Uncertainty Evaluation Method Research Articles

Validation of the sensitivity analysis method of coordinate measurement uncertainty evaluation

The paper presents the results of the tests carried out to validate a new method for evaluating the uncertainty of coordinate measurements categorised as the Sensitivity Analysis (SA). This method concerns measuring dimensions and geometrical deviations. Measurement uncertainty is evaluated on the basis of information given in the Maximum Permissible Error (MPE) formula for a Coordinate Measuring Machine (CMM). Measurement models express the measured characteristics as a function of differences of coordinates of a small number of appropriately selected points of the workpiece. If reverification test results for the CMM used are available, then the estimated uncertainty takes into account the actual accuracy of the CMM. General formulae are given to calculate the uncertainty of measurement of a circle diameter and coaxiality. The relevant experiment is based on ISO 15530-3 recommendations. Acalibrated cylindrical square was used for validation. 17 circles’ diameters and 84 different combinations of datum length and distance of the toleranced element from the datum for measuring coaxiality were adopted as validated characteristics. The validation results are presented in tables and graphs and the chi-square test for equality of variances was used to confirm that the method is correct. The validation results are positive.

Structural Reliability Analysis and Reliability Index Calculation Method Based on Measurement Uncertainty

Structural reliability is a probabilistic measure of structural reliability. Reliability indicators can be calculated from the average and standard deviation. The standard deviation only reflects the degree of dispersion of the series of measured values such as structural resistance and load effects. However, the acquisition of measurement values is related to the measurement objects, instruments, methods, conditions, and measurement personnel. It is difficult to reflect the impact of these five aspects on the measurement values of structural resistance and load effects using standard deviation. Based on this, this article deeply analyzes the measurement uncertainty evaluation theory and method and proposes to use the synthetic standard uncertainty instead of the standard deviation to calculate the standard value of the structural resistance and load effect. This article establishes the structural performance function, structural reliability calculation formula, the reliable index calculation formula, the calculation formula of variation coefficient and the calculation formula of the safety factor based on the measurement uncertainty. The conclusion of this article provides a new application approach for China national standard “Measurement Uncertainty Evaluation and Representation” and also builds a new bridge for the measurement uncertainty evaluation theory to enter the field of structural reliability analysis.

Calculation method of representative value of inorganic binder strength based on combined standard uncertainty

This paper analyzes the limitations of calculating the representative value using standard deviation. Based on the measurement uncertainty evaluation theory and method, this paper proposes to use the combined standard uncertainty to calculate the representative value instead of standard deviation. In this way, the representative values of the test results from a certain guarantee rate based on the combined standard uncertainty can reflect the degree of dispersion of the series of test data values, and can also reflect the impact on the measurement objects, instruments, methods, conditions and personnel on the test data. Taking the unbounded compressive strength and flexural tensile strength of inorganic binders on highway pavements as examples, a method of calculating representative values of unbounded compressive and flexural strength based on combined standard uncertainty is established. The establishment of article conclusions, providing a new application path for national standards “Assessment and Expression of Measurement Uncertainty.”

Uncertainty evaluation in time-dependent measurements

Data quality plays a strong role in modelling and is fundamental to ensure that obtained analyses and results are reliable. Data uncertainty is related to the measurement’s imperfections that will cause an error in the obtained numerical value. In this way, data quality could be measured through uncertainty. Although there are well-established methods for uncertainty evaluation in independent measurements, there is a gap of methods in the case of time-dependent measurements. This study aims to propose a general methodology to evaluate the uncertainty of time-dependent measurements. Fitting an appropriate model to the measurements and then resampling and refitting a model, the uncertainty estimation of each data point is possible. The approach was validated using measurements obtained from typical time series models and compared with theoretical values. Further, real data from a water system is also used to illustrate the method’ capacity for uncertainty estimation of single time measurements.

A simple and effective way to evaluate the accuracy of digital image correlation combined with scanning electron microscopy (SEM-DIC)

Digital image correlation (DIC) is a powerful technique enabling mapping of local strain fields with the spatial resolution down to a few nanometers when combined with scanning electron microscopy. However, the accuracy of strain determination is frequently unknown due to a large number of experimental parameters influencing it. Here we present a simple and time-effective method for quantitative evaluation of uncertainties in strain values obtained by DIC. By imposing a fictive hydrostatic strain a high absolute accuracy of mean strain determination is demonstrated with deviations from the target value below 0.03%. At the same time, the precision decreases strongly with the reduction of the subset and step sizes reflecting a fundamental tradeoff between the spatial resolution and trueness of local strain values.

