Comparative Analysis of Support Vector Machine Regression and Gaussian Process Regression in Modeling Hydrogen Production from Waste Effluent

Abstract

Organic-rich substrates from organic waste effluents are ideal sources for hydrogen production based on the circular economy concept. In this study, a data-driven approach was employed in modeling hydrogen production from palm oil mill effluents and activated sludge waste. Seven models built on support vector machine (SVM) and Gaussian process regression (GPR) were employed for the modeling of the hydrogen production from the waste sources. The SVM was incorporated with linear kernel function (LSVM), quadratic kernel function (QSVM), cubic kernel function (CSVM), and Gaussian fine kernel function (GFSVM). While the GPR was incorporated with the rotational quadratic kernel function (RQGPR), squared exponential kernel function (SEGPR), and exponential kernel function (EGPR). The model performance revealed that the SVM-based models did not show impressive performance in modeling the hydrogen production from the palm oil mill effluent, as indicated by the R² of −0.01, 0.150, and 0.143 for LSVM, QSVM, and CSVM, respectively. Similarly, the SVM-based models did not perform well in modeling the hydrogen production from activated sludge, as evidenced by R² values of 0.040, 0.190, and 0.340 for LSVM, QSVM, and CSVM, respectively. On the contrary, the SEGPR, RQGPR, SEGPR, and EGPR models displayed outstanding performance in modeling the prediction of hydrogen production from both oil palm mill effluent and activated sludge, with over 90% of the datasets explaining the variation in the model output. With the R² > 0.9, the predicted hydrogen production was consistent with the SEGPR, RQGPR, SEGPR, and EGPR with minimized prediction errors. The level of importance analysis revealed that all the input parameters are relevant in the production of hydrogen. However, the influent chemical oxygen demand (COD) concentration and the medium temperature significantly influenced the hydrogen production from palm oil mill effluent, whereas the pH of the medium and the temperature significantly influenced the hydrogen production from the activated sludge.

1. Introduction

In the past two decades, there has been an increasing quest for transition into a low carbon economy due to the adverse effect of the utilization of energy derived from fossil fuels on the environment [1]. The utilization of fossil-fuel-derived energy for various human activities often results in the emission of environmentally unfriendly gaseous emissions, with climate change being one of the most undesirable effects [2]. To keep global warming to no more than 2 °C, the Paris climate agreement, signed in December 2015 and also further substantiated at the recently concluded COP 26 summit held at Glasgow, aims to limit it to 1.5 °C [3]. This has pushed several urgent international concerns on the continuous utilization of fossil fuel-derived energy to the forefront. The topmost questions being presently addressed are: what should be performed to avoid dangerous thresholds of climate change, how each type of fossil fuel should be lowered, and how could the production of renewable energy be hastened to replace fossil fuels in the short term? Several strategies have been proposed to answer these questions [4]. According to Fawzy et al. [4], these strategies can be categorized into two, namely, the conventional and negative emissions. The conventional strategies for climate change mitigation include the development and deployment of renewable energy sources, increasing use of nuclear power, carbon capture, storage and utilization, and fuel switch and efficiency gain. The negative emission strategies deal with the activities such as soil carbon sequestration, afforestation, reforestation, bioenergy carbon capture, and storage.

As part of the conventional strategies, there is growing interest in the development and deployment of hydrogen energy due to its several benefits as a renewable energy source [5]. Some of the benefits include zero-emission when used in a hydrogen fuel cell, robust reliability in terms of its usage in tough climatic conditions, high efficiency compared to other forms of renewable energy sources, and lower operational cost compared to renewable energy sources such as photovoltaic solar cell [6]. Several technological pathways have been explored for hydrogen production. Some of these technological pathways are heavily reliant on the use of fossil fuel sources such as natural gas as feedstock. However, there is a growing research interest in producing hydrogen from waste sources based on the circular economy concept, as shown in Table 1.

Table 1. Summary of studies on hydrogen production from waste sources.

