Offshore Wind Power Foundation Corrosion Rate Prediction Model Based on Improved SHO Algorithm

Abstract

To improve the accuracy of offshore wind power foundation corrosion rate prediction and grasp the operation status of equipment in time, an offshore wind power foundation corrosion rate prediction model based on an improved spotted hyena optimization (SHO) algorithm is proposed in this paper. Firstly, in order to reduce the modeling workload of the offshore wind power foundation corrosion prediction model, kernel principal component analysis (KPCA) is used to extract the principal elements of the offshore wind power foundation corrosion rate. Secondly, for the problems in the SHO algorithm, it is easy to fall into local optimums, and the solution accuracy is not high; the SHO algorithm is improved by the convergence factor and Levy flight strategy, which gives the SHO algorithm stronger global search ability and convergence speed. Finally, based on the improved SHO algorithm, an offshore wind power base corrosion rate prediction model is established by optimizing the penalty parameter and kernel function parameter. Simulation results show that the average relative error, root mean square error, and global maximum relative error assimilation coefficient of the combined prediction model in this paper are 2.86%, 0.15, 3.74%, and 0.995, respectively, which are better than other corrosion prediction models.

1. Introduction

With the popularization of industrialization, traditional fossil energy as a non-renewable energy source can no longer meet the increasing energy demand [1,2]. The environmental pollution caused by fossil energy needs to be solved by the society. Therefore, it is a consensus among all sectors of society to realize the energy transition and develop non-polluting and renewable green energy sources to ease the energy pressure and reduce environmental pollution. As a renewable clean energy, wind energy has great development potential [3,4,5]. With the increasing maturity of offshore wind power technology, offshore wind power costs have dropped significantly, especially the “carbon peak” and “carbon neutral” dual-carbon target program. It is expected that more and more offshore wind farm construction projects will be implemented [6].

However, the environment in which offshore wind turbines are located is far more complex and harsh than onshore wind power. The harsh corrosive environments such as high salinity in the surface atmosphere, alternating wet and dry conditions in the seawater immersion at the submerged zone, and the attachment of marine organisms can cause serious corrosion hazards to the monopile foundations of offshore wind turbines [7,8]. The environmental loads on the monopile foundation are also much higher than those on land. In addition, the overturning bending moment caused by the towering structure of the wind turbine also exerts huge alternating tensile stresses on the monopile foundation. The corrosion, stress, and fatigue interact with each other, so the monopile foundation faces severe safety risks [9]. Therefore, researching an offshore wind power foundation corrosion rate prediction method to grasp the health state of the foundation is crucial for the operational safety of offshore wind turbines.

Monopile foundation is the most commonly used type of turbine foundation in offshore wind farms. Peralta S., Sasmito A. P., and Kumral M. focus on the hydrodynamic problems and structural strength problems that floating offshore wind turbine structures may encounter under wave and wind load, numerically analyze the pitting corrosion fatigue of floating offshore wind turbine foundations, and describe the influence of corrosion damage on the fatigue limit capacity of offshore wind turbine substructures [10]. Yang G., Chai Y., and Wang D. et al. combined the structural characteristics of offshore wind turbine monopile foundations, the corrosion environment, corrosion mechanism, and corrosion behavior of the different parts of offshore wind turbine monopile foundations located in different marine corrosive environment zones, which were analyzed and summarized [11]. For the characteristics of the various types of corrosion risks, corresponding corrosion protection measures are given. Regarding corrosion rate prediction method research, the literature [12] puts forward a kind of corrosion prediction model in the reinforcement of the concrete structures of offshore wind farms. Through indoor and outdoor experiments, machine learning, theoretical analysis, etc., the corrosion law, reaction mechanism, and judging method of steel structure are systematically researched. The above results are significant for studying offshore wind power foundation corrosion, but the model structure is complex, and it is easy to fall into the local optimal solution in the training process. L. Chen, J. Yang, and X. Lu proposed a genetic algorithm to predict the corrosion rate of metal in a place in South China [13]. Y. Jiang, H. Li, G. Yang, C. Zhang, and K. Zhao established a corrosion rate prediction model of the grounding networks by taking six influencing factors, such as resistivity, water content, salt content, and so on, as input parameters [14]. The corrosion sample capacity in the above literature is less than 100, which is a typical small sample, and the use of a BP neural network is not appropriate. For small sample data, the support vector machine fitting effect is better; the literature [15] uses the artificial bee colony algorithm to optimize the SVM parameters, the establishment of the grounding network corrosion rate prediction model, and corrosion test data to verify the practicality of the model. H. Zhao, Z. Li, S. Zhu, and Y. Yu used the extended memory factor to establish a grounding network corrosion prediction model [16]. However, the optimization algorithm has high requirements for data due to its complex structure, and the parameters of the SVM model are difficult to determine to achieve the expected results, and the algorithm has to be optimized [17,18].

The corrosion rate prediction methods for offshore wind foundations have rarely been studied. J. H. Xu, X. W. Wang, and J. J. Yang combined the structural characteristics, the corrosion environment, the corrosion mechanism, and the corrosion behavior of different parts of the foundation located in different marine corrosive environment zones, which were analyzed and summarized, and they especially analyzed the various types of corrosion risks caused by the sealing failure of the inner compartment and transition section of monopile foundation [19]. The existing studies are not comprehensive enough to analyze the influencing factors of offshore wind power foundation corrosion, and most of them are based on a single point of view and do not adequately consider the influence of various influencing factors. As a result, it is difficult to model them, which results in errors in the prediction of offshore wind power foundation corrosion. Secondly, the feature extraction of offshore wind power foundation corrosion factors as well as the data processing methods need to be improved, and the accuracy of corrosion rate prediction is yet to be further improved [17,20]. The modeling methods proposed by the above scholars all have unique advantages. Still, they are limited by the limitations of the optimization algorithm itself, which may result in the inability to accurately predict the corrosion rate for multi-factor and high-dimensional problems. In summary, the current research has the following three problems. Firstly, it is difficult to balance prediction accuracy and training time. Secondly, the screening methods for corrosive principal factors are usually based on linear problem mapping, which does not consider that the independent variables are related to each other, resulting in a poor explanatory relationship between the independent variables and the dependent variable. Thirdly, the regression algorithms used have high requirements for the number and quality of samples. At the same time, the realistically obtained corrosion data are very limited, and these algorithms have poorer predictive effects on small samples.

