Effect Of Random Measurement Errors Research Articles

A New Three-Dimensional Empirical Reconstruction Model Using a Stochastic Optimization Method

Motivated by MMS mission observations near magnetic reconnection sites, we have developed a new empirical reconstruction (ER) model of the three-dimensional (3D) magnetic field and the associated plasma currents. Our approach combines both the measurements from a constellation of satellites and a set of physics-based equations as physical constraints to build spatially smooth distributions. This ER model directly minimizes the loss function that characterizes the model-measurement differences and the model departures from linear or nonlinear physical constraints using an efficient stochastic optimization method by which the effects of random measurement errors can be effectively included. Depending on the availability of the measured parameters and the adopted physical constraints on the reconstructed fields, the ER model could be either slightly over-determined or under-determined, yielding nearly identical reconstructed fields when solved by the stochastic optimization method. As a result, the ER model remains valid and operational even if the input measurements are incomplete. Two sets of new indices associated respectively with the model-measurement differences and the model departures are introduced to objectively measure the accuracy and quality of the reconstructed fields. While applying the reconstruction model to observations of an electron diffusion region (EDR) observed by NASA’s Magnetospheric Multiscale (MMS) mission, we examine the relative contributions of the errors in the plasma current density arising from random measurement errors and linear approximations made in application of the curlometer technique. It was found that the errors in the plasma current density calculated directly from the measured magnetic fields using a linear approximation were mostly contributed from the nonlinear configuration of the 3D magnetic fields.

Correction of residence time distributions and hydraulic indexes affected by tracer release duration in surface flow constructed wetlands

In tracer experiments of surface flow constructed wetlands, residence time distributions (RTDs) are generally originated from the normalized concentration data of recovered tracers based on ideal instantaneous tracer release mode. However, this tracer release mode is commonly approximated by finite-continuous tracer release over a relatively short duration. As a result, the accuracy of RTDs and hydraulic indexes cannot be guaranteed if the RTD data and index values were still calculated based on the instantaneous release. To solve this problem, a method for correcting the original RTD data and the index values affected by tracer release duration was proposed. The correction of hydraulic indexes can be performed using analytical formulas, whereas the correction of the RTDs requires an RTD model (such as the gamma distribution and one-dimensional advection-dispersion model) or a smoothing algorithm (such as the simple moving average algorithm) to avoid the increasing effect of random measurement errors caused by the direct use of the RTD correction formulas. The correction method was successfully verified by a specially designed tracer test, and its practical application effect was exemplified. A Monte Carlo test also proved that the RTD correction owed certain robustness to tracer release instability, while the correction of some hydraulic indexes that reflect flow dispersion and comprehensive hydraulic efficiency had inferior robustness. Aside from this, the influence of tracer release duration on RTDs and hydraulic indexes without any correction was analyzed. It was found that the release duration caused the shape of the original RTDs to be more skewed in the positive direction of the x-axis and changed from “thin and high” to “fat and short”, while the duration of the release caused the positive relative errors of most indexes, which became more serious with an increase in the duration or worsening hydraulic performance. Based on these influence rules, 0.01 was defined as the threshold of the normalized release duration which needs to correct RTDs and hydraulic indexes, considering that the relative errors between the uncorrected and corrected indexes were less than 5% when the normalized duration was less than this threshold.

Effects of Random Measurement Error on Lung Cancer Screening Decisions: A Retrospective Cohort-Based Microsimulation Study

