1. Introduction
With the continual growth in global demand for mineral resources, deep-sea mining has become an important direction for resource development. The seabed is rich in mineral resources, including polymetallic nodules, cobalt-rich crusts, and hydrothermal sulfides [
1,
2]. However, its development faces numerous technical challenges. Among these, the deep-sea mining transportation system plays a crucial role in deep-sea mining. This system, responsible for transporting seabed ore or slurry to the surface, is a central hub directly affecting mining efficiency and system safety [
3]. The deep-sea mining transportation system connects the mining vehicle, intermediate storage, and the surface mothership through pipelines, with seabed collected slurry transported via flexible soft hoses and lifting hard pipes [
4]. In the deep-sea environment, the transportation pipelines are subjected to various loads, including their own weight, buoyancy, forces from waves and currents, resistance and pressure from seawater. Studying the force situation of transportation pipelines and effectively predicting other mechanical parameters based on existing monitoring data to ensure the pipelines operate within a safe load range has significant implications for designing mining operation schemes, mining vehicle path ranges, and pipeline material performance.
Due to the extreme complexity of the deep-sea environment, deep-sea mining experiments require significant financial and human resources and need to address many uncontrollable risks. Establishing mathematical models of ocean environments and system equipment through numerical simulation to study the stress conditions of transportation pipelines can yield vast amounts of simulation data for constructing predictive models of pipeline mechanical characteristics. Currently, numerical simulation methods for calculating pipeline stress primarily include the concentrated mass method [
5], finite difference method [
6], and finite element method [
7].
In the study of lifting hard pipe mechanics, American scholars such as Felippa, Chung, and Whitney have employed the finite element method to analyze the kinematic and dynamic characteristics of a 5486 m long lifting hard pipe [
8,
9,
10,
11,
12]. They used three-dimensional beam elements to build the model, which is capable of axial, bending, and torsional coupled deformation. The pipeline model includes 18 elements, 19 nodes, and 114 degrees of freedom. In subsequent studies by Chung et al., the finite element method was further applied to research the static and dynamic behavior of deep-sea mining lift pipes and their attachments [
13,
14,
15]. To reduce the vibration effects of marine hydrodynamics on lifting pipes, Chung, Cheng, and others designed several elastic damping connection devices on the pipeline and modeled the pipeline system using the finite element method and mass–spring element method for static and dynamic analysis [
16,
17,
18,
19,
20]. Moreover, Mustoe, Huttelmaier, Cheng, and others used the Discrete Element Method (DEM) for the kinetic analysis of deep-sea mining lift pipes under 2D axial and bending coupling. This discrete element pipe description method is based on a system composed of rigid bodies connected by concentrated axial and bending stiffness. Mustoe and others conducted four nonlinear dynamic analyses with a 2D DEM model of an 5486 m deep-sea mining pipeline [
21,
22]. Huttelmaier applied the Discrete Element Method to calculate a 1905 m long marine vertical pipeline, including axial and bending deformations, and compared the results with the finite element method and analytical method [
23]. Sup Hong based on the concentrated mass method and incremental iterative method, conducted a three-dimensional dynamic analysis of the deep-sea subsea mining lift pipe system, completing axial forced vibration in a vertical state and three-dimensional nonlinear dynamic analysis within the time domain [
24,
25]. Wu employed the stochastic phase spectrum method to generate random wave forces and vortex-induced excitations acting on risers in the time domain. He proposed a parametrically excited top-tensioned riser model that was simultaneously subjected to random wave and vortex-induced excitations [
26].
In the study of flexible hose mechanics, Ghadimi [
27] proposed a method for calculating the spatial shape and stress state of flexible hoses. This mathematical model principle involves dividing the hose into several mass–spring segments to analyze the force and motion relationship of the segments. Ablow and Schechter [
28] conducted a finite difference analysis on submarine cables, combined with the system dynamics characteristics to establish and solve the differential equations of the flexible cable. Bernitsas et al. derived the mathematical three-dimensional equilibrium equations for flexible hoses and utilized the U.L. method to solve the equilibrium equations through the three-dimensional large displacement finite element incremental method [
29]. Nordgren utilized the finite time integration method to analyze the situation where one end of the flexible hose was fixed and the other end was freely falling, under the assumption that the axial and shear effects of the hose were neglected [
30]. Based on the static characteristics of the hydraulic conveying pipeline, Xu obtained a three-dimensional spatial model of the hose and conducted numerical simulations on the static displacement of the hydraulic lifting pipeline under steady-state conditions [
31]. Wang utilized the OrcaFlex software to simulate the laying of a flexible pipeline with an outer diameter of 352.42 mm on the seabed at a depth of 3000 m. The study investigated the axial tension, bending moment, and stress–strain dynamics of the pipeline during the laying process and analyzed factors influencing the dynamic behavior of the pipeline [
32].
