Uncertainty Evaluation Method Research Articles

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

Uncertainty evaluation for wind speed measurement part (1): “GUM method and Monte Carlo method”

Due to the lack of analysis and research on the performance of different uncertainty evaluation methods in the field of wind speed measurement, it is difficult to choose the most favorable uncertainty evaluation method in the specific wind speed measurement, which will affect the efficiency and accuracy of results. In view of the above situation, this study applied three commonly used uncertainty evaluation methods (conventional GUM method, correlation GUM method and MCM method) to the uncertainty evaluation of wind speed measurement, and analyzed the performance of different methods to provide technical support for specific applications. Firstly, taking the pitot tube wind speed measurement system as an example, the principle and model of wind speed measurement are introduced; Secondly, explain the steps and processes of the above three methods for evaluating uncertainty; Finally, taking a 10 m/s wind speed measurement as an example, the above three methods were used (The correlation GUM method incorporates the correlation between wind tunnel stability and uniformity in its evaluation) to evaluate the uncertainty of wind speed measurement in the Pitot tube wind speed measurement system, and the evaluation results were verified and compared accordingly. The following results were obtained:1) The three uncertainty evaluation methods are all applicable to the evaluation of wind speed measurement uncertainty in this field; 2) The accuracy of evaluation results: MCM method > correlation GUM > conventional GUM, among which correlation GUM method effectively improves the accuracy of uncertainty U95 by 23 % compared to conventional GUM method; 3) Evaluation method operability: MCM method > conventional GUM > correlated GUM. Therefore, we suggest that, when evaluating the uncertainty of wind speed measurement, the MCM method should be given priority when there are high requirements for accuracy and operability. When there are difficulties in the use and promotion of MCM, but there is a high requirement for accuracy, the correlation GUM method can be used. When the accuracy requirement is not high and the calculation is not too complicated, the conventional GUM method can be used.

Estimation and Analysis of Glacier Mass Balance in the Southeastern Tibetan Plateau Using TanDEM-X Bi-Static InSAR during 2000–2014

In recent decades, glaciers in the southeastern Tibetan Plateau (SETP) have been rapidly melting and showing a large scale of glacier mass loss. Due to the lack of large-scale, high-resolution, and high-precision observations, knowledge on the spatial distribution of the glacier mass balance and the response to climate change is limited in this region. We propose a TanDEM-X bi-static InSAR (Interferometric Synthetic Aperture Radar) algorithm with a non-local mean filter method and difference strategy, to improve the precision of glacier surface elevation change detection. Moreover, we improved the glacier mass balance estimation algorithm with a correction method for multi-source system errors and an uncertainty evaluation method based on error propagation theory to reduce the uncertainty of estimations. We used 13 pairs of TanDEM-X bi-static InSAR images to obtain the glacier mass balance data for the entire SETP. The total area of glaciers monitored was 5821 km2 and the total number of glaciers monitored was 2321; the glacier surface elevation change rate was −0.505 ± 0.005 m/yr, and the glacier mass balance estimation was −454.5 ± 13.1 mm w.eq. during 2000–2014. Additionally, we analyzed the spatial distribution of the glacier mass balance within the SETP using the sub-watershed analysis method. The results showed that the mass loss rate had a decreasing trend from the southeast to the northwest. Furthermore, the temperature change and the glacier mass loss rate showed a positive correlation from the southeast to the northwest in this region. This study greatly advances our understanding of the regularities of glacier dynamics in this region, and can provide scientific support for major national goals such as the rational utilization of surrounding water resources and construction of important transportation projects.

