Advanced Mathematical and Computational Tools in Metrology and Testing XI

Alistair B Forbes, Nien-Fan Zhang;Anna Chunovkina;Sascha Eichstädt;Franco Pavese

• Publisher: WSPC
• Year: 2018
• ISBN:
  9789813274310
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

This volume contains original, refereed contributions by researchers from institutions and laboratories across the world that are involved in metrology and testing. They were adapted from presentations made at the eleventh edition of the Advanced Mathematical and Computational Tools in Metrology and Testing conference held at the University of Strathclyde, Glasgow, in September 2017, organized by IMEKO Technical Committee 21, the National Physical Laboratory, UK, and the University of Strathclyde. The papers present new modeling approaches, algorithms and computational methods for analyzing data from metrology systems and for evaluation of the measurement uncertainty, and describe their applications in a wide range of measurement areas.

This volume is useful to all researchers, engineers and practitioners who need to characterize the capabilities of measurement systems and evaluate measurement data. Through the papers written by experts working in leading institutions, it covers the latest computational approaches and describes applications to current measurement challenges in engineering, environment and life sciences.

Contents:

• Analysis of Key Comparisons with Two Reference Standards: Extended Random Effects Meta-Analysis (O Bodnar and C Elster)
• Confirmation of Uncertainties Declared by KC Participants in the Presence of an Outlier (A G Chunovkina and A Stepanov)
• Quantity in Metrology and Mathematics: A General Relation and the Problem (V A Granovskii)
• Bayesian Analysis of an Errors-in-Variables Regression Problem (I Lira and D Grientschnig)
• Triangular Bézier Surface: From Reconstruction to Roughness Parameter Computation (L Pagani and P J Scott)
• On the Classification into Random and Systematic Effects (F Pavese)
• Measurement Models (A Possolo)
• Metrology and Mathematics — Survey on a Dual Pair (K H Ruhm)
• Fundaments of Measurement for Computationally-Intensive Metrology (P J Scott)
• Study of Gear Surface Texture Using Mallat's Scattering Transform (W Sun, S Chrétien, R Hornby, P Cooper, R Frazer and J Zhang)
• The Evaluation of the Uncertainty of Measurements from an Autocorrelated Process (N F Zhang)
• Dynamic Measurement Errors Correction in Sliding Mode Based on a Sensor Model (M N Bizyaev and A S Volosnikov)
• and other papers

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

• Description of state of the art techniques for modeling measurement systems and analyzing measurement data
• Written by researchers active in institutions developing world-leading measurement capabilities
• Provides a multi-disciplinary approach to addressing measurement challenges in a wide range of applications

A B Forbes, N F Zhang, A Chunovkina, S Eichstädt, F Pavese (eds.):
Advanced Mathematical and Computational Tools in Metrology and Testing XI
Series on Advances in Mathematics for Applied Sciences, Vol. 89
© 2018 World Scientific Publishing Company (pp. 85–118)

Metrology and mathematics — Survey on a dual pair

Karl H. Ruhm

Swiss Federal Institute of Technology (ETH), Institute of Machine Tools and Manufacturing (IWF), Leonhard Strasse 21, LEE L219, Zurich, CH 8092, Switzerland
E-mail: [email protected]

When we do usual Computation in Science, especially in Metrology, we assume that we do Mathematics. This is only partly true in spite of the fact that database handling and data processing are most important indeed. The field of Measurement plus Observation is much more entangled with Mathematics. The following survey “Metrology and Mathematics” will focus on selected ideas, concepts, rules, models, and structures, each of which is of a basic mathematical nature. When doing this, it is not surprising at all that most theoretical and applicational requirements in the field can be reduced to just a few basic logical and mathematical structures. This is also true for complex processes in fields like humanity and society. Signal and System Theory (SST) supports this claim. However, such an endeavour asks for an orderly and consistent definition of quantities and processes and of their mathematical models, called signals and systems. These models represent all kinds of issues, items, and phenomena in the real world. The term model indicates the superordinate means of mathematical description, observation, and representation in Science and Technology. The question arises, what the role of Logic and Mathematics looks like in detail. The term structure will be consistently pivotal. And, as is generally known, structures are best visualised by graphical means, here called Signal Relation Graphs (SRG).

