Advanced Mathematical And Computational Tools In Metrology And Testing X

Franco Pavese, Wolfram Bremser, Anna Chunovkina, Nicolas Fischer, Alistair B Forbes

• Publisher: WSPC
• Year: 2015
• Topic: Biological Sciences
• eBook ISBN:
  9789814678636
• Subtopic: Science General
• Index: Biological Sciences

This volume contains original and refereed contributions from the tenth AMCTM Conference (http://www.nviim.ru/AMCTM2014) held in St. Petersburg (Russia) in September 2014 on the theme of advanced mathematical and computational tools in metrology and testing.

The themes in this volume reflect the importance of the mathematical, statistical and numerical tools and techniques in metrology and testing and, also keeping the challenge promoted by the Metre Convention, to access a mutual recognition for the measurement standards.

Contents:

• Fostering Diversity of Thought in Measurement Science (F Pavese and P De Bièvre)
• Polynomial Calibration Functions Revisited: Numerical and Statistical Issues (M G Cox and P Harris)
• Empirical Functions with Pre-Assigned Correlation Behaviour (A B Forbes)
• Models and Methods of Dynamic Measurements: Results Presented by St. Petersburg Metrologists (V A Granovskii)
• Interval Computations and Interval-Related Statistical Techniques: Estimating Uncertainty of the Results of Data Processing and Indirect Measurements (V Ya Kreinovich)
• Classification, Modeling and Quantification of Human Errors in Chemical Analysis (I Kuselman)
• Application of Nonparametric Goodness-of-Fit Tests: Problems and Solution (B Yu Lemeshko)
• Dynamic Measurements Based on Automatic Control Theory Approach (A L Shestakov)
• Models for the Treatment of Apparently Inconsistent Data (R Willink)
• Model for Emotion Measurements in Acoustic Signals and Its Analysis (Y Baksheeva, K Sapozhnikova and R Taymanov)
• Uncertainty Calculation in Gravimetric Microflow Measurements (E Batista, N Almeida, I Godinho and E Filipe)
• Uncertainties Propagation from Published Experimental Data to Uncertainties of Model Parameters Adjusted by the Least Squares (V I Belousov, V V Ezhela, Y V Kuyanov, S B Lugovsky, K S Lugovsky and N P Tkachenko)
• A New Approach for the Mathematical Alignment Machine Tool-Paths on a Five-Axis Machine and Its Effect on Surface Roughness (S Boukebbab, J Chaves-Jacob, J-M Linares and N Azzam)
• Goodness-of-Fit Tests for One-Shot Device Testing Data (E V Chimitova and N Balakrishan)
• Calculation of Coverage Intervals: Some Study Cases (A Stepanov, A Chunovkina and N Burmistrova)
• Application of Numerical Methods in Metrology of Electromagnetic Quantities (M Cundeva-Blajer)
• Calibration Method of Measuring Instruments in Operating Conditions (A A Danilov, Yu V Kucherenko, M V Berzhinskaya, N P Ordinartseva)
• Statistical Methods for Conformity Assessment When Dealing with Computationally Expensive Systems: Application to a Fire Engineering Case Study (S Demeyer, N Fischer, F Didieux and M Binacchi)
• Overview of EMRP Joint Reserch Project NEW06 "Traceability for Computationally-Intensive Metrology" (A B Forbes, I M Smith, F Härtig and K Wendt)
• Stable Units of Account for Economic Value Correct Measuring (N Hovanov)
• A Novel Approach for Uncertainty Evaluation Using Characteristic Function Theory (A B Ionov, N S Chernysheva and B P Ionov)
• Estimation of Test Uncertainty for TraCIM Reference Pairs (F Keller, K Wendt and F Härtig)
• Approaches for Assigning Numerical Uncertainty to Reference Data Pairs for Software Validation (G J P Kok and I M Smith)
