Optimization of the Spectral Processing of the Signal of a Precision Distance Sensor Based on a Frequency Rangefinder

We have derived an expression for the error of method in difference frequency measurements for a distance sensor based on a frequency range finder. We employed weighted average estimation for a broad class of weighting functions and examined the structure of the error. Quantitative estimates have been made for some of the components of the error. We propose an averaged characteristic for the error as the standard deviation obtained at discrete intervals of distance. A version for practical use of these results is considered.__________Translated from Izmeritelnaya Tekhnika, No. 2, pp. 21–25, February, 2005.     

基于时域加权的单位脉冲响应模型的非叠代算法

提出了一种基于时域加权的新的非叠代优化算法,用于重构经过采样示波器测量的阶跃信号、脉冲信号等。该算法构造了一个期望误差函数,由于这个期望误差函数与真实误差很接近,因此构造了新的价值函数,并使用时域加权来优化不同的波形,在减小时域振铃时有效的控制噪声放大。与误差能量,归一化方法相比,该算法经过仿真实验表明了其可行性和有效性。     

Photoemission Temperature Measurement. Two Approaches to the Determination of the Procedural Error

Two methods are proposed for determining the procedural error T based on a comparison of the ratio and difference of the radiation signals picked up by a sensor from a primary standard and an object. Those methods, theoretical and experimental, require knowledge of the sensor conversion parameter. Both methods are shown to be correct and to give the same results. Tungsten and platinum are used as samples to show the relations the principal quantities that define the photoemission temperature measurements. These relations allow the optimum conditions to be chosen for measurement in a given temperature interval, taking into account the object and the sensor parameters.     

On computational methods for variational inequalities

In this note, we focus on optimised mesh design for the Finite Element (FE) method for variational inequalities using global norm estimates for local error control. The strategies are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes (see, e.g., Rannacher et al. [19, 6, 2]), where error control for the primal problem is established by solving an auxiliary (dual) problem. In this context we blamed (cf. e.g., Rannacher and Suttmeier [18, 19]) global norm estimates being not that useful in applications. But having a closer look at the DWR-concept, one observes that in fact global (energy) error bounds can be employed to establish local error control. Our ideas and techniques are illustrated at the socalled obstacle problem.It turns out, that reliable and efficient energy error control is one main ingredient to establish useful a posteriori error bounds for local quantities. Therefore, in addition, we derive an unified approach to a posteriori error control in the energy norm for elliptic variational inequalities of first kind. Eventually, this framework is applied to Signorinis problem.     

Chain Sampling Scheme under Constant Inspection Errors

The primary aim of this paper is to extend the inspection error consideration to chain sampling schemes, an area that has not been dealt with in the literature. A mathematical model is developed to investigate the performance of chain sampling schemes under constant inspection errors. Expressions of performance measures, such as operating characteristic function, average total inspection and average outgoing quality, are derived to aid the analysis of a general chain sampling scheme, ChSP‐4A ( ) r, developed by Frishman. This study reveals that as Type I inspection error increases the probability of acceptance will decrease and as Type II inspection error increases the acceptance probability will increase. The effect of Type II error on the probability of acceptance is very marginal compared with that of Type I error, especially when the true fraction non‐conforming is small. In addition, the effects of inspection errors can be ‘eliminated’ by transforming to its equivalent perfect inspection counterpart, hence greatly reducing the complexity of the analysis. The effects of other sampling parameters are also studied to serve as a foundation for future plan designing purposes. Copyright © 2006 John Wiley & Sons, Ltd.     

Analytically determining of the absolute inaccuracy (error) of indirectly measurable variable and dimensionless scale characterising the quality of the experiment

In the following paper we present an easily applicable new method for the analytical representation of the maximum absolute inaccuracy (error) of an indirectly measurable variable f = f(x₁, x₂, ..., x_n) as a function of the maximum absolute inaccuracies (errors) of the directly measurable variables x₁, x₂, ..., x_n. Our new approach is more adequate for the objective reality. The gist of it is that in order to find the analytical form of the maximum absolute inaccuracy of the variable f we take for being fixed variables the statistical mean values of the modules of the moment velocities of alteration of f in respect of the variables x₁, x₂, ..., x_n and the numerical value of the maximum absolute inaccuracy of the variable f is found using the statistical mean values of the absolute values of the absolute inaccuracies . Having this in mind we develop the theory of errors, which we will call with what we feel is a more precise term — theory of inaccuracies. We introduce some new terms — space of the absolute inaccuracy and stochastic plane of the absolute inaccuracy of f. We also define a sample plane of the ideal absolutely accurate experiment and using it we define a universal numerical characteristic — a dimensionless scale for evaluation of the quality (accuracy) of the experiment.     

