# Data-Driven Approach to Modeling Biohydrogen Production from Biodiesel Production Waste: Effect of Activation Functions on Model Configurations

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## Abstract

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## Featured Application

**This study explored the feasibility of various multilayer perceptron configurations for modeling biohydrogen production from biodiesel production waste. Based on the best model, knowledge of how various parameters influence biohydrogen production can be employed in designing an optimized bioreactor that could maximize production processes.**

## Abstract

^{2}of 0.403 and a RMSE of 301.55. While the MLPNN configuration with the hyperbolic tangent as the hidden layer activation function and the sigmoid as the outer layer activation function yielded the best performance as indicated by an R

^{2}of 0.978 and a RMSE of 9.91. The gradient descent optimization algorithm was observed to help improve the model’s performance. All the input variables significantly influence the predicted biohydrogen. However, waste glycerol has the most significant effects.

## 1. Introduction

_{2}) emissions is a top priority in the struggle against global warming [2]. More efforts are being made towards the realization of cutting carbon emissions and alleviating the consequences of climate change [3,4,5]. Nevertheless, the energy industry must be decarbonized in order to achieve the set target. To achieve the carbon neutrality target, renewable energy initiatives have been reported to play a vital role and have the potential to provide up to 90% of the required carbon reductions [1,6]. In view of these renewable energy sources such as, solar, wind, hydro, tidal, geothermal, and biomass, have been extensively explored and reported to have a significant contribution towards attaining carbon neutrality in the future [7,8].

^{2}of 0.993. The pH of the medium was reported to have a significant influence on bioethanol production. In comparison to the support vector machine regression, the Gaussian process regression was found to have a better performance when employed to model hydrogen production from waste effluent from bioprocesses. Machine learning algorithms are also robust in evaluating the interaction of process parameters and their effect on the process output, as reported by Hossain et al. [17]. However, a comparative analysis of different machine learning algorithms for modeling hydrogen production by co-gasification of biomass and coal revealed that the artificial neural network (ANN) algorithm offers superior performance. To the best of the authors’ knowledge, the application of multilayer perceptron and radial basis function neural networks as well as the effect of activation functions on the network configuration for modeling the prediction of biohydrogen from biodiesel production waste has not been reported in the literature. Based on these premises, this study focuses on the application of different architectures of multilayer perceptron neural networks in comparison with selected radial basis function neural networks for the modeling of biohydrogen production from biodiesel production waste, with a particular focus on the effect of activation functions on model configurations.

## 2. Experimental and Model Configuration

_{2}HPO

_{4}, Endo-nutrient, and inoculum. According to the design, the concentrations of each medium element were changed. The experiment was designed to investigate the effect of Urea Endo-nutrient, Na

_{2}HPO

_{4,}and the amount of waste glycerol per liter of the medium on biohydrogen production. Experimental data consisting of 29 runs in batch mode, was employed for training various models used in this study.

_{i}denotes the center of the hidden neurons, σ denotes the width of the hidden neuron [26].

^{2}), root mean squared errors (RMSE), and the sum of squares error (SSE) were used to model performance. The level of importance (${\vartheta}_{ik}$) analysis using the Garson modified algorithm (Equation (2) was performed on the best model to determine to what extent the input variables influence the predicted model output [27].

## 3. Results and Discussion

#### 3.1. Parametric Analysis and Descriptive Statistics of the Data

_{2}HPO

_{4}in the range of 3–6 g/L while maintaining the concentration of urea between 0.1–0.175 can facilitate high biohydrogen production from waste glycerol. Figure 3d shows that the interaction between waste glycerol and Na

_{2}HPO

_{4}has the most significant effects on biohydrogen production. It can be seen that high hydrogen production (up to 20,000 mL H

_{2}/L) was facilitated using waste glycerol in the range of 5–10 g/L and Na

_{2}HPO

_{4}in the range of 6–8 g/L.

_{2}HPO

_{4}, the amount varied from 0 to 8 g/L with a mean of 3.93 g/L. The standard deviation and variance were estimated at 1.89 g/L and 3.57 g/L, respectively. The biohydrogen production was in the range of 117.46 to 1606.65 g/L, with the mean calculated as 582.98 g/L. The standard deviation and variance were calculated as 493.17 g/L and 243213.28 g/L, respectively.

#### 3.2. Model Performance

^{2}is summarized in Table 3. The RBFNN displayed great potential in predicting the biohydrogen production from waste glycerol. As shown in Figure 4a, the actual values depicted as “1” are consistent with the predicted values by RBFNN-1 depicted as “2”. On the contrary, poorer performance in the prediction of the biohydrogen from waste glycerol using the RBFNN-2 is observed in Figure 4b. Moreover, the superior performance of the RBFNN-1 model over the RBFNN-2 model can be further ascertained from the R

^{2}and RMSE values of 0.903 and 53.31, respectively, obtained for the RBFNN-1 model. This implied that RBFNN-1 had a robust prediction with fewer errors compared to RBFNN-2, which had R

^{2}and RMSE values of 0.419 and 301.55, respectively. A better performance of RBFNN-1 compared with RBFNN-2 could be attributed to the use of a standardized identity activation function compared to the non-standardized activation function used in RBFNN-2. The use of a standardized identity activation function has been reported to improve the performance of RBFNN [30]. The use of standardized identity as an activation function in the outer layer helps to prevent diminishing gradient problems and improve the computation performance of the RBFNN-1 model [31].

