Approximation Spline Functions Research Articles

Numerical modeling of thermomechanical processes in heat-resistant alloys

This article presents a numerical simulation of thermomechanical processes in heat-resistant alloys. The authors develop the law of temperature distribution along the length of the physical body, which is considered as a rod of alloy EI-617. The authors also investigated the dependence of the magnitude of the elongation of the rod from a given temperature. To do this, the rod is conditionally divided into several elements, and then the study is carried out in one area. To determine the temperature dependence, the temperature distribution field is approximated by a full polynomial of the second degree, and approximation spline functions are introduced. Using a temperature gradient for one element, the functional expression characterizing the total thermal energy is written, first for the (n-1) element, then for the last n-th element. The total thermal energy is expressed by the formula . By minimizing the total thermal energy, we obtain a system of algebraic equations for determining the nodal values of temperatures. Applying the obtained values, the elongation of the element due to thermal expansion is calculated. The relationship between the temperature T, elongation DlT , «tensile» force R , and «tensile stress» . is shown in the work. It is shown that with increasing temperature, the above values proportionally increase.

Digital filtration of flood-ebb perturbations in the signals of the hydrostatic pressure sensors of the sea level

We suggest an algorithm for digital filtration of flood-ebb perturbations (FEPs) in the signals of hydrostatic pressure sensors of the bottom and coastal sea level recorders that use approximating spline functions and provide solutions of the problems that analyze Rayleigh and tsunami wave perturbations. We considered the models of signal components from the recorders and different versions of the digital filtration algorithms for FEPs. We estimated the errors of FEP filtration for the algorithms that we considered and suggested using statistical modeling. We conclude that it is preferable to apply the algorithm based on approximation spline functions for digital filtration of the FEPs.

Optimization of Quantizer’s Segment Threshold Using Spline Approximations for Optimal Compressor Function

In this paper, the optimization of quantizer’s segment threshold is done. The quantizer is designed on the basis of approximative spline functions. Coefficients on which we form approximative spline functions are calculated by minimization mean square error (MSE). For coefficients determined in this way, spline functions by which optimal compressor function is approximated are obtained. For the quantizer designed on the basis of approximative spline functions, segment threshold is numerically determined depending on maximal value of the signal to quantization noise ratio (SQNR). Thus, quantizer with optimized segment threshold is achieved. It is shown that by quantizer model designed in this way and proposed in this paper, the SQNR that is very close to SQNR of nonlinear optimal companding quantizer is achieved.

Method of digital filtration of experimental data sequences with the use of approximation spline functions

A method of digital filtration of experimental data sequences with the use of approximation spline functions is proposed. A problem of digital filtration on the basis of such functions is posed, and its general solution is given. An example of constructing approximation spline functions with control at the ends of observation intervals is considered. Results of digital filtration of aerodynamic experimental data with the use of the method developed are described.

Microcomputer-controlled automatic titrator with analysis of results by means of spline functions

A method of controlling an automatic titrator by means of a microcomputer is described. Experimental titration data have been analysed by the use of approximative or rational spline functions.

A numerical method of finding potentiometric titration end-points by use of approximative spline functions

A new numerical method of determining potentiometric titration end-points is presented. It consists in calculating the coefficients of approximative spline functions describing the experimental data (e.m.f., volume of titrant added). The end-point (the inflection point of the curve) is determined by calculating zero points of the second derivative of the approximative spline function. This spline function, unlike rational spline functions, is free from oscillations and its course is largely independent of random errors in e.m.f. measurements. The proposed method is useful for direct analysis of titration data and especially as a basis for construction of microcomputer-controlled automatic titrators.

Approximation Theory and Spline Functions.

Approximation Theory and Spline Functions.