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Citation: Bulus, H.N. Adaptive
Neuro-Fuzzy Inference System and
Artificial Neural Network Models for
Predicting Time-Dependent Moisture
Levels in Hazelnut Shells (Corylus
avellana L.) and Prina (Oleae europaeae
L.). Processes 2024,12, 1703. https://
doi.org/10.3390/pr12081703
Academic Editor: Jie Zhang
Received: 17 July 2024
Revised: 7 August 2024
Accepted: 9 August 2024
Published: 14 August 2024
Copyright: © 2024 by the author.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
processes
Article
Adaptive Neuro-Fuzzy Inference System and Artificial Neural
Network Models for Predicting Time-Dependent Moisture
Levels in Hazelnut Shells (Corylus avellana L.) and Prina
(Oleae europaeae L.)
Halil Nusret Bulus
Department of Computer Engineering, Corlu Faculty of Engineering, Tekirdag Namik Kemal University,
Tekirdag 59860, Turkey; nbulus@nku.edu.tr
Abstract: Nowadays, in parallel with the rapid increase in industrialization and human population, a
significant increase in all types of waste, especially domestic, industrial, and agricultural waste, can
be observed. In this study, microwave drying, one of the disposal methods for agricultural waste,
such as prina and hazelnut shell, was performed. To reduce the time, energy, and cost spent on drying
processes, two recently prominent machine learning prediction methods (Artificial Neural Network
(ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS)) were applied. In this study, our aim
is to model the disposal of waste using artificial intelligence techniques, especially considering the
importance of environmental pollution in today’s context. Microwave power values of 120, 350,
and 460 W were used for 100 g of hazelnut shell, and 90 W, 360 W, and 600 W were used for 7 mm
thickness of prina. Both ANN and ANFIS approaches were applied to a dataset obtained from the
calculation of moisture content and drying rate values. It was observed that the ANFIS and ANN
models were applicable for predicting moisture levels, but not applicable for predicting drying rates.
When the coefficient of determination (R
2
), Root Mean Square Error (RMSE) and Mean Absolute
Percentage Error (MAPE) values for moisture level are examined both for ANN and ANFIS models’
predictions, it is seen that the R
2
value is between 0.981340 and 0.999999, the RMSE value is between
0.000012 and 0.015010 and the MAPE value is between 0.034268 and 23.833481.
Keywords: ANFIS; ANN; hazelnut shell; microwave drying; prina
1. Introduction
In recent times, the rapid surge in industrialization and human population has led
to a noticeable escalation in various types of waste, primarily encompassing domestic,
industrial, and agricultural waste [
1
]. These wastes either require disposal or necessitate
a reduction in their pollution load. However, their economic evaluation is of paramount
importance, and different assessment methodologies have gained significance in recent
times [2].
In Turkey, hazelnut shells are highly valued and have a high calorific value (4100–4400 cal/g)
and are widely used as a fuel, especially in regions where hazelnuts are produced. Pentosan,
which is a by-product in the petrochemical industry, such as furfural and furfuryl alcohol, is
present in hazelnut shells in an amount of 25–30%. Hazelnut shells are used to produce briquettes,
activated carbon, and industrial coal through carbonization [3].
There are many areas where olive pulp is used. Examples of these are fertilizer
and animal feed in agriculture, bitumen addition in the construction sector, and in road
construction. In addition, it is also reported in studies that it is used as fuel due to the high
energy it provides [2].
An important approach to reducing the management costs of product samples is to
reduce the weight of the products. One way to reduce product weight is to apply drying
Processes 2024,12, 1703. https://doi.org/10.3390/pr12081703 https://www.mdpi.com/journal/processes
Processes 2024,12, 1703 2 of 17
techniques. Drying the product is a technique that brings about the problem of energy
use, thus necessitating the design of energy-efficient drying systems. In addition to energy
transmission, convection, and radiation-based heating systems, microwave heating systems
that provide direct energy to materials through an electromagnetic field approach have also
been developed. This method, known as microwave drying, is widely used for treating
various types of waste due to its numerous potential advantages [4].
The microwave drying method has been applied in various ways, including meat
processing [
5
], in the food industry [
6
], with pulp [
7
], hazelnut shells [
1
] and mango
peels [8].
Energy auditing can be utilized as an important tool in assessing the life cycle of
agricultural products, serving as an initial step in recognizing plant production that leads
to increased efficiency. Energy, being a crucial input not only in agriculture but also in
various sectors, assists in enhancing productivity, increasing food security, and developing
rural economies [
9
]. When it comes to energy system modelling, what comes to mind is im-
plementing energy systems by modeling them in a computer environment and performing
analyzes on these models. Analyzes of various scenarios can be carried out through these
models [10].
Practical systems are intricate, and to ensure their optimal operation, the utilization of
models or structural and mathematical representations becomes imperative. This accounts
for the heightened prevalence of modeling practices in contemporary science. Traditional
mathematical tools are not adequately embraced for addressing indistinct and undeter-
mined systems; nevertheless, intelligent modeling methods demonstrate significant efficacy
in this domain [11].
Mathematical models are significantly used in food drying, as in many other fields.
These methods aim to describe the drying process. The use of artificial intelligence methods
is effective in developing models with high accuracy. One of the advantages of these
methods is their ease of applicability. Therefore, the popularity of using algorithms and
methods, such as Adaptive Neuro-Fuzzy Inference System (ANFIS), Artificial Neural
Networks (ANN), Fuzzy Inference System (FIS), and Genetic Algorithms (GA), is increasing
day by day [
12
]. Machine learning is significant today because the human brain is unable
to efficiently manage exponentially increasing information, thus necessitating machine
support. Artificial intelligence is a field divided into many subdisciplines. The application
of these methods in the field of drying, as in other fields, is a process that continues to be
developed. For this reason, research in this field remains valid, as in many other fields [
11
].
Currently, machine learning methods are successfully used in various fields, from
medicine to agriculture, for both current data modeling and future predictions. There are
many types of machine learning method, and ANN is one such method capable of pro-
ducing high-accuracy predictions [
13
]. The ANN prediction technique has become widely
used in many fields today. Simulating the working of the human brain in a simple manner,
ANNs hold a significant place in Artificial Intelligence Technologies. ANN methodology
has many important features, including the ability to learn from data, make generalizations,
and work with an unlimited number of variables [14].
ANNs are function networks that establish relationships similar to the relationships
between nerve cells called neurons. They have become widespread in many fields in parallel
with the development of computer technologies in recent times. In science and engineering,
they provide accurate and rapid solutions, especially for regression and classification
problems. In terms of drying technologies, ANNs are used for various purposes such
as modeling drying kinetics, dryer design and optimization, process control, and energy
control [15].
To eliminate the process and time costs of experimental procedures, accurately pre-
dicting the drying curve by modeling the behavior of the system would be a significant
advantage. Using a trained ANN for this modeling is a valid approach. Additionally,
the increasing input and output parameters due to systemic changes can also be easily
integrated into the ANN model. Moisture content, which is considered an important
Processes 2024,12, 1703 3 of 17
parameter in drying studies, allows for the measurement of the amount of water and vapor
within the material [16].
ANFIS method is a technique that emerges from the combined application of fuzzy
logic and artificial neural network principles. ANFIS can be trained with known or desired
values and utilized to calculate unknown values. Widely employed in recent years for
solving non-linear problems, ANFIS demonstrates considerable success in determining the
relationships between input and output variables [17].
In many studies, both ANFIS and ANN methods have been employed. Dash et al.
(2023) modeled the ultrasonic-assisted osmotic dehydration of cape gooseberry using AN-
FIS [
18
]. Soni et al. (2022) applied ANN to predict the friction coefficient of nuclear-grade
graphite [
19
]. Jena and Sahoo (2013) used ANN to model the propagation of mushrooms
and vegetables in a fluidized bed dryer [
20
]. Pusat et al. (2016) estimated the coal moisture
content in the convective drying process using ANFIS [
21
]. Dolatabadi et al. (2018) utilized
artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFIS) to
model the simultaneous adsorption of dye and metal ions from aqueous solutions using
sawdust [
22
]. One of the studies that designed an ANN and ANFIS system which predicts
moisture dissipation and energy consumption is that of Kaveh et al. (2018). In this study,
the author examined potatoes, garlic and melon and used a convective hot air dryer as a
drying device [23].
