Uncertainty in Acoustics

Measurement, Prediction and Assessment

Robert Peters, Robert Peters

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9780429894282
• Edition: 1
• Topic: Technik & Maschinenbau
• Subtopic: Akustiktechnik

This guide to estimating uncertainties in the measurement, prediction and assessment of noise and vibration applies across environmental noise and vibration, occupational noise and vibration exposure, and building and architectural acoustics.

The book collates information from the various Standards and from research, with explanation, examples and case studies. It enables estimation of uncertainty in the measurement and prediction of acoustic quantities, suitable for use in environmental impact and occupational exposure assessments. It is for acoustic consultants, mechanical and building service engineers, architect and building professionals and environmental health officers.

Bob Peters worked for more than forty years in acoustics and noise control – teaching, research, consultancy. He was a principal acoustic consultant with Applied Acoustic Design, a senior research fellow at London South Bank University, and a tutor on Institute of Acoustics distance learning courses.

Chapter 1

Introduction and Concepts

John Hurll

1.1 Introduction

In many aspects of everyday life, we are accustomed to the doubt that arises when estimating quantities, amounts, timings and the like. For example, if somebody asks, “What do you think the time is?” we might say, “It is about 10:15”. Use of the word “about” implies that we know that the time is not exactly 10:15 but is somewhere near it. In other words, we recognise, without really thinking about it, that there is some doubt about the time that we have estimated.

We could, of course, be a bit more specific. We could say, “It is 10:15 give or take five minutes”. The term “give or take” implies that there is still doubt about the estimate, but now we are assigning limits to the extent of the doubt. We have given some quantitative information about the doubt, or uncertainty, of our “guess”.

We will also be more confident that our estimate is within, say, five minutes of the correct time than we are that it is within, say, 30 seconds. The larger the uncertainty we assign in a given situation, the more confident we are that it encompasses the “correct” value. Hence, for that situation, the uncertainty is related to the level of confidence.

So far, our estimate of the time has been based on subjective knowledge. It is not entirely a guess, as we may have recently observed a clock or looked at our watch. However, in order to make a more objective measurement, we have to make use of a measuring instrument of some kind; in this case, we can use a timepiece of some kind. Even if we use a measuring instrument, there will still be some doubt, or uncertainty, about the result. For example, we could ask

“Is my watch accurate?”

“How well can I read it?”

“The watch is strapped to my wrist. Am I warming it up?”

So, to quantify the uncertainty of the time-of-day measurement, we will have to consider all the factors that could influence the result. We will have to make estimates of the possible variations associated with these influences. Let us consider some of these.

Is the watch accurate? In order to find out, it will be necessary to compare it with a timepiece or clock whose accuracy is better known. This, in turn, will have to be compared with an even better characterised one, and so on. This leads to the concept of traceability of measurements, whereby measurements at all levels can be traced back to agreed references. In most cases, measurements are required to be traceable to the International System of Units (SI system). This is usually achieved by an unbroken chain of comparisons to a national metrology institute, which maintains measurement standards that are directly related to SI units.

In other words, we need a traceable calibration. This calibration itself will provide a source of uncertainty, as the calibrating laboratory will assign a calibration uncertainty to the reported values. When used in a subsequent evaluation of uncertainty, this is often referred to as the imported uncertainty.

In terms of the accuracy of the watch, however, a traceable calibration is not the end of the story. Measuring instruments change their characteristics as time goes by. They “drift”. This, of course, is why regular recalibration is necessary. It is therefore important to evaluate the likely change since the instrument was last calibrated.

If the instrument has a reliable and convincing history, it may be possible to predict what the reading error will be at a given time in the future based on past results and apply a correction to the reading. This prediction will not be perfect, and therefore, an uncertainty on the corrected value will be present. In other cases, the past data may not indicate a reliable trend, and a limit value may have to be assigned for the likely change since the last calibration. This can be estimated from examination of changes that occurred in the past. Evaluations made using these methods yield the uncertainty due to secular stability, or changes with time, of the instrument. This is commonly known as “drift”.

How well can I read it? There will inevitably be a limit to which we can resolve the reading we observe on the watch. If it is an analogue device, this limit will often be imposed by our ability to interpolate between the scale graduations. If the device has a digital readout, the finite number of digits in the display – and our ability to assimilate them as they change – will define the limit. This also shows that there are human factors involved in the interpretation of measurement results. Another example of this is when a stopwatch is used – the reaction time of the operator may be significantly worse than the inherent accuracy of the stopwatch. This reveals some important issues. First, the measurement may not be independent of the operator, and special consideration may have to be given to operator effects. We may have to train the operator to use the equipment in a particular way. Special experiments may be necessary to evaluate particular effects. Additionally, evaluation of uncertainty may reveal ways in which the method can be improved, thus giving more reliable results. This is a positive benefit of uncertainty evaluation.

The watch is strapped to my wrist. Am I warming it up? Well, it certainly will be at a different temperature to the surroundings – but does this matter? All measuring instruments are, to some degree or other, influenced by the environment to which they are exposed, and it is the designers’ task to ensure that such influences are minimised. This is a general point that is applicable to all measurements. Every measurement we make has to be carried out in an environment of some kind; it is unavoidable. So we have to consider whether any particular aspect of the environment could have an effect on the measurement result. The following environmental effects are among the most commonly encountered when considering measurement uncertainty:

Ambient temperature, relative humidity and barometric pressure

Electric or magnetic fields, background charge

Gravity

Electrical supplies to measuring equipment

Presence of interfering objects (e.g. acoustic reflections, magnetic permeability)

Vibration and background noise

Light and optical reflections

Furthermore, some of these influences may have little effect as long as they remain constant, but they could affect measurement results if they are not constant.

It can be seen by now that understanding of a measurement system is important in order to identify and quantify the various uncertainties that can arise in a measurement situation. Conversely, analysis of uncertainty can often yield a deeper understanding of the system and reveal ways in which the measurement process can be improved. The points arising from such an analysis have to be asked, and answered, in order that we can devise an appropriate measurement method that gives us the information we require. Until we know the details of the method, we are not in a position to evaluate the uncertainties that will arise from that method. This leads to a most important question, one that should be asked before we even start with our evaluation of uncertainty: “What exactly is it that I am trying to measure?”

Until this qu...