A method of Gas sensor drift compensation based on intrinsic characteristics of response curve

doi:10.21203/rs.3.rs-2718240/v1

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A method of Gas sensor drift compensation based on intrinsic characteristics of response curve

https://doi.org/10.21203/rs.3.rs-2718240/v1

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published 24 Jul, 2023

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Sensor drift is an inevitable and challenging problem in gas sensing and an important problem in signal processing, as it seriously affects the detection performance and service life of sensor. In this study, a new sensor drift compensation method, which is based on intrinsic characteristic of sensory response, is proposed. The dataset for two different volatile organic compounds with a period of 36 months are employed and two kinds of features (one is steady-state feature, another is transient feature) are extracted. Their relationship is built and its change rule with sensor drift is explored. Then, drift compensation method is processed based on the change rule through iteration making the drifted sensor features adjusted to the value of month 1, which is considered as having no drift phenomenon. Moreover, the process is rapid. Finally, SVM is employed for proving the performance of the sensor drift compensation method proposed in this study. The results show the efficacy of 22 month of continuous monitoring, which has been enough for most application scenario, and almost 20% of increasement of correct classification rate of SVM after drift compensation, which indicates the effect of drift compensation method.

Physical sciences/Engineering

Physical sciences/Mathematics and computing

Signal drift

Gas sensor

Intrinsic characteristics

Relationship of features

Sensor is a way obtaining information, which is the most important and basic tool in information age. It has been largely applied in many areas^[1][2]. Gas sensor, which works based on volatiles, is an indispensable kind of sensor. Furthermore, it is a nondestructive and rapid detection way, which has aroused wide concern from researchers due to its close relation to practical applications. Because of those advantages, it has been successfully applied in many areas, such as air quality monitoring^[3], drunk driving^[4], food quality detection^[5], and so on.

Sensor drift is a phenomenon that sensory signal response would gradually and unpredictably change even exposed to the same analyte under identical condition when sensors are operated over a long period of time ^[6]. Existing types of gas sensor^[7][8] all belong to chemical sensor, where sensor drift is a serious impairment. Furthermore, sensor drift is an inevitable problem, which is the characteristic of sensor itself and has plagued the sensor research community for many years.

In general, sensor drift can be attributed to two predominant sources ^[9][10]: real drift and measurement system drift. The real drift due to the chemical and physical interaction processes of the chemical analytes, occurring at the sensing film microstructure. The measurement system drift is produced by the external and uncontrollable alterations of the experimental operating system.

Promoting anti-drift performance of sensor material and proposing a method for drift compensation are two main ways for solving sensor drift problem. Developing a new sensor material is cost-consuming and time-consuming, which make this way hard and unrealistic in recent years. By contrast, proposing a method for drift compensation is relatively easy and has high feasibility. Hence, many studies have been done for drift compensation and two main ways are proposed, which are divided based on providing reference gas or not.

Drift compensation method based on reference gas is a traditional way, whose data processing is simple and rapid. Furthermore, acceptable results could be obtained. Ziyatdinov et al.^[11] and Osuna^[12] proposed drift compensation methods based on common principal component analysis and Partial Least Square combined with reference gas, respectively. And, good results were both obtained. However, practically a new device is needed for supplying extra reference gas, which increases the detection cost and makes the detection process more complicated. Hence, it limits its application scenarios. Moreover, the choosing of reference gas is another problem.

For the drift compensation method without reference gas, it is always complex relatively. Thiago and Eduardo^[13] developed a model that using an ensemble of neural networks in a parallel way combining the weighted output of classifiers to compensate the drift. Lei and David^[14] proposed a unified framework called domain adaptation extreme learning machine for drift compensation. For this type of drift compensation method, drifted response signal is always included for model training and building combined with detection time. As the increase of detection time and classified category, the model would be more and more complex. A mount of training dataset is necessary for model building and a new model needs to be built when other application is required, which make the generalizability of this type of method not good enough. Furthermore, the model building process likes a black box, which is hard to reflect the drift characteristics and measure its reliability.

In this paper, a novel drift compensation method based on intrinsic characteristics of response signal is proposed, which is relatively simple and do not need reference gas. Moreover, classification algorithm is applied for proving the performance of the new proposed method. The aims of this paper are: (1) to explore the intrinsic characteristics of response signal; (2) to realize drift compensation through the new proposed method; (3) to evaluate the drift compensation performances through support vector machine (SVM)^[15].