The main objective of this study is to mathematically model the drying process using
experimentally obtained data from different waste materials. Simulations based on these
models aim to reduce the time and energy expended in laboratory experiments, thereby
helping to determine the most suitable conditions for the drying industry. The study
specifically aimed to develop mathematical models of the drying process using ANN and
ANFIS methods and to compare the performance of these mathematical models. In this
study, microwave energy was utilized and, as waste materials, prina, and hazelnut shells
were selected. Although it is known that both models are used together or separately in
many fields, this is one of the pioneering studies developed for modeling the drying of
food waste, particularly the waste of olives and hazelnuts, which are significant products
in Turkey.
2. Materials and Methods
2.1. Waste Samples
The hazelnut shells (Corylus avellana L.) used in this study were obtained from Ordu
Province, Turkey. Experiments were conducted at 120, 350, and 460 W microwave power
levels. According to the wet base, the first moisture value was found to be 13
±
1% on
average. In all drying experiments, hazelnut shells weighed weighing 100 g were set on the
glass plate in a thin layer form. The final moisture value was determined as 1.1 ±0.8 [1].
The prina samples for the experiments used in the ANN and ANFIS models were
taken from a factory producing olive oil in Turkey and used in the laboratory. Laboratory
setups are designed to keep microwave power at 90 W, 360 W and 600 W levels. The
thickness of the prina layers was set to 7 mm. Drying experiments were continued in the
microwave apparatus until the prina moisture reached 12% (w.b.) and measurements were
made periodically [2].
A Beko brand, 2450 MHz frequency, 800 W power, 19-L capacity, turntable microwave
oven was arranged appropriately for the drying of all products. The experiments were
conducted in triplicate for each parameter. The averages of the data were utilized.
The moisture content data over time for prina and hazelnut shell products obtained
from a microwave dryer with different power levels are provided in Tables 1and 2, re-
spectively. In Tables 1and 2, the mw value represents the moisture content on a wet basis
as a percentage, while the md value represents the moisture content on a dry basis as
a percentage. Partial data used for moisture estimation of the prina and hazelnut shell
products are provided as an example. In calculating these values, wet mass (Mw) was used
Processes 2024,12, 1703 4 of 17
as shown in Equations (1)–(3). Measurements for 75 min at 90 W for prina and 55 min at
120 W for hazelnut shell are shown.
Table 1. The time-dependent moisture content values of the prina (Oleae Europaeae L.) product at
90 W microwave power.
Drying Time (min.) Wet Weight (Mw) (g)
Moisture Content for
Dry Basis (md) (%)
Moisture Content for
Wet Basis (mw) (%)
0 149.76 0.89 0.49
5 149.72 0.89 0.49
10 149.78 0.89 0.49
15 149.77 0.89 0.49
20 149.59 0.89 0.49
25 149.60 0.89 0.49
30 149.52 0.89 0.49
40 149.60 0.89 0.49
50 149.53 0.89 0.49
55 149.50 0.89 0.49
60 149.52 0.89 0.49
65 149.48 0.89 0.49
70 149.42 0.89 0.49
75 149.41 0.89 0.49
Table 2. The time-dependent moisture content values of the hazelnut shell (Corylus avellana L.)
product at 120 W microwave power.
Drying Time (min.) Wet Weight (Mw) (g)
Moisture Content for
Dry Basis (md) (%)
Moisture Content for
Wet Basis (mw) (%)
0 100.00 0.15 0.13
5 98.00 0.13 0.11
10 95.50 0.10 0.09
15 93.50 0.07 0.07
20 92.00 0.06 0.05
25 91.00 0.05 0.04
30 90.00 0.03 0.03
35 89.50 0.03 0.03
40 89.00 0.02 0.02
45 88.50 0.02 0.02
50 88.25 0.01 0.01
55 88.00 0.01 0.01
Tables 1and 2are sample datasets illustrating the time-dependent variations of mw
and md values at specific microwave powers for prina and hazelnut shell products, re-
spectively. Considering this dataset, microwave power and time were chosen as inputs,
and mw and md were selected as outputs when creating models for ANN and ANFIS.
To enhance the sensitivity and accuracy of the models, separate models were generated
for each output value with the same learning function, transfer function, and number of
neurons. The predicted mw and md values were then used to calculate the dimensionless
moisture ratio (MR) and drying rate (DR).
2.2. Theoretical Principle
In the experimental data used to create the data set in the study, moisture content was
calculated using two different equations. Equation (1) calculated the moisture content on a
wet basis, while Equation (2) calculated this content on a dry basis. The equation used to
calculate the dimensionless moisture ratio is given in Equation (3): [24,25]
mw% = [Mw/(Mw+ Md)] ×100 (1)
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md% = (Mw/Md)×100 (2)
MR = (m/m0) (3)
where M
d
: Dry weight (g), M
w
: Wet weight (g), MR: Dimensionless moisture ratio, m:
Moisture content of sample at a specific time (g water/g wet matter), m
0
: Initial moisture
content (g water/g wet matter).
2.3. Drying Rate
The drying rate, which represents the change in moisture content of the dried product
over unit time, is calculated using Equation (4) [26,27].
DR = (md(t+∆t) −md(t))/∆t (4)
where m
d(t)
represents the moisture content at time t (kg water/kg dry matter), m
d(t+∆t)
indicates the moisture content at t + ∆t, and ∆t is the time difference (min).
2.4. Analysis Using ANN
In this study, an Artificial Neural Network (ANN) was employed to develop a formula
based on the tangent sigmoid (tansig) transfer function. MATLAB software was utilized
for creating and testing ANN models. Hence, a preferred ANN architecture consisting of
one input layer, one hidden layer, and one output layer was chosen. There is no universally
accepted rule for determining the number of neurons in the hidden layer when constructing
ANN models. In this study, preliminary experiments were conducted on waste drying trial
data with different numbers of neurons in the hidden layer. It was observed that employing
10 neurons in the hidden layer yielded better results in predicting drying rate and moisture
content values compared to using a greater number of neurons. Consequently, the number
of neurons in the hidden layer was fixed at 10 for all the ANN architectures developed in
this study.
The output layer consists of a neuron representing the mw and md separately. Input
data were divided into three segments: training, testing, and validation, randomly selected.
ANN was trained using the Levenberg–Marquardt (LM) learning algorithm. The training
of the neural network was conducted using MATLAB software. ANN is a highly effective
method in solving nonlinear optimization problems [28].
An illustration of one of the ANN architectures used in the study is shown in Figure 1.
While a linear transfer function was employed in the output layer of the created ANNs,
tanh-sigmoid transfer function was tested in the hidden layer [29].
In ANNs, neuron weights are updated following a specific learning rule throughout
the training iterations. The jth neuron receives an activation signal from the input layer,
which is a weighted sum. The formula for this weighted sum, denoted as ‘h’, is provided
in Equation (5) [30].
hj=Σiwij xi+ bj(5)
In Equation (5), the symbol ‘w
ij
’ represents the weights governing the connections
from the input layer neurons to the neurons situated within the hidden layer. ‘b
j
’ stands for
the biases associated with the neurons in the hidden layer. The variables ‘i’ and ‘j’ denote
the respective quantities of neurons within the input layer and the hidden layer.
The resultant sum is subsequently employed in the creation of the output neuron,
denoted as ‘H
j
’, through the utilization of the activation function ‘f’. Typically, the tangent
sigmoid function serves as the activation function in the hidden layer, and its mathematical
representation is provided in Equation (6).
Hj= f (hj) = 2/(1 + e−2hj)−1 (6)
Processes 2024,12, 1703 6 of 17
As a consequence, output neurons receive signals, as depicted in Equation (7), origi-
nating from hidden neurons.
yk=Σjwkj Hj+ bk(7)
In the given equations, the weight parameter used in the hidden layers is represented
by ‘wkj’ and the bias value used in these layers is represented by ‘bk’.
1
Figure 1. Illustration of the ANN architecture of MR used in the study for hazelnut shells and prina.
As shown in Figure 1, the Artificial Neural Network (ANN) consists of three layers.
The first layer, the input layer, receives the microwave power and drying time values as
inputs. The second layer, the hidden layer, is composed of 10 neurons. These neurons
are numbered from h
0
to h
9
, and the value transmitted to each neuron is calculated using
Equation (5) with the appropriate i and j values. The diagram in Figure 1illustrates one of
the ANN models, which were separately created for MR and DR predictions but share the
same architecture. In this context, the value in the output layer represents either the MR or
DR value. Equation (7) is used to obtain the calculated value in the output layer.
