Predictive Modeling of Bioenergy Production from Fountain Grass Using Gaussian Process Regression: Effect of Kernel Functions

Abstract

Experimental studies have shown that bioethanol production from biomass sources has been reported to be influenced by several process parameters. It is not entirely known, however, how the interaction of these factors affects the concentration of bioethanol production. In this study, the use of Gaussian Process Regression (GPR) in predictive modeling of bioethanol production from fountain grass has been investigated. Parametric analysis showing the interaction effect of time, pH, temperature, and yeast extract on the bioethanol production was examined. The effect of kernel functions on the performance of the GPR in modeling the prediction of bioenergy output was also examined. The study shows that the kernel function, namely, rotational quadratic (RQGPR), squared exponential (SEGPR), Matern 5/2 (MGPR), exponential (EGPR), and the optimizable (Opt.GPR.), had varying effects on the performance of the GPR. Coefficients of determination (R²) of 0.648, 0.670, 0.667, 0.762, and 0.993 were obtained for the RQGPR, SEGPR, MGPR, EGPR, OptGPR, respectively. The OptGPR with R² of 0.993 and RMSE of 45.13 displayed the best performance. The input parameters analysis revealed that the pH of the fermentation medium significantly influences bioethanol production. A proper understanding of how the various process variables affect bioethanol production will help in the real-time optimization of the process in the eventuality of scale-up.

1. Introduction

In recent years, bioenergy production from various biomass sources has received a lot of attention, and perennial grasses have emerged as a potential source of biomass for biofuel production [1,2,3]. There is less competition for food crops when perennial plants are cultivated on land that is no longer suitable for agricultural use [4,5]. In view of the imminent depletion of fossil fuels and the mounting threat posed by environmental degradation, perennial plant utilization is imperative for prioritizing the transition to an economy that is powered by bioenergies such as bioethanol [6]. A bioenergy system’s long-term viability necessitates consideration of three factors: the environment, the economy, and society at large [7]. One environmental advantage of utilizing forest biomass for bioenergy production is that it can enhance the soil carbon sink process, in which agricultural land is converted to forest land [8]. Bioenergy, being the sole renewable carbon source, is regarded as the most viable alternative to fossil energy, with the ability to reduce greenhouse gas emissions [9]. Carbon in bioenergy is typically derived from atmospheric CO₂, which is sequestered during biomass development through photosynthesis [10]. Thus, if carbon capture and storage are used in conjunction with bioenergy consumption, carbon emissions might be neutral or even negative [11]. For a low-carbon future, evaluations of biomass resources and GHG mitigation potentials are cornerstones for developing bioenergy networks [12].

The potential of bioenergy production in the form of bioethanol has been widely investigated using different feedstocks and conversion processes, as summarized in

Table 1. Bioethanol production from various feedstocks and conversion processes.

Bioenergy Type	Parameters Investigated	Conversion Process	Biofuel Produced	Reference
Seaweed	Cellulose loading, Enzyme loading, temperature, pH, and incubation term	Enzymatic hydrolysis and fermentation	9.77 g/L	[15]
Pomegranate peels	HNO3 concentration, Temperature, and hydrolysis time	Enzymatic hydrolysis and fermentation	61.45 g/L	[16]
Sunflower stalk	Concentration of NaOH, time for pretreatment	Enzymatic hydrolysis and fermentation	49.06 g/L	[17]
Microalgae	Algal biomass amount, the yeast volume, and the time of fermentation	Enzymatic hydrolysis and fermentation	18.57 g/L	[18]
Deodar sawdust	Chemical concentration, incubation time, and biomass loading	Thermochemical pretreatment method and enzymatic hydrolysis Separate hydrolysis and co-fermentation	14.25 g/L	[19]
Wheat straw	Extraction temperature, extraction time, and substrate loading	Subcritical water pretreatment and high solid hydrolysis	37.00 g/L	[20]
Pumpkin peel wastes	Hydrolysis loading substrate, α-amylase concentration, and amyloglucosidase concentration	Enzymatic hydrolysis and fermentation	84.36 g/L	[21]
Cotton stalk	Effect of pre-treatment method, enzymatic hydrolysis load, and retention time	Enzymatic hydrolysis and fermentation	9.5 g/L	[22]
Cheese whey	pH (4–6), temperature (30–36 °C), and lactose concentration	Fermentation	2.57 g/L	[23]
Oil palm frond juice	initial pH, rotation rate, and temperature.	Fermentation	0.50 g/g *	[2]

* Bioethanol yield.

