A Data-Driven Intelligent Prediction Approach for Collision Responses of Honeycomb Reinforced Pipe Pile of the Offshore Platform

Abstract

The potential collision between the ship and the pipe piles of the jacket structure brings huge risks to the safety of an offshore platform. Due to their high energy-absorbing capacity, honeycomb structures have been widely used as impact protectors in various engineering applications. This paper proposes a data-driven intelligent approach for the prediction of the collision response of honeycomb-reinforced structures under ship collision. In the proposed model, the artificial neural network (ANN) is combined with the dynamic particle swarm optimization (DPSO) algorithm to predict the collision responses of honeycomb reinforced pipe piles, including the maximum collision depth (δ_max) and maximum absorption energy (E_max). Furthermore, a data-driven evaluation method, known as grey relational analysis (GRA), is proposed to evaluate the collision responses of the honeycomb-reinforced pipe piles of offshore platforms. Results of the case study demonstrate the accuracy of the DPSO-BP-ANN model, with measured mean-square-error (MSE) of 5.06 × 10⁻⁴ and 4.35 × 10⁻³ and R² of 0.9906 and 0.9963 for δ_max and E_max, respectively. It is shown that the GRA method can provide a comprehensive evaluation of the performance of a honeycomb structure under impact loads. The proposed model provides a robust and efficient assessment tool for the safe design of offshore platforms under ship collisions.

1. Introduction

In the past decades, with the increase in the number of offshore platforms and marine traffic, the corresponding risks of collision between bypassing ships and platforms have amplified [1,2,3]. Collision accidents may cause severe damage to the structure of the platform, or even result in the collapse of the whole platform, causing huge losses and endangering the safety of the personnel. In 2009, the Ekofisk 2/4 three-legged jacket platform collided with the well workover vessel Big Orange XVIII [4], which caused severe damage to the jacket and caused ruptures in several braces. Most relevant industry standards, such as DNV [5,6], NORSOK N-003 [7] and ISO 19902 [8] refer to the ship collision accident as an important sudden risk in the design of the offshore platform. Thus, it is crucial to carry out collision response predictions and protective design measures for the offshore platform structures.

During a ship collision scenario, the pile legs and braces of offshore platforms, usually composed of tubular members, are the key components of impact protection. In order to mitigate the damage to tubular members caused by ship collision, researchers have proposed some protective measures or strengthening schemes for tubular structures. Due to their excellent anti-impact energy-absorbing capacity, honeycomb structures have been widely used in the field of impact protection [9,10,11]. In recent years, researchers [12,13] have developed a series of honeycomb structures with different geometric forms to improve better performances in anti-impact. In 2018, Gao et al. [14] proposed a negative Poisson’s ratio honeycomb structure with a double V-shaped cylindrical geometry, which can better absorb the impact energy and thus could provide better protection for the structure. In a different research work, Lin et al. [15] studied the dynamical performance of the honeycomb-reinforced pipe leg with a hexagonal honeycomb and arrow honeycomb by using the numerical simulation software ANSYS/LS-DYNA.

Structural analysis of the collision response is typically implemented using finite element (FE) numerical modelling techniques and by using commercial packages such as LS-DYNA [16,17] or ABAQUS [18] to obtain the structural dynamic responses under ship collision [19,20,21]. Travanca and Hao [16,17] used LS-DYNA to carry out a series of FE simulations for ship collision cases with three different jacket platforms. Moulas et al. [18] presented a nonlinear FEA method for evaluating the structural damage caused by ship impact. Rigueiro et al. [20] conducted numerical simulations for the process of a ship colliding with the pile leg of an offshore platform. However, finite element analysis of complex problems such as the dynamic response analysis of a platform under ship collision, becomes a daunting task due to the computational cost, the need for calibration of various parameters within the commercial package and modelling difficulties such as instabilities and non-convergence.