Evaluating Proton Dose and Associated Range Uncertainty Using Daily Cone-Beam CT.

PurposeThis study aimed to quantitatively evaluate the range uncertainties that arise from daily cone-beam CT (CBCT) images for proton dose calculation compared to CT using a measurement-based technique.MethodsFor head and thorax phantoms, wedge-shaped intensity-modulated proton therapy (IMPT) treatment plans were created such that the gradient of the wedge intersected and was measured with a 2D ion chamber array. The measured 2D dose distributions were compared with 2D dose planes extracted from the dose distributions using the IMPT plan calculated on CT and CBCT. Treatment plans of a thymoma cancer patient treated with breath-hold (BH) IMPT were recalculated on 28 CBCTs and 9 CTs, and the resulting dose distributions were compared.ResultsThe range uncertainties for the head phantom were determined to be 1.2% with CBCT, compared to 0.5% for CT, whereas the range uncertainties for the thorax phantom were 2.1% with CBCT, compared to 0.8% for CT. The doses calculated on CBCT and CT were similar with similar anatomy changes. For the thymoma patient, the primary source of anatomy change was the BH uncertainty, which could be up to 8 mm in the superior–inferior (SI) direction.ConclusionWe developed a measurement-based range uncertainty evaluation method with high sensitivity and used it to validate the accuracy of CBCT-based range and dose calculation. Our study demonstrated that the CBCT-based dose calculation could be used for daily dose validation in selected proton patients.

Uncertainty Evaluation Method and Application of Reservoir Lithofacies Proportion under the Condition of Few Wells

Abstract The proportion of different lithofacies is essential to determine the net-gross ratio, which directly affects the calculation of oil and gas reserves. Under the condition of few wells, the reliability of different lithofacies proportions obtained using well data is poor because it is difficult to estimate the uncertainty variation range of different lithofacies proportions. The present study overcomes this problem using an uncertainty evaluation method for reservoir lithofacies proportion. First, different lithofacies proportions of the reservoir are determined using the well and seismic data and are considered as the most likely estimated. Based on the lithofacies proportion, the lithofacies models of the study area are developed. Second, uniform and random methods are applied to sample the lithofacies models, and then, the probability distribution functions of different lithofacies proportions are derived. Third, the three levels of lithofacies proportions in the study area are calculated using the method of quantile and discretization of the probability distribution. Finally, we take M gas field as a sample and compare the test results of the fixed and random well structures. The results show that the sampling results of the fixed well structure model significantly deviate under the influence of the extension direction of the channel and well pattern distribution. Therefore, it is suggested to use random well structure to determine the uncertainty distribution range of lithofacies proportion.

Design of MultiChannel Parallel Dynamic Testing Virtual Instrument Based on Dynamic Measurement

With the rapid advancement of virtual instrument technology, converting the data measurement and control platform to a virtual one has become fashionable. This study focuses on dynamic measurement in order to create a multichannel parallel dynamic testing virtual instrument and then test the instrument’s performance. System login, user management, database storage, query and compression, data processing and real-time display, multifunctional analysis, remote access, and report generation modules have all been designed and implemented. A dynamic measurement uncertainty evaluation method based on quasi-Monte Carlo (MC) method is proposed in light of the common phenomenon that static is used instead of dynamic in the current evaluation process of dynamic measurement uncertainty. For this example, the actual results show that the algorithm produces very reliable and stable calculation results.

The Storage within Digital Calibration Certificates of Uncertainty Information Obtained Using a Monte Carlo Method

Supplement 1 to the ‘Guide to the expression of uncertainty of measurement’ describes a Monte Carlo method as a general numerical approach to uncertainty evaluation. Application of the approach typically delivers a large number of values of the output quantity of interest from which summary information such as an estimate of the quantity, its associated standard uncertainty, and a coverage interval for the quantity can be obtained and reported. This paper considers the use of a Monte Carlo method for uncertainty evaluation in calibration, using two examples to demonstrate how so-called ‘digital calibration certificates’ can allow the complete set of results of a Monte Carlo calculation to be reported.

