GAS SENSING DEVICE FOR SENSING ONE OR MORE GASES IN A MIXTURE OF GASES

Abstract

A gas sensing device includes chemo-resistive gas sensors, wherein each of the gas sensors generates signals corresponding to concentrations of gases in a mixture of gases; a heating arrangement for heating gas sensors according to a periodic temperature profile; a preprocessing processor for receiving the signals from each of the gas sensors and for preprocessing the received signals to generate a preprocessed signal sample for each of the gas sensors for each period of the periodic temperature profile; a feature extraction processor configured for receiving the preprocessed signal samples and for extracting for each of the periods a set of feature values from the preprocessed signal samples received for the respective period; and a gas concentration processor for receiving sets of feature values.

Claims

1. A gas sensing device for sensing one or more gases in a mixture of gases; the gas sensing device comprising: one or more chemo-resistive gas sensors, wherein each of the gas sensors is configured for generating signals (SIG) corresponding to concentrations of the one or more gases in the mixture of gases; a heating arrangement configured in such way that the gas sensors are heated according to a periodic temperature profile (STP); a preprocessing processor configured for receiving the signals from each of the gas sensors and for preprocessing the received signals (SIG) in order to generate a preprocessed signal sample (PSS) for each of the gas sensors for each period (PER) of the periodic temperature profile (STP); a feature extraction processor configured for receiving the preprocessed signal samples (PSS) and for extracting for each of the periods (PER) a set of feature values (TFV, FFV) from the preprocessed signal samples (PSS) received for a respective period (PER), wherein each of the sets of feature values (TFV, FFV) comprises one or more time domain feature values (TFV), which are based on time domain characteristics of one of the preprocessed signal samples (PSS) received for the respective period (PER), and one or more frequency domain feature values (FFV), which are based on frequency domain characteristics of one of the preprocessed signal samples (PSS) received for the respective period (PER); a gas concentration processor configured for receiving the sets of feature values (TFV, FFV), and for creating for each of the sets of feature values (TFV, FFV) a sensing result (SR) for each of the gases, wherein the gas concentration processor comprises a trained model based algorithm processor and one or more trained models for the trained model based algorithm processor, wherein at least a portion of a respective set of feature values (TFV, FFV) is fed to inputs of the trained model based algorithm processor using one of the one or more trained models, wherein the sensing results (SR) are based on output values (OV) at outputs of the trained model based algorithm processor.

2. A gas sensing device according to claim 1, wherein the preprocessing processor comprises a baseline normalization processor configured for normalizing the signals (SIG) received from the gas sensors.

3. A gas sensing device according to claim 1, wherein the preprocessing processor comprises a sine period extraction processor configured for receiving a control signal (CS) from the heating arrangement and for extracting a starting time (ST) and an end time (ET) for one of the periods (PER) from the control signal (CS).

4. A gas sensing device according to claim 1, wherein the feature extraction processor comprises a slope calculation processor configured for calculating for each of the periods (PER) a slope for each of the preprocessed signal samples (PSS) received for the respective period (PER), wherein the feature extraction processor is configured for using the slope of one of the periods (PER) as one of the time domain feature values (TFV) of the set of feature values (TFV, FFV) of the respective period (PER).

5. A gas sensing device according to claim 1, wherein the feature extraction processor comprises a sensitivity calculation processor configured for calculating for each of the periods (PER) a sensitivity for each of the preprocessed signal samples (PSS) received for the respective period (PER), wherein the feature extraction processor is configured for using the sensitivity of one of the periods (PER) as one of the time domain feature values (TFV) of the set of feature values (TFV, FFV) of the respective period (PER).

6. A gas sensing device according to claim 1, wherein the feature extraction processor comprises a time-to-frequency converting processor configured for converting each of the preprocessed signal samples (PSS) from a time domain into a frequency domain in order to calculate a spectrum (SP) for each of the preprocessed signal samples (PSS), wherein the frequency domain feature values (FFV) for a respective preprocessed signal sample (PSS) are calculated from a respective spectrum (SP).