Sources	Technological Process	Hydrogen Produced	Reference
Food waste	Gasification	1.2 tonne/h	[7]
Municipal solid waste	Electrolysis Gasification	43.1 MNm3 183 MNm3	[8]
Garden waste	Dark fermentation	97 mL of H2/g	[9]
Household waste	Hydrothermal gasification	39 wt% biohydrogen yield	[10]
Waste activated sludge	Anaerobic fermentation	46.8 ± 1.0 mL/g	[11]
Organic solid waste	Pyrolysis reforming	11.49 mmol/g	[12]
Waste activated sludge	Dark fermentation	11.01 ± 0.30 mL/g	[13]
Palm oil mill effluent	Dark fermentation	4.62 LH2/L	[14]
Palm oil mill effluent	Microbial electrolysis	92.72% biohydrogen yield	[15]
Palm oil mill effluent	Dark fermentation	3.07 ± 0.66 H2 yield mol-H2/mol-acetate	[16]

Table 1. Summary of studies on hydrogen production from waste sources.

Sources	Technological Process	Hydrogen Produced	Reference
Food waste	Gasification	1.2 tonne/h	[7]
Municipal solid waste	Electrolysis Gasification	43.1 MNm3 183 MNm3	[8]
Garden waste	Dark fermentation	97 mL of H2/g	[9]
Household waste	Hydrothermal gasification	39 wt% biohydrogen yield	[10]
Waste activated sludge	Anaerobic fermentation	46.8 ± 1.0 mL/g	[11]
Organic solid waste	Pyrolysis reforming	11.49 mmol/g	[12]
Waste activated sludge	Dark fermentation	11.01 ± 0.30 mL/g	[13]
Palm oil mill effluent	Dark fermentation	4.62 LH2/L	[14]
Palm oil mill effluent	Microbial electrolysis	92.72% biohydrogen yield	[15]
Palm oil mill effluent	Dark fermentation	3.07 ± 0.66 H2 yield mol-H2/mol-acetate	[16]

As shown in Table 1, food wastes, municipal solid wastes, garden wastes, household wastes, waste-activated sludge, organic solid wastes, and palm oil mill effluent have been employed for hydrogen production. The hydrogen was produced from various sources using technological processes such as gasification, electrolysis, dark fermentation, hydrothermal gasification, anaerobic fermentation, pyrolysis reforming, and microbial electrolysis. The amounts of hydrogen produced were observed to vary with the type of technological process used. Moreover, experimental investigations have shown that the hydrogen produced can also be influenced by various process conditions temperature, pH of the medium, influent COD concentration, light intensity, agitation speed, and so on. It is unclear from the literature the inter-relationship between the various parameters and to what extent these parameters influence hydrogen production. The constraints can be resolved using a data-driven modeling approach such as SVM and GPR.

A variety of processes have been modeled using SVM and GPR. SVM and GPR were used by Zhao et al. [17] to model hydrogen production from biomass via the water gasification process. Both the SVM and GPR displayed robust prediction performance with R² of 0.976, and 0.954, respectively. The application of SVM for the identification of leak possibilities in hydrogen fuel cell vehicles has been reported by Tian et al. [18]. The SVM modeling resulted in 95% diagnosis accuracy at constant diagnosis time. SVM has been reported to be robust in the predictive modeling of solar thermal energy systems [19]. However, the authors observed that the SVM predictive accuracy was less than other machine learning algorithms, such as random forest. Yoon and Moon [20] reported that the GPR model accurately models energy consumption in a commercial building. The modeling of hydrogen-rich syngas production from co-gasification agriculture waste using SVM and GPR has been reported by Bahadar et al. [19]. The hydrogen-rich syngas was accurately predicted by the SVM and GPR as indicated by the high R² (>0.9), indicating a strong correlation between the actual and the predicted values. To the best of the authors’ knowledge, the comparative analysis of SVM regression and GPR in modeling hydrogen production from waste effluent has not been reported in the literature. Therefore, this study focuses on the comparative analysis of SVM and GPR in modeling hydrogen production from palm oil mill effluent and activated waste sludge. The input variables sensitivity analysis on the predicted hydrogen production was also investigated.