Pyramid Bayesian Method for Model Uncertainty Evaluation of Semantic Segmentation in Autonomous Driving

With the fast-developing deep learning models in the field of autonomous driving, the research on the uncertainty estimation of deep learning models has also prevailed. Herein, a pyramid Bayesian deep learning method is proposed for the model uncertainty evaluation of semantic segmentation. Semantic segmentation is one of the most important perception problems in understanding visual scene, which is critical for autonomous driving. This study to optimize Bayesian SegNet for uncertainty evaluation. This paper first simplifies the network structure of Bayesian SegNet by reducing the number of MC-Dropout layer and then introduces the pyramid pooling module to improve the performance of Bayesian SegNet. mIoU and mPAvPU are used as evaluation matrics to test the proposed method on the public Cityscapes dataset. The experimental results show that the proposed method improves the sampling effect of the Bayesian SegNet, shortens the sampling time, and improves the network performance.

A Cluster-Based Method for Quantitative Characterization and Uncertainty Evaluation of Areal Step Height in Structured Surface Metrology

Quantitative characterization and uncertainty evaluation of areal step height is of increasing importance for semiconductor manufacturing. However, step characterizations often confront problems of repeatability and reproducibility due to fitting of upper and lower planes. To solve this problem, we propose a cluster-based method for step height characterization and uncertainty evaluation. By data reconstruction and K-means clustering, our method converts characterizing steps into approximating Euclidean distances, without necessity to fit planes. Moreover, it can evaluate uncertainties simultaneously with parameterization. The proposed method is firstly validated with synthetic data. Then two experiments respectively on nominal 5 μm and 90 nm standard artefacts are carried out. The characterization results highly conform to the calibrated values, with 0.0986% and 1.22% differences respectively. Comparing to the latest ISO method, the cluster-based method presents better performance on repeatability and reproducibility. The experimental results demonstrate that the method works well for measurement either with or without outliers.

Research Trends in the Optimization of the Master Surgery Scheduling Problem

The Master Surgery Scheduling Problem (MSSP) allocates operating theatre time to surgery groups such as medical specialities or surgeons, which is essential for daily operational planners. Many researchers have highlighted issues in the optimization of surgical scheduling problems. However, most recent reviews limited the issues at the operational level and excluded the problem characteristics such as surgery group type and schedule cyclicity. This study aims to review the state-of-the-art of MSSP and identify new trends in optimization strategies (problem characteristics and objective function), uncertainty scheduling factors (types and approaches), and solution and evaluation methods. These aspects are the key components in developing an effective MSSP optimization model. This paper reviews articles published between 2000 and 2021 that addressed MSSP, concentrating on papers between 2016 and 2021. We underlined the popularity of medical specialities as the surgery group, one-week horizon length, a cyclic schedule, multi-objective optimization and evaluation by benchmarking. The analysis shows that surgery duration is the most prominent uncertainty type, while strategies for handling this are stochastic programming, robust optimization, and fuzzy programming. We highlighted the role of heuristic approaches in addressing the MSSP’s computational complexity. This review’s trends, challenges, and potential solutions are essential for future researchers in developing optimization models for MSSP.

Evaluation of pressure and species concentration measurement using uncertainty propagation

This paper presents a probabilistic uncertainity evaluation method as described in the Guide to the Expression of Uncertainty in Measurements (GUM) and its application to probe measurements on pressure and fuel concentration. All sources of unceratinties are expressed as probability distributions. Consequently, the overall standard uncertainty of the quantity can be calculated using the Gaussian error propagation formula. The result of the uncertainty evaluation yields the most probable value of the measurand and describes its distribution in terms of rectangular (standard uncertainty) or gaussian (“expanded” uncertainty) distribution. A pitot-static probe and a fuel-concentration stem probe are used in order to demonstrate the principle of the probabilistic uncertainty evaluation method. The uncertainty induced by the pressure and concentration data acquisition system as well as the calibration of the fuel-concentration probe are included in the analysis. The overall “expanded” uncertainties for the measured and calculated values are presented as a function of different inlet fuel flows. In addition to this, the individual sources of uncertainty to the overall standard uncertainty are presented and discussed. Moreover, the transformation of standard uncertainty to “expanded” uncertainty will provide the deviation of the measurement in a 95% or 99% normal distributed interval instead of a 67% rectangular distributed interval.