Data Acquisition

The experiment was carried out during January 2019 to December 2021 (36 months) in a gas delivery platform facility. Eight gas sensors were applied for collecting dataset and two kinds of gases (Ethanol and Ethylene) were tested. The flow level of each gas was 100ml/min, ± 1% of accuracy. All the gas was stored in pressurized gas cylinders. Synthetic air was applied as background gas and two tested gases were added to it for all experiment. Furthermore, the background gas was also tested. For obtaining stable and effective results, the response of the gas sensor array was measured when the operating temperature of sensors was fixed at 400 ◦C based on the best detection parameters provided by manufacturer.

The dataset during a period of month 1, 4, 14, 16, 20, 22, 36 was collected and employed for drift compensation research. The data of month 1 was taken as the benchmark, which considered as no drift. The data of month 4 showed the characteristic of the initiating. While, the data of month 14, 16, 20 and 22 showed that of intermediate stage. The data of month 36 showed the characteristic of end stage. The number of samples collected during a period of one month for two gases are showed in Table 1 below.

Table 1

The number of samples collected during a period of one month for three gases
Month ID	Number of samples
Month ID	Ethanol	Ethylene	Total
Month 1	84	88	172
Month 4	82	170	252
Month 14	52	43	95
Month 16	28	40	68
Month 20	264	100	364
Month 22	30	30	60
Month 36	600	600	1200

Data Processing

Feature extraction

Feature extraction^[16] is an extremely important preprocessing method for exploring the data characteristic and an inevitable step for applying in real application^[17]. Figure 1 shows a typical response curve of gas sensor, which is also the data collected for feature extraction.

According to Fig. 1, for gas injection (adsorption) phase, the curve increases first, then become stable. For the cleaning (desorption) phase, the curve decreases first and then become stable. Furthermore, the trends of the original curve and drifted curve are similar. The main difference of them is the stable value and slope of response curve. The first step of this study is to find a certain rule of the difference.

On the other hand, the curve trend of desorption phase is largely depended on the characteristic of adsorption phase. Hence, for reducing the calculation quantity, the data of response curve of adsorption phase are applied for feature extraction. Four features (one steady-state and three transient features) are selected for drift compensation research in this study.

The steady-state feature is defined as the difference of the maximal response value and the baseline.

$${\text{Fs}}={\text{Max(}}R) - Min(R)$$

Where ${\text{Fs}}$ represents the steady-state feature, ${\text{Max(}}R)$ is maximal response value, $Min(R)$ is the baseline of response curve.

Its normalized version is expressed by the ratio of the maximal response value and the baseline value.

$$\left\| {{\text{Fs}}} \right\|=\frac{{Max(R) - Min(R)}}{{Min(R)}}$$

Where $\left\| {{\text{Fs}}} \right\|$ represents the normalized version of steady-state feature and is applied as Feature 1.

The transition feature reflects the dynamics of sensor response and is evaluated through the equation below.

$${\text{F}}{{\text{t}}_{\text{n}}}=\frac{{{{\text{R}}_{{\text{n+}}\alpha }}{\text{-}}{{\text{R}}_{\text{n}}}}}{{{{\text{R}}_{\text{n}}}}}$$

Where n is the detection time point, ${\text{F}}{{\text{t}}_{\text{n}}}$ represents the one unit of transition feature and the average of them is the transition feature, ${{\text{R}}_{\text{n}}}$ is response value when detection time point is n, ${{\text{R}}_{{\text{n+}}\alpha }}$ is response value of detection time point ${\text{n+}}\alpha$,$\alpha$is the moving scalar and defined as 0.1, 0.01 and 0.001, respectively. Then, three transition features are calculated through three moving scalars, respectively.

Sensor drift compensation method

The process of this method is as follows:

(1) Feature extraction and selection: Extract four features described above, and select two features (one is the steady-state feature, defined as Feature 1 and another is the transient feature, defined as Feature 2) for subsequent analysis.