Practical experimental design and uncertainty evaluation method for dimensional and form measurements using coordinate measuring machines

This study introduces a feasible method for estimating uncertainty in dimension and form measurements using a coordinate measuring machine. Herein, products with various geometries are measured and their conformity to the corresponding specifications is verified considering the measurement uncertainty. The uncertainty calculation method, which is feasible in production and consistently applicable to measurements ranging from simple to complex geometries, is in the developmental phase due to the complicated uncertainty factors in three‐dimensional measurement. Thus, this study reports the details of an experimental design that is independent of the geometric complexity of the workpiece being measured. Based on the analysis of variance, the calculation of the measurement uncertainty was formulated. Additionally, the validity of the proposed method was confirmed through a comparison experiment, demonstrating that the calibration results obtained using the proposed procedure align with those obtained via other established approaches. (140 words)

Confidence-aware reinforcement learning for energy management of electrified vehicles

The reliability of data-driven techniques, such as deep reinforcement learning (DRL) frequently diminishes in scenarios beyond their training environments. Despite DRL-based energy management strategies (EMS) having gained great popularity in optimizing the energy economy of electrified vehicles (EVs), their performance degradation in untrained contexts has not received adequate attention. This study presents a confidence-aware EMS designed to mitigate this problem and thereby enhance the overall EMS functionality. Firstly, a deep ensemble model-based uncertainty evaluation method is developed for devising a confidence assessment mechanism to measure the reliability of DRL actions. On this basis, a confidence-aware DRL-based strategy is proposed, wherein a knowledge-driven approach replaces DRL actions in instances of low confidence, aiming to improve overall performance. For validation, a fuel cell EV with complex energy flow was used as the testbed, and our proposed EMS was trained with the aim of optimizing fuel cell system energy consumption, battery longevity, and capacity maintenance. Both the confidence mechanism and the proposed EMS were evaluated using real-world driving profiles. Results suggest the established confidence mechanism accurately represents the DRL’s performance across different situations. In addition, the proposed EMS outperforms existing DRL-based EMS by 4.0% in hydrogen economy without compromising other objectives. The comprehensive architecture of the proposed amalgamation of data-driven and knowledge-driven methodologies can be effectively tailored to analogous energy management problems, thereby contributing to advancements in related fields.

Uncertainty Evaluation Based on Bayesian Transformations: Taking Facies Proportion as An Example

Many input parameters in reservoir modeling cannot be uniquely determined due to the incompleteness of data and the heterogeneity of the reservoir. Sedimentary facies modeling is a crucial part of reservoir modeling. The facies proportion is an important parameter affecting the modeling results, because that proportion directly determines the net gross ratio, reserves and sandbody connectivity. An uncertainty evaluation method based on Bayesian transformation is proposed to reduce the uncertainty of the facies proportion. According to the existing data and geological knowledge, the most probable value of the facies ratio and the prior distribution of uncertainty are estimated. The prior distribution of the facies proportion is divided into several intervals, and the proportions contained in each interval are used in facies modeling. Then, spatial resampling is carried out for each realization to obtain the likelihood estimation of the facies proportion. Finally, the posterior distribution of the facies ratio is achieved based on Bayesian transformation. The case study shows that the uncertainty interval of sandstone proportion in the study area has been reduced from [0.31, 0.59] to [0.35, 0.55], with a range reduction of 29%, indicating that the updated posterior distribution reduces the uncertainty of reservoir lithofacies proportion, thereby reducing the uncertainty of modeling results.

Time-varying uncertainty evaluation of the shock wave pressure measurements with small samples in an aerospace shock tube

Shock tube is a crucial device for the dynamic calibration of pressure sensors in aerospace and defense fields. Accurate measurement of the shock wave pressure (SWP) in the shock tube and reliable evaluation of the measurement uncertainty are the basis for improving the calibration accuracy of pressure sensors. However, the repeated measurement results of the SWP in shock tube have typical features of time-varying and small samples, leading to a poor reliability of the measurement uncertainty evaluation. To address this issue, an improved method is proposed to accurately evaluate the time-varying uncertainty of the SWP measurement results with small samples in an aerospace shock tube. The time-varying SWP measurement signals are firstly decomposed into four components by the multicomponent extraction based on signal decomposition algorithms. For the repeated SWP measurement data with small samples, a sample size expansion based on the bootstrap method is presented to reduce the mean estimation error of the four components. A time-varying uncertainty evaluation model of the four components is established based on the conjugate prior Bayesian theory. The reliable evaluation of the time-varying uncertainty of the SWP measurements is finally realized according to the uncertainty propagation principle. Simulations and the SWP measurement experiments in an aerospace shock tube are carried out to validate the performance of the proposed method. The results show that the proposed method works well in the time-varying uncertainty evaluation of the SWP measurements with small samples. Furthermore, the comparative experiments demonstrate the superiority of the proposed method over the Bessel method and the Bayesian method for the SWP measurement uncertainty evaluation in both accuracy and reliability.

