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Metrology, the science of measurement, involves the determination from experiment of estimates of the values of physical quantities, along with the associated uncertainties. In this endeavour, a mathematical model of the measurement system is required in order to extract information from the experimental data. Modelling involves model building : developing… (More)

- Valerie N. Livina, Tatiana M Martins, A. B. Forbes
- Chaos
- 2015

We apply tipping point analysis to nine observational oxygen concentration records around the globe, analyse their dynamics and perform projections under possible future scenarios, leading to oxygen deficiency in the atmosphere. The analysis is based on statistical physics framework with stochastic modelling, where we represent the observed data as a… (More)

- A. B. Forbes
- Numerical Algorithms
- 1993

This paper is concerned with generalised regression models in metrology. In experiments where much is known about the nature of the error in the measurement data, it is possible to build comprehensive mathematical models which lead to better estimates of the required parameter values. We indicate how efficient optimisation algorithms can be developed which… (More)

- R. M. Barker, A. B. Forbes
- 2001

Metrology, the science of measurement, involves the determination of physical quantities from experiment, along with estimates of their associated uncertainties. In this endeavour, a mathematical model of the measurement system is required in order to extract information from the experimental data. For the measurements to be reliable, these models must be… (More)

Fuzzy inference systems are widely used for classification and control. They can be designed from the training data. This paper describes a technique for deriving fuzzy classification rules from the interval-valued data. The technique based on a heuristic method of possibilistic clustering and a special method of the interval-valued data preprocessing.… (More)

- B. P. Butler, A. B. Forbes
- Numerical Algorithms
- 1993

The task of fitting a curve or surface to a number of related data sets is common in metrology. Thedata matching problem arises when sets of supplementary measurements are added to those of an underlying base set. Each supplementary set may have its own reference frame. This problem is formally equivalent to thedata splicing problem in which no one set… (More)

- A. B. Forbes
- 2009

This paper describes a fall-back procedure for use with the Gauss-Newton method for nonlinear least-squares problems. While the basic Gauss-Newton algorithm is often successful, it is well-known that it can sometimes generate poor search directions and exhibit slow convergence. For dealing with such situations we suggest a new two-dimensional search… (More)

- A. B. Forbes
- 2009

− This paper considers the analysis of observational data associated with the fundamental constants, in particular looking at issues of consistency and sensitivity.

- Paul J. Scott, A. B. Forbes
- Philosophical transactions. Series A…
- 2012

The aim of precision engineering is the accurate control of geometry. For this reason, mathematics has a long association with precision engineering: from the calculation and correction of angular scales used in surveying and astronomical instrumentation to statistical averaging techniques used to increase precision. This study illustrates the enabling role… (More)

− The assessment of the geometry of artefacts in length metrology is concerned with estimating dimension, form and roughness. While all three are positive quantities, the evaluation of form and roughness are problematic, mainly because the values of the parameters to be measured are often of the same order as the measurement uncertainty. Furthermore, random… (More)