Multivariate Calibration for Selective Analysis of Hydrogen Sulfide and Carbon Monoxide with Thermal Modulation of the SnO₂–PdO Sensor

Abstract

In this study, multivariate data processing during thermal modulation of the SnO₂–PdO gas sensor was performed using the multivariate calibration (MC) method. We propose to supplement this method with a procedure that allows the solving of problems of both quantitative and qualitative analysis. The advantage of the extended method (Multivariate Calibration for Selective Analysis, MCSA) compared to other methods is its modest requirements for computing resources, which allows it to be easily implemented on standard microcontrollers. The MCSA method opens up the prospect of creating compact gas analyzers of a new generation, capable of selective gas analysis in hard-to-reach places in an autonomous mode. The implementation of the MCSA method was demonstrated using the example of selective determination of hydrogen sulfide and carbon monoxide by a sensor whose temperature periodically changed from 100 to 450 °C. The training sample data were transformed by the MCSA method, which allowed for successful qualitative and quantitative analysis of the test sample data.

1. Introduction

The two main tasks of gas sensor analysis are to increase their sensitivity and selectivity. One of the most effective ways to solve these problems is to switch from steady-state operation modes of a metal oxide sensor to modulating its temperature. As we have shown earlier, a sharp change in temperature can lead to an increase in sensor sensitivity by two to three orders of magnitude [1]. In addition, temperature modulation can also increase the selectivity of the analysis performed by the sensor [2,3,4,5].

There are two fundamentally different approaches to increasing the selectivity of the analysis. One of them is to create highly selective sensors that have a significant sensitivity ratio between the target gas and the components of the system interfering with the determination. For example, when determining hydrogen sulfide, the cross-sensitivity was 5–6 orders of magnitude with respect to hydrogen, carbon monoxide, and ammonia [6]. In this case, the term “highly selective sensor” can be used. The second way to increase selectivity is to use several sensors combined into an “electronic nose” system [7,8,9,10,11]. The third way is temperature modulation of a low-selectivity sensor [12,13,14,15,16,17,18,19,20]. The first way is preferable because the use of highly selective sensors allows one to avoid the influence of any interfering components. At the same time, temperature modulation also has its advantages, including, for example, the possibility of selectively determining different gases and even gas mixtures [1,5] by a single low-selectivity sensor.

Many of these studies used a sinusoidal change in the sensor temperature [3,21,22,23] or a sawtooth change in its temperature [18]. The pulse mode with a sharp heating of the sensor also has its advantages. The first advantage is lower energy consumption by the sensor in the measurement cycle. The second advantage is the ability to sharply activate the catalyst at a time when the gas has not yet had time to desorb from the surface, which helps to increase the sensitivity of the sensor. In some studies, a feedback mechanism was used to increase sensitivity—the sensor temperature changed during the experiment depending on its resistance [19,24]. To increase sensitivity, temperature modulation of the sensor can also be combined with its light modulation due to UV radiation [25].

Each measurement cycle in the temperature modulation mode forms a vector data array, which can be similar to the vector data array of a multisensor system—an “electronic nose”. Measurements obtained by one sensor at different points in time of the measurement cycle are similar to measurements obtained by different sensors at the same point in time, so they can be processed by the same methods that are used for the “electronic nose”—the principal component method, artificial neural networks, etc. At the same time, there are fundamental differences between the multidimensional data obtained by one sensor in temperature modulation and the multidimensional data of the sensor array of the “electronic nose”. A single sensor does not form an independent set of components, but a correlated time series, allowing us to trace the functional relationship between the electrical resistance and the temperature of the sensor (in time from the beginning of the cycle). This opens up the possibility of using chemometric methods different from those used in “electronic nose” type systems [5].

In many previously published works, the authors used the Fourier transform [2,26,27,28] and the wavelet transform [23,26,29]. However, the study of these approaches did not lead to the creation of selective gas analyzers. Firstly, it was not possible to develop clear algorithms for selective analysis that could be implemented in devices. Secondly, these transformations, which are easily implemented by computer processors or specialized microchips, are not suitable for creating compact gas analyzers based on the use of simple mass-produced microcontrollers. The basis of this work is the development of a new chemometric MCSA method for processing multivariate data, which ensures high efficiency with relative simplicity of software implementation.

