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EN
In this paper, a procedure for MEMS accelerometer static calibration using a genetic algorithm, considering non-orthogonality was presented. The results of simulations and real accelerometer calibration are obtained showing high accuracy of parameters estimation.
2
Content available remote Charakterystyka akcelerometrów lotniczych
PL
W artykule przedstawiono charakterystykę porównawczą akcelerometrów lotniczych. Omówiono przeznaczenie czujników przyspieszeń stosowanych w lotnictwie oraz dokonano przeglądu ich konstrukcji ze względu na rodzaj zastosowanego przetwornika rodzaju sygnału. Zdefiniowano błędy mające wpływ na niepewność pomiaru. Analizie poddano przyrządy kilku producentów, reprezentujące różne metody pomiarowe spośród akcelerometrów klasycznych, jak i wykonanych w technologii MEMS. Wskazano sensory cechujące się najmniejszymi błędami.
EN
The article presents the comparative characteristics of aviation accelerometers. There were discussed several issues like the purpose of acceleration sensors in aviation or their design with respect to the type of signal transducer used. Errors affecting the accuracy of measurement have been defined. Instruments from several manufacturers, representing various measurement methods used in classical accelerometers as well as those with MEMS technology applied have been analysed. The sensors with the smallest errors were indicated.
3
EN
We provide sharp upper and lower bounds on the bias of trimmed means of progressively censored type II order statistics from general distributions in various scale units. The results are illustrated with numerical examples. We also discuss this problem for distributions with decreasing density or failure rate, as well as for generalized order statistics.
EN
In this paper, classes of separate and combined ratio-product estimators are proposed for estimating the finite population mean in stratified random sampling. The expressions for biases and mean squared errors (MSEs) of the proposed classes are derived to the first order of approximation. It is also verified that the proposed classes of estimators, under their optimum conditions, are equivalent to the separate regression estimator. The proposed classes of estimators are compared with the other existing estimators by using the MSE criterion, and the conditions under which the proposed classes perform better are obtained. Theoretical results are validated with the help of an empirical study.
EN
Determination of the phase difference between two sinusoidal signals with noise components using samples of these signals is of interest in many measurement systems. The samples of signals are processed by one of many algorithms, such as 7PSF, UQDE and MSAL, to determine the phase difference. The phase difference result must be accompanied with estimation of the measurement uncertainty. The following issues are covered in this paper: the MSAL algorithm background, the ways of treating the bias influence on the phase difference result, comparison of results obtained by applying MSAL and the other mentioned algorithms to the same real signal samples, and evaluation of the uncertainty of the phase difference.
EN
The paper presents the influence of the bias current value on the Active Magnetic Bearing force-current characteristic linearity.
7
Content available remote Ocena dokładności cyfrowej estymacji podstawowych parametrów sygnałów
PL
Artykuł dotyczy problematyki wyznaczania błędów estymatorów i oceny niepewności estymacji podstawowych parametrów sygnałów otrzymanych na podstawie danych spróbkowanych. Do podstawowych parametrów sygnałów zaliczamy wartość średnią, średniokwadratową skuteczną, międzyszczytową i funkcję gęstości prawdopodobieństwa.
EN
The paper focuses on errors of estimators and the measurement uncertainty of basic signals parameters set with sampled data. As basic signals parameters we regard mean, mean square, root mean square, peak-to-peak amplitude and probability density function.
EN
The error reduction technique, based on inverse transformation, for a shunt active resistance measurement using an ammeter and voltmeter is considered. When computing a corrected reading only multiplicative operations on two measurement results are used, namely squaring and division. The proposed method allows to increase resistance measurement accuracy by about two orders of magnitude what has been validated by both theoretical and experimental outcomes.