In essence, the finite element analysis method of the structural system provides a mapping relationship, which can map the input parameters (geometry, material, load, etc.) to the structural response (stress, strain, displacement, etc.). As a general and successful function-approximation method, the artificial neural network (ANN) is known to be effective in approximating complex nonlinear mapping relationships [22,23]. In recent years, ANN models have been successfully applied to structural response predictions and analyses [24,25,26,27,28,29]. Lu et al. [28] used the GA-based ANN model to predict the structural response caused by dropped object collision and carried out failure probability analysis. More recently, Li, J. et al. [29] developed an ANN model for the prediction of the peak pressure of BLEVE (Boiling Liquid Expanding Vapour Explosion). However, due to its inherent nature as a gradient-based descent algorithm, the traditional BP-ANN model inevitably leads to some shortcomings such as local optimum and the restrictions of error function derivability. Therefore, by incorporating some global optimizing algorithms such as the genetic algorithm (GA) and particle swarm optimization (PSO) into the training process of the BP algorithm, researchers have proposed a series of hybrid ANN models such as the GA-ANN model and PSO-ANN model and provided some useful results in the relevant literatures [30,31,32,33,34,35,36]. Li et al. [35] used SSA-LSTM and SSA-BP ANN models to predict the maximum pitting corrosion depth of subsea oil pipelines. Lin et al. [36] proposed a hybrid ANN model to predict the collision responses of offshore platform structures by combining the DPSO algorithm with the BP-ANN model, which also proved that the DPSO-ANN model can be regarded as an effective alternative of the time-consuming FEA method.

A fundamental issue is to how to utilize the results of collision response to carry out a data-driven assessment for the anti-impact performance of honeycomb structures. For the evaluation problem of the collision responses of honeycomb structures, researchers have proposed some common assessment indexes, such as maximum collision depth δ_max and maximum absorption energy E_max [12,14]. Grey relational analysis (GRA) is an attractive tool for addressing multi-index evaluation problems, successfully used in various engineering fields [37,38]. In this paper, GRA is used to evaluate the anti-impact performance of the honeycomb structure.

As stated above, the FEA method is normally very time-consuming, especially for the analysis and evaluation of dynamic responses of structures under ship collision. Therefore, it is very necessary to develop a fast and efficient prediction and evaluation approach for the collision responses of the honeycomb structure as an alternative to the traditional FEA methods. In order to fill the knowledge gap of fast prediction and efficient evaluation of the collision responses of the honeycomb structure, this paper aims to develop a data-driven intelligent prediction and assessment approach supporting the safety design of offshore platform structures under collision accidents. Combining with the Latin hypercube sampling (LHS) method, the DPSO algorithm is integrated into the BP-ANN model for predicting the collision responses of honeycomb-reinforced pipe piles under ship collision. Further, GRA is carried out to predict collision responses and evaluate the anti-impact performance of honeycomb-reinforced pipe piles under ship collision. This study provides an intelligent and data-driven prediction and evaluation approach for the collision responses of honeycomb-reinforced pipe piles of offshore platforms, which can also be applied to the prediction and evaluation of other marine facilities to promote intelligence and digitization in ocean engineering.

2. Methodology

2.1. Research Framework

The research framework of the proposed approach and process for prediction of the collision responses of the honeycomb structure are presented in Figure 1.

Stage 1: in this stage, for the selected collision parameters (collision velocity v_s, mass of ship m_s and collision angle φ_s), the LHS method is used to generate scenarios for the training and testing of the ANN model. Then, the specific FEA is conducted for each group of collision parameters (v_s, m_s, φ_s) in LS-DYNA to calculate the corresponding collision responses (such as maximum collision depth δ_max and maximum absorption energy E_max) of the honeycomb-reinforced pipe piles of the offshore platform. The raw data are pre-processed through mapping within a specified range, [0, 1], and is used as input and target data for the ANN model.

Stage 2: in this stage, the preprocessed data are used to train and test the ANN model. In the training process of the ANN model, the dynamic particle swarm optimization and BP algorithms are conducted, respectively, for the global optimization and local optimization of the weights and the thresholds of the ANN model. The trained DPSO-BP-ANN model can predict the collision responses of the honeycomb-reinforced pipe piles of offshore platforms faster than the conventional FEA method, especially in a multi-collision scenario investigation.

Stage 3: in this stage, the grey relational analysis (GRA) is carried out for the prediction results of the collision responses obtained via the DPSO-BP-ANN model, and a new GRA-based assessment index is established for evaluating the anti-impact performance of honeycomb-reinforced pipe piles under ship collision.

2.2. Honeycomb Reinforced Pipe Structure

The honeycomb structure was used to reinforce the pipe piles of the offshore jacket platform, as shown in Figure 2. There are some different types of honeycomb cells applied in the honeycomb structure, such as hexagonal cells and arrow cells. The hexagonal honeycomb structure is used herein, due to its availability and common usage in practice.

