Consideration Of Measurement Errors Research Articles

A Bayesian Approach For The Consideration Of Measurement Errors

Metrology is a key tool for tolerancing as it is used to determine whether dimensions are within their tolerance intervals. However, measurement errors cannot be avoided and need being accounted for. The probabilistic approach is applied to both the dimensions and their measurement errors; they are modelled as random variables and characterized by their probability density function. The probability density function of the measurement error is assumed to be known; this work is included in a research project in collaboration with a metrology company, where the engineers are able to provide us with this information. This paper describes a strategy to account for such measurement errors and (partially) correct or mitigate their effects. Through Bayesian inference, the likelihood of true values given measured values is estimated, allowing for a probabilistic correction. The proposed method is applied to numerical examples with simulated data and its relevance is discussed.

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise.

Introduction: Despite continued technological improvements, measurement errors always reduce or distort the information that any real experiment can provide to quantify cellular dynamics. This problem is particularly serious for cell signaling studies to quantify heterogeneity in single-cell gene regulation, where important RNA and protein copy numbers are themselves subject to the inherently random fluctuations of biochemical reactions. Until now, it has not been clear how measurement noise should be managed in addition to other experiment design variables (e.g., sampling size, measurement times, or perturbation levels) to ensure that collected data will provide useful insights on signaling or gene expression mechanisms of interest. Methods: We propose a computational framework that takes explicit consideration of measurement errors to analyze single-cell observations, and we derive Fisher Information Matrix (FIM)-based criteria to quantify the information value of distorted experiments. Results and Discussion: We apply this framework to analyze multiple models in the context of simulated and experimental single-cell data for a reporter gene controlled by an HIV promoter. We show that the proposed approach quantitatively predicts how different types of measurement distortions affect the accuracy and precision of model identification, and we demonstrate that the effects of these distortions can be mitigated through explicit consideration during model inference. We conclude that this reformulation of the FIM could be used effectively to design single-cell experiments to optimally harvest fluctuation information while mitigating the effects of image distortion.

Robust disturbance classification in power transmission systems with denoising recurrent autoencoders

The automated classification of grid disturbances based on phasor measurements is a key technology for the reliable operation of power transmission systems. The predominant use of simulated training data limits the applicability of existing classification approaches due to the missing consideration of measurement errors or data quality issues. To mitigate these shortcomings, this study presents a robust disturbance classification procedure incorporating denoising recurrent autoencoders within a novel two-stage training approach. The developed disturbance classification procedure is evaluated for different noise characteristics and dataset combinations created with an optimization based error model. Experimental results based on a generic power transmission system show superior performance of the proposed two-stage design compared to a conventional, one-stage model training.

Validity and reliability of Mini-Mental State Examination in Older Adults in China: Inline Mini-Mental State Examination with cognitive functions

The main aim of the study is to validate the factor structure of the Mini-Mental State Examination (MMSE) of China’s older population using the Chinese Longitudinal Healthy Longevity Survey. The validation process used the exploratory factor analysis (EFA) to determine the number of dimensions of MMSE, the confirmatory factor analysis (CFA) to confirm the factorial structure of MMSE, and the factorial invariance to conclude the factor structure does not differ between the young-old (aged 65 – 79) and old-old (aged 80 or older). The results of the EFAs suggested two possible factor structures: A six-factor and a seven-factor solution. The seven-factor confirmatory factor model turned out as the best fit by comparison to the four competing confirmatory models. Strict factorial invariance was attained for the two age groups, indicating a high level of measurement equality, a property of invariance was seldom achieved in the literature of factorial invariance studies. In comparison to the MMSE literature that focused solely on EFA that aims to establish a single summated score, the present study suggests using EFA, CFA, and factorial invariance that takes into consideration of measurement errors as the preferred procedure since it establishes the appropriate MMSE dimensionality that is in line with their respective cognitive functions.

A Numerical Procedure for Multivariate Calibration Using Heteroscedastic Principal Components Regression

Many methods have been developed to allow for consideration of measurement errors during multivariate data analyses. The incorporation of the error structure into the analytical framework, usually described in terms of the covariance matrix of measurement errors, can provide better model estimation and prediction. However, little effort has been made to evaluate the effects of heteroscedastic measurement uncertainties on multivariate analyses when the covariance matrix of measurement errors changes with the measurement conditions. For this reason, the present work describes a new numerical procedure for analyses of heteroscedastic systems (heteroscedastic principal component regression or H-PCR) that takes into consideration the variations of the covariance matrix of measurement fluctuations. In order to illustrate the proposed approach, near infrared (NIR) spectra of xylene and toluene mixtures were measured at different temperatures and stirring velocities and the obtained data were used to build calibration models with different multivariate techniques, including H-PCR. Modeling of available xylene–toluene NIR data revealed that H-PCR can be used successfully for calibration purposes and that the principal directions obtained with the proposed approach can be quite different from the ones calculated through standard PCR, when heteroscedasticity is disregarded explicitly.