To improve the accuracy of the offshore wind power foundation corrosion rate prediction and to grasp the health status of the foundation, an offshore wind power foundation corrosion rate prediction model is established based on KPCA-ISHO-LSSVM. The contributions are as follows:

(1)

The main elements of the offshore wind power foundation corrosion rate are extracted using kernel principal component analysis, which reduces the modeling workload of the offshore wind power foundation corrosion prediction model.

(2)

The improvement of the spotted hyena algorithm by the nonlinear adjustment of convergence factor and Lévy flight strategy, which accelerates the convergence speed of the algorithm and improves the optimization ability.

(3)

Based on the improved spotted hyena algorithm, the least squares support vector machine’s penalty parameter and kernel function parameter are optimized, and the offshore wind power foundation corrosion rate prediction model is established.

The organization of this paper is as follows: Section 1 analyzes the corrosion characteristics of offshore wind power foundations; Section 2 introduces the kernel principal component analysis method; Section 3 introduces the spotted hyena optimization algorithm improvement strategy; Section 4 introduces the corrosion rate prediction model for offshore wind power foundation based on ISHO-LSSVM; Section 5 is the simulation verification; and Section 6 is the conclusion.

2. Corrosion Characteristics of Offshore Wind Power Foundations

Single offshore wind turbine foundations and conduit frame foundations are mostly composed of steel structures, and the pile foundation of the high pile cap foundation is often made of steel pipe piles [21], as shown in Figure 1. The transition section and connection with the pile foundation are also often made of steel structures. It can be said that steel is the most important material used for offshore wind turbine foundations. The foundation stands tall in the marine environment and has strong corrosiveness to steel, similar to general marine structures. Its most prominent feature is the marine corrosion problem of steel. The corrosion resistance varies greatly with different exposure conditions. It is usually divided into five zones [22]. The presence of salt particles or salt mist in the marine atmospheric region leads to much greater corrosion in this area than inland areas. The splash zone has sufficient oxygen supply, sufficient sunlight, and a large amount of salt particles. During the process of dry–wet alternation and under the impact of waves, local corrosion is more severe, making it the area with the most severe corrosion.

However, the wind turbine foundation, as the supporting structure of the wind turbine, is different from harbor structures or offshore platform structures, as it combines the characteristics of high-rise structures and power machine foundations [23]. The large overturning moment with the uncertain direction of the wind turbine foundation results in significant alternating tensile stress. At the same time, the structural components of the foundation not only bear the load of the marine environment but also the dynamic load generated during the operation of the wind turbine. The interweaving effect of stress and corrosion, as well as fatigue and corrosion, is more prominent. Once local damage occurs to the anti-corrosion protection system in important parts (such as the foundation node of the jacket), it is extremely easy to cause structural damage. Therefore, there is a higher demand for the reliability and corrosion rate prediction of anti-corrosion protection measures during the lifespan of wind turbine foundations.

3. Kernel Principal Component Analysis

In order to eliminate the effect of different magnitudes in the data set, the original data are normalized to obtain the new data set. The normalization formula is as follows [21]:

$$x_j=\frac{X_j-\underset{1\le j\le n}{\min }\left\{X_j\right\}}{\underset{1\le j\le n}{\max }\left\{X_j\right\}-\underset{1\le j\le n}{\min }\left\{X_j\right\}}$$

(1)

where $x_j$ is the normalized data; $X_j$ is the original data of an eigenvector; $\underset{1\le j\le n}{\max }\left\{X_j\right\}$ and $\underset{1\le j\le n}{\min }\left\{X_j\right\}$ are the maximum and minimum values of the eigenvector, respectively.

Mapping the new dataset to gain high-dimensional space $\varphi =\left\{\varphi (x_1),\varphi (x_2),\cdots ,\varphi (x_n)\right\}$, $i=1,2,\cdots ,n$, the covariance matrix in the high-dimensional space $\varphi$ is as follows [19]:

$$C=\frac{1}{n}{\displaystyle \sum _{i=1,j=1}^n\varphi (x_i)\varphi {(x_j)}^T}=\frac{1}{n}\left[\varphi (x_1),\cdots ,\varphi (x_n)\right]\left[\begin{array}{l}\varphi (x_1)\\ ⋮\\ \varphi {(x_n)}^T\end{array}\right]=\frac{1}{n}\varphi {\varphi }^T$$

(2)

Let the kernel function be $K={\varphi }^T\varphi ={(k_{i,j})}_{n\times n}$, where $k_{i,j}=\varphi {(x_i)}^T\varphi (x_i)$. Using the kernel function, the characteristic polynomial of the covariance can be simplified to obtain the following:

$$K^2\alpha ={\lambda }_{i}K\alpha \Rightarrow K\alpha ={\lambda }_i\alpha$$

(3)

where α is a column vector of dimension n.