(2) Relationship exploration of the Feature 1 and Feature 2: Build a model of Feature 1 and Feature 2, and use parameters of this model describing their relationship. Furthermore, the parameters of all sample of Month 1 are calculated and their average is defined as A. The equation is as follow:

$${\text{F}}1(i)=1000 \times A(i) \times F2(i)$$

Where i represents the specific one sample, ${\text{F}}1(i)$ is the value of Feature 1 of sample i of Month 1, $F2(i)$ is the value of Feature 2 of sample i of Month 1, $A(i)$ is the scale coefficient of sample i. A is the average of $A(i)$.

(3) Relationship exploration of the Feature 1 of Month 1 and other months: Build a model of the Feature 1 of Month 1 and other months, and use parameters of this model describing their relationship. The parameter for all samples is calculated, respectively, and their average is defined as $B(j)$, j is 4, 14, 16, 20, 22 and 36 representing Month4, Month14, Month16, Month20, Month22, Month36, respectively. The equation is as follows:

$$B(j)=F1(1)/F1(j)$$

Where $F1(1)$ represents the average value of Feature 1 in the first month, $F1(j)$ represents the average value of feature 1 of month j. $B(j)$ could be considered as the drift degree of month j.

(4) Drift compensation: Feature 1 is the drift compensated feature and applied for next analysis in this study. Parameter $B(j)$ is the chief principal for compensation and parameter A is applied as an auxiliary parameter for improving compensation accuracy. The calculation process is as follows:

$$F3(i)(j)=F1(i)(j)/B(j)$$

Where $F1(i)(j)$ is the value of Feature 1 of sample i of month j. $F3(i)(j)$ is the value of the sample i of month j after first step of drift degree compensation, which should be similar to that of Feature 1 of Month 1.

$$P(i)(j)=F1(i)(j)/[1000 \times F2(i)(j)]$$

Where $F2(i)(j)$ is the value of Feature 2 of sample i of month j. $P(i)(j)$ is the actual scale coefficient of sample i of month j. Hence, $P(i)(j)$ should be transformed, making it as close as possible to A for drift compensation.

$$M(i)(j)=P(i)(j) \times A/P(j)$$

Where $P(j)$ is average value of $P(i)(j)$. $M(i)(j)$ could be considered as the actual scale coefficient of sample i of month j. Real drift and measurement system drift are two predominant sources causing sensor drift. The measurement system factors make the drift unpredictable. The purpose of the calculation of $M(i)(j)$ is to decrease this part of error partly.

$$N(i)(j)=(M(i)(j)+A)/2$$

Where $N(i)(j)$ is final scale coefficient, which considered both sensor itself and measure system factors inducing drift, making the compensated result more accurate.

$$G(i)(j)=F3(i)(j)/[1000 \times M(i)(j)]$$

Where $G(i)(j)$ could be considered as the compensated result of Feature 2 of sample i of month j.

$$R(i)(j)=1000 \times G(i)(j) \times N(i)(j)$$

Where $R(i)(j)$ is the final compensated value. The produce of $R(i)(j)$ combines Feature 1 and Feature 2, and considers both sensor itself and measure system factors inducing drift, which lead to more accurate results.

(5) Drift compensation for all sensors: Apply this method for all sensors and all samples. The drift compensated feature is obtained and applied for subsequence analysis.

Support Vector Machine

SVM, which is based on the Structural Risk Minimization and Statistic Learning Theory, is considered as one of the most robust and accurate methods used for classification analysis^[18]. Furthermore, it has global minimum of the error function and excellent generalization ability of the trained network^[19]. It is a linear machine working in the high dimensional feature space formed by the non-linear mapping of the n-dimensional input vector x into a K-dimensional feature space (K > n) with a function. For the results of SVM, samples are considered as points in space and mapped so that the samples of the separated categories are divided by a clear gap that is as wide as possible, which is also the optimal hyperplane to separate two classes.

In this part, the sensor drift compensation method proposed in this study is carried out and its performance is discussed according to the results of SVM. Month 1 is set as benchmark, which is considered as no drift. The objective of the drift compensation method is to make the characteristics of features of other months similar to those of month 1.

The data analyzed in this study are: eight steady features and twenty-four transient features in total, which are extracted from eight sensor response curves for representing one sample. Eight steady-state features are compensated and applied for classification analysis. Twenty-four transient features are compared and eight of them are selected as auxiliary data for drift compensation.