2. Experimental Details and Model Configuration

Two sources of waste, namely, activated sludge and palm oil mill effluent, were employed for biohydrogen production. The details of the experimental design and description have been reported in Yin and Wang [21] and Chong et al. [22]. As reported by Yin and Wang [21], Erlenmeyer flasks of 100 mL were used for batch experimental runs for biohydrogen production. Silicone rubber stoppers were used to prevent gas from escaping, 1 mol/L HCl and 1 mol/L NaOH were used to alter the pH in each batch. The temperature of the batch reactor was maintained at each stipulated value in the range of 25–40 °C by using a reciprocal shaker at 100 r/min. Each of the experimental runs was performed using 10 mL of sludge, which was pre-cultured, and 10 mL of nutrients. The culture medium was anaerobically gassed for 3 min before incubation. The cumulative hydrogen production was analyzed from each batch run using a stipulated gas chromatograph. As reported by Chong et al. [22], the experimental hydrogen production was carried out in a fermenter of 3 L in volume. The pH, temperature, and COD levels were varied based on the experimental design when introducing the POME into the fermenter. The hydrogen produced was analyzed using a gas chromatograph.

SVM and GPR with different kernel functions were employed for modeling the hydrogen production from the two waste substrates. One major advantage of the SVM regression is that it allows the specification of how much error can be tolerated in the model, and it is robust in locating a suitable hyperplane in higher dimensions to fit the data. The objective function of the SVM regression is to minimize the weight function (w) of the input variables represented in Equation (1) and the constraints represented in Equation (2).

$$\mathrm{Min} \frac{1}{2}\Vert \mathrm{w}{\Vert }^2$$

(1)

$$\left|{\mathrm{y}}_{\mathrm{i}} - {\mathrm{w}}_{\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}\right|\le \mathsf{\epsilon }$$

(2)

where ${\mathrm{y}}_{\mathrm{i}}$, ${\mathrm{x}}_{\mathrm{i}}$, and $\mathsf{\epsilon }$, targeted variable, the input variables, and the maximum error function, respectively. The architecture of the SVM regression is depicted in Figure 1. It consists of the input layer which supplies the input variables, the hidden layer, and the output layer.

Although the SVM possesses the practical merit of producing a fair estimation of its own uncertainty, the GPR, on the other hand, has the main practical advantage of accurately evaluating its own level of uncertainty. The GPR may be thought of as kernelized Bayesian linear regression, where the kernel parameterization is controlled by choice of covariance/kernel function and the data used to generate predictions. By estimating the parameters of the Gaussian distribution in a provided observed training data, the GPR predicts a posterior Gaussian distribution for targets over test points X. The probabilistic model of Gaussian process functions across the training and testing datasets (f and f*, respectively is provided by Equation (3). A block matrix of kernel similarity matrices makes up the right-hand covariance matrices in Equation (3).

$$\left[\begin{array}{c}\mathrm{f}\\ {\mathrm{f}}^{*}\end{array}\right]~\mathrm{N}\left(0, \left[\begin{array}{c}\mathrm{K} \left(\mathrm{X},\mathrm{X}\right)\\ \mathrm{K}\left({\mathrm{X}}_{*}\mathrm{X}\right)\end{array}\begin{array}{c}\mathrm{K}\left(\mathrm{X},{\mathrm{X}}_{*}\right) \\ \mathrm{K}\left({\mathrm{X}}_{*},{\mathrm{X}}_{*}\right)\end{array}\right]\right)$$

(3)

Different regression learners with kernel functions such as squared exponential (Equation (4)), exponential (Equation (5), and rotational quadratic (Equation (6)) were used and trained to compare their results.

$$\mathrm{k}\left({\mathrm{z}}_{\mathrm{i}},{\mathrm{z}}_{\mathrm{j}}\right)\mathsf{\theta }) = { \mathsf{\sigma }}_{\mathrm{j}}^2\exp \left\{-\frac{1}{2}\frac{{\left({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}^{\mathrm{T}}\left({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}{{\mathsf{\sigma }}_{\mathrm{j}}^2}\right\}$$