7. A gas sensing device according to claim 6, wherein the feature extraction processor comprises an amplitude calculation processor configured for calculating for each of the periods (PER) at least one amplitude of the spectrum (SP) of each of the preprocessed signal samples (PSS) received for the respective period (PER), wherein the feature extraction processor is configured for using at least one of the amplitudes calculated for one of the periods (PER) as one of the frequency domain feature values (FFV) of the set of feature values (TFV, FFV) of the respective period (PER).

8. A gas sensing device according to claim 6, wherein the feature extraction processor comprises a phase calculation processor configured for calculating for each of the periods (PER) at least one phase of the spectrum (SP) of each of the preprocessed signal samples (PSS) received for the respective period (PER), wherein the feature extraction processor is configured for using at least one of the phases calculated for one of the periods (PER) as one of the frequency domain feature values (FFV) of the set of feature values (TFV, FFV) of the respective period (PER).

9. A gas sensing device according to claim 6, wherein the feature extraction processor comprises a total harmonic distortion calculation processor configured for calculating for each of the periods (PER) at least one total harmonic distortion of the spectrum (SP) of each of the preprocessed signal samples (PSS) received for the respective period (PER), wherein the feature extraction processor is configured for using at least one of the total harmonic distortions calculated for one of the periods (PER) as one of the frequency domain feature values (FFV) of the set of feature values (TFV, FFV) of the respective period (PER).

10. A gas sensing device according to claim 1, wherein the preprocessing processor comprises a relative resistance extracting processor configured for extracting relative resistance changes of the gas sensors from the signals (SIG) received from the gas sensors, wherein the preprocessing processor is configured for using relative resistance changes for generating the preprocessed signal samples (PSS).

11. A gas sensing device according to claim 1, wherein the preprocessing processor comprises a relative conductance extracting processor configured for extracting relative conductance changes of the gas sensors from the signals (SIG) received from the gas sensors, wherein the preprocessing processor is configured for using relative conductance changes for generating the preprocessed signal samples (PSS).

12. A gas sensing device according to claim 1, wherein the gas sensing device comprises: a drift calculation processor configured for calculating for each of the sensors a drift of a respective sensor signal (SIG), and a feature selection processor configured for selecting for each of the sensors, based on the drift of the respective sensor, which of the feature values (TFV, FFV) of one of the sets of feature values (TFV, FFV) are fed to inputs of the trained model based algorithm processor.

13. A gas sensing device according to claim 1, wherein the periodic temperature profile (STP) is a sinusoidal temperature profile (STP).

14. A method for operating a gas sensing device for sensing one or more gases in a mixture of gases; the gas sensing device comprising one or more chemoresistive gas sensors, wherein the method comprises: using each of the gas sensors for generating signals (SIG) corresponding to concentrations of the one or more gases in the mixture of gases; using a heating arrangement in such way that the gas sensors are heated according to a periodic temperature profile (STP); using a preprocessing processor for receiving the signals (SIG) from each of the gas sensors and for preprocessing the received signals (SIG) in order to generate a preprocessed signal sample (PSS) for each of the gas sensors for each period (PER) of the periodic temperature profile (STP); using a feature extraction processor for receiving the preprocessed signal samples (PSS) and for extracting for each of the periods (PER) a set of feature values (TFV, FFV) from the preprocessed signal samples (PSS) received for a respective period (PER), wherein each of the sets of feature values (TFV, FFV) comprises one or more time domain feature values (TFV), which are based on time domain characteristics of one of the preprocessed signal samples (PSS) received for the respective period (PER), and one or more frequency domain feature values (FFV), which are based on frequency domain characteristics of one of the preprocessed signal samples (PSS) received for the respective period (PER); and using a gas concentration processor for receiving the sets of feature values (TFV, FFV), and for creating for each of the sets of feature values (TFV, FFV) a sensing result (SR) for each of the gases, wherein the gas concentration processor comprises a trained model based algorithm processor and at least one trained model for the trained model based algorithm processor, wherein at least a portion of a respective set of feature values (TFV, FFV) is fed to inputs of the trained model based algorithm processor, wherein the sensing results (SR) are based on output values (OV) at outputs of the trained model based algorithm processor.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Preferred embodiments of the invention are subsequently discussed with respect to the accompanying drawings, in which:

[0051] FIG. 1 shows a schematic view of a first exemplary embodiment of a gas sensing device according to the disclosure, which comprises four chemoresistive gas sensors;