Sensor Drift Compensation Method

Feature extraction and selection

As described above, four features are extracted from one sensor response curve. The steady-state value is defined as Feature 1. Three transient values are compared and selected based on their relevance with Feature 1, and the chosen one is defined as Feature 2. The scatter plots of Feature 1 and other three features are shown in Fig. 2.

Linear correlation leads to less calculation complex and displays a more obvious visual effect. Hence, it is applied for selecting appropriate Feature 2. As shown in Fig. 2(a), (b) and (c), all plots display strong correlation, which proves the correctness of linear relationship of these two features.

Figure 2(a), (b) and (c) are the linear relationship of Feature 1 and three transient features with 0.001, 0.01 and 0.1 of moving scalar, respectively. The fitting correlation coefficients (R²) and root mean square error (RMSE) are employed to reflect their fitting performance. According to Fig. 2, Fig. 2(a) has the best fitting performance, whose standard error is 0.06736, R² is 0.9951. By contrary, Fig. 2(c) has the worst fitting performance. The reason might be that as the increasement of the moving scalar, more uncertainty includes, which makes the data fluctuate more greatly. However, the smaller moving scalar means higher computing cost. For Fig. 2(b), its standard error is 0.1348 and R² is 0.9918, which is just a little worse than that of Fig. 2(a) and also shows good fitting performance. Hence, considering both the fitting performance and calculation complex, the feature with 0.01 of moving scalar is selected and defined as Feature 2.

Calculation of A and $B(j)$

R² and RMSE are employed again to reflect the fitting performance of Feature 1 and Feature 2, which reflect the reliability of parameter A. The values of R² and RMSE of different months and sensors are showed in Table 2 and Table 3, respectively. The values of RMSE have been normalized, making them comparable.

The fitting performance of Month 1 is the most important index for the reason of that it is the drift compensation objective. According to Table 2, the values of R² of Month 1 are all higher than 0.86, which indicates that the linear correlation of two features of Month 1 is reliable and the parameter A is able to reflect the characteristic of sensor signal response without drift. Furthermore, most values of R² are acceptable, which proves the feasibility of linear correlation of two features again. According to Table 3, the values of RMSE of Month 1 are all less than 0.12, which means a good fitting performance. For all the values in Table 3, most of RMSE are less than 0.15, which also proves the existence of linear correlation of two features.

According to Tables 2 and 3, the fitting performance of Month 1 is the best. For other months, the values of R² and RMSE are fluctuated and most of their fitting performances are worse than that of Month 1, which reflects that sensor drift happened and it is partly uncertainty and unpredictable. The reason might be environment and measurement system factors, whose uncertainty makes the sensor drift fluctuated.

Table 2

The value of R² of different months and sensors
Month ID	S1	S2	S3	S4	S5	S6	S7	S8
Month 1	0.9836	0.9811	0.9356	0.9435	0.9914	0.991	0.8769	0.8695
Month 4	0.7889	0.4307	0.0363	0.7590	0.6049	0.7219	0.5398	0.4874
Month 14	0.6677	0.6154	0.6828	0.7126	0.3071	0.0239	0.9763	0.8528
Month 16	0.9083	0.992	0.7255	0.7538	0.6742	0.6532	0.4625	0.4743
Month 20	0.9474	0.9862	0.7234	0.7420	0.6006	0.7508	0.5739	0.7648
Month 22	0.8322	0.1798	0.9684	0.9385	0.1864	0.1986	0.5421	0.5775
Month 36	0.9777	0.9363	0.7930	0.8000	0.4411	0.4181	0.7581	0.7476

Table 3

The value of RMSE of different months and sensors
Month ID	S1	S2	S3	S4	S5	S6	S7	S8
Month 1	0.0358	0.0300	0.1127	0.1110	0.0426	0.0368	0.0692	0.0677
Month 4	0.0493	0.0989	0.2468	0.3109	0.2161	0.2245	0.0727	0.0786
Month 14	0.0384	0.0376	0.0317	0.0308	0.1177	0.1150	0.0195	0.0218
Month 16	0.0130	0.0089	0.0671	0.0620	0.0381	0.0417	0.0939	0.0939
Month 20	0.0058	0.0071	0.0266	0.0257	0.0199	0.0269	0.0420	0.0411
Month 22	0.1491	0.1647	0.1479	0.1523	0.1876	0.2078	0.1891	0.1908
Month 36	0.0068	0.0075	0.0111	0.0107	0.0138	0.0138	0.0114	0.0115

Parameter A reflects the relationship of two features of one sensor. The values of parameter A with different sensors and months are calculated by Eq. (4) and presented for showing drift phenomena directly and analyzing the drift rule of sensor. Their trends with different sensors and months show in Fig. 3 below.