Self-reported tobacco pack-year history plays a large role in decisions about low-dose CT screening for lung cancer, yet is challenging to measure accurately. To what extent does random measurement error in pack-year information impact screening decisions and screening effectiveness? Retrospective cohort study of 10,449 patients with pack-year history documented at least twice between October 2013 and July 2017 across 8 academic Veterans Affairs sites. Outcome measures included (1) observed reliability of pack-year information based on all repeat measures for the study population and (2) each person's statistically "true" pack-year information based on best linear unbiased predictor from a multilevel linear random effects model. To examine how unreliability leads to misclassification of screening eligibility and inaccuracy in estimating lung cancer risk, we simulated pack-year observations for each person, first comparing simulated pack-year and lung cancer risk values with true values, then comparing outcomes when basing screening decisions on unreliable pack-year information vstrue information. Reliability of assessing pack-year information in routine practice varied across sites. Thus, we examined the clinical impact of two different levels of reliability, based on the range of intraclass correlation coefficients observed. Using a≥ 30-pack-year threshold led to a high rate of eligibility misclassifications (48.1%misclassified with higher reliability pack-year information and 60.7%misclassified with lower reliability information). However, using a lung cancer risk threshold leads to fewer misclassifications (47.3%-49.7%misclassified when using lower reliability pack-year information) and maintains screening effectiveness better when using unreliable pack-year information. Random error in real-world pack-year assessments leads to a substantial rate of misclassifying who should be offered CT screening if a≥ 30-pack-year criterion is used. However, using a lung cancer risk threshold mitigates the impact of unreliable pack-year information. Decision-makers concerned about the impact of unreliable pack-year information should consider using risk-based approaches to CT screening.

Sensor Network Robustness Using Model-Based Data Reconciliation for Continuous Tablet Manufacturing

Advances in continuous manufacturing in the pharmaceutical industry necessitate reliable process monitoring systems that are capable of handling measurement errors inherent in all sensor technologies and detecting measurement outliers to ensure operational reliability. The purpose of this work was to demonstrate data reconciliation (DR) and gross error detection methods as real-time process management tools to accomplish robust process monitoring. DR mitigates the effects of random measurement errors, while gross error detection identifies nonrandom sensor malfunctions. DR is an established methodology in other industries (i.e., oil and gas) and was recently investigated for use in drug product continuous manufacturing. This work demonstrates the development and implementation of model-based steady-state data reconciliation on 2 different end-to-end continuous tableting lines: direct compression and dry granulation. These tableting lines involve different equipment and sensor configurations, with sensor network redundancy achieved using equipment-embedded sensors and in-line process analytical technology tools for the critical process parameters and critical quality attributes. The nonlinearity of the process poses additional challenges to solve the steady-state data reconciliation optimization problem in real time. At-line and off-line measurements were used to validate the framework results.

Sensitivity studies on a novel nuclear forensics methodology for source reactor-type discrimination of separated weapons grade plutonium

Abstract A recently published nuclear forensics methodology for source discrimination of separated weapons-grade plutonium utilizes intra-element isotope ratios and a maximum likelihood formulation to identify the most likely source reactor-type, fuel burnup and time since irradiation of unknown material. Sensitivity studies performed here on the effects of random measurement error and the uncertainty in intra-element isotope ratio values show that different intra-element isotope ratios have disproportionate contributions to the determination of the reactor parameters. The methodology is robust to individual errors in measured intra-element isotope ratio values and even more so for uniform systematic errors due to competing effects on the predictions from the selected intra-element isotope ratios suite. For a unique sample-model pair, simulation uncertainties of up to 28% are acceptable without impeding successful source-reactor discrimination. However, for a generic sample with multiple plausible sources within the reactor library, uncertainties of 7% or less may be required. The results confirm the critical role of accurate reactor core physics, fuel burnup simulations and experimental measurements in the proposed methodology where increased simulation uncertainty is found to significantly affect the capability to discriminate between the reactors in the library.

Steady-State Data Reconciliation Framework for a Direct Continuous Tableting Line.