[0052] FIG. 2 illustrates an exemplary period of a periodic temperature profile provided by a heating arrangement and a signal provided by a chemoresistive gas sensor heated according to the periodic temperature profile;

[0053] FIG. 3 shows a schematic view of a second exemplary embodiment of a gas sensing device according to the disclosure, which comprises four chemoresistive gas sensors;

[0054] FIG. 4 illustrates an exemplary plot of an exemplary relative estimation error as a function of the drift rate for different sets of feature values;

[0055] FIG. 5 shows an exemplary graphene multi-gas sensor array according to the disclosure;

[0056] FIG. 6 illustrates an exemplary implementation of the feature extraction for a periodic sensor signal;

[0057] FIG. 7 illustrates an exemplary preprocessed signal sample and a spectrum derived therefrom;

[0058] FIGS. 8A, 8B, 8C, and 8D illustrate exemplary training steps for a trained model using linear discriminant analysis;

[0059] FIG. 9 illustrates exemplary plots of exemplary time domain feature values and of exemplary frequency domain feature values for a specific gas concentration profile; and

[0060] FIG. 10 illustrates an exemplary plot of an exemplary relative estimation error and of an exemplary R2 score for time domain feature values and for frequency domain feature values as a function of time.

[0061] Equal or equivalent elements or elements with equal or equivalent functionality are denoted in the following description by equal or equivalent reference numerals.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0062] In the following description, a plurality of details is set forth to provide a more thorough explanation of embodiments of the present disclosure. However, it will be apparent to those skilled in the art that embodiments of the present disclosure may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form rather than in detail in order to avoid obscuring embodiments of the present disclosure. In addition, features of the different embodiments described hereinafter may be combined with each other, unless specifically noted otherwise.

[0063] FIG. 1 shows a schematic view of a first exemplary embodiment of a gas sensing device 1 according to the disclosure, which comprises four chemoresistive gas sensors 2.

[0064] The gas sensing device 1 is configured for sensing one or more gases in a mixture of gases. The gas sensing device 1 comprises: [0065] one or more chemoresistive gas sensors 2, wherein each of the gas sensors 2 is configured for generating signals SIG corresponding to concentrations of the one or more gases in the mixture of gases; [0066] a heating arrangement 3 configured in such way that the gas sensors 2 are heated according to a periodic temperature profile STP; [0067] a preprocessing processor 4 configured for receiving the signals SIG from each of the gas sensors 2 and for preprocessing the received signals SIG in order to generate a preprocessed signal sample PSS for each of the gas sensors 2 for each period PER of the periodic temperature profile STP; [0068] a feature extraction processor 5 configured for receiving the preprocessed signal samples PSS and for extracting for each of the periods PER a set of feature values TFV, FFV from the preprocessed signal samples PSS received for the respective period PER, wherein each of the sets of feature values TFV, FFV comprises one or more time domain feature values TFV, which are based on time domain characteristics of one of the preprocessed signal samples PSS received for the respective period PER, and one or more frequency domain feature values FFV, which are based on frequency domain characteristics of one of the preprocessed signal samples PSS received for the respective period PER; [0069] a gas concentration processor 6 configured for receiving the sets of feature values TFV, FFV, and for creating for each of the sets of feature values TFV, FFV a sensing result SR for each of the gases, wherein the gas concentration processor 6 comprises a trained model based algorithm processor 7 and one or more trained models 8 for the trained model based algorithm processor 7, wherein at least a portion of the respective set of feature values TFV, FFV is fed to inputs 9 of the trained model based algorithm processor 7 using one of the one or more trained models 8, wherein the sensing results SR are based on output values OV at outputs 10 of the trained model based algorithm processor 7.

[0070] According to embodiments of the disclosure the preprocessing processor 4 comprises a baseline normalization processor 11 configured for normalizing the signals SIG received from the gas sensors 2.

[0071] According to embodiments of the disclosure the preprocessing processor 4 comprises a sine period extraction processor 12 configured for receiving a control signal CS from the heating arrangement 3 and for extracting a starting time ST and an end time ET for one of the periods PER from the control signal CS.

