Predicting H₂S emission from gravity sewer using an adaptive neuro-fuzzy inference system Open Access

Domestic wastewater is transported to water resource recovery facilities via the underground pipelines (or tunnels) called sanitary sewers. During transportation, the attachment and subsequent growth of microorganisms on the submerged surfaces of the sewer occur, which leads to the formation of a biological slime layer, more often named biofilm. The biofilm's deeper regions (closer to the sewer walls) are mostly inhabited by anaerobic microorganisms because oxygen penetration is limited by the outer region of the biofilm. Microbial activity of sulfate-reducing organisms – obligate anaerobes – within the biofilm's deeper regions reduces sulfate (SO₄²⁻) to hydrogen sulfide (H₂S) (Gutierrez et al. 2016; Li et al. 2019). The formation of H₂S depends on the presence of readily biodegradable chemical oxygen demand and sulfur compounds in the sewers (Park et al. 2014). According to Carrera et al. (2016), domestic wastewater usually contains SO₄²⁻ in a concentration range of 40–200 mg SO₄²⁻/L (equals to 13.3–66.7 mg SO₄²⁻-S/L).

The H₂S product in the biofilm can be diffused to the bulk liquid phase and – when the sewer runs partially full – can then be released to the overlaying gas phase if the supporting factors such as high-turbulence flow, low pH, and high temperature of the liquid phase are prevailed (Yongsiri et al. 2004a; Jiang et al. 2017; Wu et al. 2018; Zuo et al. 2019). In the case of sufficient ventilation of sewer, H₂S can be released to the air; this gas has an extremely unpleasant smell (rotten egg odor) with a very low odor detection threshold (0.0001–0.03 ppm) and causes a detrimental impact on human health, ranging from eye irritation and headaches at lower levels (1–10 ppm) and sudden death at levels >1,000 ppm (Salehi & Chaiprapat 2019). In the case of insufficient ventilation of sewer, H₂S is accumulated in the sewer atmosphere (the confined air space above the flow surface) and subsequently adsorbed on the sewer moist walls (unsubmerged walls) where it can be oxidized by the action of Thiobacilli-generating sulfuric acid (H₂SO₄) (Huber et al. 2016; Jiang et al. 2017). The H₂SO₄ product is the major cause of the corrosion of cement and metal materials in sewers (Jiang et al. 2015, 2016; Wu et al. 2018; Fytianos et al. 2020). The corrosion of sewer networks is an increasing universal concern because it has the potential to cost the wastewater industry billions of dollars to maintain and rehabilitate the damaged sewers. As an example, the Sanitation Districts of Los Angeles County estimated an annual total cost of US$13.75 billion to perform rehabilitation and the maintenance of the corroded sanitary sewers in the United States (García et al. 2020).

Several predictive models to estimate H₂S emission from gravity sewers have been developed since the early 1970s. They can be categorized into the following two main groups: (1) modified sewer re-aeration models in which the overall mass transfer coefficient of H₂S replaces the overall mass transfer coefficient of oxygen and (2) models estimating H₂S emission rate as a function of hydraulic conditions (Carrera et al. 2016). Some examples of the first group are those developed by Parkhurst & Pomeroy (1972), United States Environmental Protection Agency (USEPA) (1974), Taghizadeh-Nasser (1986), Jensen (1995), and Yongsiri et al. (2003, 2004a, 2004b, 2005). Examples of the second group of the models are the ones proposed by Lahav et al. (2004, 2006). The critical parameter in these second group models is velocity gradient – adapted from the mixing theory – that is linked to the head loss in the sewer.

Yet, despite all these developments and efforts made to model H₂S emission from gravity sewers, to the best of the authors' knowledge, the application of an adaptive neuro-fuzzy inference system (ANFIS) has never been exploited. The ANFIS models have advantages over the theoretical/empirical models for complex nonlinear systems because they are constructed based only on a dataset of the input and output variables of the system under consideration, without requiring prior knowledge of the interrelationship between the variables. In addition, they have been proved as a robust modeling tool for nonlinear complex systems with high generalization power. Therefore, the present study aimed – for the first time – to fill this research gap. An ANFIS model based on grid partitioning (GP)/subtractive clustering (SC) of the input domain (will be referred to hereafter as ANFIS-GP and ANFIS-SC, respectively) was developed to predict H₂S emission from a gravity sewer using the experimental data reported in Lahav et al. (2006). The predictive abilities of the ANFIS-GP and ANFIS-SC models were compared with each other and with that of the conventional multiple regression by means of two descriptive statistics, including the coefficient of determination (R²) and root-mean-squared error (RMSE). In addition, the two ANFIS models were compared with each other in terms of complexity (i.e., number of rules and parameters).

