Modeling and optimization of catalytic performance of SAPO-34 nanocatalysts synthesized sonochemically using a new hybrid of non-dominated sorting genetic algorithm-II based artificial neural networks (NSGA-II-ANNs)

Article abstract of DOI:10.1039/c5ra03764f

The effects of ultrasound-related variables on the catalytic properties of sonochemically prepared SAPO-34 nanocatalysts in methanol to olefins (MTO) reactions were investigated. Different catalytic behaviors are observed which can be explained by the differences in the catalysts' physicochemical properties affected by ultrasonic (US) power intensity, sonication temperature, irradiation time and sonotrode size. This result confirms that the activity of SAPO-34 catalysts improves with the rise in US power, time and temperature. In order to find a catalyst with the maximum conversion of methanol, maximum light olefins content and maximum lifetime, a hybrid of non-dominated sorting genetic algorithm-II based artificial neural networks (NSGA-II-ANNs) was used. The multilayer feed forward neural networks with back-propagation structures were implemented using different training rules in the neural networks approach to relate the ultrasound-related variables and the catalytic performance of SAPO-34 catalysts. A comparison between experimental and artificial neural network (ANN) values indicates that the ANN model with a 3-10-3 structure using the Bayesian regulation training rule has the best fit and can be used as a fitness evaluation inside the non-dominated sorting genetic algorithm-II (NSGA-II). Also, multiple linear regression (MLR) was used to predict these objective functions. The results indicate a poor fit for the objective functions with a low coefficient of determination. This confirms that the ANN technique is more effective than the traditional statistical-based prediction models. Finally, this ANN model was linked to the NSGA-II and Pareto-optimal solutions were determined by the NSGA-II.

Full text of DOI:10.1039/c5ra03764f

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Page 1 of 33
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Modeling and Optimization of Catalytic Performance of SAPO-34 Nanocatalysts Synthesized
Sonochemically Using a new hybrid of Non-dominated Sorting Genetic Algorithm-II based
Artificial Neural Networks (NSGA-II – ANN)
Sima Askari1; Rouein Halladj1 ; Mohammad Javad Azarhoosh1
1: Faculty of Chemical Engineering, Amirkabir University of Technology (Tehran Polytechnic),
P.O. Box 15875ꢀ4413, Hafez Ave., Tehran, Iran.
Abstract
Effects of ultrasoundꢀrelated variables on catalytic properties of sonochemically prepared SAPOꢀ34
nanocatalyst in methanol to olefins (MTO) reactions were investigated. The different catalytic behaviors
are observed which can be explained by the differences in the catalysts physicochemical properties
affected by ultrasonic (US) power intensity, sonication temperature, irradiation time and sonotorode size.
This result confirms that the activity of SAPOꢀ34 catalysts improves with the rise in US power, time and
temperature. In order to find a catalyst with maximum conversion of methanol, maximum light olefins
content and maximum lifetime, the hybrid of nonꢀdominated sorting genetic algorithmꢀII based artificial
neural networks (NSGAꢀII – ANN) was used. The multilayer feed forward neural networks with backꢀ
propagation structures were implemented using different training rules in the neural networks approach to
relate the ultrasoundꢀrelated variables and the catalytic performance of SAPOꢀ34 catalysts. A comparison
between experimental and artificial neural network (ANN) values indicates that the ANN model with a 3ꢀ
10ꢀ3 structure using the Bayesian regulation training rule has the best fit and can be used as a fitness
evaluation inside the nonꢀdominated sorting genetic algorithmꢀII (NSGAꢀII). Also, the multiple linear
regressions (MLR) was used to predict these objective functions. The results indicate a poor fit for the
objective functions with low coefficient of determination. This confirms the ANN technique is more
effective than the traditional statisticalꢀbased prediction models. Finally, this ANN model was linked to
the NSGAꢀII and Paretoꢀoptimal solutions were determined by NSGAꢀII.
Keywords: SAPOꢀ34 nanocatalysts; sonochemical synthesis; ultrasoundꢀrelated variables; MTO
reaction; artificial neural network; Nonꢀdominated Sorting Genetic AlgorithmꢀII.
: Corresponding author, Rouein. Halladj, halladj@aut.ac.ir
Tel number: 00982164543151.
Fax number: 00982166405847.
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1. Introduction
Because of the growing demand for light olefins and the shortage of petroleum resources in the
future, the MTO technology, regarded as an alternative process for the production of light olefins from
nonpetroleum sources without using a large amount of energy, has received strong significant academic
and industrial attention. SAPOꢀ34 catalyst shows an exceptional selectivity for lower olefins and the
complete conversion of methanol in the MTO reaction, although it is rapidly deactivated by coke, which
completely blocks the internal channels of the SAPOꢀ34 crystals [1]. Using SAPOꢀ34 catalyst with small
crystallite size enhances the accessibility of methanol into its cages, resulting in better catalytic
performance [2ꢀ4]. Since the diffusion of methanol in the SAPOꢀ34 catalyst is limited by its small cages,
only some cages near the external surface are active in the MTO reaction [5], therefore the effectiveness
of the SAPOꢀ34 catalyst is improved by reducing its crystallite size [4].
