This section gives an overview of measurement uncertainty and errors and critically reviews different existing in-situ measurement error propagation techniques, prior to presenting the error propagation method developed and proposed for this thesis.
3.3.4.1. Sources of error and uncertainty
Uncertainty in in-situ heat-flux measurements can be associated with measurement
techniques used (for example, where air temperatures are measured), as well as the addition of constant surface thermal resistances where surface temperatures are used - see Section 3.3.3. In addition, uncertainty in obtaining a whole element U-value is associated with the number of point-values used to estimate this whole element U-value and how representative the observed point-values are of the entire fabric element (Section 3.3.2). Uncertainty with in-situ field measurements is also associated with seasonal influences and the natural variability of heat-flow through a construction element (and is affected by timing of the monitoring campaign) - this is further discussed below.
Moreover, like all field measurements using instruments, in-situ heat-flux measurements are affected by the conditions of measurement and instruments used, which have errors
associated with them. It is for these reasons that, even when measuring over sufficiently long periods, the in-situ method in non-steady state conditions is not a high precision method (BSI, 2014). The act of measuring affects what is being measured: for instance, placing a heat-flux sensor on a surface inherently affects the characteristics of what is being attempted to be measured (Childs, 1999), leading, for example, to random or systematic deflection and reflection errors. This means that measurement results can only ever be an estimate of the true value rather than the actual true value. It is therefore important that these errors are as best as possible accounted for as this affects the measurement results, confidence in findings and comparability between different sources, published literature, specifications, standards, models (JCGM, 2008, Czichos, 2011) and comparison of the heat-flow reduction potential of intervention measures. For example, it is generally accepted that the difference between measurements (and hence also the efficacy of interventions) is only 'demonstrated' if measurement uncertainties do not overlap (Taylor, 1997).
However, the exact number of errors and of possible confounders, and the magnitude of their effect is not known, despite influencing the estimated result. These errors can be systematic or random. Systematic errors usually relate to accuracy and spread the readings around some displaced, but not true value (Squires, 2001) and cannot be controlled for by repeated measurements (Taylor, 1997). Systematic errors include instrument accuracy (how close it is certified to a known value), instrument erroneous calibration, research practice and design (e.g. differences in sensor fixings), and their exact influence is usually unknown but should instead be minimised for by careful research design and practice. Though small, the systematic additional influence of the thermal resistance of the heat-flux sensor itself of 6.25 x 10-3 m2K/W (Hukseflux, 2012) can be accounted for by adjusting for (i.e. deducting this factor) in R- and U-value estimations, as has been done in this research. Systematic errors could be only present (or absent) in certain conditions and could be systematic for each sensor but random between sensors or for a collection of sensors, making error estimation difficult. Random errors, usually associated with the precision (or repeatability) of
measurements, are equally likely to be positive or negative and are always present in an experiment and causes "successive readings to spread about the true value of the quantity"
(Squires, 2001). Random errors can be reduced by repeated measurements and might be revealed statistically from the spread/variation of repeated measurements (Taylor, 1997).
Random error sources include equipment set-up and researcher and occupant influence, though these might also be systematic errors or have systematic components. Usually results are accurate if they are "relatively free from systematic errors, and precise if the random error is small" (Squires, 2001) - clearly both are important.
Slightly different errors are estimated in different standards and are summarised in Appendix 3.D., adapted from Pelsmakers (2012). Given that ISO-9869 (BSI, 2014) is the UK and EU accepted protocol, its identified errors are summarised below, and was used in this thesis as a basis for uncertainty estimation.
As described in Section 3.3.3. there is difficulty to measure accurate temperatures which reflect the heat-flow path and this will create uncertainty, estimated at ±5% by ISO-9869 for
"temperature variations within the space and differences between air and radiant
temperatures"(BSI, 2014). In addition, there will be instrument errors (±5%, (BSI, 2014)) and contact errors (±5%, (BSI, 2014)) could arise if leaving a small gap between the sensor and the surface and (or) changing the airspeed around the sensor; contact error was found to be ≤2%
with airspeeds up to 1m/s (Bales, 1985). It should also be noted that airflow through the floor board gaps could create turbulence around the sensors and also affect any airflow between the sensors and the surface, though the airspeed around the sensors is unknown and this uncertainty is uncharacterised.
The mounting of the sensor on the surface changes the heat-flow that goes through the undisturbed surface, which can lead to operational deflection errors (Cesaratto et al., 2011, Childs, 1999, Trethowen, 1986); it is estimated by ISO-9869 (BSI, 2014) at ±2 to ±3% error though a slightly larger deflection error of ±4% is suggested by Doran (2008). Furthermore, masking tape smoothed over the sensor's edges can minimise "the differences in turbulent flow over the sensor compared to the adjacent wall." (Bales, 1985). Similar fixing strategies are likely to be relevant for floor sensor fixings. Additionally, ISO-9869 (BSI, 2014) estimates a
±10% error for "errors caused by the variations over time of the temperatures and heat-flow", i.e.
natural variability.
However, the natural variability of a U-value is not a measurement error but a real
characteristic of an element's actual thermal transmittance in dynamic situations; i.e.
U-values are not constant but change when subject to e.g. changes in radiation and airflow over time. To discuss this conceptual difference, it can be helpful to think of the identified errors as 'intrinsic' and 'extrinsic errors' (Bales, 1985) and separate these from the natural variability of U-values - as categorised in Table 8. Intrinsic errors are those related to instrument accuracy, while extrinsic properties are associated and contingent on the measurement application and technique used (Bales, 1985), i.e. related to measuring conditions. For example extrinsic errors come from how ambient temperatures are determined and from sensor fixing methods such as deflection and contact errors.
Instrument error
±3% Operational/deflection error ±10% Natural variability U
±5% Contact error
±5% Temperature sensor location measurement error; only for U-values4 when air temperatures used.
Total ISO-9869 error
- Equation 41. - see also Section 3.3.4.2.
Table 8. Summary of ISO-9869 estimated measurement uncertainties; categorisation by author.
As surface temperatures are used for estimation of R-values (BSI, 2014), the latter ±5% error 'temperature location measurement error' is considered applicable only to U-value estimates (D'Amelio, 2012a) where air temperatures are generally used - this is further discussed in Section 3.3.4.3.
3.3.4.2. Different error propagation methods
Following on from the previous overview of ISO-9869 estimated errors, an overview is provided here of the ISO-9869 error propagation method as well as Baker's (2011) error propagation technique as this is used by several other researchers in the UK, followed by any other techniques.
3 Often 'accuracy' issues tend to be systematic errors; instrument documentation tends to state instrument calibration accuracy as a ± value; the ± value suggests random error, which it is for a range of sensors, but systematic (but unknown in which direction) per sensor. Given that this systematic error is known, and its direction could be either way, it might be offset by other random errors, hence combination in the quadratic sum with other (random) errors is appropriate. Taylor (1997, p106-107) argues that systematic errors combined with random errors in quadrature could be combined to give a "reasonable estimate of our total uncertainty, given that our apparatus has systematic uncertainties we could not eliminate". Other systematic calibration errors can however occur in determining the accuracy of instruments, which could lead to an offset in the instrument accuracy, which is often only revealed when measuring the same quantity with different sensors side-by-side or upon
re-calibration.
4 The ±5% error is not directly stated in ISO-9869 but interpreted from the addition of another ±5% error in the quadratic sum and arithmetic sum not accounted for above - as also interpreted by D'Amelio (2012a).