Measurement Error Theory Research Articles

Опыт применения цифровых нивелиров и программного обеспечения CREDO НИВЕЛИР для мониторинга инженерных сооружений

Purpose: To present the experience of working with digital levels at a construction site during long-term settlement monitoring settlement of both engineering structures under construction and in operation in conditions of tight time constraints, a significant amount of work, limited resources and adverse observation conditions with the simultaneous need to perform them with high accuracy. Methods: Theory of measurement errors, least squares method, parametric adjustment method. Results: It is shown that digital levels of various manufacturers, although they are used to solve various geodetic problems, and the work of many authors is devoted to the study of the influence of various factors on the accuracy of the result obtained by them, but in real production conditions a number of such factors cannot be excluded, which leads to a deterioration in the accuracy of the leveling results. Practical recommendations for mathematical processing of leveling networks built by digital levels in the CREDO NIVELIR software environment are developed, non-standard types of settlement marks are proposed with an indication of the methodology for performing observations when using them. Based on the known dependence of the tilt angle of the digital level on the ambient temperature, an original method for its determination is proposed, including situations when the obtained value exceeds its compensation limits by the level software. It is shown that the conclusions obtained on the basis of the experience of working with digital levels make it possible to increase the accuracy of such work, as well as reduce their labor intensity, when monitoring the settlement of engineering structures. Practical significance: The conclusions and results presented in the article have been obtained on the basis of long-term control of the settlement of both engineering structures under construction and in operation and can be implemented by engineering and geodetic construction support.

Application of Duhamel's convolution integral in computer measurement systems

The paper is a new approach to the Duhamel's convolution integral. It contains a brief description of the Duhamel's convolution integral and an overview of applications of this integral. The scientific novelty presented in the work is the original algorithm for determining the frequency characteristic, together with its mathematical justification as well as with hardware and software implementation. The proposed algorithm was used in computer measurement systems enabling the determination of Bode and Nyquist characteristics of objects used in automation. The measurement system was built by the authors on the basis of the proposed algorithm. Measurements were carried out using it. During the measurements of the selected automation object, actual results were obtained and referenced to theoretical results. Then their correctness was assessed using the theory of measurement errors. In this way, the correctness of the mathematical considerations concerning the application of the Duhamel's convolution integral in computer measurement systems enabling the determination of the frequency characteristics of objects used in automation was confirmed.

Using the fundamentals of the theory of measurement errors in performing geodesic measurement and calculation works

In this article, the tasks of the theory of measurement errors during geodetic measurement and calculation practices, equal and unequal measurements and measurement errors, i.e. deviations from the actual values of the measured quantity as a result of measurement issues aimed at elucidating the work and their classifications are covered. Also, the criteria of measurement accuracy, expressions for their determination, as well as the procedure for processing one quantity measured with equal accuracy and a sample example of its implementation are given.

Определение точности геодезических измерений при реконструкции исторических объектов

Purpose: To consider the issue of the assignment of marking work accuracy at reconstruction stage of a technically complex object. To show the need in accuracy preliminary calculation. After the assignment of geodetic measurement accuracy, to perform geodetic network designing in Credo.dat software package. To determine leveling class that satisfies formed requirements. Methods: Measurement error theory, least squares method, parametric adjustment method, modeling of geodetic networks using package of applied programs. Results: Requirements for the accuracy of marking works were established based on the ones of current regulatory documents. The sequence of the formation of requirements for definition of accuracy in geodetic staking base locations and requirements for the accuracy of used geodetic instruments is considered. Separately, the accuracy of planned and altitudinal geodetic networks is calculated. The possibility to apply class III leveling program when creating altitudinal network to meet accuracy established requirements is shown. Practical significance: The sequence of geodetic work accuracy assignment during historical object reconstruction is outlined on a particular example, the proposed methodology can be recommended for a practical use.

Comparison of three approaches for computing measurement uncertainties

Abstract This paper compares three approaches for computing measurement uncertainties: GUM’s confidence interval (CI) based approach, Bayesian approach, and probability interval (PI) based approach in a recently proposed unified theory of measurement errors and uncertainties. The key concepts underlying the three approaches are discussed. The similarities of and differences between the three approaches are explored. We focus on a simple problem that is often encountered in practice: Type A and Type B evaluation of uncertainty with a small number of observations. The logical frameworks of the three approaches for the problem considered are discussed. Some misinterpretations of and confusion about several statistical concepts involved in uncertainty analysis are clarified. We conclude that the PI-based approach is superior to both the GUM’s CI-based approach and Bayesian approach. The revision of the GUM should adopt the PI-based approach for computing measurement uncertainties.

