Abstract
This paper presents an alternative method for predicting biochar yields from biomass thermochemical processes. As biochar is considered a renewable and sustainable energy source, it has received more attention. Several methods have been presented to predict biochar, such as neural network (NN) and least square support vector machine (LS-SVM). However, each of them has its own drawbacks, such as getting stuck in a local optimum, which occurs in NN, and lack of uncertainty and time complexity, as in LS-SVM. Therefore, this paper avoids this limitation by using a hybrid method between the adaptive neuro-fuzzy inference system (ANFIS) and gray wolf optimization (GWO) algorithm. The proposed method is called ANFIS-GWO, which consists of two stages. In the first stage, GWO is used to learn the parameters of ANFIS using the training set. Meanwhile, in the second stage, the testing set is used to evaluate the performance of the proposed ANFIS-GWO method. Three experiments were performed to assess the performance of the proposed method. The first experiment used a set of UCI (University of California, Irvine) benchmark datasets to evaluate the effectiveness of ANFIS-GWO. The aim of the second experiment was to evaluate the performance of the proposed ANFIS-GWO method to predict biochar yield from manure pyrolysis. The third experiment aimed to estimate the values of input parameters of pyrolysis that maximize biochar production. The obtained results were compared to those of other methods, such as ANFIS using gradient descent, practical swarm optimization, genetic algorithm, whale optimization algorithm, sine-cosine algorithm, and LS-SVM. The results of the ANFIS-GWO method were >35% of the standard ANFIS and also better than those of other methods.
1 Introduction
The world’s energy use has increased >10-fold during the 20th century. Energy purchases account for 5–10% of the entire national product in developed economies. However, in some of those countries, imports of fossil fuel may cost over half the value of overall exports. These economic realities are unsustainable, and pose a challenge to sustainable development [50]. Furthermore, fossil fuel is decreasing dramatically; therefore, the use of renewable energy from various sources has significantly grown in recent years. The renewable energy sources include biomass, solar radiation, ocean waves, wind, geothermal heat, and others.
Biochar is considered an attractive renewable energy source [51]. It is created from biomass through thermochemical methods, the yields of which rely on the methodological circumstances. Pyrolysis is the most popular process used to produce biochar [22]. Based on residence time and heating rate, pyrolysis is classified into two kinds: slow and fast. Biochar is created from biomass by using slow pyrolysis through a comparatively long residence period and a low heating degree, whereas fast pyrolysis uses a high heating degree and little residence period to yield a biochar.
The most attractive feature of biochar is its ability to represent a sustainable, inexpensive, and easy-to-produce method. Also, biochar has many applications in the economic-, technical-, soil-, and climate-related aspects [4, 21, 26, 31, 47]. These applications include oil amendment, energy, gas storage, water purification, and catalysis. Biochar can be used as a precursor for creating a catalyst for syngas made from the gasification of biomass, which includes a substantial quantity of tar [9]. Increase in agricultural productivity by using biochar for soil improvement can be translated into an increase in soil fecundity [40].
The prediction of biochar may be considered an optimization problem, where various artificial intelligence models are implemented to predict sustainable and renewable energy, such as solar energy [33, 37], wind energy [10], hydropower [32], bioenergy [39], geothermal energy [49], and hybrid systems [24].
Several artificial intelligence algorithms have been applied in many renewable energy applications, such as the artificial NN (ANN) [27, 46]. However, ANN has some drawbacks, such as it may get stuck in a local point; thus, the least square support vector machine (LS-SVM) is used as a method to resolve the drawbacks of ANN [8]. The performance of the LS-SVM model in predicting biochar was higher than the performance of the ANN model. Cao et al. [8] gave two reasons for this result: (i) LS-SVM uses the structural risk minimization principle that works to minimize an upper limit for the error of generalization instead of minimizing the error of training. In the other words, ANN uses the empirical risk minimization principle. (ii) LS-SVM can achieve a globally optimal solution, but ANN could not in most cases.