Keywords: Metrology, Measurement, Observation, Mathematics, Stochastics, Statistics, Signal and System Theory, Model, Structure, Relation, Signal, System.

Introduction

One should think that Metrology, as Measurement Science and Technology, is somehow comparable to Pure Mathematics and Applied Mathematics. Pure Mathematics follows purely abstract goals. In principle, Measurement Science does so too, but only seldom. Most Pure Sciences, including Measurement Science, are in need of mathematical support, and rely or have to rely on Applied Mathematics: As a fact, Metrology is interested in Applied Mathematics, but very seldom in Pure Mathematics, which fosters top-down frameworks (bird perspective) and allows holistic views. On the contrary, applicational topics in everyday measurement life utilise bottom-up frameworks (frog perspective), allowing “only” highly specialised and thus limited based insight. In summary, so-called abstract needs in Measurement Science call for concepts and results of Applied Mathematics. Thus, Pure Mathematics and Measurement Science do not reside on the same level. This is all common feeling, may be considered natural, and at least comprehensible.

Measurement Science aims at descriptions of past, present and future states. It either regards unrealistically the whole, hypothetical infinitely large real world, or rather realistically the particular, bounded, tangible small real world. The sensory process together with the observation process may serve as an example of such a restricted real process. It acts as a subsection of Measurement Technology in data acquisition and data processing.

In order to succeed in such a description of real world measurement and observation processes, we have to “download” abstract concepts, methods, and procedures from superior scientific insights, which are delivered by Measurement Science. They emerge in form of terms, rules, standards, definitions, analytics, inter- and extrapolations, procedures, best practises, trade-offs, calculations, refinements, corrections, tricks, programs with coding and decoding, and so on.

It may be surprising that all these abstract and manifold artefacts are fostered by few concepts, methods and tools, presented in the next sections.

These concepts, methods, and tools are first and foremost of a logical and mathematical character indeed. This is even true, if we at times do not have enough quantitative information about structures and parameters of the processes under investigation. Nevertheless, they stand by in the background. A first informal statement concerning a relation (interaction, dependence, association, correlation, assignment, coherence) between well-defined quantities of interest is at present sufficient for subsequent, determined, quantitative activities: Such a preliminary black box mode proves truly convenient in practise. Of course, we finally have to know, which of the concepts, methods and tools in the wide field of Applied Mathematics may best serve our particular, narrow needs, a challenge to be supported beforehand by Measurement Education.

Normally, the metrological community enjoys mathematical concepts only reluctantly, unless they come in form of shortly useful “cooking recipes”. One reason for this aversion of becoming committed in mathematical fields may be lacking overview and skills concerning the superior, holistic, and systematic principles and structures, which Mathematics readily provides to everybody. Admittedly, the principal structure of cause and effect is widely accepted [2, 4], but a deeper engagement in theoretical and practical consequences and possibilities is often missing; another challenge to be met by Measurement Education. Besides, amazing analogies can be detected as to many Philosophers of Science respecting their commitment to logical and mathematical structures.

Often, direct consequences result from such reservations. Design and realisation are studied from scratch and invented anew, although solutions are ready for use from generalising background sources. An outstanding example is the important task of error correction, which is once and for all offered by the structure of an inversion procedure of a mathematical model. However, who cares?

The following sections describe and recommend some selected mathematical concepts and structures, which primarily refer to measurement and observation procedures. This is not too demanding an endeavour, since most theoretical and applicational requirements in the field may, surprisingly enough, be reduced to about half a dozen main structures according the motto “Keep it Simple”. This is also true for complex processes: Signal and System Theory (SST) supports this claim. In this presentation, the path to this concept will be gradually prepared. Moreover, the main aim will be, to create the impression that such a holistic approach serves even way beyond Natural and Technological Sciences.