A probabilistic uncertainty evaluation method for turbomachinery probe measurements

The paper presents a probabilistic uncertainty evaluation method described in the Guide to the Expression of Uncertainty in Measurement (GUM) [1] and its application to the field of Turbomachinery probe measurement techniques. All sources of uncertainties contributing to a measurement result are expressed in terms of probability distributions. Consequently, the overall standard uncertainty of the result can be calculated using the Gaussian error propagation formula. The result of the uncertainty evaluation yields the most probable value of the measurand and describes its distribution in terms of standard or extended uncertainties. A pneumatic five-hole-probe measurement technique has been chosen to show the principle of the probabilistic uncertainty evaluation method. The complete signal chain including the probe calibration, the modeling and the application in the turbine has been included in the analysis. The overall uncertainties of the measured flow angles and flow total and static pressures are presented as a function of the flow Mach number. In addition, the contribution of the individual sources of uncertainty to the overall standard uncertainty is shown. Based on this break down of uncertainties optimization options of the measurement chain are suggested.

A Novel Method for Estimating Residual Model Parameters to Evaluate Uncertainty in Scattering Parameter Measurements

In this paper, we present a novel method for estimating the parameters of residual models, which are widely used to evaluate the measurement uncertainty of the scattering parameters measured by a vector network analyzer (VNA). Conventionally, the parameters of the residual model are obtained using the ripple method with an air line, where the insulator that distinguishes the inner and outer lines of the coaxial line is air. However, due to inaccuracies caused by losses from air lines, the usable range of frequencies is limited. In addition, methods using the invariance property of the cross-ratio of complex numbers result in overestimation, because the maximum error boundary is calculated. Above all, since both methods estimate only the magnitude uncertainty, the phase uncertainty estimation is not rigorous, and the correlation between the magnitude and the phase cannot be estimated. In contrast, the proposed method calculates the parameters of the residual model directly from the calibration standards uncertainty, including the phase as well as magnitude, achieving the same result as the VNA error model. The proposed parameter estimation for residual models can also easily propagate to the uncertainty of other measurements, since it can obtain the correlation between magnitude and phase as well as the cross-frequency. In this paper, we compared the parameters of the residual model using the proposed method, the conventional ripple method, and the invariance property of the cross-ratio of complex numbers. For validation, the uncertainty obtained using the residual model with the proposed parameter estimation was compared to the results from the VNA error model. The two uncertainties showed excellent agreement for highly reflective and matched devices, respectively. Finally, we discuss how to effectively manage the calibration and measurement capabilities of scattering parameters using the proposed uncertainty evaluation method.

GUM method for evaluation of measurement uncertainty: BPL long wave time service monitoring

This paper constitutes the first report on the uncertainty evaluation based on Guide to the expression of Uncertainty in Measurement (GUM) method for BPL long wave time service monitoring. First, the applicability of the GUM method was considered from two perspectives: the BPL long wave time service monitoring model and the monitoring data distribution. A complete monitoring measurement model was then established. Subsequently, the uncertainty sources were analyzed via Type A and Type B evaluation. The bootstrap method was used to compare and verify the standard uncertainty evaluation by the GUM method. Thus, the uncertainty results for BPL time service monitoring were obtained under the existing monitoring model and equipment conditions. Furthermore, this paper also provides certain suggestions for improving the quality of time service monitoring. This work is expected to facilitate methods and provide guidance for evaluating the uncertainty in corresponding monitoring systems of other land-based time service systems.

Measurement uncertainty evaluation procedures and applications for various types of multichannel rotating-element spectroscopic ellipsometers.

A universal measurement uncertainty evaluation procedure is required for different types of multichannel rotating-element spectroscopic ellipsometers (RE-SEs) used in modern semiconductor industry. Herein, an improved uncertainty evaluation procedure, based on the universal measurement model functions and implicit function theorem, is introduced for unknown optical parameters of a sample. In addition, we develop a measurement standard instrument that can solve the error problems related to the basic principles of the multichannel RE-SEs used in the industrial field and present an example of applying the proposed uncertainty evaluation method to this standard instrument. Accordingly, the measurement performance for several types of real-time RE-SEs can be quantitatively compared. It can also be used for standardization, instrumentation, and measurement optimization.

