Normal Measurement Error Research Articles

Error Analysis of Normal Surface Measurements Based on Multiple Laser Displacement Sensors.

The robotic drilling of assembly holes is a crucial process in aerospace manufacturing, in which measuring the normal of the workpiece surface is a key step to guide the robot to the correct pose and guarantee the perpendicularity of the hole axis. Multiple laser displacement sensors can be used to satisfy the portable and in-site measurement requirements, but there is still a lack of accurate analysis and layout design. In this paper, a simplified parametric method is proposed for multi-sensor normal measurement devices with a symmetrical layout, using three parameters: the sensor number, the laser beam slant angle, and the laser spot distribution radius. A normal measurement error distribution simulation method considering the random sensor errors is proposed. The measurement error distribution laws at different sensor numbers, the laser beam slant angle, and the laser spot distribution radius are revealed as a pyramid-like region. The influential factors on normal measurement accuracy, such as sensor accuracy, quantity and installation position, are analyzed by a simulation and verified experimentally on a five-axis precision machine tool. The results show that increasing the laser beam slant angle and laser spot distribution radius significantly reduces the normal measurement errors. With the laser beam slant angle ≥15° and the laser spot distribution radius ≥19 mm, the normal measurement error falls below 0.05°, ensuring normal accuracy in robotic drilling.

Optimizing fault diagnosis for electric vehicle battery systems: Improved Giza pyramids construction and advanced gradient boosting decision trees

This manuscript proposes an online multi-fault diagnostic technique for the series string batteries in electric vehicles to identify and diagnose external/internal short circuits, sensor faults, and connection fault detection. The proposed technique combines the Improved Giza Pyramids Construction and Gradient Boosting Decision Trees. Many variables, including road conditions, electromagnetic interference, and driving habits, may complicate the battery fault system, multi-parameter or non-linear coupling, making it challenging to diagnose faults properly by using a single parameter in the real operation of an electric vehicle. The voltage fluctuation data is collected by simulating a battery discharging and charging investigation in a vibration setting. By deconstructing and rebuilding the discrete wavelet transform, the proposed approach removes voltage signal noise. To categorize the fault state, the voltage change, co-variance and variance matrixes, and voltage characteristics are employed as input-values in the improved Giza pyramids construction, and gradient boosting decision trees technique. The Improved Giza pyramids construction technique is utilized to detect fault signals and determine the degree of the defect. The cell faults are separated from other faults using the Gradient Boosting Decision Trees approach by identifying the surrounding voltages with fault flags. Furthermore, the correlation coefficient of the nearby voltage difference and current isolates connection and voltage sensor defects. The multi-fault diagnosis approach may prevent erroneous fault detection and offer high resilience to battery inconsistencies and normal measurement errors of state of health, ambient temperature, and state of charge. The projected control theme is evaluated on the MATLAB platform and its performance is assessed. The performances of the proposed method are compared with existing techniques like Artificial Bee Colony, Differential Evolution, Improved Giza Pyramids Construction and Particle Swarm Optimization. The efficiency of the Artificial Bee Colony, Differential Evolution, Particle Swarm Optimization, and Improved Giza Pyramids Construction and proposed technique is 82.237 %, 79.265 %, 87.1029 %, 89.023 % and 95.4501 %.

A new linear measurement method for the geometric error of CNC machine tools—Normal measurement method

In order to efficiently identify the geometric error parameters of CNC machine tools, a new geometric error model was established by analyzing the rigid body degrees of freedom error decomposition method in multi-body kinematics theory. Based on this, a novel measurement method called the normal measurement method was proposed. Taking the Y-axis as an example, measurement experiments were conducted on terms of pitch error and yaw error in the geometric error. The results show that the error accuracy identified by the normal measurement method and error model is consistent with traditional linear measurement methods. Furthermore, it has the advantages of a simple measurement process, low error dispersion, and good error prediction value tracking. It provides a new and effective approach for the detection and identification of geometric errors, laying the foundation for improving machine tool machining accuracy.

Extrapolation estimation for nonparametric regression with measurement error

AbstractFor the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the regression functions. By applying the conditional expectation directly to the kernel‐weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function, if the bandwidth is less than the SD of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications.

A Novel Method for Pose and Position Calibration of Laser Displacement Sensors.

Laser displacement sensors are widely used in the aviation industry for the purpose of surface normal measurements. The measurement of a surface normal depends on prior knowledge of the poses and positions of the sensors, which are obtained through calibration. This paper introduces a new parameter to the traditional calibration procedure, to reduce the calibration error, and explores the factors affecting calibration using the Monte Carlo method. In the experiment, the normal measurement error of the probe consisted of four sensors after calibration was less than 0.1∘, which satisfied the established requirements. This paper indicates the boundary conditions for a successful calibration and validates the proposed method, which provides a new method for the pose and position calibration of laser displacement sensors and other similar sensors.