Reliable process monitoring in real-time remains a challenge for the pharmaceutical industry. Dealing with random and gross errors in the process measurements in a systematic way is a potential solution. In this paper, we present a process model-based framework, which for given sensor network and measurement uncertainties will predict the most likely state of the process. Thus, real-time process decisions, whether for process control or exceptional events management, can be based on the most reliable estimate of the process state. Reliable process monitoring is achieved by using data reconciliation (DR) and gross error detection (GED) to mitigate the effects of random measurement errors and non-random sensor malfunctions. Steady-state data reconciliation (SSDR) is the simplest forms of DR but offers the benefits of short computational times. We also compare and contrast the model-based DR approach (SSDR-M) to the purely data-driven approach (SSDR-D) based on the use of principal component constructions. We report the results of studies on a pilot plant-scale continuous direct compression-based tableting line at steady-state in two subsystems. If the process is linear or mildly nonlinear, SSDR-M and SSDR-D give comparable results for the variables estimation and GED. SSDR-M also complies with mass balances and estimate unmeasured variables. SSDR successfully estimates the true state of the process in presence of gross errors, as long as steady state is maintained and the redundancy requirement is met. Gross errors are also detected while using SSDR-M or SSDR-D. Process monitoring is more reliable while using the SSDR framework.

Random measurement error: Why worry? An example of cardiovascular risk factors.

With the increased use of data not originally recorded for research, such as routine care data (or ‘big data’), measurement error is bound to become an increasingly relevant problem in medical research. A common view among medical researchers on the influence of random measurement error (i.e. classical measurement error) is that its presence leads to some degree of systematic underestimation of studied exposure-outcome relations (i.e. attenuation of the effect estimate). For the common situation where the analysis involves at least one exposure and one confounder, we demonstrate that the direction of effect of random measurement error on the estimated exposure-outcome relations can be difficult to anticipate. Using three example studies on cardiovascular risk factors, we illustrate that random measurement error in the exposure and/or confounder can lead to underestimation as well as overestimation of exposure-outcome relations. We therefore advise medical researchers to refrain from making claims about the direction of effect of measurement error in their manuscripts, unless the appropriate inferential tools are used to study or alleviate the impact of measurement error from the analysis.

Dynamic characterizations of underwater structures using noncontact vibration tests based on nanosecond laser ablation in water: evaluation of passive vibration suppression with damping materials

Recently, the demand for higher performing underwater structures under diverse conditions has increased. Examples include improved precision and speed of the position control of robot manipulators. To prevent the control spillover problems when active controls are used, a control system is typically constituted with a low-pass filter to eliminate all modes except for the target modes. However, experimentally measuring the dynamic properties of an underwater structure in an environment where the structure and a fluid continuously influence each other is difficult. We have recently proposed a noncontact vibration testing method for dynamic characterizations of underwater structures in which the response to a laser ablation excitation force is measured by laser Doppler vibrometer. Integrating passive control using a vibration-damping material affixed onto the underwater structure and active control constituted with the low-pass filter may realize a more cost-effective system. To develop this combined control into a practical method, the reliability of the measured frequency response function must be validated. Additionally, the applicable frequency range must be expanded to encompass the high-frequency region (several tens of kHz) so that the vibration suppression quality of underwater structures can be evaluated. Herein we quantify the effect of random measurement errors on the measured frequency response function with a reliability factor based on the concept of coherence functions. Using the measured frequency response function with a reliability factor, we demonstrated that our method can evaluate passive vibration suppression effect of an underwater structure with a damping material in high-frequency ranges up to 20 kHz.

Application of Monte Carlo method to statistical testing in deformation analysis based on robust M-estimation

In deformation analysis of geodetic control networks, it is important to know whether the estimated displacement value of a given point is the effect of displacement or only the effect of random measurement errors. The F-test of statistical significance is used to answer this question. This test is applied both in conventional deformation analysis (CDA) based on least square (LS) estimation and in deformation analysis based on robust M-estimation. Unfortunately, the F-test is strongly flawed in the latter case. As a consequence, its results are significantly different here than assumed/expected. This paper analyses how flawed the F-test is and proposes a new solution. First, the algorithm of the global and local F-tests was derived. It was then demonstrated that for deformation analysis based on robust M-estimation, this algorithm has theoretical flaws. Next, it was shown how these problems can be solved numerically. The basis of the solutions proposed involves the use of stochastic simulations and, more specifically, the Monte Carlo (MC) method. Moreover, it was noted that other statistical test problems which also occur in deformation analysis based on robust M-estimation can be solved using present-day computers. The numerical approach can be a good support here in the selection of the proper significance level as well as in the correct performance of the test sensitivity analysis. All theoretical discussions were verified on an example simulated control network.