[0072] According to embodiments of the disclosure the feature extraction processor 5 comprises a slope calculation processor 13 configured for calculating for each of the periods PER a slope for each of the preprocessed signal samples PSS received for the respective period PER, wherein the feature extraction processor 5 is configured for using the slope of one of the periods PER as one of the time domain feature values TFV of the set of feature values TFV, FFV of the respective period PER.

[0073] According to embodiments of the disclosure the feature extraction processor 5 comprises a sensitivity calculation processor 14 configured for calculating for each of the periods PER a sensitivity for each of the preprocessed signal samples PSS received for the respective period PER, wherein the feature extraction processor 5 is configured for using the sensitivity of one of the periods PER as one of the time domain feature values TFV of the set of feature values TFV, FFV of the respective period PER.

[0074] According to embodiments of the disclosure the feature extraction processor 5 comprises a time-to-frequency converting processor 15 configured for converting each of the preprocessed signal samples PSS from a time domain into a frequency domain in order to calculate a spectrum SP for each of the preprocessed signal samples PSS, wherein the frequency domain feature values FFV for the respective preprocessed signal sample PSS are calculated from the respective spectrum SP.

[0075] According to embodiments of the disclosure the feature extraction processor 5 comprises an amplitude calculation processor 16 configured for calculating for each of the periods PER at least one amplitude of the spectrum SP of each of the preprocessed signal samples PSS received for the respective period PER, wherein the feature extraction processors is configured for using at least one of the amplitudes calculated for one of the periods PER as one of the frequency domain feature values FFV of the set of feature values TFV, FFV of the respective period PER.

[0076] According to embodiments of the disclosure the feature extraction processor 5 comprises a phase calculation processor 17 configured for calculating for each of the periods PER at least one phase of the spectrum SP of each of the preprocessed signal samples PSS received for the respective period PER, wherein the feature extraction processor 5 is configured for using at least one of the phases calculated for one of the periods PER as one of the frequency domain feature values FFV of the set of feature values TFV, FFV of the respective period PER.

[0077] According to embodiments of the disclosure the feature extraction processor 5 comprises a total harmonic distortion calculation processor 18 configured for calculating for each of the periods PER at least one total harmonic distortion of the spectrum SP of each of the preprocessed signal samples PSS received for the respective period PER, wherein the feature extraction processor 5 is configured for using at least one of the total harmonic distortions calculated for one of the periods PER as one of the frequency domain feature values FFV of the set of feature values TFV, FFV of the respective period PER.

[0078] In a further aspect, the disclosure refers to a method for operating a gas sensing device 1 for sensing one or more gases in a mixture of gases, wherein the gas sensing device 1 comprises one or more chemoresistive gas sensors 2, wherein the method comprises the steps of: [0079] using each of the gas sensors 2 for generating signals SIG corresponding to concentrations of the one or more gases in the mixture of gases; [0080] using a heating arrangement 3 in such way that the gas sensors 2 are heated according to a periodic temperature profile STP; [0081] using a preprocessing processor 4 for receiving the signals SIG from each of the gas sensors 2 and for preprocessing the received signals SIG in order to generate a preprocessed signal sample PSS for each of the gas sensors 2 for each period PER of the periodic temperature profile STP; [0082] using a feature extraction processor 5 for receiving the preprocessed signal samples PSS and for extracting for each of the periods PER a set of feature values TFV, FFV from the preprocessed signal samples PSS received for the respective period PER, wherein each of the sets of feature values TFV, FFV comprises one or more time domain feature values TFV, which are based on time domain characteristics of one of the preprocessed signal samples PSS received for the respective period PER, and one or more frequency domain feature values FFV, which are based on frequency domain characteristics of one of the preprocessed signal samples PSS received for the respective period PER; [0083] using a gas concentration processor 6 for receiving the sets of feature values TFV, FFV, and for creating for each of the sets of feature values TFV, FFV a sensing result SR for each of the gases, wherein the gas concentration processor 6 comprises a trained model based algorithm processor 7 and at least one trained model 8 for the trained model based algorithm processor 7, wherein at least a portion of the respective set of feature values TFV, FFV is fed to inputs 9 of the trained model based algorithm processor 7, wherein the sensing results SR are based on output values OV at outputs 10 of the trained model based algorithm processor 7.