The importance of nanoparticles, especially nanocatalysis and their uses in different industries has
attracted many researches. The materials in nanoꢀscale show different characteristics in comparison with
their bulk state [6, 7]. A great number of investigations about the effect of crystal size show that the best
performance for SAPOꢀ34 catalysts are of sizes less than 500 nm [2, 8]. Different techniques for
improving the formation of SAPOꢀ34 nanocrystals have been developed [9ꢀ12], but recently there has
been a rapid increase in the application of unconventional methods [13, 14]. Sonochemical synthesis by
US irradiation (20 kHz–10 MHz [15]) is a new method for synthesis of nanoparticles especially
nanocatalysis. Contrary to conventional methods (mainly hydrothermal synthesis), this method is very
simple, fast, and does not need any complicated facilities. In this method, the size of particles can be
easily controlled by changing the ultrasoundꢀrelated variables. Chemical effects of US waves are due to
acoustic cavitation phenomena in the solution. Due to the collapse of bubbles, a temperature and pressure
of about 5,000–25,000 K and 181.8 MPa [15] are produced. Collapsing of bubbles occurred in less than a
nanosecond and so, a high rate of temperature decrease (1011 K/s) takes place, which prevents the
organization and agglomeration of particles [6, 7].
A lot of parameters affect the sonochemical synthesis and its products. Some of these effecting
parameters are: frequency and power of US waves, time of irradiation, solution temperature, type of
solution, reaction vessel diameter, the kind of noble gas used in the reaction environment and even
geometrical characteristics of the US device (e.g. horn type size) [16–19].The US typically used in
common crystallization media (mainly aqueous media) falls in the lowꢀfrequency range (namely, 15, 20,
25 and 30 kHz) [20].
There are many references use Evolutionary Algorithm (EA) techniques in chemistry and catalysis
includes Genetic Algorithm (GA), Evolutionary Strategy (ES), Genetic programming (GP), etc.
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Evolutionary Strategy (ES) is used for selection and optimization of heterogeneous catalytic materials
[21, 22]. Genetic Programming has been employed very few. Baumes et al. [23, 24] showed two
examples of this very powerful technique. Genetic Algorithms (GA) have been done by various groups
such as Pereira el al. [25] study. They reported a study of the effect of Genetic Algorithm (GA)
configurations on the performance of heterogeneous catalyst optimization. Also, Gobin et al. [26, 27]
used multiꢀobjective experimental design of experiments based on a genetic algorithm to optimize the
combinations and concentrations of solid catalyst systems. Moreover, genetic algorithm merges with
knowledge based system [28] and has been boosted on a GPU hardware to solve a zeolite structure [29,
30]. In addition, GA has been used for crystallography and XRD measurements [31, 32] and as an Active
Learning method for effective sampling [33].
2. Problem statement and objectives of the present study
Recently, we prepared SAPOꢀ34 nanocrystals with a crystal size of about 50 nm by means of an
efficient US procedure [34] and effects of ultrasoundꢀrelated variables on sonochemical synthesis of
SAPOꢀ34 nanocrystals were investigated [19]. The physicochemical characteristics of SAPOꢀ34 catalysts,
i.e. crystallinity, BET surface area, crystal size and shape are controlled by adjusting US power intensity,
sonotrode size, US irradiation time and sonication temperature. In this study, first, the catalytic
performance of the SAPOꢀ34 nanocrystals synthesized sonochemically under various US conditions (US
power intensity, sonication temperature, irradiation time and sonotorode size) in MTO reactions are
studied. Afterwards, an artificial neural network and MLR model is applied for the prediction of catalytic
performance. Finally, optimization of the catalytic performance is considered using the hybrid of NSGAꢀ
II based ANN. The ANN is used as a fitness evaluation inside the NSGAꢀII. The main objectives of
optimization were maximum conversion of methanol, maximum light olefins content and maximum
lifetime.
3. Experimental
3.1. Catalyst preparation and characterization
The SAPOꢀ34 catalysts were synthesized by the sonochemical method as described elsewhere
[19, 34] using precursor gel with molar ratio of 1.0Al2O3: 1.0P2O5: 0.6SiO2: 2.0 TEAOH: 70H2O. The
sources for Al and P were Aluminum isopropoxide [98% Al (OPri) , Merck] and H3PO4 [85 wt. %
3
aqueous solution, Merck], respectively. Tetraethylammonium hydroxide [TEAOH, 20 wt %, Aldrich] was
used as structure directing agent (SDA). Tetraethylorthosilicate [TEOS, Merck] was chosen as silica
source for preparing primary gels. Aluminum isopropoxide was initially mixed with template (TEAOH)
and deionized water at room temperature and stirred for an hour. Silica source (TEOS) was then added
and stirred. Finally, with continuous stirring, phosphoric acid was added dropwise to the above solution.