Improving the accuracy of analysis when using multivariate data can be achieved by using multivariate calibration algorithms [30,31,32]. Typically, this method of processing vector data is used only for quantitative analysis [33,34,35]. Currently, new methods for synthesizing metal oxide materials with increased chemisorption activity are being developed to create next-generation semiconductor sensors [36,37,38,39]. Sol–gel synthesis is most often used to solve practical problems, and SnO₂ continues to be the most common sensor material. Sensors based on it with palladium additives are widely used for commercial purposes and are the objects of further scientific research [40,41,42,43,44].

2. Materials and Methods

2.1. Synthesis and Characterization of Tin Dioxide Nanopowder

Sol–gel synthesis was used to create the gas-sensitive layer of the sensor. The first stage consisted of obtaining a highly dispersed sol of tin acid H₂SnO₃ by reacting tin (IV) acetate Sn(CH₃COO)₄ with a concentrated solution of ammonia NH₃. In the second stage, tin acid H₂SnO₃ was isolated by centrifugation and dried at a temperature of 120 °C. In the third stage, the obtained tin acid powder was calcined at a temperature of 500 °C, as a result of which tin acid H₂SnO₃ decomposed to tin dioxide nanopowder SnO₂ [5].

Transmission electron microscopy was used to evaluate the geometric dimensions of the nanoparticles of the tin dioxide SnO₂ used. The Carl Zeiss Libra 120 microscope was used. Characterization of SnO₂ tin dioxide nanopowder was performed by X-ray Diffraction (XRD) using an ARL X`TRA device operating in Bragg–Brentano geometry. The XRD patterns registration was performed in the θ-θ mode and the samples were placed on silicon substrates with a “zero background”. An X-ray tube with a copper anode (CuKα) was used as a source and discrimination of inelastically scattered radiation was performed by a semiconductor energy-dispersive detector with a resolution of 250 eV with a cooler on Peltier elements. To eliminate reflections from the substrate, the samples were tilted by 5° relative to the primary beam. The LaB₆ sample was used as an instrumental standard. The obtained diffraction patterns were decoded using the Powder Diffraction File (PDF-2) database.

2.2. Production of Gas-Sensitive Material SnO₂–PdO

At the first stage, tetraamminepalladium (II) nitrate [Pd(NH₃)₄](NO₃)₂ was added to nanodispersed tin dioxide SnO₂. At the second stage, the resulting nanopowder was mixed with a solution of ethylcellulose in terpineol to obtain a paste, which was applied to a special dielectric substrate containing platinum electrodes and a platinum heater. The sensor electrodes are two platinum pads 500 µm wide with a gap of 200 µm between the pads. The gas-sensitive layer was applied to these pads and the gap between them. Over the past years, we have manufactured and tested a wide range of electrode designs on various dielectric substrates and have consistently confirmed that, with correct calibration, the sensitivity and selectivity of the sensor are virtually independent of the geometric variations in the electrodes.

We estimated the sensor temperature by the resistance of the sensor heater with a previously determined temperature coefficient of its resistance α = 0.00295 K⁻¹. At the third stage, the substrate with a thin layer of paste applied to it was calcined at a temperature of 750 °C, as a result of which a gas-sensitive layer SnO₂–PdO was formed from the paste, which included 97% SnO₂ and 3% PdO (by weight) [5]. At the fourth stage, after the formation of the gas-sensitive layer, the sensor was soldered to the TO-8 housing (Figure 1).

2.3. Experimental Methodology with the Manufactured Gas Sensor

In this work, we used calibration gas mixtures of hydrogen sulfide H₂S with synthetic air, carbon monoxide CO with synthetic air, and hydrogen H₂ with synthetic air with concentrations of 10 and 200 ppm. The required concentrations were created by mixing the flows of the calibration gas mixture and synthetic air using a set of gas pressure regulators and mass flow controllers “Bronkhorst”, Ruurlo, Netherlands and “Eltochpribor”, Moscow, Russia.