. Feedstocks such as seaweed, pomegranate peels, sunflower stalk, microalgae, deodar sawdust, wheat straw, pumpkin peel wastes, cotton stalk, cheese whey, and oil palm frond juice have been employed for producing bioethanol. The various feedstocks were converted to bioethanol using enzymatic hydrolysis, thermochemical pretreatment, and fermentation. The effect of process parameters such as cellulose loading, enzyme loading, temperature, pH, incubation term, HNO₃ concentration, the concentration of NaOH, Algal biomass amount, yeast volume, biomass loading, and type of pre-treatment method on the bioethanol production were investigated. The bioethanol produced varied with the conversion methods, the conditions of the process, and the nature of the feedstock. The studies showed that enzymatic hydrolysis and fermentation of pumpkin peel wastes, pomegranate peels, seaweed, sunflower stalk, and microalgae resulted in bioethanol production of 84.36 g/L, 61.45 g/L, 9.5 g/L, 49.06 and 18.57 g/L, respectively. Thermochemical pretreatment, enzymatic hydrolysis, and co-fermentation of deodar sawdust resulted in bioethanol production of 14.25 g/L.

The aforementioned processes showed the great potential of bioethanol production from the feedstocks investigated. However, the ways various parameters interact to influence the bioethanol production is still receiving research attention. The huge amount of data generated during the experimental runs can be employed using a data-driven predictive modeling approach. One such approach that has been widely used in the literature is Gaussian process regression (GPR). GPR is able to directly represent the uncertainty of the model. This suggests that GPR provides an opportunity to use a distribution for the prediction value, rather than just a single value as the prediction. Neural networks do not immediately consider this degree of uncertainty. When working with GPR, it offers a flexible opportunity to incorporate previous information and specifics about the form of the model by employing a variety of kernel functions. In supervised machine learning applications, GPR, as a nonparametric machine learning algorithm, employs a Bayesian approach to multi-factor regression analysis. GPR provides the capacity to work with minimal datasets and provide uncertainty measures on predictions. Huang et al. [13] reported that the GPR algorithm was robust in predicting short-term renewable energy consumption in China. Bahadar et al. [14] displayed great potential in predicting hydrogen-rich syngas by biomass and coal co-gasification techniques. To the best of the authors’ knowledge, the use of GPR for predictive modeling of bioenergy production from fountain grass considering the effect of kernel functions has not been reported. This study, therefore, focuses on the predictive modeling of bioenergy production from fountain grass, considering the effect of kernel functions on the GPR model. The development of an efficient and comprehensive predictive model for bioethanol production from fountain grass can provide significant reference information for policymakers and the renewable energy industry.

2. Materials and Methods

The bioethanol was produced from fountain grass powder using K. oxytoca bacteria as described by Lin et al. [24]. The K. oxytoca bacteria, which was extracted from lignocellulose-degrading microflora, was employed for converting the fountain grass powder directly to bioethanol. The experimental runs were designed to investigate the influence of fermentation time, the initial pH of the liquid medium, the cultivation temperature, and the yeast extract on the bioethanol concentration.

The GPR is a non-parametric, kernel-integrated, probabilistic model that can be trained using the fitrgp function in the regression learner’s environment of MATLAB 2019 a (MathWorks Inc., Portola Valley, CA, USA) [25]. The GPR model can be expressed, as in Equation (1), in the form of a vector [26].

$$P\left(y|f,X\right)~N\left(y\right)|H\beta +f, {\sigma }^{2}I)$$

(1)

Using the fitrgp function, parameters such as β (the basis function), σ² (the noise variance), and θ (hyperparameters) of the kernel function can be estimated during the GPR training. During the training, the basis function, the kernel function, as well as the initial values of the parameters were specified.

K-fold cross-validation was employed to evaluate the GPR model performance [27]. The K-fold cross-validation technique was used to estimate a model’s performance in the absence of any input data. When the data are insufficient and there is a need to gain a reasonable estimate of training and generalization error, this approach is advantageous. The use of the K-fold cross-validation helped to overcome the challenges of underfitting and overfitting [28]. Using the K-fold cross-validation, a model may be trained with hyperparameters that have the best possible values. The K-fold cross-validation method ensures that a proportion of the samples is used once for training and validation (as part of a test fold). In comparison to the holdout technique, this provides a more accurate picture of the model’s performance. To avoid overfitting, which can occur when a model is trained using all the data, and to ensure that the model is generalized, it is possible to “test” the model on K distinct data sets using K-fold cross-validation. During the model configuration, the dataset was divided into two proportions for training and testing. The dataset for training was subsequently split into K-folds, where part of the K-fold (K-1) is employed for training while the remaining proportion is employed for validation. The performance of the models was evaluated using the coefficient of determination (R²), root mean square (RMSE) error, and mean absolute errors (MAE). The R² measures the extent of predictability of the GPR model output in the range of 0 to 1. An R² of 0 implies the output of the process cannot be predicted by the model while an R² of 1 implies a perfect prediction of the model output. The RMSE is a residual standard deviation that is employed to measure prediction errors. The residuals provide a measurement of the distance of the data points from the regression line, which provides a measurement of how dispersed these residuals are. In other words, it indicates the degree to which the data are concentrated around the line of best fit. For a model, the MAE is the sum of the total individual prediction errors in a test set divided by the number of test cases.

