Particle Swarm Optimization AlgorithmExtreme Learning Machine (PSOELM) Model for Predicting Resilient Modulus of Stabilized Aggregate Bases
Abstract
:1. Introduction
2. Research Data and Methods
2.1. Description of Used Data and Variables
2.2. Theoretical Backgrounds and Model Development
2.2.1. PSO
Algorithm 1: The PSO algorithm for optimization problem of ddimensional decision variables. 

2.2.2. ANN
2.2.3. ELM
2.2.4. Hybridization (PSOANN, PSOELM)
Algorithm 2: The algorithmic flow of PSOELM. 

2.2.5. Model Development and Performance Assessment
3. Results and Discussion
4. Concluding Remarks
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Dataset  Variable  Mean  Median  Min.  Max.  SD  SK  KU 

Training  WD  12.57  8.00  0.00  30.00  11.19  −1.13  0.49 
CSAFR  0.25  0.13  0.11  0.51  0.18  −1.47  0.73  
DMR  3.26  3.37  2.34  4.63  0.71  −0.94  0.39  
σ_{3}  69.35  69.00  0.00  138.00  49.60  −1.34  −0.02  
σ_{d}  173.50  208.00  69.00  277.00  78.73  −1.40  −0.02  
M_{r}  3690.88  3422.00  585.00  9803.00  1862.06  1.42  1.12  
Testing  WD  13.32  16.00  0.00  30.00  11.10  −1.19  0.35 
CSAFR  0.26  0.13  0.11  0.51  0.19  −1.67  0.58  
DMR  3.28  3.37  2.34  4.63  0.73  −1.07  0.34  
σ_{3}  71.94  69.00  0.00  138.00  47.16  −1.22  −0.04  
σ_{d}  167.89  138.00  69.00  277.00  75.06  −1.26  0.11  
M_{r}  3668.12  3443.00  773.00  9644.00  1861.16  1.65  1.15 
Model  r^{2}  RMSE  MAE 

PSOANN (Train)  0.640  1117.367  881.90 
PSOANN (Test)  0.597  1184.155  929.18 
KELM (Train)  0.692  1064.782  804.90 
KELM (Test)  0.674  1075.378  815.94 
PSOELM (Train)  0.981  253.439  191.66 
PSOELM (Test)  0.963  369.592  280.00 
Model  Input Variables  r^{2}  RMSE  MAE 

1  WD, CSAFR, DMR, ${\sigma}_{3}$ and ${\sigma}_{d}$  0.981  253.439  191.66 
2  WD, CSAFR, DMR and ${\sigma}_{3}$  0.948  415.554  299.43 
3  WD, CSAFR, DMR and ${\sigma}_{d}$  0.973  304.451  204.98 
4  WD, CSAFR and DMR  0.921  521.08  378.71 
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Kaloop, M.R.; Kumar, D.; Samui, P.; Gabr, A.R.; Hu, J.W.; Jin, X.; Roy, B. Particle Swarm Optimization AlgorithmExtreme Learning Machine (PSOELM) Model for Predicting Resilient Modulus of Stabilized Aggregate Bases. Appl. Sci. 2019, 9, 3221. https://doi.org/10.3390/app9163221
Kaloop MR, Kumar D, Samui P, Gabr AR, Hu JW, Jin X, Roy B. Particle Swarm Optimization AlgorithmExtreme Learning Machine (PSOELM) Model for Predicting Resilient Modulus of Stabilized Aggregate Bases. Applied Sciences. 2019; 9(16):3221. https://doi.org/10.3390/app9163221
Chicago/Turabian StyleKaloop, Mosbeh R., Deepak Kumar, Pijush Samui, Alaa R. Gabr, Jong Wan Hu, Xinghan Jin, and Bishwajit Roy. 2019. "Particle Swarm Optimization AlgorithmExtreme Learning Machine (PSOELM) Model for Predicting Resilient Modulus of Stabilized Aggregate Bases" Applied Sciences 9, no. 16: 3221. https://doi.org/10.3390/app9163221