Estimating Deformation of Geogrid-Reinforced Soil Structures Using Hybrid LSSVR Analysis

Abstract

The study of displacement plays a key role in the planning of geosynthetic reinforced soil structures. Nevertheless, the literature stresses the promise of artificial intelligence technologies in tackling geotechnical engineering difficulties. The major purpose of this work was to evaluate the potential utilize of machine learning-based approaches in forecasting the deformation of geogrid-reinforced soil structure (Dis). This study introduces and verifies novel techniques that integrate the reptile search algorithm (RSA) and equilibrium optimizer (EO) with least squared Support Vector Regression (LSSVR). Afterward, a total of 166 finite element analyses conducted in the literature were used in order to create the dataset. The aim of the application of optimization algorithms was to find the optimal values of the penalty factor (c) and the width (g) of the kernel function for LSSVR. The results show that both the $LSSVR_E$ and $LSSVR_R$ algorithms have a good chance of correctly forecasting the $Dis$. Considering the $TIC$ index, a remarkable reduction was concluded, a reduction from 0.0393 $\left( {LSSVR_E } \right)$ to 0.0215 $\left( {LSSVR_R } \right)$ in train phase, and from 0.0222 $\left( {LSSVR_E } \right)$ to 0.0088 $\left( {LSSVR_R } \right)$ in the test phase. A comprehensive index named $OBJ$ concluded 1.8003 for $LSSVR_E$, and an almost a half reduction at 0.9257 for $LSSVR_R$.

Appendix

Algorithm 1. $EO$’s steps [82]

1.	Initialize the particles $C_i (i = 1,2,3, \ldots ,N)$ population
2.	Fix the four particles’ suitable value in $equilibrium pool, C_{{\mathrm{eq}}} ,$ a great value
3.	Fix value of variables $a_1 = 2;a_2 = 1;GP = 0.5;$
4.	While $\left( {it < t_{max} } \right)$
5.	For every $i$ particle
6.	Calculate the particle’s suitable value if $\left( {\vec{C}_i } \right)$
7.	Updating $C_{{\mathrm{eq}}} , if \vec{C}_i$ finer
8.	End for
9.	$\vec{C}_{avg} = \left( {\vec{C}_{{\mathrm{eq(1)}}} + \vec{C}_{{\mathrm{eq(2)}}} + \vec{C}_{{\mathrm{eq(3)}}} + \vec{C}_{{\mathrm{eq(4)}}} } \right)/4$
10.	The equilibrium pool $\vec{C}_{{\mathrm{eq.pool}}} = \left[ {\vec{C}_{{\mathrm{eq(1)}}} ,\vec{C}_{{\mathrm{eq(2)}}} ,\vec{C}_{{\mathrm{eq(3)}}} ,\vec{C}_{{\mathrm{eq(4)}}} ,\vec{C}_{{\mathrm{eq(avg)}}} } \right]$
11.	Finish the memory-saving
12.	By Eq. (7), calculate $t$
13.	For every $i$ particle
14.	Choose a nominee at random from $\vec{C}_{{\mathrm{eq.pool}}}$
15.	Make the two vectors $\vec{r}$ and $\vec{\lambda }$ at random
16.	By Eq. (6), calculate $\vec{F}$
17.	By Eq. (10), calculate $p_i^t$
18.	By Eq. (9), calculate $G_0^t$
19.	End for
20.	$it$++
21.	End while

Algorithm 2. The $RSA$’s framework [83]

1: Input: The parameters of $RSA$ including the sensitive parameter $\alpha$, $\beta$, crocodile size ($N$), and the maximum generation $T_{Max}$.

2: Initializing $n$ crocodile, $z_i$ and calculate $f_i$.

3: Determine the best crocodile $best_j$.

4: while ($t \le T_{Max}$.) do

5: Update the $ES$ by Eq. (15).

6: for $i = 1$ to $N$ do

7: for $i = 1$ to $N$ do

8: Calculate the $\eta$, $R, P$ by Eqs. (13), (14), and (16).

9: if $t \le \frac{{T_{Max} }}{4}$ then

10: $x_{i,j} \left( {t + 1} \right) = best_j \left( t \right) - \eta_{i,j} \left( t \right) \times \beta - R_{i,j} \left( t \right) \times r$.

11: else if $\frac{{T_{Max} }}{4} \le t < \frac{{2 \times T_{Max} }}{4}$

12: $x_{i,j} \left( {t + 1} \right) = best_j \left( t \right) \times z_{r_1 ,j} \times Es\left( t \right) \times r$.

13: else if $\frac{{2 \times T_{Max} }}{4} \le t < \frac{{3 \times T_{Max} }}{4}$

14: $x_{i,j} \left( {t + 1} \right) = best_j \left( t \right) \times P_{i,j} \left( t \right) \times r$.

15: else

16: $x_{i,j} \left( {t + 1} \right) = best_j \left( t \right) - \eta_{i,j} \left( t \right) \times \varepsilon - R_{i,j} \left( t \right) \times r$.

17: end if

18: end for

19: end for

20: Find the best crocodile.

21: $t = t + 1$.

22: end while

23: Output: The best crocodile.