2.3. Latin Hypercube Sampling (LHS)

Selection of the training samples with high representativeness is a key influencing factor for the training of the ANN model. However, the random sampling method commonly used could not guarantee that the training samples generated would cover the entire variable space well, especially for the situations of multi-variable and small training samples. Latin hypercube sampling (LHS) is a method that can be used to generate random samples well-distributed evenly over the entire variable space. Moreover, the LHS method can significantly reduce the number of training samples needed to achieve the training accuracy of the ANN model. In order to generate well-distributed training sample coverage of the entire variable space for the ANN model, LHS is used to generate training samples with high representativeness scattering in the entire domain of the design variables.

In this study, we consider the factors affecting the collision responses of honeycomb-reinforced pipe piles under ship collision, including the collision velocity v_s, the mass of ship m_s and the collision angle φ_s. According to the value range of each collision parameter, the LHS is used to generate 50 collision scenarios in total, in which 40 collision scenarios are randomly selected for training of the ANN model. The remaining 10 collision scenarios are used for testing of the ANN model.

2.4. Artificial Neural Network (ANN) Model

In this study, we adopt a three-layer neural network model: (i) input layer, (ii) hidden layer and (iii) output layer. The neuron number of each layer is denoted by n, m and l, respectively. The neurons in different layers of the neural network are connected via the activation function, weights W₁, W₂ and thresholds θ₁, θ₂. Here, the sigmoid function is selected as the activation function:

$$f(x)=1/(1+e^{-x})$$

(1)

In the training process of the ANN model, the weights W₁, W₂ and thresholds θ₁, θ₂ of the neural network are defined as the optimization variables. These weighting factors are iteratively adjusted using the optimization algorithm and during the learning and recall processes. This ensures that outputs of the ANN model can approximate target outputs of the training samples gradually.

To define the approximation accuracy of the ANN model output to the target output, the mean square error (MSE) of the neural network is adopted and regarded as the objective function of the optimization algorithm:

$$MSE=\frac{1}{S\times l}{\displaystyle \sum _{p=1}^S{\displaystyle \sum _{k=1}^l{(y{t}_{p,k}-y{r}_{p,k})}^2}}$$

(2)

where yt_p,k and yr_p,k are the outputs of the ANN model and target outputs of the training sample, respectively, and S is the number of training samples.

2.5. Dynamic Particle Swarm-BP (DPSO-BP) Optimization

In order to optimize the weights W₁, W₂ and thresholds θ₁, θ₂ of the ANN model, the dynamic particle swarm optimization and BP algorithms are used to perform global optimization and local optimization, respectively. Particle swarm optimization (PSO) is a swarm intelligence optimization algorithm and is inspired by flocks of birds or insects. In order to further improve the performance of the PSO algorithm, dynamic particle swarm optimization (DPSO) is utilized via dynamically adjusting inertia factor, ω, and acceleration factors c₁, c₂. The velocity and location of each particle in the DPSO algorithm are updated using the following formulae

$$V_i(k+1)=\omega (k)V_i(k)+c_1(k)r_1(P_i-X_i)+c_2(k)r_2(P_g-X_i{)}_{ }$$

(3)

$$X_i(k+1)=X_i(k)+V_i(k+1)$$

(4)

where V_i(k) and X_i(k) represent the velocity and location of t-th particle at the k-th iteration step, respectively; the inertia factor ω(k) and acceleration factors c₁(k), c₂(k) are adjusted according to the linear decreasing model [31,32].

Upon completion of the global optimization in the DPSO algorithm, the BP algorithm is exploited to carry out a local optimization for weights W₁, W₂ and thresholds θ₁, θ₂. The BP algorithm is a kind of gradient-based descent algorithm with better local convergence, and the adjustments of the weight and threshold are given as the following formulas:

$$\Delta W=\eta (k)\frac{\partial MSE}{\partial W},\begin{array}{cc}& \Delta \theta =\eta (k)\frac{\partial MSE}{\partial \theta }\end{array}$$

(5)

where ΔW and Δθ are the adjustments of the weight and threshold, respectively; η(k) is the dynamic learning rate that is adjusted according to MSE during the iteration [31,32].