The cumulative contribution of each factor c is calculated, and the main influence factor can be determined by extracting the q main elements with higher contribution, and the formula for h is as follows [18]:

$$c=\frac{{\displaystyle \sum _{i=1}^q{\lambda }_i}}{{\displaystyle \sum _{i=1}^n{\lambda }_i}}$$

(4)

Usually, the requirement is satisfied when the cumulative contribution c is greater than 85% [14]. Using Equation (4) to determine the principal components, for any sample x, the reconstructed nonlinear sample F_i can be obtained by performing a high-dimensional mapping of its eigenvalue α and eigenvector u_i as follows:

$$F_i=u_i^T\varphi (x)=[{\displaystyle \sum _{i=1}^n{\alpha }_i}\varphi (x_i){]}^T={\alpha }^T{[k(x_1,x),\cdots ,k(x_i,x)]}^T$$

(5)

4. Spotted Hyena Optimization Algorithm Improvement Strategy

4.1. Spotted Hyena Optimization Algorithm

In 2018, the Indian scholar Gaurav Dhiman proposed the spotted hyena optimizer (SHO). The predatory process of the spotted hyena populations involves four stages. The principle of the SHO is as follows:

(1) Encirclement process: The spotted hyena is able to acutely perceive the location, which is as follows [14]:

$$D_h=\left|B\cdot P_p(t)-P(t)\right|$$

(6)

$$B=2\cdot r_1$$

(7)

where D_h is the distance; t is the number of iterations; Pp is the position of the prey; P(t) is the position; B is the swing factor; r₁ is a uniformly distributed random number; r₁ ∈ [0, 1].

The spotted hyena individual position update formula is as follows [6]:

$$P(t+1)=P_p(t)-E\cdot D_h$$

(8)

$$E=2\cdot h\cdot r_2-h$$

(9)

$$h=5-5\cdot \frac{t}{NI}$$

(10)

where E is the convergence factor, r₂ has the same meaning as r₁, h is the control factor, and N_I is the maximum number of iterations.

(2) Hunting process: The spotted hyenas belong to a group of animals and complete the hunt by trusting each other and exchanging information to determine the location of prey. This process is as follows [15]:

$$D_h=\left|B\cdot P_p(t)-P_k\right|$$

(11)

$$P_k=P_h-E\cdot D_h$$

(12)

$$C_h=P_k+P_{k+1}+\cdots +P_{k+N}$$

(13)

where P_h is the first optimal position; and C_h is the set containing N optimal solutions. Where the expression for N is as follows:

$$N=Coun{t}_{nos}(P_h,P_{h+1},P_{h+2},\cdots ,P_h+M)$$

(14)

where M is a random vector in between [0.5, 1]; nos defines the number of feasible solutions.

(3) The process of attacking prey (local search): When hunting is completed, it starts to attack the prey, and the condition of attacking the prey is reached. The mathematical expression of this process is as follows:

$$P_h(t+1)=\frac{C_N}{N}$$

(15)

where P_h(t + 1) is the preserved optimal solution.

(4) Search process (global search): The spotted hyena searches for the prey according to the position in the set of optimal solutions C_h. When the convergence factor is satisfied, it will spread out to search for the prey with a better position, which is a mechanism that facilitates the SHO to carry out global search.

Compared with other optimization algorithms, SHO has fewer parameters, simple operation, good stability, and higher solution accuracy. However, its optimization ability relies on the two random parameters B and E to regulate, and during the optimization process, the SHO also suffers from falling into local optimums and insufficient solution accuracy.

4.2. Nonlinear Adjustment of Convergence Factors

When the SHO is iteratively calculated, the control factor h adopts a linearly decreasing adjustment strategy, but in fact, the change in h is nonlinear; in order to better reflect the algorithm’s optimization process, this paper introduces a nonlinear adjustment strategy as follows [24,25,26]:

$$h(t)=5-5{\left[\frac{1}{e-1}(e^{\frac{t}{NI}}-1)\right]}^Q$$

(16)

where e is the natural logarithm, Q is the attenuation coefficient, and the larger Q is, the more h attenuates.

Through the improvement, the control factor h realizes a nonlinear decrease from five to zero. At the beginning of the algorithm iteration, h is slowly decreasing, which is better decaying compared to the original control factor, and is favorable for the algorithm to perform the global search. In the late iteration, the improved h decays faster, which makes the population closer to the optimal solution.

4.3. Levi’s Flight Strategy

Lévy flight is a kind of non-Gaussian stochastic process, which is more stochastic and can explain certain stochastic phenomena in nature [22]. This kind of step size adjustment can not only increase the population diversity, but also help the population to reach the global optimal solution. Therefore, the introduction of the Lévy flight strategy in the optimization algorithm is conducive to increasing the population diversity and expanding the search range.

To enhance the optimization performance, the Lévy flight strategy is introduced in the SHO and acts on the stochastic factors r₁ and r₂ of the SHO as follows [15]:

The swing factor is defined as Equation (17):

$$B=2\cdot Levy\cdot r_1$$

(17)

The convergence factor is defined as Equation (18):

$$E=2\cdot h\cdot Levy\cdot r_2-h$$

(18)

where Levy is the search path.

5. Corrosion Rate Prediction Model for Offshore Wind Power Foundation Based on ISHO-LSSVM

LSSVM is a machine learning method for solving nonlinear regression problems. LSSVM is characterized by the small number of samples required and high regression accuracy, and is now widely used to solve nonlinear regression problems [23].

For the acquired data sample set $\{x_i,y_i\},i=1,2,\cdots n$, where $x_i$ is the input quantity and $y_i$ is the output quantity. The objective function of LSSVM to solve the optimization problem is as follows:

$$\left\{\begin{array}{l}\min J(w,b,e)=\frac{1}{2}{w}^{T}w+\frac{1}{2}C{\displaystyle \sum _{i=1}^m{\zeta }_i^2}\hfill \\ \mathrm{s}.\mathrm{t}. y_i\left[w^T\phi \left(x_i\right)+b\right]=1-{\zeta }_i^2\hfill \end{array}\right.$$

(19)

where $\phi$ is the nonlinear mapping; $w$ is the hyperplane weight vector; b is the bias factor; C is the penalty coefficient; and ${\zeta }_i$ is the slack variable.

