Uncertainty Evaluation of the Electrical Transient Rise Time

This paper deals with the uncertainty evaluation of the rise time of one pulse of an electrical fast transient burst (EFT/B), as carried out by the National Institute of Metrology, Quality and Technology (Inmetro) of Brazil. The main goal is to analyse the impact of two uncertainty sources not included in the uncertainty budget example in IEC 61000-4-4 standard, and not very well explored in the literature: Voltage Measurement and Horizontal Accuracy. The uncertainty sources considered in this evaluation were: the oscilloscope’s resolution and calibration of the voltage scale (Voltage Measurement) and the time scale (Horizontal Accuracy); the bandwidth of the measurement system; the oscilloscope sampling rate; and the repeatability of ten different measurements. Two sets of measurements were taken from two different oscilloscope settings: in the first one, the interpolation function was enabled, and in the other one was disabled. In both cases two components stood out for their huge relative contribution: time reading and repeatability. Considered together, these two components added up approximately 87% of the expanded uncertainty for interpolated samples, and 95% for non-interpolated samples. Also, the results indicate that the oscilloscope interpolation function (OIF), if available, should be used, as the expanded uncertainty decreases by 27% due to a better oscilloscope resolution. A discussion of the uncertainty budget example in Annex C of IEC 61000-4-4 is presented. In conclusion, once the OIF is enabled, the two additional uncertainty components discussed in this paper should be considered in the uncertainty budget. They should not be neglected since the combined relative contribution of these components is larger than the relative contribution of repeatability.

Predictive Continuum Constitutive Modeling of Unfilled and Filled Rubbers

The general CSE model fits Treloar’s uniaxial extension test and predicts unfitted uniaxial compression, equibiaxial extension, biaxial extension, pure shear, and simple shear tests. As a newly proposed method, the general CSE model, along with the stress-softening ratio, the residualstretch ratio, and the weighted piecewise two-point interpolation function, fits the Cheng–Chen’s test and the Diani–Fayolle–Gilormini’s test in cyclic uniaxial extension at different pre-stretches and predicts corresponding responses at untested pre-stretches. Physical mechanisms of the Mullins effect have also been predicted based on the evolution of constitutive parameters.

Graph-directed random fractal interpolation function

"Barnsley introduced in [1] the notion of fractal interpolation function (FIF). He said that a fractal function is a (FIF) if it possess some interpolation properties. It has the advantage that it can be also combined with the classical methods or real data interpolation. Hutchinson and Ruschendorf [7] gave the stochastic version of fractal interpolation function. In order to obtain fractal interpolation functions with more exibility, Wang and Yu [9] used instead of a constant scaling parameter a variable vertical scaling factor. Also the notion of fractal interpolation can be generalized to the graph-directed case introduced by Deniz and  Ozdemir in [5]. In this paper we study the case of a stochastic fractal interpolation function with graph-directed fractal function."

Research on 3D Improved Extended Finite Element Method for Electric Field of Liquid Nitrogen with Bubbles

In this paper, the improved extended finite element method (XFEM) for analyzing the three-dimensional (3D) electric field is presented. The interface between two media is described by using a four-dimensional (4D) level set function. For elements with multiple interfaces, the local level set method is used to improve the accuracy. By using weak discontinuous enrichment function and moving level set function, the interpolation function is modified. The new interpolation function makes it unnecessary to repeat the mesh generation when a moving interface occurs. The cost of calculation is greatly reduced. The reliability of 3D improved XFEM in the electric field is verified through numerical calculation examples of single bubble, multi-bubbles, and moving deformed bubble in liquid nitrogen.

An Investigation on using Lagrange, Newton and Least Square Methods for Generating Nonlinear Interpolation Function for the Measuring Instruments

This research is considered the milestone for metrologists to choose the appropriate method for determination of the nonlinear interpolation function for the measuring instruments. Three methods of generating the interpolation polynomial equations were investigated; Newton, Lagrange, and Least Square method. The response of the measuring instruments under investigation was calculated and compared with the experimental results. Least Square method was found that it is the most accurate and most realistic approach to determine the interpolation polynomial function for the measuring instruments. It is recommended to use Least Square method rather than other methods to interpolating the polynomial equation. This recommendation is very important for metrologist as well as for measuring instruments applicant. This article is millstone to determine the response of the measuring instrument at non calibrated points in the calibrated range.

A Concretization of an Approximation Method for Non-Affine Fractal Interpolation Functions

The present paper concretizes the models proposed by S. Ri and N. Secelean. S. Ri proposed the construction of the fractal interpolation function(FIF) considering finite systems consisting of Rakotch contractions, but produced no concretization of the model. N. Secelean considered countable systems of Banach contractions to produce the fractal interpolation function. Based on the abovementioned results, in this paper, we propose two different algorithms to produce the fractal interpolation functions both in the affine and non-affine cases. The theoretical context we were working in suppose a countable set of starting points and a countable system of Rakotch contractions. Due to the computational restrictions, the algorithms constructed in the applications have the weakness that they use a finite set of starting points and a finite system of Rakotch contractions. In this respect, the attractor obtained is a two-step approximation. The large number of points used in the computations and the graphical results lead us to the conclusion that the attractor obtained is a good approximation of the fractal interpolation function in both cases, affine and non-affine FIFs. In this way, we also provide a concretization of the scheme presented by C.M. Păcurar .