PL
Celem pracy jest wyznaczenie rzeczywistej wariancji wartości oczekiwanej skwantowanego sygnału i porównanie takiej wariancji z estymatorami tej wielkości obliczanymi metodą klasyczną oraz na podstawie funkcji autokorelacji. W pracy zdefiniowano postać estymatora wartości oczekiwanej sygnału. Na tej podstawie wyznaczono jego wariancję. Do badań zastosowano skwantowane próbki sygnału oraz momenty zmiennej losowej. Założono, że próbki sygnału zostały skwantowane w przetworniku analogowo-cyfrowym (A-C) typu zaokrąglającego o idealnej charakterystyce kwantowania. W charakterze przykładu przedstawiono wyniki obliczeń wariancji dla sygnału sinusoidalnego, sygnałów losowych o rozkładach: równomiernym oraz Gaussa.
EN
In the paper there is presented a way of determining the variance of the expected value estimator based on the signal autocorrelation function. The expected signal value estimator is defined and the estimator variance is determined. For investigations there were used quantized samples of signal and moments of random variable. There was assumed that the signal was sampled by an ideal AC round-off converter. As an example there are given the results of variance calculations for sinusoidal, Gaussian and uniform PDF (Probability Density Function) signals. The paper is divided into three paragraphs. Paragraph 1 comprises a brief introduction to the research problems. There is given a definition of the expected signal value estimator, calculated on the basis of quantized data (Eq. 2). There are defined the initial conditions allowing calculation of the estimator characteristics. In Paragraph 2 the variance (Eq. 3) of the estimator (Eq. 2) calculated on the basis of moments (Eq. 7) and the autocorrelation function (Eq. 8) are determined. There are also presented the definitions of variance estimators of the expected signal value estimator calculated with use of the classic method (Eq. 11) and autocorrelation function (Eq. 12). Because both estimators have bias, there are given definitions (Eq. 14, 15) for the case when only quantization has an influence on the variance bias. In subparagraphs 2.1 - 2.3 there are presented exemplary results of calculating the variance (Eq. 3) of the estimator (Eq. 2) for the examined signals. For each signal a definition of the characteristic function (Eq. 16, 19, 22) is given. On the basis of the characteristic function definitions, the detailed formulas (Eq. 17, 20, 23) calculated from the random variable moments are derived. (Fig. 1-3) shows charts of the variance. There are defined the formulas (Eq. 18, 21, 24) allowing calculations of the mean square error. Exemplary results are given in Tables 1 and 2. The investigation results are summarized in Paragraph 3. They show that the accuracy of calculation results of the expected signal value estimator variance obtained with use of the classic method and those from the autocorrelation function is the same.
PL
Artykuł dotyczy problematyki oceny wpływu kwantowania na niepewność estymatora wartości oczekiwanej sygnału. Zdefiniowano postacie estymatorów wartości oczekiwanej oraz wariancji tego parametru. Wyznaczono obciążenia estymatorów. Oceniono wpływ kwantowania na niepewność estymatora wartości oczekiwanej. Do badań zastosowano skwantowane próbki sygnału oraz momenty zmiennej losowej. Konwersja sygnału przeprowadzono z zastosowaniem kwantyzatora typu zaokrąglającego o idealnej charakterystyce kwantowania.
EN
The paper deals with the problem of evaluation of quantization influence on the signal mean value estimator uncertainty on the basis of digital measuring data. In order to evaluate the uncertainty ,there have been used the quantized samples and moments of a random variable as well as the Widrow theory of quantization. The round-off quantizer of the ideal quantizing characteristic has been applied. The paper is divided into four sections. In the first section there is given Eq. (2) describing the mean value estimator obtained from the quantized data. In the second section the bias of the mean value estimator is described by Eq. (5) and shown in Fig.1. The mean value estimator (2) with and without bias (5) is shown in Fig.2. The mean value estimator variance is given by Eq. (6) and shown in Fig.3. In the next section there are presented Eqs. (21)-(23) describing the quantization influence on the mean value estimator uncertainty obtained from the moments and quantized data. The quantization influence on the mean value estimator uncertainty is studied in two independent cases, with and without bias, and shown in Fig.6. It has been shown that for a sinusoidal signal Eq. (21) is a suppressed oscillating function of the amplitude. Moreover, it has been proved that by increasing the sample size Eqs. (22) and (23) can be brought to 1. In the last section the results of investigations are summarized.