As shown in Fig. 3, parameter A’s trends of all sensors are similar, which reflects the similarity of drift phenomena. Moreover, the value of parameter A increases first, then fluctuates and finally decreases. For first several months, sensor drift might be influenced by both real drift and measurement system drift, which causes uncertainty and unpredictable. Hence, the values of parameter A fluctuate during this time. Then, drift caused by real drift become dominated with time goes, which has a certain trend and leads to the decrease of the value of parameter A. The results indicate that all sensors have similar drift rule and prove that parameter A is a suitable parameter exhibiting it.

$B(j)$ , which reflects the relationship of the Feature 1 of Month 1 and other months, is an important parameter for drift compensation and employed to judge drift degree. The value trends of $B(j)$ with different sensors and months show in Fig. 4 below.

As shown in Fig. 4, the trends of the values of $B(j)$ for all sensors are also similar. It fluctuates first, then become stable. Moreover, the value of $B(j)$ during month 14 to 20 decreases greatly, which increases the drift compensation difficulty. The reason of its trend rule is similar to that of A. The results indicated that all sensors had similar drift pattern, and could be able to compensate using one method. Furthermore, for the standard error of $B(j)$, most of them are less than 10% of $B(j)$, which proves that the overall situation is satisfactory and parameter $B(j)$ is effective.

Drift compensation

According to the description above, the relationship between two features of month 1, 4, 14, 16, 20, 22 and 36 is presented. The values of parameter A and $B(j)$ are given. Then, the values of $R(i)(j)$ are calculated according to the equations (6)-(11) and the drift compensated features for all samples are easily obtained.

In this part, the characteristics of initial and compensated features of sensor 1 detecting Ethanol in month 14 are discussed as an example, and their values are compared with that of month 1. Furthermore, their average and standard error are calculated for increasing analyzing reliability.

The results show that the average of initial feature of month 14 is 5537.32, and its standard error is 2270.74. After drift compensation, its average value become 10599.53, and its standard error is 5740.68. The difference indicates that the drift compensation method influences the initial data greatly. By comparison, the average value of month 1 is 11149.45, and its standard error is 5102.03, which is similar to the feature dataset after drift compensation. The results prove the effect of the drift compensation method proposed in this study. Furthermore, the drift compensation features of other months also have similar characteristics, which indicates that the drift compensation method proposed in this study is reliable with high probability.

SVM

After the calculation process above, Feature 1 of all sensors and samples have been compensated. In this part, SVM is applied for classification and the classification performances of original dataset and drift compensated dataset are compared for proving the effect of drift compensation method.

For SVM, 180 samples (60 samples for Ethanol, Ethylene and background air) of Month 1 were selected and applied for building classification model. The reason was that the data of month 1 was taken as the benchmark, which was considered as no drift. Hence, the performance of SVM built based on the data of Month 1 could reflect the drift degree. Moreover, the same number of samples of each group helps to balance the importance of each group and improve the classification performance of SVM model. The kernel function was set as Radial Basis Function. For obtaining the optimal SVM model, two parameters, penalty parameter c and kernel parameter g, were optimized through grid search method with the growth of c and g at an interval of 2.5 for obtaining the best c and g. Five-fold cross-validation was applied to estimate the performance of each parameter and the parameters with best cross-validation accuracy were picked. Figure 5 shows the performance of SVM with different combinations of c and g. As shown in Fig. 5, 100% of classification correct rate is obtained when c = 0.1768 and g = 32, which are therefore applied for testing process.

Then, SVM built in previous sentence was applied for classification and the total samples showed in Table 1 were involved. Table 4 presents the results of SVM based on the original dataset and dataset after compensated.

As shown in Table 4, the correct classification rates of the dataset of Month 1 are both 100%, which indicates that SVM has good classification performance and proves the effect of SVM. For other months, the original data could be considered as drifted one, whose correct classification rate is lower than that of Month 1. Furthermore, the classification performances of compensated data are better than that of the original data for all months.