(4)

$$\mathrm{k}\left({\mathrm{z}}_{\mathrm{i}}, {\mathrm{z}}_{\mathrm{j}}\right)\mathsf{\theta }) = {\mathsf{\sigma }}_{\mathrm{j}}^2\exp \left\{-\frac{\sqrt{\left({\left({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}^{\mathrm{T}}({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}}{{\mathsf{\sigma }}_{\mathrm{j}}^{ }}\right\}$$

(5)

$$\mathrm{k}\left({\mathrm{z}}_{\mathrm{i}},{\mathrm{z}}_{\mathrm{j}}\right)\mathsf{\theta }) = { \mathsf{\sigma }}_{\mathrm{j}}^2 {\left\{1 + \frac{{\sqrt{\left({\left({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}^{\mathrm{T}}({\mathrm{z}}_{\mathrm{i}} - {\mathrm{z}}_{\mathrm{j}}\right)}}^2}{2{\mathsf{\alpha }\mathsf{\sigma }}_{\mathrm{j}}^2}\right\}}^{-\mathsf{\alpha }}$$

(6)

where ${\mathsf{\sigma }}_{\mathrm{j}},$ ${\mathsf{\sigma }}_{\mathrm{f}},$ are the characteristic length scale and the signal standard deviation for a covariance function $\mathrm{k}\left({\mathrm{z}}_{\mathrm{i}},{\mathrm{z}}_{\mathrm{j}}\right)$. ${\mathrm{z}}_{\mathrm{i}}{ \mathrm{and} \mathrm{z}}_{\mathrm{j}}$ are d-by-1 vectors. $\mathsf{\alpha }$ is the positive-valued scale-mixture parameter.

Different features and k-fold validations, as well as hyperparameter settings, were used to train the SVM and GPR models in the MATLAB environment. All the models were trained with distinct feature frames and parameters in mind. The SVM and GPR model performance were evaluated using root mean square error (RMSE), coefficient of determination (R²), and mean absolute errors (MAE). The MSE is a measure of how closely a regression line follows a collection of data points. This is accomplished by squaring the distances between the points on the plots and the regression line. The RMSE is a measure of the residuals’ standard deviation (prediction errors). The RMSE is also useful in quantifying the amount of variance that exists around the models. It can be represented by Equation (7). The R² is a statistical metric that assesses the extent to which variations in one variable can be explained by changes in another one (Equation (8)). The MAE of the models with regard to a test set is the average of all individual prediction errors on all instances in the test set (Equation (9)).

$$\mathrm{RMSE} = \sqrt{\frac{\sum {\left({\ddot{\mathrm{Y}}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}$$

(7)

where ${\ddot{\mathrm{Y}}}_{\mathrm{i}}$ and ${\mathrm{Y}}_{\mathrm{i}}$ are predicted and actual value of the hydrogen, n is the number of observed runs.

$${\mathrm{R}}^2=\frac{\mathrm{Expand} \mathrm{variation} \mathrm{in} \mathrm{Y}}{\mathrm{Total} \mathrm{variation} \mathrm{in} \mathrm{Y}} = 1-\frac{{\sum }_{\mathrm{i} = 1}^{\mathrm{n}}{\left({\hat{\mathrm{y}}}_{\mathrm{i}} - {\mathrm{y}}_{\mathrm{i}}\right)}^2}{{\sum }_{\mathrm{i} = 1}^{\mathrm{n}}{\left({\mathrm{y}}_{\mathrm{i}} - {\bar{\mathrm{y}}}_{\mathrm{i}}\right)}^2}$$

(8)

where ${\hat{\mathrm{y}}}_{\mathrm{i}}$ depicts the mean of the actual values of the hydrogen produced, ${\mathrm{y}}_{\mathrm{i}}$ is the actual value of the hydrogen produced and ${\bar{\mathrm{y}}}_{\mathrm{i}}$ is a given point on the regression line.