Introducing the Lagrangian operator ${\alpha }_i$, the Lagrangian function is obtained as follows:

$$L(w,b,e,\alpha )=J(w,b,e)-{\displaystyle \sum _{i=1}^m{\alpha }_i}\left\{y_i\left[w^T\phi \left(x_i\right)+b\right]-1+e_i\right\}$$

(20)

The partial derivatives of Equation (20) are solved, and then the substitutions $\phi {(x)}^{\mathrm{T}}\phi (x)$ in the partial derivatives are made to finally obtain the expression of the classification function of the LSSVM:

$$y(x)=\mathrm{sign}\left[{\displaystyle \sum _{i=1}^m{\alpha }_i}{y}_{i}K\left(x,x_i\right)+b\right]$$

(21)

The penalty parameter C and the kernel function parameter $\sigma$ are two very important parameters of LSSVM, which have a great influence on the regression fitting effect of LSSVM. In order to obtain a better fitting effect, it is necessary to find the optimization of C and $\sigma$. The ISHO-LSSVM prediction model is used to predict the current system state.

The corrosive environment of offshore wind power operation is very harsh; the high humidity and high salinity of the sea surface atmospheric area, the dry and wet alternation of the splash zone and tidal zone, and the seawater immersion and seabed attachment of the submerged area, and other harsh corrosive environments will cause serious corrosion hazards to the monopile foundation of the offshore wind turbine, and the environmental load of the monopile foundation is much higher than that of land, and its corrosion rate affects a large number of factors with a certain degree of correlation between the various factors. In order to reduce the modeling workload of the offshore wind turbine foundation corrosion prediction model, KPCA is used to process the corrosion rate influencing factors of the offshore wind turbine foundation, downsizing the sample data in high dimensional space, eliminating the spatial correlation and redundancy of data, and extracting the main data of the main nonlinear characteristics of the principal elements. Using the convergence factor nonlinear adjustment and Lévy flight strategy to improve SHO and improve the performance of SHO’s optimization, and using ISHO to optimize the parameters of LSSVM to establish the offshore wind power base corrosion rate prediction model based on the KPCA-ISHO-LSSVM, the modeling process is shown in Figure 2.

The steps for forecasting are as follows:

(1)

Obtain sample data. According to the factors affecting the corrosion rate of offshore wind power foundations, the relevant data are collected.

(2)

Normalization. To eliminate the error affected by the different scales of the influencing factors, the sample data are normalized to obtain the data set $x_1,x_2,\cdots ,x_n$.

(3)

KPCA dimensionality reduction. KPCA is used to downsize the data set $x_1,x_2,\cdots ,x_n$ to obtain the reconstructed indexes $F_1,F_2,\cdots ,F_m$.

(4)

ISHO parameter optimization. Use ISHO to optimize C and $\sigma$ of LSSVM. The process of ISHO can be seen in Figure 3.

(5)

Set the initial values and search ranges of penalty parameters C and kernel function parameters, and set the population size of the spotted hyena.

(6)

Calculate the current optimal position and check if there are any spotted hyena individuals that are beyond the boundaries and adjust them if any.

(7)

Calculate the individual fitness value of the spotted hyena after the position update and compare it with the fitness value of the previous generation to retain the best position of the spotted hyena.

(8)

Update the group of spotted hyenas until the spotted hyena position under the individual optimal fitness value is searched.

(9)

If the algorithm reaches the termination condition, output the best spotted hyena position, i.e., the optimal solution of C and $\sigma$; otherwise repeat steps (5) to (9).

(10)

The optimal solution of C and $\sigma$ is assigned to LSSVM, which is utilized to predict the corrosion rate of offshore wind power foundations.

Figure 3. Optimization flow chart of ISHO.

Figure 3. Optimization flow chart of ISHO.

After the prediction is completed, the prediction model needs to be evaluated, and in this paper, the average relative error, the root mean square error, the global maximum relative error, and the coefficient of determination are used to make a comprehensive evaluation of the prediction effect of the model, and their calculation formulas are as follows:

$${\epsilon }_{\mathrm{MAPE}}=\frac{1}{N}{\displaystyle \sum _{i=1}^N\left|\frac{y_i-{y_i}^{\ast }}{y_i}\right|}\times 100\%$$

(22)

$${\epsilon }_{\mathrm{RMSE}}=\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^N{(y_i-{y_i}^{\ast })}^2}}$$

(23)

$${\epsilon }_{\mathrm{MAX}}=\max \left|\frac{y_i-{y_i}^{\ast }}{y_i}\right|\times 100\%$$

(24)

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^N{({y_i}^{\ast }-y_i)}^2}}{{\displaystyle \sum _{i=1}^N{(y_i-\overline{y_i})}^2}}$$

(25)

where N is the sample capacity of the test set, $y_i$ is the actual value of corrosion rate, ${y_i}^{\ast }$ is the predicted value of corrosion rate, and $\overline{y_i}$ is the average value of corrosion rate.

6. Experimental Verification and Analysis

To verify the effectiveness of the proposed approach, simulation analysis is carried out based on the actual collected data. Based on the data provided by the project “Aguiyang Engineering Corporation Limited Key Scientific Research Project (YJ2023-13)”, seawater data were collected from 15 offshore wind farms and 72 sets of sample data are shown in

Table A1. Seventy-two sets of raw sample data.