In the study, drying time and applied power are provided as inputs to the ANN, while
the network is expected to predict mw and md to calculate the moisture content and drying
rate. For each ANN trial, 80% of the total drying trial data were used for training the
network, 15% of training data for validation during training iterations, and 15% of training
data were randomly selected as test data to assess the model’s predictive accuracy. After
the training, testing and validation processes were completed, the remaining 20% of the
data obtained from the experimental studies were given to the ANN model to predict. The
closeness between the actual measured values and the model’s predictions was evaluated
using commonly used regression metrics in machine learning applications, including the
coefficient of determination (R
2
) and error terms such as Root Mean Square Error (RMSE)
and Mean Absolute Percentage Error (MAPE) [26].
The results of the m
w
and m
d
tests were examined using analysis of variance, de-
pending on the microwave power level (one-way ANOVA). To see if the differences were
significant, the LSD (Least Significant Different) test was used.
2.5. Analysis Using ANFIS
ANFIS models have a five-layer structure, with three hidden layers located between
the input and output layers. These three hidden layers respectively encompass input
membership functions, rules, and output membership functions. Additionally, it is known
that they include backpropagation algorithms in the Sugeno and Mamdani fuzzy logic
classes [31].
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Figure 2shows the ANFIS architecture with five layers, consisting of two inputs and
one output.
Processes 2024, 12, x FOR PEER REVIEW 7 of 18
The results of the m
w
and m
d
tests were examined using analysis of variance, depend-
ing on the microwave power level (one-way ANOVA). To see if the differences were sig-
nificant, the LSD (Least Significant Different) test was used.
2.5. Analysis Using ANFIS
ANFIS models have a five-layer structure, with three hidden layers located between
the input and output layers. These three hidden layers respectively encompass input
membership functions, rules, and output membership functions. Additionally, it is known
that they include backpropagation algorithms in the Sugeno and Mamdani fuzzy logic
classes [31].
Figure 2 shows the ANFIS architecture with five layers, consisting of two inputs and
one output.
Figure 2. ANFIS Model Structure for MR.
Fuzzification Layer: This layer fuzzifies the inputs of the system using membership
functions. The changes in membership degrees are determined by the membership func-
tions.
O
1,i
= µ
Ai
(x), i = 1, 2 (8)
O
1,i
= µ
Bi-2
(x), i = 3, 4 (9)
µ
Ai
and µ
Bi-2
are the degrees of membership functions for fuzzy sets A
i
and B
i
[32].
Rule Layer: Each node in this layer represents the rules and their number based on
the Takagi–Sugeno fuzzy system. The output of each rule node is the product of the mem-
bership degrees coming from the first layer.
O
2,i
= w
i
= µ
Ai
(x) × µ
Bi-2
(y), i = 1, 2, 3, 4 (10)
w
i
, represents the firing strength for each rule [32].
Normalization Layer: The outputs of this layer are expressed as normalized firing
strengths.
O
3,i
= w
= w
i
/Σ
i
w
i
(11)
w
repsents the normalized firing strength.
Defuzzification Layer: This layer converts the fuzzy values back to crisp values, and
the contribution of each node to the model output is determined in this layer.
O
4,i
= w
f = w
(p
i
x + q
i
y + r
i
) (12)
p
i
, q
i
and r
i
constitute the parameter set of this node [33].
Figure 2. ANFIS Model Structure for MR.
Fuzzification Layer: This layer fuzzifies the inputs of the system using membership
functions. The changes in membership degrees are determined by the membership functions.
O1,i =µAi (x), i = 1, 2 (8)
O1,i =µBi-2 (x), i = 3, 4 (9)
µAi and µBi-2 are the degrees of membership functions for fuzzy sets Aiand Bi[32].
Rule Layer: Each node in this layer represents the rules and their number based
on the Takagi–Sugeno fuzzy system. The output of each rule node is the product of the
membership degrees coming from the first layer.
O2,i = wi=µAi (x) ×µBi-2 (y), i = 1, 2, 3, 4 (10)
wi, represents the firing strength for each rule [32].
Normalization Layer: The outputs of this layer are expressed as normalized firing
strengths.
O3,i =wi=wi/Σiwi(11)
wirepsents the normalized firing strength.
Defuzzification Layer: This layer converts the fuzzy values back to crisp values, and
the contribution of each node to the model output is determined in this layer.
O4,i =wifi=wi(pix+qiy+ri)(12)
pi, qiand riconstitute the parameter set of this node [33].
Output Layer: There is only one node in this layer. The output values of the nodes
from the previous layer are summed to obtain the actual output value of the ANFIS system.
O5,i =Σiwifi=Σiwifi/Σiwi(13)
The experimental datasets, consisting of 35 datasets for hazelnut and 1598 datasets
for prina, were divided into two parts: 80% for training and 20% for validating the ANFIS
model. Each dataset included two independent variables as inputs and one dependent
variable as the output. Three membership function nodes were assigned to each indepen-
dent variable.
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The experimental data were fitted into a first-order Takagi–Sugeno model to train
the ANFIS model. Input and output membership functions (MFs) were selected based
on minimizing the Root Mean Square Error (RMSE) during ANFIS training, utilizing two
methods: backpropagation and a hybrid approach combining forward and backward
passes [34].
2.6. Statistical Analysis
The closeness between the actual measured values and the model estimates was as-
sessed using the coefficient of determination (R
2
) and error metrics (Root Mean Square
Error (RMSE) and Mean Absolute Percentage Error (MAPE)), which are commonly em-
ployed in machine learning applications for regression analysis (Equations (14)–(16)). In
this study, the parameters of the models were estimated through nonlinear regression
analysis conducted using MATLAB. The predictive performance of the developed ANFIS
models was evaluated based on the determination coefficient (R
2
), RMSE, and MAPE.
The model exhibiting the highest R
2
, lowest RMSE, and MAPE below 10% demonstrated
superior performance in predicting md and mw values to calculate MR and DR against
drying time. [4,7,35].
MAPE = 1/N ×Σi(MRexp,i −MRpre,i)/MRexp,i (14)
RMSE = √(1/N ×Σi((MRexp,i −MRpre,i)2/(MRexp,i −MRavg,i)2)) (15)
R2= 1 −Σi((MRexp,i −MRpre,i)2/(MRexp,i −MRavg,i)2)×N (16)
where MR
teo,i
is the ith predicted moisture ratio, MR
exp,i
is the ith experimental moisture
ratio, and MRavg,i is the average experimental moisture ratio.
The results of the MR and DR tests were subjected to analysis of variance (ANOVA),
depending on the microwave power level (one-way ANOVA). To ascertain the significance
of differences, Tukey’s test was applied. All statistical analyses were performed using SPSS
(PASW Statistics 18, SPSS Ltd., Hong Kong, China). Significant differences were defined as
those with p-values less than 0.05.
3. Results
Drying data obtained experimentally for both prina and hazelnut shells was used to
create an ANN model and train the model. This developed ANN model used a neural net-
work structure with a single hidden layer, containing two input variables and, accordingly,
one output variable, to independently predict the time-dependent mw and md to calculate
moisture and drying rate of the selected products. While the input data of the developed
ANN model consist of the drying time of the products and the microwave power values
applied to the products, the output data of the model include mw and md.
One of the issues addressed in this study is the creation of an ANN model that is
compatible with experimental data for MR and DR parameters and includes the drying
characteristics of hazelnut shells and prina. A model was successfully implemented,
allowing the generation of drying curves without the need for experimentation under
various drying conditions in a conveyor dryer. Consequently, MR and DR parameters can
be effectively estimated for hazelnut shell and prina drying.
The moisture ratios of hazelnut shell and prina obtained at different drying times,
using three tests, are illustrated in Figures 3and 4. The reduction in drying time associated
with an increase in drying power can be attributed to the elevated water vapor pressure
within the samples, promoting the migration of moisture. The moisture ratios of prina
and hazelnut shell exhibited a rapid decline as the drying time increased. The persistent
decrease in the moisture ratio implies that diffusion plays a dominant role in internal mass
transfer. Similar findings were noted in experiments involving drilling sludge, zucchini
slices and hazelnut shell [1,4,26].