Table 4

Results of SVM based on the original data and compensated data
Month ID	original data	compensated data
Month 1	100%	100%
Month 4	83.73%	96.83%
Month 14	74.74%	88.42%
Month 16	66.18%	85.29%
Month 20	56.04%	93.38%
Month 22	63.33%	85%
Month 36	70.67%	74.17%

As shown in Table 4, for original data, its correct classification rates decrease as time goes overall. The reason might be that the drift phenomenon become more and more obvious, making SVM model lose efficacy gradually and leading to the decrease of its correct classification rate. For Month 20, its correct classification rate was 56.04%, which indicated the uselessness of SVM model for the classification of original data. For the compensated data, the correct classification rate of compensated data obtains more than 20% of increasement compared with that of original data except Month 36 and the average of them reaches to 89.78%, which indicate that drift compensation method has good performance. However, the correct classification rate also decrease as time goes, which indicates that the drift degree could influence the effect of drift compensation method and its influence became bigger with time goes.

As to certain month, the correct classification rates of Month 20 and 22 were low for original data. By contrast, the value of $B(j)$, which was the main parameter for drift compensation, also decreased quickly in Fig. 4. Hence, the reason for the results might be that original data of Month 20 and 22 drifted too much and had beyond the limit of SVM model. On the other hand, for compensated data, their classification correct rates are both acceptable, which indicate that the drift compensation method is still worked in Month 22. For Month 36, the correct classification rate of original data is 70.67%, which seems not bad. But, the correct classification rate of compensated data is 74.17%, which is just a little higher than that of original data. By contrast, the values of A and $B(j)$ of month 1 and 36 are similar as shown in Tables 3 and 4. Hence, sensor drift phenomena of month 36 had not followed the drift rule and parameters A and $B(j)$ couldn’t display its characteristic accurately, which make the drift compensation method not work well and the correct classification rates of original data and compensated data are similar. Furthermore, we assume that the similarity of parameters A and $B(j)$ of month 1 and 36 is a coincidence, which make the correct classification rate higher than that of month 20 and 22.

According to the discussion above, the drift compensation method proposed in this study is effective when the continuous monitoring time less than 22 month, which has been enough for most application scenario. Hence, the drift compensation method proposed in this study achieves great development of correct classification rate and has practical significance.

Sensor drift is an inevitable problem in continuous monitoring application. In this study, a new drift compensation method, which is based on the intrinsic characteristics of response signal, is proposed. The dataset of month 1 is considered as standard data and was the object of drift compensation. The results showed that the characteristic of compensated dataset is similar to that of dataset of month 1, which indicated the efficacy of this method. SVM is applied for verifying the performance of drift compensation method. The results show almost 20% improvement of correct classification rate, reaching to 89.78%, and the efficacy of 22 month of continuous monitoring, which has been enough for most application scenario. According to the results above, it is proved that the drift compensation method proposed in this study is effective and this study provides another way for sensor drift compensation.

Data availibility

The data that support the findings of this study are available from State Grid Corporation of China but restrictions apply to the availability of these data, which were used under license for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of State Grid Corporation of China.

Acknowledgments

The author acknowledges the financial support of Zhejiang Provincial Natural Science Foundation of China through Project Q23C130001. We also acknowledge the support and assistance from laboratory engineers at the Department of Biosystems Engineering, Zhejiang University.

Author contributions

Y.S. and Y.Z. conceived of the presented idea and the experiments. Y.Z. planned and conducted experiments. Y.S. analyzed the experimental data, and designed the figures. All authors discussed the results and contributed to the final manuscript.

Competing interests

The authors declare no competing interests.

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No competing interests reported.

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A method of Gas sensor drift compensation based on intrinsic characteristics of response curve

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Data Acquisition And Processing

Data Acquisition

Data Processing

Feature extraction

Sensor drift compensation method

Support Vector Machine

Results And Discussion

Sensor Drift Compensation Method

Feature extraction and selection

Calculation of A and \(B(j)\)

Drift compensation

SVM

Conclusion

Declarations

Data availibility

Acknowledgments

Author contributions

Competing interests

References

Additional Declarations

Status:

Journal Publication

Version 1