Sample No.	PH Value	$\mathbf{Ion} \mathbf{Mass} \mathbf{Concentration}/\mathbf{mg}\cdot {\mathbf{L}}^{-1}$
		${\mathbf{Na}}^{\mathbf{+}}$	${\mathbf{Mg}}^{\mathbf{2}\mathbf{+}}$	${\mathbf{Ca}}^{\mathbf{2}\mathbf{+}}$	${\mathbf{K}}^{\mathbf{+}}$	${\mathbf{NO}}_{\mathbf{3}}^{\mathbf{-}}$	${\mathbf{Br}}^{\mathbf{-}}$	${\mathbf{Cl}}^{\mathbf{-}}$	${\mathbf{SO}}_{\mathbf{4}}^{\mathbf{2}\mathbf{+}}$	${\mathbf{HCO}}_{\mathbf{3}}^{\mathbf{-}}$	${\mathbf{F}}^{\mathbf{-}}$
1	7.91	2238.26	348.16	206.55	129.82	1.31	44.45	1327.28	323.16	116.83	0.24
2	7.66	2036.13	379.93	200.26	203.27	7.13	31.90	1260.06	301.21	135.37	0.73
3	7.66	2126.99	324.64	230.65	204.24	3.75	38.32	1235.92	282.76	139.21	0.66
4	7.11	2079.74	280.90	184.18	112.17	5.86	32.61	1095.35	275.83	109.75	0.14
5	8.20	2203.06	356.86	180.34	75.95	3.32	34.89	1200.45	272.87	126.43	0.07
6	8.05	2092.34	352.99	194.56	71.73	2.72	33.33	1110.04	277.56	148.75	0.11
7	8.42	2093.29	378.85	199.96	149.55	3.72	37.33	1110.89	270.35	135.10	0.40
8	7.58	2251.04	307.69	200.04	139.15	4.67	44.29	1182.38	268.61	166.55	0.11
9	8.25	2009.35	350.50	215.10	213.20	8.32	33.81	1185.95	251.53	164.80	0.39
10	7.23	2269.88	289.54	187.51	160.54	6.79	41.89	1005.79	275.46	132.85	0.23
11	8.36	2150.76	389.83	227.22	196.36	7.99	42.12	1337.89	278.20	115.25	0.31
12	8.45	2165.70	388.05	226.22	152.89	5.51	41.42	1121.73	332.87	177.63	0.14
13	7.06	2041.95	338.46	235.14	88.61	8.40	35.78	1206.93	313.07	128.07	0.50
14	8.39	2034.41	315.73	223.75	70.53	2.45	35.02	1143.15	272.08	112.30	0.46
15	7.11	2014.69	344.74	219.18	205.04	9.49	41.48	1161.25	295.00	173.66	0.01
16	8.17	2158.54	347.08	214.58	128.94	3.54	34.61	1099.25	309.11	148.48	0.15
17	8.11	2045.60	305.14	224.61	80.67	9.38	33.86	1348.56	290.87	112.99	0.10
18	7.38	2072.77	375.27	212.90	165.36	8.94	42.57	1000.23	293.01	139.10	0.41
19	8.26	2346.29	299.24	180.61	137.91	5.15	31.60	1051.99	271.93	137.06	0.56
20	8.32	2342.69	379.39	197.19	197.74	5.77	44.45	1026.08	329.00	168.69	0.12
21	7.58	2229.56	347.49	238.50	93.39	7.74	36.24	1211.59	319.43	144.41	0.19
22	7.11	2117.48	300.45	181.01	164.68	5.66	34.89	1142.87	271.17	128.07	0.41
23	7.29	2174.76	365.91	192.76	101.16	2.72	41.88	1182.86	251.45	112.10	0.56
24	7.13	2304.59	340.51	222.32	178.80	3.57	42.64	1137.51	257.50	174.07	0.35
25	7.79	2066.46	300.06	175.50	105.44	6.86	43.55	1178.54	291.39	119.55	0.11
26	8.29	2090.58	352.56	209.19	145.48	5.40	35.14	1127.39	275.18	135.26	0.56
27	8.15	2025.40	318.88	195.57	152.68	7.32	39.50	1013.45	303.50	167.91	0.58
28	7.86	2252.02	366.31	234.50	161.86	4.54	41.84	1025.18	301.61	160.49	0.57
29	8.25	2221.12	352.78	181.18	86.58	9.05	43.93	1310.35	271.39	179.89	0.24
30	7.07	2121.29	304.09	177.98	171.63	9.42	30.59	1239.06	329.98	164.17	0.17
31	7.28	2057.52	384.06	238.16	105.97	6.11	37.01	1259.99	275.26	143.48	0.40
32	7.15	2078.03	354.04	201.38	197.13	5.86	30.92	1304.22	300.91	183.60	0.39
33	7.95	2096.11	351.18	210.37	127.33	3.08	35.87	1302.04	323.26	103.43	0.19
34	8.29	2076.18	377.74	185.71	183.33	6.28	44.90	1066.20	267.38	174.57	0.47
35	7.20	2258.74	356.25	198.95	179.97	2.54	34.81	1264.56	293.88	181.48	0.32
36	7.46	2110.75	332.17	228.98	173.39	5.22	34.56	1316.49	321.35	168.06	0.21
37	7.98	2043.77	339.98	171.12	127.01	4.81	43.45	1330.64	297.69	123.32	0.55
38	7.99	2346.96	294.51	220.46	174.67	2.11	34.16	1190.28	268.59	108.87	0.28
39	7.89	2340.17	321.24	231.59	110.50	8.58	32.79	1336.60	294.30	126.18	0.10
40	8.24	2173.86	285.35	232.50	162.94	3.69	44.44	1290.95	274.93	160.94	0.19
41	7.42	2130.65	368.97	215.50	156.55	4.38	32.93	1197.14	260.17	181.86	0.12
42	7.11	2263.43	367.82	197.49	135.18	8.17	30.92	1018.90	266.40	134.82	0.17
43	7.17	2070.97	386.19	233.17	77.63	3.45	30.76	1216.82	273.08	155.66	0.46
44	7.80	2276.86	320.24	229.05	179.89	9.24	41.16	1023.68	322.32	173.73	0.41
45	7.21	2046.12	288.48	171.78	149.41	9.95	38.02	1129.15	301.83	118.52	0.25
46	8.19	2251.92	364.10	228.78	212.03	7.75	33.58	1096.08	267.93	161.85	0.13
47	7.20	2265.67	351.33	208.22	146.93	9.97	34.25	1251.08	255.02	147.07	0.21
48	8.09	2263.75	388.69	172.11	144.19	6.15	40.47	1272.56	304.71	112.48	0.24
49	7.67	2297.51	321.39	229.37	75.48	3.97	41.28	1264.80	267.92	104.53	0.10
50	7.81	2043.87	314.92	191.69	70.78	5.84	31.59	1174.21	303.64	138.71	0.57
51	8.19	2129.47	287.58	234.90	173.18	9.87	39.36	1172.94	315.14	128.88	0.20
52	7.53	2104.12	346.24	198.08	207.96	9.84	36.55	1234.40	258.62	126.66	0.55
53	7.67	2036.26	388.39	200.50	144.44	3.95	32.09	1340.48	269.20	101.94	0.46
54	8.48	2030.80	386.03	208.92	107.70	6.28	34.10	1113.40	285.19	176.82	0.27
55	8.14	2161.99	372.01	228.92	71.83	5.12	38.02	1147.17	309.01	104.46	0.52
56	7.53	2238.30	356.86	230.48	106.66	9.99	43.21	1016.68	258.10	118.04	0.16
57	7.32	2293.92	376.84	205.78	142.10	8.67	36.28	1067.72	284.13	129.92	0.17
58	7.74	2032.72	330.86	228.04	176.36	7.27	42.01	1257.12	250.49	155.79	0.19
59	7.14	2251.72	328.00	189.51	88.31	9.81	35.57	1169.14	278.13	116.77	0.24
60	7.08	2091.21	349.00	215.91	201.05	3.67	41.83	1316.71	291.07	167.70	0.28
61	8.29	2117.25	358.03	212.61	120.57	6.68	44.92	1002.34	321.71	140.49	0.12
62	8.41	2127.78	284.88	181.71	159.75	8.55	41.45	1110.21	258.29	184.98	0.18
63	7.74	2313.92	345.67	225.29	122.94	2.31	34.14	1079.63	256.49	102.50	0.28
64	7.93	2031.73	343.09	197.34	109.36	8.47	40.11	1175.68	304.94	163.11	0.15
65	7.84	2333.33	301.16	200.82	206.99	4.05	39.85	1098.16	255.61	155.94	0.49
66	7.45	2011.62	382.75	178.74	99.49	3.77	33.53	1192.98	304.10	125.90	0.60
67	8.35	2113.42	336.93	236.25	165.39	9.06	44.75	1121.94	309.74	114.10	0.24
68	7.98	2314.67	331.24	218.33	97.02	6.41	40.35	1125.20	299.20	138.92	0.21
69	7.58	2226.41	305.70	208.50	77.43	2.31	33.74	1228.85	301.13	148.67	0.11
70	7.77	2326.32	327.45	185.25	198.94	4.25	30.83	1139.43	305.80	126.63	0.26
71	8.32	2297.34	303.43	177.62	186.81	7.62	32.86	1256.10	322.48	117.24	0.25
72	8.46	2010.86	352.25	193.70	142.60	2.80	41.04	1335.83	315.15	104.43	0.29

