T J Esward

Deconvolution filters for the analysis of dynamic measurement processes: a tutorial

Analysis of dynamic measurements is of growing importance in metrology as an increasing number of applications requires the determination of measurands showing a time-dependence. Often linear time-invariant (LTI) systems are appropriate for modelling the relation between the available measurement data and the required time-dependent values of the measurand. Estimation of the measurand is then carried out by deconvolution.This paper is a tutorial about the application of digital deconvolution filters to reconstruct a time-variable measurand from the measurement signal of a LTI measurement apparatus. The goal of the paper is to make metrologists aware of the potentialities of digital signal processing in such cases. A range of techniques is available for the construction of a digital deconvolution filter. Here we compare various approaches for a form of dynamic model that is relevant to many metrological applications and we discuss the consequences for these approaches of the different ways in which information about the LTI system may be expressed. We consider specifically the methods of minimum-phase all pass decomposition, asynchronous time reversal using the exact inverse filter and the construction of stable infinite impulse response and finite impulse response approximate inverse filters by a least squares approach in the frequency domain. The methods are compared qualitatively by assessing their numerical complexity and quantitatively in terms of their performance for a simulated measurement task.Taking into account numerical complexity and underlying assumptions of the methods, we conclude that when a continuous model of the LTI system is available, or when the starting point is a set of measurements of the frequency response of a system, application of least squares in the frequency domain for the construction of an approximate inverse filter is to be preferred. On the other hand, asynchronous time reversal filtering using the exact inverse filter appears superior when a discrete model of the LTI system is available and when causality of the deconvolution filter is not an issue.

A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system

This paper is concerned with bringing together the topics of uncertainty evaluation using a Monte Carlo method, distributed computing for data parallel applications and pseudo-random number generation. A study of a measurement system to estimate the absolute thermodynamic temperatures of two high-temperature blackbodies by measuring the ratios of their spectral radiances is used to illustrate the application of these topics. The uncertainties associated with the estimates of the temperatures are evaluated and used to inform the experimental realization of the system. The difficulties associated with determining model sensitivity coefficients, and demonstrating whether a linearization of the model is adequate, are avoided by using a Monte Carlo method as an approach to uncertainty evaluation. A distributed computing system is used to undertake the Monte Carlo calculation because the computational effort required to evaluate the measurement model can be significant. In order to ensure that the results provided by a Monte Carlo method implemented on a distributed computing system are reliable, consideration is given to the approach to generating pseudo-random numbers, which constitutes a key component of the Monte Carlo procedure.

Mathematical modelling to support traceable dynamic calibration of pressure sensors

This paper focuses on the mathematical modelling required to support the development of new primary standard systems for traceable calibration of dynamic pressure sensors. We address two fundamentally different approaches to realizing primary standards, specifically the shock tube method and the drop-weight method. Focusing on the shock tube method, the paper presents first results of system identification and discusses future experimental work that is required to improve the mathematical and statistical models. We use simulations to identify differences between the shock tube and drop-weight methods, to investigate sources of uncertainty in the system identification process and to assist experimentalists in designing the required measuring systems. We demonstrate the identification method on experimental results and draw conclusions.

The application of self-validation to wireless sensor networks

Self-validation is a valuable tool for extending the operating range of sensing systems and making them more robust. Wireless sensor networks suffer many limitations meaning that their efficacy could be greatly improved by self-validation techniques. We present two independently developed data analysis techniques and demonstrate that they can be applied to a wireless sensor network. Using an acoustic ranging application we demonstrate an improvement of more than ten-fold in the uncertainty of a single measurement where multiple sensor readings are appropriately combined. We also demonstrate that of the two methods for determining a largest consistent subset one is more rigorous in dealing with correlation, and the other more suited to time-series data.