Extrapolation estimation in parametric regression models with measurement error

For the general parametric regression models with covariates contaminated with normal measurement errors, an alternative method to the traditional simulation extrapolation algorithm is proposed to estimate the unknown parameters in the regression function. By applying the conditional expectation directly to the target function, the proposed algorithm successfully removes the simulation step, by generating an estimation equation either for immediate use or for extrapolating, thus providing a possibility of reducing the computational time or the Monte Carlo simulation error. Large sample properties of the resulting estimator, including the consistency and the asymptotic normality, are thoroughly discussed. Potential wide applications of the proposed estimation procedure are illustrated by examples, simulation studies, as well as a real data analysis.

Wiener degradation models with scale-mixture normal distributed measurement errors for RUL prediction

When the field collected data is biased by unexpected errors due to sensors and measurement, simple Wiener process may fail to correctly estimate the true degradation path. Most existing studies assume additive Gaussian errors in the true degradation path to account for the effects of measurement errors. This assumption is prone to unexpected outliers during the data collection. To achieve a robust estimation for the underlying degradation process, we propose to model the measurement errors using a family of thick-tailed distributions, called Scale-Mixture Normal (SMN) distributions. The SMN distribution can be expressed as a Gaussian hierarchy structure, which is more robust to unexpected outliers. We develop an efficient Expectation-Maximum (EM) algorithm incorporating the Variational Bayesian method to estimate the model parameters. We also derive the distribution of the remaining useful life for online monitoring. The efficiency of the model is verified by Monte Carlo simulations, and the performance of the proposed model on real data is illustrated by the application on hard disk drivers and thrust ball bearing degradation data.

Online multi-fault detection and diagnosis for battery packs in electric vehicles

Rapid detection and accurate diagnosis of faults are essential to safe operation of battery packs in electric vehicles. However, the misdiagnosis happens occasionally because of similar signatures of cell faults, sensor faults and connection faults. In this paper, an online multi-fault diagnostic method is proposed based on a non-redundant crossed-style measurement circuit and improved correlation coefficient method. In the measurement circuit, each sensor measures the voltage sum of two neighboring cells and one connection part without increasing the hardware cost. The correlation coefficient method is used to catch fault signatures and assess the fault degree. By applying these two methods, the cell faults can be distinguished from other faults by identifying the correlation coefficient of neighboring voltages with fault flags. Furthermore, connection faults and voltage sensor faults are isolated by the correlation coefficient of the neighboring voltages difference and current. The multi-fault diagnostic method can avoid false fault detection among different faults, and ensure high robustness to normal measurement errors and battery inconsistencies of ambient temperature, state of charge, and state of health. The feasibility and advantage are validated by theoretical analysis and comparative study of experimental results.

A two-piece normal measurement error model

In the context of measurement error models, the true unobservable covariates are commonly assumed to have a normal distribution. This assumption is replaced here by a more flexible two-piece normal distribution, which allows for asymmetry. After setting-up a general formulation for two-piece distributions, we focus on the case of the normal two-piece construction. It turns out that the joint distribution of the actual observations (the multivariate observed covariates and the response) is a two-component mixture of multivariate skew-normal distributions. This connection facilitates the construction of an EM-type algorithm for performing maximum likelihood estimation. Some numerical experimentation with two real datasets indicates a substantial improvement of the present formulation with respect to the classical normal-theory construction, which greatly compensates the introduction of a single parameter for regulation of skewness.

Recovery of the three-dimensional wind and sonic temperature data from a physically deformed sonic anemometer

Abstract. A sonic anemometer reports three-dimensional (3-D) wind and sonic temperature (Ts) by measuring the time of ultrasonic signals transmitting along each of its three sonic paths, whose geometry of lengths and angles in the anemometer coordinate system was precisely determined through production calibrations and the geometry data were embedded into the sonic anemometer operating system (OS) for internal computations. If this geometry is deformed, although correctly measuring the time, the sonic anemometer continues to use its embedded geometry data for internal computations, resulting in incorrect output of 3-D wind and Ts data. However, if the geometry is remeasured (i.e., recalibrated) and to update the OS, the sonic anemometer can resume outputting correct data. In some cases, where immediate recalibration is not possible, a deformed sonic anemometer can be used because the ultrasonic signal-transmitting time is still correctly measured and the correct time can be used to recover the data through post processing. For example, in 2015, a sonic anemometer was geometrically deformed during transportation to Antarctica. Immediate deployment was critical, so the deformed sonic anemometer was used until a replacement arrived in 2016. Equations and algorithms were developed and implemented into the post-processing software to recover wind data with and without transducer-shadow correction and Ts data with crosswind correction. Post-processing used two geometric datasets, production calibration and recalibration, to recover the wind and Ts data from May 2015 to January 2016. The recovery reduced the difference of 9.60 to 8.93 ∘C between measured and calculated Ts to 0.81 to −0.45 ∘C, which is within the expected range, due to normal measurement errors. The recovered data were further processed to derive fluxes. As data reacquisition is time-consuming and expensive, this data-recovery approach is a cost-effective and time-saving option for similar cases. The equation development can be a reference for related topics.