$$\mathrm{MAE} = \frac{{\sum }_{\mathrm{i} = \mathrm{n}}^{\mathrm{n}}\left|{\ddot{\mathrm{Y}}}_{\mathrm{i}}{}_{ } - {\mathrm{Y}}_{\mathrm{i}}\right|}{\mathrm{n}}$$

(9)

The independent variable importance analysis was conducted to determine the influence of the input parameters on the model output. The relative importance of the input parameters for a single response variable can be determined by deconstructing the model weights. Finding all weighted connections between the nodes of interest can reveal the relative relevance (or degree of association) of a certain explanatory variable for the response variable. That is, the weights that relate a certain input node to the response variable are identified in the hidden layer. The weights determine the relative importance of the information that is processed in the network so that the weights minimize input variables that have no relationship to a response variable.

3. Results and Discussion

3.1. Performance Analysis of the SVM and GPR Models

Figure 2 portrays the actual and predicted hydrogen production from the palm oil mill effluent, the details of the predictor importance analysis based on the measured values, and the predictor’s importance analysis. As shown in Figure 1, the SVM models integrated with the linear (LSVM), quadratic (QSVM), and cubic (CSVM) kernel functions did not display a notable performance in the predicting the hydrogen production from the activated sludge. The predicted hydrogen production from the three models was not consistent with the actual values, as indicated in Figure 1. As summarized in

Table 2. Comparative analysis of the SVM and GPR in predicting the hydrogen production.

Substrate	Performance Matrix	LSVM	QSVM	CSVM	FGSVM	RGPR	SEGPR	DEGPR
	RMSE	0.148	0.135	0.111	0.020	0.00258	0.00258	0.00258
Palm oil mill effluent	R2	−0.010	0.150	0.143	0.980	0.999	0.999	0.999
	MAE	0.125	0.113	0.095	0.019	0.00145	0.00145	0.00145
	RMSE	1000.1	918.19	830.3	133.39	13.222	13.222	173.26
Sludge	R2	0.040	0.190	0.340	0.980	0.999	0.999	0.970
	MAE	786.29	701.36	598.64	128.05	6.102	6.102	89.332

, the LSVM, QSVM, and CSVM poorly predict hydrogen production. This can be confirmed by the R² values of −0.01, 0.150, and 0.143 for LSVM, QSVM, and CSVM, respectively. This implies that a small fraction of the variations of the predicted hydrogen production is explained by the LSVM, QSVM, and CSVM. The incorporation of the exponential kernel function significantly improves the predictability of the SVM in modeling the prediction of hydrogen production. The performance of the SFVM model can be confirmed from the R² of 0.980, which implies that the model can explain over 90% variant in the predicted hydrogen production with minimized errors, as indicated by the RMSE and MAE values in Table 2.

The GPR models incorporated with rotational, squared exponential, and quadratic, exponential kernel functions displayed superior performance compared to the SVM models. As shown in Figure 2a, the predicted hydrogen agrees with the observed values. This can further be confirmed by the R² value of 0.999, which implies that over 90% variation in the predicted hydrogen can be explained by the models. The hydrogen production from the palm oil mill effluent is observed to be significantly influenced in the low-temperature range of 23–30 °C, as depicted in Figure 2b. This phenomenon is typical of photocatalytic reactions for hydrogen production, as reported by Hisatomi et al. [23]. Furthermore, a positive influence observed at pH of 5.7, 7, and 8 is an indication that the palm oil mill effluent at the stipulated pH could enhance hydrogen production. Karimi et al. [24] reported that hydrogen production from glycerol, ethanol, and methanol is positively influenced by pH of 7.5–8.5. Using palm oil mill effluent with a high concentration of COD was observed to promote high hydrogen production, as shown in Figure 2b. Zhu et al. [25]) reported that the use of waste molasses with high COD concentration significantly enhances hydrogen production. The overall level of importance analysis of the various parameters is depicted in Figure 2c. It can be seen that the reaction temperature has the greatest influence on the predicted hydrogen production from the palm oil mill effluent. This is followed by the influent COD concentration, while the pH has the least influence.