Nevertheless, LS-SVM suffers from some drawbacks, such as its performance is highly dependent on the selected kernel function. Also, it is relatively slow because the parameters of SVM must be tuned by conducting a coarse grid search and then a fine grid search. It cannot use the fuzzy rules as the change rules between the biochar characteristics and operating conditions occur in a fuzzy manner. Therefore, the fuzzy set theory is applied to address these cases [29]. Therefore, fuzzy sets have many interests in renewable energy issues [48], and the fuzzy inference system was used widely in renewable energy. A fuzzy-based model uses logical operators and IF-THEN rules in order to build qualitative relationships between its variables. The neuro-fuzzy systems combine the advantages of each of fuzzy logic and ANN in one model, through applying the ANN in adapting rule-based fuzzy systems. A particular model in neuro-fuzzy systems is the adaptive neuro-fuzzy inference system (ANFIS), which has achieved great outcomes in modeling non-linear functions. The membership function parameters of ANFIS are obtained from a dataset that defines the system operation. The ANFIS uses the features of the dataset to learn, and modifies the system parameters based on an error criterion [23]. The ANFIS has recorded many successful implementations in predicting the results of renewable energy, such as in solar energy [41], wind energy [1, 3], and bioenergy [13, 18].
However, the ANFIS model has some drawbacks when it is used for real applications; these drawbacks result from training the parameters of the memberships function and weights between layers of the ANFIS model. The gradient descent approaches are popular algorithms that are used to learn the parameters of ANFIS. However, in each repetition, the gradient is computed and its performance is affected by the initial point. Also, it can get stuck in the local point and therefore is not a global solution for parameters that can be determined [23]. To solve these drawbacks, meta-heuristics like genetic algorithm (GA) [30] and particle swarm optimization (PSO) [16, 45] were applied. However, GAs have always been criticized for their slow convergence speed, whereas PSO could encounter premature convergence at the later stage of the search process and is sensitive to neighborhood topology. Thus, the gray wolf optimization (GWO) algorithm is used to deal with this issue [36].
The GWO is a new meta-heuristic that emulates the behavior of gray wolves in nature [36]. In GWO, four kinds of wolves (i.e. α, β, δ, and ω) are utilized, where α wolves control the β, which in turn control the δ, whereas all the higher wolves control the ω wolves. There are three steps used to mimic the hunting behaviors (i.e. tracking, encircling, and attacking the prey). The GWO algorithm has a small number of parameters compared to other algorithms, and its performance has been established in several applications, such to enhance the performance of an NN, as in Refs. [17, 38]. Also, Robandi [42] used GWO to estimate photovoltaic parameters. It is applied to solve the system reliability optimization as in Ref. [25], which provides better results than other algorithms. In addition, it has been applied in optimizing support vector machines and clustering applications [6] (for more applications, see Ref. [20]). From the promised results of GWO in these applications, we decide to use it in this paper.
The main contributions of the current work are to (i) improve the performance of ANFIS through learning its parameters using the GWO algorithm, and (ii) to apply the improved ANFIS model as a new prediction method for renewable energy production, especially biochar production. Therefore, the proposed method for predicting biochar, which is called ANFIS-GWO, consists of two stages: (i) training ANFIS and (ii) testing. In the first stage, the ANFIS parameters are estimated using the GWO algorithm in which each solution of the population of GWO contains the parameter’s value. Meanwhile, the ANFIS-GWO algorithm is evaluated in the second phase by using the testing set (which is not used before in the training stage) as input and then predicting the output and computing the performance.
This paper is arranged as follows: in Section 2, the standard ANFIS model, GWO, and fuzzy C-means (FCM) are explained. In Section 3, the proposed method is introduced. Section 4 gives the experimental results and discussion. The conclusion is given in Section 5.
2 Preliminaries
2.1 ANFIS
Jang [23] introduced ANFIS, which is a hybrid model that combines fuzzy logic and NNs. ANFIS is based on the Takagi-Sugeno inference model that creates a non-linear mapping from input to the output space by using fuzzy IF-THEN rules. The ANFIS model contains five layers, as shown in Figure 1.