2.6. Grey Relational Analysis (GRA) Evaluation

As stated in the introduction section, grey relational analysis (GRA) is an attractive tool for addressing the multi-index evaluation problem. Here, A denotes the original evaluation matrix:

$$\mathit{A}=\left(\begin{array}{cccc}{a}_{1,1}& a_{1,2}& \cdots & a_{1,l}\\ a_{2,1}& a_{2,2}& \cdots & a_{2,l}\\ ⋮& ⋮& & ⋮\\ a_{S,1}& a_{S,2}& \cdots & a_{S,l}\end{array}\right)$$

(6)

where each row of matrix A represents an evaluation object denoted by r_i = (a_i,1, a_i,2,…, a_i,l) (i = 1, 2, …, S), and each column of matrix A represents an evaluation index denoted by c_j = (a_1,j, a_2,j,…, a_S,j)^T. In GRA evaluation, we first need to define a virtual optimal ideal solution as the reference sample, denoted by r₀ = (a_0,1, a_0,2,…, a_0,r), and then to calculate the grey correlation coefficient g_i,j of each element a_i,j in the evaluation matrix A (each index of each sample) to reference sample r₀:

$$g_{i,j}=\frac{\underset{1\le k\le S}{\min }\underset{1\le t\le l}{\min }\left|a_{0,t}-a_{k,t}\right|+\rho \underset{1\le k\le S}{\max }\underset{1\le t\le l}{\max }\left|a_{0,t}-a_{k,t}\right|}{\left|a_{0,j}-a_{i,j}\right|+\rho \underset{1\le k\le S}{\max }\underset{1\le t\le l}{\max }\left|a_{0,t}-a_{k,t}\right|}, \left(i=1, 2, \dots ,S,j=1, 2, \dots ,l\right)$$

(7)

where ρ represents the resolution coefficient. Further, the GRA assessment index could be defined by calculating the grey relational grade G_i of the evaluation object:

$$G_i=\mathit{w}\cdot {\mathit{g}}_i{}^T$$

(8)

where G_i is the GRA assessment index of the ith evaluation object r_i = (a_i,1, a_i,2,…, a_i,l); w is the weight vector of the evaluation indexes, denoted by w = (w₁,w₂,…,w_l); g_i is the grey correlation coefficient vector of the ith evaluation object, denoted by g_i = (g_i,1, g_i,2,…g_i,l). It means that the quantitative evaluation could be conducted for each evaluation object r_i = (a_i,1, a_i,2,…, a_i,l) by utilizing the GRA index G_i.

3. FE Model and Collision Scenarios

3.1. FE Model

To demonstrate the procedure and efficiency of the model, a case study of a four-legged jacket platform is presented herein. The corresponding FE model and the mesh are shown in Figure 3a. The hexagonal honeycomb structure is modelled in the vicinity of one of the piles of the jacket platform. The honeycomb-reinforced pile structure in the collision scenario is displayed in Figure 3b. The validation, calibration and mesh sensitivity of the FEA is published in a previous study by the current authors [15].

3.2. Collision Scenarios

3.2.1. Collision Parameters

As stated in Section 2.3, the collision velocity v_s, the mass of the ship m_s, and the collision angle φ_s (as shown in Figure 4) are the chosen collision parameters. The added mass coefficient is introduced to consider the influence of the surrounding water. The collision parameters are listed in

Table 1. The ranges of collision parameters.

Collision Parameter	Range
Ship collision velocity, vs	0–2 m/s
Mass of ship, ms	3000–5000 tons
Added mass coefficient, ca	1.05
Collision angle, φs	0°, 15°, 30°, 45°, 60°

.

3.2.2. Collision Scenarios via LHS Sampling

A total of 50 groups of collision scenarios were generated using the LHS sampling method, in which 40 collision scenarios were randomly selected for the training of the DPSO-BP-ANN model, and the remaining 10 groups were used for the testing of the DPSO-BP-ANN model. The training and testing scenarios are represented in

Table 2. 40 groups of collision scenarios for training selected via LHS sampling.