Identification of materials in a hyperbolic annular fin for a given temperature requirement

This article deals with the prediction of parameters in an annular hyperbolic fin with temperature-dependent thermal conductivity. Three parameters such as thermal conductivity, variable conductivity coefficient and the surface heat transfer coefficient have been predicted for satisfying a prescribed temperature distribution on the surface of fin. This is achieved by a hybrid differential evolution-nonlinear programming optimization method. The effect of random measurement errors is also considered. It is observed from the present inverse analysis that many feasible materials exist satisfying the given temperature distribution, thereby providing engineering flexibility in selecting any material from the available choices. For a given material, this is possible by regulating the surface heat transfer coefficient.

Forward and inverse solutions of a conductive, convective and radiative cylindrical porous fin

This paper deals with the numerical study of a conductive, convective and radiative cylindrical porous fin. At first, Runge–Kutta method-based numerical solution is obtained for calculating the temperature distribution, and then an inverse problem is solved for estimation of unknown parameters. Five critical parameters such as the porosity, emissivity, solid thermal conductivity, thickness and the permeability have been simultaneously predicted for satisfying a prescribed temperature distribution on the surface of the porous fin. This is achieved by solving an inverse problem using the hybrid evolutionary–nonlinear programming optimization algorithm. The effect of random measurement errors between ±10% has been considered. The estimated values of non-dimensional entities such as porosity and surface emissivity are found to be approximately within the range, 0.28–0.92 and 0.27–0.75, respectively. Additionally, the thermal conductivity, thickness and the permeability are found to be almost between 17 and 140W/mK, 8.7×10−4 to 0.007m and 2×10−11 to 5×10−8m2, respectively. The present study reveals that many feasible combinations of available materials satisfy the same temperature field, thus providing an opportunity for selecting any combination from the available alternatives. Moreover, the hybrid method is found to perform better and yield relatively faster convergence than individual methods. The sensitivity analysis reveals that the effect of fin permeability on the temperature field is considerably high than other parameters.

Application of decomposition method and inverse prediction of parameters in a moving fin

The application of the Adomian decomposition method (ADM) is extended to study a conductive–convective and radiating moving fin having variable thermal conductivity. Next, through an inverse approach, ADM in conjunction with a binary-coded genetic algorithm (GA) is also applied for estimation of unknown properties in order to satisfy a given temperature distribution. ADM being one of the widely-used numerical methods for solving non-linear equations, the required temperature field has been obtained using a forward method involving ADM. In the forward problem, the temperature field and efficiency are investigated for various parameters such as convection–conduction parameter, radiation–conduction parameter, Peclet number, convection sink temperature, radiation sink temperature, and dimensionless thermal conductivity. Additionally, in the inverse problem, the effect of random measurement errors, iterative variation of parameters, sensitivity coefficients of unknown parameters are investigated. The performance of GA is compared with few other optimization methods as well as with different temperature measurement points. It is found from the present study that the results obtained from ADM are in good agreement with the results of the differential transformation method available in the literature. It is also observed that for satisfactory reconstruction of the temperature field, the measurement error should be within 8% and the temperature field is strongly dependent on the speed than thermal parameters of the moving fin.

Estimating true standard deviations.

Estimating true standard deviations.

‘Maybe I'm not as good as I think I am.’ How qualification users interpret their examination results

