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Recursive Neural Network–Particle Swarm Versus Nonlinear Multivariate Rational Function Algorithms for Optimization of Biodiesel Derived from Hevea brasiliensis

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Abstract

This research reports the application of recursive neural network–particle swarm (RNN–PS) and nonlinear multivariate rational function (NLMRF) algorithms for optimization of biodiesel derived from non-edible feedstock of Hevea brasiliensis. Nonlinear auto-regressive with external input (NARX) model was applied with four input variables: time (45–65 min), process temperature (45–65 °C), methanol/oil molar proportion (4:1–12:1) and catalyst dosage (0.5–1.5 wt%), one target (biodiesel yield) and two delays. The RNN showed better correlation (SSE = 21.14 and R2 = 0.98) than the three NLMRFs (SSE > 300 and R2 < 0.63). Optimum conditions obtained with RNN–PS hybrid heuristic model were 60.55 min, 70 °C, methanol/oil molar ratio of 6.89 and catalyst concentration of 1.5wt% with a maximum biodiesel yield of 92.77wt% and experimental validation of 92.52 wt%. Sensitivity analysis result shows that the level of the impact of the input variables on the independent responses follows the order: catalyst concentration (43.77%) > reaction time (24.22%) > methanol/HBSO molar ratio (21.89%) > reaction temperature (10.12%). RNN–PS exhibited high capability in excellent capturing of mapping, great diversity trajectory search, rapid convergence and intrinsic guidance strategy. Functional groups, fatty acid compositions and physicochemical characteristics of the biodiesel obtained using Fourier transform infrared (FTIR), gas chromatography flame ionization detector (GC-FID) and American Standard for Material Testing (ASTMD) methods show that the quality of the biodiesel agreed with international standards. RNN–PSO is therefore proposed as a meta-heuristic and reliable optimization tool for developing a viable and sustainable route for biodiesel fuel production.

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Abbreviations

\({A}_{\mathrm{IS}}\) :

Area under thri-internal standard peak (µV*sec)

\({M}_{\mathrm{IS}}\) :

Weight of applied internal standard (mg)

\({\Sigma }_{\mathrm{A}}\) :

Summed area under peak for fatty acids (µV/sec)

X 1 :

Reaction time (min)

a 0–a 14 :

Coefficients to be determined

X 2 :

Reaction temperature (°C)

X 3 :

Methanol/HBSO molar ratio

C 1,C 2 :

Weights of local global information

CV:

Coefficient of variance

X 4 :

Catalyst concentration (wt%)

GA:

Genetic algorithm

gBest:

Best position of swarm

h:

Hidden layers

I :

Input layers

k :

Input neurons

M :

Mass of biodiesel sample (mg)

m :

Hidden neurons

M FAME :

Average molecular mass of biodiesel

n h :

Number of hidden neurons

n :

Output neurons

NARX:

Nonlinear auto-regressive with external input

n i :

Number of input neurons

NLMRF :

Nonlinear multivariate rational function

o:

Output layers

P:

Particles current position

pBest:

Best position of particle

PSO:

Particle swarm optimization

r 1,r 2 :

Two random variables

S j :

Significance of the jth input parameter

V :

Particle velocity

W :

Weight

W FAME :

Produced biodiesel (mg)

X 1-X 4 :

Independent variables

Y :

Actual response

Y m :

Mean of the actual response

Y p :

Predicted response

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Acknowledgements

The authors are thankful to Springboard Laboratories, Awka, and NOTAP/PZ laboratory, Alex Ekwueme Federal University Ndufu Alike, Abakaliki, for the availability of laboratory apparatus and analytical equipment.

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Only the authors funded this research.

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Authors and Affiliations

  1. Chemical Engineering Department, Alex Ekwueme Federal University, Ndufu Alike, P.M.B. 1010, Abakaliki, Nigeria

    Chizoo Esonye & Cyril Sunday Ume

  2. Chemical Engineering, Department Nnamdi, Azikiwe University, P.M.B. 5025, Awka, Nigeria

    Okechukwu Donminic Onukwuli

  3. Delta State Polytechnique, Ogwashiukwu, Asaba, Nigeria

    Okolie Charles Ubaka

  4. Institute of System Science, Durban University of Technology, Durban, South Africa

    Okon Anietie Etim

  5. Michael Okpara University of Agriculture, Umudike, Nigeria

    Chinedu Mathew Agu

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  1. Chizoo Esonye
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Correspondence to Chizoo Esonye.

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Esonye, C., Onukwuli, O.D., Ubaka, O.C. et al. Recursive Neural Network–Particle Swarm Versus Nonlinear Multivariate Rational Function Algorithms for Optimization of Biodiesel Derived from Hevea brasiliensis. Arab J Sci Eng 48, 15979–15998 (2023). https://doi.org/10.1007/s13369-023-07947-x

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