PL
Artykuł przedstawia problematykę obliczania wartości oczekiwanej, obciążenia i wariancji cyfrowego estymatora funkcji autokorelacji sygnałów. Pokazano, że estymator funkcji autokorelacji nie jest zgodny oraz, że jest obciążony dodatkową, wynikającą z kwantowania składową. Pokazano, że funkcja gęstości kompensuje przesunięcie funkcji autokorelacji, co oznacza, że określenie na postawie momentów obciążenia i wariancji estymatora możliwe jest jedynie w tych punktach funkcji autokorelacji, które odpowiadają wartości średniokwadratowej sygnału. Przedstawiono wyniki oszacowań obciążenia i wariancji cyfrowego estymatora funkcji autokorelacji dla wybranych klas sygnałów. Do obliczeń zastosowano opracowany na potrzeby prowadzonych badań wielobitowy wirtualny korelator sygnałów.
EN
In the paper there are discussed problems of estimation of the expected value, bias and variance of the digital estimator of the signal autocorrelation function. It is shown that the autocorrelation function estimator is not consistent and that the density function compensates the autocorrelation function delay. It means that determination of the bias and variance of the estimator basing on the so-called moments is possible only in these points of the autocorrelation function which are the mean square value of the signal. There are presented the results of estimation of the bias and variance of the autocorrelation function digital estimator for selected classes of signals. In order to perform calculations, there was designed a dedicated, multi-bit, virtual correlator of signals. The paper is divided into 3 sections. Section 1 contains a short introduction to the issues of this paper. In Section 2 there are presented the definitions of the autocorrelation function and the autocorrelation function estimator of a signal and quantized signal - Eqs. (2-4). Next, there is calculated the estimator's expected value - Eqs. (5, 6). There is determined the bias of the autocorrelation function digital estimator caused by quantization Eq. (7). In the next part of paper there is shown that the signal distribution density function compensates the autocorrelation function delay - Eq. (11). There is also calculated the estimator's mean square error - Eq. (20). The mean square error and variance from Eq. (17) allows evaluating the estimator consistency. Table 1 presents the results of analysis of the bias and variance of the autocorrelation function digital estimator for a sinusoidal signal with noise. There are analysed the following types of noise: Gaussian, uniform probability density function (PDF) and triangular PDF signal. In Section 3 the investigation results are summarized. The obtained results show the importance of investigations on autocorrelation function degradation caused by quantization.
PL
Artykuł przedstawia problematykę obliczania wartości oczekiwanej, obciążenia i wariancji cyfrowego estymatora wartości średniej sygnałów przypadkowych. W rzeczywistych sytuacjach pomiarowych estymacja obciążenia i wariancji, wymaga najczęściej wielokrotnego powtarzania eksperymentu pomiarowego. Nie są przy tym sformułowane kryteria dotyczące dokładności prowadzonych oszacowań. Zaprezentowane w pracy wzory omijają problem niejednoznaczności oszacowań i umożliwiają, na podstawie momentów, obliczenie obciążenia i wariancji cyfrowego estymatora wartości średniej sygnałów.
EN
In the paper there is discussed a problem of estimation of the expected value, bias and variance of the mean value digital estimator of random signals. In real measurement tasks the estimation of the variance and bias values requires numerous repetitions of measurement experiments. Moreover, there are no clear criteria of the estimation accuracy. The equations formulated in this paper allow avoiding the problem of the estimation uncertainty and calculating the bias and variance of the digital estimator of the mean value signals basing on the so called moments. The paper is divided into 4 sections. Section 1 contains a short introduction to the issues of this paper. In Section 2 there is given a definition of the digital estimator of the mean value signal. The estimator's expected value is calculated - Eq. (2). On the basis of Eq. (2), the bias caused by quantization is given by Eq. (4). The variance is described by Eq. (7), while the mean square error by Eq. (8). It allows evaluating the consistency estimator. The variance of the mean value Eq. (13) is determined basing on the Widrow theory of quantization Eq. (10-12). In the next section there is presented an example of determining the bias - Eq. (17) and variance Eq. (20) of the mean value digital estimator of a Gaussian signal. The characteristic function of the Gaussian signal is given by Eq. (15). Table 1 presents the result of calculating the mean value variance for varying signal amplitude and increasing A/D resolution. Section 4 summarizes the investigations and presents some concluding remarks. There are discussed applications of the obtained expressions to evaluation of the measurement result uncertainty of the most important signal parameters.
