Efficient and Effective Gas Sensor Calibration with Randomized Gas Mixtures

Introduction The selective quantification of target gases in complex mixtures is an important part of numerous applications of chemical gas sensors. To this end, the data is usually evaluated with statistical models using lab calibration data. In most cases, the experimental design exposes the sensor to only a few fixed concentration levels, either one gas at a time or a limited number of pre-determined combinations [1]. This approach neglects masking effects and gas interactions as well as the risk of overfitting due to systematic influences. We present a calibration method based on randomized gas mixtures in which all calibration gases are present at each calibration point, with concentrations drawn from well-defined distributions reflecting the targeted application. Using indoor air quality monitoring as an example, we show that this method is superior to the classic “sequential” approach as well as flexible and easy to configure. Method The relevant gases for the measurement of indoor air quality can be divided into two groups: background (zero air, humidity and inorganic gases) and (very) volatile organic compounds ((V)VOC). Figure 1 illustrates the generation of randomized gas mixtures. The aim of the evaluation could be the quantification of TVOC (total VOC, here approximated by few gases as VOCsum). Alternatively, the (V)VOCs can be sub-divided into interferent and target VOCs with the aim of quantifying toxic or carcinogenic substances (here benzene and formaldehyde). As our current gas mixing system [2] is limited to six gases, two representatives were selected for inorganic background gases (hydrogen H2, carbon monoxide CO), interferent VOCs (acetone, toluene) and target VOCs (formaldehyde, benzene), respectively. The randomized gas mixtures were generated with a Python script and the distributions of the individual gases can be found in [3]. A total of 800 different mixtures were tested with each offered to the sensors for 20 min. For comparison with a sequential calibration strategy (ascending concentration values, one gas at a time), we also measured such a calibration profile. Each gas was offered at four different concentrations for 20 min each and this sequence was repeated three times at different humidity (Table 2). A total of eleven different sensors were tested, of which only the AS-MLV-P2 (ams AG) sensor is shown here. The sensor was operated in temperature cycles (TCO) [4]. For feature extraction mean and slope values were calculated for 120 equidistant ranges of each cycle. The best 20 features are selected using a principal component analysis to prevent overfitting. The quantification of the desired target value is carried out with partial least squares regression (PLSR). To compare the ability to quantify each individual gas in the given mixture, a performance value of performance = std(c(g))/RMSEP(g) - 1 is defined [3] where std(c(g)) is the standard deviation of the concentration distribution of gas g and RMSEP(g) is the root mean square error (RMSE) of the concentration prediction of the PLSR model for this gas. Results Figure 2 shows an example of a PLSR model for acetone trained with 100 randomized gas exposures (grey). The RMSE is calculated from 100 additional random gas exposures (dashed lines). The blue dots show the points predicted for 100 more gas exposures that were not used in training and validation. A good agreement of the test data set with the training data can be seen. To calculate the performance for the individual regression models (Table 2), the models are trained, validated and tested with a data set of 400 randomized gas mixtures. The highest performance (8.58) among individual gases is achieved for CO, i.e. the AS-MLV-P2 can quantify CO accurately in a variable background of all other gases. To compare randomized and sequential calibration (Table 3), three combinations are investigated: (1) training/validation randomized, testing randomized; (2) training/validation randomized, testing sequential; and (3) training/validation sequential, testing randomized. Validation is always performed with 6-fold cross-validation. For a fair comparison, randomized mixtures with all gases in the same concentration range as the sequential measurements were chosen. The best overall performance is achieved for randomized training with randomized testing with performance results well above one for five target gases whereas sequential training with randomized testing achieves the worst performance with a non-zero performance result only for CO. The randomized data is obviously more challenging to predict, which is expected due to the more realistic background. At the same time, this allows a more efficient training, as one data point for each gas is obtained from each gas mixture. Sequential calibration cannot provide a model for any target gas which is able to predict the more realistic random mixtures. The presented randomized calibration generates reliable models from a few gas exposures for a whole series of target gases and is, therefore, much more effective. For the calibration of mixtures, it is also much more efficient than combinatorial approaches. The presented method thus offers a promising approach for the successful transition of chemical sensors from the laboratory into the field. References [1] Wolfrum et al., Calibration transfer among sensor arrays designed for monitoring volatile organic compounds in indoor air quality, IEEE Sensors Journal, 6(2006), 1638–1643. doi:10.1109/JSEN.2006.884558. [2] Helwig et al., Gas mixing apparatus for automated gas sensor characterization, Measurement Science and Technology, 2014, 25(5), 055903–055903, doi:10.1088/0957-0233/25/5/055903. [3] Bastuck, dissertation, Saarland University and Linköping University (2019). doi:10.3384/diss.diva-159106. [4] Schütze, Sauerwald, Dynamic operation of semiconductor sensors, in: Semiconductor Gas Sensors, Woodhead Publishing, 2nd Edition, 2020, doi:10.1016/B978-0-08-102559-8.00012-4. Figure 1