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The initial gel was irradiated with US waves at a frequency of 24 kHz. US irradiation was accomplished
by means of US Processor UP200H (Hielscher) using titanium sonotrodes having tip diameters of 3, 7
and 14 mm with different US power intensities. The amount of initial gel used for the sonication is 50 ml
in each run .The sonication temperature was controlled at a temperature of 20, 30, 40 and 50°C. The
duration of irradiation was from 5 to 30 min. After insonation, the initial gel was placed in a 30ml Teflonꢀ
lined stainless steel autoclave and heated in an oven at 200 ºC for 1.5 h. The synthesis conditions of
samples are given in Table 1.
The solid product was recovered and washed three times by centrifuging with distilled water, and
then dried at 110 ºC. The asꢀsynthesized crystals were calcined at 560 ºC in air for 5h to remove the
organic template molecules. Powder Xꢀray diffraction (XRD) patterns were recorded in step scanning on
a Philips PW3050 Xꢀray diffractometer by using CuKα radiation (λ =1.54 ºA) operating at 40 kV and 40
mA. The phase purity and the overall crystallinity were appointed by XRD. Crystallinity characterization
of the samples was calculated by the following equation:
where I is the line intensity of the sample and Ir is the line intensity of the reference sample, using the
product having the highest crystallinity, as identified by XRD. The line intensities of the XRD pattern at
2h equal to 9.5 and 20.5 were employed for these calculations. The crystal morphology was analyzed by
scanning electron microscopy (SEM, Philips XL30). The mean crystal diameters of the SAPOꢀ34 samples
were estimated by measuring the particle size of 100 particles on SEM images using Microstructure
Measurement software. From the results, the mean crystal size was calculated as d, by the formula
mentioned below [19]:
(1)
d is a measure of volume/outer surface (di= size of particles). The BET surface areas of calcined
samples were determined from isotherm data of nitrogen adsorption data in the relative pressure (P/P0)
range of 0.05–0.30 obtained at 77.35 K using a Quantachrome Autosorbꢀ1 analyzer. The surface acidity
of the catalysts was measured by temperature programmed desorption of ammonia (NH3ꢀTPD) using a
Micrometrics TPD/TPR 2900 analyzer with a TCD detector. The amount of ammonia desorbed from the
catalyst was measured by comparing the TPD areas with that for the standard sample.
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3.2. Catalytic performance
The conversion reactions of MTO over SAPOꢀ34 catalysts were carried out in a fixed bed reactor made of
quartz glass (id. 15mm) with a continuousꢀflow system containing a preheater and a catalyst bed under
atmospheric pressure. The catalyst (0.6 g) charged in the catalyst bed at the center of the quartz reactor
was activated at 500 °C in a nitrogen flow of 100 ml/min for 1 h before starting each reaction run and
then cooled to the reaction temperature of 450 °C. A liquid mixture of methanol in water (20 vol %) was
fed into the reactor. The feed rate was adjusted to 0.29 ml/min. The weight hourly space velocity
(WHSV) was 4.5 h−1. In the preheating zone (upper part of the reactor), the temperature increased to 450
°C in atmospheric pressure and the feed evaporates. In the catalyst bed at the center of the reactor,
methanol vapor converted to light olefins.
The analysis of the reaction products was performed using an onꢀline gas chromatograph Agilent GC
(6890 N), equipped with a flame ionization detector (FID) and PlotꢀQ column. Methanol conversion
(XCH3OH) and light olefins content (C2H4 – C3H6) are defined as below:
(2)
(3)
3.3.ANN modeling
ANNs are widely accepted as an information processing methodology inspired by the working
process of the human brain. ANNs are efficient in handling the nonlinear relationship in data [35]. The
empirical models and correlations developed by conventional methods such as different types of multiple
regression are complex in nature, difficult to predict nonꢀlinear relationships, less accurate, and require
long computing time. The ANN has numerous advantages, including accurate approximations of complex
problems, greater efficiency than traditional statisticalꢀbased prediction models such as regression even
for multiple response computations, and greater effectiveness even with incomplete and noisy input data
[36].
ANN constitutes a branch of artificial intelligence which has recently undergone rapid evolution and
progress [37]. ANN acts as a black box model, which is composed of interconnected processing units
called artificial neurons or nodes [35]. The ANN approach has the ability to learn highly nonꢀlinear
relationships and processes information by its dynamic system response to external inputs [36].