• Uncertainty Evaluation for a Computationally Expensive Model of a Sonic Nozzle (G J P Kok and N Pelevic)
• EllipseFit4HC: A MATLAB Algorithm for Demodulation and Uncertainty Evaluation of the Quadrature Interferometer Signals (R Köning, G Wimmer and V Witkovský)
• Considerations on the Influence of Test Equipment Instability and Calibration Methods on Measurement Uncertainty of the Test Laboratory (A S Krivov, S V Marinko and I G Boyko)
• A Cartesian Method to Improve the Results and Save Computation Time in Bayesian Signal Analysis (G A Kyriazis)
• The Definition of the Reliability of Identification of Complex Organic Compounds Using HPLC and Base Chromatographic and Spectral Data (E V Kulyabina and Yu A Kudeyarov)
• Uncertainty Evaluation of Fluid Dynamic Simulation with One-Dimensional Riser Model by Means of Stochastic Differential Equations (E A O Lima, S B Melo, C C Dantas, F A S Teles and S Soares Bandiera)
• Simulation Method to Estimate the Uncertainties of ISO Specifications (J-M Linares and J M Sprauel)
• Adding a Virtual Layer in a Sensor Network to Improve Measurement Reliability (U Maniscalco and R Rizzo)
• Calibration Analysis of a Computational Optical System Applied in the Dimensional Monitoring of a Suspension Bridge (L L Martins, J M Rebordão and A S Ribeiro)
• Determination of Numerical Uncertainty Associated with Numerical Artefacts for Validating Coordinate Metrology Software (H D Minh, I M Smith and A B Forbes)
• Least-Squares Method and Type B Evaluation of Standard Uncertainty (R Palenčár, S Ďuriš, P Pavlásek, M Dovica, S Slosarčík and G Wimmer)
• Optimising Measurement Processes Using Automated Planning (S Parkinson, A Crampton and A P Longstaff)
• Software Tool for Conversion of Historical Temperature Scales (P Pavlásek, S Ďuriš, R Palenčár and A Merlone)
• Few Measurements, Non-Normality: A Statement on the Expanded Uncertainty (J Petry, B De Boeck, M Dobre and A Peruzzi)
• Quantifying Uncertainty in Accelerometer Sensitivity Studies (A L Rukhin and D J Evans)
• Metrological Aspects of Stopping Iterative Procedures in Inverse Problems for Static-Mode Measurements (K K Semenov)
• Inverse Problems in Theory and Practice of Measurements and Metrology (K K Semenov, G N Solopchenko and V Ya Kreinovich)
• Fuzzy Intervals as Foundation of Metrological Support for Computations with Inaccurate Data (K K Semenov, G N Solopchenko and V Ya Kreinovich)
• Testing Statistical Hypotheses for Generalized Semiparametric Proportional Hazards Models with Cross-Effect of Survival Functions (M A Semenova and E V Chimitova)
• Novel Reference Value and DOE Determination by Model Selection and Posterior Predictive Checking (K Shirono, H Tanaka, M Shiro and K Ehara)
• Certification of Algorithms for Constructing Calibration Curves of Measuring Instruments (T Siraya)
• Discrete and Fuzzy Encoding of the ECG-Signal for Multidisease Diagnostic System (V Uspenskiy, K Vorontsov, V Tselykh and V Bunakov)
• Application of Two Robust Methods in Inter-Laboratory Comparisons with Small Samples (E T Volodarsky and Z L Warsza)
• Validation of CMM Evaluation Software Using TraCIM (K Wendt, M Franke and F Härtig)
• Semi-Parametric Polynomial Method for Retrospective Estimation of the Change-Point of Parameters of Non-Gaussian Sequences (S V Zabolotnii and Z L Warsza)
• Use of a Bayesian Approach to Improve Uncertainty of Model-Based Measurements by Hybrid Multi-Tool Metrology (N-F Zhang, B M Barnes, R M Silver and H Zhou)
• Application of Effective Number of Observations and Effective Degrees of Freedom for Analysis of Autocorrelated Observations (A Zieba)