A Nonlinear Observer SOC Estimation Method Based on Electrochemical Model for Lithium-Ion Battery

As the global environmental pollution and energy crisis become more serious, lithium-ion batteries (LIB) received an increasing research interest due to their low self-discharge rates, long cycle life, and high power density for the transportation applications. Battery management system (BMS) plays an essential part for the LIB system as it can guarantee an efficient and stable operation through LIB state of charge (SOC) estimation. In this article, a nonlinear observer with terminal voltage feedback injection (VFNO) is designed based on the electrochemical single particle (SP) model to monitor the SOC of LIB. The convergence of the SP-VFNO system in consideration of measurement error is proved in terms of Lyapunov stability theory. The current, the terminal voltage, and the SOC reference value are measured in the battery testing system. Besides, the extended Kalman filter (EKF) based on both the SP model and the second-order resistor-capacitor (SORC) model to estimate SOC is adopted for comparison. The experimental results indicate that the proposed SP-VFNO method has superiority with a faster convergence rate and a higher estimation precision, which can help the accurate SOC estimation for BMS in practical application.

Nonlinear Step-Stress Accelerated Degradation Modeling and Remaining Useful Life Estimation Considering Multiple Sources of Variability

In the absence of sufficient degradation data of long-lifetime and highly reliable products, a step-stress accelerated degradation model based on nonlinear diffusion process is proposed to estimate the remaining useful life (RUL), with the advantage of requiring small sample size and short test time. For multiple uncertainties caused by inherent properties, individual differences, measurement equipment performance and artificial deviations in the degradation process, this model considers the temporal variability, unit-to-unit variability and measurement errors in both performance degradation and covariates. To estimate the RUL, we derive an analytical approximation to the first hitting time (FHT) of the nonlinear diffusion process crossing a predetermined threshold with the consideration of measurement errors. Based on maximum likelihood estimation (MLE), a modified simulation and extrapolation (SIMEX) method, called MLE-SIMEX, is developed for estimating unknown parameters in the established model. The usefulness of the proposed model is demonstrated by a simulation case and a real-world example. The results reveal that considering nonlinearity and multiple sources of variability in the step-stress accelerated degradation process can improve the model fitting and the accuracy of RUL estimation.

Краткосрочное прогнозирование процессов качки корабля с учетом ошибок измерений

Краткосрочное прогнозирование процессов качки корабля с учетом ошибок измерений

把握力調整能力の定量的評価デバイスにおける測定誤差の検討

把握力調整能力の定量的評価デバイスにおける測定誤差の検討

Damage Detection Using Improved Direct Stiffness Calculations — A Case Study

The improved direct stiffness calculation (DSC) is a simple and relatively practical technique to estimate the bending stiffness along beam-type structures based on modal parameters and thus to assess damage in the structure. Application of this technique to a real continuous bridge, named Truckee River Bridge (TRB) in California, is presented in this paper. Comparing the stiffness estimated from baseline condition with that obtained from different damage scenarios in consideration of measurement errors, the damage location and its severity were reliably estimated. Moreover, the improved DSC technique is extended to detect the damage with material nonlinearity, which is simulated with pushover and time-history analyses using one earthquake event. The results of this case study show that the DSC is valid and efficient for identifying the damage with material nonlinearity in beam-type bridges using low-order mode shapes, which is advantageous for in-suit structural health monitoring applications.

Process performance evaluation based on Taguchi capability index with the consideration of measurement errors

Most research works related to process capability analysis are carried out under the assumption of no gauge measurement errors. Unfortunately, such an assumption does not adequately accommodate real-world situations even with modern, highly sophisticated measuring instruments and devices. Estimating and testing process capability without considering gauge measurement errors may often lead to unreliable decisions. Thus, how to accurately measure process performance in the presence of measurement errors becomes a critical and essential task. This article applies the concept of generalised confidence intervals to evaluate process performance based on Taguchi capability index Cpm with the consideration of measurement errors. To investigate the performance of the proposed method, a series of simulations was undertaken. A sensitivity study on the effects of ignoring measurement errors was also carried out. The results reveal that the proposed method performs very well for evaluating process performance when measurement errors are present or not.