Processes 2024,12, 1703 9 of 17
Processes 2024, 12, x FOR PEER REVIEW 9 of 18
lowing the generation of drying curves without the need for experimentation under vari-
ous drying conditions in a conveyor dryer. Consequently, MR and DR parameters can be
effectively estimated for hazelnut shell and prina drying.
The moisture ratios of hazelnut shell and prina obtained at different drying times,
using three tests, are illustrated in Figures 3 and 4. The reduction in drying time associated
with an increase in drying power can be aributed to the elevated water vapor pressure
within the samples, promoting the migration of moisture. The moisture ratios of prina
and hazelnut shell exhibited a rapid decline as the drying time increased. The persistent
decrease in the moisture ratio implies that diffusion plays a dominant role in internal mass
transfer. Similar findings were noted in experiments involving drilling sludge, zucchini
slices and hazelnut shell [1,4,26].
Figures 3 and 4 present the experimental moisture ratio alongside predictions from
ANN and ANFIS models for the respective test data points. It is evident that the system
is highly effective in accurately estimating moisture ratio values across all experimental
conditions.
(a) (b)
Figure 3. Comparison of ANN and Experimental Moisture Content Changes: (a) Hazelnut Shell, (b)
Prina.
(a) (b)
Figure 4. Comparison of ANFIS and Experimental Moisture Content Changes: (a) Hazelnut Shell,
(b) Prina.
While designing the ANN architecture, various neuron numbers were experimented
with in preliminary studies conducted on the data from hazelnut shell and prina drying
experiments. It was observed that employing 10 neurons in the hidden layer yielded superior
results compared to using a larger number of neurons for estimating both mw and md.
Model predictions and experimental measurements were observed to have the same
trends and overlap. Upon examination of the numerical values, it is evident that the Mois-
Figure 3. Comparison of ANN and Experimental Moisture Content Changes: (a) Hazelnut Shell,
(b) Prina.
Processes 2024, 12, x FOR PEER REVIEW 9 of 18
lowing the generation of drying curves without the need for experimentation under vari-
ous drying conditions in a conveyor dryer. Consequently, MR and DR parameters can be
effectively estimated for hazelnut shell and prina drying.
The moisture ratios of hazelnut shell and prina obtained at different drying times,
using three tests, are illustrated in Figures 3 and 4. The reduction in drying time associated
with an increase in drying power can be aributed to the elevated water vapor pressure
within the samples, promoting the migration of moisture. The moisture ratios of prina
and hazelnut shell exhibited a rapid decline as the drying time increased. The persistent
decrease in the moisture ratio implies that diffusion plays a dominant role in internal mass
transfer. Similar findings were noted in experiments involving drilling sludge, zucchini
slices and hazelnut shell [1,4,26].
Figures 3 and 4 present the experimental moisture ratio alongside predictions from
ANN and ANFIS models for the respective test data points. It is evident that the system
is highly effective in accurately estimating moisture ratio values across all experimental
conditions.
(a) (b)
Figure 3. Comparison of ANN and Experimental Moisture Content Changes: (a) Hazelnut Shell, (b)
Prina.
(a) (b)
Figure 4. Comparison of ANFIS and Experimental Moisture Content Changes: (a) Hazelnut Shell,
(b) Prina.
While designing the ANN architecture, various neuron numbers were experimented
with in preliminary studies conducted on the data from hazelnut shell and prina drying
experiments. It was observed that employing 10 neurons in the hidden layer yielded superior
results compared to using a larger number of neurons for estimating both mw and md.
Model predictions and experimental measurements were observed to have the same
trends and overlap. Upon examination of the numerical values, it is evident that the Mois-
Figure 4. Comparison of ANFIS and Experimental Moisture Content Changes: (a) Hazelnut Shell,
(b) Prina.
Figures 3and 4present the experimental moisture ratio alongside predictions from
ANN and ANFIS models for the respective test data points. It is evident that the system
is highly effective in accurately estimating moisture ratio values across all experimental
conditions.
While designing the ANN architecture, various neuron numbers were experimented
with in preliminary studies conducted on the data from hazelnut shell and prina drying
experiments. It was observed that employing 10 neurons in the hidden layer yielded
superior results compared to using a larger number of neurons for estimating both mw
and md.
Model predictions and experimental measurements were observed to have the same
trends and overlap. Upon examination of the numerical values, it is evident that the
Moisture Ratio values, presented as a function of drying time, align well with both the
experimental results and the predictions made by the ANN and ANFIS models. Similar
results were reported by Bulu¸s et al. (2023) and Levent et al. (2023) in the ANN model for
MR [26,36].
Microwave heating allows for faster mass transfer within the product and generates
more heat due to volumetric heating at higher powers. The variation in moisture content
with drying rate is shown in Figures 5and 6. Consistent with the findings of Bulu¸s et al.
(2023), an increase in wavelength power corresponds to an increase in drying rate [
26
].
Although the drying rate is initially rapid in the early stages of the drying process, it
subsequently slows down in the later stages.
Processes 2024,12, 1703 10 of 17
Processes 2024, 12, x FOR PEER REVIEW 10 of 18
ture Ratio values, presented as a function of drying time, align well with both the experi-
mental results and the predictions made by the ANN and ANFIS models. Similar results
were reported by Buluş et al. (2023) and Levent et al. (2023) in the ANN model for MR
[26,36].
Microwave heating allows for faster mass transfer within the product and generates
more heat due to volumetric heating at higher powers. The variation in moisture content
with drying rate is shown in Figures 5 and 6. Consistent with the findings of Buluş et al.
(2023), an increase in wavelength power corresponds to an increase in drying rate [26].
Although the drying rate is initially rapid in the early stages of the drying process, it sub-
sequently slows down in the later stages.
When comparing the estimated moisture content with the drying rate values, it was
observed that they were not consistent.
(a) (b)
Figure 5. Variation and Estimation of Drying Rate for ANN: (a) Hazelnut Shell, (b) Prina.
(a) (b)
Figure 6. Variation and Estimation of Drying Rate for ANFIS: (a) Hazelnut Shell, (b) Prina.
Although random pieces of the datasets were taken for validation, training, and test-
ing in the tool used, this process was also performed manually before using the tool. For
the construction of the Artificial Neural Network model, two inputs, time and microwave
power of hazelnut shell and prina, were chosen, while md and mw were designated as
outputs separately.
In the ANN model with a single hidden layer, the hidden layer utilized the tangent
sigmoid function as its activation function, and the transfer function employed a linear
transfer function. The learning algorithm employed was the Levenberg–Marquardt algo-
rithm (trainlm). Through analysis of results obtained from multiple experiments involv-
ing the hidden layer, the number of neurons was determined to be 10. Figure 7 displays
the error log graph of the ANN training.
Figure 5. Variation and Estimation of Drying Rate for ANN: (a) Hazelnut Shell, (b) Prina.
Processes 2024, 12, x FOR PEER REVIEW 10 of 18
ture Ratio values, presented as a function of drying time, align well with both the experi-
mental results and the predictions made by the ANN and ANFIS models. Similar results
were reported by Buluş et al. (2023) and Levent et al. (2023) in the ANN model for MR
[26,36].
Microwave heating allows for faster mass transfer within the product and generates
more heat due to volumetric heating at higher powers. The variation in moisture content
with drying rate is shown in Figures 5 and 6. Consistent with the findings of Buluş et al.
(2023), an increase in wavelength power corresponds to an increase in drying rate [26].
Although the drying rate is initially rapid in the early stages of the drying process, it sub-
sequently slows down in the later stages.
When comparing the estimated moisture content with the drying rate values, it was
observed that they were not consistent.
(a) (b)
Figure 5. Variation and Estimation of Drying Rate for ANN: (a) Hazelnut Shell, (b) Prina.
(a) (b)
Figure 6. Variation and Estimation of Drying Rate for ANFIS: (a) Hazelnut Shell, (b) Prina.
Although random pieces of the datasets were taken for validation, training, and test-
ing in the tool used, this process was also performed manually before using the tool. For
the construction of the Artificial Neural Network model, two inputs, time and microwave
power of hazelnut shell and prina, were chosen, while md and mw were designated as
outputs separately.
In the ANN model with a single hidden layer, the hidden layer utilized the tangent
sigmoid function as its activation function, and the transfer function employed a linear
transfer function. The learning algorithm employed was the Levenberg–Marquardt algo-
rithm (trainlm). Through analysis of results obtained from multiple experiments involv-
ing the hidden layer, the number of neurons was determined to be 10. Figure 7 displays
the error log graph of the ANN training.