A novel uncertainty evaluation method based on the particle filter and beta distribution for data with unknown distribution.

Uncertainty evaluation for unknown distribution data is a key problem to be solved in uncertainty evaluation theory. To evaluate the measurement uncertainty of data with unknown distributions, a novel uncertainty evaluation method based on the particle filter (PF) and beta distribution is proposed in this paper. A beta distribution with wide adaptability was adopted as the distribution type of measurement results, the parameters of the beta distribution were taken as the parameters to be estimated, and a state-space model was established. The PF method, suitable for non-Gaussian data, was utilized to obtain the estimates of the parameters of the beta distribution according to the measurement results. Finally, the best estimates of the measurement results and their uncertainty were calculated using the beta distribution parameters. Simulation results show that the proposed method is adaptive to accurately evaluate the measurement uncertainties of data, especially for non-Gaussian distribution data or asymmetrically distributed data. Multiple evaluation results show that the method has good robustness. The experimental results for the drift errors of a laser interferometer show that the uncertainty result of the proposed method is consistent with the Monte Carlo method. This method is suitable for a variety of distribution types that can be characterized through beta distribution and can solve the optimal estimation and uncertainty evaluation of most measurement results with unknown distribution types.

Evaluation of Measurement Uncertainty for Fourth Axis Error Calibration of Coordinate Measuring Machines

According to the calibration method defined in the specification, a measurement uncertainty evaluation method for the fourth axis error calibration results of coordinate measuring machines is proposed. Establish a measurement uncertainty evaluation model based on calibration methods and analyze the sources of each uncertainty. Based on measurement examples, the evaluation process of measurement uncertainty for the fourth axis error calibration of coordinate measuring machines is elaborated.

Modelling a deep network using CNN and RNN for accident classification

There is a rapid evolution in highway investigation due to the increased usage of vehicles. Recently, various investigators have huge attention to the Intelligent Transportation System (ITS). Predicting a particular image plays a crucial role in digital image processing. However, this process is more challenging due to its changing viewpoints, illumination, colour, shape, etc. This work concentrates on modelling a novel deep learning (DL) approach. Initially, a deep-Convolutional Neural Network (D–CNN)–based sample-level classifier is proposed iteratively to measure the sampling uncertainty. Here, the uncertainty evaluation method is integrated with the sample learning process for training the robust sample classifier. The proposed D-CNN model has the competency to identify the abnormal activities and feature representation simultaneously. Subsequently, Deep Recurrent Neural Network (D-RNN) is proposed to examine the feature representation from the bag of samples and generates the final classification output by considering the local and global sampling aggregately. The simulation is performed using MATLAB 2020a and the proposed D-CNN and D-RNN model provides better trade-off with the classification accuracy compared to other approaches. The model accuracy is 92.9%, sensitivity is 76.40%, and specificity is 100% which is substantially higher than other approaches.

