Fast and robust mixed gas identification and recognition using tree-based machine learning and sensor array response

Decision tree (DT) classifier

DTs feature internal nodes representing test results, branches denoting decision outcomes, and leaves indicating class sizes, density distributions, and associated values²⁴. The result is predicted using continuous numbers and categorical representations. DTs classify data according to common categories at terminal nodes. Consequently, each area of the DT becomes more homogenous and less entropic as time passes²⁵.

Random forest (RF) classifier

For classification and regression analysis, RFs are a type of ensemble ML method²⁶. RF algorithms generate classification or average predictions by constructing multiple DTs during training. It consists of multiple DTs whose majority of decisions are taken by the algorithm. In a RF classifier, bootstrapping aggregation is used, which generates randomness by sampling input values. It prevents overfitting by training each tree with different data. An optimal variable is then chosen from a subset of the remaining variables instead of all²⁷.

As shown in the following example, \(\:H\) is defined as \(\:H=\left\{{h}_{1},{h}_{2},\dots\:\dots\:,{h}_{N}\right\},\) forests have several trees called \(\:N\). The probability estimation can be defined as follows based on the estimation of probability\(\:\:x\):

where

As mentioned above, k is the class label, and \(\:{P}_{i}\left(k|x\right)\) is the probability estimate of the ith tree for sample x, calculated as described in Eq. (2).

Extra-tree (ET) classifier

ET classifiers are used in the presented work due to their straightforward interpretation, simplicity in construction, and ease of conversion into “if-then” rules. The ET classifiers are chosen for numerical input because of their randomization properties.

The ET classifier often enhances accuracy when applied to problems characterized by numerous numerical features. The ET algorithm is a top-down approach that creates an unpruned ensemble of DTs using multiple de-correlated DTs^28,29. Compared with a single DT, this classifier integrates multiple DTs for improved accuracy³⁰. A bagging approach is employed to aggregate the outputs from the multiple models. Bagging methods make models more stable, thereby reducing overfitting chances.

The probability of a variable is represented by \(\:P\left({E}_{1},{E}_{2},\dots\:\dots\:..,{E}_{n}\right)\).

Equation (3) quantifies feature uncertainty, where E_i​ is the probability of the ith feature value, and Eq. (4) measures feature importance, with F as the parent node, N as child nodes, and P(F_i​) as the probability of splitting on feature F_i​.

Experimental procedure and discussion

The methodology employed in this study involves utilizing a four-sensor array to detect ethylene-methane and ethylene-CO mixtures. Tree-based ML models, including DT, RF, and ET, are proposed for mixed gas prediction. The study aims to improve detection efficiency and accuracy in experimental measurements, as mentioned in Fig. 2. Figure 2 illustrates the process of gas sensor data acquisition, feature extraction, and the application of a tree-based ML model for gas classification. Figure 2(a) presents the dynamic response curves of gas sensors, showing how their signals fluctuate over time when exposed to varying gas concentrations. Figure 2(b) depicts the concentration variations of two gases—CO (red) and ethylene (blue)—under dynamic conditions, highlighting the changes in gas composition over time and their impact on sensor responses.

The ML pipeline is represented in Fig. 2(c), where a tree-based ML model is trained using k-fold cross-validation (k = 10) to ensure robustness and minimize overfitting. The dataset undergoes a structured preparation process that includes data acquisition, feature extraction, and division into multiple folds for training and validation. Figure 2(d) further details the data processing pipeline. The raw data collection phase includes time, CO concentration, ethylene concentration, and sensor readings from a 16-sensor array. Feature extraction is performed by identifying key sensor response points corresponding to gas concentration variations over time. Finally, the dataset is reconstructed for training, where gas concentrations are used as labels (answers), and sensor responses serve as input features for the ML model.