This paper will present the ANFIS model structure followed by the methodology describing the data processing and modeling approach for the ANFIS-GP, ANFIS-SC, and multiple regression models. Then, results of the three models are compared and discussed, and finally, the paper ends with the conclusions.

ANFIS, originally introduced by Jang (1993), is a knowledge-based system that deals with a number of conditional statements (commonly known as IF-THEN rules) and a set of input–output data of the system under consideration. It is used to describe the input–output behavior of complex nonlinear and uncertain problems that are difficult or complicated to be modeled using the mathematical approaches. The ANFIS model combines two soft computing techniques – artificial neural network (ANN) and fuzzy inference system (FIS) – in a single framework. In fact, the ANFIS model has a potential to capture the strengths of these two techniques: the adaptive and learning ability of ANN and the ability of FIS in knowledge representation and interpretation with the help of fuzzy IF-THEN rules (Jang 1993; Jang et al. 1997). The mathematical background of ANFIS model is described in detail below.

For simplicity, let us suppose that the FIS under consideration has two inputs (each with two fuzzy sets) and one output. For the first-order Takagi–Sugeno FIS (Takagi & Sugeno 1985), a typical rule set with two fuzzy IF-THEN rules can be expressed in the following form:

As seen from expressions (1) and (2), each fuzzy IF-THEN rule is composed of two parts, namely the IF part, which is known as antecedent (or premise) part, and the THEN part, which is called the consequent (or conclusion) part. Hence, the parameters pertaining to the fuzzy sets A_i and B_i are referred to as antecedent parameters, and the set {α_i, β_i, γ_i} is referred to as the consequent parameters.

Figure 1 illustrates the architecture of a typical ANFIS model, which is functionally equivalent to a two input single-output first-order Takagi–Sugeno FIS with two fuzzy rules.

As seen in Figure 1, the ANFIS model is a feed-forward neural network consisting of six distinct functional blocks (more often called layers), in which each layer is composed of a set of processing elements named nodes (neurons or elements). The nodes are connected together by links that indicate the signal flow direction from one node to another. Each node applies a specific function on its incoming signals and sends out the product, which is an input for the next layer. Owing to space limitation, the detailed description of each layer is provided in Supplementary Material.

One of the most crucial steps in the establishment of an ANFIS model is the structure identification, which involves the selection of an appropriate MF, the assignment of an optimal number of MFs to each input variable, and the determination of the number of fuzzy rules. To achieve this aim, two different techniques have been developed with focus on partitioning of the input space: (i) GP and (ii) SC. A brief description of the theoretical background of these two techniques is presented in the following subsections.

A GP technique refers to dividing a multi-dimensional input space into rectangular subspaces using an axis-paralleled partition with respect to the number and the type of MFs in each dimension, which are set by the user. Each rectangular subspace, called the fuzzy region, is specified by a fuzzy rule. The total number of fuzzy rules is equal to the number of all possible combinations of the MFs of all inputs (Benmouiza & Cheknane 2019; Babanezhad et al. 2020). For instance, applying GP on a data space comprised of N inputs (x₁, x₂,…, x_N) generates M₁×M₂×…×M_N fuzzy rules, where M_i denotes the number of MFs for the ith input x_i for i= 1 to N. Therefore, for a given input space, an increase in the number of MFs per input leads to a remarkable increase in the number of fuzzy rules accordingly, and consequently, an increase in the number of trainable parameters so that the computational load of the model raises.

SC, originally proposed by Chiu (1994), is an effective and rapid one-pass technique by which a large dataset is organized and categorized. In other words, the dataset is split into a number of homogeneous groups, named as clusters, such that the identical data points belong to the same cluster. The number of generated clusters is the same as the number of fuzzy rules (Rahnema et al. 2019). Applying the SC technique on a data space creates a number of clusters whose centers are used to identify the MFs, in the form of ‘gaussmf’, for the inputs (Asadi et al. 2020). This technique has gained remarkable attention because the fuzzy rules can be automatically created rather than the GP technique using which the manual selection of the number of input MFs in advance is a prerequisite to generate fuzzy rules. In addition, the SC technique prevents the problem of combinatorial explosion of the fuzzy rules in the case of a high-dimensional dataset. In other words, it reduces the rule-base complexity of the ANFIS models (Kumar et al. 2017). A brief description of the SC technique is given below (Heddam et al. 2019).