The disposition of this survey starts with selected mathematical tools to describe quantities and processes in a general way. These two basic terms represent any sort of phenomena and items on the real world side: The term mathematical model, concerning these two terms, stands for the superior means of abstract description, behaviour, and representation in Science and Technology.

Above all, the most tantalising omnipresent claims “Our mathematical universe” [10] or “Why our world is mathematical” [11] remains. Such popular statements will be commented shortly in the concluding section.

1 Assumptions and Preconditions

We will consider Measurement and Observation Procedures [9] and will use their common terminology. Fortunately, after slight adaptations of terminology and corresponding statements, the presented concepts prove valid in other fields too. Additionally, we assume that all quantities to be measured and observed are well defined, in spite of the fact that there are always severe discussions about definitions and meanings of quantities.

The well-known Cause and Effect Principle allows multiple quantities as causes, considered as inputs to the process. They may even occur correlated. We may also recognise multiple quantities as effects, ...

Table of contents

• Cover Page
• Title Page
• Copyright
• Contents
• Foreword
• Analysis of key comparisons with two reference standards: Extended random effects meta-analysis
• Confirmation of uncertainties declared by KC participants in the presence of an outlier
• Quantity in metrology and mathematics: A general relation and the problem
• Bayesian analysis of an errors-in-variables regression problem
• Triangular Bézier surface: From reconstruction to roughness parameter computation
• On the classification into random and systematic effects
• Measurement models
• Metrology and mathematics — Survey on a dual pair
• Fundaments of measurement for computationally-intensive metrology
• Study of gear surface texture using Mallat’s scattering transform
• The evaluation of the uncertainty of measurements from an autocorrelated process
• Dynamic measurement errors correction in sliding mode based on a sensor model
• The Wiener degradation model with random effects in reliability metrology
• EIV calibration of gas mixture of ethanol in nitrogen
• Models and algorithms for multi-fidelity data
• Uncertainty calculation in the calibration of an infusion pump using the comparison method
• Determination of measurement uncertainty by Monte Carlo simulation
• A generic incremental test data generator for minimax-type fitting in coordinate metrology
• NLLSMH: MCMC software for nonlinear least-squares regression
• Reduced error separating method for pitch calibration on gears
• Mathematical and statistical tools for online NMR spectroscopy in chemical processes
• A new mathematical model to localize a multi-target modular probe for large-volume metrology applications
• Soft sensors to measure somatic sensations and emotions of a humanoid robot
• Bayesian approach to estimation of impulse-radar signal parameters when applied for monitoring of human movements
• Challenging calculations in practical, traceable contact thermometry
• Wald optimal two-sample test for right-censored data
• Measurement
• Sensitivity analysis of a wind measurement filtering technique
• The simulation of Coriolis flowmeter tube movements excited by fluid flow and exterior harmonic force
• Indirect light intensity distribution measurement using image merging
• Towards smart measurement plan using category ontology modelling
• Analysis of a regional metrology organization key comparison: Preliminary consistency check of the linking-laboratory data with the CIPM key comparison reference value
• Stationary increment random functions as a basic model for the Allan variance
• Modelling a quality assurance standard for emission monitoring in order to assess overall uncertainty
• Integrating hyper-parameter uncertainties in a multi-fidelity Bayesian model for the estimation of a probability of failure
• Application of ISO 5725 to evaluate measurement precision of distribution within the lung after intratracheal administration
• Benchmarking rater agreement: Probabilistic versus deterministic approach
• Regularisation of central-difference method when applied for differentiation of measurement data in fall detection systems
• Polynomial estimation of the measurand parameters for samples from non-Gaussian distributions based on higher order statistics
• EIV calibration model of thermocouples
• Modeling and evaluating the distribution of the output quantity in measurement models with copula dependent input quantities
• Bayesian estimation of a polynomial calibration function associated to a flow meter
• Dynamic measurement errors correction adaptive to noises of a sensor
• Author index
• Keyword index