Figure 6. Variation and Estimation of Drying Rate for ANFIS: (a) Hazelnut Shell, (b) Prina.
When comparing the estimated moisture content with the drying rate values, it was
observed that they were not consistent.
Although random pieces of the datasets were taken for validation, training, and testing
in the tool used, this process was also performed manually before using the tool. For the
construction of the Artificial Neural Network model, two inputs, time and microwave
power of hazelnut shell and prina, were chosen, while md and mw were designated as
outputs separately.
In the ANN model with a single hidden layer, the hidden layer utilized the tangent
sigmoid function as its activation function, and the transfer function employed a linear
transfer function. The learning algorithm employed was the Levenberg–Marquardt algo-
rithm (trainlm). Through analysis of results obtained from multiple experiments involving
the hidden layer, the number of neurons was determined to be 10. Figure 7displays the
error log graph of the ANN training.
Figure 7shows the graphical representation of the mean square error of the models
selected as the optimal system. The mean square error is shown to prove the accuracy of the
training process. As a result of the experiments, the lowest verification mean square error
was marked in the 12th epoch for hazelnut shells and in the 490th epoch for prina. The circle
in the figure indicates the point where the validation performance is optimal (i.e., where the
lowest error value is reached). The regression graphs given in Figure 8show the regression
outputs created for the test, validation and training data allocated for the ANN model from
the experimental (target) data obtained. This graph also gives the regression output for all
data. For hazelnuts with training mean square error < 0.0005, correlation coefficients of
0.9984, 0.9705, 0.9992 and 0.9848 were obtained for training, testing, validation and general
data, respectively. The fact that the correlation coefficient is close to one indicates that there
Processes 2024,12, 1703 11 of 17
is an acceptable fit in the data sets. Considering these, the developed ANN network model
predicted the moisture rate and drying rate to a level close to reality [37].
Processes 2024, 12, x FOR PEER REVIEW 11 of 18
(a) (b)
Figure 7. ANN performance validation plot: (a) Hazelnut Shell, (b) Prina.
Figure 7 shows the graphical representation of the mean square error of the models
selected as the optimal system. The mean square error is shown to prove the accuracy of
the training process. As a result of the experiments, the lowest verification mean square
error was marked in the 12th epoch for hazelnut shells and in the 490th epoch for prina.
The circle in the figure indicates the point where the validation performance is optimal
(i.e., where the lowest error value is reached). The regression graphs given in Figure 8
show the regression outputs created for the test, validation and training data allocated for
the ANN model from the experimental (target) data obtained. This graph also gives the
regression output for all data. For hazelnuts with training mean square error < 0.0005,
correlation coefficients of 0.9984, 0.9705, 0.9992 and 0.9848 were obtained for training, test-
ing, validation and general data, respectively. The fact that the correlation coefficient is
close to one indicates that there is an acceptable fit in the data sets. Considering these, the
developed ANN network model predicted the moisture rate and drying rate to a level
close to reality [37].
Figure 7. ANN performance validation plot: (a) Hazelnut Shell, (b) Prina.
Processes 2024, 12, x FOR PEER REVIEW 12 of 18
(a) (b)
Figure 8. ANN correlation plots for training, validation, testing and overall network processes: (a)
Hazelnut Shell, (b) Prina.
ANFIS was employed to predict the md and mw of hazelnut shell and prina under
varying microwave power and over time. ANFIS, based on the Takagi–Sugeno fuzzy in-
ference system, consists of two main components: membership functions and fuzzy infer-
ence rules. Membership functions map each point in the input space to a membership
value (or degree of membership) in the combined fuzzy set, ranging from 0 to 1. Fuzzy
inference rules are a set of if–then rules that define the nature of the output values.
In this research, 1598 data points obtained from experimental results—comprising
1278 (80%) for training and 320 (20%) for testing—were utilized in the ANFIS model.
“fuzzy tool” was used to create the MATLAB application of the specified model and the
model was created based on the same input parameters as the ANN model.
Figures 9 and 10 illustrates the training and test datasets derived from experimentally
obtained data in hazelnut shell and prina drying, focusing on the specified rate for both
ANFIS models. In these figures, the dot represents the test data and the circle represents
the training data. The two models, each featuring two inputs and one output, underwent
500 training rounds with the given datasets. The resulting training error graph is presented in
Figure 11 and 12, showcasing the evolution of the training error throughout the training pro-
cess. The data predicted by the fuzzy network exhibit similarity to the actual data.
(a) (b)
Figure 8. ANN correlation plots for training, validation, testing and overall network processes:
(a) Hazelnut Shell, (b) Prina.
ANFIS was employed to predict the md and mw of hazelnut shell and prina under
varying microwave power and over time. ANFIS, based on the Takagi–Sugeno fuzzy
inference system, consists of two main components: membership functions and fuzzy
inference rules. Membership functions map each point in the input space to a membership
value (or degree of membership) in the combined fuzzy set, ranging from 0 to 1. Fuzzy
inference rules are a set of if–then rules that define the nature of the output values.
Processes 2024,12, 1703 12 of 17
In this research, 1598 data points obtained from experimental results—comprising
1278 (80%) for training and 320 (20%) for testing—were utilized in the ANFIS model. “fuzzy
tool” was used to create the MATLAB application of the specified model and the model
was created based on the same input parameters as the ANN model.
Figures 9and 10 illustrates the training and test datasets derived from experimentally
obtained data in hazelnut shell and prina drying, focusing on the specified rate for both
ANFIS models. In these figures, the dot represents the test data and the circle represents
the training data. The two models, each featuring two inputs and one output, underwent
500 training rounds with the given datasets. The resulting training error graph is presented
in Figures 11 and 12, showcasing the evolution of the training error throughout the training
process. The data predicted by the fuzzy network exhibit similarity to the actual data.
Processes 2024, 12, x FOR PEER REVIEW 12 of 18
(a) (b)
Figure 8. ANN correlation plots for training, validation, testing and overall network processes: (a)
Hazelnut Shell, (b) Prina.
ANFIS was employed to predict the md and mw of hazelnut shell and prina under
varying microwave power and over time. ANFIS, based on the Takagi–Sugeno fuzzy in-
ference system, consists of two main components: membership functions and fuzzy infer-
ence rules. Membership functions map each point in the input space to a membership
value (or degree of membership) in the combined fuzzy set, ranging from 0 to 1. Fuzzy
inference rules are a set of if–then rules that define the nature of the output values.
In this research, 1598 data points obtained from experimental results—comprising
1278 (80%) for training and 320 (20%) for testing—were utilized in the ANFIS model.
“fuzzy tool” was used to create the MATLAB application of the specified model and the
model was created based on the same input parameters as the ANN model.
Figures 9 and 10 illustrates the training and test datasets derived from experimentally
obtained data in hazelnut shell and prina drying, focusing on the specified rate for both
ANFIS models. In these figures, the dot represents the test data and the circle represents
the training data. The two models, each featuring two inputs and one output, underwent
500 training rounds with the given datasets. The resulting training error graph is presented in
Figure 11 and 12, showcasing the evolution of the training error throughout the training pro-
cess. The data predicted by the fuzzy network exhibit similarity to the actual data.
(a) (b)
Figure 9. ANFIS distribution of test and training data of the adsorption process: (a) for MR, (b) for
DR (Hazelnut Shell).
Processes 2024, 12, x FOR PEER REVIEW 13 of 18
Figure 9. ANFIS distribution of test and training data of the adsorption process: (a) for MR, (b) for
DR (Hazelnut Shell).
(a) (b)
Figure 10. ANFIS distribution of predicted and experimental data of the adsorption process: (a) for
MR, (b) for DR (Prina).
(a) (b)
Figure 11. (a) MR and (b) DR prediction error rate for 500 training rounds (Hazelnut Shell).
The blue dots in Figures 11 and 12 show the error value for each epoch.
(a) (b)
Figure 12. (a) MR and (b) DR prediction error rate for 500 training rounds (Prina).
The ANFIS rules were established through the training of the developed models, as
depicted in Figures 13 and 14. Specifically, Figures 13a and 14a illustrate the rules formu-
lated for the estimation of the mw parameter, while Figures 13b and 14b showcase the
rules generated for the estimation of the DR parameter. In total, nine rules were derived
from the training process and subsequently utilized for making predictions.