After the density measure of each data point is determined, the data point with the highest density measure is selected to be the first cluster center.

This process – searching new cluster centers – is repeated with respect to the three criteria as given in Table 1. Once the clustering process is complete, a fuzzy IF-THEN rule is assigned to each cluster; the antecedent of the fuzzy rules are created by projecting the clusters onto each dimension in the input space (Chiu 1994, 1997).

It has been proven by numerous studies that the hybrid algorithm – that integrates the error backpropagation and the least squares estimation (LSE) methods – is highly efficient in optimizing ANFIS parameters (Chen et al. 2018; Kashyap et al. 2019). Each iteration (epoch) of the hybrid algorithm is composed of two passes, including a forward pass and a backward pass. In the forward pass, the functional signals (the nodes output) go forward until the defuzzification layer wherein the LSE method is used to determine the consequent parameters under the condition that the antecedent parameters are held fixed. Then, the error between target and ANFIS-predicted values is computed. If this error is greater than the pre-specified threshold, the backward pass starts. In the backward pass, the error signals are propagated from the output layer backward to the input layer and gradient descent is used to tune the antecedent parameters, while the consequent parameters remain fixed. The output of the ANFIS is computed by employing the consequent parameters determined in the forward pass. The details and mathematical background of this algorithm can be found in Jang (1993) and Jang et al. (1997).

The data used in this study were obtained from the study of Lahav et al. (2006). Briefly, Lahav et al. (2006) operated an artificial gravity-flow sewer (a 27-m-long PVC pipe with an internal diameter of 0.16 m) using sulfide-containing water with an initial sulfide concentration of 20.4–27.2 mg S/L. The authors established an empirical equation describing dissolved sulfide in the aqueous phase of the sewer pipe as a function of temperature and hydraulic conditions (c.f. Table 2 presenting the range of temperature and hydraulic conditions used in the experimental runs).

To construct an ANFIS/MLR model in this study, x₁–x₇ were considered as the input variables, while the total sulfide in the aqueous phase of the sewer pipe (y) was the only output variable (c.f. Table 2 for the notation x_i for i= 1–7). The dataset consists of a total number of 596 input–output data pairs as given in Supplementary Material, Table S1. The input–output data pairs will be referred to hereafter as patterns); the jth pattern contains a collection of eight data points as {x_1j, x_2j,…, x_7j, y_j} for j= 1–596.

Before using the original (raw) dataset to construct ANFIS models, a two-step data pre-processing approach was applied. The first step involved normalizing the entire data points, while the second step dealt with splitting the normalized dataset. A detailed description of each respective step is given below.

After obtaining the normalized dataset, it was randomized and subsequently divided into three disjoint subsets including training, validation, and testing subsets. In this study, 416 patterns corresponding to about 70% of the dataset were assigned to training subset, while the remaining 30% of the dataset (i.e., 180 patterns) were split into two equal halves, termed validation and testing subsets. The training subset was used to develop the ANFIS models. The validation subset was served in conjunction with the training subset to prevent the ANFIS models from overfitting the training data. The testing subset was utilized to assess the accuracy and effectiveness of the trained (developed) ANFIS models for predicting the output.

The training, validation, and testing subsets were stored in the workspace of MATLAB^® (version 8.3.0.532, R2014a) (The MathWorks Inc., Natick, MA, USA) in the form of arrays, in which each row consists of a pattern with the last column (from left to right) indicating the output value and the remaining columns representing inputs' values.

This section presents three different modeling approaches, including ANFIS-GP, ANFIS-SC, and multiple regression models, applied for predicting H₂S emission from the gravity sewer.

To develop the ANFIS-GP model, the ANFIS Editor GUI (graphical user interface) of the Fuzzy Logic Toolbox in the framework of MATLAB^® (version 8.3.0.532, R2014a) was used. The ‘anfisedit’ was typed in the MATLAB command window to display the ANFIS Editor GUI, which includes four distinct panels, namely (i) load data, (ii) generate FIS, (iii) train FIS, and (iv) test FIS. Initially, the training, validation, and testing subsets were loaded from the MTALAB workspace into the ANFIS Editor GUI, and then, an initial FIS was created by choosing the GP technique. For the system under consideration in this study, various ANFIS-GP models were tried. It is important to note that the following points were taken into account to choose the best model as the one with minimum error:

• All possible combinations of the input variables were tested. Table 3 presents the combinations of input variables used for the model's development.

