# An Intelligent Warning Method for Diagnosing Underwater Structural Damage

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Gray Level Co-Occurrence Matrix

#### 2.2. Feature Parameters

#### 2.3. SOM Networks Model

#### 2.4. Learning Steps

- (i)
- Initialization: Set the [0,1] random value as the initial connection weight between the input neuron and the output neuron. A set, S
_{j}, of outputting neighboring neurons is selected, wherein S_{j}(0) represents a set of neighboring neurons of neuron j at time t = 0, and S_{j}(t). - (ii)
- Set the input of the neural network: Make the sample feature parameters into the following matrix and input them to the SOM network:$$X\left(n\right)={[{x}_{1}\left(n\right),{x}_{2}\left(n\right),{x}_{3}\left(n\right)\cdots {x}_{N-1}\left(n\right),{x}_{N}\left(n\right)]}^{T}.$$
- (iii)
- Calculate the Euclidean distance: Input layer neurons, i, into mapping layer neurons’, j, available Euclidean distance, d
_{ij}, indicated as:$${d}_{ij}=\Vert X-{W}_{j}\Vert =\sqrt{{\displaystyle \sum _{i=1}^{n}{[{x}_{i}(t)-{w}_{ij}(t)]}^{2}}}.$$In the equation, w_{ij}is the weight of the input layer neuron, i, to the mapping layer neuron, j. W_{j}is the connection weight of the neuron, j, on the mapping layer. - (iv)
- Obtain the winning neuron: The position of the winning neuron can be obtained by calculating the minimum Euclidean distance between the input vector and the weight vector. When the input vector is X and the winning neuron is denoted by c, the formula is expressed as:$$\Vert X-{W}_{c}\Vert =\underset{i}{\mathrm{min}}\Vert X-{W}_{i}\Vert ,\text{}i=1,2,3\cdots M-1,M,$$
_{c}is the weight of the winning neuron, c. W_{i}is the connection weight of the neuron, i, on the mapping layer. - (v)
- Adjust weight: The connection weight of the input neuron and all neurons in the competition neighborhood are corrected by Equation (6):$$\Delta {w}_{ij}={w}_{ij}(t+1)-{w}_{ij}(t)=\eta (t)[{x}_{i}(t)-{w}_{ij}(t)].$$Among them, t is the continuous time, and the learning rate at time t is $\eta (t)$. $\eta (t)=\frac{1}{t}$ or $\eta (t)=0.2(1-\frac{t}{1000})$. The value range of $\eta (t)$ is [0,1].
- (vi)
- Determine whether the output result meets the expected requirements: If the result meets the previously set requirements, then end; if not, return to step (ii) to continue.

## 3. Experiment and Result Analysis

#### 3.1. Image Acquisition and Processing

#### 3.2. Triangle Algorithm

- Step 1:
- The initial range of the factor of the generative criterion is determined according to the properties of the micro-damage image.
- Step 2:
- Confirm the generative angle, θ, by the theory of image rotation invariant. In Figure 5, the sequence A is he generative step length, d, g
_{1}-g_{n n}is the sequence B image gray level, g, g_{1}-g_{n}. - Step 3:
- The sequence A is linked to the sequence B, and θ is then joined to sequence A and sequence B, respectively.
- Step 4:
- Extract all d
_{n}-θ-g_{t}combinations. Then, a triangular combination can form.

- (1)
- Generative angle, θ: The average of directions of 0°, 45°, 90°, and 135°.
- (2)
- Image gray level: g
_{t}= 2^{m}^{+2}, among them, t = m + 2, t is taken as the integer of [1,6]. - (3)
- Generative step length, d: Take the integer of [1,6].

#### 3.3. Optimization of Generative Criterion

_{n}-θ-g

_{t}, of the underwater structure micro-damage is n is 5, t is 7, and θ is taken as the average of the four directions of 0°, 45°, 90°, and 135°.

#### 3.4. Establishing a Standard Sample Label

_{5}-θ-g

_{7}, among them, θ takes 0°, 45°, 90°, and 135°). The DFS method establishes screening criteria for screening parameters by observing the trend of the characteristic parameters of different diagnostic types. The screening criteria are determined according to the size of the intersection interval of different types of damages: The smaller the crossover interval, the better the screening results, and the parameters are suitable for establishing a diagnostic model; otherwise, the parameter is not suitable for diagnosing underwater structural damage. Figure 9, Figure 10 and Figure 11 shows the screening results.

_{1}, entropy, P

_{2}, variance of grayscale, P

_{3}, correlation, P

_{4}, inverse matrix, P

_{5}, variance, P

_{6}, significant clustering, P

_{7}, and sums of mean, P

_{8}, were screened. Therefore, the DFS method could effectively solve these problems of characteristic parameter selection. The standard values of each parameter are given in Table 2.

#### 3.5. Training Network Model

#### 3.6. Application and Validation

## 4. Conclusions

_{5}-θ-g

_{7}, which was the texture average of distance, delta = 4, four directions (0°, 45°, 90°, 135°), and image gray level, g = 128.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 7.**Tendency of d (when g = 2

^{8}). Sample 1–9 represents nine sample images of certain types of defects.

