# Prediction of Pile Axial Bearing Capacity Using Artificial Neural Network and Random Forest
## 4 Machine Learning Methods
### Artificial Neural Network (ANN)  
Artificial neural network (ANN) has emerged over the past four decades as a powerful and versatile computational tool for organizing and correlating knowledge [52]. ANN has been proved a useful prediction tool in solving many types of problems, usually difficult to address using conventional numerical and statistical approaches [53]. [PERSON], the mathematician, and [PERSON], the neuroscientist, are the first two scientists who developed the idea of ANN-based on the structure of the human brain [54]. The ANN has been proved to exhibit a strong ability to handle complex problems in which the relationships between input(s) and output(s) are complex or nonlinear [55]. This computational technique is capable of recognizing, capturing, and mapping features, the so-called 'patterns' in a set of data, primarily due to high neuronal interconnections that process much information in parallel [53]. The structure of ANN consists of several layers (input, hidden, and output layers) connected together by different link weights through hidden nodes [55]. In each node, the activation function is applied. The node net input is obtained by summing the weights of the connection as well as a bias [44]. The back-propagation is the most popular manner to train ANN among different learning algorithms [56]. In addition, many other rules of study have been introduced and extended to this day [57; 58].  
This fact shows that ANN has many advantages and is widely used in different fields, especially in the field of construction engineering [59; 60]. Moreover, numerous investigations on the determination of bearing capacity using ANN have been conducted [55; 57; 58; 60]. In the work of [PERSON] and [PERSON] [61], the author predicted the total capacity of concrete spun pipe piles by using stress-wave data to buildthe ANN-based predictive model. Based on the conclusion, the predictive performance given by ANN was more reliable compared to supporting vector machines (SVM). [PERSON] and [PERSON] [62] proposed an ANN-based predictive model of cohesionless soil pile bearing efficiency. A number of 80 cases of axial load were used, and the results showed that the correlation coefficient (R) equaled to 0.92, showing the reliability of the ANN-based predictive model. Besides, numerous investigations on the behavior of pile bearing using ANN also pointed out a better prediction performance compared with analytical and empirical methods [53; 60; 61; 62]. A schematic diagram of neural network could be illustrated in Figure 4. In the ANN algorithm, the multi-layer network is generally shown to operate most effectively, because it can simulate nonlinear processes. Neural computing's main principle is the decomposition of the relationship between inputs and output into a series of linearly separable steps using hidden layers. Three distinct steps in developing an ANN-based solution could be summarized as [63]:  
Step 1: Transformation or scaling of data;  
Step 2: Definition of network architecture, where the number of hidden layers, the number of neurons in each layer, and the connectivity between neurons are determined. The network architecture selection could be depicted from Figure 4;  
Step 3: Train the network to respond correctly a given set of inputs, this step is considered as the development of neural network (Figure 5);