In Figures 13 and 14 the blue tones assist in visualizing the extent to which specific
rules influence the output. A darker shade in the output column indicates an increase in
the ruleʹs weight or impact. On the other hand, the sections corresponding to inputs use
yellow and red colors to indicate the influence and validity of these rules on the inputs.
Figure 10. ANFIS distribution of predicted and experimental data of the adsorption process: (a) for
MR, (b) for DR (Prina).
Processes 2024, 12, x FOR PEER REVIEW 13 of 18
Figure 9. ANFIS distribution of test and training data of the adsorption process: (a) for MR, (b) for
DR (Hazelnut Shell).
(a) (b)
Figure 10. ANFIS distribution of predicted and experimental data of the adsorption process: (a) for
MR, (b) for DR (Prina).
(a) (b)
Figure 11. (a) MR and (b) DR prediction error rate for 500 training rounds (Hazelnut Shell).
The blue dots in Figures 11 and 12 show the error value for each epoch.
(a) (b)
Figure 12. (a) MR and (b) DR prediction error rate for 500 training rounds (Prina).
The ANFIS rules were established through the training of the developed models, as
depicted in Figures 13 and 14. Specifically, Figures 13a and 14a illustrate the rules formu-
lated for the estimation of the mw parameter, while Figures 13b and 14b showcase the
rules generated for the estimation of the DR parameter. In total, nine rules were derived
from the training process and subsequently utilized for making predictions.
In Figures 13 and 14 the blue tones assist in visualizing the extent to which specific
rules influence the output. A darker shade in the output column indicates an increase in
the ruleʹs weight or impact. On the other hand, the sections corresponding to inputs use
yellow and red colors to indicate the influence and validity of these rules on the inputs.
Figure 11. (a) MR and (b) DR prediction error rate for 500 training rounds (Hazelnut Shell).
The blue dots in Figures 11 and 12 show the error value for each epoch.
Processes 2024,12, 1703 13 of 17
Processes 2024, 12, x FOR PEER REVIEW 13 of 18
Figure 9. ANFIS distribution of test and training data of the adsorption process: (a) for MR, (b) for
DR (Hazelnut Shell).
(a) (b)
Figure 10. ANFIS distribution of predicted and experimental data of the adsorption process: (a) for
MR, (b) for DR (Prina).
(a) (b)
Figure 11. (a) MR and (b) DR prediction error rate for 500 training rounds (Hazelnut Shell).
The blue dots in Figures 11 and 12 show the error value for each epoch.
(a) (b)
Figure 12. (a) MR and (b) DR prediction error rate for 500 training rounds (Prina).
The ANFIS rules were established through the training of the developed models, as
depicted in Figures 13 and 14. Specifically, Figures 13a and 14a illustrate the rules formu-
lated for the estimation of the mw parameter, while Figures 13b and 14b showcase the
rules generated for the estimation of the DR parameter. In total, nine rules were derived
from the training process and subsequently utilized for making predictions.
In Figures 13 and 14 the blue tones assist in visualizing the extent to which specific
rules influence the output. A darker shade in the output column indicates an increase in
the ruleʹs weight or impact. On the other hand, the sections corresponding to inputs use
yellow and red colors to indicate the influence and validity of these rules on the inputs.
Figure 12. (a) MR and (b) DR prediction error rate for 500 training rounds (Prina).
The ANFIS rules were established through the training of the developed models,
as depicted in Figures 13 and 14. Specifically, Figures 13a and 14a illustrate the rules
formulated for the estimation of the mw parameter, while Figures 13b and 14b showcase
the rules generated for the estimation of the DR parameter. In total, nine rules were derived
from the training process and subsequently utilized for making predictions.
Processes 2024, 12, x FOR PEER REVIEW 14 of 18
(a) (b)
Figure 13. Rules created for ANFIS Models: (a) MR and (b) DR (Hazelnut Shell).
(a) (b)
Figure 14. Rules created for ANFIS Models: (a) MR and (b) DR (Prina).
Comparative analysis revealed that the ANFIS model exhibited a closer alignment of
predicted md values with experimental data when compared to the ANN model. Con-
versely, the ANN model demonstrated superior performance in predicting MR values.
This observation aligns with findings from a study on mango slices, where the Takagi–
Sugeno fuzzy model was employed to estimate effective diffusivity, yielding similar re-
sults [38]. Additionally, Buluş et al., 2023 reported that the combination of fuzzy logic and
neural networks proves to be a suitable and reliable approach for modeling and predicting
the drying kinetics of drilling sludge [26].
The aim is to achieve the closest R2 value to 1 and RMSE and MAPE values closest to
0. For R2, ANN and ANFIS values ranging from 0.981340 to 0.999999 imply a high level of
correlation. A MAPE < 0.10 indicates high accuracy in prediction, 0.10–0.20 indicates good
prediction, 0.20–0.50 indicates reasonable prediction, and MAPE > 0.50 indicates lack of
accuracy in prediction [13]. As seen in Table 3, the MAPE values indicate both good and
reasonable predictions.
Table 3. RMSE, MAPE and R2 values of training and testing dataset for mw.
ANN
Training
Hazelnut shell RMSE 0.001418
Prina 0.000012
Hazelnut shell MAPE 13.124759
Prina 0.034268
Hazelnut shell R2 0.996091
Prina 0.999999
Test
Hazelnut shell RMSE 0.007535
Prina 0.001332
Hazelnut shell MAPE 21.047262
Figure 13. Rules created for ANFIS Models: (a) MR and (b) DR (Hazelnut Shell).
Processes 2024, 12, x FOR PEER REVIEW 14 of 18
(a) (b)
Figure 13. Rules created for ANFIS Models: (a) MR and (b) DR (Hazelnut Shell).
(a) (b)
Figure 14. Rules created for ANFIS Models: (a) MR and (b) DR (Prina).
Comparative analysis revealed that the ANFIS model exhibited a closer alignment of
predicted md values with experimental data when compared to the ANN model. Con-
versely, the ANN model demonstrated superior performance in predicting MR values.
This observation aligns with findings from a study on mango slices, where the Takagi–
Sugeno fuzzy model was employed to estimate effective diffusivity, yielding similar re-
sults [38]. Additionally, Buluş et al., 2023 reported that the combination of fuzzy logic and
neural networks proves to be a suitable and reliable approach for modeling and predicting
the drying kinetics of drilling sludge [26].
The aim is to achieve the closest R2 value to 1 and RMSE and MAPE values closest to
0. For R2, ANN and ANFIS values ranging from 0.981340 to 0.999999 imply a high level of
correlation. A MAPE < 0.10 indicates high accuracy in prediction, 0.10–0.20 indicates good
prediction, 0.20–0.50 indicates reasonable prediction, and MAPE > 0.50 indicates lack of
accuracy in prediction [13]. As seen in Table 3, the MAPE values indicate both good and
reasonable predictions.
Table 3. RMSE, MAPE and R2 values of training and testing dataset for mw.
ANN
Training
Hazelnut shell RMSE 0.001418
Prina 0.000012
Hazelnut shell MAPE 13.124759
Prina 0.034268
Hazelnut shell R2 0.996091
Prina 0.999999
Test
Hazelnut shell RMSE 0.007535
Prina 0.001332
Hazelnut shell MAPE 21.047262
Figure 14. Rules created for ANFIS Models: (a) MR and (b) DR (Prina).
In Figures 13 and 14 the blue tones assist in visualizing the extent to which specific
rules influence the output. A darker shade in the output column indicates an increase in
the rule’s weight or impact. On the other hand, the sections corresponding to inputs use
yellow and red colors to indicate the influence and validity of these rules on the inputs.
Comparative analysis revealed that the ANFIS model exhibited a closer alignment
of predicted md values with experimental data when compared to the ANN model. Con-
versely, the ANN model demonstrated superior performance in predicting MR values. This
Processes 2024,12, 1703 14 of 17
observation aligns with findings from a study on mango slices, where the Takagi–Sugeno
fuzzy model was employed to estimate effective diffusivity, yielding similar results [
38
].
Additionally, Bulu¸s et al., (2023) reported that the combination of fuzzy logic and neural
networks proves to be a suitable and reliable approach for modeling and predicting the
drying kinetics of drilling sludge [26].