No.	vs (m/s)	ms (103 ton)	φs (°)	No.	vs (m/s)	ms (103 ton)	φs (°)
1	1.341	4.318	0	21	0.355	4.115	30
2	1.582	3.196	60	22	1.146	4.572	15
3	0.047	4.696	15	23	1.838	3.730	0
4	1.474	4.761	30	24	1.897	3.897	45
5	0.933	4.855	45	25	0.828	3.111	60
6	0.141	4.623	0	26	0.799	3.383	45
7	1.090	4.445	15	27	1.355	4.220	15
8	0.605	4.009	60	28	1.690	3.613	30
9	0.316	3.433	30	29	0.995	4.745	60
10	0.677	3.785	45	30	0.735	3.294	0
11	0.454	3.313	45	31	1.977	4.923	0
12	0.595	3.099	0	32	0.245	4.076	60
13	0.063	4.848	15	33	0.250	4.255	15
14	1.613	3.567	60	34	0.433	4.960	45
15	0.872	3.520	30	35	0.535	3.463	30
16	1.291	3.674	60	36	1.547	3.847	45
17	1.720	3.964	45	37	1.435	3.946	0
18	1.185	4.165	15	38	0.198	4.396	15
19	1.243	3.011	0	39	1.925	4.460	60
20	1.039	4.536	30	40	1.762	3.203	30

and

Table 3. 10 groups of collision scenarios for testing selected via LHS sampling.

No.	vs (m/s)	ms (103 ton)	φs (°)	No.	vs (m/s)	ms (103 ton)	φs (°)
1	1.648	3.367	0	6	0.507	4.969	45
2	0.252	3.067	15	7	1.558	4.609	60
3	0.051	3.621	45	8	1.980	4.092	15
4	1.379	3.897	30	9	0.835	3.464	30
5	0.664	4.259	60	10	1.165	4.593	0

, respectively.

4. Results and Discussions

4.1. Results of Collision Response Obtained from the FEA

For each group of collision parameters in Table 2 and Table 3, an explicit FEA of the collision scenario is carried out in LS-DYNA. Each group of collision response results consist of two variables: (1) the maximum collision depth δ_max, and (2) maximum absorption energy E_max. The collision response results of the FEA are represented in

Table 4. Collision response results of training samples obtained via FEA.

No.	δmax (m)	Emax (MJ)	No.	δmax (m)	Emax (MJ)
1	0.606	2.28007	21	0.244	0.249996
2	0.672	2.26494	22	0.589	2.10122
3	0.068	0.00461146	23	0.719	2.89533
4	0.733	2.54346	24	0.853	2.96361
5	0.604	1.72075	25	0.443	1.02603
6	0.096	0.0363084	26	0.479	1.02249
7	0.578	1.94234	27	0.652	2.31342
8	0.377	0.711563	28	0.73	2.53065
9	0.205	0.169672	29	0.574	1.81793
10	0.439	0.830656	30	0.367	0.757749
11	0.299	0.332752	31	0.825	3.52636
12	0.296	0.460952	32	0.177	0.122338
13	0.088	0.00874403	33	0.203	0.126513
14	0.71	2.41313	34	0.341	0.455302
15	0.488	1.27668	35	0.319	0.491481
16	0.621	2.02566	36	0.702	2.43963
17	0.776	2.73135	37	0.609	2.30004
18	0.594	2.05965	38	0.171	0.0809198
19	0.529	1.77956	39	0.873	3.17622
20	0.584	1.8563	40	0.716	2.49124

and

Table 5. Collision response results of testing samples obtained via FEA.

No.	δmax (m)	Emax (MJ)	No.	δmax (m)	Emax (MJ)
1	0.606	2.28007	6	0.244	0.249996
2	0.672	2.26494	7	0.589	2.10122
3	0.068	0.00461146	8	0.719	2.89533
4	0.733	2.54346	9	0.853	2.96361
5	0.584	1.8563	10	0.716	2.49124

, respectively, for the training samples and testing samples.

4.2. Predictions of Collision Response Using DPSO-BP-ANN Model

4.2.1. Training and Testing Performance of DPSO-BP-ANN Model

The DSPO-BP-ANN model is established as stated in Section 2.4 and Section 2.5. A total of 40 groups of training data in Table 2 and Table 4 were used to train the DSPO-BP-ANN model, and 10 groups of testing data in Table 3 and Table 5 were used for testing the model. The MSE and coefficients of determination R² are outlined in

Table 6. MSE and R² of DPSO-BP-ANN models for training and testing.

