Journal articles: 'Random measurement error'

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Kroc, Edward. "Generalized measurement error: Intrinsic and incidental measurement error." PLOS ONE 18, no. 6 (June 29, 2023): e0286680. http://dx.doi.org/10.1371/journal.pone.0286680.

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In this paper, we generalize the notion of measurement error on deterministic sample datasets to accommodate sample data that are random-variable-valued. This leads to the formulation of two distinct kinds of measurement error: intrinsic measurement error, and incidental measurement error. Incidental measurement error will be recognized as the traditional kind that arises from a set of deterministic sample measurements, and upon which the traditional measurement error modelling literature is based, while intrinsic measurement error reflects some subjective quality of either the measurement tool or the measurand itself. We define calibrating conditions that generalize common and classical types of measurement error models to this broader measurement domain, and explain how the notion of generalized Berkson error in particular mathematicizes what it means to be an expert assessor or rater for a measurement process. We then explore how classical point estimation, inference, and likelihood theory can be generalized to accommodate sample data composed of generic random-variable-valued measurements.

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Madan, Hennadii, Franjo Pernuš, and Žiga Špiclin. "Reference-free error estimation for multiple measurement methods." Statistical Methods in Medical Research 28, no. 7 (January 31, 2018): 2196–209. http://dx.doi.org/10.1177/0962280217754231.

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We present a computational framework to select the most accurate and precise method of measurement of a certain quantity, when there is no access to the true value of the measurand. A typical use case is when several image analysis methods are applied to measure the value of a particular quantitative imaging biomarker from the same images. The accuracy of each measurement method is characterized by systematic error (bias), which is modeled as a polynomial in true values of measurand, and the precision as random error modeled with a Gaussian random variable. In contrast to previous works, the random errors are modeled jointly across all methods, thereby enabling the framework to analyze measurement methods based on similar principles, which may have correlated random errors. Furthermore, the posterior distribution of the error model parameters is estimated from samples obtained by Markov chain Monte-Carlo and analyzed to estimate the parameter values and the unknown true values of the measurand. The framework was validated on six synthetic and one clinical dataset containing measurements of total lesion load, a biomarker of neurodegenerative diseases, which was obtained with four automatic methods by analyzing brain magnetic resonance images. The estimates of bias and random error were in a good agreement with the corresponding least squares regression estimates against a reference.

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Müller, Andreas Michael, and Tino Hausotte. "Analysis of the random measurement error of areal 3D coordinate measurements exclusively based on measurement repetitions." tm - Technisches Messen 88, no. 2 (January 27, 2021): 71–77. http://dx.doi.org/10.1515/teme-2020-0087.

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Abstract The measurement uncertainty characteristics of a measurement system are an important parameter when evaluating the suitability of a certain measurement system for a specific measurement task. The measurement uncertainty can be calculated from observed measurement errors, which consist of both systematic and random components. While the unfavourable influence of systematic components can be compensated by calibration, random components are inherently not correctable. There are various measurement principles which are affected by different measurement error characteristics depending on specific properties of the measurement task, e. g. the optical surface properties of the measurement object when using fringe projection or the material properties when using industrial X-ray computed tomography. Thus, it can be helpful in certain scenarios if the spatial distribution of the acquisition quality as well as uncertainty characteristics on the captured surface of a certain measurement task can be found out. This article demonstrates a methodology to determine the random measurement error solely from a series of measurement repetitions without the need of additional information, e. g. a reference measurement or the nominal geometry of the examined part.

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Hutcheon, J. A., A. Chiolero, and J. A. Hanley. "Random measurement error and regression dilution bias." BMJ 340, jun23 2 (June 23, 2010): c2289. http://dx.doi.org/10.1136/bmj.c2289.

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Leinonen, Jaakko, Eero Laakkonen, and Leila Laatikainen. "Random measurement error in visual acuity measurement in clinical settings." Acta Ophthalmologica Scandinavica 83, no. 3 (June 8, 2005): 328–32. http://dx.doi.org/10.1111/j.1600-0420.2005.00469.x.

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Zhai, Xiaochun, Songhua Wu, Bingyi Liu, Xiaoquan Song, and Jiaping Yin. "Shipborne Wind Measurement and Motion-induced Error Correction of a Coherent Doppler Lidar over the Yellow Sea in 2014." Atmospheric Measurement Techniques 11, no. 3 (March 5, 2018): 1313–31. http://dx.doi.org/10.5194/amt-11-1313-2018.

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Abstract. Shipborne wind observations by a coherent Doppler lidar (CDL) have been conducted to study the structure of the marine atmospheric boundary layer (MABL) during the 2014 Yellow Sea campaign. This paper evaluates uncertainties associated with the ship motion and presents the correction methodology regarding lidar velocity measurement based on modified 4-Doppler beam swing (DBS) solution. The errors of calibrated measurement, both for the anchored and the cruising shipborne observations, are comparable to those of ground-based measurements. The comparison between the lidar and radiosonde results in a bias of −0.23 ms−1 and a standard deviation of 0.87 ms−1 for the wind speed measurement, and 2.48, 8.84∘ for the wind direction. The biases of horizontal wind speed and random errors of vertical velocity are also estimated using the error propagation theory and frequency spectrum analysis, respectively. The results show that the biases are mainly related to the measuring error of the ship velocity and lidar pointing error, and the random errors are mainly determined by the signal-to-noise ratio (SNR) of the lidar backscattering spectrum signal. It allows for the retrieval of vertical wind, based on one measurement, with random error below 0.15 ms−1 for an appropriate SNR threshold and bias below 0.02 ms−1. The combination of the CDL attitude correction system and the accurate motion correction process has the potential of continuous long-term high temporal and spatial resolution measurement for the MABL thermodynamic and turbulence process.

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Gertner, George Z. "The sensitivity of measurement error in stand volume estimation." Canadian Journal of Forest Research 20, no. 6 (June 1, 1990): 800–804. http://dx.doi.org/10.1139/x90-105.