Feasibility Study of Performance Assessment Gauge for Freeform Measurement

Recent product components have been designed as a combination of complex forms for advanced functionality. Such high degree-of-freedom forms are shaped by various manufacturing processes. In the industrial supply chain, the deviation of a manufactured form from its designed form must be verified to ensure product quality. Three-dimensional (3D) measuring systems are typically used for verification. To validate the product manufacturing performance accurately, a measurement procedure that can derive the measurands of forms with small measurement uncertainty is necessitated. For simple geometries such as flats, spheres, and cylinders, precise measurement and uncertainty evaluation methods have been established; however, those for complex forms are still being developed. In this study, measurement uncertainty is assessed by measuring a calibrated gauge and comparing the measured with calibrated values. Several gauges configured with basic geometric elements have been proposed as a reference for complex form measurements, and some issues remain. Some of the gauges do not sufficiently simulate the forms of actual product components, whereas other gauges are difficult to calibrate with small uncertainties. Herein, we discuss a possible approach for solving these problems in the metrology of complex forms using 3D measuring systems. First, a new gauge concept is proposed. The gauge is designed by extracting the complex features of the actual product form and segmenting the gauge’s form into various circular arc curvatures. The geometric parameters are well calibrated, and the measurable angular range of the curvature is not limited. A representative gauge based on this concept is described. Next, a robust and small-uncertainty calibration method for complex-form objects is described. The area encompassing the target cross-section is measured, and an envelope is generated on the probe tip mechanical surface from the probe tip centers to determine the measured surface. Finally, the calibration and measurement uncertainty evaluation for the geometric parameters of the new gauge are quantitatively presented. It is verified that the proposed calibration procedure is applicable to freeform measurements, and that both simple and complex forms can be measured within a 1.5 μm uncertainty.

Uncertainty evaluation method of the scattering matrix measurements for the polarized scanning nephelometer

The polarized scanning nephelometer (PSN) is an instrument for measuring the multiangle scattering matrix of aerosol particles. Prior to being used, its measurement accuracy should be first verified. However, due to the complexity of the errors involved, it is very difficult to evaluate the measurement accuracy of the instrument reasonably, which limits the application of the PSN. In this work, taking di-ethyl-hexyl-sebacate droplets as an example, an uncertainty evaluation method of the scattering matrix measurements for the PSN is proposed. According to the measurement characteristics, the sources of uncertainty are divided into systematic effects and random effects. The corresponding evaluation method is then proposed for these two uncertainty categories, and the uncertainty introduced by systematic effects is investigated in depth via the Monte Carlo method. The evaluation results clearly show the variation trend of each uncertainty component as a function of the scattering angle in different matrix elements. The combined uncertainty is calculated and analyzed, and the result shows that the measurement uncertainty of the instrument is less than 0.0185, which verifies the accuracy of the instrument. This method can provide a reference for the accuracy evaluation of similar instruments.

Uncertainty propagation for dropout-based Bayesian neural networks

Uncertainty evaluation is a core technique when deep neural networks (DNNs) are used in real-world problems. In practical applications, we often encounter unexpected samples that have not seen in the training process. Not only achieving the high-prediction accuracy but also detecting uncertain data is significant for safety-critical systems. In statistics and machine learning, Bayesian inference has been exploited for uncertainty evaluation. The Bayesian neural networks (BNNs) have recently attracted considerable attention in this context, as the DNN trained using dropout is interpreted as a Bayesian method. Based on this interpretation, several methods to calculate the Bayes predictive distribution for DNNs have been developed. Though the Monte-Carlo method called MC dropout is a popular method for uncertainty evaluation, it requires a number of repeated feed-forward calculations of DNNs with randomly sampled weight parameters. To overcome the computational issue, we propose a sampling-free method to evaluate uncertainty. Our method converts a neural network trained using dropout to the corresponding Bayesian neural network with variance propagation. Our method is available not only to feed-forward NNs but also to recurrent NNs such as LSTM. We report the computational efficiency and statistical reliability of our method in numerical experiments of language modeling using RNNs, and the out-of-distribution detection with DNNs.