13
Content available remote Effect of bias in ferroelectric-antiferroelectric relaxation
EN
The ferroelectric-antiferroelectric transition in greyscale generation of antiferroelectric liquid crystal displays (AFLC) is a heterogeneous process. The process has been described as the growth of finger-like domains [1]. We have previously studied the ferroelectric-antiferroelectric phase transition, relaxation that follows the data pulse in surface stabilized asymmetric antiferroelectric liquid crystal displays using biasless video frequency waveforms [2]. This relaxation involves an intensity decay of the light transmitted by a pixel and depends on several parameters such as surface stabilization, rotational viscosity of the AFLC, magnitude of the data pulse, and bias voltage. The usual multiplexed driving of AFLC displays leads to long-term stabilisation of the grey levels induced by the data pulses within the selection time. However, depending on the bias level, alternative greyscale mechanisms may be obtained by allowing the grey levels to decay during the frametime. These greyscales may be advantageous in some instances since they improve the dynamic response of the AFLC device and reduce the reset time of the waveform. In this study we extend the previous work to include the effect of bias. We present the measured data, in terms of growth pattern and speed and present an extension of the previously model on order to explain the results.
PL
Artykuł przedstawia wymagania dotyczące walidacji metod badawczych, definicje cech charakterystycznych metod badawczych oraz sposoby przedstawiania dowodów na spełnienie wymagań dotyczących konkretnego zastosowania metody badawczej.
EN
The article presents requirements concerning validation of research methods, definitions of characteristic features of research methods, as well as ways of presenting evidence of fulfilling the requirements concerning a specific use of a research method.
EN
Extremes of stream flow and precipitation are commonly modeled by heavy-tailed distributions. While scrutinizing annual flow maxima or the peaks over threshold, the largest sample elements are quite often suspected to be low quality data, outliers or values corresponding to much longer return periods than the obser-vation period. Since the interest is primarily in the estimation of the right tail (in the case of floods or heavy rainfalls), sensitivity of upper quantiles to largest elements of a series constitutes a problem of special concern. This study investigated the sen-sitivity problem using the log-Gumbel distribution by generating samples of different sizes (n) and different values of the coefficient of variation by Monte Carlo ex-periments. Parameters of the log-Gumbel distribution were estimated by the prob-ability weighted moments (PWMs) method, method of moments (MOMs) and maximum likelihood method (MLM), both for complete samples and the samples deprived of their largest elements. In the latter case, the distribution censored by the non-exceedance probability threshold, FT , was considered. Using FT instead of the censored threshold T creates possibility of controlling estimator property. The effect of the FT value on the performance of the quantile estimates was then examined. It is shown that right censoring of data need not reduce an accuracy of large quantile estimates if the method of PWMs or MOMs is employed. Moreover allowing bias of estimates one can get the gain in variance and in mean square error of large quantiles even if ML method is used.
EN
The derivation of frequent subgraphs from a dataset of labeled graphs has high computational complexity because the hard problems of isomorphism and subgraph isomorphism have to be solved as part of this derivation. To deal with this computational complexity, all previous approaches have focused on one particular kind of graph. In this paper, we propose an approach to conduct a complete search for various classes of frequent subgraphs in a massive dataset of labeled graphs within a practical time. The power of our approach comes from the algebraic representation of graphs, its associated operations and well-organized bias constraints to limit the search space efficiently. The performance has been evaluated using real world datasets, and the high scalability and flexibility of our approach have been confirmed with respect to the amount of data and the computation time.