The descriptive statistics of the datasets shown in

Table 2. Descriptive statistics of the predictors and the output.

Parameters	Range	Minimum	Maximum	Mean	Std. Deviation	Variance
Time (h)	192.00	144.00	336.00	240.00	43.67	1906.76
pH	4.00	5.00	9.00	7.00	0.91	0.83
Temperature (K)	20.00	293.00	313.00	303.00	4.55	20.69
Yeast extract (mg/L)	8000.00	2500.00	10,500.00	6500.00	1819.44	3,310,344.83
bioethanol concentration (mg/L)	398.21	73.79	472.00	238.34	128.62	16,542.49

consist of combinations of the input parameters, namely, fermentation time, the pH of the medium, the temperature, yeast extract, and the targeted parameters (bioethanol concentration). The dataset values consist of time (144–336 h), pH (5–9), temperature (293–313 K), and yeast extract (2500–10,500 mg/L).

3. Results and Discussion

3.1. Parametric Analysis and Effect of Interaction of Process Factors on Bioethanol Production

The effect of factor interaction between pH and time; temperature and time; yeast extract and time; yeast extract and temperature; yeast extract and pH; yeast extract and pH on the bioethanol concentration are depicted in Figure 1. The plots were generated using the three-dimensional mesh functions in Sigma plot graphical software. The three-dimensional plot showing the effect of two factors at a time on the bioethanol concentration was generated while keeping the factor constant. It can be seen that the three input parameters had varying levels of influence on the bioethanol production from the fountain grass. An increase in bioethanol concentration was noticeable at pH of 5.0–7.0 and fermentation time of 160–240 h, as shown in Figure 1a. The bioethanol production was favorable at a temperature range of 290–305 K, as shown in Figure 1b. Yeast extract in the range of 2000–6000 mg/L was observed to be suitable for an increase in bioethanol concentration, as revealed in Figure 1c. The interaction between the pH and time; temperature and time; yeast extract and time produced a high concentration of bioethanol (Figure 1a–c) (>300 mg/L). Conversely, the interaction between yeast extract and temperature; yeast extract and pH; yeast extract and pH resulted in a lower concentration of bioethanol (<300 mg/L).

3.2. Performance Evaluation and Comparative Analysis of the Models

The performance of the RQGPR as a function of the dispersion and regression plots is depicted in Figure 2. In Figure 2a, the observed and the RQGPR-predicted bioethanol concentration were not consistent. As indicated in the regression plot in Figure 2b, only 64.8% of the datasets could explain the variation in the model output. The performance matrix summarized in

Table 3. Performance matrix of the various models.

Performance Matrix	RQGPR	SEGPR	MGPR	EGPR	OptiGPR
R2	0.648	0.670	0.667	0.762	0.993
RMSE	63.15	62.93	63.13	63.11	45.13
MAE	50.65	48.29	48.43	48.44	32.07
Prediction speed (obs/s)	2000	1600	1800	1500	1500
Training time (s)	2.61	6.50	2.43	2.67	65.95

reveals that the RQGPR model had the highest predictive errors with RMSE and MAE values of 63.15 and 50.65 respectively. With the R² of 0.648, it implies that the RQGPR model was not robust in modeling and generalizing the prediction of bioethanol production from fountain grass.

Figure 3 shows the performance of the SEGPR as a function of dispersion and regression plots. The measured and SEGPR-predicted bioethanol were not consistent, as indicated in Figure 3a. Only 67% of the datasets could explain the variance in the model output, as seen in the regression plot in Figure 3b. However, the SEGPR model had improved performance compared to the RQGPR model as indicated by the R², RMSE, and MAE values of 0.670, 62.93, and 48.29, respectively, according to the performance matrix shown in Table 3. This implies there was a slight effect of incorporating squared exponential kernel functions into the GPR. Just like the RQGPR, the SEGPR model was not robust in predicting and generalizing the prediction of bioethanol production from fountain grass.