An age-structured state-space stock–recruit model for Pacific salmon (Oncorhynchusspp.)

We describe an age-structured state-space model for stock–recruit analysis of Pacific salmon data. The model allows for incorporation of process variation in stock productivity, recruitment, and maturation schedules, as well as observation error in run abundance, harvest, and age composition. Explicit consideration of age structure allows for realistic depiction of system dynamics and sample design, more complete use of recent data, and forecasts that consider sibling relationships. A Bayesian framework is adopted, implemented with Markov chain Monte Carlo methods, which provides an enhanced ability to incorporate auxiliary information, convenient and rigorous consideration of measurement error and missing data, and a more complete assessment of uncertainty. We fit the model to annual upstream weir counts, commercial and recreational harvest estimates, and age composition data from Chinook salmon (Oncorhynchus tshawytscha) in Karluk River, Alaska. For the case study, the model is configured with a Ricker stock–recruit relationship, autoregressive lag-1 productivity, and Dirichlet age-at-maturity. Details of alternate configurations are also described. We introduce the optimal yield probability profile as an objective tool for informing the selection of escapement goals based on yield considerations and describe alternative versions useful for addressing other management questions.

Generalized Inference for Measuring Process Yield With the Contamination of Measurement Errors—Quality Control for Silicon Wafer Manufacturing Processes in the Semiconductor Industry

The yield index Spk provides an exact measure of process yield for normally distributed processes, and it has been popularly accepted by many engineers and shop floor controllers as communication tools for evaluating and improving the manufacturing quality. Most research works related to Spk are carried out under the assumption of no gauge measurement errors. Unfortunately, such an assumption does not accommodate real situations closely even with modern and highly sophisticated measuring instruments. Conclusions drawn from process capability analysis without considering measurement errors are hence unreliable. Recently, Wang studied the impact of the process yield estimation and judgment on the true process yield in the presence of measurement errors and indicated that the presence of measurement errors in the data leads to different behaviors of the estimator according to the entity of the contamination degree. To remedy this, this paper applies the concept of generalized pivotal quantities to construct generalized confidence intervals for Spk with consideration of measurement errors. A series of simulations was undertaken to evaluate the performance of the proposed generalized inference method. The results reveal that the generalized inference method performs very well for measuring process yield in the presence of measurement errors.

An Improved Direct Stiffness Calculation Technique for Damage Detection of Bending Structures

In this paper, a practical application for a continues beam-type bridge, the Truckee river bridge, California, to test the validity of the improved DSC method in the identification of the bridge damage after severe loading such as that caused by an earthquake was discussed. Comparing the calculated stiffness from the improved DSC method with that from design data of the bridge based on the numerical simulation with different damage scenarios in consideration of measurement errors, the location and severity of the damage in the bridge can be accurately and reliably detected. The pushover and seismic damage assessment analysis shows that the improved DSC is valid and efficient for damage detection in highway bridges.

Nonlinear Elasto-Mammography for Characterization of Breast Tissue Properties

Quantification of the mechanical behavior of normal and cancerous tissues has important implication in the diagnosis of breast tumor. The present work extends the authors' nonlinear elastography framework to incorporate the conventional X-ray mammography, where the projection of displacement information is acquired instead of full three-dimensional (3D) vector. The elastic parameters of normal and cancerous breast tissues are identified by minimizing the difference between the measurement and the corresponding computational prediction. An adjoint method is derived to calculate the gradient of the objective function. Simulations are conducted on a 3D breast phantom consisting of the fatty tissue, glandular tissue, and cancerous tumor, whose mechanical responses are hyperelastic in nature. The material parameters are identified with consideration of measurement error. The results demonstrate that the projective displacements acquired in X-ray mammography provide sufficient constitutive information of the tumor and prove the usability and robustness of the proposed method and algorithm.

QMRA and decision-making: Are we handling measurement errors associated with pathogen concentration data correctly?