The aim is to achieve the closest R
2
value to 1 and RMSE and MAPE values closest to
0. For R
2
, ANN and ANFIS values ranging from 0.981340 to 0.999999 imply a high level of
correlation. A MAPE < 0.10 indicates high accuracy in prediction, 0.10–0.20 indicates good
prediction, 0.20–0.50 indicates reasonable prediction, and MAPE > 0.50 indicates lack of
accuracy in prediction [
13
]. As seen in Table 3, the MAPE values indicate both good and
reasonable predictions.
Table 3. RMSE, MAPE and R2values of training and testing dataset for mw.
ANN
Training
Hazelnut shell RMSE 0.001418
Prina 0.000012
Hazelnut shell MAPE 13.124759
Prina 0.034268
Hazelnut shell R20.996091
Prina 0.999999
Test
Hazelnut shell RMSE 0.007535
Prina 0.001332
Hazelnut shell MAPE 21.047262
Prina 0.393607
Hazelnut shell R20.986629
Prina 0.999983
ANFIS
Training
Hazelnut shell RMSE 0.003098
Prina 0.003752
Hazelnut shell MAPE 15.026398
Prina 0.991405
Hazelnut shell R20.981340
Prina 0.999893
Test
Hazelnut shell RMSE 0.008599
Prina 0.015010
Hazelnut shell MAPE 23.833481
Prina 4.036180
Hazelnut shell R20.982586
Prina 0.997862
The obtained values were subjected to Analysis of Variance (ANOVA) to assess the
statistical significance of differences between the means, and LSD test was used for post
hoc analysis. The results revealed that the difference among DR values was statistically
significant at the 1% significance level, as determined by the LSD test. It was also observed
that it was significant for DR, as seen in Tables 4and 5.
Processes 2024,12, 1703 15 of 17
Table 4. m
w
and DR mean values and significance groups for Experimental, ANN and ANFIS
(Hazelnut).
Moisture Content on Wet Basis (mw) Drying Rate (DR)
Microwave Power Microwave Power
Method 120 350 460 120 350 460
Experimental
0.0818 b 0.0460 ı 0.0501 g 0.2849 c 0.6551 c 108.5156 a
ANN 0.0779 c 0.0506 f 0.0532 d 0.4056 c 65.3113 b 108.6989 a
ANFIS 0.0870 a 0.0478 h 0.0514 e 0.2722 c 65.1814 b 109.0025 a
LSD
(p≤0.01) 0.0002 5.895
F value 5.622 ** 247.479 **
** Significant at the 1% level, LSD: Least Significant Difference, Means with the same letter are not significantly
different from each other.
Table 5. m
w
and DR mean values and significance groups for Experimental, ANN and ANFIS (Prina).
Moisture Content on Wet Basis (m
w
)
Drying Rate (DR)
Microwave Power Microwave Power
Method 120 350 460 120 350 460
Experimental 0.4784 b 0.3026 c 0.2529 e 0.7107 g 8.4550 e 10.9548 b
ANN 0.4783 b 0.3034 c 0.2529 e 0.9611 fg 8.3724 e 10.5489 c
ANFIS 0.4814 a 0.3035 c 0.2563 d 1.0832 f 9.5280 d 19.5755 a
LSD (p≤0.01) 0.0012 0.3172
F value 11.455 ** 1383.370 **
** Significant at the 1% level, LSD: Least Significant Difference, Means with the same letter are not significantly
different from each other.
Upon thorough examination of all the tables, it is evident that the values generated
by the ANN and ANFIS models exhibit close proximity to each other. Statistically, means
labeled with the same letter, as determined by the F test, indicate that they are significantly
different from one another.
4. Discussion
In this study, the drying characteristics of residues from two different food products
were modeled using two different artificial intelligence techniques. In this context, networks
were designed to predict moisture content and drying ratio values. The obtained results
indicate that the prediction of moisture content was particularly successful.
Thanks to these results, the findings based on both products will allow for the pre-
diction of drying process values of harvested products without the need for laboratory
conditions. Although there are studies in the literature on drying parameters using artificial
intelligence techniques [
12
], including those using ANN [
13
–
15
], ANFIS [
17
], and both
techniques [18–22], the number of studies focusing on food waste is relatively lower. This
study aims to provide insights into the drying process applied for the storage or reuse of
food waste.
The modeling results indicate that the predictions regarding moisture content are
more effective compared to the drying rate, as evident from the graphs. Therefore, future
studies should not only explore different artificial intelligence techniques but also aim to
achieve an optimal number of experimental results to effectively train the networks.
5. Conclusions
This study involves the development of ANN and ANFIS models to predict moisture
content and drying rate values of hazelnut shells and olive pomace. The objective of
creating these models is to enable the storage or reuse of products without conducting
Processes 2024,12, 1703 16 of 17
drying processes in a laboratory setting. One of the goals is to eliminate the costs associated
with experimental setups. The energy costs in a laboratory setting for microwave drying
of hazelnut shells have been approximately calculated as 0.25 kWh for 75 min at 120 W,
0.22 kWh for 20 min at 350 W, and 0.20 kWh for 15 min at 460 W.
To develop the models, 80% of the drying data obtained in the laboratory for both
products were used for training the model, and 20% were set aside for validation. The
R-squared (R
2
), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error
(RMSE) values were calculated for the results. For moisture content, it was seen that the R
2
value ranged from 0.981340 to 0.999999, the RMSE value ranged from 0.000012 to 0.015010,
and the MAPE value ranged from 0.034268 to 23.833481.
These values indicate that both models produce results close to reality when consider-
ing the moisture content parameter. However, for the drying rate, the prediction values
obtained with both models did not match the actual values as closely, as shown by the
resulting graphs.
Funding: This research received no external funding.
Data Availability Statement: Dataset available on request from the authors.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Moralar, A.; Çelen, S. Evaluation of Thermal and Drying Characteristics of Dried Hazelnut (Corylus avellana L.) Shell Waste.
Philipp. Agric. Sci. (PAS) 2022,105, 159–168. [CrossRef]
2.
Çelen, S.; Akta¸s, T.; Karabeyo˘glu, S.S.; Akyildiz, A. Drying Behaviour of Prina (Crude Olive Cake) Using Different Type of Dryers.
Dry. Technol. 2016,34, 843–853. [CrossRef]
3.
Dönmez, ˙
I.E.; Selçuk, S.; Sargın, S.; Özdeveci, H. Chemical composition of chestnut, hazelnut and pistachios fruits rind. Turk. J.
For. 2016,17, 174–177. [CrossRef]
4.
Tınmaz Köse, E.; Çelen, S.; Çelik, S.Ö. Conventional and microwave drying of hydrocarbon cutting sludge. Environ. Prog. Sustain.
Energy 2019,38, 13104. [CrossRef]
5.
Erden, G. Combination of alkaline and microwave pretreatment for disintegration of meat processing wastewater sludge. Environ.
Technol. 2013,34, 711–718. [CrossRef]
6.
Bezsedes, S.; Laszlo, Z.; Szabo, G.; Hodur, C. Effects of microwave pretreatments of the anaerobic digestion of food industrial
sewage sludge. Environ. Prog. Sustain. Energy 2011,30, 486–492. [CrossRef]
7.
Çelen, S.; Akta¸s, T.; Karabeyo˘glu, S.S.; Akyıldız, A. Drying of prina using microwave energy and determination of appropriate
thin layer drying model. J. Tekirdag Agric. Faculty 2015,12, 21–31.
8.
Nagel, A.; Neidhart, S.; Kuebler, S.; Elstner, P.; Anders, T.; Korhummel, S.; Tanja, S.; Kienzle, S.; Winkler, C.; Qadri, S.; et al.
Applicability of fruit blanching and intermittent microwave-convective belt drying to industrial peel waste of different mango
cultivars for the recovery of functional coproducts. Ind. Crops Prod. 2017,109, 923–935. [CrossRef]
9.
Ghorbani, R.; Mondani, F.; Amirmoradi, S.; Feizi, H.; Khorramdel, S.; Teimouri, M.; Sanjani, S.; Anvarkhah, S.; Aghel, H. A
Case Study of Energy Use and Economical Analysis of Irrigated and Dryland Wheat Production Systems. Appl. Energy 2011,88,
283–288. [CrossRef]
10.
Nabavi-Pelesaraei, A.; Rafiee, S.; Hosseini-Fashami, F.; Chau, K. Predictive Modelling for Energy Management and Power Systems
Engineering; Artificial Neural Networks and Adaptive Neuro-fuzzy Inference System in Energy Modeling of Agricultural Products
Chapter 11; Candice Janco Publisher: Amsterdam, The Netherlands, 2021.