	MSE of Training Samples	R2 of Training Samples	MSE of Test Samples	R2 of Test Samples
Maximum collision depth	9.17 × 10−5	0.9982	5.06 × 10−4	0.9906
Maximum absorption energy	7.25 × 10−4	0.9993	4.35 × 10−3	0.9963

.

Figure 5 and Figure 6 present regression diagrams of the results of DPSO-BP-ANN model against the results of the FEA.

The results of MSE and R² demonstrate that the DPSO-BP-ANN model has good performance for both training and testing samples.

4.2.2. Prediction Results of DPSO-BP-ANN Model

The trained DPSO-BP-ANN model was applied to predict the collision responses for the training and testing samples. The prediction results are listed in

Table 7. Prediction results of DPSO-BP-ANN model for training samples.

No.	δmax (m)	Emax (MJ)	No.	δmax (m)	Emax (MJ)
1	0.598	2.31044	21	0.255	0.26049
2	0.668	2.29116	22	0.605	2.07022
3	0.091	0.02273	23	0.724	2.89908
4	0.734	2.59349	24	0.832	2.96517
5	0.589	1.73250	25	0.453	1.00267
6	0.109	0.02503	26	0.465	1.04364
7	0.584	1.94893	27	0.634	2.27394
8	0.386	0.68931	28	0.732	2.51790
9	0.208	0.20089	29	0.581	1.81308
10	0.429	0.85609	30	0.370	0.75509
11	0.289	0.32877	31	0.829	3.43211
12	0.292	0.44537	32	0.174	0.12060
13	0.088	0.02342	33	0.191	0.11463
14	0.716	2.42005	34	0.341	0.43507
15	0.492	1.28216	35	0.330	0.49736
16	0.618	2.02600	36	0.708	2.38823
17	0.782	2.69315	37	0.611	2.32231
18	0.591	2.02691	38	0.157	0.07696
19	0.529	1.77600	39	0.860	3.20933
20	0.587	1.88795	40	0.717	2.51321

and

Table 8. Prediction results of DPSO-BP-ANN model for testing samples.

No.	δmax (m)	Emax (MJ)	No.	δmax (m)	Emax (MJ)
1	0.645	2.44266	6	0.401	0.61892
2	0.159	0.14548	7	0.783	2.69604
3	0.112	0.05066	8	0.830	3.19637
4	0.649	2.19267	9	0.475	1.17844
5	0.422	0.90463	10	0.587	2.07228

and compared with the collision response results of the FEA (Table 4 and Table 5).

Figure 7 and Figure 8 present comparisons between the DPSO-BP-ANN and FEA. A reasonable correlation between the DPSO-BP-ANN and FEA is observed. The DPSO-BP-ANN model is shown to be an efficient alternative for the conventional FEA method and can predict the collision responses of the honeycomb-reinforced pipe piles reliably.

4.3. Effects of Collision Parameters on the Predictive Results

Figure 9 shows curves of maximum collision depth δ_max and maximum absorption energy E_max varying with the collision velocity under five different ship masses of 3000, 3500, 4000, 4500, and 5000 tons. It is seen that both δ_max and E_max increase significantly with the collision velocity increasing, which means that the collision velocity is a key factor influencing the collision responses of honeycomb-reinforced pipe piles. In a low-velocity collision, the influence of the mass of the impactor (the ship) on both δ_max and E_max is not significant. Conversely, in the situation of a high-velocity collision, both δ_max and E_max under the collisions of large tonnage ships increase significantly. Thus, with the high-velocity collision of large tonnage ships, the collision protection requires a meticulous design and protective planning.

Figure 10 presents the curves of the maximum collision depth δ_max and maximum absorption energy E_max against the collision angle under five different collision velocities (0.4, 0.8, 1.2, 1.6, and 2.0 m/s). At low-velocity collisions (0.4 m/s), the influence of the collision angle on δ_max are slight, and δ_max increases significantly with an increase in the collision angle under medium- and high-velocity collisions. The maximum absorption energy E_max initially increases and then decreases with the increasing of the collision angle in the contexts of medium- and low-velocity collisions, and E_max reaches the peak value when the collision angle is in the range of 20–30 degrees. At high-velocity collisions, E_max initially decreases rapidly and then surges slightly with an increase in the collision angle.