Background: Assessment grades are ‘estimates’ of ability or performance and there are many reasons why an awarded grade might not meet a candidate's expectations, being either better or poorer than anticipated. Although there may be some obvious reasons for grade discrepancies, such as a lack of preparation or under-performance, there are a number of technical issues to consider, such as the potential effects of random measurement error, human error and grade misclassification. However, traditionally, there has been limited information available to the public about such issues. Purpose: This study formed part of a two-year investigation into the reliability of public examination outcomes in England and the current paper explores participants’ narratives relating to one of the themes that emerged from the study of public perceptions of assessment reliability. It examines how individuals interpreted and rationalised their examination results, particularly those that failed to meet expectations, and discusses the impact that such results may have on individuals’ academic self-concept. Sample and method: Ten focus groups were conducted across five qualification user groups: two each with employees, employers, teachers, trainee teachers, and job-seekers (74 participants in total). A flexible discussion schedule was employed to explore participants’ experiences and perceptions of assessment reliability. Main findings: Participants tended to internalise ‘blame’ for results that were poorer than expected by constructing explanations that focused on a perceived lack of preparation, ability or knowledge. These experiences appeared to have a negative impact on individuals' academic self-concept. Secondary school teacher participants shared experiences of marking, technical and standard setting errors, and were more aware than other qualification user groups of the external factors that can impact on assessment outcomes. Conclusion: Examination results that are poorer than expected can threaten individuals’ academic self-concept, confidence in their ability, and influence their study and career intentions and opportunities. A better understanding of educational measurement issues may offer individuals a more informed framework for understanding their examination results, especially where results do not meet expectations.

Error Propagation in Contact Resistivity Extraction Using Cross-Bridge Kelvin Resistors

The cross-bridge Kelvin resistor is a commonly used method for measuring contact resistivity (ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ). For low ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> , the measurement has to be corrected for systematic error using measurements of contact resistance, semiconductor sheet resistance, and device dimensions. However, it is not straightforward to estimate the propagation of random measurement error in the measured quantities on the extracted ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> . In this paper, a method is presented to quantify the effect of random measurement error on the accuracy of ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> extraction. This is accomplished by generalized error propagation curves that show the error in ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> caused by random measurement errors. Analysis shows that when the intrinsic resistance of the contact is smaller than the semiconductor sheet resistance, it becomes important to consider random error propagation. Comparison of literature data, where ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> <; 5 ·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> Ω · cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> has been reported, shows that care should be taken since, even assuming precise electrical data, a 1% error in the measurement of device dimensions can lead to up to ~ 50% error in the estimation of ρ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> .

Estimating the timing of diet shifts using stable isotopes

Stable isotope analysis has become an important tool in studies of trophic food webs and animal feeding patterns. When animals undergo rapid dietary shifts due to migration, metamorphosis, or other reasons, the isotopic composition of their tissues begins changing to reflect that of their diet. This can occur both as a result of growth and metabolic turnover of existing tissue. Tissues vary in their rate of isotopic change, with high turnover tissues such as liver changing rapidly, while relatively low turnover tissues such as bone change more slowly. A model is outlined that uses the varying isotopic changes in multiple tissues as a chemical clock to estimate the time elapsed since a diet shift, and the magnitude of the isotopic shift in the tissues at the new equilibrium. This model was tested using published results from controlled feeding experiments on a bird and a mammal. For the model to be effective, the tissues utilized must be sufficiently different in their turnover rates. The model did a reasonable job of estimating elapsed time and equilibrial isotopic changes, except when the time since the diet shift was less than a small fraction of the half-life of the slowest turnover tissue or greater than 5-10 half-lives of the slowest turnover tissue. Sensitivity analyses independently corroborated that model estimates became unstable at extremely short and long sample times due to the effect of random measurement error. Subject to some limitations, the model may be useful for studying the movement and behavior of animals changing isotopic environments, such as anadromous fish, migratory birds, animals undergoing metamorphosis, or animals changing diets because of shifts in food abundance or competitive interactions.

Flow-mediated dilation in human brachial artery after different circulatory occlusion conditions.