The performance of the SVM and GPR models in predicting hydrogen production from activated sludge is depicted in Figure 3. As shown in Figure 3a, the SVM incorporated with linear, quadratic, and cubic kernel functions did not show impressive performance in modeling the prediction of the hydrogen production from activated sludge. The poor performance of the LSVM, QSVM, and CSVM is depicted by the large deviation of the predicted hydrogen production and the actual values obtained from the activated sludge. With R² of 0.04, 0.190, and 0.340 obtained using the LSVM, QSVM, and CSVM models, respectively, for predicting the hydrogen production, a large portion of the datasets cannot explain the variation in the model output (predicted hydrogen). Hence, the models are not suitable for modeling the relationship between the input parameters and hydrogen production. Moreover, large prediction errors indicated by the RMSE and the MAE values also confirm the poor predictability of the LSVM, QSVM, and CSVM models. However, the incorporation of the fine Gaussian kernel functions into the SVM significantly improves the performance, as indicated by the R² of 0.980. This is an indication that 98% of the datasets can explain the variation in the model output. Hence, the predicted hydrogen production is consistent with the actual values obtained from the activated sludge.

All the three kernel functions incorporated into the GPR showed impressive performance in predicting the hydrogen production from the activation sludge. The predicted hydrogen production is in proximity to the actual values as indicated by the R². R² of 0.999, 0.999, and 0.990 were obtained for the RGPR, SEGPR, and DEGPR, respectively. This indicates that the datasets can explain the variation in the model output with minimized prediction errors, as indicated by the RMSE and MAE values. As indicated by the R² and the prediction errors, the RGPR, SEGPR, and DEGPR models are robust in modeling the non-linear relationship between the input parameters and the process output. Based on the GRP models, the level of importance analyses depicted in Figure 3a,b revealed that the hydrogen production from the activated sludge is significantly influenced by the temperature, pH, and glucose concentration. In Figure 3b, a positive influence at a temperature of 25 °C implies an enhanced hydrogen production at the stipulated temperature. Furthermore, hydrogen production from the activated sludge is most favored at a pH of 5 and glucose concentration of 20 g/L. The overall analysis of the level of importance of the input parameters revealed that the pH of the medium plays a vital role in influencing the model output. This is followed by the temperature and the glucose concentration.

The three-dimensional plots showing the comparison between the actual and predicted hydrogen produced from palm oil mill effluent and activated sludge are depicted in Figure 4 and Figure 5. The interaction effect of the two most significant factors, which are: influent COD concentration and temperature for hydrogen produced from the palm oil mill effluent, as well as pH and temperature for hydrogen produced from activated sludge, were also displayed on the plots. In Figure 4a–g, the actual hydrogen produced was compared with the predicted values using LSVM, QSVM, CSVM, FGSVM, RGPR, SEGPR, and DEGPR models. Figure 4a,b revealed that the actual hydrogen (dome shape) is not consistent with the predicted values (flat shape) by the LSVM and QSVM. Improved consistency between the actual and predicted is, however, observed using the CSVM model as depicted in Figure 4c. Figure 4d–g show a high degree of consistency between the actual and predicted hydrogen from the palm oil mill effluent. The plots also show that the two factors significantly influence the hydrogen produced from the oil palm mill effluent. An increase in the influent COD concentration up to 50 mg/L resulted in a corresponding increase in the amount of hydrogen produced per day. Similarly, optimum hydrogen production from the palm oil mill effluent is favorable at 32 °C. The interaction between the influent COD concentration and the temperature peaked at maximum hydrogen production of 1.1 m³ hydrogen per day.