To create a mixture of ethanol C₂H₅OH vapors with synthetic air, a special setup was used, which contained a 150 mL macro syringe, the piston of which moved automatically at a controlled speed. The required number of drops of ethanol solution in water were added to the macro syringe using a chromatographic syringe (1 μL). After equilibrium was established in the macro syringe chamber, the piston slowly pushed the gas mixture into the tee, where it was further diluted with synthetic air.

At the beginning of each measurement cycle, the manufactured sensor was heated from 100 °C to 450 °C over a period of 2 s, and then cooled from 450 °C to 100 °C over a period of 13 s. The measurement cycles lasting 15 s were continuously repeated. Figure 2 shows the change in sensor temperature over two measurement cycles (curve 1).

The air temperature was 25 ± 2 °C with a relative humidity of about 33%. As a rule, in studies of gas sensors of this type, the influence of the ambient temperature is usually considered negligible. The possibilities of the method for increasing the selectivity of analysis using temperature modulation of a semiconductor sensor were demonstrated in previous articles, for example, in [1]. There we showed that the influence of air humidity for sensors of this type with the above-mentioned temperature modulation is also not critical for the task of analyzing gas mixtures.

3. Results

3.1. Morphological and Composition Characterization

The image of SnO₂ nanopowder obtained by transmission electron microscopy is shown in Figure 3, allowing us to estimate the grain size at 7–10 nm.

The diffraction pattern of SnO₂ powder nanoparticles is shown in Figure 4. The left ordinate axis shows the PDF-2 database card information for the tetragonal modification of SnO₂. The experimentally obtained XRD data are shown on the right ordinate axis. It was found that the SnO₂ sample corresponds to the tetragonal SnO₂ phase (PDF card 21–1250). The coherent scattering region estimated using the Debye–Scherrer formula was 5.04 nm.

We have previously shown that the mismatch between the crystallite sizes determined by XRD and the grain size determined by transmission electron microscopy is explained by the composite nature of the grains, which have a core–shell structure [45].

3.2. Selective Determination of Hydrogen Sulfide

As shown in Figure 2, the analyzed gases have individual resistance–time dependences, which allows for both quantitative and qualitative gas analysis.

Figure 5 shows the change in sensor resistance over one measurement cycle for seven different hydrogen sulfide concentrations in the air. The dots in the figure mark a set of sensor electrical resistance values at a time of 10 s from the start of the cycle. Sixty electrical resistance values were taken from each of these seven curves. During the first five seconds of the cycle, when the changes were most significant, electrical resistance values were selected every 0.1 s—a total of 50 values. During the next 10 s, electrical resistance values were selected every second—another 10 values were selected. Thus, for each of the curves included in the 15 s measurement cycle, 60 electrical resistance values were selected.

One of the typical approaches to solving problems of qualitative analysis of multivariate data is to use a combination of principal component analysis (PCA) for efficient reduction in data dimensionality and any of the classification or regression methods [5], which requires a very resource-intensive projection of the observed data matrix of dimension md into the principal component space with an a priori complexity estimate as O(md²), where m is the number of observations (the number of measurement cycles) in the training sample and d is the original dimension of the observed vectors (the number of points recorded in one measurement cycle). The proposed MCSA method allows one to exclude the PCA transformation as the most computationally expensive operation by solving the classification problem using regression models for each of the analyte gases in the training set, which gives an a priori complexity estimate of the MCSA method as O(kcn²), where k is the number of analyte gases in the training sample, c is the number of parameters in the regression model, and n is the number of points for constructing the regression model. Taking into account typical values of key parameters, the MCSA method is able to reduce the computational complexity of the problem of qualitative analysis by 10³–10⁶ times.

Usually, regression models are built for electrical resistance from concentration $R=f\left(\phi \right)$. Since our main goal was to synthesize algorithms for an automatic gas analyzer, in order to reduce the number of microcontroller operations, we built regression dependences of concentration on electrical resistance $\phi =f^{-1}\left(R\right)$. Mathematically, such regression models are equivalent, but by inverting the function, the computational complexity of the algorithm can be reduced.

