Humidity sensor calibration
When used over a wide range of relative humidity and temperature, hygrometers require large calibration data sets. For these, calibration equations provide useful summaries of complex sensor behaviour to users. Large data-sets combined with slow sensor response can mean humidity calibrations can take days to complete. MSL is investigating ways to reduce calibration time through more efficient use of transient calibration data.
One of the busiest areas of humidity sensor development is that of electrical impedance sensors that exploit a hygroscopic material whose dielectric properties alter as it absorbs water molecules. Calibration of these sensitive devices presents particular challenges.
Studies at MSL in collaboration with Spain’s national humidity laboratory INTA (Instituto Nacional de Técnica Aeroespacial) have identified a number of factors that influence the sensor or instrument response at the calibration measurement-point and contribute to the uncertainty. These include hysteresis and time constants of both calibration chamber and sensor; mismatch between the measured test temperature and the temperature in the immediate proximity of the sensor; and mismatch between the conditions of calibration and the subsequent conditions of use. Other conditions under laboratory control include: the period the sensor is exposed to constant conditions before data is logged (soak-time); flow-rate of air past the sensor; number and range of setpoints and pre-conditioning of instrument before changing setpoint.
The implications of immersion and self-heating effects on the calibration of relative humidity probes is not clearly understood. Our study has shown that the flow of heat to or from the test point can have two effects: (1) the temperature at the sensor differs from that of the surroundings and as a result the relative humidity at the sensor will also be different, and (2) the effect of temperature on the electronics located within the probe affects its electrical characteristics. As in thermometry, if the sensor is used under conditions nominally identical to those of calibration, immersion errors can be accounted for and practically eliminated.
The response of a relative humidity hygrometer is non-linear, complex and sensitive to many parameters including sensor temperature, thermal gradients, sensor speed, hysteresis, contamination and condensation.
In collaboration with the Netherlands national metrology institute NMi –VSL (NMi Van Swinden Laboratorium) MSL has investigated the use of calibrations equations for humidity applications. A humidity calibration requires measurements of the response R to reference humidity h and temperature t at sufficient points to ensure conditions of use are sampled. Figure 1 shows corrections, h – R, as calibration coverage increases.
(a) Simple 5-point calibration reveals quadratic structure.
(b) Hysteresis is sampled by stepping up and down in RH.
(c) Calibration cycle repeated at different temperatures
As a summary of the data, the calibration equation expresses the calibrated or corrected humidity H in terms of t and R. It enables interpolation between data points and estimation of the uncertainty associated with non-repeatability, irreproducibility and hysteresis. We have found the polynomial
to be sufficiently general to cover most calibrations. The parameters bj are determined from the calibration points (hi, Ri, ti) using the method of least squares The equation form varies because the originally linearized sensor response becomes more complex through contamination and adjustment as the instrument ages. The fitted equation minimises the standard deviation of the residuals s and yields statistically significant parameters and corrections. Insignificant parameters are set to zero and the fit repeated.
Equations quadratic in R (first three terms of (1)) can be fitted to the sets of data in Figure 1(a) and (b). For these fits, the residual error and calibration uncertainty is shown in Figure 2(a) and (b). The calibration uncertainty includes that associated with the reference, the device under test and the fitting procedure. While the residual error is small in Figure 2(a), the calibration uncertainty is severely optimistic since hysteresis has not been sampled. Hysteresis is evident in the residual error structure in Figure 2(b). Here the uncertainty is realistic provided the device is used at the calibration temperature.
Figure 2 Residual error and expanded uncertainty for fits to data in Figure 1.
In Figure 1 (c), corrections for calibration measurements taken at 5 different temperatures show that there is a clear temperature effect, which, if not corrected will lead to substantial error. As is reflected in Figure 2(c), the data is well fitted by a relative humidity-temperature calibration equation using all coefficients of (2). The expanded uncertainty is not much larger than that for the single temperature calibration but the resulting calibration equation allows traceable measurement over the full range of temperature for which the instrument is used.
Long response times and complex response can require lengthy calibration times in order to adequately characterise the hygrometer response.
During a calibration, the relative humidity is changed many times with set-points stepping up and down the humidity scale. The set-points (or a subset) may be repeated at different temperatures. In calibrations at MSL, the generator, chamber and sensor response are sampled continuously. Following a set-point transition, some time (30 – 60 mins) is allowed for the humidity generator, the calibration chamber and the sensor to come to an approximate thermodynamic equilibrium before the “steady state” humidity response is sampled over a period of 5 minutes or so. Thus, although much data is available and collected through the continuous monitoring, only a fraction (perhaps 10% to 15%) is actually used for the calibration analysis (see Figure 3).
Figure 3: The relative humidity (thick line) and temperature (thin line) response of a sensor monitored during a calibration. During a normal calibration, only a short section of data at the end of each “steady state” period is used (symbolised by “□” and “∆”).
Total Data Calibration (TDC) is the method whereby all data logged during the calibration is used to characterise, and hence calibrate, the sensor response. This requires an adequate model of the sensor response that includes time constants, hysteresis and steady state response. Since the model can be fitted to all data collected, not just to that collected at the end of a lengthy soak, set-point transitions can be made well before the system has reached equilibrium and thus calibration time can be significantly decreased. Furthermore, since for particular sensor types, typical time-constants and hysteresis behaviour will be derived, these may be used as starting points to calibrations of that type of sensor, further reducing the amount of data needing to be collected.
The challenges to be addressed include
- Determining an adequate model of hysteresis.
- Modelling the response of the sensor to single step wetting and drying transitions (over a range of humidity) and then any sequence of applied humidity transitions.
- Fitting the model to full and reduced calibration data in real time.
Determination of measurement sequences that minimise calibration time.
For further information on humidity sensor calibration, contact Jeremy Lovell-Smith
Benyon, R.; Lovell-Smith, J.W.; Mason, R.S.*; Vicente, T. 2001. "State of the art calibration of relative humidity sensors". Proceedings of TEMPMEKO 2001, 8th International Symposium on Temperature and Thermal Measurements in Industry and Science, Berlin, 2001. 1003-1008.
Lovell-Smith, J.W.; Benyon, R. 2002. "Immersion error in relative humidity probes". Papers from the 4th International Symposium on Humidity and Moisture ISHM2002, Taipei, 389-396. .
Lovell-Smith, J.; Neilsen, J. 2004. "Calibration equations for humidity applications". Proceedings of TEMPMEKO 2004, 9th International Symposium on Temperature and Thermal Measurements in Industry and Science, Cavtat,. 645-950.