Similarly, in Figure 5a–g, the actual hydrogen produced from activated sludge was compared to the predicted values using LSVM, QSVM, CSVM, FGSVM, RGPR, SEGPR, and DEGPR models. Figure 5a,b show that the actual hydrogen (dome shape) does not match the LSVM and QSVM predicted values (flat shape). The CSVM model, as shown in Figure 5c, improves the consistency between the actual and predicted values. Figure 5d–g indicate that the actual and predicted hydrogen from the activated sludge is quite consistent compared to Figure 5a,b. The plots also illustrate that the two most significant factors (pH and temperature) have a considerable impact on the amount of hydrogen produced from the activated sludge. When the pH was increased to 8.2, the amount of hydrogen produced per liter increased proportionally. At 32 °C, optimal hydrogen production of the activated sludge was attained.

3.2. Comparison of the Best Model with Literature and Practical Implications of the Study

The appraisal of the best models utilized for modeling hydrogen production from palm oil mill effluent and activated sludge waste with those reported in the literature are summarized in Table 3. As summarized in Table 3, various data-driven modeling techniques such as multilayer perceptron neural network (MLPNN), Levenberg–Marquardt neural network, scaled conjugate gradient neural network (SCGNN), least-square SVM, backpropagation neural network (BPNN), Ensemble Tree, ANN incorporated with sigmoid function and ANN incorporated with hyperbolic tangent function has been employed in modeling various processes. The performance of the FGSVM, RGPR, SEGPR, and DEGPR used in modeling hydrogen production from palm oil mill effluent and activated sludge wastes is comparable with the models reported in the literature, as indicated by the R² values. The R² of 0.999 obtained for the RGPR, SEGPR, and DEGPR models are consistent with that reported for modeling hydrogen production from biomass gasification [22], commercial proton exchange membrane fuel cell [23], photocatalytic hydrogen production from ethanol [24], hydrogen production through water-gas shift reaction [26], and hydrogen production by catalytic steam methane reforming [27]. This is an indication of the sturdiness of the GPR in modeling non-linear complex processes. The slight variation in the performance of the SVM and GPR used in modeling formic acid electro-oxidation with the present study could be a result of different model inputs, the datasets, and the complexity of the process. Furthermore, the SVM algorithm performs poorly compared to the GPR, possibly due to the lack of inbuilt mechanisms to handle datasets where target classes overlapped.

Table 3. Comparison of the best model with literature.

S/N	Process	Model	Performance Matrix	Reference
1	Hydrogen production from Palm oil mill effluent	RGPR, SEGPR, DEGPR	R2 = 0.999, RMSE = 0.00258 R2 = 0.999, RMSE = 0.00258 R2 = 0.999, RMSE = 0.00258	This study
2	Hydrogen production from waste activated sludge	FGSVM RGPR SEGPR	R2 = 0.980, RMSE = 133.290 R2 = 0.999, RMSE = 3.222 R2 = 0.999, RMSE = 13.222	This study
3	Hydrogen production via biomass gasification	SVM KNN Decision tree	R2 = 0.997, RMSE = 1.631 R2 = 0.991, RMSE = 0.991 R2 = 0.991, RMSE = 0.944	[28]
4	Commercial proton exchange membrane fuel cell	SVM MLP	R2 = 0.977, RMSE = 0.050 R2 = 0.995, RMSE = 0.03	[29]
5	Photocatalytic hydrogen production from ethanol	LMNN SCGNN	R2 = 0.998, RMSE = 1.32 × 10−15 R2 = 0.997, RMSE = 2.21 × 10−15	[30]
6	Hydrogen production through water-gas shift reaction	LSSVM	R2 = 0.998, RMSE = 0.0069	[31]
7	Co-gasification techniques for producing hydrogen	SQGPR RQGPR	R2 = 0.980, RMSE = 0.0089 R2 = 0.980, RMSE = 0.0088	[32]
8	PEM fuel cell systems	BPNN	R2 = N.R, RMSE = 0.02334	[33]
9	Formic acid electro-oxidation	SVM, Ensemble Tree, and GPR	R2 = 0.820, RMSE = N.R R2 = 0.830, RMSE = N.R R2 = 0.850, RMSE = N.R	[34]
10	Catalytic steam methane reforming to hydrogen	ANN with Sigmoid function ANN with Hyperbolic Tangent function	R2 = 0.997, RMSE = 0.652 R2 = 0.984, RMSE = 0.348	[31]

N.R. Not reported.