**Figure 8.**Form of g (when d = 5). Sample 1–9 represents nine sample images of certain types of defects.

**Figure 15.**Micro-damage image. (

**a**) Micro-honeycombs; (

**b**) Micro-voids; (

**c**) Micro-cracks; (

**d**) Micro-depressions.

NO. | Parameters | Calculation Formulas | Texture Characteristic |
---|---|---|---|

T_{1} | Angular second moment | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}{p}^{2}(i,j,d,\theta )}$ | The uniformity of gray distribution and degree of texture. |

T_{2} | Sums of average | $\sum _{k=2}^{2g}k\times {P}_{X}}(k)$ | The change of brightness. |

T_{3} | Sums of variance | $\sum _{k=2}^{2g}{(k-{T}_{2})}^{2}{P}_{X}}(k)$ | Texture period size. |

T_{4} | Maximum probability | $\underset{i,j}{MAX[}p(i,j,d,\theta )]$ | The distribution of the main texture. |

T_{5} | Sums of entropy | $-{\displaystyle \sum _{k=2}^{2g}{P}_{X}(k)\times \mathrm{log}[{P}_{X}}(k)]$ | Texture complexity. |

T_{6} | Variance | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}{(i-m)}^{2}p(i,j,d,\theta )}$ | Texture periodicity. |

T_{7} | Variance of grayscale | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}[{(i-j)}^{2}\times {p}^{2}(i,j,d,\theta )}}]$ | Texture distribution. |

T_{8} | Correlation | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}[(i\times j\times p(i,j,d,\theta )-{u}_{1}}}\times {u}_{2}]/({d}_{1}\times {d}_{2})$ | The main direction of the texture. |

T_{9} | Inverse matrix | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}p(i,j,d,\theta )/[1+{(i-j)}^{2}]}$ | Local texture changes. |

T_{10} | Cluster shadow | ${{\displaystyle \sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}[(i-{u}_{1})+(j-{u}_{2})]}}}^{3}\times p(i,j,d,\theta )$ | Texture uniformity. |

T_{11} | Significant clustering | ${{\displaystyle \sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}[(i-{u}_{1})+(j-{u}_{2})]}}}^{4}\times p(i,j,d,\theta )$ | Texture uniformity. |

T_{12} | Entropy | $\sum _{i=1}^{g}{\displaystyle \sum _{j=1}^{g}p{(i,j,d,\theta )}^{2}\times {\mathrm{log}}_{10}p(i,j,d,\theta )}$ | Texture randomness. |

Damage Type | P_{1} | P_{2} | P_{3} | P_{4} | P_{5} | P_{6} | P_{7} | P_{8} |
---|---|---|---|---|---|---|---|---|

Micro-honeycombs | 0.45219 | 1.23347 | 0.341173 | 0.659015 | 1.487459 | 16074.99305 | 0.6085123 | 2113537.15 |

Micro-depressions | 0.735626 | 0.844082 | 0.245272 | 0.986124 | 1.270514 | 16039.67163 | −0.23044 | 2113536.83 |

Micro-voids | 0.966008 | 0.645785 | 0.155829 | 3.719458 | 1.034531 | 16113.92133 | 0.185468 | 2113536.14 |

Micro-cracks | 0.561931 | 0.114353 | 0.047756 | −1.768837 | 1.1816 | 16103.60313 | −0.487734 | 2113536.55 |

Parameters | Value | |||||||
---|---|---|---|---|---|---|---|---|

Input Layer Node | x_{1} | x_{2} | x_{3} | x_{4} | x_{5} | x_{6} | x_{7} | x_{8} |

P_{1} | P_{2} | P_{3} | P_{4} | P_{5} | P_{6} | P_{7} | P_{8} | |

Weight | 0.125 | |||||||

Neighborhood shape | Hexagon, R = 3 | |||||||

Neurons | 64 | |||||||

Training steps | 10, 50, 100, 200, 500,1000 |

Number of Training Steps | Micro-Honeycombs | Micro-voids | Micro-depressions | Micro-cracks | Clustering Result |
---|---|---|---|---|---|

10 | 55 | 37 | 37 | 55 | 50% |

50 | 43 | 37 | 37 | 55 | 75% |

100 | 43 | 1 | 37 | 37 | 75% |

200 | 49 | 1 | 16 | 64 | 100% |

500 | 49 | 1 | 16 | 64 | 100% |

1000 | 49 | 1 | 16 | 64 | 100% |

Damage Type | Sample Classification Number | Classification Accuracy |
---|---|---|

Micro-honeycombs | 36, 41, 42, 43, 44, 49, 50, 51, 52, 57, 58, 59 | 80% |

Micro-voids | 1, 2, 3, 4, 9, 10, 17, 18, 19, 20, 25, 26, 27, 33, 34, 35 | 93.33% |

Micro-depressions | 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 29 | 100% |

Micro-cracks | 30, 31, 32, 38, 39, 40, 45, 46, 47, 48, 54, 55, 56, 61, 62, 63, 64 | 86.66% |

Unknown situation | 53, 60 | - |

28 | - | |

37 | - |

Damage Type | Sample Number |
---|---|

Micro-honeycombs | 1–10 |

Micro-voids | 11–20 |

Micro-depressions | 21–30 |

Micro-cracks | 31–40 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Li, K.; Wang, J.; Qi, D.
An Intelligent Warning Method for Diagnosing Underwater Structural Damage. *Algorithms* **2019**, *12*, 183.
https://doi.org/10.3390/a12090183

**AMA Style**

Li K, Wang J, Qi D.
An Intelligent Warning Method for Diagnosing Underwater Structural Damage. *Algorithms*. 2019; 12(9):183.
https://doi.org/10.3390/a12090183

**Chicago/Turabian Style**

Li, Kexin, Jun Wang, and Dawei Qi.
2019. "An Intelligent Warning Method for Diagnosing Underwater Structural Damage" *Algorithms* 12, no. 9: 183.
https://doi.org/10.3390/a12090183