• The ‘gaussmf’, one of the most commonly used MFs in the literature, was tested for each input (note that only two MFs were assigned to each input in order to make the models as simple as possible).

• Takagi–Sugeno FIS in the form of a first-order polynomial function was used.

Each ANFIS-GP model was trained with the training subset using the hybrid algorithm, and the model error (called training error) was determined; the training error goal was set to zero. At each epoch, the model validation error was also calculated. An epoch, at which the validation error started to rise while the training error continued to decrease, was considered as a sign to terminate iterating the training algorithm because of the occurrence of overfitting. In the case that both the training and validation errors continued to decrease while the number of the epochs increased, the learning algorithm stopped iterating whenever the training error goal achieved; otherwise, the iterating progressed up to an epoch beyond which the training error value remained constant. When none of these three stopping criteria was met, the learning algorithm continued iterating up to a pre-defined number of epochs (100 epochs).

From Equations (9) and (10), it can be seen that the closer the RMSE to zero and R² to unity, the smaller the difference between and ⁠. In other words, the model perfectly fits the data when the R² value is equal to unity and the RMSE value is equal to zero.

Once the training process was complete, the trained (developed) model was subjected to the testing phase, so that the testing subset (unseen data during the training/validation process) was fed to the model in order to assess the predictive ability of the model by means of the two aforementioned statistical indices (R² and RMSE; see Equations (9) and (10)).

Note that when the model training and testing phases were complete, the normalized output values of the model were anti-normalized to their original values by reversing transformation of Equation (7).

The ANFIS-SC model was constructed in the same manner as the ANFIS-GP, except that the number of MFs per input was automatically determined instead of specifying by the user. In the FIS generation panel of the ANFIS Editor GUI, the SC technique was selected and the MATLAB default values for the clustering parameters were selected (r= 0.50, λ = 1.25, AR= 0.50, RR= 0.15; MATLAB^® version 8.3.0.532, R2014a). Note that the training phase parameters, including the number of training epochs, training error goal, the type of output MF, training algorithm, and training stopping criteria, were the same as those used for the ANFIS-GP model. In addition, the model testing phase was performed similar to that for the ANFIS-GP model.

The multiple regression-based analysis was also performed for predicting H₂S emission from the gravity sewer. The experimental data were evaluated by means of DataFit software (trial version 9.1.32, Copyright^© 1995–2014, Oakdale Engineering, PA, USA), which contains 242 types of regression models. As the regression models were solved, they were automatically ranked based on the goodness of fit. In addition, t-ratios and p-values were estimated to assess the significance of the model coefficients (p < 0.05 was considered statistically significant). It should be pointed out that the training subset was served to estimate the regression model coefficients, while the testing subset was applied to evaluate the models’ prediction accuracy in terms of R² and RMSE given by Equations (9) and (10).

In this study, various modeling approaches were applied to predict H₂S emission from a gravity-flow sewer as a function of temperature and hydraulic conditions.

First, two different ANFIS models, namely ANFIS-GP and ANFIS-SC, were constructed based on the first-order Takagi–Sugeno FIS. The hybrid-learning algorithm was employed to train the models. The inputs to the models were temperature, pipe's slope, flow rate, hydraulic depth, mean flow velocity, liquid volume fraction in the pipe, and time, while models’ output was H₂S emission from the aqueous phase of the sewer. The data used were taken from the experimental study of Lahav et al. (2006). Models’ performances were assessed with two descriptive statistical indicators, namely R² and RMSE.

Second, multiple regression models were established whose results were compared with those of the ANFIS-GP and ANFIS-SC models.

To estimate H₂S emission from the gravity-flow sewer pipe, 63 ANFIS-GP models were developed whose training, validation, and testing results in terms of R² and RMSE are presented in Table 4. In addition, the number of fuzzy rules and the total number of parameters (linear and nonlinear) for each model are given.

It can be seen from Table 4 that the ANFIS-GP models M₁, M₂,…,M₅₆ offer good performance with R² values in the range of 0.9514–0.9960 and 0.9442–0.9943, and RMSE values in the range of 2.306–8.013 and 2.460–7.671, for validation and testing phases, respectively. Note that models M₅₇ to M₆₃ were found to be inappropriate because the creation of models M₅₇ to M₆₂ and model M₆₃ resulted in a total number of 472 and 1,052 parameters, respectively, which was greater than the size of the training subset (equals to 416 input–output data pairs). From the results in Table 4, the ANFIS-GP models (M₁, M₂,…,M₆), which use only one of the input variables (X₁, X₂, or X₆) in combination with the input variable X₇, can efficiently estimate H₂S emission. Among these models, model M₁ is ranked as the best ANFIS-GP model, which gives R² and RMSE values of 0.9714 and 6.141, respectively, for the validation phase, and the R² value of 0.9715 and the RMSE value of 5.481 for the testing phase. This reveals that the input variable X₁, denoted as temperature, seems to be more effective variable for predicting H₂S emission.

