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The planning stages of dredging require comprehensive and detailed analyses. Identifying the dredging environment is one of the important points. A three-dimensional (3D) geological modeling technology has been shown to be a robust tool for representing and analyzing the conditions of geology. From a general perspective, a 3D model is established by some spatial surfaces. Based on a dredging project, this study investigated the estimation capability of an interpolation method of triangulation combined with BP neural network, for modeling a rock layer surface. The performance of the proposed model is compared with some conventional methods in the literature. The results showed that this interpolation method is effective to be employed for surface modeling of the rock layer.

A reasonable judgment about the location of all soil types in the dredging area is one of the most important elements for the planning of maritime dredging operations, as the material to be dredged determines the selection of dredging equipment and drives the productivity computations [

Surface modeling needs some necessary information, such as real data at sampled sites and predicted values at unsampled sites. Interpolation is the process of predicting the values of attributes at unsampled sites. Many researchers have carried out studies on interpolation methods for the purpose of providing an optimum model structure [

In addition, some scholars try to apply artificial intelligence technology to the study of spatial interpolation methods. Lin and Chen proposed an attribute interpolation method based on radial basis function networks and variograms [

There are three types of 3D models which are wireframe, surface, and solid models, and these models completely and unambiguously define the stratigraphy for the site being modeled [

Triangulation interpolation is the most common and simplest interpolation method, especially in geographic information systems. For this method, the equation of a simple planar surface is

The triangular region surrounded by the three points is called the natural neighbors [

Inverse distance weighting interpolation is a method in which the distance between the interpolation point and the sample point is used as the weight [

A neural network, constructed under the inspiration of biological neural networks, is a data processing model with a large amount of interconnecting artificial neuronst [

Figure

Three-layer BP network structure.

The interpolation method of triangulation combined with BP neural network, which is used for surface modeling in this study, actually contains two interpolation processes. Figure

Steps of the interpolation method of triangulation combined with BP neural network: (a) scattered measured data points; (b) random virtual data points; (c) all triangles formed with data points as vertices.

The interpolation method of triangulation combined with BP neural network is applied in the 3D geological modeling of a dredging area. This area, which has a design excavation depth of 13.5 m, is located at one coast of China, and the main dredged materials are soil and rock. Compared with soil, rock excavation is more difficult and requires higher construction costs. Therefore, the 3D model research mainly focuses on the rock layer, and the amount of excavation is paid special attention. A total of 12 boreholes can be used for model establishment. To make the method more general, a reference point (B01) is determined, and the coordinate of which is defined as (

Project area and borehole information.

The establishment and training of BP neural networks are implemented using computer software. Quasi-Newton algorithm is used for network training, and some relative parameters are shown in Table

Parameter settings.

Parameter | Value |
---|---|

Maximum number of training | 1000 |

Count of hidden layers | 8 |

Learning rate | 0.01 |

Training requirements accuracy | 0 |

Figure

Borehole distribution.

The operation results of BP neural network are shown in Figures

Error performance curve.

Regression analysis chart of sample data.

As mentioned above, 2 boreholes are used for testing. Table

Comparison of the 3 interpolation methods.

Borehole number | Location | Interpolation method | Number of borehole for calculation | Elevation of boundary between soil layer and rock layer (m) | ||
---|---|---|---|---|---|---|

Actual | Predicted | |||||

B11 | 470.55 | 118.36 | Triangulation | B05, B07, B08 | −5.9 | −5.97 |

Inverse distance weighting | All | −12.28 | ||||

BP neural network | All | −5.9 | ||||

Triangulation | B05, B06, B11 | −11.47 | ||||

B12 | 262.15 | 146.36 | Inverse distance weighting | All | −10.3 | −11.23 |

BP neural network | All | −10.3 |

In addition, the BP neural network also provides a way to estimate the maximum error of the elevation of boundary between the soil layer and rock layer. If

In this study,

In the modeling based on triangulation interpolation, the number and distribution of boreholes have a great impact on the partitioning of natural neighbors. Therefore, it can be inferred that the virtual drilling arrangement is an important part in the modeling using the interpolation method of triangulation combined with BP neural network. 4 steps of virtual drilling arrangements are made in this paper, aiming at obtaining a more accurate 3D model. Figure

Steps of virtual drilling arrangement. (a) Step 1. (b) Step 2. (c) Step 3. (d) Step 4.

Figure ^{3}, compared to step 3. This result has reached the owner’s request, and the final statistic of rock is 362,131 m^{3}.

Amount of rocks in each step.

After completing the arrangement of virtual drilling, the 3D model can be established, as shown in Figure

3D model of the dredging area: (a) front view; (b) vertical view.

Sensitively generated surface models have a crucial importance for the optimum planning and 3D modeling. In this study, a new interpolation method is used for modeling a surface of the rock layer. Based on a dredging project, the result is compared with 2 conventional interpolation methods.

As a result, some merits of the interpolation method of triangulation combined with BP neural network have been recorded. First, this method has provided more accurate results. Second, it gives a way to calculate the maximum error of interpolation points, and the training accuracy rate of BP neural network is considered to be closely related to the error.

Finally, the 3D model of the dredging area is established using this new interpolation method, and the statistic of rock is determined. This case of application aims to provide a new example for material reserve estimation.

The data used to support the findings of this study are available from the corresponding author upon request.

The BP neural network calculation has been done by using the MATLAB2016a software, The relative code is wrote by the corresponding author of this paper, and the name of code is sci-code. The repository link is

The authors declare that they have no conflicts of interest.