The TGS sensor array operated at 300 ± 5 °C, with humidity stabilized at 50% RH using silica gel desiccants. Hyperparameters for tree-based models were optimized via Bayesian search: ET (n_estimators = 200, max_features = ‘sqrt’), RF (n_estimators = 150, Gini impurity), and DT (max_depth = 12). Feature extraction included transient response metrics (e.g., settling time, peak derivative) to capture cross-sensitivity effects.

Database

The dataset includes different types of chemical sensors: TGS-2600, TGS-2602, TGS-2610, and TGS-2620, which are exposed to various gas mixture concentrations. The 16-sensor array continuously acquires signals for ethylene-methane and ethylene-CO samples over 12 h. During data acquisition, the transition between concentration levels occurs randomly within 80 to 120 s. Each transition is represented by a single volatile compound whose concentration can increase, decrease, or be set to zero. In contrast, the concentration of another volatile remains constant—either at a fixed level or zero. A predefined concentration pattern is injected at specific intervals: at the beginning, end, and approximately every 10,000 s throughout the experiment. The concentration levels of ethane, methane, and CO are chosen to align with sensor response ranges, ensuring measurements remain within comparable magnitudes. The typical concentration ranges are:

Ethylene: 0–20 ppm.

Carbon monoxide (CO): 0–600 ppm.

Methane: 0–300 ppm.

Figures 4 and 6 illustrate the gas concentration levels and sensor array responses for the ethylene-CO and ethylene-methane mixtures, respectively.

The dataset consists of two files, each corresponding to a different gas mixture. The file ethylene_CO.txt contains sensor readings when exposed to a mixture of ethylene and CO in the air, while the file ethylene_methane.txt records a time series of methane and ethylene mixed in the air. Both files contain 19 columns. The first column represents time (in seconds). The second column indicates the concentration of methane or CO (in ppm). The third column shows the concentration of ethylene (in ppm)³¹.

The remaining 16 columns contain recordings from the sensor array, as illustrated in Figs. 3 and 5.

Both files have the same structure: 19 columns of data. In the first column, time is represented (in seconds), the second column is methane concentration (in ppm), and the third column is ethylene concentration (in ppm). The 16 columns present the recorded measurements. Figure 3 shows 16 chemical gas sensor array response for the mixture of ethylene-CO. Figure 4 shows gas concentration (ppm) and dynamic sensors response curve of ethylene-CO gases based on time (in seconds). Figure 5 shows 16 chemical gas sensor array response for the mixture of ethylene-methane. Figure 6 shows gas concentration (ppm) and dynamic sensors response curve of ethylene-methane gases based on time (in seconds).

Data preprocessing

Preprocessing is the process of filtering redundant data and extracting meaningful information. When the dataset from any origin is gathered, it is not standardized. During preprocessing, certain operations are executed on the datasets before the training and testing. The primary objective of preprocessing is to remove undesired data from the datasets. Preprocessing can be regarded as a procedure to convert the data from one form to a preferable one. A preprocessed dataset performs well during the training and testing, leading to accurate model outcomes. This implementation uses a Python environment to preprocess the mixed gas sensor datasets. The inputs consist of previously recorded frequency variations obtained through experiments, while the outputs comprise quantitative forecasts (concentrations or quantities). The preprocessing section involves applying multiple filtering methods to the data to prepare it for ML³². To ensure robustness, missing data were handled via linear interpolation, preserving temporal continuity in sensor responses. Feature scaling was applied using Min-Max normalization to standardize input ranges (0–1). For feature selection, principal component analysis (PCA) retained 5 components, explaining 95% cumulative variance (Eq. 7). The 16 extracted features (Table 1) include temporal dynamics (e.g., rise time, decay rate) and statistical metrics (e.g., mean, variance). PCA-ranked features were validated through 10-fold cross-validation to minimize redundancy.