Layers of the ANFIS Model.
The crisp inputs x and y to the node of the first layer and the output
where Ai and Bi are the membership values of the generalized Gaussian membership function defined as [23]
where pi and σi are the premise parameters. In the second layer, the node’s output is the firing strength of a rule, as
The node’s output in the third layer is the normalized firing strength as
The node in layer 4 is an adaptive node, and its output is computed as
where pi, qi, and ri are the consequent parameters of the node i. In the last layer, there exists only one node whose output is computed by using the following equation:
There are two sets of adjustable parameters of the ANFIS model: the premise and the consequent parameters. The least square method (LSM) can be used to determine the fitness values of the consequent parameters. However, if the premise parameters are not steady, the search space will be wider and the convergence of training will be slower. Therefore, the hybrid learning techniques can be used to overcome this problem. One of these hybrid learning algorithms is the hybrid between the back-propagation algorithm and the LSM. This algorithm involves a two-step process [23].
In the first one, if the premise parameters are steady, the functional signals will propagate to layer 4, where the LSM specifies the consequent parameters. Thereafter, the consequent parameters will be kept fixed.
The adaptation methods of most fuzzy inference systems rely on the back-propagation algorithm that is applied to deal with parameter optimization in general. This traditional optimization technique can get trapped in a local optimum. To fix this problem, evolutionary methods like GA have been widely applied. Nevertheless, these methods could not achieve the promised results in all experimental cases and need much computation time; therefore, we use the GWO algorithm to determine the optimal weights of ANFIS and reduce the time complexity.
2.2 GWO Algorithm
The GWO algorithm is a swarm algorithm that emulates the social hierarchy of wolves [36], wherein wolves aim to determine the location of prey. The hierarchy of wolves consists of three layers: the first is the α wolves that correspond to the fittest wolves; meanwhile, the other two layers are called β and δ wolves, which represent the second and third best wolves, respectively. Therefore, these wolves are responsible for searching for prey in the search space, while the other wolves follow them. Three steps are used to simulate the hunting behavior: (i) encircling, (ii) tracking, and (iii) attacking the prey. The definition of encircling is given in Eq. (7) [36]:
where D is the distance between the wolf X and the prey Xp, while F and A represent the coefficient vectors that are computed as follows:
where r1 and r2 represent random vectors that belong to the interval
The position of any wolf X in the current population can be updated, as in Figure 2, according to the position of α, β, and δ as
Updating the Wolves’ Positions in the GWO Algorithm.
where
2.3 FCM Clustering Method
The most important concept in ANFIS is defining the number of membership functions. This can be considered a clustering problem; therefore, the FCM is used to achieve a small number of fuzzy rules. FCM is a clustering method; it was improved by Bezdek et al. [7], who determined the degree of data belonging to different clusters through minimizing the following objective function:
where r > 1 is a real number,
This iteration will stop when
3 Proposed Method
This section introduces the proposed method for predicting the biochar yield from manure pyrolysis. This model is based on a hybrid between the GWO and ANFIS. It is called ANFIS-GWO, in which the parameters of the ANFIS are determined by using the GWO algorithm. This model has five layers similar two traditional ANFIS. The nodes in layer 1 are represented by input variables (heating rate, pyrolysis temperature, holding time, moisture content, sample mass). The nodes in layer 2 are the membership functions of the input variables. The fuzzy logic rules are represented by the nodes in layer 3. The nodes of layer 4 use the consequent part of the Takagi-Sugeno-Kang model. The output of layer 5 is the biochar. In the learning stage, the GWO is used to determine the best value of the weights between layers 4 and 5, as well as to train the membership function according to the input variable.