Knowledge of the variability in pathogen or indicator concentrations over time at a particular location (e.g. in drinking water sources) is essential in implementation of concentration-based regulations and in quantitative microbial risk assessment. Microbial enumeration methods, however, are known to yield highly variable counts (even among replicates) and some methods are prone to substantial losses (i.e. only a fraction of the target microorganisms in a sample are observed). Consequently, estimated microorganism concentrations may be biased and only a fraction of the variability that is observed in temporally distributed concentration estimates is due to variability in concentration itself. These issues have often been ignored in the past, and approaches to integrate knowledge about the measurement error associated with enumeration methods into decisions have not been standardized. Here, an existing model that describes variability in microorganism counts as a function of sample volume and the analytical recovery of the enumeration method is expanded to include temporal concentration variability and sample-specific recovery information. This model is used to demonstrate that microorganism counts and analytical recovery are not independent (as has often been assumed), even if the correlation is obscured by other sources of variability in the data. It is also used as an experimental design tool to evaluate strategies that may yield more accurate concentration estimates. Finally, the model is implemented in a Bayesian framework (with a Gibbs sampling algorithm) to quantify temporal concentration variability with appropriate consideration of measurement errors in the data and the analytical recovery of the enumeration method. We demonstrate by simulation that this statistical approach facilitates risk analyses that appropriately model variability in microorganism concentrations given the available data and that it enables decisions based on quantitative measures of uncertainty.

Defensible Progress Monitoring Data for Medium- and High-Stakes Decisions

Within a response to intervention model, educators increasingly use progress monitoring (PM) to support medium- to high-stakes decisions for individual students. For PM to serve these more demanding decisions requires more careful consideration of measurement error. That error should be calculated within a fixed linear regression model rather than a classical test theory model, which has been more common. Seven practical skills are described for improving the use of PM data for medium- to high-stakes decisions: (a) estimating a static performance level in PM, (b) fitting a level of confidence to an educational decision, (c) expressing an estimated score ( Yhat) with its measurement error, (d) judging reliable improvement from one time to a later time, (e) properly using slope versus trendedness, (f) expressing “rate of improvement” (slope) with error, and (g) controlling autocorrelation. An example data set and PM graphs are used to illustrate each.

Regression-based process monitoring with consideration of measurement errors

Multivariate process monitoring and fault detection is an important problem in quality improvement. Most existing methods are based on a common assumption that the measured values of variables are the true values, with limited consideration of the various types of measurement errors embedded in the data. On the other hand, research on measurement errors has been conducted from a pure theoretical statistics point of view, without any linking of the modeling and analysis of measurement errors with monitoring and fault detection objectives. This paper proposes a method for multivariate process monitoring and fault detection considering four types of major measurement errors, including sensor bias, sensitivity, noise and dependency of the relationship between a variable and its measured value on some other variables. This method includes the design of new control charts based on data with measurement errors, and identification of the maximum allowable measurement errors to fulfill certain fault detectability requirements. This method is applicable to processes where the natural ordering of the variables is known, such as for cascade or multistage processes, and processes where the causal relationships among variables are known and can be described by a Bayesian network. The method is demonstrated in two industrial processes.

In-situ alignment calibration of attitude and ultra short baseline sensors for precision underwater positioning

Positioning accuracy of an ultra short baseline (USBL) tracking system is significantly reduced with the increase of alignment errors in the installation of sensors. Although techniques for sensor alignment calibration have been developed, they are either complex or lacking in rigor. This study proposes an algorithm to estimate the angular misalignments of a USBL transceiver relative to attitude sensors. The numerical algorithm is based on the positioning errors caused by heading, pitch, and roll misalignments, respectively, when running a circular survey around a seabed transponder. The positioning errors introduced by the angular misalignments outline an iterative scheme of estimating the roll alignment error first, next the heading alignment error, and then finally the pitch alignment error. This makes possible the efficient estimation of all angular misalignments with a high degree of accuracy. With the consideration of measurement error and executing a non-centered and non-perfect circle around the true transponder position, numerical simulations are performed to validate the effectiveness of the proposed algorithm. The simulation results show that the proposed algorithm is robust to the effects of measurement error, non-centered circles, and non-perfect circles. Moreover, the estimates converge fairly quickly, and can be achieved with good accuracy in only a few iterations.

What They See Is What We Get

Several alternative response formats are available to the web survey designer, but the choice of format is often made with little consideration of measurement error. The authors experimentally explore three common response formats used in web surveys: a series of radio buttons, a drop box with none of the options initially displayed until the respondent clicks on the box, and a scrollable drop box with some of the options initially visible, requiring the respondent to scroll to see the remainder of the options. The authors reversed the order of the response options for half the sample. The authors find evidence of response order effects but stronger evidence that visible response options are endorsed more frequently, suggesting that visibility may be a more powerful effect than primacy in web surveys. The results suggest that the response format used in web surveys does affect the choices made by respondents.