# An Intelligent Warning Method for Diagnosing Underwater Structural Damage
## 2 Methodology
### SOM Networks Model  
The self-organizing map neural network (SOM); strengthening central neurons and inhibiting peripheral neurons is a unique property of biological neuronal systems. The patterns of competition between neurons is a mechanism formed by the brain's self-organization [37]. SOM retains the spatial topology of input neurons due to its unique neighborhood characteristics and obtains the best mapping by continuously adjusting the connection weights of winning neurons and neighboring neuron network nodes [38]. The SOM neural network closely combines the phenomenon of enhancing the center and suppressing the surrounding of the biological neuron system with the self-organization characteristics of the human brain. Therefore, SOM retains the topology of the network and can be based on limited sample space failure detection, effectively reducing the need for spatial samples in the intelligent diagnostic system. Figure 2 shows a typical self-organizing feature mapping network model consisting of an input layer and a contention layer. The input layer contains \(n\) neurons, and the competition layer is a two-dimensional planar array composed of \(m\times n\) neurons [39]. This section utilizes SOM to identify micro-damage structures.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**NO.** & **Parameters** & **Calculation Formulas** & **Texture Characteristic** \\ \hline T\({}_{1}\) & Angular second moment & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}p^{2}(i,j,d,\theta)\) & The uniformity of gray distribution and degree of texture. \\ \hline T\({}_{2}\) & Sums of average & \(\sum\limits_{k=2}^{2g}k\times P_{X}(k)\) & The change of brightness. \\ \hline T\({}_{3}\) & Sums of variance & \(\sum\limits_{k=2}^{2g}\left(k-T_{2}\right)^{2}\!P_{X}(k)\) & Texture period size. \\ \hline T\({}_{4}\) & Maximum probability & \(\underset{i,j}{MAX}[p(i,j,d,\theta)]\) & The distribution of the main texture. \\ \hline T\({}_{5}\) & Sums of entropy & \(\sum\limits_{k=2}^{2g}p_{X}(k)\times\log[P_{X}(k)]\) & Texture complexity. \\ \hline T\({}_{6}\) & Variance & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}(i-m)^{2}p(i,j,d,\theta)\) & Texture periodicity. \\ \hline T\({}_{7}\) & Variance of grayscale & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}\left[(i-j)^{2}\times p^{2}(i,j,d, \theta)\right]\) & Texture distribution. \\ \hline T\({}_{8}\) & Correlation & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}\left[(i\times j\times p(i,j,d,\theta )-u_{1}\times u_{2}\right]/(d_{1}\times d_{2})\) & The main direction of the texture. \\ \hline T\({}_{9}\) & Inverse matrix & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}p(i,j,d,\theta)/[1+(i-j)^{2}]\) & Local texture changes. \\ \hline T\({}_{10}\) & Cluster shadow & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}\left[(i-u_{1})+(j-u_{2})\right]^{3} \times p(i,j,d,\theta)\) & Texture uniformity. \\ \hline T\({}_{11}\) & Significant clustering & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}\left[(i-u_{1})+(j-u_{2})\right]^{4} \times p(i,j,d,\theta)\) & Texture uniformity. \\ \hline T\({}_{12}\) & Entropy & \(\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}p(i,j,d,\theta)^{2}\times\log_{10}p( i,j,d,\theta)\) & Texture randomness. \\ \hline \hline \end{tabular} Note: \(g\) takes a power of 2, \(u_{1}=\sum\limits_{i=1}^{g}\sum\limits_{j=1}^{g}p(i,j,d,\theta)\), \(u_{2}=\sum\limits_{j=1}^{g}j\sum\limits_{i=1}^{g}p(i,j,d,\theta)\), \({d_{1}}^{2}=\sum\limits_{i=1}^{g}\left(i-u_{1}\right)^{2}\sum\limits_{j=1}^{ g}p(i,j,d,\theta)\), \({d_{2}}^{2}=\sum\limits_{j=1}^{