Table 3. Comparison of the best model with literature.

S/N	Process	Model	Performance Matrix	Reference
1	Hydrogen production from Palm oil mill effluent	RGPR, SEGPR, DEGPR	R2 = 0.999, RMSE = 0.00258 R2 = 0.999, RMSE = 0.00258 R2 = 0.999, RMSE = 0.00258	This study
2	Hydrogen production from waste activated sludge	FGSVM RGPR SEGPR	R2 = 0.980, RMSE = 133.290 R2 = 0.999, RMSE = 3.222 R2 = 0.999, RMSE = 13.222	This study
3	Hydrogen production via biomass gasification	SVM KNN Decision tree	R2 = 0.997, RMSE = 1.631 R2 = 0.991, RMSE = 0.991 R2 = 0.991, RMSE = 0.944	[28]
4	Commercial proton exchange membrane fuel cell	SVM MLP	R2 = 0.977, RMSE = 0.050 R2 = 0.995, RMSE = 0.03	[29]
5	Photocatalytic hydrogen production from ethanol	LMNN SCGNN	R2 = 0.998, RMSE = 1.32 × 10−15 R2 = 0.997, RMSE = 2.21 × 10−15	[30]
6	Hydrogen production through water-gas shift reaction	LSSVM	R2 = 0.998, RMSE = 0.0069	[31]
7	Co-gasification techniques for producing hydrogen	SQGPR RQGPR	R2 = 0.980, RMSE = 0.0089 R2 = 0.980, RMSE = 0.0088	[32]
8	PEM fuel cell systems	BPNN	R2 = N.R, RMSE = 0.02334	[33]
9	Formic acid electro-oxidation	SVM, Ensemble Tree, and GPR	R2 = 0.820, RMSE = N.R R2 = 0.830, RMSE = N.R R2 = 0.850, RMSE = N.R	[34]
10	Catalytic steam methane reforming to hydrogen	ANN with Sigmoid function ANN with Hyperbolic Tangent function	R2 = 0.997, RMSE = 0.652 R2 = 0.984, RMSE = 0.348	[31]

N.R. Not reported.

The SVM and GPR-based models can be incorporated into the design process of the hydrogen production process from palm oil mill effluent and activated sludge waste in the case that a scale-up process is necessary. Having the knowledge of how each of the input parameters influences the process outputs utilizing SVM and GPR-based models will help to identify how resources should be correctly allocated. In addition, a suitable control measure may be incorporated into the whole operation to cut down on the amount of wasted energy and resources.

4. Conclusions

The bulk of wastewater has a large proportion of readily biodegradable organic components, which allows it to avoid the need for pre-treatment and lets it be utilized directly as a possible substrate in hydrogen production bioreactors. This helps to overcome the necessities for the pre-treatment stage. This study has demonstrated the application of SVM and GPR models incorporated with different kernel functions for modeling the production of hydrogen production from palm oil mill effluent and activated sludge. The incorporation of the linear, quadratic, and cubic kernel function to the SVM did not result in any significant improvement in the predictive performance of the hydrogen production from the palm oil mill effluent and activated sludge, as indicated by the low R² values and high prediction errors based on the RMSE and MAE. The GPR models with the various kernel functions show better performance in modeling the prediction of the hydrogen production from the palm oil mill effluent and the activated sludge. The predicted hydrogen was consistent with the actual values. The input parameters were found to significantly influence the hydrogen produced from the two sources. The level of importance study revealed that all the input parameters are important in the process of producing hydrogen. However, the concentration of COD in the influent water and the temperature of the medium had a substantial impact on the amount of hydrogen that was produced from palm oil mill effluent. On the other hand, the pH of the medium and the temperature had a substantial impact on the amount of hydrogen that was produced by the activated sludge. This study could serve as a reference point in the case of a scale-up; real-time optimization of the hydrogen production from waste effluent will be made possible with a thorough understanding of how various process factors influence the process.