The empirical coefficients a and b were determined for the power multiplicative model describing the relationship between the observed values of the analyte gas concentration $\left\{{\phi }_i\right\}$ and the sensor resistance values $\left\{R_i\right\}$ at different points in time during the measurement cycle (Figure 6):

$${\phi }_i\left(R_i|t=10\right)=a·R_i^b·{\epsilon }_i \mathrm{for} i=1,2,\dots ,n,$$

(1)

where ${\epsilon }_i$ is the stochastic coefficient corresponding to the deviation of the observed concentration of the analyte gas from its predicted concentration and $n=60$ is the number of observations in the training part of the sample. Note that dependencies similar to (1) are typical for the description of sorption processes and can be written not only in the natural form of the power multiplicative model (1), but also in the linearized form of the logarithmic additive model $\log {\phi }_i=\log a+b\log R_i+\log {\epsilon }_i$, which can be seen in Figure 6, where a logarithmic scale is used for both axes.

Statistical estimates of the coefficients a and b for model (1) were also obtained for other sets $\left\{{\phi }_i\right(R_i\left)\right\}$ of concentrations and electrical resistances of the sensor, corresponding to other moments in the measurement cycle. The training set included a total of 60 sets of sensor resistances with 7 resistance values in each, corresponding to hydrogen sulfide concentrations of 0.5 ppm, 1 ppm, 2 ppm, 5 ppm, 10 ppm, 20 ppm, and 50 ppm. Thus, the array of electrical resistance values $\left\{R_i\right\}$, containing 420 values, was reduced to an array of coefficients $(a,b)$ of model (1) containing 120 values.

To control the quality of the model, a test part of the sample was formed from the data of experiments that were not included in the training part of the sample. In each test, 60 resistance values were used, corresponding to the same points in time as in the training part of the sample. For each of the 60 values of the sensor resistance $\left\{R_i\right\}$, the corresponding values of the concentration of the gas-analyte $\left\{{\phi }_i\right\}$ were determined using Equation (1) and the previously found coefficients $(a,b)$, while the coefficients and the resistance of the sensor corresponded to the same points in time from the beginning of the measurement cycle. Based on the found concentration values $\left\{{\phi }_i\right\}$, the sample mean $\overline{\phi }$ and relative standard deviation S_r were determined. The qualitative analysis procedure was performed by weighing the relative standard deviation with a certain critical value:

$$S_r={\displaystyle \frac{1}{\overline{\phi }}}\sqrt{{\displaystyle \frac{1}{m-1}}{\sum }_{j=1}^m{\left({\phi }_j-\overline{\phi }\right)}^2}<S_0.$$

(2)

In particular, if the relative standard deviation (2) satisfied the inequality H₀: S_r < 0.45, then the main hypothesis H₀ was accepted that the analyte is hydrogen sulfideH₂S, otherwise the alternative hypothesis H₁: S_r ≥ 0.45 was accepted that the analyte is any other gas. Analyzing the results of our experiments, we can see that the critical value S₀ = 0.45 provides excellent separation of the relative standard deviations for all concentrations of the target gas H₀: S_r < 0.45 from the relative standard deviations for all concentrations of other analyte gases H₀: S_r ≥ 0.45. As a result, we can formulate an empirical hypothesis that the critical value of the relative standard deviation S₀ = 0.45 minimizes the sum of the probabilities of statistical errors of type I and II.

As shown in Figure 7, for all tests with hydrogen sulfide, the relative standard deviation value satisfied the hypothesis H₀: S_r < 0.45, and for all tests with other analytes, on the contrary, H₁: S_r ≥ 0.45. Thus, it was possible to conduct a qualitative analysis for conventionally single-component mixtures of hydrogen sulfide H₂S with air, without statistical errors of types I and II the determination mixtures with air of different concentrations of hydrogen sulfide H₂S (green squares), carbon monoxide CO (blue squares), hydrogen H₂ (red squares), or ethanol C₂H₅OH (black squares), which entered the research chamber during experiments.

3.3. Selective Determination of Carbon Monoxide

Figure 8 shows the change in sensor resistance during one measurement cycle for seven different concentrations of carbon monoxide in the air. The set of sensor electrical resistance values at 10 s from the start of the cycle is marked with dots in the figure. Just as in the selective determination of hydrogen sulfide, sets of empirical coefficients $(a,b)$ were determined for the model (1). By analogy with the training set for hydrogen sulfide H₂S, the training set for carbon monoxide CO included the sensor resistance values $\left\{R_i\right\}$ at time t = 10 s corresponding to the following concentrations of CO in the air $\left\{{\phi }_i\right\}$: 1 ppm, 2 ppm, 5 ppm, 10 ppm, 20 ppm, 50 ppm, 100 ppm.

