## 4 Data Analysis Framework Application
### Irregular Waves and Data Processing  
Although all 6 DOFs were captured during the test, only 4 DOFs are employed to maintain the consistency of the framework with the ongoing research developed for advancing ships using the state-of-the-art simulator data available in the MARTITIME SIMULATION CENIRE of AMC. As such, surge and sway vectors additively formed vector \(\xi\), to represent translational response features, whereas roll and yaw-shaped vector \(\psi\) denotes the spatial response to induced waves. The size of observation window is selected to be 40 s corresponding to 8000 samples. To further condense the features within the scalograms, a max-pooling filter is applied on the original 256 to 256 matrix which essentially condenses the matrix size based on the filter window size according to Equation (11). In this respect, different window size has been utilized to investigate the effect of matrix resolution on computational cost and validation accuracy. \[\text{MaxPooling(X)}_{\text{i,j}}=\text{max}_{\text{a,b}=0}^{f-1}\text{X}_{ \text{(i}\times\text{s}+\text{a}),\text{(j}\times\text{s}+\text{n})} \tag{11}\]  
Given the input feature map represented as X, which is an image with dimensions (Widthinput, Heightinput), or more accurately, the matrix of wavelet coefficient, and f as the size of the max pooling window with a stride of s, i, and j iterating over the spatial dimension. Figure 11 indicates the original and lower resolution scalogram through the max pooling operation. As can be seen despite the resolution lost, the features as the vector of summative normalized wavelet coefficient are almost identical. On this basis, the down-sampled matrix is employed for the primary part of the investigation, which will be discussed in the next section. In the next stage, the features within the normalized vector of K split into two vectors of A and B to form the features array respective to the wave class given in Table 3. Simply, the first array A is characterized by black pixels as minor wavelet value below 0.5, and the second array B includes the normalized wavelet coefficient above 0.5. Figure 12 summarizes the data processing mechanism. To perform statistical tests on features of data with respect to the projection planes and to examine entropy on each plane, the wave data in Table 3 is processed with a max-pooling operation of window size 32 that reduces the resolution of the features from 256 to 8 vectors. Subsequently, the one-way Analysis of Variance (ANOVA) statistical test is carried out on raw data, A and B. Generally, ANOVA is a statistical method utilized to assess differences among the means of multiple groups. Specifically, the one-way ANOVA determines if there are statistically significant variations among the means of three or more independent groups [30]. The test has been carried out on raw data, white and black planes. As such, the features with higher variance possess higher entropy and are more functional for classification. As can be witnessed in Figure 13, the projection has enhanced the variance of features substantially. However, augmenting the current set with additional attributes  
Figure 11: The scalogram with original size (**a**) and the down sampled image as the result of max pooling operation (**b**) with the relevant normalized feature representation in the bottom. Figure 12: Schematic representation of data analysis process. that contribute extra variance can potentially enhance the entropy, particularly if these attributes are endogenous and intrinsic to the data's characteristics. In this order, the resolution has been increased in max-pooling to the window of size 8 corresponding to 32 features, where a higher number of features facilitates the comparison of nuances through exploratory and statistical analysis. Numerous studies have been conducted, and three images depicting the response to the same temporal segment were selected as representative samples.