Regarding the ANFIS-GP models that use more than two input variables (models M₇, M₈,…,M₅₆), model M₂₄ (shown in bold italic in Table 4) whose input is a set of X₁, X₂, X₅, and X₇ variables yields the smallest RMSE of 2.459 for the testing phase (R² = 0.9943).

It can be concluded that the prediction performance of the ANFIS-GP model M₁ whose input variables are X₁ and X₇ is enhanced by the addition of variables X₂ and X₅ to the input data.

A scatter diagram of the measured and the predicted values of H₂S emission for testing subset using the ANFIS-GP model M₂₄ is shown in Figure 2.

It is evident from Figure 2(a) that the data points on the plot dispersed close to the 45° line (often called the 1:1 line or the 100% correlation line) with the R² value of 0.994. This indicates that only 0.6% of the total variability in the response could not be explained by the model. In addition, the measured data and the model predictions are plotted versus the number of patterns, as illustrated in Figure 2(b). It is clear from Figure 2(b) that there is a small discrepancy between the measured data and the predictions, which confirms high predictive ability of the ANFIS-GP model M₂₄.

A total of 63 ANFIS-SC models were developed to predict H₂S emission. The performance of each model through training, validation, and testing phases in terms of R² and RMSE is presented in Table 5. The number of fuzzy rules and the total number of parameters (linear and nonlinear) for each model are also provided.

As seen in Table 5, the ANFIS-SC models (M₁, M₂,…,M₆), which deal with only one of the input variables (X₁, X₂, or X₆) in combination with the input variable X₇, displays good prediction accuracy for estimating H₂S emission.

Among these models, the model M₁ which uses {X₁ and X₇} as input sets was found to be the best model, which yields R² and RMSE values of 0.9749 and 5.760, respectively, for the validation phase, and the R² value of 0.9748 and the RMSE value of 5.156 for the testing phase. This finding is in good agreement with that of the obtained results using the ANFIS-GP model M1, suggesting that the input variable X₁ (temperature) is the major variable for predicting H₂S emission for the system under consideration.

Concerning the ANFIS-SC models that have more than two input variables (models M₇, M₈,…, M₆₃), the model M₅₀ (shown in bold italic in Table 5) whose input is a set of X₁, X₃, X₅, X₆, and X₇ variables produces the smallest RMSE value of 2.514 for the testing phase (R²= 0.9940). This indicates that {X₁, X₃, X₅, X₆, and X₇} is the optimum set of input variables for estimating H₂S emission from the gravity-flow sewer pipe under the conditions considered in this study.

The prediction performance of the trained model (ANFIS-SC model M₅₀) against the testing subset is visualized in Figure 3. This figure indicates an excellent agreement between the measured data and the model-predicted values with the R² value of 0.9940.

In the regression analysis, among 242 regression models examined for predicting H₂S emission from the gravity sewer, an exponential model (called Model 1) – whose mathematical definition is given in Table 6 – offered the best performance. A summary of the regression analysis of Model 1, including the standard error of the estimate, residual sum of squares (RSS), and R², is tabulated in Table 6. In addition, Table 6 represents a summary of the regression analysis of two first-order polynomial models (called Models 2 and 3). As seen in this table, Models 1 clearly outperformed the Models 2 and 3 with R² and RSS values of 0.966 and 1.235, respectively, against the R² value of 0.742 and the RSS value of 9.458 achieved by Model 2, and the R² value of 0.547 and the RSS value of 16.601 achieved by Model 3 (the smaller RSS, the better the model performs, and vice versa in the case of R²). The estimated regression coefficient values together with standard error, t-ratios, and the corresponding p-values for the best-fit model (Model 1) are summarized in Table 7. The larger t-ratio, the more significant parameter in the regression model. In addition, the parameter whose p-value is the least is considered the most significant parameter affecting the model response. As seen in Table 7, parameters X₁, X₃, X₄, X₆, and X₇ showed a significant influence (p < 0.05) on the model response, among which X₁ (temperature) and X₇ (time) had more importance than the other parameters, whereas parameters X₂ and X₅ were found to be statistically non-significant (p > 0.05).