[0084] The overall algorithm flow starts with collecting the measured signals SIG, which may be resistance data of the respective sensor 2. An inversion of the resistance signals is performed if they appear to have a more linear conductance drift than resistance drift. In a preprocessing processor 4, the signals SIG are normalized with a baseline and individual sine periods PER are confined for the feature extraction processor 5. The extracted features TFV, FFV are then used as input to a trained model based algorithm processor 7 that performs the actual prediction of gas concentrations.

[0085] FIG. 2 illustrates an exemplary period of a periodic temperature profile STP provided by a heating arrangement 3 and a signal SIG provided by a chemoresistive gas sensor 2 heated according to the periodic temperature profile STP.

[0086] According to embodiments of the disclosure the periodic temperature profile STP is a sinusoidal temperature profile STP.

[0087] As shown in FIG. 2, the signal SIG, which refers to the conductance of the sensor 2, follows the sinusoidal temperature profile STP to some extend but is distorted in comparison. This distortion is more pronounced when the sensor 2 comes in to contact with higher gas concentrations and is not present if there is no sensor reactive gas present. The added distortion increases the information content in the signal SIG, which can be exploited to improve gas detection. By transforming the signal SIG, for example via Fourier transformation, into the frequency domain, frequency domain feature values FFV that capture this information can be extracted, e.g., the total harmonic distortion (THD) and the phase shift of the fundamental frequency component.

[0088] Frequency domain feature values FFV extracted in the frequency domain based on the dynamic of the signal SIG offer various advantages. One of them is the observation that in the event of changing gas concentrations, the impact on the dynamic of the signal SIG is immediate whereas the resistance change shows some hysteresis. The frequency domain features values FFV therefore offer a quick response to changes of the signal SIG. Another advantage is that the amount of distortion is independent from baseline changes (where by baselines the initial value of the sensor resistance in the presence of clean air is meant) and thus the corresponding frequency domain feature values FFV have the attribute of added robustness against drift in the signal SIG of the sensor 2. Furthermore, under a certain mode of operation (max. temperature, period length), it was observed that the distortion of the signal SIG is only experienced for ozone (O3) whereas it is not visible for other sensor reactive gases like nitrogen dioxide (NO2). This in turn yields frequency domain feature values FFV that are highly selective to ozone and show less cross-sensitivity to other gases, which can be efficiently exploited by judiciously designed signal processing.

[0089] FIG. 3 shows a schematic view of a second exemplary embodiment of a gas sensing device 1 according to the disclosure, which comprises four chemoresistive gas sensors 2.

[0090] According to embodiments of the disclosure the preprocessing processor 4 comprises a relative resistance extracting processor 19 configured for extracting relative resistance changes of the gas sensors 2 from the signals SIG received from the gas sensors 2, wherein the preprocessing processor 4 is configured for using the relative resistance changes for generating the preprocessed signal samples PSS.

[0091] According to embodiments of the disclosure the preprocessing processor 4 comprises a relative conductance extracting processor 20 configured for extracting relative conductance changes of the gas sensors 2 from the signals SIG received from the gas sensors 2, wherein the preprocessing processor 4 is configured for using the relative conductance changes for generating the preprocessed signal samples PSS.

[0092] According to embodiments of the disclosure the gas sensing device 2 comprises: [0093] a drift calculation processor 21 configured for calculating for each of the sensors 2 a drift of the respective sensor signal SIG, and [0094] a feature selection processor 22 configured for selecting for each of the sensors 2, based on the drift of the respective sensor 2, which of the feature values TFV, FFV of one of the sets of feature values TFV, FFV are fed to the inputs 9 of the trained model based algorithm processor 7.

[0095] FIG. 3 describes an embodiment of the gas sensing device 1 with a flow diagram. Starting with the signal SIG provided by the sensor 2, the resistance or the conductance of the sensor 2 is extracted. The latter provides a better visual alignment with the heating temperature, as seen in FIG. 2, but mainly the choice whether to use resistance or conductance as basis for further processing steps should be made based on which shows the more linear behavior over time (linear resistance drift vs. linear conductance drift) for the best overall performance and stability.

