# Prediction of Depth of Seawater Using Fuzzy C-Means Clustering Algorithm of Crowdsourced SONAR Data

^{*}

## Abstract

**:**

## 1. Introduction

- The fuzzy-logic-based FCM algorithm was implemented in the field to predict depth data.
- The proposed method obtained more accurate depth data by clustering the data, which is experimentally proven.
- To obtain accurate results, the proposed model divided the data into the parts (blocks) with sizes approximately 100 to 100 m by location of the data measurements according to domain knowledge.
- The accuracy of the proposed model was measured by calculating the mean absolute error of the mean value of each block of the real data and the FCM value of each block.

## 2. Related Works

## 3. Materials and Methods

#### 3.1. Observation Technology of Depth of Seawater

#### 3.1.1. SONAR

#### 3.1.2. Crowdsourced Bathymetry

- Vessels should be equipped with a global navigation satellite system (GNSS) for the calculation of the location and single-beam echo sounders (SBAS) for measurement of depth.
- The equipment (software and hardware) of the vessels must meet the recommendations of the IMO on performance standards so that vessels have the ability to gather bathymetric data (along with location and time) of standardized reliability.
- The collected data from GNSS and SBES on ships will be transferred to the National Marine Electronics Association (NMEA) and must be saved on board. Saved data will be transferred from vessels to the trusted node.For the purpose of achieving the required level of standardization, the IHO Data Center for Digital Bathymetry accepts bathymetric information in specific (default) formats. These formats are the CSV, XYZT, or GeoJson format. The XYZT format contains longitude, latitude, depth, and time. On depth measurement, the vertical distance between the line of the water surface and the thrust position of the SONAR transducer can play a significant role. Therefore, the IHO automatically recommends setup sensors according to the issue. The data collected in this way have a significant value in a whole range of activities related to improving seabed mapping.

#### 3.2. Problem Analysis

#### 3.3. Possible Solutions

#### 3.4. Proposed Method

#### 3.4.1. Fuzzy C-Means Clustering

- Clustering algorithm based on partition-k-means, k-medoids, PAM, CLARA, CLARANS
- Clustering algorithm based on hierarchy—BIRCH, CURE, ROCK, chameleon
- Clustering algorithm based on fuzzy theory—FCM, FCS, MM
- Clustering algorithm based on distribution—DBCLASD, GMM
- Clustering algorithm based on density—DBSCAN, OPTICS, Mean-shift
- Clustering algorithm based on graph theory—CLICK, MST
- Clustering algorithm based on grid—STING, CLIQUE
- Clustering algorithm based on fractal theory—FC
- Clustering algorithm based on model—COBWEB, GMM, SOM, ART

- Clustering algorithm based on kernel—kernel k-means, kernel SOM, kernel FCM, SVC, MMC, MKC
- Clustering algorithm based on ensemble—methods for generating the set of clusters: 4 types of consensus function: CSPA, HGPA, MCLA, VM, HCE, LAC, WPCK, sCSPA, sMCLA, sHBGPA
- Clustering algorithm based on swarm intelligence—ACO_based (LF), PSO_based, SFLA_based, ABC_based
- Clustering algorithm based on quantum theory—QC, DQC
- Clustering algorithm based on spectral graph theory—SM, NJW
- Clustering algorithm based on affinity propagation—AP
- Clustering algorithm based on density and distance—DD
- Clustering algorithm for spatial data—DBSCAN, STING, Wavecluster, CLARANS
- Clustering algorithm for data stream—STREAM, CluStream, HPStream, DenStream
- Clustering algorithm for large-scale data-k-means—BIRCH, CLARA, CURE, DBSCAN, DENCLUE, Wavecluster, FC

**Step****1.**- Set values for
**c**(number of clusters),**m**(fuzziness exponent),**ε** **Step****2.**- Initialize fuzzy partition matrix $\mathit{U}=\left[{\mathit{u}}_{\mathit{i}\mathit{j}}\right],{\mathit{U}}^{\left(\mathbf{0}\right)}$
**Step****3.**- At
**k**-step: calculate the**c**cluster centers(centroids) ${\mathit{C}}^{\left(\mathit{k}\right)}=\left[{\mathit{c}}_{\mathit{j}}\right]$ with ${\mathit{U}}^{\left(\mathit{k}\right)}$. Where ${\mathit{c}}_{\mathit{j}}$ calculates with Equation (3) **Step****4.**- Calculate and update membership matrix ${\mathit{U}}^{\left(\mathit{k}\right)},{\mathit{U}}^{\left(\mathit{k}+\mathbf{1}\right)}$
**.**Equation (2) **Step****5.**- If $\mathit{max}\left\{\Vert {\mathit{U}}^{\left(\mathit{k}+\mathbf{1}\right)}-{\mathit{U}}^{\left(\mathit{k}\right)}\Vert \right\}$
**< ε**then stop, otherwise set**k = k+1**and return to Step 3