^{2}value of 0.920 and a low RMSE value of 21.48. Minimal errors were obtained from training and testing the MLPNN-1 with the experimental data. However, improved performance in the predictability of the model was obtained using MLPNN-3, MLPNN-4, and MLPNN-5, as indicated by the R

^{2}values of 0.969, 0.954, and 0.939, respectively, and low RMSE values. This implied that the nature of the activation function used in the hidden and outer layers significantly influenced the model’s performance [32]. Using the scaled conjugate gradient optimization algorithm, the MLPNN-3 with hyperbolic tangent as the hidden layer activation function and sigmoid as the outer layer activation function had the best predictive performance, as indicated by an R

^{2}of 0.969. It is obvious that using hyperbolic tangent as an activation function at the hidden and outer layers did not result in good predictability by the model, as indicated by an R

^{2}of 0.433.

^{2}value, which was greater than 0.940, MLPNN-7 with hyperbolic tangent as the hidden layer activation function and Sigmoid as the outer layer activation function displayed the best performance, as indicated by an R

^{2}of 0.978 and a RMSE of 9.91. This performance was consistent with the best configuration using the scaled gradient descent optimization algorithm. For all the models, the actual values of the volume of biohydrogen produced per liter of waste glycerol were in close proximity with the predicted values, as shown in Figure 6a–e. The training and testing of the experimental data in the models resulted in low errors, as indicated by the low SSE values.

_{2}PO

_{4}, had varying levels of influence on the predicted biohydrogen production. However, waste glycerol with the highest level of importance value of 0.542 had the most significant influence on the predicted biohydrogen production.

#### 3.3. Comparison of the Best Model with Literature and Implications of the Study

^{2}value of 0.978 and the lowest RMSE value of 9.91 mL H

_{2}/L of biodiesel waste. The robust performance of the model in modeling the prediction of biohydrogen production could be attributed to the unique characteristics of the hyperbolic tangent as well as the activation at the hidden layer [35]. The hyperbolic activation function enables rapid network convergence at the hidden layer, thereby complementing the sigmoid activation function and facilitating a robust prediction [36]. The sigma activation function’s primary goal is to keep the predicted or output value inside a certain bound, which contributes to the model’s effectiveness and precision [37]. Besides, it is generally accepted that the best method for optimizing neural networks and other machine-learning algorithms is using gradient descent. Gradient descent as an iterative optimization algorithm has the advantage of reducing the cost function to obtain a model that can accurately predict a targetted output [38]. The difference between the model’s anticipated output and the actual output was measured by the cost function (C) or the loss function.

^{2}and low RMSE values. The slight variation in the performance indicator of the best model in this study and those reported in the literature can be attributed to the peculiarity of the datasets, the differences in training algorithms, and the nature of activation functions.

## 4. Conclusions

^{2}value of 0.978.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Contour plots showing the interaction between (

**a**) urea and waste glycerol (

**b**) Endo-nutrient and urea (

**c**) Na

_{2}HPO

_{4}and urea (

**d**) Na

_{2}HPO

_{4}and waste glycerol.

**Figure 5.**Comparison between the actual and predicted biohydrogen using (

**a**) MLPNN-1 (

**b**) MLPNN-2 (

**c**) MLPNN-3 (

**d**) MLPNN-4 (

**e**) MLPNN-5 (

**f**) MLPNN-6 with a scaled conjugate gradient optimization algorithm.

**Figure 6.**Comparison between actual and predicted biohydrogen using (

**a**) MLPNN-7 (

**b**) MLPNN-8 (

**c**) MLPNN-9 (

**d**) MLPNN-10 (

**e**) MLPNN-11 (

**f**) MLPNN-12 with a gradient descent optimization algorithm.

**Figure 7.**Analysis of the relative importance of input variables on predicted biohydrogen production.

Model | The Activation Function in the Hidden Layer | The Activation Function in the Outer Layer | Optimization Algorithm for Training | Number of Units in the Hidden Layers |
---|---|---|---|---|

MLPNN 1 | Hyperbolic tangent | Identity | Scaled conjugate gradient | 10 |

MLPNN 2 | Hyperbolic tangent | Hyperbolic tangent | Scaled conjugate gradient | 10 |