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A method is given for approximating and evaluating the consequences of random and nonrandom errors in the independent variables of a nonlinear tree volume function that is used in the estimation of stand volume based on a simple random sample of plots. Sampling error, regression function error, and measurement error are accounted for with the method presented. An application is given where relatively moderate amounts of measurement error in the independent variables of a tree volume function can cause a relatively large reduction in the accuracy of estimated stand volume.

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Zhou, Jun Wei, Lin He, and Rong Wu Xu. "Typical Errors Analysis in Frequency Response Function Measurement." Applied Mechanics and Materials 419 (October 2013): 470–76. http://dx.doi.org/10.4028/www.scientific.net/amm.419.470.

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FRF measurements can suffer from various errors. The effect of deterministic errors become more prominent compared to random errors in FRF measurement. Excitation and sensor misalignment is the most common source of deterministic error, so mathematic model is established and the effect on FRF estimation was analyzed for senor and excitation misalignment situations. Finite element model simulation reveals that misalignment error can have the least effect on the dominant FRFs and a stronger effect on lesser FRFs, beside that it also results in the appearance of false peaks in the measured FRFs.

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Rigdon, Edward E. "Demonstrating the effects of unmodeled random measurement error." Structural Equation Modeling: A Multidisciplinary Journal 1, no. 4 (January 1994): 375–80. http://dx.doi.org/10.1080/10705519409539986.

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Hasebe, Satoshi. "Random Measurement Error in Assessing Compensatory Ocular Countertorsion." Archives of Ophthalmology 121, no. 12 (December 1, 2003): 1805. http://dx.doi.org/10.1001/archopht.121.12.1805.

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Klems, J. H. "Measurement of Fenestration Net Energy Performance: Considerations Leading to Development of the Mobile Window Thermal Test (MoWitt) Facility." Journal of Solar Energy Engineering 110, no. 3 (August 1, 1988): 208–16. http://dx.doi.org/10.1115/1.3268259.

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We present a detailed consideration of the energy flows entering a building space and the effect of random measurement errors on determining fenestration performance. Estimates of error magnitudes are made for a passive test cell; we show that a more accurate test facility is needed for reliable measurements on fenestration systems with thermal resistance 2–10 times that of single glazing or with shading coefficients less than 0.7. A test facility of this type, built at Lawrence Berkeley Laboratory, is described. The effect of random errors in this facility is discussed and computer calculations of its performance are presented. The discussion shows that, for any measurement facility, random errors are most serious in nighttime measurements, and systematic errors are most important in daytime measurements. It is concluded that, for this facility, errors from both sources should be small.

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Eastwood, Annette, Will G. Hopkins, Pitre C. Bourdon, Robert T. Withers, and Christopher J. Gore. "Stability of hemoglobin mass over 100 days in active men." Journal of Applied Physiology 104, no. 4 (April 2008): 982–85. http://dx.doi.org/10.1152/japplphysiol.00719.2007.

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The purpose of this study was to investigate the suggestion in a recent meta-analysis that variability in hemoglobin mass increases when time between measurements increases from days to months. Hemoglobin mass of six active men was measured with the carbon monoxide method every 1–6 days for 100–114 days (42 ± 3 measurements, mean ± SD). Measurement error for each individual's series was estimated from the standard deviation of consecutive pairwise changes and compared with his total error (standard deviation of all values). Linear trends and periodicities in each series were quantified by regression and spectral analysis. Series with known random error and periodicity were also simulated and analyzed. There were clear differences in the pairwise error of measurement between subjects (range 1.4–2.7%). For five men, there was little difference between the total and pairwise errors; their mean ratio (1.06, 90% confidence limits 0.96–1.17) was less than ratios for simulated sinusoidal series with random error of 2%, amplitude of 2%, and periods of 20–100 days (ratios 1.13–1.21). Spectral analysis clearly revealed such periodicities in the simulated series but not in the series of these subjects. The sixth man, who had donated blood 12 days before commencing measurements, showed errors, trend, and periodicity consistent with gradual restoration of hemoglobin mass. Measurement error of hemoglobin mass does not increase over 100 days. Consequently, hemoglobin mass may be suitable for long-term monitoring of small changes that might occur with training or erythropoietin abuse, taking into consideration the small differences between athletes in errors and trends.

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Korobko, A., and O. Nazarko. "The Uncertainty of Measurements as a Tool for Evaluating the Adequacy of the Mathematical Measurement Model." Metrology and instruments, no. 1 (March 25, 2019): 51–55. http://dx.doi.org/10.33955/2307-2180(1)2019.51-55.

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The article offers a new way of estima-ting the influence of random and methodical errors to the result of measurement for the measurement uncertainty index. The ratio of the difference between theo-retical and experimental data is proposed from the average error of their determination for the quantitative indicator of the influence of methodical error. The ratio of the uncertainty in the measurement of experimental data to the uncertainty in measuring theoretical data for a quantitative measure of the effect of a random error is proposed. These indicators are based on the assumption that the theoretical and experimental data are normally distributed. The theoretical distribution va-ries within the total uncertainty of measurement of type B of the parameter under study. The physical essence of the indicator of the influence of the metho-dical error is the probability with which the results of measuring the average value of the indicator (determined experimentally) are within the li-mits of a possible deviation of the theoretical value of this indicator. Figure — 3. Table 1. References — 14.

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14

Guo, Tian Tai, Xiao Xiao Wang, Hui Zou, Bo Hong, Jun Zhao, and Ming Kong. "Application of Self-Calibration in Flatness Assessment." Advanced Materials Research 605-607 (December 2012): 1054–57. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.1054.

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A self-calibration algorithm is described that allows the separation of the flatness error of two-dimensional profiling stages through the combination with a flat artifact whose accuracy is unknown. The calibration requires performing three independent measurements with different orientations of the same artifact to make mathematical models. Then the self-calibration algorithm was simulated using Matlab. The simulation results show that when there is no random measurement noise, this algorithm can realize exact calibration of the flatness error of the stage, while in the presence of random measurement noise, the algorithm introduces a calibration error of about the same size as the random measurement noise itself.