Based on fundamental mechanics research, significant progress and breakthroughs have been achieved in recent years in the prediction and estimation of mechanical properties. Buljak, Maier, and others used inverse analysis to diagnose the mechanical properties and structures of materials, which aids in assessing potentially deteriorated material performance and mechanical damage within structures [
33]. The combination of “drilling” methods with indentation tests and inverse analysis has been utilized to evaluate residual stress and mechanical properties, effectively reducing the additional damage and costs typically associated with conventional diagnostic procedures for structural components [
34]. Zhang developed a stress prediction model based on synthesized nonlinear coefficients, which can effectively assess the stress state of specimens [
35]. Song proposed a multimodal fusion prediction model that integrates material microstructure information and compositional data, providing a promising solution for the measurement and prediction of material properties [
36].
Despite the rich force analysis provided by past research, there remains a significant challenge in force prediction, especially in quickly predicting under conditions of insufficient monitoring data. This paper aims to address this issue by establishing a simulation model of the deep-sea mining system and conducting static and dynamic simulation analyses on lifting hard pipes and hoses, further building a predictive model of pipeline mechanical characteristics based on the BP neural network, thereby providing guidance for the safety and reliability of the deep-sea mining transportation system.
2. Deep-Sea Mining Transportation Pipeline Mechanics Analysis
The deep-sea mining transportation pipeline, serving as a vital hub transporting seabed-collected polymetallic nodules to the surface and connecting the mining vehicle, intermediate storage, and mining ship, plays a critical role in system operation safety. To further investigate the motion laws and stress characteristics of the transportation pipeline in deep-sea mining operations and establish its mechanical prediction model, this section conducts static and dynamic analyses of the deep-sea mining transportation pipeline. This will provide a theoretical reference for subsequent simulation analysis and predictive model construction.
2.1. Static Analysis of Deep-Sea Mining Transportation Pipeline
The deep-sea transportation pipeline is considered a slender structure in marine engineering. Its static analysis usually employs the catenary equation [
37]. The application of catenary theory [
38] allows for a precise analytical calculation of the pipeline. Considering a differential segment,
, the catenary model is illustrated in
Figure 1. Here,
represents the gravitational force per unit length of the pipeline,
denotes the angle between the pipeline unit’s tangent and the horizontal direction, and
and
are, respectively, the vertical and horizontal components of tension.
Based on the force balance analysis, the following is concluded:
Assuming the constant
, substituting
into Equation (2) yields
In the equation,
, and substituting this into Equation (3) yields
Integrating Equation (4) yields
2.2. Dynamic Analysis of Deep-Sea Mining Transport Pipelines
This study is based on the Euler–Bernoulli beam theory [
39] to analyze the dynamics of deep-sea transport pipelines, considering the coupling of the fluid and pipeline. It is assumed that the deformation of the transport pipeline is a small displacement, and the internal fluid is an ideal incompressible fluid. By analyzing the forces on the pipeline element
, the motion control equations of the transport pipeline in a three-dimensional coordinate system are obtained. As shown in
Figure 2,
Figure 2a illustrates the force analysis on the pipeline wall, where
is the axial tension of the pipeline,
is the pressure of the internal fluid on the wall,
is the frictional resistance of the internal flow on the wall, and
is the shear force of the pipeline.
Figure 2b depicts the force analysis on the internal fluid of the pipeline.