Experimental data not included in the training set were also used to test the model. As shown in Figure 9, for all tests with carbon monoxide, the relative standard deviation was less than the specified critical level H₀: S_r < 0.45, and for all tests with other analytes, the opposite was true, H₁: S_r ≥ 0.45. Thus, it was possible to conduct a qualitative analysis for conventionally single-component mixtures of carbon monoxide with air without statistical errors of types I and II.

4. Discussion

In prior publications [1,5], we explored various methods for processing multidimensional data, such as a selective analysis algorithm leveraging principal component analysis. An attempt to implement this PCA-based algorithm on a microcontroller for an industrial gas analyzer failed due to insufficient hardware resources. A similar limitation was encountered with artificial neural networks. Drawing on this experience, we developed the MCSA algorithm, which is specifically designed for constrained hardware environments.

In the MCSA algorithm proposed here, when processing test experiment data, in addition to the average concentration value, the relative standard deviation S_r of the concentration values for the analyzed part of the sample is also found. As shown above, the relative standard deviation will not exceed the critical level in S_r < S₀ if the test experiment was carried out for the same analyte gas for which the training sample was constructed. However, for other analyte gases, the relative standard deviation will exceed the critical level S_r ≥ S₀, since the parameters of model (1) were estimated using the training part of the sample for different concentrations of the target components—hydrogen sulfide H₂S and carbon monoxide CO, respectively, which generates a large dispersion in the concentration estimates.

From the point of view of machine learning theory, the solution to the problem of qualitative gas analysis based on comparison with the “critical value” of some metric calculated from sample data is a special case of the well-known “decision tree” method. The “critical value” is estimated empirically, based on the training sample data, and the correctness of the estimates obtained is verified using the test sample data. The representativeness of the data in the training and test samples ensures the correctness of the solution to practical problems with a given degree of uncertainty.

From the data shown in Figure 7, we note that (a) choosing S_r > 0.51 will increase the number of false-positive classifications (i.e., the proportion of type I statistical errors) and that (b) choosing S_r < 0.39 will increase the number of false-negative classifications (i.e., the proportion of type II statistical errors). The mean between these boundaries, S₀ = 0.45, was taken as the critical value that minimizes the probabilities for type I and type II statistical errors. As shown in Figure 7 and Figure 9, the qualitative analysis task was successfully solved for gas concentrations above 10 ppm, and in some cases, even below 10 ppm.

5. Conclusions

Temperature modulation of a semiconductor sensor opens up possibilities for creating a new generation of gas analyzers—inexpensive, compact, providing selective analysis in an autonomous mode in hard-to-reach places. At the same time, existing methods for processing multidimensional sensory data [1,5] are complex and require sufficiently productive microprocessors for their implementation.

In practice, there are two different tasks of selective gas analysis. The first of them is the qualitative and quantitative analysis of conventionally single-component mixtures, for example, hydrogen sulfide in the air or carbon monoxide in the air. In this case, it is assumed that the probability of the joint presence of different analytes in the air is negligibly small. If this assumption is incorrect, then a more complex task arises—determining the composition of two- or multi-component gas mixtures.

The methodology presented in this paper, although focused on the identification of a conventionally single-component gas mixture, also has the potential to determine the composition of multi-component mixtures, a task we have previously addressed using more computationally intensive data processing methods [1]. Extending the MCSA method to the analysis of two-component gas mixtures would require the collection of an expanded array of multivariate sensory data on the responses of mixtures with calibrated component ratios, which is the subject of our planned future research.

The novelty of the results presented in this article can be seen in the MCSA method—a chemometric method for analyzing multivariate sensor data. The proposed approach is applicable not only to the analysis of semiconductor sensor data, but also in other areas of analytical chemistry, for example, when processing spectral data. In addition, the proposed algorithm can be used to solve problems of applied mathematics related to identifying whether a curve belongs to a given family. Such problems can be typical for research in materials science, industrial safety, and ecology.