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Romanova, M. A., and M. V. Mamchenko. "Method and Algorithm for Estimating the Maximum Total Error of an Automotive LiDAR." Journal of Physics: Conference Series 2096, no. 1 (November 1, 2021): 012179. http://dx.doi.org/10.1088/1742-6596/2096/1/012179.

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Abstract The article proposes a method and an appropriate algorithm for estimating the error of the measurements of the LiDAR as a technical measurement system to “include” this evaluation in the given accuracy. A generic model for the LiDAR’s measurements is described, a mathematical model of the measurements with the total values of random and systematic errors is given. Based on this method the algorithm for estimating the maximum total error (not exceeding the accuracy of the measurement) is formed. The algorithm complies both with the mathematical description presented in the article, and the methodology described in Russian standard GOST R 8.736-2011. On the basis of the calculated estimate of the weighted average error, it is possible to construct a technical device, that provides a three-fold reserve in terms of measurement accuracy.

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16

Chiasson, Paul. "Interpretation of Falling-Head Tests in Presence of Random Measurement Error." ISRN Civil Engineering 2012 (June 7, 2012): 1–10. http://dx.doi.org/10.5402/2012/871467.

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Field data are tainted by random and several types of systematic errors. The paper presents a review of interpretation methods for falling-head tests. The statistical robustness of each method is then evaluated through the use of synthetic data tainted by random error. Six synthetic datasets are used for this evaluation. Each dataset has an average relative error for water elevation Z, respectively, of 0.04%, 0.11%, 0.22%, 0.34%, 0.45%, and 0.90% (absolute errors on elevation are, respectively, 0.10, 0.25, 0.50, 1.0, and 2.0 mm for a range of water elevation change of 150 mm during test). Each synthetic dataset is composed of 40 synthetic tests (each test consisting of 18 data couples of synthetic falling-head measurements). Results show that the Z-t method is the most accurate and precise, followed by the Hvorslev method when a correction is applied and the velocity method when appropriately interpreted. Advice on how to interpret falling-head tests tainted by random error concludes the study.

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Wang, H., R. J. Barthelmie, P. Doubrawa, and S. C. Pryor. "Errors in radial velocity variance from Doppler wind lidar." Atmospheric Measurement Techniques 9, no. 8 (August 29, 2016): 4123–39. http://dx.doi.org/10.5194/amt-9-4123-2016.

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Abstract. A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Using both statistically simulated and observed data, this paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10 %.

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Duan, Xiu Yun, and Yu Huang. "Research on Method of Random Error Separation Based on Wavelet Transform and Frequency Bands Character." Applied Mechanics and Materials 347-350 (August 2013): 3950–53. http://dx.doi.org/10.4028/www.scientific.net/amm.347-350.3950.

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a new method of random error separation based on wavelet transform and the frequency bands character of measurement data is proposed. Approximates the random error with the detail components of the wavelet decomposition, determines the optimal decomposition level on the frequency intervals between the random errors and other components, and finally gets the random error by reconstructing all the detail components. The method is simply and efficient, avoids the indirect error with modeling and indirect methods, and computer simulation proves the robustness of the separation results.

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Williams, P. J. S., A. Etemadi, I. W. McCrea, and H. Todd. "Errors due to random noise in velocity measurement using incoherent-scatter radar." Annales Geophysicae 14, no. 12 (December 31, 1996): 1480–86. http://dx.doi.org/10.1007/s00585-996-1480-x.

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Abstract. The random-noise errors involved in measuring the Doppler shift of an 'incoherent-scatter' spectrum are predicted theoretically for all values of Te/Ti from 1.0 to 3.0. After correction has been made for the effects of convolution during transmission and reception and the additional errors introduced by subtracting the average of the background gates, the rms errors can be expressed by a simple semi-empirical formula. The observed errors are determined from a comparison of simultaneous EISCAT measurements using an identical pulse code on several adjacent frequencies. The plot of observed versus predicted error has a slope of 0.991 and a correlation coefficient of 99.3%. The prediction also agrees well with the mean of the error distribution reported by the standard EISCAT analysis programme.

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Alpert, Nathaniel M., W. Craig Barker, Andrew Gelman, Stephen Weise, Michio Senda, and John A. Correia. "The Precision of Positron Emission Tomography: Theory and Measurement." Journal of Cerebral Blood Flow & Metabolism 11, no. 1_suppl (March 1991): A26—A30. http://dx.doi.org/10.1038/jcbfm.1991.33.

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The limits of quantitation with positron emission tomography (PET) are examined with respect to the noise propagation resulting from radioactive decay and other sources of random error. Theoretical methods for evaluating the statistical error have been devised but seldom applied to experimental data obtained on human subjects. This paper extends the analysis in several ways: (1) A Monte Carlo method is described for tracking the propagation of statistical error through the analysis of in vivo measurements; (2) Experimental data, obtained in phantoms, validating the Monte Carlo method and other methods are presented; (3) A difference in activation paradigm, performed on regional CBF (rCBF) data from five human subjects, was analyzed on 1.6-cm diameter regions of interest to determine the mean fractional statistical error in PET tissue concentration and in rCBF before and after stereotactic transformation; and (4) A linear statistical model and calculations of the various statistical errors were used to estimate the magnitude of the subject-specific fluctuations under various conditions. In this specific example, the root mean squared (RMS) noise in flow measurements was about three times higher than the RMS noise in the concentration measurements. In addition, the total random error was almost equally partitioned between statistical error and random fluctuations due to all other sources.

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van den Tillaart, Sander P. M., Martijn J. Booij, and Maarten S. Krol. "Impact of uncertainties in discharge determination on the parameter estimation and performance of a hydrological model." Hydrology Research 44, no. 3 (December 27, 2012): 454–66. http://dx.doi.org/10.2166/nh.2012.147.

