## Methodology
### Simulation of RBF ANN Model for Estimating Body Dimensions  
The radical basic function (RBF) ANN is one of the feedforward neural networks with simple structure and has the advantages of approximating any non-linear function with arbitrary accuracy and fast convergence [16,18]. Therefore, the predictive model proposed in this study was constructed based on RBF ANN with the architecture composed of an input layer, hidden layer, and output layer. In this paper, the simulation process included eight steps as follows. **Step 1**: Distributed the element of \(X=[x(I),\,x(2),\,\ldots,\,x(p)]^{T}\) to the input layer. Where, \(X\) was a matrix of inputting samples; \(p\) was the number of input samples. **Step 2**: Calculated the inputs of the hidden layer;  
\[hi_{j}(k)=\sum_{1}^{n}w_{ij}x_{i}(k),\,\,j=1,2,\ldots,h \tag{1}\]  
where, \(hi_{j}(k)\) was the inputs of the \(k\)th inputting sample in the \(j\)th node of hidden layer, \(k=1,\,2,\,\ldots,\,\)\(p\); \(w_{ij}\) was the linkage weights between input layer and hidden layer. For the RBF ANN, the linkage weights between the input layer and the hidden layer were set to 1. **Step 3**: Calculated the cluster centers \(\{c_{1},\,c_{2},\,\ldots,\,c_{h}\}\) and the parameter \(\sigma\) in the hidden layer;  
For the RBF ANN, the outputs of the hidden layer were activated by a radial Gauss function \(G\):  
\[G(x(k),c_{i})=exp\left[-\frac{\|x(k)-c_{i}\|}{2\sigma^{2}}\right],\,\,i=1,2, \ldots,h \tag{2}\]  
where, \(c_{i}\) was the \(i\)th cluster center in the hidden layer; \(\sigma\), also known as spread, was the smoothing parameter, \(\|\cdot\|\) was the representative of the Euclidean norm. Thus, the cluster centers \(\{c_{1},\,c_{2},\,\ldots,\,c_{h}\}\) and the parameter \(\sigma\) was set to 1.0 initially in this study. The cluster centers \(\{c_{1},\,c_{2},\,\ldots,\,c_{h}\}\) were determined by the K-means algorithm. The operational procedures were as follows:  
1. An initial set of cluster centers \(\{c_{1},\,c_{2},\,\ldots,\,c_{h}\}\) was chosen from the inputs of hidden layer randomly;
2. Each of the input of hidden layer was assigned to its closest cluster center according to the Euclidean metrics;
3. New cluster centers were computed as the means of the \(K\)th cluster;
4. If the position of any cluster center changed, return to (2), otherwise, stop. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**SN**} & \multicolumn{4}{c}{**Input Data**} & \multicolumn{4}{c}{**Output Data**} \\ \cline{2-13}  & **W** & **A** & **H** & **ST** & **WH** & **AH** & **HH** & **CH** & **KH** & **C** & **T** & **K** \\ \hline
8 & 82.7 & 80.9 & 90.3 & 169.4 & 100.7 & 91.4 & 78.7 & 71.0 & 45.9 & 74.5 & 54.3 & 36.6 \\
9 & 74.5 & 86.3 & 91.9 & 176.0 & 109.4 & 85.0 & 84.2 & 79.3 & 51.3 & 79.6 & 50.3 & 36.6 \\
10 & 80.6 & 84.3 & 90.3 & 171.1 & 105.5 & 97.0 & 82.2 & 77.9 & 47.1 & 79.2 & 51.4 & 36.4 \\
11 & 88.5 & 87.6 & 91.6 & 163.6 & 101.3 & 89.8 & 80.3 & 73.6 & 45.6 & 75.7 & 51.3 & 36.4 \\
12 & 92.1 & 95.4 & 95.4 & 166.0 & 104.3 & 96.8 & 78.8 & 73.3 & 42.7 & 84.0 & 53.4 & 37.7 \\
13 & 77.9 & 78.6 & 85.2 & 165.2 & 104.5 & 97.2 & 76.5 & 73.4 & 44.0 & 79.0 & 46.4 & 35.2 \\
14 & 87.1 & 87.6 & 91.6 & 166.3 & 100.8 & 90.3 & 80.0 & 70.3 & 43.3 & 80.9 & 52.8 & 37.5 \\
15 & 75.5 & 81.0 & 92.4 & 173.1 & 108.9 & 98.4 & 83.6 & 79.5 & 48.0 & 79.7 & 51.2 & 37.3 \\
16 & 80.3 & 87.3 & 94.5 & 175.6 & 108.3 & 98.0 & 83.3 & 79.2 & 50.4 & 80.2 & 55.4 & 37.2 \\
17 & 71.0 & 72.8 & 83.8 & 156.3 & 97.0 & 80.3 & 74.0 & 70.0 & 42.0 & 71.5 & 50.9 & 37.1 \\
18 & 74.7 & 82.3 & 87.2 & 159.0 & 96.4 & 84.3 & 74.5 & 69.4 & 41.5 & 73.9 & 49.8 & 34.4 \\
19 & 92.8 & 97.3 & 96.0 & 164.1 & 100.2 & 86.9 & 78.3 & 71.5 & 42.3 & 82.4 & 56.6 & 38.2 \\
20 & 82.9 & 83.5 & 90.9 & 183.2 & 116.4 & 104.4 & 92.2 & 90.0 & 53.2 & 79.9 & 54.4 & 36.2 \\ \hline \hline \end{tabular} Note: SN is sample number. For W, A, H, ST, WH, AH, HH, CH, C, T, K, please refer to Figure 2 and Table 1.  
\end{table}