11.
Ojediran, J.O.; Okonkwo, C.E.; Adeyi, A.J.; Adeyi, O.; Olaniran, A.F.; George, N.E.; Olayanju, A.T. Drying characteristics of yam
slices (Dioscorea rotundata) in a convective hot air dryer: Application of ANFIS in the prediction of drying kinetics. Heiyon 2020,
6, e03555. [CrossRef]
12.
Omari, A.; Behroozi-Khazaei, N.; Sharifian, F. Drying kinetics and artificial neural network modeling of the mushroom drying
process in a microwave-hot air dryer. J. Food Process Eng. 2018,41, e12849. [CrossRef]
13.
Kacar, ˙
I.; Korkmaz, C. Prediction of agricul-tural drying using multi-layer perceptron network, long short-term memory network
and regression methods. Gümü¸shane Univ. J. Sci. Technol. 2022,12, 1188–1206.
14. Ataseven, B. Forecasting by using artificial neural networks. Öneri Derg. 2013,10, 101–115.
15.
Yıldız, A.K.; Ta¸sova, M.; Polatcı, H. The Use of Radial-Based Artificial Neural Networks in Modelling Drying Kinetics. Turk. J.
Agric.-Food Sci. Technol. 2020,8, 511–514.
16.
Fabani, M.P.; Capossio, J.P.; Roman, M.C.; Zhu, W.; Rodriguez, R.; Mazza, G. Producing non- traditional flour from watermelon
rind pom-ace: Artificial neural network (ANN) modeling of the drying process. J. Environ. Manag. 2021,281, 111915. [CrossRef]
[PubMed]
Processes 2024,12, 1703 17 of 17
17.
Turan, E.; Genço˘glu, M.T.; Karabiber, A. The calculation of surface leakage currents on the high voltage insulators by using ANFIS
method. Turk. J. Nat. Sci. 2015,4, 16–20.
18.
Dash, K.K.; Sundarsingh, A.; Bhagyaraj, G.V.S.; Pandey, V.K.; Kovacs, B.; Mukarram, S.A. Modelling of ultrasonic assisted osmotic
dehydration of cape gooseberry using adaptive neuro-fuzzy inference system (ANFIS). Ultrason. Sonochem. 2023,96, 106425.
[CrossRef]
19.
Soni, A.; Yusuf, M.; Beg, M.; Hashmi, A.W. An application of Artificial Neural Network (ANN) to predict the friction coefficient
of nuclear grade graphite. Mater. Today Proc. 2022,68, 701–709. [CrossRef]
20.
Jena, S.; Sahoo, A. ANN modeling for diffusivity of mushroom and vegetables using a fluidized bed dryer. Particuology 2013,11,
607–613. [CrossRef]
21.
Pusat, S.; Akkoyunlu, M.T.; Pekel, E.; Akkoyunlu, M.C.; Özkan, C.; Kara, S.S. Estimation of coal moisture content in convective
drying process using ANFIS. Fuel Process. Technol. 2016,147, 12–17. [CrossRef]
22.
Dolatabadi, M.; Mehrabpour, M.; Esfandyari, M.; Alidadi, H.; Davoudi, M. Modeling of simultaneous adsorption of dye and
metal ion by sawdust from aqueous solution using of ANN and ANFIS. Chemom. Intell. Lab. Syst. 2018,181, 72–78. [CrossRef]
23.
Kaveh, M.; Sharabiani, V.R.; Chayjan, R.A.; Taghinezhad, E.; Bbaspour-Gilandeh, Y.; Golpour, I. ANFIS and ANNs Model for
Prediction of Moisture Diffusivity and Specific Energy Consumption Potato, Garlic and Cantaloupe Drying Under Convective
Hotair Dryer. Inf. Process. Agric. 2018,5, 372–387. [CrossRef]
24. Tınmaz Köse, E. Drying of drilling cutting: Emphasis on energy consumption and thermal analysis. Processes 2019,46, 43–53.
25.
Çelen, S.; Arda, S.O.; Karata¸ser, M.A. Modeling of Drying Behavior Using Microwave Conveyor Dryer Assisted Solar Energy.
El-Cezerî J. Sci. Eng. 2018,5, 267–271.
26.
Bulu¸s, H.N.; Moralar, A.; Çelen, S. Modeling of The Moisture Content and Drying Rate of The Zucchini (Cucurbita pepo L.) In A
Solar Hybrid Dryer with Ann and Anfis Methods. Philipp. Agric. Sci. (PAS) 2023,106, 293–305. [CrossRef]
27.
Darıcı, S.; ¸Sen, S. Kivi meyvesinin kurutulmasında kurutma havası hızının kurumaya etkisinin incelenmesi. Tesisat Mühendisli˘gi
2012,130, 51–58.
28.
Thant, P.P.; Robi, P.S.; Mahanta, P. ANN Modelling for Prediction of Moisture Content and Drying Characteristics of Paddy in
Fluidized Bed. Int. J. Eng. Appl. Sci. (IJEAS) 2018,5, 257245.
29.
Kurtulmu¸s, F.; Polat, A.; ˙
Izli, N. Yapay sinir a˘gları kullanarak kayısının farklı kurutma yöntemleriyle kurutulmasında kuruma
hızı ve nem oranı parametrelerinin modellenmesi. ÇOMÜ Ziraat Fakültesi Derg. 2020,8, 261–269. [CrossRef]
30.
Madic, M.; Marinkovic, V.; Radovanovic, M. Mathematical modeling and optimization of surface roughness in turning of
polyamide based on artificial neural network. Mechanika 2012,18, 574–581. [CrossRef]
31.
Didekova, Z.; Kajan, S. Applications of Intelligent Hybrid Systems in Matlab. In Proceedings of the Technical Computing Prague
2009: 17th Annual Conference Proceedings, Prague, Czech Republic, 19 November 2009.
32.
Imran, M.; Alsuhaibani, S.A. A neuro-fuzzy inference model for diabetic retinopathy classification. In Intelligent Data Analysis for
Biomedical Applications: Challenges and Solutions; Academic Press: Cambridge, MA, USA, 2019; pp. 147–172. [CrossRef]
33.
Majumdar, A. Adaptive neuro-fuzzy systems in yarn modelling. In Soft Computing in Textile Engineering; Woodhead Publishing:
Sawston, UK, 2010; pp. 159–177. [CrossRef]
34.
Pusty, K.; Dash, K.K.; Giri, S.; Bhagya Raj, G.V.S.; Tiwari, A.; Shaikh, A.M.; Bela, K. Ultrasound assisted phytochemical extraction
of red cabbage by using deep eutectic solvent: Modelling using ANFIS and optimization by genetic algorithms. Ultrason.
Sonochem. 2024,102, 106762. [CrossRef]
35.
Olatunji, O.M.; Horsfall, I.T.; Ukoha-Onuoha, E.; Osa-aria, K. Application of hybrid ANFIS-based non-linear regression modeling
to predict the %oil yield from grape peels: Effect of process parameters and FIS generation techniques. Clean. Eng. Technol. 2022,
6, 100371. [CrossRef]
36.
Levent, M.; Bulu¸s, H.N.; Moralar, A.; Çelen, S. Fındık Kabu˘gu Kurutma Parametre Tahmininde Yapay Sinir A˘gı Modellerinin
Kar¸sıla¸stırılması. In Bilgisayar Ve Elektronik Bilimlerinde Güncel Geli¸smeler 2; Yav¸san, E., Kahya, E., ¸Sim¸sek, M.A., Eds.; ˙
Iksad
Publishing House: Ankara, Turkey, 2023; pp. 24–46.
37.
Onu, C.E.; Nwabanne, J.T.; Ohale, P.E.; Asadu, C.O. Comparative analysis of RSM, ANN and ANFIS and the mechanistic
modeling in eriochrome black-T dye adsorption using modified clay. S. Afr. J. Chem. Eng. 2021,36, 24–42. [CrossRef]
38.
Vaquiro, H.A.; Bon, J.; Diez Diez, J.L. Fuzzy logic application to drying kinetics modeling. In Proceedings of the 17th IFAC World
Congress, COEX, Seoul, Republic of Korea, 6–11 July 2008; Volume 41, pp. 2206–2211. [CrossRef]
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