Filling the gaps: Gaussian mixture models from noisy, truncated or incomplete samples

Astronomical data often suffer from noise and incompleteness. We extend the common mixtures-of-Gaussians density estimation approach to account for situations with a known sample incompleteness by simultaneous imputation from the current model. The method, called GMMis, generalizes existing Expectation-Maximization techniques for truncated data to arbitrary truncation geometries and probabilistic rejection processes, as long as they can be specified and do not depend on the density itself. The method accounts for independent multivariate normal measurement errors for each of the observed samples and recovers an estimate of the error-free distribution from which both observed and unobserved samples are drawn. It can perform a separation of a mixtures-of-Gaussian signal from a specified background distribution whose amplitude may be unknown. We compare GMMis to the standard Gaussian mixture model for simple test cases with different types of incompleteness, and apply it to observational data from the NASA Chandra X-ray telescope. The python code is released as an open-source package at https://github.com/pmelchior/pyGMMis

Endpoint estimation for observations with normal measurement errors

This paper investigates the estimation of the finite endpoint of a distribution function when the observations are contaminated by normally distributed measurement errors. Under the framework of Extreme Value Theory, we propose a class of estimators for the standard deviation of the measurement errors as well as for the endpoint. Asymptotic theories for the proposed estimators are established while their finite sample performance is demonstrated by simulations. In addition, we apply the proposed methods to the outdoor long jump data to estimate the ultimate limit for human beings in the long jump.

Bayesian inference in measurement error models from objective priors for the bivariate normal distribution

In regression analysis, when the covariates are not exactly observed, measurement error models extend the usual regression models toward a more realistic representation of the covariates. It is common in the literature to directly propose prior distributions for the parameters in normal measurement error models. Posterior inference requires Markov chain Monte Carlo (MCMC) computations. However, the regression model can be seen as a reparameterization of the bivariate normal distribution. In this paper, general results for objective Bayesian inference under the bivariate normal distribution were adapted to the regression framework. So, posterior inferences for the structural parameters of a measurement error model under a great variety of priors were obtained in a simple way. The methodology is illustrated by using five common prior distributions showing good performance for all prior distributions considered. MCMC methods are not necessary at all. Model assessment is also discussed. Results from a simulation study and applications to real data sets are reported.

A Discriminant Function Approach to Adjust for Processing and Measurement Error When a Biomarker is Assayed in Pooled Samples

Pooling biological specimens prior to performing expensive laboratory assays has been shown to be a cost effective approach for estimating parameters of interest. In addition to requiring specialized statistical techniques, however, the pooling of samples can introduce assay errors due to processing, possibly in addition to measurement error that may be present when the assay is applied to individual samples. Failure to account for these sources of error can result in biased parameter estimates and ultimately faulty inference. Prior research addressing biomarker mean and variance estimation advocates hybrid designs consisting of individual as well as pooled samples to account for measurement and processing (or pooling) error. We consider adapting this approach to the problem of estimating a covariate-adjusted odds ratio (OR) relating a binary outcome to a continuous exposure or biomarker level assessed in pools. In particular, we explore the applicability of a discriminant function-based analysis that assumes normal residual, processing, and measurement errors. A potential advantage of this method is that maximum likelihood estimation of the desired adjusted log OR is straightforward and computationally convenient. Moreover, in the absence of measurement and processing error, the method yields an efficient unbiased estimator for the parameter of interest assuming normal residual errors. We illustrate the approach using real data from an ancillary study of the Collaborative Perinatal Project, and we use simulations to demonstrate the ability of the proposed estimators to alleviate bias due to measurement and processing error.

Simulation extrapolation estimation in parametric models with Laplace measurement error

The normal-error-based simulation extrapolation (N-SIMEX) procedure provides a simulation-based method to remove or reduce the bias in estimators of parameters in measurement error models. This paper shows that the N-SIMEX procedure only works for the normal measurement error and does not work for Laplace measurement error. A new L-SIMEX procedure is particularly designed to remove or reduce the Laplace measurement errors in parametric models. Unlike in the N-SIMEX procedure where the measurement error is removed or reduced by adding independent normal errors controlled by the scale parameter, the proposed procedure removes or reduces the Laplace measurement error by adding a noise variable which is a difference between two independent gamma random variables, and where the noise level is governed by the shape parameter. Heuristic and rigorous arguments are provided to justify the proposed method and a Jackknife-type estimation procedure is provided to estimate the variance of the L-SIMEX estimate. Simulation studies and a real data example are presented to demonstrate the proposed estimation procedure. A finite sample comparison with some revised moment estimators of Hong and Tamer is also included.

