Stability Analysis of Breakwater Armor Blocks Based on Deep Learning

Abstract

This paper aims to use deep learning algorithms to identify and study the stability of breakwater armor blocks. It introduces a posture identification model for fender blocks using a Mask Region-based Convolutional Neural Network (R-CNN), which has been enhanced by considering factors affecting breakwater fender blocks. Furthermore, a wave prediction model for breakwaters is developed by integrating Bidirectional Encoder Representations from Transformers (BERTs) with Bidirectional Long Short-Term Memory (BiLSTM). The performance of these models is evaluated. The results show that the accuracy of the Mask R-CNN and its comparison algorithms initially increases and then decreases with higher Intersection Over Union (IOU) thresholds, peaking at 95.16% accuracy at an IOU threshold of 0.5. The BERT-BiLSTM wave prediction model maintains a loss value around 0.01 and an accuracy of approximately 90.00%. These results suggest that the proposed models offer more accurate stability assessments of breakwater armor blocks. By combining the random forest prediction model with BiLSTM, the wave characteristics and fender posture can be predicted better, offering reliable decision support for breakwater engineering.

1. Introduction

Breakwaters are among the most vital structures for safeguarding coastal regions and ports. They play a key role in protecting coastlines from wave impact and erosion. Analyzing the stability of breakwaters is important for several reasons.

• It is used to assess the ability of breakwaters to resist wave forces. This ensures structural integrity over time.
• It ensures the breakwaters are safe and capable of protecting coastal regions from waves. This reduces the risk of flooding and erosion.
• It helps in the optimal design of breakwaters, which permits experts to prefer suitable materials and construction methods.

One of the crucial elements in ensuring a breakwater’s efficient operation and long-term dependability is its stability [1,2]. In the traditional design method, engineers mainly rely on the analysis method based on physical models and empirical formulas when designing breakwater armor blocks [3,4,5]. Over the past several years, numerous studies have been conducted to analyze the stability of rubble-mound breakwaters. The relation between waves and the stability of armor units is highly complex and cannot be accurately represented analytically. Therefore, many researchers have focused on developing empirical formulas that account for various physical characteristics of structures and waves. Hudson [6] introduced a straightforward stability formula based on regular wave tests using dimensionless analysis, which calculates the weight of a breakwater’s armor unit. Although a modified version of this formula remains in use, it does not account for important parameters such as storm duration, wave period, and damage level. Thompson and Shuttler [7] and Ahrens [8] incorporated both regular and irregular waves in their extensive tests to examine breakwater stability. Vidal et al. [9] studied the impact of wave height on breakwater stability and recommended considering the average height of the 50 highest waves instead of the average of the top ‘n’ waves. They conducted physical model tests and developed a formula to predict the stability number of rubble-mound breakwaters. However, these studies often rely on linear assumptions and simplified conditions, while coastal systems are inherently complex. As a result, these empirical formulas cannot accurately predict the stability number or address the uncertainties involved in this context. It is difficult to accurately capture the influence of complex nonlinear behavior and environmental factors on block stability [10]. Under this background, it is of great significance to analyze the stability of breakwater armor blocks by using a method based on deep learning.

The quick growth of deep learning technology in recent years has given the engineering sector new options to expand beyond the boundaries of conventional approaches. Deep learning technology can accurately capture complex nonlinear relations and patterns by learning many data points and patterns and improve the prediction ability of block stability [11,12,13]. Although some studies use the deep learning method to analyze the stability of structures, there is still a lack of systematic and comprehensive research in the specific case of breakwater armor blocks.

Therefore, the purpose of this paper is to explore the application of deep learning methods in the stability analysis of breakwater armor blocks, thus providing engineers with an accurate, reliable, and efficient tool for predicting and evaluating the stability of breakwater armor blocks. The innovation of this paper lies in the introduction of a deep learning model to analyze the stability of breakwater armor blocks, which has achieved a more comprehensive consideration of the influence of various factors on block stability. The effect of increasing the stability forecast ability of breakwater armor blocks is finally realized through the verification and analysis of a large quantity of experimental data.

The major contributions of the work are summarized as follows.

We introduce deep learning models for the stability analysis of breakwater armor blocks.