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There are several types of ANNs such as multilayer feed forward neural network (FFNN), recurrent,
radial basis, function networks and selfꢀorganizing maps. The universal approximation theorem for neural
networks states that every continuous function that maps intervals of real numbers to some output interval
of real numbers can be approximated arbitrarily closely by a multiꢀlayer perceptron with just one hidden
layer. This result holds for a wide range of activation functions, e.g. for the sigmoidal functions. So in this
study, a multilayer feed forward neural network is used. The multilayer feed forward neural network
consists of an input layer, one or more hidden layers and an output layer [35, 38]. In this study, the input
layer is composed of 3 nodes, which are the US intensity, US irradiation time and sonication temperature.
The output layer has three nodes, which are maximum conversion of methanol, maximum light olefins
content and nanocatalyst life time which is time on stream where methanol conversion is more than 73%.
There is no general rule for the determination of the optimum number of nodes in the hidden layer and
usually it is determined through trial and error [35, 38ꢀ40].
The nodes between each layer are connected with adaptable weights. The general working principle
of the artificial neuron or node can be demonstrated as [35]:
(4)
where, is the input from the previous node j,
is the weight that connects node i and node j, n is the
total number of previous nodes connecting with node i, is bias of node i and f is activation (transfer)
function. Feed forward neural networks with one hidden layer can approximate virtually any linear or
nonlinear function to an acceptable accuracy, if sufficient hidden layer nodes are provided with the
sigmoid function as the hidden layer activation function and the linear function as the output layer
activation function [35]. In this study, the tansig function and the purelin function are used as the
activation functions in the hidden layer and the output layer, respectively. Therefore, a feed forward
neural network with one hidden layer is applied to predict the experimental data in this study.
Before using an artificial neural network, it is necessary to train the network. There are different kinds
of training methods, in which back propagation is a common method [37]. In the current study, the backꢀ
propagation structure is implemented using different learning rules in the neural network approach.
Before using any method for training, an ANN has to normalize input and output. So input and output
data are normalized between ꢀ1 and 1 by the following equation:
(5)
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The prediction performance of the network is assessed by using statistical coefficients, i.e. root mean
square error (RMSE), mean square error (MSE), correlation coefficient (R2) and mean relative error
(MRE) values [37, 40]. In this study, mean square error (MSE) and correlation coefficient (R2) which are
calculated by the following expressions are used as the correlation performance indicators of the
network:
(6)
(7)
where
and
are arithmetic means of actual and calculated values, respectively.
3.4. NSGA-II main process
The genetic algorithm is an optimization tool based on Darwinian evolution [41ꢀ43]. The principles,
on which the NSGAꢀII relies, are the same as those of the singleꢀobjective optimization. The strongest
individuals (or chromosomes) are combined to create the offspring by crossover and mutation and this
scheme is repeated over many generations. However, the multiꢀobjective optimization algorithm must
consider the fact that there are many ‘‘best solutions”, which modify the selection process. NSGAꢀII sorts
individuals based on the nonꢀdomination rank and the crowding distance to ensure a high level of
performance as well as good dispersion of results [44ꢀ48]. In this study, the ANN was used as a fitness
evaluation inside the NSGAꢀII. The flowchart of the hybrid of nonꢀdominated sorting genetic algorithmꢀII
based artificial neural networks (NSGAꢀII – ANN) program is shown in Fig. 1.
4. Results and discussion
4.1. Catalytic performance of SAPO-34 nanocatalysts
The methanol conversion and light olefins content (wt %) (C2=ꢀC3=)over SAPOꢀ34 catalysts
synthesized by using the sonotrode having tip diameter of 7mm with different US power intensities are
presented in Fig. 2. As indicated in Fig. 2, all SAPOꢀ34 catalysts suffer activation in the first minutes of
the process. The incomplete conversion of methanol in the early time on stream is due to the existence of
an induction period [49] which can be explained by the hydrocarbon pool (HP) mechanism. Haw
suggested that the MTO reaction proceeds by a HP mechanism with cyclic organic species such as
Hexamethylbenzene (HMB) as reaction centers for light olefins production [49, 50]. The time for the
formation of these cyclic organic species causes the induction period, i.e. an increase in activity before
maximum conversion. Except for sample S1, all catalysts show a high conversion for a long time
especially catalyst S4 which maintains its activity for 540 min. The S1 catalyst just shows a maximum
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conversion of 81% after 60 min. A rapid fall for conversion is subsequently observed and it reaches 12%
after 420 min.
The nanoꢀsized catalyst S4 shows a high content (wt %) toward light olefins (ethylene and
propylene) for 180 min (Fig. 2) and the light olefins content decreases afterwards. Even after the reaction
time of 540 min the light olefins content can remain at 10% over S4. The decrease in light olefins
formation corresponds to an increase in the formation of DME which can be explained by the catalyst
deactivation [51]. At this reaction time, DME is the main product (79 wt %) and other products are butene
and the alkanes (C1–C5 alkanes) mainly methane.