Readership: Researchers, graduate students, academics and professionals in metrology.
Key Features:

• Unique consolidated series of books (started in 1993) in mathematics, statistics and software specifically for metrology and testing
• Authors are among the most prominent in the metrology and testing fields
• No competing books in the same comprehensive field

Advanced Mathematical and Computational Tools in Metrology and Testing X Edited by F. Pavese, W. Bremser, A. Chunovkina, N. Fischer and A. B. Forbes © 2015 World Scientific Publishing Company (pp. 38–49)

INTERVAL COMPUTATIONS AND INTERVAL-RELATED STATISTICAL TECHNIQUES: ESTIMATING UNCERTAINTY OF THE RESULTS OF DATA PROCESSING AND INDIRECT MEASUREMENTS

V. KREINOVICH

Computer Science Department, University of Texas at El Paso, El Paso, Texas 79968, USA
E-mail: [email protected]
http://www.cs.utep.edu/vladik

In many practical situations, we only know the upper bound Δ on the measurement error: |Δx| ≤ Δ. In other words, we only know that the measurement error is located on the interval [−Δ, Δ]. The traditional approach is to assume that Δx is uniformly distributed on [−Δ, Δ]. In some situations, however, this approach underestimates the error of indirect measurements. It is therefore desirable to directly process this interval uncertainty. Such “interval computations” methods have been developed since the 1950s. In this paper, we provide a brief overview of related algorithms and results.

Keywords: interval uncertainty, interval computations, interval-related statistical techniques

1. Need for Interval Computations

Data processing and indirect measurements. We are often interested in a physical quantity y that is difficult (or impossible) to measure directly: distance to a star, amount of oil in a well. A natural idea is to measure y indirectly: we find easier-to-measure quantities x₁, …, x_n related to y by a known relation y = f(x₁, …, x_n), and then use the results

_i of measuring x_i to estimate

:

This is known as data processing.

Estimating uncertainty of the results of indirect measurements: a problem. Measurements are never 100% accurate. The actual value x_i of i-th measured quantity can differ from the measurement result

_i; in other words, there are measurement errors

Because of that, the result

= f(

₁, …,

_n) of data processing is, in general, different from the actual value

It is desirable to describe the error

of the result of data processing. For this, we must have information about the errors of direct measurements.

Uncertainty of direct measurements: need for overall error bounds (i.e., interval uncertainty). Manufacturers of a measuring instrument (MI) usually provide an upper bound Δ_i for the measurement error: |Δx_i| ≤ Δ_i. (If no such bound is provided, then

_i is not a measurement, it is a wild guess.)

Once we get the measured value

_i, we can thus guarantee that the actual (unknown) value of x_i is in the interval

For example, if

_i = 1.0 and Δ_i = 0.1, then x_i ∈ [0.9, 1.1].

In many practical situations, we also know the probabilities of different values Δx_i within this interval. It is usually assumed that Δx_i is normally distributed with 0 mean and known standard deviation.

In practice, we can determine the desired pr...