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Uncertainties in discharge determination may have serious consequences for hydrological modelling and resulting discharge predictions used for flood forecasting, climate change impact assessment and reservoir operation. The aim of this study is to quantify the effect of discharge errors on parameters and performance of a conceptual hydrological model for discharge prediction applied to two catchments. Six error sources in discharge determination are considered: random measurement errors without autocorrelation; random measurement errors with autocorrelation; systematic relative measurement errors; systematic absolute measurement errors; hysteresis in the discharge–water level relation and effects of an outdated discharge–water level relation. Assuming realistic magnitudes for each error source, results show that systematic errors and an outdated discharge–water level relation have a considerable influence on model performance, while other error sources have a small to negligible effect. The effects of errors on parameters are large if the effects on model performance are large as well and vice versa. Parameters controlling the water balance are influenced by systematic errors and parameters related to the shape of the hydrograph are influenced by random errors. Large effects of discharge errors on model performance and parameters should be taken into account when using discharge predictions for flood forecasting and impact assessment.

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Miao, Yu, Hongye Su, Rong Gang, and Jian Chu. "Industrial Processes: Data Reconciliation and Gross Error Detection." Measurement and Control 42, no. 7 (September 2009): 209–15. http://dx.doi.org/10.1177/002029400904200704.

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Process data plays a vital role in industrial processes, which are the basis for process control, monitoring, optimization and business decision making. However, it is inevitable that process data measurements will be corrupted by random errors. Therefore, data reconciliation has been developed to improve accuracy of process data by reducing the effect of random errors. Unfortunately, reconciled values would be deteriorated by gross errors, which may be present during measurement. Therefore, gross error detection is necessary to guarantee the efficiency of data reconciliation, which has been developed to identify and eliminate gross errors in process data. In this paper, a review of data reconciliation and gross error detection and relevant industrial applications are presented. As the efficiency of data reconciliation and gross error detection largely depends upon the locations of sensors, sensor networks design is also included in the review. Meanwhile, some achievements of the authors are also included.

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Westfall, James A., and Paul L. Patterson. "Measurement variability error for estimates of volume change." Canadian Journal of Forest Research 37, no. 11 (November 2007): 2201–10. http://dx.doi.org/10.1139/x07-082.

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Using quality assurance data, measurement variability distributions were developed for attributes that affect tree volume prediction. Random deviations from the measurement variability distributions were applied to 19 381 remeasured sample trees in Maine. The additional error due to measurement variation and measurement bias was estimated via a simulation study for various components of volume change. In comparison with sampling error, the error due to measurement variation was relatively small. When biases in measurements had contradictory effects on the calculation of individual tree volume, there was little additional error, however, systematic biases produced substantial error increases. The proportion of measurement variation error attributable to diameter at breast height and tree species classification was small relative to that attributable to bole (merchantable) height and percent cull attributes, which composed the preponderance of uncertainty due to measurement variation. The greatest impacts were associated with the accretion component, which was subject to measurement variation and bias at both the initial and subsequent measurements.

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Su, Wei Peng, Yong Sheng Hao, and Qi Chang Li. "ARMA-AKF Model of MEMS Gyro Rotation Data Random Drift Compensation." Applied Mechanics and Materials 321-324 (June 2013): 549–52. http://dx.doi.org/10.4028/www.scientific.net/amm.321-324.549.

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Application of MEMS angular rate gyro attitude when monitoring for long-term, zero-point drift and random error in cumulative points after long-term monitoring errors can significantly increase the measurement error. Using ARMA model of MEMS gyros random drift modeling and error compensation method using Adaptive Kalman Filter, which increases gyro attitude measurement of long-term reliability Last experiment. The method in accordance with the principle of time series analysis, integration of observations and estimates of actual system so that it can reflect the influence of external disturbance and noise on the system. It can also reflect the influence of system disturbance on actual system performance improves estimation precision.

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Nusser, Sarah M., Nicholas K. Beyler, Gregory J. Welk, Alicia L. Carriquiry, Wayne A. Fuller, and Benjamin M. N. King. "Modeling Errors in Physical Activity Recall Data." Journal of Physical Activity and Health 9, s1 (January 2012): S56—S67. http://dx.doi.org/10.1123/jpah.9.s1.s56.

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Background:Physical activity recall instruments provide an inexpensive method of collecting physical activity patterns on a sample of individuals, but they are subject to systematic and random measurement error. Statistical models can be used to estimate measurement error in activity recalls and provide more accurate estimates of usual activity parameters for a population.Methods:We develop a measurement error model for a short-term activity recall that describes the relationship between the recall and an individual’s usual activity over a long period of time. The model includes terms for systematic and random measurement errors. To estimate model parameters, the design should include replicate observations of a concurrent activity recall and an objective monitor measurement on a subsample of respondents.Results:We illustrate the approach with preliminary data from the Iowa Physical Activity Measurement Study. In this dataset, recalls tend to overestimate actual activity, and measurement errors greatly increase the variance of recalls relative to the person-to-person variation in usual activity. Statistical adjustments are used to remove bias and extraneous variation in estimating the usual activity distribution.Conclusions:Modeling measurement error in recall data can be used to provide more accurate estimates of long-term activity behavior.

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Andrich, David, and Pender Pedler. "A law of ordinal random error: The Rasch measurement model and random error distributions of ordinal assessments." Measurement 131 (January 2019): 771–81. http://dx.doi.org/10.1016/j.measurement.2018.08.062.

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Mayr, Andreas, Matthias Schmid, Annette Pfahlberg, Wolfgang Uter, and Olaf Gefeller. "A permutation test to analyse systematic bias and random measurement errors of medical devices via boosting location and scale models." Statistical Methods in Medical Research 26, no. 3 (April 24, 2015): 1443–60. http://dx.doi.org/10.1177/0962280215581855.

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Measurement errors of medico-technical devices can be separated into systematic bias and random error. We propose a new method to address both simultaneously via generalized additive models for location, scale and shape (GAMLSS) in combination with permutation tests. More precisely, we extend a recently proposed boosting algorithm for GAMLSS to provide a test procedure to analyse potential device effects on the measurements. We carried out a large-scale simulation study to provide empirical evidence that our method is able to identify possible sources of systematic bias as well as random error under different conditions. Finally, we apply our approach to compare measurements of skin pigmentation from two different devices in an epidemiological study.