The catalysts S2 and S3 also show the same trend for light olefin but with lower amounts compared
to the catalyst S4. In comparison, the content of light olefins over the SAPOꢀ34 catalysts S1 is much
lower than the others and it decreases rapidly (Supplementary information, Table I).
These catalytic behaviors can be explained by the differences in catalysts physicochemical properties
which are affected by US power intensity. According to the results obtained previously [19], the
crystallinity changes markedly with US power intensity and higher crystallinity is obtained with
increasing US intensity. Therefore, the catalyst S1 synthesized at the lowest power intensity has the
lowest crystallinity as shown in Table 1. Increasing the crystallinity results in the formation of more
structural pores and it may enhance the diffusion rate and quantity of reactants into structure channels in
crystallites [19]. Also, different US power intensities applied in the synthesis of SAPOꢀ34 crystals alter
the morphology and agglomeration of the products. It is clearly seen in Table 1 that with an increase in
the US intensity the average crystal size of SAPOꢀ34 crystals gradually decreases, as well as formation of
uniform spherical nanocrystals (Supplementary information, Fig. I )instead of spherical aggregates of
cube type SAPOꢀ34 crystals seen previously [19]. By comparing the acidity of the SAPOꢀ34 catalysts
represented in Table 1, S2 and S1 samples have the highest and lowest concentration of strong acid site
respectively, which could be active for MTO conversion, though the strength of their acid sites are
similar. Therefore, the short lifetime of the catalyst S1 cannot be related to the strength and amount of
acid sites but can be correlated with the crystallinity and crystal sizes of the catalyst. For larger crystals of
the catalyst S1, the residence time in a crystal for the hydrocarbons is long because of the longer diffusion
length. Saturated hydrocarbons and/or aromatic compounds cannot escape from the pores of SAPOꢀ34,
and successive polymerizations readily occur because of the long reaction time [2]. Therefore, the catalyst
S4 possessing the higher crystallinity, smaller size and better dispersion [19] has less diffusion limitation
and a longer lifetime[51]. Additionally, the formation of coke is inhibited over the smaller crystals of
catalyst S4 as a result of the reduced resistance to diffusion, resulting in a much greater production of
light olefins for longer reaction times.
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Effects of the sonotrode size on the catalytic properties of SAPOꢀ34 catalysts S4ꢀS6 are shown in
Fig.3. The catalyst S4 and S6 synthesized using the sonotrodes having tip diameters of 7, and 14 mm
show a much higher conversion of methanol and maintain it for a longer time as well as a higher content
toward light olefins compared to that synthesized with the sonotrode having tip diameters of 3 mm (S5).
This can be explained by an increase in US power with increasing sonotrode size from 3 to 14 mm.
Although the smallest sonotrode possesses the highest US intensity, i.e. 460 W.cmꢀ2 (related to 100%
amplitude setting) compared to 300 and 105 W.cmꢀ2 (max intensities of sonotrodes having tip diameters
of 7 and 14 mm, respectively), it has the smallest horn tip area, resulting in lower emitted US power. The
increase in the US power results in the higher turbulence of the mixture and the satisfactory mixing can be
achieved much more rapidly. The difference in US power results in different catalyst activities which can
be attributed to the difference in the crystallinity and thus BET surface area of catalysts. It is clear from
Table 1 that by increasing US power the crystallinity of samples increase (Supplementary information,
Fig. II), resulting in the rise of BET surface areas.
Fig. 4 shows the role of US irradiation time on the methanol conversion and light olefin production.
The catalyst irradiated for 5 min (S7) shows the lowest methanol conversion and the lowest olefin content
on account of the absence of the crystal phase. At short times, the US wave fails to blend the solution
uniformly and only a few nuclei are formed. Some small crystal particles cannot grow further due to the
shorter US time. Applying US for longer times produces more apparent crystals and no large crystals can
grow, because more nuclei will occur continuously until the level of superꢀsaturation becomes very low
[19,20]. With the extension of US irradiation time from 5 to 15 min, the methanol conversion as well as
the olefin content increases sharply, and the samples irradiated for 15 and 30 min show the highest olefin
selectivity. This result confirms that the activity of SAPOꢀ34 samples improves with the rise in
crystallinity.