Table of contents

• Cover Page
• Title
• Copyright
• Foreword
• Contents
• Fostering Diversity of Thought in Measurement Science
• Polynomial Calibration Functions Revisited: Numerical and Statistical Issues
• Empirical Functions with Pre-Assigned Correlation Behaviour
• Models and Methods of Dynamic Measurements: Results Presented by St. Petersburg Metrologists
• Interval Computations and Interval-Related Statistical Techniques: Estimating Uncertainty of the Results of Data Processing and Indirect Measurements
• Classification, Modeling and Quantification of Human Errors in Chemical Analysis
• Application of Nonparametric Goodness-of-Fit Tests: Problems and Solution
• Dynamic Measurements Based on Automatic Control Theory Approach
• Models for the Treatment of Apparently Inconsistent Data
• Model for Emotion Measurements in Acoustic Signals and Its Analysis
• Uncertainty Calculation in Gravimetric Microflow Measurements
• Uncertainties Propagation from Published Experimental Data to Uncertainties of Model Parameters Adjusted by the Least Squares
• A New Approach for the Mathematical Alignment Machine Tool-Paths on a Five-Axis Machine and Its Effect on Surface Roughness
• Goodness-of-Fit Tests for One-Shot Device Testing Data
• Calculation of Coverage Intervals: Some Study Cases
• Application of Numerical Methods in Metrology of Electromagnetic Quantities
• Calibration Method of Measuring Instruments in Operating Conditions
• Statistical Methods for Conformity Assessment When Dealing with Computationally Expensive Systems: Application to a Fire Engineering Case Study
• Overview of EMRP Joint Reserch Project NEW06 “Traceability for Computationally-Intensive Metrology”
• Stable Units of Account for Economic Value Correct Measuring
• A Novel Approach for Uncertainty Evaluation Using Characteristic Function Theory
• Estimation of Test Uncertainty for TraCIM Reference Pairs
• Approaches for Assigning Numerical Uncertainty to Reference Data Pairs for Software Validation
• Uncertainty Evaluation for a Computationally Expensive Model of a Sonic Nozzle
• EllipseFit4HC: A MATLAB Algorithm for Demodulation and Uncertainty Evaluation of the Quadrature Interferometer Signals
• Considerations on the Influence of Test Equipment Instability and Calibration Methods on Measurement Uncertainty of the Test Laboratory
• A Cartesian Method to Improve the Results and Save Computation Time in Bayesian Signal Analysis
• The Definition of the Reliability of Identification of Complex Organic Compounds Using HPLC and Base Chromatographic and Spectral Data
• Uncertainty Evaluation of Fluid Dynamic Simulation with One-Dimensional Riser Model by Means of Stochastic Differential Equations
• Simulation Method to Estimate the Uncertainties of ISO Specifications
• Adding a Virtual Layer in a Sensor Network to Improve Measurement Reliability
• Calibration Analysis of a Computational Optical System Applied in the Dimensional Monitoring of a Suspension Bridge
• Determination of Numerical Uncertainty Associated with Numerical Artefacts for Validating Coordinate Metrology Software
• Least-Squares Method and Type B Evaluation of Standard Uncertainty
• Optimising Measurement Processes Using Automated Planning
• Software Tool for Conversion of Historical Temperature Scales
• Few Measurements, Non-Normality: A Statement on the Expanded Uncertainty
• Quantifying Uncertainty in Accelerometer Sensitivity Studies
• Metrological Aspects of Stopping Iterative Procedures in Inverse Problems for Static-Mode Measurements
• Inverse Problems in Theory and Practice of Measurements and Metrology
• Fuzzy Intervals as Foundation of Metrological Support for Computations with Inaccurate Data
• Testing Statistical Hypotheses for Generalized Semiparametric Proportional Hazards Models with Cross-Effect of Survival Functions
• Novel Reference Value and DOE Determination by Model Selection and Posterior Predictive Checking
• Certification of Algorithms for Constructing Calibration Curves of Measuring Instruments
• Discrete and Fuzzy Encoding of the ECG-Signal for Multidisease Diagnostic System
• Application of Two Robust Methods in Inter-Laboratory Comparisons with Small Samples
• Validation of CMM Evaluation Software Using TraCIM
• Semi-Parametric Polynomial Method for Retrospective Estimation of the Change-Point of Parameters of Non-Gaussian Sequences
• Use of a Bayesian Approach to Improve Uncertainty of Model-Based Measurements by Hybrid Multi-Tool Metrology
• Application of Effective Number of Observations and Effective Degrees of Freedom for Analysis of Autocorrelated Observations
• Author Index
• Keywords Index