On the estimation of Weibull's parameters in brittle materials

The parameters in Weibull's specific risk function are estimated using several methods, both in compression and in bending. To this end, several formulae are employed for different values of the limiting stress _L. The parameters are estimated by minimizing ² in order to compare the capacity of the different formulae for approximating these parameters. In the case of bending, the error committed when obtaining the parameters from a uniform-stress-field Weibull function is of the order of 100%.     

Quantitative estimation of measurement errors for general technological parameters

Results are presented on the metrological characteristics of multichannel data-acquisition systems (DAS) that perform indirect measurements. General and typical structures are given for such DAS, which are represented by mathematical models for the errors in processing the data in them. An analysis is presented of the dependence of the error on the DAS parameters and input signals.Translated from Izmeritelnaya Tekhnika, No. 10, pp. 16–20, October, 2004.     

The Specific Nature of Measurements and of the Tolerance Monitoring of Measurements. A Discussion

The concepts of measurement accuracy and the reliability of the results of monitoring are discussed. A classification is proposed for the multiparametric monitoring of measurements in terms of the nature of the relationship between the monitored parameters. The results are given of investigations of the dependence of the probability of monitoring errors on the number of monitored parameters using the method of simulation modeling.     

A generalized model for the uniaxial isothermal deformation of a viscoelastic body

Summary Using the notion of a fractional derivative we formulate a new model for a uniaxial deformation of a visco-elastic body. The basic assumption is that all derivatives ₍₎ with respect to time of the stress depend (with specified weighting factor) on all derivatives ₍₎ with respect to time of the strain (multiplied with another weighting factor), for 01. In this respect our model is a generalization of the Zener model, i.e., it is a Zener fractional model with infinitely many terms. The relation between stress and strain is given in explicit form. For two specific choices of parameters the behavior of the model under suddenly applied stress (creep) and suddenly applied strain (stress relaxation) are examined.     

Measurement Procedure Error of a Distance Gauge Based on a Frequency-Modulated Range Finder with Weighted Smoothing of the Digitization Error

The potential capabilities of a weighted method of smoothing the digitization error of a distance gauge based on a frequency-modulated range finder are considered. Exact analytic relations for the measurement error produced with the use of a weighting function of arbitrary form are obtained. For certain special cases, concrete quantitative calculations are performed and the results compared to theoretical estimates given in the literature as well as to estimates of the error found by means of computation simulation.     

An explicit residual‐type error estimator for ‐quadrilateral extended finite element method in two‐dimensional linear elastic fracture mechanics

This paper deals with explicit residual a posteriori error estimation analysis for ‐quadrilateral extended finite element method (XFEM) discretizations applied to the two‐dimensional problem of linear elastic fracture mechanics. The result is twofold. First, to enable estimation procedures with application to XFEM, a specific quasi‐interpolation operator of averaging type is constructed. The main challenge here arises from the different types of enrichments implemented, and hence, to impose the constant‐preserving property of the interpolation operator on an element, we use the idea of an extension operator. An upper bound on the discretization error measured in the energy norm and associated local error indicators are then constructed and analyzed. The second result follows from the error analysis and concerns an alternative choice of branch functions used in XFEM applications. In particular, the branch functions have to be chosen to fulfill the divergence‐free conditions within the crack tip element and traction‐free boundary conditions on the crack faces. Then, the corresponding XFEM solution gains a better accuracy with less degrees of freedom. Finally, numerical examples are provided with comparative results. Copyright © 2012 John Wiley & Sons, Ltd.     