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Short, Margaret B., and Bradley P. Carlin. "Multivariate spatiotemporal CDFs with random effects and measurement error." Bayesian Analysis 1, no. 3 (September 2006): 595–624. http://dx.doi.org/10.1214/06-ba120.

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Xiao, Ming Zhu. "Estimating Measurement Error Based on Evidence Theory." Advanced Materials Research 548 (July 2012): 839–42. http://dx.doi.org/10.4028/www.scientific.net/amr.548.839.

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Measurement error is traditionally represented with probability distributions. Although probabilistic representations of measurement error have been successfully employed in many analyses, such representations have been criticized for requiring more refined knowledge with respect to the existing error than that is really present. As a result, this paper proposes a general framework and process for estimating the measurement error based on evidence theory. In this research cumulative belief functions (CBFs) and cumulative plausibility functions (CPFs) are used to estimate measurement error. The estimation includes two steps:(1) modeling the parameters by means of a random set, and discrediting the random set to focal elements in finite numbers; (2)summarizing the propagation error. An example is demonstrated the estimation process.

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Singh, Ravi Shankar, Helko van den Brom, Stanislav Babaev, Sjef Cobben, and Vladimir Ćuk. "Estimation of Impedance and Susceptance Parameters of a 3-Phase Cable System Using PMU Data." Energies 12, no. 23 (November 30, 2019): 4573. http://dx.doi.org/10.3390/en12234573.

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This paper proposes a new regression-based method to estimate resistance, reactance, and susceptance parameters of a 3-phase cable segment using phasor measurement unit (PMU) data. The novelty of this method is that it gives accurate parameter estimates in the presence of unknown bias errors in the measurements. Bias errors are fixed errors present in the measurement equipment and have been neglected in previous such attempts of estimating parameters of a 3-phase line or cable segment. In power system networks, the sensors used for current and voltage measurements have inherent magnitude and phase errors whose measurements need to be corrected using calibrated correction coefficients. Neglecting or using wrong error correction coefficients causes fixed bias errors in the measured current and voltage signals. Measured current and voltage signals at different time instances are the variables in the regression model used to estimate the cable parameters. Thus, the bias errors in the sensors become fixed errors in the variables. This error in variables leads to inaccuracy in the estimated parameters. To avoid this, the proposed method uses a new regression model using extra parameters which facilitate the modeling of present but unknown bias errors in the measurement system. These added parameters account for the errors present in the non- or wrongly calibrated sensors. Apart from the measurement bias, random measurement errors also contribute to the total uncertainty of the estimated parameters. This paper also presents and compares methods to estimate the total uncertainty in the estimated parameters caused by the bias and random errors present in the measurement system. Results from simulation-based and laboratory experiments are presented to show the efficacy of the proposed method. A discussion about analyzing the obtained results is also presented.

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Lou, Qun, Junhao Lv, Lihua Wen, and Jinyou Xiao. "Time-space Domain Elimination Method of High-Temperature Thermal Disturbance Test Error." Journal of Physics: Conference Series 2285, no. 1 (June 1, 2022): 012028. http://dx.doi.org/10.1088/1742-6596/2285/1/012028.

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Abstract The digital image correlation (DIC) test method has been widely used in structural deformation measurement due to its non-contact and full-field. However, eliminating the effects of temperature-induced thermal disturbance is a primary challenge in high-temperature DIC measurements. In this paper, the measurement error is regarded as the superposition of zero-mean random error and non-zero mean system error, a time-space domain disturbance error elimination method is proposed to eliminate the adverse effects of thermal disturbance. Firstly, the noise images are averaged in the time domain to reduce the DIC matching error caused by zero-mean random noise. Then the noise displacement field is locally weighted quadratically smoothed in the space domain to eliminate the non-zero mean system error. The experimental results show that the proposed method can improve the high-temperature deformation measurement accuracy compared with the single-domain processing method. This paper will provide a new method for improving the measurement accuracy in DIC full-field deformation measurement under a high-temperature environment.

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Borshchov, P. I. "MINIMIZATION OF RANDOM ERROR OF DIGITAL METHOD OF MEASUREMENT OF AMPLITUDE OF A SINUSOIDAL SIGNA." Praci Institutu elektrodinamiki Nacionalanoi akademii nauk Ukraini 2022, no. 62 (August 18, 2022): 55–60. http://dx.doi.org/10.15407/publishing2022.62.055.

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The errors of measuring the amplitude of sinusoidal signals by the method based on calculating the sum of the ratios of digital samples of instantaneous signal values to the sines of the phase angles corresponding to the sampling moments are investigated. A mathematical expression for determining the total random measurement error using the values of the parameters of the error components is obtained. It is shown that there is a minimum value of the total random measurement error as a function of the number of instantaneous signal values taken into account. The method of reducing the level of random error to the desired level is given. The method can be used to create metrological support for measuring the parameters of electrical signals at low and infralow frequencies, including industrial frequency. Ref. 7, fig. 4, table.

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Vorotnikov, I. N., M. A. Mastepanenko, Sh Zh Gabrielyan, S. V. Mishukov, and V. V. Varlamov. "Improving a parameter determination method for multielement bi-poles used in digital dielcometric hygrometer of agricultural products." IOP Conference Series: Earth and Environmental Science 996, no. 1 (February 1, 2022): 012032. http://dx.doi.org/10.1088/1755-1315/996/1/012032.

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Abstract The article examines the possibility of determining the parameters of multi-element bi-pole using the author’s method of aggregate measurements. Mathematical modeling of measuring circuits is performed, the random error of the results of measurements of parameters of a four-element bi-pole by the Monte Carlo method is estimated and determination result of the methodological and random components of the measurement errors of parameters of circuit elements is presented. The relevance of the application of the combined method of research with measurements in steady-state and transient modes for determining the moisture content of agricultural products is justified. The reduction of the resulting methodological error and the possibility of reducing the number of analog-to-digital transformations without deteriorating the target accuracy are proved.