. The 72 sets of data were normalized based on Equation (1) due to the large magnitude differences between the different types of influencing factors. KPCA was used to calculate the cumulative contribution of each factor. The results of KPCA algorithm processing are shown in

Table 1. Results of KPCA analyses.

Principal Component	Eigenvalue	Variance Contribution/%	Cumulative Variance Contribution/%
PH value	1.8652	40.75	40.75
${\mathrm{SO}}_4^{2+}$	0.9532	26.52	67.27
${\mathrm{NO}}_3^{-}$	0.5236	10.24	77.51
${\mathrm{Mg}}^{2+}$	0.4123	7.23	84.74
${\mathrm{HCO}}_3^{-}$	0.2596	6.53	91.27
${\mathrm{Na}}^{+}$	0.1321	3.35	94.62
${\mathrm{Ca}}^{2+}$	0.0952	1.95	96.57
${\mathrm{Cl}}^{-}$	0.0526	1.85	98.42
${\mathrm{K}}^{+}$	0.0412	0.71	99.13
${\mathrm{Br}}^{-}$	0.0241	0.54	99.67
${\mathrm{F}}^{-}$	0.0091	0.33	100

. The first 60 groups are regarded as the training set, while the last 10 groups are the test set, which can effectively evaluate and validate the generalization performance of models or algorithms based on this data while ensuring that the data are fully utilized.

According to the basic principle of the preferential selection of the kernel principal components of influencing factors using KPCA, if the sum of the contribution rates of some influencing factors exceeds 85%, these factors can be used instead of all the factors for the corrosion rate prediction study. As can be seen in Table 1, the cumulative contribution rate of PH value, ${\mathrm{SO}}_4^{2+}$, ${\mathrm{NO}}_3^{-}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{HCO}}_3^{-}$ has reached more than 85%. Therefore, these five influencing factors are selected as the key indicators of offshore wind power foundation corrosion for the next prediction study. According to the coefficient matrix of the principal components to reorganize the data, the sample data were reorganized from the previous eleven-dimensional data to five-dimensional data. The reorganized sample data are shown in

Table A2. Sample data after reorganization.

