## 4 Results
### Development of an Artificial Neural Network-Based Equation
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{_dl_/**t**} & \multirow{2}{*}{_I/D_} & \multicolumn{5}{c}{\(\sigma_{c}\)/\(\sigma_{y}\)} \\ \cline{3-7}  & & **0.2** & **0.4** & **0.5** & **0.6** & **0.7** \\ \hline \multirow{4}{*}{0.2} & 0.2 & 0.88 & 0.85 & 0.79 & 0.74 & 0.61 \\  & 0.4 & 0.85 & 0.82 & 0.77 & 0.70 & 0.59 \\  & 0.6 & 0.84 & 0.79 & 0.75 & 0.68 & 0.56 \\  & 0.8 & 0.83 & 0.78 & 0.74 & 0.66 & 0.54 \\  & 1.2 & 0.81 & 0.77 & 0.73 & 0.65 & 0.53 \\ \hline \multirow{4}{*}{0.4} & 0.2 & 0.80 & 0.76 & 0.71 & 0.67 & 0.59 \\  & 0.4 & 0.75 & 0.71 & 0.68 & 0.62 & 0.54 \\  & 0.6 & 0.70 & 0.68 & 0.65 & 0.61 & 0.53 \\  & 0.8 & 0.68 & 0.66 & 0.64 & 0.60 & 0.52 \\  & 1.2 & 0.65 & 0.63 & 0.62 & 0.59 & 0.52 \\ \hline \multirow{4}{*}{0.5} & 0.2 & 0.77 & 0.73 & 0.69 & 0.64 & 0.56 \\  & 0.4 & 0.67 & 0.65 & 0.62 & 0.58 & 0.50 \\  & 0.6 & 0.61 & 0.60 & 0.58 & 0.54 & 0.47 \\  & 0.8 & 0.58 & 0.57 & 0.56 & 0.53 & 0.46 \\  & 1.2 & 0.55 & 0.54 & 0.53 & 0.52 & 0.46 \\ \hline \multirow{4}{*}{0.6} & 0.2 & 0.72 & 0.69 & 0.66 & 0.61 & 0.53 \\  & 0.4 & 0.59 & 0.57 & 0.55 & 0.52 & 0.45 \\  & 0.6 & 0.53 & 0.51 & 0.49 & 0.47 & 0.41 \\  & 0.8 & 0.49 & 0.47 & 0.46 & 0.45 & 0.40 \\  & 1.2 & 0.45 & 0.45 & 0.44 & 0.43 & 0.39 \\ \hline \multirow{4}{*}{0.8} & 0.2 & 0.58 & 0.56 & 0.55 & 0.52 & 0.44 \\  & 0.4 & 0.39 & 0.37 & 0.36 & 0.34 & 0.28 \\ \cline{1-1}  & 0.6 & 0.32 & 0.30 & 0.29 & 0.28 & 0.24 \\ \cline{1-1}  & 0.8 & 0.28 & 0.27 & 0.26 & 0.25 & 0.22 \\ \cline{1-1}  & 1.2 & 0.25 & 0.24 & 0.24 & 0.23 & 0.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: FEA results of corroded X65 pipeline for ANN training dataset. Figure 7: The architecture of ANN in MATLAB. \[\left(y\right)_{n}=\frac{\left(y_{max}-y_{min}\right)(x-x_{min})}{\left(x_{max}-x_{ min}\right)}+y_{min} \tag{5}\]  
where, \(y\) is the normalisation value ranging from \(-1\) to \(1\) and \(x\) is denormalization value ranging according to its dataset. After training the ANN, the weights and biases were adjusted for output predictions with the lowest errors. The connections between the input, output, hidden neurons, and their weights and biases were mathematically expressed, as shown in Equations (6)-(8). \[\left[ \begin{array}{c}h_{1,1}\\ h_{1,2}\\ h_{1,3}\\ h_{1,4}\\ h_{1,5}\\ h_{1,6}\end{array} \right]=\left[ \begin{array}{ccccc}0.0290&-0.3112&0.2976&-0. 0501&0.0044\\ -1.0552&0.4619&1.5820&2.0369&0.4190\\ -0.2548&0.4752&-0.0036&0.0093&-2.7614\\ 2.1350&0.2060&0.1957&-0.3347&1.3200\\ -0.1720&0.2548&0.7511&-0.1147&-0.0504\\ 0.9064&1.3703&0.7865&-0.5071&-0.8183\\ \end{array} \right]\left[ \begin{array}{c}(UTS)_{n}\\ (d/t)_{n}\\ (l/D)_{n}\\ (w/t)_{n}\\ (\sigma_{c}/\sigma_{y})_{n}\end{array} \right]+\left[ \begin{array}{c}0.4439 \\ 2.8125\\ 2.1760\\ 0.6014\\ 0.0232\\ 1.8972\end{array} \right] \tag{6}\]  
\[\left[ \begin{array}{c}h_{2,1}\\ h_{2,2}\\ h_{2,3}\\ h_{2,4}\\ h_{2,5}\\ h_{2,6}\end{array} \right]=\left[ \begin{array}{ccccc}0.8994&-0.5208&-0.1017&1. 6657&0.5182&0.8874\\ -1.1137&-0.4861&-1.3240&0.2724&0.7561&1.0007\\ -1.4525&0.7080&-0.4520&0.6728&1.4434&-0.7388\\ -0.9694&-1.0553&1.5402&-1.8413&1.0336&-1.9841\\ 0.2574&-0.2465&-0.6022&-0.4447&0.6712&0.8255\\ -2.5687&-0.0788&0.2776&-0.4032&-2.4040&0.4544\\ \end{array} \right]\left[ \begin{array}{c}a(h_{1,1})\\ a(h_{1,2})\\ a(h_{1,3})\\ a(h_{1,4})\\ a(h_{1,5})\\ a(h_{1,6})\end{array} \right]+\left[ \begin{array}{c}-1.9775\\ 1.9334\\ 0.4981\\ 0.3314\\ -0.2197\\ -2.2699\end{array} \right] \tag{7}\]  
\[\left[ \begin{array}{ccccc}0.7767&-1.4787&-0.8224&-0.5620&1.2112&1.3954\\ \end{array} \right]\left[ \begin{array}{c}a(h_{2,1})\\ a(h_{2,3})\\ a(h_{2,4})\\ a(h_{2,5})\\ a(h_{2,6})\end{array} \right]+\left[ \begin{array}{c}2.2849\\ \end{array} \right]\right\} \tag{8}\]  
where, \(a(x)\) is hyperbolic tangent sigmoid transfer function,  
\[a(x)=\frac{2}{(1+e^{-2x})-1}\text{ or }\tanh(x)\]  
and \(f(x)\) is linear transfer function,  
\[f(x)=x\]  
To ensure the reliability of the assessment equations, an unseen dataset was used to validate the method and determine its performance.