A unified theory of measurement errors and uncertainties

This paper presents a unified theory of measurement errors and uncertainties. The proposed theory unifies the theory of errors with the theory of measurement uncertainties and merges some of the best practices in error and uncertainty analysis. The unified theory is based entirely on the frequentist statistics. It recovers the traditional classification of random and systematic errors (as the primary classification) and retains the GUM’s Type A and Type B classification (as the secondary classification). The unified theory employs two new estimators (presented in this paper) for estimating the expanded uncertainty: one for direct measurements and the other for indirect measurements. The Welch–Satterthwaite formula is no longer needed because these two new estimators do not need the effective degrees of freedom (DOF) of the total (i.e. combined) standard uncertainty. This significantly simplifies uncertainty analysis and avoids the difficulty and subjectivity in determining the DOF of a Type B component and the limitations of the Welch–Satterthwaite formula. Jensen’s inequality theoretically guarantees that the two new estimators are conservative. Numerical analyses and test examples suggest that the two new estimators are only slightly conservative. This paper demonstrates the validity and effectiveness of these two new estimators and provides a comprehensive comparison with existing methods. The unified theory is easy to understand and easy to use; it provides reliable and realistic estimates of uncertainties.

Evaluation criteria of landslide stability

The theoretical issues related to the definition of the landslide movement for rectilinear and circular cylindrical sliding surfaces are considered. Based on the concepts of the theory of measurement errors, an analysis of the impact of the parameters on the landslide velocity is performed. The formulas obtained allow us to calculate the speeds of landslides during seismic and atmospheric action.

The new concepts of measurement error theory

In current measurement theory, there are various logical and philosophical troubles, and the evaluation concepts of measurement error are various and inconsistent among different schools. This paper throws away the shackle of the current measurement theories and concepts, and re-discusses basic measurement concepts. By proving a new measurement error theory that any error is a bias and follows random distribution, this paper points out the misunderstanding of traditional measurement theory, subverts the traditional error category theory, gives out a new interpretation of measurement uncertainty concept, proposes abolishing the concept system of precision, trueness, and accuracy, and thereby achieves the united measurement concept system across all the disciplines, including geodesy, geomatics, metrology, instrumentation, and so on.

Spatial regression with covariate measurement error: A semiparametric approach.

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.

Accounting for unknown foster dams in the genetic evaluation of embryo transfer progeny.

Animals born by embryo transfer (ET) are usually not included in the genetic evaluation of beef cattle for preweaning growth if the recipient dam is unknown. This is primarily to avoid potential bias in the estimation of the unknown age of dam. We present a method that allows including records of calves with unknown age of dam. Assumptions are as follows: (i) foster cows belong to the same breed being evaluated, (ii) there is no correlation between the breeding value (BV) of the calf and the maternal BV of the recipient cow, and (iii) cows of all ages are used as recipients. We examine the issue of bias for the fixed level of unknown age of dam (AOD) and propose an estimator of the effect based on classical measurement error theory (MEM) and a Bayesian approach. Using stochastic simulation under random mating or selection, the MEM estimating equations were compared with BLUP in two situations as follows: (i) full information (FI); (ii) missing AOD information on some dams. Predictions of breeding value (PBV) from the FI situation had the smallest empirical average bias followed by PBV obtained without taking measurement error into account. In turn, MEM displayed the highest bias, although the differences were small. On the other hand, MEM showed the smallest MSEP, for either random mating or selection, followed by FI, whereas ignoring measurement error produced the largest MSEP. As a consequence from the smallest MSEP with a relatively small bias, empirical accuracies of PBV were larger for MEM than those for full information, which in turn showed larger accuracies than the situation ignoring measurement error. It is concluded that MEM equations are a useful alternative for analysing weaning weight data when recipient cows are unknown, as it mitigates the effects of bias in AOD by decreasing MSEP.

Research on the Measurement Error of MWIR Average Atmospheric Transmittance

The atmospheric transmittance in mid-wavelength infrared (MWIR) band reflects the characteristics of atmospheric particles, which is typically used in MWIR imaging system correction and data extraction. MWIR imager is wide spectral band instrument and its measuring output is usually affected by broadband atmospheric transmittance which is usually considered as average influence, therefore it is exactly of great importance to study the measurement of MWIR average atmospheric transmittance, which is valuable for MWIR images correction and application. A measurement error model of MWIR atmospheric transmittance was proposed according to the measuring method of the broadband average atmospheric transmittance. Because the transmittance measurement principle mentioned in this paper is indirect measurement, some direct input data are needed to be acquired through infrared imager, blackbody, etc. Finally, combining the measurement error theory with data of the experiments, the MWIR atmospheric transmittance and its measurement error are extracted. The results show that the MWIR atmospheric transmittance measured value is reasonable according to the empirical value in sunny day. And the measurement error objectively reflects most aspects of the test, exactly proving the validity of the measurement experiment.