Different magnitudes and durations of postocclusion reactive hyperemia were achieved by occluding different volumes of tissue with and without ischemic exercise to test the hypotheses that flow-mediated dilation (FMD) of the brachial artery would depend on the increase in peak flow rate or shear stress and that the position of the occlusion cuff would affect the response. The brachial artery FMD response was observed by high-frequency ultrasound imaging with curve fitting to minimize the effects of random measurement error in eight healthy, young, nonsmoking men. Reactive hyperemia was graded by 5-min occlusion distal to the measurement site at the wrist and the forearm and proximal to the site in the upper arm. Flow was further increased by exercise during occlusion at the wrist and forearm positions. For the two wrist occlusion conditions, flow increased eightfold and FMD was only 1 to 2% (P > 0.05). After the forearm and upper arm occlusions, blood flow was almost identical but FMD after forearm occlusions was 3.4% (P < 0.05), whereas it was significantly greater (6.6%, P < 0.05) and more prolonged after proximal occlusion. Forearm occlusion plus exercise caused a greater and more prolonged increase in blood flow, yet FMD (7.0%) was qualitatively and quantitatively similar to that after proximal occlusion. Overall, the magnitude of FMD was significantly correlated with peak forearm blood flow (r = 0.59, P < 0.001), peak shear rate (r = 0.49, P < 0.002), and total 5-min reactive hyperemia (r = 0.52, P < 0.001). The prolonged FMD after upper arm occlusion suggests that the mechanism for FMD differs with occlusion cuff position.

Effects of exposure measurement error when an exposure variable is constrained by a lower limit.

Epidemiologic studies routinely suffer from bias due to exposure measurement error. In this paper, the authors examine the effect of measurement error when the exposure variable of interest is constrained by a lower limit. This is an important consideration, since often in epidemiologic studies an exposure variable is constrained by a lower limit such as zero or a nonzero detection limit. In this paper, attenuation of exposure-disease associations is defined within the framework of a classical model of uncorrelated additive error. Then, the special case of nonlinearity due to the effect of a lower threshold is examined. A general model is developed to characterize the effect of random measurement error when there is a lower threshold for recorded values. Findings are illustrated under the assumption that the true exposure follows the lognormal and gamma distributions. The authors show that the direction and magnitude of bias in estimated exposure-response associations depends on the population distribution of the exposure, the magnitude of the recording threshold, the value assigned to below-threshold measurement results, and the variance in the measured exposure due to random measurement error.

Study of surface nuclear magnetic resonance inverse problems

Motivated by the recent application of the Earth-field nuclear magnetic resonance (NMR) technique to the detection and mapping of subsurface groundwater (to depths of 100 m or so), and making use of a recently developed theory of the method, we consider in detail the resulting inverse problem, namely the inference of the subsurface water distribution from a given sequence of NMR voltage measurements. We consider the simplest case of horizontally stratified water distributions in a horizontally stratified conducting Earth. Inversion methods based both on the singular value decomposition (SVD) and Monte Carlo are used and compared. The effects of random measurement errors and of systematic errors in the assumed subsurface conductivity structure are studied. It is found that an incorrectly modeled highly conducting layer leads to a “screening effect” in which the water content of layers lying below it is severely underestimated. We investigate also the ability of different source-receiver loop geometries to provide complementary information that may improve a combined inversion. Finally, inversion of experimental data from Cherry Creek, CO, USA is performed. Since only the absolute magnitude of the NMR voltage is measured accurately, a nonlinear Monte Carlo inversion is performed.

Determining the mass density along magnetic field lines from toroidal eigenfrequencies

Toroidal eigenfrequencies can be used to remotely sense the equatorial mass density ρeq and the density dependence along a magnetic field line. Here we present improvements to the method of Schulz [1996], which allows ρeq and the power law index α (for mass density along a field line ∝ R−α, where R is the radial distance from the center of the Earth) to be determined from the y intercept and slope of a plot of toroidal frequency versus toroidal harmonic number n. Our modifications include a model form for eigenfrequencies with a fractional precision of 0.0005 for −6 ≤ α ≤ 6 and 2 ≤ L ≤ 8 (accuracy is doubtful beyond L = 5) and an iterative procedure for getting more accurate results than those found using Schulz's method. In addition, we do an analysis of the effect of random measurement errors. Observed frequencies need to be accurate to ∼6% (3%) of the fundamental frequency in order to determine ρeq (α) to a precision of 30% (unity). We then apply our method to data generated using the Global Core Plasma Model for plasmaspheric mass density; our analysis demonstrates clearly how the α index represents the mass density dependence on the outer part of the field line (R/(LRE) ≳ 2/3).