MLPNN 3 | Hyperbolic tangent | Sigmoid | Scaled conjugate gradient | 10 |

MLPNN 4 | Sigmoid | Identity | Scaled conjugate gradient | 10 |

MLPNN 5 | Sigmoid | Hyperbolic tangent | Scaled conjugate gradient | 10 |

MLPNN 6 | Sigmoid | Sigmoid | Scaled conjugate gradient | 10 |

MLPNN 7 | Hyperbolic tangent | Identity | gradient descent | 10 |

MLPNN 8 | Hyperbolic tangent | Sigmoid | gradient descent | 10 |

MLPNN 9 | Hyperbolic tangent | Hyperbolic tangent | gradient descent | 10 |

MLPNN 10 | Sigmoid | Identity | gradient descent | 10 |

MLPNN 11 | Sigmoid | Hyperbolic tangent | gradient descent | 10 |

MLPNN 12 | Sigmoid | Sigmoid | gradient descent | 10 |

RBFNN-1 | Softmax | Identity | ordinary | 10 |

RBFNN-2 | Softmax | Standardized identity | standard | 10 |

Parameters | Range | Minimum | Maximum | Mean | Standard Deviation | Variance |
---|---|---|---|---|---|---|

Waste glycerol (g/L) | 36.58 | 0.23 | 36.81 | 21.39 | 7.43 | 55.27 |

Urea (g/L) | 0.20 | 0.05 | 0.25 | 0.15 | 0.05 | 0.00 |

Endo-nutrient (mL/L) | 0.40 | 0.00 | 0.40 | 0.19 | 0.10 | 0.01 |

Na_{2}HPO_{4} (g/L) | 8.00 | 0.00 | 8.00 | 3.93 | 1.89 | 3.57 |

HP (mL H_{2}/L) | 1489.19 | 117.46 | 1606.65 | 582.98 | 493.17 | 243,213.28 |

Model | RMSE | SSE-Training | SSE-Testing | R^{2} |
---|---|---|---|---|

RBFNN-1 | 53.31 | 1.253 | 0.024 | 0.903 |

RBFNN-2 | 212.25 | 3.082 | 0.017 | 0.736 |

MLPNN-1 | 21.48 | 1.083 | 0.021 | 0.920 |

MLPNN-2 | 51.99 | 4.052 | 0.000 | 0.433 |

MLPNN-3 | 12.66 | 0.034 | 0.010 | 0.969 |

MLPNN-4 | 88.14 | 0.567 | 0.074 | 0.954 |

MLPNN-5 | 59.26 | 0.358 | 0.038 | 0.939 |

MLPNN-6 | 29.63 | 0.028 | 0.018 | 0.957 |

MLPNN-7 | 258.12 | 0.250 | 0.207 | 0.965 |

MLPNN-8 | 9.91 | 0.027 | 0.003 | 0.978 |

MLPNN-9 | 38.43 | 0.317 | 0.076 | 0.934 |

MLPNN-10 | 43.72 | 0.493 | 0.198 | 0.948 |

MLPNN-11 | 16.20 | 0.111 | 0.006 | 0.977 |

MLPNN-12 | 15.09 | 0.035 | 0.019 | 0.959 |

Model-Type | Objective | RMSE | R^{2} | Reference |
---|---|---|---|---|

MLPNN (Hyperbolic tangent as the hidden layer activation function and sigmoid as the outer layer activation function | To model the prediction of biohydrogen production from biodiesel production waste | 9.91 | 0.978 | This study |

MLP coupled with imperialist competitive algorithm | To model geothermal power generation | 2.24 | 0.997 | Khosravi and Syri [39] |

MLP coupled with levenberg marquardt training algorithm | To model hydrogen solubility in hydrocarbon fuels | 0.02 | 0.993 | Mohammadi et al. [40] |

MLPNN | To model the prediction of corrosion inhibition performances of ionic liquids | 5.47 | 0.970 | Quadri et al. [41] |

MLP- coupled with levenberg marquardt training algorithm | To model the interfacial tension of hydrogen-brine system | 0.18 | 0.999 | Ng et al. [42] |

MLP coupled with levenberg marquardt training algorithm and Sigmoid function as activation function | To model lignin extraction from oil palm biomass | 1.13 | 0.993 | Rashid et al. [43] |

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**MDPI and ACS Style**

Hossain, S.S.; Ayodele, B.V.; Alhulaybi, Z.A.; Alwi, M.M.A.
Data-Driven Approach to Modeling Biohydrogen Production from Biodiesel Production Waste: Effect of Activation Functions on Model Configurations. *Appl. Sci.* **2022**, *12*, 12914.
https://doi.org/10.3390/app122412914

**AMA Style**

Hossain SS, Ayodele BV, Alhulaybi ZA, Alwi MMA.
Data-Driven Approach to Modeling Biohydrogen Production from Biodiesel Production Waste: Effect of Activation Functions on Model Configurations. *Applied Sciences*. 2022; 12(24):12914.
https://doi.org/10.3390/app122412914

**Chicago/Turabian Style**

Hossain, SK Safdar, Bamidele Victor Ayodele, Zaid Abdulhamid Alhulaybi, and Muhammad Mudassir Ahmad Alwi.
2022. "Data-Driven Approach to Modeling Biohydrogen Production from Biodiesel Production Waste: Effect of Activation Functions on Model Configurations" *Applied Sciences* 12, no. 24: 12914.
https://doi.org/10.3390/app122412914