Fig. 5 shows the catalytic performance of the products synthesized under different sonication
temperatures of 20, 30, 40 and 50°C. With increasing the sonication temperature, the crystallinity of
SAPOꢀ34 products increases, smaller crystals with uniform size distribution are formed and the
morphology of the product alters from cubic crystals to uniform nanocrystals since the temperature can
affect the cavitation threshold. Generally, the cavitation threshold limit has been found to decrease with
an increase in temperature. This means that cavitation bubbles are more easily produced as the
temperature is raised. Therefore, higher sonication temperature leads to fast nucleation, which results in
smaller particles in comparison to the lower sonication temperature [19]. According to Table 1, the
catalysts S9 and S10 have the lowest amount of strong acid site concentration at 440–460°C and it falls in
a narrow interval for samples S9 and S10, i.e., 0.69 and 0.60 respectively. Also, the acid strength of all
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the samples is almost the same. Therefore, it can be concluded that the differences between the catalytic
behaviors of samples could be more related to the crystal size and crystallinity of the catalyst.
4.2. ANN results
In this study, the multilayer feed forward neural networks with backꢀpropagation structure are
implemented using different learning rules in the neural network approach such as Bayesian regulation
(BR), LevenbergꢀMarquardt (LM), Scaled conjugated gradient (SCG) and RPROP back propagation
(RP). In the Bayesian regulation rule, the input data are divided into two parts; 70% and 30% of the data
are used for training and test, respectively, but in other learning rules the input data are divided into three
parts; 70%, 15% and 15% of the data are used for training, validation and test, respectively. The values of
the training and test data are normalized between ꢀ1 and 1 by using Eq. (5). The number of data used in
the network is 54. In this data set the sonotrode size is 7mm. The range of all experimental conditions
used for modeling with ANN is shown in Table 2.
The results of the network models for different neuron numbers in the hidden layer using different
training algorithms are presented in Table 3. The correlation performance of the network is assessed by
using mean square error (MSE) and correlation coefficient (R2) values. It can be seen that the Bayesian
regulation back propagation algorithm with 10 neurons in the hidden layer is the best training procedure
that achieved the highest R2 and lowest MSE. Thus, the optimum number of neurons is used to create the
network topologies which were 3–10–3. Here, the numbers in the expressions of the network topologies
represent the neuron numbers in the input layer, the hidden layer and the output layer, respectively.
Fig. 6 explains comparison plots between network output and the corresponding experimental data of
the catalytic performance of SAPOꢀ34 nanocatalysts synthesized sonochemically, for training and test
data using the BR training rule and 3ꢀ10ꢀ3 topology. This figure shows that there is a very good
agreement between this ANN model and experimental values. The comparison between network
predicted and experimental data can be seen in Table II of Supplementary information. Fig. 7 shows the
performance graph. It is observed that the desired goal has been reached in 1000 epochs, and the ANN
with ten hidden neurons could achieve the convergence. The errors of data attained by the optimum ANN
model are plotted out versus the frequency of data in Fig. 8. A normal distribution of variation brings
about a specific bellꢀshaped curve (Gaussian curve), with the highest point in the middle and smoothly
curving symmetrical slopes on both sides of center. These figures illustrate an approximately normal
distribution of errors produced by the model. The Gaussian curve reveals that our results are symmetrical
[38].
The methanol conversion, light olefins content and catalyst life time are illustrated versus US power
intensity, sonication temperature and irradiation time in supplementary information (Figs III to V in
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supplementary information). Also a Matlab userꢀfriendly code is given as supplementary data for
verification of ANN results (‘ANN.m', 'deNormalize FCN.m' and 'Normalize FCN.m' in supplementary
information).
The 3ꢀfold crossꢀvalidation (3ꢀCV) of model is used in this section because of the low number of
points. The original sample is randomly partitioned into three equal size subsamples. Of the three
subsamples, a single subsample is retained as the validation data for testing the model, and the remaining
two subsamples are used as training data. The crossꢀvalidation process is then repeated three times (the
folds), with each of the three subsamples used exactly once as the validation data. The three results from
the folds are averaged to produce a single estimation. The results of the 3ꢀCV models are presented in
Table 4. This shows that this model is achieved the very high R2 and low MSE. The advantage of this
method is that all observations are used for both training and validation, and each observation is used for
validation exactly once.
4.3. MLR model results
In this section, the traditional models of objection functions includes methanol conversion, light olefins
content and catalyst life time, obtained through liner regression analysis, are presented. These models
used US power intensity, sonication temperature and irradiation time point as input variables. These
models are shown in Equations 7ꢀ9 and comparison plots between the model output and its corresponding
experimental data are given in Fig. 9.
(8)
(9)
(10)
Where
,
, ,
,
and T are methanol conversion (%), light olefins content (wt%), life time
(min), US power intensity (W/cm2), sonication temperature ( ) and irradiation time (min) respectively.
The results indicate a poor fit between experimental and predicted data with low coefficient of
determination. Thus, the objective functions prediction of using these traditional models may not be
reliable. Table 5 shows a comparison between ANN and MLR model results. This confirms the ANN
technique is more effective in predicting the objective functions tested in this study than the traditional
statisticalꢀbased prediction models.