The force balance equation for the small section of the pipeline wall in
Figure 2a is as follows, where Equation (6) represents the Z-direction balance equation, and Equation (7) represents the Y-direction balance equation:
In the equations, represents the circumference inside the conveying pipeline, is the mass per unit length of the conveying pipeline, is the acceleration due to gravity, is the cross-sectional area outside the conveying pipeline, is the pressure acting on this outer cross-section, is the density of the fluid outside the conveying pipeline, represents the buoyancy acting on the outer cross-section, is the damping coefficient, shear force , where is the bending stiffness of the conveying pipeline, is the static water pressure, and is the external force acting on the Y-direction conveying pipeline.
The force balance equation for the fluid element in
Figure 2b is as follows, where Equation (8) represents the Z-direction balance equation, and Equation (9) represents the Y-direction balance equation:
In the equations, represents the cross-sectional area inside the conveying pipeline, is the internal fluid pressure, and is the mass per unit length of the internal fluid in the conveying pipeline.
Combining Equations (6) and (8), the following expression is derived:
In the equation,
represents the fluid velocity inside the conveying pipeline. Assuming
is the total length of the conveying pipeline, integrating Equation (10) from
to
yields the following expression:
In the equation,
is the tension at the top of the conveying pipeline, and
is the internal fluid pressure of the conveying pipeline. From Equations (7), (9) and (11), the
y-direction and
x-direction motion equations of the conveying pipeline can be obtained as follows:
In the equation, and are the forces exerted on the conveying pipeline in the x and y directions by the fluid.
5. Conclusions
Based on the analysis of the mechanical theory of deep-sea mining transportation pipelines, this paper establishes a simulation model for deep-sea mining systems and conducts static and dynamic analyses of the deep-sea mining transportation pipelines. It innovatively combines 64 sets of working condition test schemes through orthogonal experiments and establishes, for the first time, a pipeline mechanical characteristic prediction model based on the BP neural network. The main work and conclusions of this paper are as follows:
- (1)
In the OrcaFlex 11.0 software, an overall interactive simulation analysis model of the deep-sea mining system is established. A static analysis of the lifting hard pipe and hose is conducted to obtain key parameters of the pipeline’s mechanical characteristics. Using an orthogonal experimental design, a total of 64 sets of experimental conditions are combined to analyze the dynamic simulation of the deep-sea mining transportation pipeline system. A total of 32,064 sets of simulated sensor data are obtained for training and testing the mechanical prediction model of the pipeline.
- (2)
A predictive model is constructed based on the BP neural network for the effective tension at the top of the lifting hard pipe, the effective tension at the position of 107.5 m along the hose, the bending radius at the position of 132.5 m along the hose, and the bending moment. The impact of ocean current speed and angle on the mechanical parameters of the hose is studied, and the mechanical parameters of each node of the hose are predicted. The trained BP neural network model has average absolute error (MAE) and root mean square error (RMSE) values close to 0, with correlation coefficients close to 1. There is a strong linear positive correlation between the predicted values and the simulated values. The trained neural network model can serve as a predictive model for the mechanical characteristics of the transportation pipeline. By inputting sensor data, it can predict the changes in the mechanical parameters of critical points in the transportation pipeline, ensuring that the tension of the lifting hard pipe, hose tension, bending radius of the hose, and bending moment remain within safe limits. In the event of safety risks, adjustments to the mining operation plan can be made promptly to avoid pipeline failure, breakage, or excessive bending deformation.
Currently, in actual deep-sea mining operations, the sensor parameters related to the mechanical properties of the conveying pipelines that can be monitored include wind speed, wave period, significant wave height, current speed, current angle, and the strain of the pipeline. This paper innovatively takes the dynamic simulation results of multiple working conditions from the earlier orthogonal experiment combinations as simulation sensor data. By employing machine learning methods, a predictive model of pipeline mechanical properties is constructed for the first time, with the monitorable sensor parameters serving as input for model training. This model predicts mechanical parameters that are difficult to monitor in actual deep-sea mining operations. It analyzes the variation patterns of mechanical parameters of the conveying pipeline under different environmental loads to ensure that the pipeline operates within the mechanical parameter range designed for the pipeline. This study can ensure the safety of deep-sea mining operations by predicting the performance of pipelines in extreme marine environments, identifying and addressing potential structural weaknesses in advance, and helping to extend the service life of pipeline systems. In addition, predicting mechanical properties can promote an efficient exploitation of deep-sea resources and support the goal of sustainable development.