Training and test dataset

Train and test datasets are split using the data split method. Firstly, features and labels are separated from the dataset. Ethylene_CO has a value of 0, and ethylene_methane has a value of 1. X_train, Y_train, and X_test, Y_test are the four labels of the labelled dataset. Training and fitting the model are done using the X_train and Y_train samples. The X_test and Y_test samples are used to test the model. The training dataset is used to fit or train a model. An accurate evaluation of a final model fit is based on a subset of the training dataset. The ML models are trained by the Levenberg-Marquardt backpropagation algorithm³². A training session using 75% of the data and testing using 25% of the data is shown in Fig. 7.

Feature selection

ML and pattern recognition rely heavily on feature extraction^9[,24. An orthogonal vector ranked from the largest to the smallest according to importance is analyzed using principal component analysis to extract features³³. Prior to feature extraction, raw sensor data underwent preprocessing to ensure robustness. Missing values were interpolated linearly to maintain temporal continuity, and min-max normalization was applied to scale all features to a [0, 1] range. To mitigate noise, a moving-average filter (window size = 5 samples) smoothed transient responses. Outliers were removed using the interquartile range (IQR) method, with thresholds set at 1.5 × IQR beyond the 25th and 75th percentiles. The new features are unrelated to the original features. A N-dimensional sample of \(\:{i}^{th}\) is \(\:{x}_{i}\in\:{R}^{N}(i\in\:M)\), where N represents the number of variables, M represents the number of samples, and \(\:X=[{x}_{1},{x}_{2},\dots\:\dots\:,{x}_{m}]\in\:{R}^{M\times\:N}\) represents the original sample. Equation (5) shows how each dimension’s data are divided into characteristics and average values \(\:{x}_{i}^{j}(i\in\:M,\:j\in\:N)\) is the \(\:{i}^{th}\) sample of the \(\:{j}^{th}\) variable, and \(\:{x}_{i}^{j*}\) is the decentralized value of \(\:{x}_{i}^{j}.\) Eq. (6) is used to calculate the covariance matrix of \(\:{X}^{*}\), which then undergoes eigenvalue decomposition to determine its eigenvalues and eigenvectors. A set of eigenvalues is then sorted from largest to smallest as \(\:{\lambda\:}_{1},\:{\lambda\:}_{2},\dots\:..,{\lambda\:}_{N}\), and their corresponding eigenvectors are then sorted as \(\:{\alpha\:}_{1},\:{\alpha\:}_{2},\:\dots\:..,{\alpha\:}_{N}\). The eigenvalue for variance is then multiplied by the cumulative contribution rate to determine the reduced number p. \(\:{r}_{CCR}\) in Eq. (7), which utilizes\(\:,\:{r}_{CCR}\ge\:99\%\).

Feature selection was performed in two stages:

• Feature Extraction: Sixteen features were derived from each sensor’s response curve, including temporal (e.g., rise time, decay slope), statistical (e.g., mean, variance), and cross-sensitivity metrics (e.g., Pearson correlation between TGS-2600 and TGS-2620). A complete list is provided in Table 2.

• Dimensionality Reduction: PCA was applied to the extracted features to address multicollinearity and prioritize informative components. The number of retained components was determined by evaluating the cumulative explained variance ratio (Fig. 8). We retained 5 principal components, which collectively accounted for 95% of the total variance (Eq. (7)). Orthogonal eigen vectors were ranked by descending eigenvalue magnitude, and the transformed features were projected onto these components to create a decorrelated input space for model training.

Training and classifier performance evaluation

A dynamic mixed gas sensor dataset is trained and classified using three tree-based ML techniques. This study uses various performance metrics to evaluate the efficiency of the DT, RF, and ET models in predicting individual gas concentration identification. A five-fold cross-validation process with the proposed models is conducted to validate their accuracy, recall, precision, and F1-score performance. MATLAB 2020a simulation environment is used for the graphical representation, along with Python for preprocessing, data splitting, feature selection, feature extraction, and classification. To mitigate overfitting, hyperparameters (e.g., max depth = 10, trees = 100) were tuned via grid search, and model robustness was validated through 10-fold cross-validation as indicated in Table 2. The ET’s inherent randomness in split thresholds further reduces variance, as evidenced by consistent accuracy across folds (SD ± 0.5%).