Improvement of Polynomial Methods for Reproducing Functional Dependences

A comparative analysis is made of polynomial methods of reproducing functions. Recommendations on reducing the errors and/or increasing the interpolation interval for Newton polynomials are proposed in a general form and also using the example of the sin function.     

Three- and six-wave procedure for measuring total ozone content with complete compensation of the aerosol error for the Dobson spectrophotometer

Almost total compensation of the aerosol error for the Dobson spectrophotometer used for measuring the overall ozone content is shown to be possible. A functional diagram of the device is provided together with theoretical substantiation of aerosol error compensation.Translated from Izmeritelnaya Tekhnika, No. 9, pp. 62–64, September 2004.     

A Gamma–normal series truncation approximation for computing the Weibull renewal function

This paper presents a series truncation approximation for computing the Weibull renewal function. In the proposed model, the n-fold convolution of the Weibull Cdf is approximated by a mixture of the n-fold convolutions of Gamma and normal Cdfs. The mixture weight can be optimally determined and fitted into a very accurate linear function of Weibull shape parameter β. Major advantages of the proposed model include:

(a) The proposed model and its parameters can be directly written out. Using the proposed model, the renewal density and variance functions can be easily evaluated.

(b) The proposed model includes Gamma and normal series truncation models as its special cases. It is easy to be implemented in Excel. The series converges fairly fast.

(c) Over the range of β(0.87,8.0), the maximum absolute error is smaller than 0.01; and over , the maximum absolute error is smaller than 0.0037.

(d) The model can be easily extended to non-Weibull case with some additional work.

Identification of embedded interlaminar flaw using inverse analysis

The integrity of a composite laminate can be greatly affected by an existence of embedded interlaminar flaw. In general, identification of such a flaw often requires expensive tools and tedious processes. The aim of the present work is to develop a novel method with the aid of an intelligent post-processing scheme, thereby not relying on those sophisticated experiments. Essentially the proposed procedure utilizes an inverse analysis to estimate unknown delamination parameters from limited measurements. The procedure first constructs approximate functions relating the delamination parameters to measurement parameters. Then, a multi-dimensional minimization technique is adopted to search for the best estimates of unknown parameters corresponding to the lowest value of error objective function. In the present verification and simulation analyses, surface strains at discrete locations on a composite laminate under three-point bending are selected as the input measurements. Although reasonable estimates are obtained with these measurements, to increase their accuracy, the deflection at load point is also included as measurement input. Additional improvements are observed when those measurements under multiple loading conditions are included. A detailed error sensitivity analysis is also carried out to confirm the methods robustness. These results suggest the current method to be one of the alternate identification approaches for detecting a single embedded delamination in composite laminates.     

Calculation of the errors of an inductive voltage divider with a balancing winding

A procedure for calculating the errors of the transfer factor due to the fact that the parameters of the sections of an inductive voltage divider with a balancing winding are not identical is proposed. The results of experimental investigations are presented.Translated from Izmeritelnaya Tekhnika, No. 10, pp. 40–43, October, 2004.     

Estimated incapability index: reliability and decision making with sample information

The process incapability index , which provides an uncontaminated separation between information concerning the process precision and process accuracy, has been proposed to measure process performance for industry applications. In this paper, we investigate the reliability of the natural estimator computationally, based on the ‐level confidence relative error for various sample sizes. We also develop a decision‐making procedure for judging if the process satisfies the preset quality requirement. The investigation is useful to the practitioners in determining the sample sizes required in their applications for the decisions reliable to the desired level. Copyright © 2002 John Wiley & Sons, Ltd.     

Determining double-K fracture parameters of concrete for compact tension and wedge splitting tests using weight function

The paper presents use of universal form of weight functions for determining the double-K fracture parameters and on compact test and wedge splitting test specimens. The proposed method enables to obtain a closed form expression of cohesion toughness of concrete specimens. A comparison with existing analytical method shows that the weight function method for determination of double-K fracture parameters yields results without any appreciable error. Significant influence of initial notch to depth (a₀/D) ratio on the double-K fracture parameters is not also observed. Finally, a possible definition of brittleness of concrete using double-K fracture parameters is proposed.