The proposed method starts by normalizing the dataset and dividing it into two groups (training and testing). Then, the FCM is used to define the number of clustering (i.e. the number of membership functions). The next step is constructing the ANFIS using the FCM output. The parameters in ANFIS are updated based on the GWO algorithm, where the GWO explores different regions of the search space that has many local minima and then reduces the domain of search to the area that contains the global solution. In the training phase, the error information between the actual output and the corresponding predicted values are used to update the parameters (weights between layers 4 and 5 and parameters of Gaussian membership function). Where the GWO starts by generating a population X, the population with a random position for each wolf the size of X is set to N and dimension D, which represents the number of ANFIS parameters. Then, the objective function for a solution inside the population X is computed and the value of α, β, and γ are updated based on the smallest three fitness functions. The objective function (obj) in our model is defined as
where y and ŷ are the original biochar value and its predicted value, respectively. This function represents the summation of the square error between the predicted biochar value ŷ and the original value (y). Therefore, the best solution is that which has the minimum objective function value.
The next step in the GWO algorithm is to update the position of other solutions according to the value of α, β, and γ using Eqs. (11)–(13). These steps previously performed are still repeated until the stop condition is satisfied. Then, the best solution is passed to the ANFIS model. The training phase is completed if the stop conditions (maximum number of iterations and error less than the small value) are satisfied. Then, the ANFIS is constructed based on the parameters coming from the best solution. In the testing phase, the test data set is applied to the proposed method that predicts the output (biochar) based on input parameters and evaluates the performance of the model. The proposed method is explained in Figure 3.
Proposed ANFIS-GWO Method.
4 Experimental Results and Discussion
In this study, three experiments were performed to test the performance of ANFIS-GWO. The first one was applied to evaluate the performance of the proposed method in achieving a minimum error using six regression datasets that are collected from the UCI (University of California, Irvine) repository [28]. The results of this experiment are recorded in Section 4.3. The second experiment was applied to predict a biochar yield from manure pyrolysis, and it is explained in Section 4.4. The last one was used to estimate the values of input parameters of pyrolysis that maximize the biochar production, as in Section 4.5.
4.1 Performance Measures
To assess the performance of the proposed ANFIS-GWO method and to test the quality of solutions, several measures were used, which are defined as follows:
Mean square error (MSE): measures the dispersion of the data around zero. It is computed as
(18)where
Mean absolute error (MAE): measures the mean absolute deviation of the values of the output from the values of the target. It is computed as
(19)where
Root MSE (RMSE): the square of MSE to measure the dispersion of the data around zero, as in the following equation:
(20)Average absolute percent relative error (AAPRE): computes the relative absolute deviation of the predicted output from the experimental output; the lowest AAPRE value indicates the most accurate prediction. It is defined mathematically as follows:
(21)Coefficient of determination (R2): measures the relationship between the experimental data and the predicted data, and the algorithm that has R2 value closer to 1. R2 is defined as
(22)The highest R2 value indicates the most accurate prediction.
Standard deviation (SD):
(23)
4.2 Experimental Settings
In all experiments, a 10-fold cross-validation method was used to divide the data into training and testing sets. The 10-fold cross-validation split the data into 10 groups, assigning nine groups as the training set and one group as the testing set. These processes are repeated 10 times until all groups become a testing set. The output is computed as the average of the total 10 runs.
The experiments were implemented in Matlab R2014b and MS Windows 10 (64 bit) over Intel Core2Duo processor and 4 MB of RAM. The parameters of all optimization algorithms were set as follows: size of the population (n) = 25, maximum iteration = 100, lower bound = −5, and upper bound = 5. These parameters were used for fair comparison between the algorithms. However, we found that in the case of increasing the population size to become >25, the performance increased little but the algorithms took very large CPU time(s). Also, we noticed that, if the population size decreased to <25, the performance is decreased (the same for the maximum number of iterations).
4.3 Experiment Series 1: Evaluating the Performance of ANFIS-GWO
In this section, six datasets are used to evaluate the performance of the proposed method (ANFIS-GWO), which are collected from the UCI repository [28]. The descriptions of these datasets are given in Table 1. In the following experiment, we refer to the Yeast, Wine, AirfoilSelfNoise, Forestfires, Heart, and Housing datasets as Dataset1, Dataset2, Dataset3, Dataset4, Dataset5, and Dataset6, respectively. In tables and figures, ANFIS-GWO, ANFIS-PSO, and ANFIS-GA are referred to as GWO, PSO, and GA, respectively. The results of the proposed ANFIS-GWO method are compared with the other three algorithms, namely ANFIS-PSO [5], ANFIS-GA [44], and the original ANFIS.