The scatter diagram of the measured data and the predicted values using Model 1 (see Tables 6 and 7 for the model equation and the estimated coefficients values) for the testing subsets is depicted in Figure 4. As seen in Figure 4(a), a good linear correlation (R²= 0.964 and RMSE = 6.14) was obtained between the measured data and the model-predicted values. This indicates that only about 3.6% of the viability in the response could not be explained by the model.

In addition, a comparative graphical representation for the measured data and the model-predicted values is displayed in Figure 4(b). It appears from Figure 4(b) that there is small difference between the measured predicted values. It can be deduced that Model 1 could be accurate enough to correctly predict H₂S emission from the gravity sewer under consideration in this study.

It can be seen from Tables 4 and 5 that both the best ANFIS-GP model M₂₄ and the best ANFIS-SC model M₅₀ tested on the testing subset produced R² and RMSE values of 0.99 and approximately 2.5, respectively, whereas the best nonlinear regression model (Model 1) – tested against the same dataset – provided R² of 0.96 and RMSE of 6.14; the smaller RMSE, the better the model performs, and vice versa in the case of R². Therefore, the proposed ANFIS-GP models M₂₄ and ANFIS-SC M₅₀ performed better than Model 1 in predicting H₂S emission from the sewer. When comparing the results obtained from the ANFIS-GP model M₂₄ and the ANFIS-SC model M₅₀ (c.f. Tables 4 and 5), it is clear that the R² and RMSE values of the two models are relatively similar. However, the ANFIS-GP model M₂₄ possessed 16 fuzzy rules and 96 parameters, which were fewer than those of the ANFIS-SC model M₅₀ (number of fuzzy rules = 20; number of parameters = 320). This implies that the complexity level of the structure of the ANFIS-GP model M24 was simpler than that of the ANFIS-GP model M₅₀. Therefore, between these two models, the ANFIS-GP model M₂₄ was a better choice for the prediction of H₂S emission.

For such a gravity-flow sewer system as considered in this study, the relationship between the input variables and the output (H₂S emission) is described by nonlinear complex mathematical formulas, which are often expensive to solve. In addition to the complexity, the overall mass transfer coefficient of H₂S is quite difficult to be determined accurately and is usually involved in laboratory and pilot trials. Hence, some simplifying assumptions are incorporated which may result in an underestimation of the H₂S emission rate. The proposed ANFIS models here, possessed strong generalization and prediction ability, were established based on only an actual measured set of input variables and the corresponding output, without taking into account any information regarding the relationship between the input variables and the H₂S emission rate. This implies that these models, called easy-to-use black-box models, could be an attractive and useful tool that is worth considering for predicting H₂S emission from gravity sewer. These models could offer great benefits because using which engineers and asset managers can evaluate the possible odor and corrosion problems through the design phase and operation of sewers. In addition, it enables them to formulate appropriate strategies to control and mitigate H₂S emission to the air or buildup in the sewers atmosphere in order to reduce health risk and minimize sewers corrosion.

This study successfully demonstrated the construction of the competing models to predict H₂S emission from a gravity sewer without the need for in-depth knowledge of H₂S emission mechanism. For the first time, the ability of the ANFIS-GP/ANFIS-SC approaches was revealed for this application. The ANFIS-GP and ANFIS-SC models developed were compared with the (non-)linear regression models. ANFIS-GP and ANFIS-SC models performed better than the (non-)linear regression models with a prediction accuracy of >99%. However, the ANFIS-GP model was found to be much simpler due to the creation of fewer fuzzy rules. This validates the ANFIS-GP model as a valuable computational tool for predicting H₂S emission from gravity sewers.

This research was funded by Prince of Songkla University and the Ministry of Higher Education, Science, Research and Innovation, Thailand, under the Reinventing University Project (Grant Number REV64061). The authors thank the support from the Department of Civil and Environmental Engineering, and Research and Development Office, Prince of Songkla University, Thailand. We also thank the support from Biogas and Biorefinery Laboratory at the Faculty of Engineering, and PSU Energy Systems Research Institute, Prince of Songkla University, Thailand.

R.S. (Ph.D., a postdoctoral fellow) developed the models, analyzed and interpreted the results, and wrote the manuscript. S.C. (Professor) reviewed and edited the manuscript.

The authors declare no conflicts of interest.

All relevant data are included in the paper or its Supplementary Information.