Sample No.	PH Value	${\mathbf{Mg}}^{2+}$	${\mathbf{NO}}_3^{-}$	${\mathbf{SO}}_4^{2+}$	${\mathbf{HCO}}_3^{-}$
1	3.8667	1.4723	1.5334	1.7113	1.1347
2	0.9639	3.3851	−0.5092	1.3585	1.9899
3	3.2178	1.2275	4.5877	1.8631	1.8452
4	3.6379	1.3956	3.2653	2.6756	0.0835
5	2.6605	1.4138	0.8012	−0.3450	−1.6430
6	−0.7152	0.6434	1.2457	4.5684	−0.2847
7	2.7125	1.4111	1.3295	−0.0465	3.1502
8	1.4475	1.4377	1.0151	−0.3530	1.6834
9	1.3440	2.3981	1.2038	0.6798	3.9931
10	1.5487	1.4955	3.8252	3.5191	1.3049
11	1.1278	4.4259	4.0803	−0.0458	2.4452
12	1.8761	1.9738	1.8543	0.8789	−0.1415
13	1.0710	1.3474	−0.8690	1.4715	−0.6221
14	−0.5449	1.8240	0.2439	0.7325	3.3775
15	2.5506	1.3922	1.2119	4.1506	1.1611
16	1.9410	1.0044	1.0387	1.9385	3.7135
17	−1.1983	4.2355	3.8587	1.5143	3.8503
18	1.4657	2.8330	4.5500	−1.4133	2.1842
19	1.6368	0.4111	1.2701	3.8163	3.2054
20	−0.0681	2.0270	0.5875	0.1574	1.4655
21	1.3528	3.6093	1.6547	1.6997	3.5525
22	1.0196	−0.9618	1.1812	2.3189	1.0002
23	−0.6334	3.4965	1.7354	−1.2712	−0.1615
24	0.8840	2.5330	1.4664	0.1676	0.4845
25	1.2855	−0.7190	3.6406	1.8047	1.4044
26	1.5093	1.9563	2.5178	1.0232	2.3792
27	0.1170	4.1509	3.6051	1.8205	0.1858
28	4.3603	3.4290	1.9341	1.1619	1.8012
29	1.3271	2.0159	1.7142	3.0885	1.3008
30	4.1483	1.9901	−1.7808	1.4474	1.9034
31	1.2267	1.3241	4.0494	0.5719	1.5424
32	1.5910	4.1414	1.4887	1.9710	2.0941
33	1.0090	1.3422	2.2230	2.5956	4.3108
34	−0.5153	1.4028	0.8700	2.4284	0.4382
35	−0.5839	1.3993	0.3940	−0.5932	1.2052
36	3.3077	2.4555	0.5273	1.6901	4.3718
37	1.8809	0.3851	1.3116	1.4645	3.8325
38	−1.2419	−0.8737	0.4045	0.4332	−1.3403
39	4.5197	2.4452	−0.5362	1.8641	−1.3256
40	2.9916	−0.3838	−1.4375	3.9473	−1.2102
41	1.8133	1.6818	1.4645	−1.0576	1.5785
42	1.5323	1.9895	−0.4454	2.5103	2.9246
43	0.3773	3.2531	0.1623	−1.2305	1.5117
44	1.7237	1.5461	1.2343	2.9519	1.2744
45	2.7996	1.1701	1.3667	1.7061	1.5965
46	3.3535	0.6347	2.3013	1.3888	1.9898
47	3.5015	1.8914	1.7656	3.3636	1.9091
48	−0.4978	1.8224	−1.1664	4.2226	1.4734
49	1.8082	−0.0855	−0.6743	−0.1832	−0.7854
50	2.8001	0.7136	2.7971	1.4468	0.2061
51	−0.1693	1.0677	1.5799	0.9540	4.1168
52	1.3731	3.9771	−1.0960	3.4502	−0.9775
53	−0.9404	4.7953	3.3717	1.3110	4.7877
54	3.4656	1.5696	3.8690	1.3556	1.9154
55	1.3066	0.3734	4.6552	−0.9089	3.8551
56	1.3848	1.0737	−0.7851	0.0726	−1.2623
57	−0.5064	1.3327	1.1752	1.0100	1.0897
58	−0.8443	−0.0952	−0.0844	1.4798	1.7999
59	−0.6794	−0.3741	0.2110	3.2230	4.0719
60	3.7750	2.2032	0.6601	1.9699	3.4242
61	1.9985	1.5485	3.8154	1.8493	4.4840
62	−0.5110	1.2685	1.9218	−1.0822	2.1844
63	1.1061	1.2407	2.2131	0.9143	1.3326
64	3.4188	1.3210	1.1136	2.6456	−0.6040
65	−1.5663	1.3232	2.1802	1.3925	0.3722
66	1.5363	−0.3021	−0.2141	−0.4896	1.6825
67	2.7397	1.9967	1.3049	−0.1274	0.7298
68	1.4288	2.7448	1.7961	1.9226	1.0469
69	1.2406	3.8171	0.1451	1.8871	−0.2190
70	1.4798	1.1895	3.9302	1.0689	1.3047
71	1.1092	1.7501	1.8874	4.0020	−0.2864
72	−1.0091	1.0085	1.0856	0.6599	2.6047

.

Using the training set for training, the ${\epsilon }_{\mathrm{RMSE}}$ of the samples is used as the fitness function of the optimization objective, and the improved SHO algorithm is applied to optimize the C and $\sigma$ of the LSSVM, with the initial values of the C and $\sigma$ set to 100 and 1, respectively, and the search ranges are both [0, 1000]. The iteration curves of the ISHO and the SHO are shown in Figure 4.

In Figure 4, the fitness value of each algorithm decreases with the increase in iteration number, but ISHO can achieve the minimum mean square error in fewer iterations. SHO also achieves a better fitness value in fewer iterations, but the ability to find the optimal solution is still inferior to that of ISHO. The initial fitness value of ISHO is lower than that of SOA, which indicates that after the optimization of Lévy’s flight strategy, the initial positional quality of the population has been improved. ISHO reaches the minimum fitness value after 25 iterations, when the corresponding optimal solutions C and $\sigma$ are 58.47 and 2.16, respectively.

The optimal values C = 58.47 and $\sigma$ = 2.16 found by ISHO are assigned to LSSVM to predict the test set data. To further validate the superiority of the offshore wind power base corrosion rate prediction method based on the KPCA-ISHO-LSSVM model, comparative analyses are conducted with the KPCA-SHO-LSSVM, KPCA-ISHO-BP, KPCA-PSO-LSSVM, and ISHO-ELM models. The settings of SHO and LSSVM in the SHO-LSSVM model are consistent with this study; the settings of KPCA and ISHO in the KPCA-ISHO-BP model are consistent with this study, and the BP network structure is 3-9-1; the settings of KPCA and LSSVM in the KPCA-PSO-LSSVM model are consistent with this study, and the PSO parameters of the search space dimension are 2, the weight factor is 2, and the acceleration factor is 0.9 and 0.4, respectively; and the ISHO-ELM model settings are consistent with this study, and the ELM model network structure is 10-28-1. The prediction results are shown in Figure 5 and

Table 2. Results of model evaluation indicators.