Description of the Six Datasets Used to Evaluate the Proposed Method.
| Code name | Dataset name | Attribute number | Instance number |
|---|---|---|---|
| Dataset1 | Yeast | 8 | 1484 |
| Dataset2 | Wine | 13 | 178 |
| Dataset3 | AirfoilSelfNoise | 6 | 1503 |
| Dataset4 | Forestfires | 13 | 517 |
| Dataset5 | Heart | 13 | 303 |
| Dataset6 | Housing | 13 | 506 |
The experiments were applied 15 times, and the average of all measures are recorded in Table 2 and Figures 4–7.
Results of ANFIS-GWO Over Six Datasets against Three Algorithms.
| Dataset | Algorithm | MSE | RMSE | MAE | Time |
|---|---|---|---|---|---|
| Dataset1 | GWO | 0.03290 | 0.18106 | 0.13120 | 45.54160 |
| PSO | 0.03322 | 0.18203 | 0.12499 | 46.86776 | |
| GA | 0.03386 | 0.18369 | 0.13146 | 43.55836 | |
| ANFIS | 2.45680 | 1.56283 | 1.02184 | 30.63989 | |
| Dataset2 | GWO | 0.01496 | 0.12173 | 0.09816 | 35.86977 |
| PSO | 0.01656 | 0.12831 | 0.10301 | 36.20687 | |
| GA | 0.01622 | 0.12660 | 0.10128 | 36.39580 | |
| ANFIS | 0.30172 | 0.51610 | 0.32813 | 11.56986 | |
| Dataset3 | GWO | 0.01608 | 0.12671 | 0.09875 | 31.13066 |
| PSO | 0.01168 | 0.10800 | 0.08258 | 26.91375 | |
| GA | 0.01500 | 0.12238 | 0.09444 | 30.07782 | |
| ANFIS | 0.06087 | 0.21176 | 0.16457 | 9.97239 | |
| Dataset4 | GWO | 0.00146 | 0.03332 | 0.01739 | 37.00145 |
| PSO | 0.00413 | 0.06071 | 0.02144 | 47.11759 | |
| GA | 0.00402 | 0.05797 | 0.02055 | 37.31711 | |
| ANFIS | 7.06525 | 1.94732 | 0.21341 | 22.18185 | |
| Dataset5 | GWO | 0.04390 | 0.20857 | 0.15655 | 35.51686 |
| PSO | 0.05130 | 0.22547 | 0.16682 | 37.21948 | |
| GA | 0.04626 | 0.21367 | 0.15858 | 36.25798 | |
| ANFIS | 6.54830 | 1.64775 | 0.56228 | 19.37667 | |
| Dataset6 | GWO | 0.01101 | 0.10477 | 0.07590 | 46.51049 |
| PSO | 0.01122 | 0.10501 | 0.07123 | 43.33064 | |
| GA | 0.01052 | 0.10221 | 0.07191 | 48.34658 | |
| ANFIS | 0.06536 | 0.21647 | 0.08408 | 28.60306 |
Boldface indicates the best result.
Results of the MSE Measures.
Results of the MAE Measures.
Results of the RMSE Measures.
Results of Time Complexity.
From Table 2 and Figures 4–7, we can conclude that ANFIS-GWO outperformed the other algorithms in four datasets out of six in terms of MSE and RMSE, whereas it outperformed three datasets out of six in terms of MAE. Meanwhile, ANFIS-PSO came in second place. According to the time complexity, we can see that the original ANFIS is faster than all other compared algorithms, although it fails to obtain the smallest error in all datasets and the differences in the time complexity between it and the other algorithms are still small. Thus, we excluded its results from our comparison because although it has the best time complexity, it has the worst performance. According to the time complexity, it can be seen that ANFIS-GWO achieved the lowest time complexity in three datasets out of six, whereas ANFIS-PSO came in second place followed by ANFIS-GA.