[0096] The following feature extraction processor 5 works both for resistance and for conductance. After the feature extraction processor 5, feature values TFV, FFV may be selected based on the application and their drift behavior to be fed to inputs 9 of the trained model based algorithm processor 7. If the sensor 2 is stable over time, all available features values TFV, FVV may be used to provide the most information to the trained model 8 which results in the best possible performance. If the sensor 2 experiences strong drift, which results in a large baseline offset, the information of the time domain feature values TFV degenerates. Consequently, only frequency domain feature values FFV may be used to have a stable and robust performance even under such conditions. For each scenario an individual trained model 8 may be used that is specifically trained for the chosen set of feature values TFV, FFV.

[0097] FIG. 4 illustrates an exemplary plot of an exemplary relative estimation error as a function of the drift rate for different sets of feature values TFV, FFV. FIG. 4 shows an example of how different sets of feature values TFV, FFV perform differently in the presence of a linear upward resistance drift. Depending on the drift rate (dR, in Ohm per second) different sets of feature values TFV, FFV may be selected as a tradeoff between performance, complexity and generalization capabilities to other gases.

[0098] The task of characterizing the drift can be seen as part of the overall design procedure for the gas sensing device 1. Here accelerated stress tests may be carried out to describe the long term behavior of the gas sensing device 1 and thus its ageing properties. Alternatively, the gas sensing device 1 can be operated in the field and observed over a long period of time (e.g., months) until its drift properties are fully described and correlated to other environmental factors. Last but not least, also the observation of the own data can be leveraged to understand if the drift is linear or not, for example by comparing long term and short term (few days) derivative trends or by correlating drifting and non-drifting features.

[0099] FIG. 5 shows an exemplary graphene multi-gas sensor array according to the disclosure. Each sensor 2.1, 2.2, 2.3 and 2.4 in the array is heated by a heat source of a heating arrangement 3, whose temperature is being controlled according to a periodic temperature profile. In other embodiments, the sensors 2.1, 2.2, 2.3 and 2.4 in the array are heated by a plurality of heat sources. For example, each of the sensors 2.1, 2.2, 2.3 and 2.4 could be heated individually by one heat source of the plurality of the heat sources.

[0100] The sensors 2.1, 2.2, 2.3 and 2.4 form a multi-gas sensor array, where a base material comprising graphene is functionalized with different chemicals (e.g., Pd, Pt, and MnO2) for dissimilar selectivity. The interaction between graphene sheets and absorbed gas analytes would influence the electronic structure of the material, resulting in altered charge carrier concentrations and changed electrical conductance or resistance respectively. Meanwhile, due to different sensitivity towards various gas molecules resistances of the sensors 2.1, 2.2, 2.3 and 2.4 also change in disparate patterns, making it possible to analyze complicated gas mixtures with one single sensor array.

[0101] FIG. 6 illustrates an exemplary implementation of the extraction of the feature values TFV, FFV for a (distorted) periodic signal SIG of the sensor 2, which is a sinusoidal signal SIG. The extraction of the feature values TFV, FFV is performed on single sine periods PER at a time. First, the slope is extracted, which may be used both directly as a time domain feature value TFV, representing the rate of change, as well as to flatten the waveform of the signal SIG. By subtracting the slope proportional to the length of the period PER, the individual sine periods PER are flattened, meaning the resulting sine periods PER are stationary. As a next step, the mean value of each period PER is calculated, which is the next time domain feature value TFV, representing the average conductance (or resistance) normalized to a baseline and is called sensitivity. As a final step in the time domain, the mean is subtracted from the periods PER of the signal SIG, removing the remaining DC offset of the periods PER of the signal SIG. The resulting periods PER of the signal SIG are then further processed in the frequency domain using a fast Fourier transform (FFT) algorithm in order to produce the spectrum of the respective period PER. The main features are the amplitude and the phase of the individual harmonics as well as the total harmonic distortion (THD). The calculation of the frequency domain feature values can be described as follows:

[0102] The definition for the total harmonic distortion used here is the ratio of the square root of the quadratic sum of the amplitude of the higher order harmonics to the fundamental frequency. For practicality a limit for the harmonics considered can be set, e.g. 10 harmonic components, which should result in no noticeable loss of information.

[0103] If feature values TFV, FFV are extracted one period PER after the other, the length of the periods PER is effectively setting the output rate of the sensing results SR. To overcome this a sliding window with the length of the periods PER and overlap between periods PER can be applied, practically allowing any rate of features extraction over time necessary for the application. For example, shifting the sliding window by one minute, results in a new set of feature values TFV, FFV produced every minute independent of the length of the periods PER.