Model	${\mathit{\epsilon }}_{\mathbf{MAPE}}$		${\mathit{\epsilon }}_{\mathbf{RMSE}}$		${\mathit{\epsilon }}_{\mathbf{MAX}}$		${\mathit{R}}^2$
	Training Set	Test Set	Training Set	Test Set	Training Set	Test Set	Training Set	Test Set
KPCA-ISHO-LSSVM	1.03	2.86	0.06	0.15	3.35	3.74	0.998	0.995
KPCA-SHO-LSSVM	2.71	6.31	0.1	0.77	9.21	9.97	0.991	0.98
KPCA-ISHO-BP	2.44	5.09	0.09	0.3	7.16	6.31	0.994	0.984
KPCA-PSO-LSSVM	1.94	4.33	0.25	0.26	4.78	5.82	0.996	0.99
ISHO-ELM	1.06	5.1	0.49	0.74	7.45	6.45	0.992	0.989

.

In Figure 5, the SHO-LSSVM model shows the highest prediction error, primarily due to its longer computation time and vulnerability to dimensional explosion and catastrophe. In addition, the prediction accuracy of the ISHO-ELM model is slightly worse compared to KPCA-PSO-LSSVM and KPCA-ISO-BP. This is related to the poor mapping effect of the ELM model in dealing with high-dimensional data, which does not retain the hidden variable information well and cannot express the nonlinear dependencies well, resulting in biased prediction results. Compared with KPCA-SHO-LSSVM, KPCA-ISO-BP, KPCA-PSO-LSSVM, and ISHO-ELM, the predicted values of the improved pre-prediction method in this paper match the actual values better. This indicates that by using the kernel function to map the sample data into the high-dimensional space and finding its subspace in the high-dimensional space for dimensionality reduction, the main element extraction accuracy is higher, effectively reducing the redundancy of the data features and improving the prediction effect of the model. Comparing the prediction effect before and after the improvement of the algorithm, it can be seen that the improved algorithm has higher prediction accuracy, improves the speed and accuracy of the model solution, and does not fall into the situation of local optimization.

To make a reasonable evaluation of the prediction accuracy of the combination model proposed in this study, this combination model is comprehensively compared with other common models, and the error changes are shown in Figure 6.

Through comparison, it can be found in Figure 6 that the errors of each group of the prediction results of the combined model proposed in this study are smaller than the other five models. The maximum relative error is less than 4%, which proves that its generalization ability is relatively good. The results of the various types of prediction errors and the coefficients of determination of the models of the five prediction models are shown in Table 2.

In Table 2, for the training set data, the ISHO-LSSVM model has a smaller error, a larger coefficient of determination, and a better training effect than the other models. For the test set data, the ${\epsilon }_{\mathrm{MAPE}}$, ${\epsilon }_{\mathrm{RMSE}}$, and ${\epsilon }_{\mathrm{MAX}}$ index of the ISHO-LSSVM model are smaller than the other three prediction models, in which the average relative error is 2.86%, which is 54.7% less than that of the SHO-LSSVM model, which shows that the model prediction accuracy is higher; the ${\epsilon }_{\mathrm{RMSE}}$ and ${\epsilon }_{\mathrm{MAX}}$ are 0.15 and 3.74%, respectively, which are 80.5% and 62.5% less than the SHO-LSSVM model. It can be seen that the volatility of the model prediction is smaller; from the coefficient of determination, the coefficient of determination of the ISHO-LSSVM model is 0.995, which is larger than that of the other three models. In summary, the corrosion rate prediction method of offshore wind power based on KPCA-ISHO-LSSVM proposed in this paper can further improve the corrosion rate prediction accuracy, and verify the correctness and superiority of the proposed corrosion rate prediction model.

7. Conclusions

In this paper, an offshore wind power foundation corrosion rate prediction method is proposed. The principal elements of offshore wind power foundation corrosion rate are extracted using the kernel principal component analysis, and the new dataset is mapped to a high-dimensional space by mapping function, which reduces the modeling workload of the offshore wind power foundation corrosion prediction model. The SHO algorithm is improved by the convergence factor nonlinear adjustment and Lévy flight strategy, and the penalty parameters and kernel function parameters of the least squares support vector machine are optimized based on the improved spotted hyena algorithm. The simulation results are as follows:

(1) With the KPCA approach, it is found that for the offshore wind power foundation, ${\mathrm{SO}}_4^{2+}$, ${\mathrm{NO}}_3^{-}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{HCO}}_3^{-}$ are some of the factors that have the greatest impact on corrosion. The data dimensionality reduction, under the premise of guaranteeing the prediction accuracy, effectively simplifies the network structure of the corrosion rate prediction model, greatly reducing its arithmetic volume and speeding up the calculation speed.

(2) The SHO algorithm is improved by the convergence factor nonlinear adjustment and Lévy flight strategy, and it is used to optimize the LSSVM model, which improves the convergence speed and prediction accuracy. The algorithm reaches the minimum fitness value after 25 iterations. The average relative error, root mean square error, and global maximum relative error homogenization coefficients of the combined prediction model in this paper are 2.86%, 0.15, 3.74%, and 0.995, respectively, which are better than those of the other corrosion prediction models.

With the approach proposed in this paper, we can grasp the foundation’s health state for offshore wind turbines’ operational safety. Due to the complexity and variability of the marine environment, more factors affect the corrosion rate of the substrate, and certain indicators are difficult to measure and quantify. In future research, the matrix corrosion data will be analyzed and predicted based on comprehensive indicators to improve the accuracy of the corrosion rate prediction further. At the same time, after obtaining accurate corrosion rate prediction results, it is necessary to carry out subsequent corrosion prevention design. The development of anti-corrosion measures will be studied in the future.