To provide more evidence about the quality of the ANFIS-GWO method in prediction, a non-parametric Wilcoxon rank sum test was used. It was applied to the analysis of the median of the ANFIS-GWO with the median of the compared algorithms according to the RMSE measure at a significance level 0.05. The value p < 0.05 indicates that there is a statistically significant difference between ANFIS-GWO and the other algorithms. The results of the Wilcoxon test are listed in Table 3, and it can be observed that there are statistically significant differences between ANFIS-GWO and the compared algorithms in general. In this context, there was a statistical difference between ANFIS-GWO and the original ANFIS over all experiments, whereas there were statistical differences between ANFIS-GWO and both ANFIS-PSO and ANFIS-GA in all experiments except for Dataset1 and Dataset6, and except for Dataset5 for ANFIS-GA.
Results of the Wilcoxon Statistical Test.
| Dataset | PSO | GA | ANFIS |
|---|---|---|---|
| Dataset1 | 0.455 | 0.263 | 0.000 |
| Dataset2 | 0.038 | 0.042 | 0.000 |
| Dataset3 | 0.000 | 0.038 | 0.001 |
| Dataset4 | 0.001 | 0.003 | 0.000 |
| Dataset5 | 0.047 | 0.648 | 0.000 |
| Dataset6 | 1.000 | 0.246 | 0.034 |
4.4 Experiment Series 2: Predicting Biochar Yield
In this experiment, the proposed algorithm was used to improve the prediction performance of the biochar yield. However, this section starts with the problem formulation, followed by the results of the comparison algorithms.
4.4.1 Problem Formulation
The prediction of biochar yield is considered a non-linear regression problem, as there are several parameters that are influenced by the production of biochar. For example, the dataset used in this study was taken from Ref. [8] and consists of 33 records; each record has five operating parameters. These parameters are the pyrolysis temperature (°C), holding time (min), heating rate (°C min−1), percentage of moisture content (%), and sample mass (g), in which the pyrolysis temperature (x1) is constrained in the range 400 °C to 600 °C, heating rate (x2) in the range 4 to 16 °C min−1, holding time (x3) in the range 40–100 min, moisture content (x4) in the range 45 to 85%, and sample mass (x5) in the range 5–20 g. The objective function fit that maximizes biochar production is defined as
4.4.2 Results and Discussion
To evaluate the ANFIS-GWO in predicting biochar yield, it is compared with the original ANFIS and seven optimized ANFIS with different meta-heuristic algorithms, i.e. PSO, GA, grasshopper optimization algorithm (GOA) [43], sine-cosine algorithm (SCA) [34], whale optimization algorithm (WOA) [35], and flower pollination algorithm (Flower) [52], as well as LS-SVM and regression NN [8]. These algorithms were selected because they achieved good results in previous works [2, 11, 12, 14, 15, 19]. The parameter settings of these algorithms are listed in Table 4.
Parameter Setting of the Algorithms.
| Algorithm | Parameter values |
|---|---|
| GWO | |
| GA | |
| PSO | |
| GOA | |
| SCA | a = 2 |
| WOA | |
| Flower | Proximity probability = 0.8 |
| ANFIS | ErrorGoal = 0, initial step size = 0.01 |
The first step in this experiment is to determine the optimal number of membership functions (clusters) by using the FCM method. Therefore, the FCM is applied at different cluster number values, and the results are shown in Figure 8. From this figure, it can be concluded that the optimal numbers of memberships are 3 and 6 with RMSE 0.32 and 0.31, respectively; hence, we set the number of memberships to 6.
Results to Determine the Optimal Number of Clusters of FCM.