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Jiang, Tammy, Jaimie L. Gradus, Timothy L. Lash, and Matthew P. Fox. "Addressing Measurement Error in Random Forests Using Quantitative Bias Analysis." American Journal of Epidemiology 190, no. 9 (February 1, 2021): 1830–40. http://dx.doi.org/10.1093/aje/kwab010.

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Abstract Although variables are often measured with error, the impact of measurement error on machine-learning predictions is seldom quantified. The purpose of this study was to assess the impact of measurement error on the performance of random-forest models and variable importance. First, we assessed the impact of misclassification (i.e., measurement error of categorical variables) of predictors on random-forest model performance (e.g., accuracy, sensitivity) and variable importance (mean decrease in accuracy) using data from the National Comorbidity Survey Replication (2001–2003). Second, we created simulated data sets in which we knew the true model performance and variable importance measures and could verify that quantitative bias analysis was recovering the truth in misclassified versions of the data sets. Our findings showed that measurement error in the data used to construct random forests can distort model performance and variable importance measures and that bias analysis can recover the correct results. This study highlights the utility of applying quantitative bias analysis in machine learning to quantify the impact of measurement error on study results.

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Negre, Alicia, Renaud Mathevet, Benoit Chalopin, and Sébastien Massenot. "Unexpected optimal measurement protocols in Bell's inequality violation experiments." American Journal of Physics 91, no. 1 (January 2023): 64–73. http://dx.doi.org/10.1119/5.0102516.

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Bell's inequality violation experiments are becoming increasingly popular in the practical teaching of undergraduate and master's degree students. Bell's parameter S is obtained from 16 polarization correlation measurements performed on entangled photons pairs. We first report here a detailed analysis of the uncertainty u( S) of Bell's parameter taking into account coincidence count statistics and errors in polarizers' orientation. We show using both computational modeling and experimental measurement that the actual sequence of the polarizer settings has an unexpected and strong influence on the error budget. This result may also be relevant to measurements in other settings in which errors in parameters may have non-random effects in the measurement.

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Shy, Sarah, Hyungsuk Tak, Eric D. Feigelson, John D. Timlin, and G. Jogesh Babu. "Incorporating Measurement Error in Astronomical Object Classification." Astronomical Journal 164, no. 1 (June 13, 2022): 6. http://dx.doi.org/10.3847/1538-3881/ac6e64.

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Abstract Most general-purpose classification methods, such as support-vector machine (SVM) and random forest (RF), fail to account for an unusual characteristic of astronomical data: known measurement error uncertainties. In astronomical data, this information is often given in the data but discarded because popular machine learning classifiers cannot incorporate it. We propose a simulation-based approach that incorporates heteroscedastic measurement error into an existing classification method to better quantify uncertainty in classification. The proposed method first simulates perturbed realizations of the data from a Bayesian posterior predictive distribution of a Gaussian measurement error model. Then, a chosen classifier is fit to each simulation. The variation across the simulations naturally reflects the uncertainty propagated from the measurement errors in both labeled and unlabeled data sets. We demonstrate the use of this approach via two numerical studies. The first is a thorough simulation study applying the proposed procedure to SVM and RF, which are well-known hard and soft classifiers, respectively. The second study is a realistic classification problem of identifying high-z (2.9 ≤ z ≤ 5.1) quasar candidates from photometric data. The data are from merged catalogs of the Sloan Digital Sky Survey, the Spitzer IRAC Equatorial Survey, and the Spitzer-HETDEX Exploratory Large-Area Survey. The proposed approach reveals that out of 11,847 high-z quasar candidates identified by a random forest without incorporating measurement error, 3146 are potential misclassifications with measurement error. Additionally, out of 1.85 million objects not identified as high-z quasars without measurement error, 936 can be considered new candidates with measurement error.

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Stupakova, Ekaterina. "Experimental test of the sample reduction random error formula." Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal, no. 4 (June 25, 2021): 37–44. http://dx.doi.org/10.21440/0536-1028-2021-4-37-44.

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Introduction. An immediate estimate of the accidental error of sample reduction can only be made if the measurement method of execution is zero. This can be achieved by imitating the grains of a useful component with markers fully extracted from the reduced sample. The markers can be larger than 44 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 4. 2021 ISSN 0536-1028 the maximum size of the sample material and are extracted from the sample using screens. Markers whose granulometric composition matches the sample composition should be extracted completely from the reduced sample using a hand magnet in the case. Methodology. A small number of markers of the correct shape imitates forgeable gold grains or d99 platinum. A much larger number of free-form markers simulate the granulometric composition of a sample in the –1+0.5 mm class. It is necessary to find a form factor linking the particles real volume with the cube volume. For magnetite markers, the form factor is 0.4. Results and analysis. The samples have been reduced with regular shaped and free-form markers, which makes it possible to experimentally determine the error of reduction. Theoretical formulas found errors for the conditions of experiments. For experiments with the regular shaped markers, a 54.77– 58.43% relative reduction error has been obtained according to 480 parallel measurements. Theoretically determined 57.64% relative error falls into this range. Similar relative reduction errors with free-form markers are 8.82–10.00% and 9.15%. Conclusion. The fairness of the reduction error analytical formula has been directly evaluated for the first time. The reduction error analytical formula can be applied when analyzing the schemes of sample preparation.

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Lappi, Juha. "Estimating the distribution of a variable measured with error: stand densities in a forest inventory." Canadian Journal of Forest Research 21, no. 4 (April 1, 1991): 469–73. http://dx.doi.org/10.1139/x91-063.

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If a variable is measured (or estimated) with error, then the distribution of the measurements is flatter than the true distribution. The variance of a measured variable is the sum of the true variance and the measurement error variance. If we shrink measured values towards their mean so that the variance will be equal to the true population variance, or its estimate, the obtained empirical distribution is more similar to the true distribution than is the distribution of measured values. To estimate the population variance, an estimate of the variance of measurement errors is required. If stand densities are measured by counting trees on fixed area or angle gauge plots, then a first approximation for the measurement (sampling) error variance can be computed assuming random (Poisson) spatial pattern of trees. The suggested estimation method is illustrated using an assumed distribution of stand densities.