EN
Applying the methodology described in Strupczewski et al. (2005a; this issue), the performance of various parsimonious models combined with three estima-tion methods versus Flood Parent Distributions is comparatively assessed by simulation experiments. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) are used as alternative methods. Five four-parameter Specific Wakeby Distributions (SWaD) are employed to serve as Flood Parent Distributions and forty Distribution/Estimation (D/E) procedures are included in respect to the estimation of upper quantiles. The relative bias (RB), relative root mean square error (RRMSE) and reliability of procedures are used for the assessment of the relative performance of alternative procedures. Parsimonious two-parameter models generally perform better for hydrological sample sizes than their three-parameter counterparts with respect to RRMSE. How-ever, the best performing procedures differ for various SWaDs. As far as estimation methods are concerned, MOM usually produces the smallest values of both RB and RRMSE of upper quantiles for all competing methods. The second place in rank is occupied by LMM, whereas, MLM produces usually the highest values. Considerable influence of sampling bias on the value of the total bias has been ascertained. The improper choice of a model fitted to SWaD samples causes that the reliability of some three-parameter parsimonious D/E procedures does not always rise with the sample size. Also odd is that True model does not always give one hundred percent reliability for very large samples, as it should. This means that estimating algorithms still require improvements.
EN
Applying the methodology described in Strupczewski et al. (2005a; this is-sue), the performance of various parsimonious models combined with three estimation methods versus Flood Parent Distributions is comparatively assessed by simulation experiments. Moments (MOM), L-moments (LMM) and maximum likelihood (MLM) are used as alternative methods. Five four-parameter Specific Wakeby Distributions (SWaD) are employed to serve as Flood Parent Distributions and forty Distribution/Estimation (D/E) procedures are included in respect to the estimation of upper quantiles. The relative bias (RB), relative root mean square error (RRMSE) and reliability of procedures are used for the assessment of the relative performance of alternative procedures. Parsimonious two-parameter models generally perform better for hydrological sample sizes than their three-parameter counterparts with respect to RRMSE. How-ever, the best performing procedures differ for various SWaDs. As far as estimation methods are concerned, MOM usually produces the smallest values of both RB and RRMSE of upper quantiles for all competing methods. The second place in rank is occupied by LMM, whereas, MLM produces usually the highest values. Considerable influence of sampling bias on the value of the total bias has been ascertained. The improper choice of a model fitted to SWaD samples causes that the reli-ability of some three-parameter parsimonious D/E procedures does not always rise with the sample size. Also odd is that True model does not always give one hundred percent reliability for very large samples, as it should. This means that estimating algorithms still require improvements.
PL
W pracy przedstawiono algorytm wyznaczania wymaganego napięcia wstępnego oraz składowych odkształceń dla układu łożyskowego obciążonego siłą zewnętrzną. Metoda polega na wykorzystaniu programu zapisanego w języku Fortran do wygenerowania procedury graficznej zapisanej w języku AutoLISP, pozwalającej na wizualizację uzyskanych wyników obliczeń w środowisku edytora graficznego AutoCAD
EN
The paper presents the algorithm of numerical determine of the necessary assenbly stressing of cone bearing-system with the external force. Fortran language is proposed here as a programming tool to generation of the graphical procedure in AutoLISP, which enables a visualization of the calculation result in the graphical environment of AutoCAD.
PL
W pracy przedstawiono algorytm graficznego wyznaczania wymaganego napięcia wstępnego dla układu łożyskowego obciążonego siłą zewnętrzną. Metoda polega na wykorzystaniu programu zapisanego w języku Fortran do wygenerowania procedury graficznej zapisanej w języku AutoLISP, pozwalającej na wizualizację uzyskanych wyników obliczeń w środowisku edytora graficznego AutoCAD.
EN
The paper presents the algorithm of graphical determine of the necessary assenbly stressing of cone bearing-system with the external force. Fortran language is proposed here as a programming tool to generation of the graphical procedure in AutoLISP, which enables a visualization of the calculation result in the graphical environment of AutoCAD.
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