A data-driven model for production prediction of strongly heterogeneous reservoir under uncertainty

Production forecasting plays an important role in the reservoir development process. This task is challenging due to complex spatial and temporal correlations (e.g., inter-well interference and forward-backward linkages temporally). Most existing work tried to solve this problem by mining the impact of historical production conditions on the future production from the perspective of time series analysis. While such works gain satisfactory prediction accuracy, they cannot take the effect of well interference into account. In this study, we revisit the problem of production prediction from strongly heterogeneous reservoirs, aiming to improve the prediction accuracy by leveraging the breakthroughs of deep learning techniques. A new data-driven model is proposed to predict the production of each oil well, where the key novelty is to mine the inter-well interference relationships from the graph perspective. First, based on four constructed inter-well relationship graphs (well pattern structure graph, distance graph, similarity graph, and injection-production relationship graph), a Multi-Graph Convolutional Network (MGCN) is built to capture the spatial interactions of the wells. Then, a Long Short-Term Memory (LSTM) network is used to capture the complex temporal correlations. Finally, to make the model consider more production influencing factors, a Fully Connected Network (FCN) is utilized to fuse spatiotemporal correlations with other production influencing factors to predict production. Besides, considering the uncertainty of the data, an uncertainty evaluation method for predicting production is developed using Latin hypercube sampling and Monte Carlo methods. For evaluation and verification, the proposed model is applied to two case studies of numerical models and actual oilfields. The data of the actual oilfield are preprocessed by the proposed ensemble empirical mode decomposition (EEMD) component threshold denoising method. The optimal hyperparameters in the model are determined by Bayesian optimization algorithm. A series of experiments demonstrated that the proposed method has minimal prediction error and can predict the production with different probabilities, which can reduce the development risk.

B[formula omitted]N[formula omitted]: Resource efficient Bayesian neural network accelerator using Bernoulli sampler on FPGA

A resource efficient hardware accelerator for Bayesian neural network (BNN) named B2N2, Bernoulli random number based Bayesian neural network accelerator, is proposed. As neural networks expand their application into risk sensitive domains where mispredictions may cause serious social and economic losses, evaluating the NN’s confidence on its prediction has emerged as a critical concern. Among many uncertainty evaluation methods, BNN provides a theoretically grounded way to evaluate the uncertainty of NN’s output by treating network parameters as random variables. By exploiting the central limit theorem, we propose to replace costly Gaussian random number generators (RNG) with Bernoulli RNG which can be efficiently implemented on hardware since the possible outcome from Bernoulli distribution is binary. We demonstrate that B2N2 implemented on Xilinx ZCU104 FPGA board consumes only 465 DSPs and 81661 LUTs which corresponds to 50.9% and 14.3% reductions compared to Gaussian-BNN (Hirayama et al., 2020) implemented on the same FPGA board for fair comparison. We further compare B2N2 with VIBNN (Cai et al., 2018), which shows that B2N2 successfully reduced DSPs and LUTs usages by 50.9% and 57.9%, respectively. Owing to the reduced hardware resources, B2N2 improved energy efficiency by 7.50% and 57.5% compared to Gaussian-BNN (Hirayama et al., 2020) and VIBNN (Cai et al., 2018), respectively.

Evaluation of Uncertainty in Determination of Lead in Milk and Dairy Products by Atomic Absorption Spectrometry

In the field of food safety inspection, researchers should fully consider the impact of measurement uncertainty to ensure the accuracy of the results, Especially when it affects the determination of detection results.This study is to establish the mathematical model of uncertainty, Synthesize and expand each uncertainty component .Finally, the uncertainty evaluation method for the determination of lead in milk and dairy products by atomic absorption spectrometry was established. Take milk powder as an example, the uncertainty of graphite furnace atomic absorption spectrometry method 1 in GB 5009.12-2017 National Food Aafety Standard Determination of Lead in Foods was evaluated by referring to JJF 1059.1-2012 Evaluation and Expression of Measurement Uncertainty. When the standard result of lead content in milk was 0.095 mg/kg, the synthetic standard uncertainty of the determination result was 0.0022 mg/kg, k=2, and the extended uncertainty was 0.005 mg/kg, and the result could be expressed as (0.095±0.005) mg/kg. The uncertainty of measurement results is mainly due to the uncertainty component introduced by test repeatability and standard solution concentration. Therefore, in the actual testing work, the accuracy and reliability of the results can be ensured by increasing the number of standard working fluid, using glass instruments with higher accuracy, and increasing the number of parallel samples.