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Trevizan, Rodrigo D., Cody Ruben, Aquiles Rossoni, Surya C. Dhulipala, Arturo Bretas, and Newton G. Bretas. "μPMU-Based Temporal Decoupling of Parameter and Measurement Gross Error Processing in DSSE." Electricity 2, no. 4 (October 2, 2021): 423–38. http://dx.doi.org/10.3390/electricity2040025.

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Simultaneous real-time monitoring of measurement and parameter gross errors poses a great challenge to distribution system state estimation due to usually low measurement redundancy. This paper presents a gross error analysis framework, employing μPMUs to decouple the error analysis of measurements and parameters. When a recent measurement scan from SCADA RTUs and smart meters is available, gross error analysis of measurements is performed as a post-processing step of non-linear DSSE (NLSE). In between scans of SCADA and AMI measurements, a linear state estimator (LSE) using μPMU measurements and linearized SCADA and AMI measurements is used to detect parameter data changes caused by the operation of Volt/Var controls. For every execution of the LSE, the variance of the unsynchronized measurements is updated according to the uncertainty introduced by load dynamics, which are modeled as an Ornstein–Uhlenbeck random process. The update of variance of unsynchronized measurements can avoid the wrong detection of errors and can model the trustworthiness of outdated or obsolete data. When new SCADA and AMI measurements arrive, the LSE provides added redundancy to the NLSE through synthetic measurements. The presented framework was tested on a 13-bus test system. Test results highlight that the LSE and NLSE processes successfully work together to analyze bad data for both measurements and parameters.

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Okuyama, Eiki, and Masayuki Ito. "Combination of Double Scale Measurements for Large Scale Surface Profile Measurement." Applied Mechanics and Materials 870 (September 2017): 197–202. http://dx.doi.org/10.4028/www.scientific.net/amm.870.197.

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In the field of surface profile measurement, many software datums were proposed. When a measured surface profile is large, the number of sampling point becomes large. As the result, the influence of the random error becomes large. To decrease the error propagation, the concept of the division of the length datum is applied to the integration method for surface profile measurement. Analytical results and simulation show when integration method is used as the software datum for surface profile measurement, combination of the large scale integration method and short scale integration method is useful to decrease the error propagation.

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Miao, En Ming, Ya Yun Gong, Tian Ju Cheng, and Peng Cheng Niu. "A Way to Improve Eddy Current Sensor Measurement Accuracy." Applied Mechanics and Materials 160 (March 2012): 47–52. http://dx.doi.org/10.4028/www.scientific.net/amm.160.47.

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Eddy current sensor is widely used in engineering applications.When it was calibrated, generally used random error analysis method,but this will expand the range of measurement errors and limit its engineering applications.In this paper, we use a new error analysis method to analyze upper and lower limit of multiple batches measurement data. At the same time, catching up with a criterion for the measurement time. This can obtain the measurement accuracy more precise and have good practical value.

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R. Ziyatdinov, Rustem, and Leisan R. Zakirova. "Application of Measurement Signal Reduction to Improve Measurement Accuracy." International Journal of Engineering & Technology 7, no. 4.36 (December 9, 2018): 1035. http://dx.doi.org/10.14419/ijet.v7i4.36.24948.

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Most modern technical tasks require high precision measurements. To do this, it is necessary to analyze the causes of errors and take measures to reduce their influence on the accuracy of measurements. The causes of errors are very diverse and cannot always be identified. However, some systematic components of the measurement error can be described and calculated mathematically. In this case, the task of reducing the signal at the output of a measuring device to the form it would have when using an “ideal” device is reduced to calculating a certain linear operator which product to the measured signal allows obtaining the minimum systematic error. In this paper, the application of the reduction method is given by the example of a measuring instrument for the degree of polarization of light radiation which comprises three measuring channels for measuring the intensity of linearly polarized radiation. Each channel is built with the use of three operational amplifiers. The main errors of a measuring channel that can be described and determined are the errors of the operational amplifiers associated with the bias voltages and temperature drift. In real measuring systems there are much larger of such components. However, the use of computer equipment for modeling systems and processes, as well as measurements, removes all restrictions on the possibilities of processing the obtained data in a software way. With the help of computer technology it is possible to reduce the influence of perturbing effects and systematic errors, and also to eliminate gross errors. The random component of an error can be reduced by increasing the number of measurements and carrying out statistical data processing.

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Hoffman, J. B., and K. R. Grimm. "Far-field uncertainty due to random near-field measurement error." IEEE Transactions on Antennas and Propagation 36, no. 6 (June 1988): 774–80. http://dx.doi.org/10.1109/8.1179.

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Kim, Yeaji, Leonardo Antenangeli, and Justin Kirkland. "Measurement Error and Attenuation Bias in Exponential Random Graph Models." Statistics, Politics and Policy 7, no. 1-2 (December 20, 2016): 29–54. http://dx.doi.org/10.1515/spp-2016-0001.

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AbstractExponential Random Graph Models (ERGMs) are becoming increasingly popular tools for estimating the properties of social networks across the social sciences. While the asymptotic properties of ERGMs are well understood, much less is known about how ERGMs perform in the face of violations of the assumptions that drive those asymptotic properties. Given that empirical social networks rarely meet the strenuous assumptions of the ERGM perfectly, practical researchers are often in the position of knowing their coefficients are imperfect, but not knowing precisely how wrong those coefficients may be. In this research, we examine one violation of the asymptotic assumptions of ERGMs – perfectly measured social networks. Using several Monte Carlo simulations, we demonstrate that even randomly distributed measurement errors in networks under study can cause considerable attenuation in coefficients from ERGMs, and do real harm to subsequent hypothesis tests.

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Nkurunziza, Sévérien. "Shrinkage strategy in stratified random sample subject to measurement error." Statistics & Probability Letters 81, no. 2 (February 2011): 317–25. http://dx.doi.org/10.1016/j.spl.2010.10.020.