Study on Error Compensation of Human Motion Analysis System

Human motion capture system based on a new kind of error compensation technology was developed and used this to assess human motion. On the basis of three-dimensional reconstruction and some essential factors influencing on the measurement accuracy, the measurement error theory and the modified and improved human motion analysis system was established. The experimental data indicate that the measurement precision of the modified and improved system is more precise than the original system on human motion measurement and capturing.

Quantifying and handling errors in instrumental measurements using the measurement error theory

AbstractMeasurement error modelling is used for investigating the influence of measurement/sampling error on univariate predictions of water content and water‐holding capacity (reference measurement) from nuclear magnetic resonance (NMR) relaxations (instrumental) measured on two gadoid fish species. This is a new way of using the measurement error theory. Reliability ratios illustrate that the models for the two fish species are influenced differently by the error. However, the error seems to influence the predictions of the two reference measures in the same way. The effect of using replicated x‐measurements is illustrated by simulated data and by NMR relaxations measured several times on each fish. The standard error of the physical determination of the reference values is lower than the standard error of the NMR measurements. In this case, lower prediction error is obtained by replicating the instrumental measurements. A new general formula is given for how to correct the least squares regression coefficient when a different number of replicated x‐measurements is used for prediction than for calibration. It is shown that the correction should be applied when the number of replicates in prediction is less than the number in calibration. This can be relevant for on‐line applications and in other situations where it is important to make fast measurements in the prediction phase. Copyright © 2004 John Wiley & Sons, Ltd.

Adjustment for Regression Dilution in Epidemiological Regression Analyses

PURPOSE: The term “regression dilution” describes the dilution/attenuation in a regression coefficient that occurs when a single measured value of a covariate is used instead of the usual or average value over a period of time. This paper reviews the current knowledge concerning a simple method of adjusting for regression dilution in single and multiple covariate situations and illustrates the adjustment procedure.METHODS: Formulation of the regression dilution problem as a measurement error problem allows existing measurement error theory to be applied to developing methods of adjustment for regression dilution. This theory leads to a precise method of adjustment for linear regression and approximate methods for logistic and Cox proportional hazards regression. The method involves obtaining the naive estimates of coefficients by assuming that covariates are not measured with error, and then adjusting these coefficients using reliability estimates for the covariates. Methods for estimating the reliability of covariates from the reliability and main study data and a method for the calculation of standard errors and confidence intervals for adjusted coefficients are described.RESULTS: An illustration involving logistic regression analysis of risk factors for death from cardiovascular disease based on cohort and reliability data from the Busselton Health Study shows that the different methods for estimating the adjustment factors give very similar adjusted estimates of coefficients, that univariate adjustment procedures may lead to inappropriate adjustments in multiple covariate situations, whether or not other covariates have intra-individual variation, and when the reliability study is moderate to large, the precision of the estimates of reliability coefficients has little impact on the standard errors of adjusted regression coefficients.CONCLUSIONS: The simple method of adjusting regression coefficients for “regression dilution” that arises out of measurement error theory is applicable to many epidemiological settings and is easily implemented. The choice of method to estimate the reliability coefficient has little impact on the results. The practice of applying univariate adjustments in multiple covariate situations is not recommended.

Wrapped distributions and measurement errors

For a random variableX and α>0 letUα≔nα (X)−X, wherenα(x)=n∈Z iffx∈(nα−α/2,nα+α/2]. Random variables of this type are important in the theory of measurement errors. We derive formulas for the distribution ofUα and apply them to the case X∼N(θ,σ2). General conditions for the unimodality ofUα are given. The correlation of the measurement errorsX−E (X) andUα (X) is seen to beO (αj) withj depending on the smoothness and asymptotic behavior of the density ofX. This gives a precise sense to the assertion that scale errors upwards and downwards are averagely well-balanced. In the normal case the density ofUα is shown to be constant up to\(o (e^{ - C\alpha ^{ - 2} } )\), as α→0.

An Experimental Approach to the Teaching of the Theory of Measurement Errors

The mathematics of error analysis, though reviewed in measurements books and laboratory manuals, is rarely experimentally applied at an elementary level. An approach based on experiments that investigate and specifically illustrate measurement errors on a basic level is described. The purpose in introducing these experiments on an elementary level is to develop in the student both an ability to understand and analyze experiments and data with respect to errors, and an understanding of the interrelationship between the theory and the experimental implementation of a measurement. Furthermore, there is a need for the student to be able to design measuring systems and develop techniques with minimal complexity to satisfy specific accuracy and tolerance requirements. This approach is implemented by a sequence of experiments, two of which are described in detail. The first of these experiments, "Measurement Errors," is concerned with error weights and the concepts of accuracy, precision, resolution, and consistency of measurements and measuring systems. In the second experiment described, the principles of digital and analog measurements and their associated errors are investigated.