We present the development of a Mask R-CNN-based model for the accurate identification of the posture and positioning of fender blocks.

We designed a wave prediction model combining BERT and BiLSTM, achieving high prediction accuracy and low loss value.

The overall organizational structure of this paper is as follows. Section 1, the introduction, introduces the background of breakwaters in the field of coastal and port protection, puts forward research questions, and leads to the motivation and goal of this paper. Section 2, the literature review, summarizes and analyzes the previous research methods related to the stability analysis of breakwater armor blocks and the application of deep learning algorithms and explains the innovation and differences of this paper. Section 3, the method section, analyzes the influencing factors on the stability of breakwater armor blocks and constructs a model for identifying the posture and postural variation of breakwater armor blocks based on a Mask Region-based Convolutional Neural Network (R-CNN) and a breakwater wave prediction based on Bidirectional Encoder Representations from Transformer (BERT) and Bi-directional Long Short-Term Memory (BiLSTM). Section 4, the results and discussion, discusses and analyzes the performance of the model and compares it with previous studies, which reflects the value of this paper. Section 5 summarizes the main findings of this paper, points out the limitations of this paper, and puts forward suggestions for further research.

2. Literature Review

As an important part in the field of ocean engineering ports and coastal protection, many scholars have carried out relevant research on its stability analysis. Vidal et al. [9] studied armor damage caused by the wave climate. This was investigated using the wave height parameter. Experiments have been conducted using lab tests with sea states possessing several wave height distributions. It has been observed that wave height can be used to compute the evolution of damage using different sets of sea states. Van Gent et al. [14] proposed a neural network-based method to model wave overtopping discharges for several ranges of coastal structures. Their work made use of a dataset retrieved from the physical model tests in the European project CLASH. Their work also applied the resampling method for assessing uncertainties.

Romano et al. [15] investigated the factors influencing wave overtopping. The variability in wave overtopping discharge is influenced by several factors, including the random starting phases of incident wave sequences and the lengths of these sequences. Their work presented an experimental study conducted in the wave flume of Roma Tre University, where 153 small-scale laboratory tests simulated eight different spectra to observe varying levels of overtopping. The use of a random number generator to seed the starting phases allowed for a detailed examination of how variability in wave overtopping discharge changes with the dimensionless freeboard.

Musumeci et al. [16] devised a method for monitoring damage to rubble-mound breakwaters. This approach is based on fully automated monitoring utilizing 3D cameras. This method is able to measure damage over time quickly because of its non-invasive nature. Experimental results show that the method does not rely on a camera sensor and can be adopted for any 3D dataset of rubble-mound breakwater. This leads to an increase in estimating damage to breakwaters.

Vieira et al. [17] presented a critical review of armored breakwaters in terms of wave overtopping and hydraulic stability. They identified some degree of uncertainty in wave overtopping and hydraulic stability. The knowledge gaps and the future scope of this field have been investigated. Stagnitti et al. [18] studied the hydraulic response of damaged and rubble-mound breakwaters and presented a prediction tool based on numerical simulations to investigate the wave overtopping issue of structures with an asymmetrical armor slope. Their work also contributes to the development of a large dataset for the tuning of broadly usable wave overtopping prediction analysis.

Stagnitti et al. [19] presented a Structure from Motion (SfM) technique for analyzing damage to cube-armored breakwaters. This work relies on the assessment of the characteristics of the macro- and micro-roughness of the armor layer. This work also combines the damage requirements used in the existing techniques with armor surface roughness characteristics. Galiatsatou et al. [20] and Campos et al. [21] elucidated the methods of developing suitable mitigation measures for the advancement of rubble-mound breakwaters safeguarding harbors. These methods were based on reliability analysis, which includes the construction of probability distribution functions by considering several climatic conditions such as waves, the rise in sea level, and storm surges.

Sujantoko et al. [22] analyzed the stability of concrete block anchors on steep slope floating breakwaters. The research results provide insight into the behavior and stability of breakwater systems. Zhao et al. [23] discussed the phenomenon of wave climbing and attenuation under wave impact. The interaction between waves and structures was studied and analyzed, and the effectiveness of fence slope protection in reducing wave climbing was evaluated. The research results provided valuable information about wave attenuation and dissipation characteristics of breakwater systems. Hasan et al. [24] conducted an experimental study on the stability of concrete block slope protection on a suspended geotechnical tubular breakwater under high waves. The research focuses on evaluating the stability of slope protection under wave load and discusses the influence of wave characteristics on the stability of slope protection. The research results provide insight into the stability behavior and effect of concrete block slope protection.