The MGPR’s performance as a function of dispersion and regression graphs is shown in Figure 4. As seen in Figure 4a, the observed and MGPR predicted bioethanol were not consistent. The regression plot in Figure 4b revealed that only 66.7% of the datasets could explain the variation in the model output. According to the performance matrix provided in Table 3, the MGPR model has a better performance than the RQGPR model but is inferior to the SEGPR model, as evidenced by the R2, RMSE, and MAE values of 0.667, 63.13, and 48.43, respectively. This suggests that introducing Matern 5/2 kernel functions into the GPR had a little effect. The MGPR model, like the SEGPR and RQGPR, was not effective at predicting and generalizing bioethanol production from fountain grass.

Improved performance in predicting the bioethanol concentration was observed by incorporating the exponential function into the GPR, as shown in Figure 5. The observed and EGPR predicted bioethanol were dispersedly consistent, as seen in Figure 5a. Only 76.2% of the datasets could explain the variance in the model output, according to the regression plot in Figure 5b. The EGPR model outperforms the RQGPR, SEGPR, and MGPR models as indicated by the R², RMSE, and MAE values of 0.762, 63.11, and 48.44 respectively, displayed in the performance matrix presented in Table 3. This indicates that adding exponential kernel functions had a significant effect on the GPR.

Further optimization of the model is required for better performance. The optimizable GPR model performance is depicted in Figure 6. Both the predicted and the observed bioethanol production were consistent as indicated by the high R² value of 0.993. This implies that over 99% of the dataset could explain the variation in the optimized model output with minimal predictive errors as indicated by the least RMSE and MAE values 45.13 and 32.07, respectively. The performance of the optimized GPR showed that it can be employed for predictive modeling and generalization of the bioethanol production from the fountain grass.

The performance of the optimized GPR model in this study was consistent with what has been reported in the literature for predictive modeling of various processes. Fang et al. [29] reported that an optimized GPR model improved the prediction of CO₂ emissions compared to back propagation neural networks. Deng et al. [25] also reported the robustness of the GPR in predictive modeling of the state of charge of lithium-ion battery packs. The optimized SEGPR model properly predicted the battery pack’s state of charge and fulfilled the needs of real-world applications. Adun et al. [30] revealed that optimizable GPR has displayed great potential in modeling the prediction of the thermophysical properties of hybrid nanofluids for solar thermal applications. The optimizable GPR model displayed superior predictive performance with an R² of 0.999. Baraldi et al. [31] also demonstrated that the optimizable GPR has a high capability to model nuclear component degradations.

3.3. Input Parameters Importance Analysis and Study Implications

The level of importance assessed via an importance analysis of the effects of input parameters on the predicted bioethanol is depicted in Figure 7. It can be seen that the input parameters, namely, fermentation time, pH of the medium, temperature, and the yeast extract, had a significant influence on the predicted bioethanol. This was indicated by the importance values of 0.20, 0.31, 0.24, and 0.25, respectively. This implies that each of the parameters influenced the bioethanol production from the fountain grass. Nasirpour et al. [32] reported that factors such as fermentation time and temperature influence high enzymatic conversion and bioethanol production from sugarcane bagasse. Additionally, the pH of the fermentation medium has been reported to influence bioethanol production [33]. An input factors analysis revealed that the pH of the fermentative medium had the most significant impact on bioethanol production from the fountain grass. This was followed by the yeast extract, temperature, and time. The detailed parameters estimates based on the synaptic weights are depicted in Figure 7b. The bioethanol production is most favorable at 240 h, pH of 9, the temperature of 300 K, and yeast extract of 4500 mg/L. The application of machine learning algorithms such as GPR can harness the enormous potential of renewable energy [34]. The renewable energy industry would be left behind were GPR not adopted for the full transition process. When it comes to quickly executing complicated processes such as operational safety, material and energy optimization machine learning models outperform humans well. Machine learning models are fantastic for a fast transition to a bioenergy economy.

4. Conclusions

This study has demonstrated the application of Gaussian Process Regression (GPR) in predictive modeling of bioethanol production from fountain grass. The interaction between the impact of time, pH, temperature, and the yeast extract on on-bioethanol synthesis was investigated using parametric analysis. The impact of kernel functions on the GPR’s performance in modeling biofuel prediction was also investigated. The study found that several kernel functions, such as rotational quadratic (RQGPR), squared exponential (SEGPR), Matern 5/2 (MGPR), exponential (EGPR), and optimizable (OptGPR), had different impacts on the GPR’s performance. The RQGPR, SEGPR, MGPR, EGPR, and OptGPR, respectively, had coefficients of determination (R²) of 0.648, 0.670, 0.667, 0.762, and 0.993. The GPR-opt had the best performance, with an R² of 0.993 and an RMSE of 45.13. The pH of the fermentation medium had a considerable impact on bioethanol production, according to the input parameters analysis. In the case of scale-up, a thorough understanding of how various process factors impact bioethanol production would aid in real-time process optimization.