[0104] After the feature extraction processor 5, the feature values TVF, FFV are used as input to a trained model based algorithm processor 7 to make actual predictions on gas concentration levels. The recurrent neural network illustrated in FIG. 1 has proven to be a sound choice for many scenarios, as it performs well on the time-series data provided by the gas sensor 2.

[0105] FIG. 7 illustrates an exemplary preprocessed signal sample PPS and a spectrum SP derived therefrom. It can be seen, that the sinusoidal preprocessed signal sample PPS is clearly distorted. Moreover, it can be seen that the spectrum SP comprises a fundamental frequency f.sub.1 and ten harmonics f.sub.2 to f.sub.11.

[0106] FIGS. 8A, 8B, 8C, and 8D illustrate exemplary training steps for a trained model 8 using linear discriminant analysis.

[0107] If, for example, less data is available to train a neural network, other approaches such as a model based on linear discriminant analysis (LDA) for feature transformation and dimensionality reduction and a simple exponential or polynomial regression function are viable as well. The features based on the periodic heater mode work just as well with classical machine learning approaches as they do with neural networks.

[0108] FIG. 9 illustrates exemplary plots of exemplary time domain feature values TFV and of exemplary frequency domain feature values FFV for a specific gas concentration profile, which comprises nitrogen dioxide and ozone, and which is shown top-left. The mean normalized conductivities G0 to G3 of the four sensors 2.1 to 2.4 of FIG. 5 are shown middle-left and the corresponding slopes m_G0 to m_G3 are shown bottom-left. The conductivities G0 to G3 and the slopes m_G0 to m_G3 may be used as time domain feature values TFV.

[0109] The corresponding amplitudes fft_abs1_G0 to fft_abs1_G3 of the fundamental frequency are shown top-right, the corresponding total harmonic distortions fft_thd_G20 to fft_thd_G23 are shown middle-right, and the corresponding phases fft_angle1_G0 to fft_angle1_G3 are shown bottom-right. The amplitudes fft_abs1_G0 to fft_abs1_G3, the total harmonic distortions fft_thd_G20 to fft_thd_G23, and the phases fft_angle1_G0 to fft_angle1_G3 may be used as frequency domain feature values.

[0110] It is visible that especially the total harmonic distortions fft_thd_G20 to fft_thd_G23 and the phases fft_angle1_G0 to fft_angle1_G3 of the fundamental frequency show a strong correlation to the ozone concentration. They are however barely responsive to nitrogen dioxide which is due to the specific mode of operation (temperature, period length). When comparing the total harmonic distortions fft_thd_G20 to fft_thd_G23 and the phases fft_angle1_G0 to fft_angle1_G3 with the mean normalized conductivities G0 to G3, it is visible that the frequency domain feature values offer a much faster response and return quickly to the initial value when the ozone concentration goes to zero. The mean normalized conductivities G0 to G3 on the other hand are susceptible to slow response and drift, which makes it less robust on its own.

[0111] FIG. 10 illustrates an exemplary plot of an exemplary relative estimation error and of an exemplary R2 score for time domain feature values TFV and for frequency domain feature values FFV as a function of time. FIG. 10 shows the performance improvement obtained in terms of relative error (“Rel. Error FD Features”) and R2 score (“R2 score FD Features”) when using the newly extracted frequency domain feature values FFV versus the relative error (“Rel. Error TD Features”) and the and R2 score (“R2 score TD Features”) of the time domain feature values TFV in the presence of drifting signals SIG in the field. Time domain feature values TFV include the slope and sensitivity illustrated also in FIG. 4 and extracted prior to the time-to-frequency processor 15.

[0112] Although some aspects have been described in the context of an apparatus, it is clear that these aspects also represent a description of the corresponding method, where a block or device corresponds to a method step or a feature of a method step. Analogously, aspects described in the context of a method step also represent a description of a corresponding block or item or feature of a corresponding apparatus.

[0113] The above described is merely illustrative, and it is understood that modifications and variations of the arrangements and the details described herein will be apparent to others skilled in the art. It is the intent, therefore, to be limited only by the scope of the impending claims and not by the specific details presented by way of description and explanation above.