Saha et al. [25] studied the analysis of the stability number of rubble-mound breakwaters using machine learning-based approaches such as ensemble learning and deep neural networks. Their work makes use of ensemble learning to analyze the features and forecast the stability number using fully connected deep neural networks. Experimental results using Ven der Meer’s [26] dataset show that the deep learning-based approach outperforms well.

Damage level estimation is one of the important tasks in the stability analysis of breakwaters. This permits us to have an economic design and safe coastal structures. Saha and De [27] use a deep artificial neural network model to estimate the damage level of rubble-mount breakwaters. Experimental results using Ven der Meer’s [AR2] dataset illustrate that this work reduces the error in damage level estimation.

Saha et al. [28] proposed a machine learning-based method to predict the damage level of rubble-mound breakwaters. In this research work, machine learning algorithms such as Random Forest, Adaboost, Support vector regression, gradient boosting, and deep artificial neural networks were utilized to compare the performance to estimate the damage level of breakwaters. Additionally, feature analysis is performed to identify the relationship between the variables.

Numerous academics have undertaken pertinent studies on the use of deep learning in the engineering area as a result of the swift development of information technology. Nieves et al. [29] used the deep learning method to predict regional coastal sea level changes. A deep learning algorithm was used to analyze meteorological and ocean data and predict future sea level change. The results showed that the deep learning model could provide an accurate prediction of regional coastal sea level change. Calkoen et al. [30] compared the effects of traditional methods and deep learning methods in predicting beach evolution by using coastline data obtained by historical satellites. The study’s findings demonstrated that deep learning techniques performed better than conventional ones and could offer more precise and trustworthy predictions of beach evolution. The shifting tendency of the coastline was examined by Fogarin et al. [31] using remote sensing data and deep learning algorithms. The findings proved that remote sensing and deep learning might be used to accurately assess the short-term evolution trend of the Venice shoreline, providing crucial data and aiding in decision-making for coastal management and conservation. Ali et al. [32] used a deep learning algorithm to predict asphaltene stability in crude oil. The correlation between the characteristics of crude oil samples and asphaltene stability was analyzed by a deep learning algorithm. The results showed that the deep learning algorithm could accurately predict asphaltene stability in crude oil.

Traditional methods focus on the analysis of breakwater stability, particularly in assessing the performance of armor blocks. These methods typically rely on empirical formulas, physical model tests, and simplified analytical approaches to estimate factors such as wave forces, armor stability, and overall structural integrity. This manuscript focuses specifically on introducing modern deep learning techniques into the domain of coastal engineering, with a particular emphasis on rubble-mound breakwaters, including fender block-armored configurations. Through the research and analysis of the above studies, it is found that traditional methods are mostly used to analyze the stability of breakwater armor blocks, but there are still limitations in the modeling of complex nonlinear behavior and environmental factors. This experiment tried to explore the potential of deep learning as a complementary tool for enhancing the accuracy, efficiency, and automation of breakwater stability analysis. Meanwhile, deep learning is widely used in engineering, and it can better capture the influence of complex nonlinear relations and environmental factors on stability, such as in [29,31,32]. However, the application of deep learning to the stability analysis and prediction of breakwater armor blocks is extremely rare. Therefore, this paper introduces deep learning and applies it to the prediction and stability analysis of breakwater armor blocks. By learning many experimental data and models, the prediction ability of block stability is improved, and new perspectives and tools are provided for engineering practice.

3. Research Model

3.1. Analysis of Influencing Factors on the Stability of Breakwater Armor Blocks

With economic development in coastal areas, investment in coastal engineering projects is increasing, and the accompanying engineering risks are also increasing, which are also being paid more and more attention to by people [33]. A breakwater can prevent seawater from flooding the protected area behind it, keep the water level in the port stable, and provide a guarantee for ships to dock safely and load and unload goods. The environment where the breakwater is located is very harsh, and it directly bears the impact of waves [34,35,36].