Performance of the Proposed Method against Other Algorithms.
| GWO | PSO | GA | GOA | SCA | WOA | Flower | ANFIS | LS-SVM | NN | |
|---|---|---|---|---|---|---|---|---|---|---|
| RMSE | 0.259 | 0.263 | 0.263 | 0.388 | 0.294 | 0.311 | 0.307 | 0.720 | 0.365 | 0.835 |
| AAPRE | 4.525 | 4.688 | 6.106 | 7.967 | 5.791 | 5.981 | 5.965 | 4.945 | 4.945 | 9.662 |
| R2 | 0.980 | 0.976 | 0.974 | 0.826 | 0.928 | 0.883 | 0.969 | 0.348 | 0.963 | 0.804 |
| SD | 0.0463 | 0.0479 | 0.0478 | 0.0839 | 0.0494 | 0.0519 | 0.0767 | 0.1824 | − | − |
| Time | 9.857 | 10.118 | 11.373 | 180.55 | 9.859 | 10.685 | 10.110 | − | − | − |
Boldface indicates the best result.
Comparison between the Sample Case of Predicted Data and Target Data.
| System output (predicted data) |
Target data |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Improved ANFIS using |
||||||||||
| GWO | PSO | GA | GOA | SCA | WOA | Flower | ANFIS | LS-SVM | NN | |
| 3.995 | 4.199 | 4.011 | 4.240 | 3.897 | 3.848 | 4.018 | 3.952 | 3.990 | 3.870 | 3.97 |
| 7.732 | 7.459 | 7.638 | 7.581 | 7.587 | 7.478 | 7.659 | 6.207 | 7.390 | 5.410 | 7.28 |
| 7.014 | 7.877 | 6.942 | 6.776 | 6.814 | 7.015 | 6.951 | 6.288 | 6.700 | 7.360 | 7.36 |
| 5.631 | 5.596 | 5.593 | 5.189 | 5.604 | 5.755 | 5.558 | 6.432 | 5.590 | 4.770 | 5.35 |
| 5.183 | 4.972 | 5.121 | 5.273 | 5.196 | 5.055 | 5.171 | 6.070 | 4.900 | 6.550 | 4.98 |
| 3.317 | 3.383 | 3.246 | 3.132 | 3.278 | 3.138 | 3.228 | 2.876 | 3.260 | 3.790 | 3.53 |
| 1.653 | 1.727 | 1.814 | 2.209 | 1.990 | 2.051 | 1.848 | 1.749 | 2.150 | 1.950 | 1.94 |
| 4.554 | 4.464 | 4.516 | 4.437 | 4.828 | 4.488 | 4.537 | 4.857 | 4.490 | 4.860 | 4.55 |
| 3.670 | 3.897 | 3.658 | 3.645 | 3.301 | 3.435 | 3.525 | 3.624 | 3.700 | 3.690 | 3.79 |
| 7.974 | 8.677 | 7.786 | 7.240 | 7.535 | 7.550 | 7.733 | 6.627 | 7.400 | 7.530 | 8.24 |
The results of the proposed method against nine models are presented in Tables 5 and 6 and Figures 9 and 10, which are the average of 15 independent runs. From Table 5, it can be concluded that, first, when the proposed method was compared with the original ANFIS model and the optimized ANFIS models, it had the best values of RMSE and AAPRE. Therefore, its performance is >35% of the original ANFIS. Second, when the proposed method was compared with five optimized ANFIS models, regression NN, and LS-SVM, it also had the best results in terms of all measures.
Accuracy of All Algorithms According to R2 Measure.
Predicted Data of All Algorithms against the Target (Real) Data.
Moreover, in terms of R2, the result of the proposed method was better than that of all other algorithms, as shown in Figures 9 and 10. These figures indicate that the results of ANFIS-GWO were nearest to the target data compared with the original ANFIS and all other models.
To test the stability of the models, the standard division measure was calculated and listed in Table 5. From this table, it can be seen that the optimized ANFIS with GWO had the best value and showed a high stability against the other models.
From the above results, in general, it can be noticed that when meta-heuristic techniques were used to learn the parameters of ANFIS, the performance of the ANFIS model improved in terms of RMSE, R2, and SD.