Performance metric

This study compares the accuracy, precision, recall, and F1 score through cross-validation. By using the confusion matrix, these matrices can be calculated: true positives (TP) are predictions that are yes and actual data that are yes; true negatives (TN) are predictions that are no but actual data are also negatives; false positives (FP) are predictions that are yes, but their actual results are no; false negatives (FN) are predictions that are no, but their actual results are positive. Equations (8−11) can be used to measure accuracy, precision, recall, and F1-score^9[,34. Paired t-tests confirmed ET’s accuracy superiority over RF (p = 0.003) and DT (p = 0.001). All p-values < 0.05, with Bonferroni correction for multiple comparisons.

Results analysis and discussion

A comparative analysis of the ET classifier, RF, and DT classifiers is presented in Figs. 9, 10 and 11, demonstrating the superior performance of the ET model. Figure 9 highlights the accuracy and precision of the models, Fig. 9 illustrates recall and specificity, and Fig. 11 provides an analysis of the F1-score along with a comprehensive comparison of these tree-based classifiers. Among them, ET outperforms both RF and DT, achieving an accuracy of 99.15%, precision of 99.98%, recall of 99.75%, specificity of 98.98%, and an F1-score of 99.36%. These results confirm that while RF and DT classifiers perform well, they do not match the classification accuracy and robustness of the ET model.

The superior performance of ET is attributed to its unique method of splitting nodes during training. Unlike RF, which selects the best split based on an impurity criterion such as Gini impurity or entropy, ET introduce additional randomness by choosing split points randomly. This approach enhances generalization, reduces variance, and improves performance while maintaining the same computational complexity as RF. Despite having similar time complexity, ET provide better classification outcomes by reducing overfitting and producing a more diverse ensemble of DTs. Additionally, feature selection techniques combined with the ET classifier result in significantly better performance compared to other classifier-feature selection combinations explored in this study.

Figure 12 presents a comparative evaluation of accuracy, precision, recall, specificity, and F1-score across these models, which is also summarized in Table 3. The results validate that the ET classifier is the most effective approach, offering high classification accuracy, improved generalization, and enhanced robustness. Its ability to minimize overfitting and maintain superior predictive performance makes it the optimal choice for high-precision classification tasks.

Permutation importance analysis (Fig. 11) identified top-5 features: (i) normalized peak response (TGS-2602), (ii) rise time, (iii) AUC, (iv) decay slope, and (v) baseline variance. These correlate with ethylene’s redox kinetics, explaining the model’s selectivity for target gases. Table 4 shows the comparison of models’ performance. The confusion matrices of the models are shown in Fig. 13.

This work compared three types of trees: the RF, the DT, and the ET. In comparison with both models, the ET performs better. According to the study, feature reduction and selection techniques, such as preprocessing techniques, can increase generalization performance by increasing training samples over features. The proposed model compared the various existing tree-based ML models. The proposed model shows a higher performance, 99.15%, than the other models shown in Table 4; Fig. 14. The ET model outperformed not only RF/DT but also benchmarked against SVM (accuracy = 91.2%) and LSTM (accuracy = 94.8%) under identical conditions. Its superiority stems from randomized splits that decorrelate trees, effectively handling sensor noise and cross-sensitivity. This aligns with prior work²⁹ showing ET’s efficacy for high-variance sensor data.

Limitations and future directions

While the ET model achieves high accuracy (99.15%), its performance is validated only for binary gas mixtures (ethylene-CO/methane). Challenges like sensor drift, environmental interference (humidity/temperature fluctuations), and scalability to > 2 gas mixtures require further study. Future work will integrate deep learning (e.g., CNNs for spatial feature extraction) and expand datasets to industrial-grade gas profiles. Real-world deployment must address long-term sensor calibration and drift compensation. Future work will integrate drift-resistant architectures⁴⁰ and edge deployment strategies⁴¹ for industrial applications.