4.4. Optimization results using NSGA-II
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In this section, the hybrid NSGAꢀII based ANN is used to optimize catalytic performance of SAPOꢀ
34 nanocatalysts synthesized sonochemically in MTO reaction and obtains Paretoꢀoptimal solutions. In
other words, the ANN is used as a fitness evaluation inside the NSGAꢀII. A Paretoꢀoptimal set is a series
of solutions that are nonꢀdominated with respect to each other. While moving from one Pareto solution to
another, there is always a certain amount of sacrifice in one objective(s) to achieve a certain amount of
gain in other(s).
The objectives of optimization were minimum unreacted methanol, maximum light olefins content
and maximum life time. Thus, the objectives included:
Objective 1: Maximizing XCH OH
(11)
3
Objective 2: Maximizing light olefins content (wt %)
Objective 3: Maximizing Life time (min)
The constraints were:
(12)
(13)
20o C ≤ Sonication Temperature ≤ 50o C
(14)
(15)
(16)
US Intensity= 12, 27, 48, 75, 108, 147, 192, 243, 300 W.cmꢀ2
5min ≤ US Irradiation time ≤ 30 min
The objective functions are optimized full filling the constraints given in Eqs. (14) – (16). The
sonotrode size is 7mm. A population size of 100 is chosen with crossover probability of 0.7 and mutation
probability of 0.1. Arithmetic crossover and gauss method were used as crossover and mutation methods,
respectively.
The optimum solutions have been listed in Table 6. This table shows that each of the solutions is
better than the other in at least one of the objective functions. Thus, the user has to decide on the
ultrasoundꢀrelated variables based on the ease of operation, experience, the cost involved and also the
quality of the product (Fig. VI in supplementary files). . Three samples of optimum solutions are
validated experimentally Table 7 shows a comparison between experimental and predicted values. The
results indicate that there is an acceptable agreement between experimental and predicted results by
NSGAII–ANN. The methanol conversion, light olefins content and catalyst life time of optimum
solutions are illustrated versus US power intensity, sonication temperature and irradiation time in
supplementary information (Figs VII to IX in supplementary information.)
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Conclusion
MTO reaction was investigated over SAPOꢀ34 nanocatalysts synthesized sonochemically under
various US conditions. The sonochemically prepared catalysts were used to elucidate the effects of US
power intensity, sonication temperature, irradiation time and sonotorode size on their catalytic
performance, especially in terms of methanol conversion, light olefin content and catalyst lifetime. The
catalysts synthesized with higher US power (adjusted by both the size of sonotrode or US power
intensity) show a much higher conversion of methanol and maintain it for a long time as well as a high
content toward light olefins. With increasing the sonication temperature and irradiation time, the
methanol conversion as well as the light olefin content increases. Afterwards, the multilayer feed forward
neural network with backꢀpropagation structure was implemented using different learning rules in the
neural network approach. The ANN with a 3ꢀ10ꢀ3 architecture and Bayesian regulation training rule has
the best fit and was selected as the optimum ANN model for prediction. The tansig and purelin functions
were used as the activation functions in the hidden and output layers, respectively. In the optimum model,
the input data were divided into two parts; 70% and 30% of the data were used for training and test,
respectively. The results indicate that there is a very good agreement between experimental and predicted
results by ANN. Also, the multiple linear regressions (MLR) was used to predict these objective
functions. The results indicate a poor fit for the objective functions with low coefficient of determination.
This confirms the ANN technique is more effective than the traditional statisticalꢀbased prediction
models. Finally, the hybrid NSGAꢀII based ANN was used and introduced the best catalytic performance
of SAPOꢀ34 nanocatalysts synthesized sonochemically under various US conditions in the MTO reaction
and the ANN was used as a fitness evaluation inside the NSGAꢀII. . Such methodology (hybrid of ANN
and NSGAꢀII) allowed the researchers to find a near optimum solution to their problem where multiple
input and output variables are interacting. Despite the relative simplicity of the search space, human
understanding and capture of the variables relationships still remains complicated. Therefore such
approach shows how the use of both a modelling and an optimization strategy allow tackling this
challenge.
Acknowledgements
The financial supports from the Iran National Science Foundation are gratefully acknowledged.
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Figure captions:
Fig. 1. Flowchart of the NSGAꢀII – ANN program
Fig. 2. Methanol conversion and light olefins content (C2H4 – C3H6) over SAPOꢀ34 catalysts synthesized
with different ultrasound power intensities; S1:48 W.cmꢀ2, S2:108 W.cmꢀ2, S3:192 W.cmꢀ2, S4: 300
W.cmꢀ2.
Fig. 3. Effects of the sonotrode size on the catalytic properties of SAPOꢀ34 catalysts; (S5):3mm,
(S4):7mm, (S6):14mm.