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Matsulevich, O. V., A. P. Kren, T. A. Pratasenia, and M. N. Delendik. "Evaluation of the error of indirect measurements of physical-mechanical characteristics of materials by dynamic indentation method." Proceedings of the National Academy of Sciences of Belarus, Physical-Technical Series 65, no. 4 (December 31, 2020): 487–95. http://dx.doi.org/10.29235/1561-8358-2020-65-4-487-495.

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The metrological problems of measuring the physic and mechanical characteristics of materials by dynamic indentation are considered. It is shown that the estimation of measurement error demanding the creation of the reference blocks is ineffective due to the wide variety of controlled materials and a wide range of changes in their properties. A technique has been developed for evaluating the accuracy of measurements based on the errors of individual parameters included in the calculation equation, i.e. by determining the error of indirect measurements. The technique is based on the estimation of the boundaries of the random error of the measured characteristics of the material and the non-excluded systematic errors of the parameters that are used for the calculations of needed characteristics. The results of experimental studies are presented, indicating that due to the different character of the dependencies of hardness and elastic modulus, the error in measuring the elastic modulus exceeds the error in measuring hardness. In addition, it was found that the error in measuring the characteristics of materials by the dynamic indentation method exceeds the measurement error by the static indentation method and can be reduced by increasing the accuracy of the equipment used for the registration of impact process. The obtained values of the physic and mechanical characteristics of the materials and the values of the measurement error show that the dynamic indentation method can effectively solve the problem of non-destructive testing of hardness, elastic modulus, and strain hardening exponent of metals and products with an appropriate error.

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Matsulevich, O. V., A. P. Kren, T. A. Pratasenia, and M. N. Delendik. "Evaluation of the error of indirect measurements of physical-mechanical characteristics of materials by dynamic indentation method." Proceedings of the National Academy of Sciences of Belarus, Physical-Technical Series 65, no. 4 (December 31, 2020): 487–95. http://dx.doi.org/10.29235/1561-8358-2020-65-4-487-495.

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The metrological problems of measuring the physic and mechanical characteristics of materials by dynamic indentation are considered. It is shown that the estimation of measurement error demanding the creation of the reference blocks is ineffective due to the wide variety of controlled materials and a wide range of changes in their properties. A technique has been developed for evaluating the accuracy of measurements based on the errors of individual parameters included in the calculation equation, i.e. by determining the error of indirect measurements. The technique is based on the estimation of the boundaries of the random error of the measured characteristics of the material and the non-excluded systematic errors of the parameters that are used for the calculations of needed characteristics. The results of experimental studies are presented, indicating that due to the different character of the dependencies of hardness and elastic modulus, the error in measuring the elastic modulus exceeds the error in measuring hardness. In addition, it was found that the error in measuring the characteristics of materials by the dynamic indentation method exceeds the measurement error by the static indentation method and can be reduced by increasing the accuracy of the equipment used for the registration of impact process. The obtained values of the physic and mechanical characteristics of the materials and the values of the measurement error show that the dynamic indentation method can effectively solve the problem of non-destructive testing of hardness, elastic modulus, and strain hardening exponent of metals and products with an appropriate error.

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Zhang, Fan. "Modeling Study on Random Error of Fiber Optic Gyro." Applied Mechanics and Materials 239-240 (December 2012): 167–71. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.167.

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An accurate modeling method for the random error of the fiber optic gyro (FOG) is presented. Taking the FOG in the inertial measurement unit of one specific inertial navigation system as the subject investigated, the method is composed of the data acquisition, preprocessing, establishing the FOG AR(2) model and performing Kalman filtering based on the model. The filtering result and the Allan variance analysis of FOG prove that the method effectively reduces the FOG random error, decreasing the angle random walk, zero-bias instability, rate random walk, angular rate ramp and quantification noise of FOG signals to less than one half of the corresponding values before the filtering of FOG random errors, which improves the accuracy of FOG.

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McAvoy, Gregory E. "Measurement Models for Time Series Analysis: Estimating Dynamic Linear Errors-in-Variables Models." Political Analysis 7 (1998): 165–86. http://dx.doi.org/10.1093/pan/7.1.165.

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This article uses state space modeling and Kalman filtering to estimate a dynamic linear errors-in-variables model with random measurement error in both the dependent and independent variables. I begin with a general description of the dynamic errors-in-variables model, translate it into state space form, and show how it can be estimated via the Kalman filter. I report the results of a simulation in which the amount of random measurement error is varied, to demonstrate the importance of estimating measurement error models and the superiority that Kalman filtering has over regression. I use the model in a substantive example to examine the effects of public opinion regarding nuclear power on the enforcement decisions of the Nuclear Regulatory Commission. I then estimate a dynamic linear errors-in-variables model using multiple indicators for the latent variables and compare simulations of this model to the single indicator model. Finally, I provide substantive examples which examine the effect of people's economic expectations on their approval of the president and their approval of government more generally.

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Farre, R., M. Rotger, and D. Navajas. "Estimation of random errors in respiratory resistance and reactance measured by the forced oscillation technique." European Respiratory Journal 10, no. 3 (March 1, 1997): 685–89. http://dx.doi.org/10.1183/09031936.97.10030685.

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The forced oscillation technique (FOT) allows the measurement of respiratory resistance (Rrs) and reactance (Xrs) and their associated coherence (gamma2). To avoid unreliable data, it is usual to reject Rrs and Xrs measurements with a gamma2 <0.95. This procedure makes it difficult to obtain acceptable data at the lowest frequencies of interest. The aim of this study was to derive expressions to compute the random error of Rrs and Xrs from gamma2 and the number (N) of data blocks involved in a FOT measurement. To this end, we developed theoretical equations for the variances and covariances of the pressure and flow auto- and cross-spectra used to compute Rrs and Xrs. Random errors of Rrs and Xrs were found to depend on the values of Rrs and Xrs, and to be proportional to ((1-gamma2)/(2 x N x gamma2))1/2. Reliable Rrs and Xrs data can be obtained in measurements with low gamma2 by enlarging the data recording (i.e. N). Therefore, the error equations derived may be useful to extend the frequency band of the forced oscillation technique to frequencies lower than usual, characterized by low coherence.

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Journal articles on the topic 'Random measurement error'

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