A Backtracking Approach to Minimal Cost Feature Selection of Numerical Data

In data mining applications, one of the most fundamental problems is feature selection, which can improve the generalization capability of patterns. Recent developments in this field have led to a renewed interest in cost-sensitive feature selection. Minimal cost feature selection is devoted to obtain a trade-off between test costs and misclassification costs. However, this problem has been addressed on only nominal data. In this paper, we consider numerical data with measurement errors and propose a backtracking approach for this problem. First, we build a data model with normal distribution measurement errors. In order to deal with this model, the neighborhood of each data item is constructed through the confidence interval. Compared with discretized intervals, neighborhoods are more reasonable to maintain the information of data. And then, we redefine the minimal total cost feature selection problem on the neighborhood model. Finally, a backtracking algorithm with three effective pruning techniques is proposed to deal with this problem. Experimental results indicate that the pruning techniques are effective, and the algorithm is efficient for datasets with nearly one thousand objects.

Test-Cost-Sensitive Attribute Reduction of Data with Normal Distribution Measurement Errors

The measurement error with normal distribution is universal in applications. Generally, smaller measurement error requires better instrument and higher test cost. In decision making, we will select an attribute subset with appropriate measurement error to minimize the total test cost. Recently, error-range-based covering rough set with uniform distribution error was proposed to investigate this issue. However, the measurement errors satisfy normal distribution instead of uniform distribution which is rather simple for most applications. In this paper, we introduce normal distribution measurement errors to covering-based rough set model and deal with test-cost-sensitive attribute reduction problem in this new model. The major contributions of this paper are fourfold. First, we build a new data model based on normal distribution measurement errors. Second, the covering-based rough set model with measurement errors is constructed through the “3-sigma” rule of normal distribution. With this model, coverings are constructed from data rather than assigned by users. Third, the test-cost-sensitive attribute reduction problem is redefined on this covering-based rough set. Fourth, a heuristic algorithm is proposed to deal with this problem. The experimental results show that the algorithm is more effective and efficient than the existing one. This study suggests new research trends concerning cost-sensitive learning.

Cost-Sensitive Feature Selection of Numeric Data with Measurement Errors

Feature selection is an essential process in data mining applications since it reduces a model’s complexity. However, feature selection with various types of costs is still a new research topic. In this paper, we study the cost-sensitive feature selection problem of numeric data with measurement errors. The major contributions of this paper are fourfold. First, a new data model is built to address test costs and misclassification costs as well as error boundaries. It is distinguished from the existing models mainly on the error boundaries. Second, a covering-based rough set model with normal distribution measurement errors is constructed. With this model, coverings are constructed from data rather than assigned by users. Third, a new cost-sensitive feature selection problem is defined on this model. It is more realistic than the existing feature selection problems. Fourth, both backtracking and heuristic algorithms are proposed to deal with the new problem. Experimental results show the efficiency of the pruning techniques for the backtracking algorithm and the effectiveness of the heuristic algorithm. This study is a step toward realistic applications of the cost-sensitive learning.

Likelihood inference in generalized linear mixed measurement error models

The generalized linear mixed models (GLMMs) for clustered data are studied when covariates are measured with error. The most conventional measurement error models are based on either linear mixed models (LMMs) or GLMMs. Even without the measurement error, the frequentist analysis of LMM, and particularly of GLMM, is computationally difficult. On the other hand, Bayesian analysis of LMM and GLMM is computationally convenient in both cases without and with the measurement error. Recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. As an application of data cloning, we conduct a frequentist analysis of GLMM with covariates subject to the measurement error model. The performance of the proposed approach which yields the maximum likelihood estimation is evaluated by two important real data types, Normal and logistic linear mixed measurement error models, and also through simulation studies.

A goodness-of-fit test of logistic regression models for case-control data with measurement error

We study goodness-of-fit tests for logistic regression models for case-control data when some covariates are measured with error. We first study the applicability of traditional test methods for this problem, simply ignoring measurement error, and show that in some scenarios they are effective despite the inconsistency of the parameter estimators. We then develop a test procedure based on work of Zhang (2001) that can simultaneously test the validity of logistic regression and correct the bias in parameter estimators for case-control data with nondifferential classical additive normal measurement error. Instead of using the information matrix considered by Zhang (2001), our test statistic uses preselected functions to reduce dimensionality. Simulation studies and an application illustrate its usefulness. Copyright 2011, Oxford University Press.