## 4 Discussion and Results
The congruity between the RASE values of the training and validation sets suggests consistent and reliable performance across various datasets. The SSE represents the sum of the squared differences between the predicted values and the actual values. The SSE for the training data is 5,649,332.2, and the SSE for the validation data is 2,834,219.7. The correctness of the model is supported by these figures, as well as the strong R\({}^{2}\) values. The congruity in RASE and MAD values between the training and validation stages implies that the model exhibits strong generalisation capabilities towards unfamiliar input. This is a crucial element of prognostic models, as it indicates their dependability in practical situations where the model needs to generate precise forecasts on data that it has not been exposed to during its training. Due to the low SSE, the model's predictions closely align with the actual observations, providing more evidence of its efficiency. To determine the effectiveness and strength of the suggested methodology, a comparison analysis was performed against existing methodologies described in the literature as follows:  
* A method was presented by [5] that uses data fusion with stage division to forecast the RUL of a system. This method, called an ensemble RUL prediction method, has been shown to achieve considerable gains in accuracy. The utilisation of bootstrap forests and hyperbolic tangent neural networks in our approach yields similar re \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**(a) Training Process**} & \multicolumn{2}{c}{**(b) Validation Process**} \\ \hline
**Measures** & **Value** & **Measures** & **Value** \\ \hline R\({}^{2}\) & 0.9967847 & R\({}^{2}\) & 0.9967703 \\ RASE & 1.2688147 & RASE & 1.2710539 \\ MAD & 0.8863745 & MAD & 0.8882592 \\ -LogLikelihood & 5814721.2 & -LogLikelihood & 2910018 \\ SSE & 5649332.2 & SSE & 2834219.7 \\ Sum Freq & 3509140 & Sum Freq & 1754307 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Prediction results for NtanH(3)NBoost(20) on both training and validation datasets. \begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Measures**} & \multicolumn{1}{c}{**Description**} \\ \hline RASE & Gives the root average squared error. When the response is nominal or ordinal, the differences are between 1 and \(p\), where \(p\) is the predicted probability of the response level. \\ \hline Mean Abs Dev (MAD) & It quantifies the average absolute difference between expected and observed values, irrespective of their direction. It is a reliable indicator of the extent to which these faults are distributed. \\ \hline Misclassification rate (MR) & The misclassification rate (MR) is a metric employed in classification problems to quantify the proportion of inaccurate predictions out of the total number of predictions made. It is a simplistic approach to assessing the frequency of the model’s inaccuracies. \\ \hline -Loglikelihood & Provides the negative of the loglikelihood \\ \hline SSE & Gives the error sums of squares. It is only available when the response is continuous. \\ \hline Sum Freq & It represents the complete analysis of observations. When a neural network variable Freq is supplied, the Sum Freq function sums the frequency column values. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._sults while providing increased adaptability and resilience in managing nonlinear deterioration patterns. * Ref. [2] conducted a comprehensive analysis of predictive maintenance for defence fixed-wing aircraft, emphasising the importance of flexible and precise prognostic models. The hybrid model we have developed successfully integrates numerous prediction algorithms to ensure both high accuracy and reliability. * Ref. [29] criticised the reliability prediction techniques used in avionics applications, highlighting the constraints of conventional methods in dynamic and intricate settings.