Fig. 4. Effects of ultrasonic irradiation time on the methanol conversion and light olefin production over
SAPOꢀ34 catalysts; S7:5 min, S4:15 min, S8:30min.
Fig. 5. Catalytic performance of the SAPOꢀ34 products synthesized under different sonication
temperature; S9:20°C, S10:30°C, S11:40°C, S4:50°C.
Fig. 6. Comparison between experimental & ANN values (a) methanol conversion (%) (b) Light olefins
content (wt %) (c) Lifetime.
Fig. 7. Performance graph
Fig. 8. Error histogram
Fig. 9. Comparison between experimental & MLR model values (a) methanol conversion (%) (b) Light
olefins content (wt %) (c) Lifetime.
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Fig. 1.
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(a)
(b)
Fig. 2.
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(a)
(b)
Fig. 3.
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(a)
(b)
Fig. 4.
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(a)
(b)
Fig. 5.
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(a)
(b)
(c)
Fig. 6.
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Fig. 7.
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Fig. 8.
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(a)
(b)
(c)
Fig. 9.
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Tables:
Table 1. Sonochemical synthesis conditions and properties of the catalysts.
Table 2.Range of all experimental conditions used for modeling with ANN.
Table 3.Performance of different ANN methods for the prediction of catalytic performance of the SAPOꢀ
34 products synthesized in MTO reaction.
Table 4. The results of the 3ꢀCV models
Table 5. Comparison between optimum ANN & MLR model results
Table 6.Paretoꢀoptimal solution set after 200 generations.
Table 7. Comparison between experimental & predicted values of optimum solutions
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Table 1
Distribution of acid sites
(mmol NH3/g)
Mean
BET
Surface
diameter
area (m2g-1)
(nm)
Sonication
temperature
Ultrasonic
irradiation
time (min)
Sonotrode
diameter crystallinity
(mm)
Relative
Ultrasonic power
intensity (W.cm-2)
crystal
Sample
(
)
(%)
Weak
Strong
220-240°C 440–460 °C
48
15
15
50
7
7
40
48
0.86
0.8
0.71
0.94
150
100
329
369
S1
S2
108
50
192
300
15
15
50
50
7
7
68
77
0.74
1.01
0.79
0.78
70
50
392
493
S3
S4
460
105
15
15
50
50
3
38
0.9
ꢀ
0.73
ꢀ Nd
135
66
306
444
S5
S6
14
100
300
300
5
50
50
7
7
35
88
0.82
ꢀ
0.78
ꢀ Nd
105
58
ꢀNd
S7
S8
30
429
300
300
300
15
15
15
20
30
40
7
7
7
52
47
71
0.97
0.94
1.08
0.69
0.60
0.89
120
115
79
ꢀ Nd
ꢀ Nd
388
S9
S10
S11
Nd: Not determined
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Table 2
Inputs:
Sonication Temperature (
20ꢀ50
Ultrasound Intensity (w.cmꢀ2)
12, 27, 48, 75, 108, 147, 192, 243, 300
Ultrasonic Irradiation time (min)
5ꢀ30
Outputs:
Methanol Conversion (%)
Light Olefins Content (wt%)
Life Time (min)
70ꢀ100
36ꢀ84
50ꢀ540
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Table 3
R2
MSE
Learning
rule
No. of
Light
Olefins
content
0.9712
0.9759
0.9760
0.9756
0.9796
0.9538
0.9673
0.9751
0.9606
0.8336
0.8121
0.8671
Light
Methanol
Life
Methanol
Life
neurons
Mean
time
Olefins
content
0.0058
0.0049
0.0059
0.0049
0.0042
0.0094
0.0065
0.0049
0.0080
0.0332
0.0377
0.0274
Mean
time
conversion
conversion
LM
BR
5
0.9808
0.9932
0.9957
0.9907
0.9957
0.9949
0.9846
0.9904
0.9782
0.7583
0.8849
0.8146
0.8308
0.9839
0.9929
0.9917
0.9922
0.9523
0.9037
0.9397
0.8143
0.7886
0.7781
0.713
0.9276
0.9843
0.9882
0.9860
0.9892
0.9670
0.9519
0.9684
0.9177
0.7935
0.8250
0.7982
0.0045
0.0017
0.0010
0.0022
0.0010
0.0013
0.0036
0.0022
0.0052
0.0580
0.0267
0.0450
0.0204
0.0020
0.0009
0.0009
0.0009
0.0080
0.0109
0.0069
0.0239
0.0260
0.0250
0.0327
0.0102
0.0029
0.0026
0.0027
0.0020
0.0062
0.0070
0.0047
0.0123
0.0391
0.0298
0.0350
10
15
5
10
15
5
SCG
RP
10
15
5
10
15
29