Software simulation of a lock-in amplifier with application to the evaluation of uncertainties in real measuring systems

Lock-in amplifiers are widely used in metrology to extract a sinusoidal component of a known frequency from a signal that is noisy, returning estimates of the amplitude and phase of the component. A number of questions arise regarding the use by metrologists of the results returned by a lock-in amplifier. For example, what uncertainties should be associated with the estimates returned? How do these uncertainties vary as the signal-to-noise ratio changes? How do instrument errors affect the estimates and the associated uncertainties? In this paper a software simulation tool is described that may be used to process simulated or real (measured) signals, with the user allowed to associate uncertainties with the values of parameters that define the simulated signal and with those that define the operation of the instrument. The results of applying the software simulation tool to both simulated signals and real signals from infrared radiation and nanoindentation experiments are described.

Aggregating measurement data influenced by common effects

The requirement to aggregate measurement data, in the case where each measured value corresponds to nominally the same quantity, is important throughout metrology. Correlation associated with measured values is shown to arise in a number of measurement problems, with examples taken from the areas of interlaboratory comparisons, including key comparisons, the calibration of measuring systems and instruments, wireless sensor networks and prediction on the basis of different models. Consideration is given to the effect that correlation has on the determination of an aggregated estimate of the measured quantity, and on testing the consistency of measurement data. Approaches to quantifying the correlation associated with measured values are presented, and a formulation is given of the problem of determining the largest consistent subset of data having associated correlation. Results for three measurement problems are given, concerned with an interlaboratory comparison of noise in a coaxial line, the calibration of a thermometer and the analysis of data arising from a wireless sensor network.

Calculation of the distortion coefficient and associated uncertainty of PTB and LNE 1?GPa pressure balances using finite element analysis?EUROMET project 463

Results for pressure distortion coefficients (λ) obtained by five national metrology institutes with finite element methods (FEM) for PTB and LNE 1 GPa piston–cylinder units are presented. For the PTB unit they demonstrate good agreement of the FEM and the experimental distortion coefficients but rather large differences in the uncertainties, pressure distributions, gap profiles and piston fall rates. The reasons for differences between the theoretical real-gap and experimental λ obtained for the LNE unit require further clarification. The uncertainty of the gap geometry is identified as the main uncertainty source.

A model for characterizing the frequency-dependent variation in sensitivity with temperature of underwater acoustic transducers from historical calibration data

The performance of underwater electroacoustic transducers often depends on water temperature and, for accurate calibrations, it is necessary to take account of this influence on measurement data. Doing so is particularly important for open-water calibration facilities where the environmental conditions cannot be controlled and seasonal variations in temperature can contribute significant measurement uncertainty. This paper describes the characterization of the sensitivity of underwater electroacoustic transducers in terms of their variation with water temperature. A model containing adjustable parameters is developed for providing frequency-dependent temperature coefficients whose use enables measurement data to be corrected for temperature. Estimates of these coefficients are determined by applying the model to the time history of measurement data obtained over a period of several years. The influence of seasonal temperature variation can then be separated from the slow temporal drift in the transducer sensitivity. The uncertainties associated with the corrected sensitivity values are evaluated.

Measurement and simulation of clock errors from resource-constrained embedded systems

Resource-constrained embedded systems such as wireless sensor networks are becoming increasingly sought-after in a range of critical sensing applications. Hardware for such systems is typically developed as a general tool, intended for research and flexibility. These systems often have unexpected limitations and sources of error when being implemented for specific applications. We investigate via measurement and simulation the output of the onboard clock of a Crossbow MICAz testbed, comprising a quartz oscillator accessed via a combination of hardware and software. We show that the clock output available to the user suffers a number of instabilities and errors. Using a simple software simulation of the system based on a series of nested loops, we identify the source of each component of the error, finding that there is a 7.5 × 10−6 probability that a given oscillation from the governing crystal will be miscounted, resulting in frequency jitter over a 60 µHz range.

Getting software right

Ian Rutt is right to stress the importance of software engineering in the development of scientific software (August p22). Before beginning to develop any software code, you have to assess the possible damage to your personal standing – and to the reputation and finances of your employer – from getting the software wrong. In addition, failing to plan the software-development process from the start can often lead to erroneous results, much wasted time and expensive code re-writes.