**5. Results and discussion**

Theoretically, a specific model can be obtained when the model parameters are correctly selected and updated. The optimum values are obtained by trial and error


**Table 3.** *Model optimum modeling parameters.*

*Evaluation of Liquefaction-Induced Settlement Using Random Forest and REP Tree Models:… DOI: http://dx.doi.org/10.5772/intechopen.94274*

using parameter setting. The optimum value for each machine learning parameter is illustrated in **Table 3**. In the proposed RF and REP Tree models the most significant parameters are the number of seeds and the minimum total weight of instances in a leaf during the modeling process.

The RF and REP Tree predictive results were obtained from the datasets for training and testing datasets. The MAE, RMSE and correlation coefficient (*r*) were subsequently determined on the basis of the Eqs. (4)–(6) shown in **Figure 2** that depicts RF and REP Tree models performance, respectively. For the RF model the

**Figure 2.** *Comparison of MAE, RMSE, and* r *values from the RF and REP tree models.*

differences, and the correlation coefficient (*r*) is a statistical measure representing the percentage of the variance for a model a dependent variable that's described by

> *n* X*n i*¼1

s

*<sup>i</sup>*¼<sup>1</sup>ð Þ *xi* � *<sup>x</sup>*

respectively, *x* and *y* are the mean values of the observed and predicted values respectively, and *n* is the total number of samples. MAE can be given as a more natural and unambiguous index compared with RMSE to quantify errors between the estimated and actual observed values [25, 26]. RMSE was used as a standard statistical metric to assess output of a model [27]. The larger correlation coefficient (*r*) and lower mean absolute error (MAE) values, and the root mean squared error

Theoretically, a specific model can be obtained when the model parameters are correctly selected and updated. The optimum values are obtained by trial and error

RF Minimum total weight of instances in a leaf: 1; minimum portion of the variance of all the data to be present in a node to be split in regression tress: 0.001; random number seed

REP Tree Maximum tree depth: �1; minimum total instance weight in the leaf: 2; minimum likelihood of variance: 0.001; fold number: 3; seed number: 1

1 *n* X*n i*¼1

*yi* � *xi* � � �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*<sup>i</sup>*¼<sup>1</sup>ð Þ *xi* � *<sup>x</sup> yi* � *<sup>y</sup>* � � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup>P*<sup>n</sup>*

*yi* � *xi* � �<sup>2</sup>

*<sup>i</sup>*¼<sup>1</sup> *yi* � *<sup>y</sup>* � �<sup>2</sup> <sup>q</sup> (6)

� (4)

*N***1(60)** *CSR* **Settlement (mm)**

th sample of the data

(5)

an independent variable, and their expressions are as follows [24]:

**(m)**

Training Minimum 1 16 0 0.21 0

Testing Minimum 1 16 7 0.29 0

**Unit Weight (kN/m<sup>3</sup> )**

Maximum 20 21 25 0.39 3.4 Mean 10.50 18.85 13.14 0.31 0.89 Standard deviation 5.80 1.89 9.14 0.05 0.92

Maximum 20 21 25 0.35 2.6 Mean 10.5 19.4 15.55 0.3255 0.93

Standard deviation 5.92 1.76 6.66 0.01 0.65

*RMSE* ¼

P*<sup>n</sup>*

where *yi* and *xi* are the observed and predicted value of *i*

P*<sup>n</sup>*

*r* ¼

**Dataset Statistical parameter Depth**

*Natural Hazards - Impacts, Adjustments and Resilience*

*Statistical parameters of the training and testing datasets.*

**Table 2.**

(RMSE) present a higher accuracy of predicted results.

used to pick attributes: 1; K value: 0

**5. Results and discussion**

**Algorithm Parameters**

*Model optimum modeling parameters.*

**Table 3.**

**264**

*MAE* <sup>¼</sup> <sup>1</sup>