Evaluating intraocular lens power formula constant robustness using bootstrap algorithms.

Bootstrapping is a modern technique mostly used in statistics to evaluate the robustness of model parameters. The purpose of this study was to develop a method for evaluation of formula constant uncertainties and the effect on the prediction error (PE) in intraocular lens power calculation with theoretical-optical formulae using bootstrap techniques. In a dataset with N=888 clinical cases treated with the monofocal aspherical intraocular lens (Vivinex, Hoya) constants for the Haigis, the Castrop and the SRKT formula were optimised for the sum of squared PE using nonlinear iterative optimisation (interior point method), and the formula predicted spherical equivalent refraction (predSEQ) and the PE were derived. The PE was bootstrapped NB=1000 times and added to predSEQ, and formula constants were derived for each bootstrap. The robustness of the constants was calculated from the NB bootstrapped models, and the predSEQ was back-calculated from the NB formula constants. With bootstrapping, the 90% confidence intervals for the a0/a1/a2 constants of the Haigis formula were -0.8317 to -0.5301/0.3203 to 0.3617/0.1954 to 0.2100, for the C/H/R constants of the Castrop formula they were 0.3113 to 0.3272/0.1237 to 0.2149/0.0980 to 0.1621, and for the A constant of the SRKT formula they were 119.2320 to 119.3028. The back-calculated PE from the NB bootstrapped formula constants standard deviation for the mean/median/mean absolute/root mean squared PE were 5.677/5.735/0.401/0.318 e-3 dpt for the Haigis formula, 5.677/5.735/0.401/0.31829 e-3 dpt for the Castrop formula and 14.748/14.790/0.561/0.370 e-3 dpt for the SRKT formula. We have been able to prove with bootstrapping that nonlinear iterative formula constant optimisation techniques for the Haigis, the Castrop and the SRKT formulae yield consistent results with low uncertainties of the formula constants and low variations in the back-calculated mean, median, mean absolute and root mean squared formula prediction error.

An integrated lifetime prediction method for double-nut ball screws subject to preload loss failure mode

Existing lifetime prediction methods for ball screws are mainly based on the failure mechanism modeling, while the accuracy is quite limited due to the need for a large number of failure samples and the ignorance of the uncertainty during the failure evolution. Therefore, we proposed an integrated lifetime prediction method for the double-nut ball screws utilizing both the degradation mechanism model and the uncertainty evaluation method. The Bayesian inference is used to update the posterior distribution of the wear coefficient on the basis of the condition monitoring data. The posterior distribution of wear coefficient gets narrower with more degraded preload data acquired, which indicates the uncertainty of the wear coefficient due to different material properties and working conditions is decreased. The experimental results showed that, without the need for a large number of failure samples, the proposed integrated lifetime prediction method for double-nut ball screws achieved much higher accuracy than existing methods.

Uncertainty analysis of velocity field calibration in wind tunnels based on GUM and MCM

The flow quality of wind tunnel is an important index to judge the performance of the wind tunnel, and it directly determines whether the aircraft can obtain high-quality test data, and directly relates to the ability of the wind tunnel to be applied to basic aerodynamic research. Velocity field calibration is necessary in flow field calibration and an important prerequisite for the accurate simulation of Mach number in wind tunnel tests. In this paper, the GUM method and the MCM method are used to compare and analyze the uncertainty of velocity field calibration of the high-speed wind tunnel, and the uncertainty of the Mach number in the range of 0.6 to 4 is solved. The uncertainty evaluation results of the two methods are basically the same, and are equivalent to the wind tunnel Mach number control accuracy value, which verifies the correctness of the evaluation results of the velocity field calibration uncertainty of high-speed wind tunnel, and the MCM method results verify the direct applicability of the GUM method for uncertainty evaluation in similar application scenarios.

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.