#### 3.4.2. Experiment Parameters and Environment

- OS: Windows 10 Pro
- Processor: Intel(R) Core (TM) i7-10700 CPU @2.90 GHz
- RAM: 32 GB
- System Type: 64 bit
- Platform: Jupyter Notebook (Python)

#### 3.4.3. Data Training Method

- Define minimum and maximum coordinates (latitude, longitude).
- Divide the whole training zone into the blocks. The approximate size of the blocks should be 100 to 100 m.
- Sort blocks that have more than 200 data points. If there are fewer data points in the blocks, no use of FCM in that block.
- Implement FCM to each block.
- Compare with real data.

## 4. Results

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The first printed map of ocean depths with information provided from the USS Dolphin (1853).

**Figure 4.**Example of measuring of same seabed: (

**a**) accurate measuring; (

**b**) inaccurate measuring when there is an obstacle while measuring; (

**c**) inaccurate measuring when there is a strong wave in sea surface.

**Figure 6.**(

**a**) One-dimensional dataset, (

**b**) membership value of k-means, (

**c**) membership value of FCM.

**Figure 10.**Example of 2, 3, and 5 clustering results. (

**a**) and (

**b**) are examples of two cluster results; (

**c**) and (

**d**) are examples of three cluster results; (

**e**) and (

**f**) are examples of five cluster results.

**Figure 11.**Example of clustering of blocks that has less or no real data. (

**a**) The value of the clustering result is 5.8 m. (

**b**) The value of the clustering result is 6.3 (m).

Latitude | Longitude | Depth(m) |
---|---|---|

35.136863 | 129.192551 | 10 |

35.136863 | 129.192551 | 11 |

35.136863 | 129.192551 | 20 |

35.136863 | 129.192551 | 23 |

35.136863 | 129.192551 | 21 |

35.136863 | 129.192551 | 20 |

Device_id | Time | Latitude | Longitude | Depth |
---|---|---|---|---|

SY-T02 | 2020-02-27 11:19:03 | 35.0001678466797 | 128.919357299805 | 14.5 m |

SY-T02 | 2020-02-28 10:10:28 | 35.0003662109375 | 128.919677734375 | 14.5 m |

SY-T04 | 2019-08-27 09:50:45 | 35.0004158020020 | 128.919662475586 | 26.4 m |

SY-T05 | 2019-02-27 08:19:08 | 35.0001335144043 | 128.919326782227 | 26.5 m |

SY-T02 | 2019-01-21 12:11:50 | 35.0006332397461 | 128.919570922852 | 25.5 m |

SY-T04 | 2018-09-23 07:23:07 | 35.0006484985352 | 128.919067382812 | 9.8 m |

SY-T03 | 2020-04-21 13:11:50 | 35.0006332397461 | 128.919570922852 | 25.7 m |

SY-T04 | 2021-01-10 17:13:09 | 35.0006484985352 | 128.919067382812 | 10.2 m |

By Mean Value of Each Block | By FCM Value of Each Block | |
---|---|---|

Mean Absolute Error | 2.09 m | 1.67 m |

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**MDPI and ACS Style**

Kamolov, A.A.; Park, S. Prediction of Depth of Seawater Using Fuzzy C-Means Clustering Algorithm of Crowdsourced SONAR Data. *Sustainability* **2021**, *13*, 5823.
https://doi.org/10.3390/su13115823

**AMA Style**

Kamolov AA, Park S. Prediction of Depth of Seawater Using Fuzzy C-Means Clustering Algorithm of Crowdsourced SONAR Data. *Sustainability*. 2021; 13(11):5823.
https://doi.org/10.3390/su13115823

**Chicago/Turabian Style**

Kamolov, Ahmadhon Akbarkhonovich, and Suhyun Park. 2021. "Prediction of Depth of Seawater Using Fuzzy C-Means Clustering Algorithm of Crowdsourced SONAR Data" *Sustainability* 13, no. 11: 5823.
https://doi.org/10.3390/su13115823