## 4 Data Analysis Framework Application
### Performance in Transition  
Another practical issue frequently addressed for ML/DL models in the context of seakeeping is the capability of the trained model to timely detect transitions from one condition to another. This issue has been addressed in [31; 32] as one of the main challenges in Sea State Estimation (SSE) using vessel motions. The origination of this issue is discussed in [15]. In short, the ML and DL models need to be trained by many permutations of input-output data, enabling them to perfectly detect the transition from one specific condition to another. However, the more scenarios in the dataset, the higher the computational  
Figure 19: Clusters scatter for two features with respect to the known wave classes.  
Figure 20: (**a**,**b**) The indication of LDA for clusters classification.  
Figure 21: (**a**) The indication of quadratic (**a**) and linear (**b**) discriminant analysis for clusters classification of engineered features.  
costs. The problem is more pronounced for sequential time stamps. To give a simple mathematical representation, in case of only two input-output sets of data (wave-response) represented by F\({}_{\text{(1,H)}}\) and G\({}_{\text{(1,H)}}\) of observation window of H size, all permutations of F and G are required to be trained. This corresponds to H! number of permutations that are needed to be trained for only two inputs, which increases exponentially by increasing the scenarios. Indeed, the essential shortcoming in the data analysis framework has imposed some constraints which impede the capability for instantaneous acquisition of changes. To this end, the current feature engineering setup has been tested to explore its functionality in transitioning from one force to another. A scenario has been set up using 470 s of each wave class to investigate the estimation throughout and during the transition from one wave to another.  
The estimation results are depicted in Figure 22, with transitions marked by black dotted boxes. Clearly, the current setup has effectively distinguished between wave classes or input forces during transitions, indicating a high sensitivity of the trained model to each class. However, to mitigate misclassification within each scenario, the most cost-effective approach is to utilize the Move-mode mechanism, as per [23], which effectively smoothens the estimation process. However, this mechanism comes with the expense of adding time lag to estimation, which is 10 s for Figure 22 and 3 s for Figure 23. In summary, the current featured engineered framework allowed fair estimation of input force (wave) using system (sphere) responses (4 DOFs) for deterministic purposes in 40 s with negligible computational expenses. The easiness of the current framework allows the inclusion of many wave scenarios to replicate real-world phenomena while preserving the nuanced features of the input-output relationship for training machine learning models. Aside from that, the proposed model can be easily reinforced or updated with negligible training time and the augmentation of new data.  
Figure 22: Indication of estimation in transition between waves (dotted boxes indicate transition time stamps).