In terms of computational time, the proposed model had the lowest run time than other models due to the ability of GWO to explore and exploit the population in less time than the other algorithms.
For a deeper analysis of the performance of the proposed method, the convergence curves were considered and illustrated in Figure 11 to show the convergence behavior of the algorithms. From this figure, it can be seen that the GWO came in fourth place after GA, PSO, and WOA. Nevertheless, GWO reached the best fitness value compared with all other algorithms.
Convergence Curve of All Optimization Algorithms.
The sample cases of the predicted data are arranged in Table 6, which shows the effectiveness of the proposed method against that of the other models.
These results imply that the proposed ANFIS-GWO model improves the performance and efficiency of ANFIS by utilizing the strengths of the GWO algorithm, which led to good accuracy and stability compared with the other models.
4.5 Experiment Series 3: Estimating the Values of Input Parameters of Pyrolysis
In this experiment, the performance of the proposed ANFIS-GWO method is evaluated by using it to estimate the values of input parameters of pyrolysis that maximize the biochar production. The problem formulation in this experiment is the same as in the previous one except for the input parameters, which here are considered unknown; only the biochar yield value is given in Eq. (24). Solving the biochar production approach is a challenge; the GWO algorithm is used to solve the approach in Eq. (24). To evaluate the performance of the proposed method, the average of the RMSE for 15 runs is computed. The estimated values of the input parameters of pyrolysis are illustrated in Table 7. According to the results in Table 7, it can be concluded that the proposed ANFIS-GWO model has high accuracy to estimate the input parameters that can reach the required biochar production.
Estimating the Values of Input Parameters.
| Pyrolysis temperature (°C) | Heating rate (°C min−1) | Holding time (min) | Moisture content (%) | Sample mass (g) | Biochar mass (g) | RMSE | |
|---|---|---|---|---|---|---|---|
| Target | 500 | 12 | 40 | 55 | 20 | 7.28 | 0.34 |
| Estimated | 500.46 | 11.89 | 39.63 | 55.27 | 19.60 | ||
| Target | 500 | 12 | 60 | 55 | 10 | 3.9 | 0.49 |
| Estimated | 500.91 | 12.53 | 59.78 | 55.13 | 9.88 | ||
| Target | 500 | 12 | 60 | 65 | 10 | 4.24 | 0.30 |
| Estimated | 499.45 | 11.78 | 59.89 | 65.31 | 9.97 | ||
| Target | 450 | 8 | 40 | 85 | 15 | 5.35 | 0.40 |
| Estimated | 449.61 | 8.45 | 40.09 | 84.38 | 14.78 | ||
| Target | 600 | 12 | 60 | 45 | 10 | 3.77 | 0.53 |
| Estimated | 600.0 | 12.33 | 60.79 | 44.19 | 10.07 |
5 Conclusions and Future Works
In this study, the improvement of the ANFIS based on the GWO algorithm has been proposed to enhance the prediction performance of the biochar yield, where this process is considered an optimization problem. Therefore, several machine learning methods have been proposed to solve this problem, such as NN and LS-SVM. All of these previous methods have their shortcomings that will affect the performance of the prediction. Thus, the proposed ANFIS-GWO model avoids these limitations and was used to improve the performance of the prediction of the biochar yield from manure pyrolysis. The experimental results showed that the ANFIS-GWO model for the UCI dataset is better than other algorithms in terms of the performance measure. Meanwhile, for the prediction of biochar yield, the proposed ANFIS-GWO had the best values of RMSE and AAPRE, which were 0.259 and 4.525, respectively. Therefore, its accuracy is >35% of the standard ANFIS, and its results are also better than those of ANFIS-PSO, ANFIS-GA, LS-SVM, and regression NN. Moreover, the values of input parameters that maximize the biochar production were estimated using the GWO algorithm and showed good results.
Based on the promising results of the proposed model, in future works, it can be applied to different other applications such as quantitative structure-activity relationship, solar radiation, and biogas production.
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