Surfaces

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