4.4. Evaluations of the Collision Reponse

Prior to the conduct of the GRA evaluation the original data of collision responses are transformed to benefit-type and standardized data [36]. Then, as stated in Section 2.6, the grey relational analysis (GRA) evaluation is carried out for the preprocessed data. Since all the data for evaluating has been transformed to benefit-type data, a larger value for the GRA index G_i is derived which provides a better evaluation of the collision response results.

In this section, the effects of the collision parameters on the GRA evaluation results are analyzed. Figure 11 presents the three-dimensional scatter diagram of the GRA evaluation results with regard to the collision angle and the corresponding mass of the ship. As shown in Figure 11, under the collision of a small tonnage ship, the GRA index reflects the better performance of honeycomb-reinforced pile structures, which is consistent with our common understanding of honeycomb sandwich structures. Additionally, the influence of the collision angle on the GRA index is not significant under the collision of large tonnage ships. Conversely, for the collision of the small tonnage ship, the GRA index first increases and then decreases with the increasing of collision angle, and the GRA index reaches optimal performance at a collision angle of 30°.

Figure 12 presents the three-dimensional scatter diagram of GRA evaluation results with regard to the collision velocity and mass of the ship. The combined effects of the collision velocity and mass of the ship on the GRA index are apparent. At low-velocity collisions, as opposed to high-velocity collisions, the mass has a larger influence on the GRA index. Moreover, the GRA index reaches optimal performance in the situation of a low-velocity collision with small tonnage ships.

Figure 13 presents the three-dimensional scatter diagram of GRA evaluation results with regard to the collision velocity and collision angle. The influence of collision velocity on GRA index is significant, and the GRA index increases with a decrease in the collision velocity. The influence of the collision angles on the GRA index is not noteworthy at high-velocity collisions. Conversely, under the situation of low-velocity collisions, the GRA index first increases and then decreases at larger angles, and the GRA index reaches optimal performance when it is close to a 30° collision angle.

5. Conclusions

This paper proposed a data-driven intelligent approach for the prediction of the collision responses of honeycomb-reinforced pile structures under ship collisions. The proposed DPSO-BP-ANN model as an alternative to the conventional FEA methods is combined with the LHS sampling to predict the collision responses. Additionally, a data-driven GRA evaluation method was proposed to evaluate the collision responses of honeycomb-reinforced piles under ship collision scenarios. The most important findings from the current investigation are:

(1)

The DPSO-BP-ANN model combined with the LHS can reasonably predict the results of the FEA in both training samples and testing samples. MSEs of the training samples are 9.17 × 10⁻⁵ and 7.25 × 10⁻⁴, respectively, for the two response variables (δ_max and E_max), and the coefficients of determination R² are 0.9982 and 0.9993, respectively, for δ_max and E_max. In the testing samples, the MSEs are 5.06 × 10⁻⁴ and 4.35 × 10⁻³, respectively, for δ_max and E_max, and the coefficients of determination R² are 0.9906 and 0.9963, respectively, for δ_max and E_max.

(2)

At low-velocity collisions, the mass of the ship does not have a large influence on either δ_max and E_max. Conversely, in a high-velocity collision, both δ_max and E_max are significantly affected by the mass of the impacting ship. This demonstrates the high risks involved in a high-velocity collision incident with a large tonnage ship. In the situation of low-velocity collisions (0.4 m/s and below), the influence of the collision angle on δ_max is marginal, whereas δ_max increases significantly with the collision angle and becomes more detrimental in medium- and high-velocity collisions. E_max initially increases and subsequently decreases with the surge in angle in medium- and low-velocity collisions. E_max reaches a peak value between 20° to 30° collision angles.

(3)

The GRA index fluctuates with an increase and decrease in the collision angles, in small tonnage ships or at low-velocity collisions. The GRA index reaches an optimal performance at a collision angle of around 30°. Therefore, for the situations of the low-velocity approaching of small tonnage ships, it is recommended to keep the direction angle at about 30 degrees, to optimize the protective performance of the honeycomb structure. In low-velocity collisions, the influence of the mass of the ship on the GRA index is more substantial than that at a high-velocity collision.

The current work aimed to develop an intelligent and data-driven approach for the fast prediction and evaluation problem of collision responses of honeycomb-reinforced pile structures. The models and approaches proposed in this study are deemed to provide an efficient tool for engineers in the safe design of offshore facilities prone to collision incidents.