A rubble-mound breakwater typically consists of several layers:

The core is the innermost layer of the breakwater, usually made of large rocks or concrete blocks, providing the primary structural support.

Filter layers are layers of smaller rocks or granular material placed around the core to prevent erosion and filter out fine particles, ensuring stability.

The armor layer is the outermost layer of the breakwater, comprising large, specially shaped blocks known as armor blocks. These blocks absorb wave energy and protect the underlying layers from erosion.

The toe berm is a sloping or stepped section at the base of the breakwater designed to dissipate wave energy and reduce scouring.

The crest structure is the topmost part of the breakwater, often designed with a specific shape or profile to deflect waves and minimize overtopping.

These components work together to provide stability and protection against wave action, thereby safeguarding coastal areas from erosion and flooding.

Armor layer stability refers to the ability of the protective layer of armor blocks on a breakwater to resist wave forces, erosion, and displacement. This stability is crucial for ensuring the overall integrity and effectiveness of the breakwater structure in mitigating coastal erosion and wave action. Several factors influence armor layer stability, including the size, shape, and weight of the armor blocks, as well as their arrangement and placement pattern. The interaction between the blocks, as well as with the underlying layers of the breakwater such as the core and filter layers, also plays a significant role.

Generally, the stability of breakwater armor blocks is affected by many factors, as shown in Figure 1. In Figure 1, the stability of breakwater armor blocks is mainly affected by wave, current, soil mechanics, block geometry, and foundation bed [37,38,39,40,41]. The specific influence modes of each factor are shown in

Table 1. The influence mode of each factor on breakwater armor blocks.

Influence Factor	Description	Influence Mode
Wave characteristics	Wave height, period, incident angle, and spectrum characteristics	Affect the force and displacement of the block
Water flow characteristics	Velocity, direction, scouring, vortex formation	Affect the stability and failure of the block
Soil mechanical properties	Strength, shear parameters, pore water pressure, type, and composition	Affect the shear strength and bearing capacity of soil
Geometric characteristics of block	Geometry, size, arrangement, block spacing and connection	Affect block stability and interaction between blocks
Characteristics of foundation bed	Bed hardness, bed stability, bed deformability, settlement, and erosion. The armor blocks are not placed directly on the foundation bed. Instead, intermediary layers like filter layers or bedding materials are typically incorporated between the foundation bed and the armor blocks.	Affect block support and displacement

.

Among all the influencing factors, waves are one of the most important driving forces for the stability of breakwater armor blocks. Factors such as wave height, period, incident angle, and spectrum characteristics will affect the force and stability of the block. Large waves and long-period waves may exert a greater dynamic load on the block, increasing the displacement and overturning risk of the block [42]. Therefore, this paper mainly starts with the wave, which is the main influencing factor, and meanwhile identifies the position and postural variation of breakwater armor blocks, which has achieved the effect of exploring the stability of breakwater fender blocks.

3.2. Identification and Analysis of Face Protection Block Posture Using Mask R-CNN

The identification of the posture and postural variation in breakwater armor blocks has important application value in breakwater engineering, which can help engineers monitor and evaluate the position, inclination angle, and rotation angle of the block in real time and provide accurate data support for maintenance and management [43]. Mask R-CNN is an object detection and instance segmentation algorithm based on deep learning, which increases pixel-level segmentation ability based on object detection [44,45]. Through Mask R-CNN, the precise positioning and contour segmentation of the armor block can be realized, thus obtaining more detailed and comprehensive pose information [46]. The specific posture recognition framework of the face pad based on Mask R-CNN is shown in Figure 2.

The input data for the algorithm include high-resolution images of the breakwater structures, particularly focusing on the armor blocks. These images are used to train and test the deep learning models. The outputs of the algorithm include predictions about the stability and potential displacement of the armor blocks under various wave conditions. This involves identifying which blocks are likely to become unstable and providing a stability score or a probability of failure for each block. The frame, as shown in Figure 2, can realize position and orientation positioning, case segmentation, and automatic detection of the cover block through position and orientation recognition of the cover block based on Mask R-CNN. The Mask R-CNN algorithm uses the network structure of combining ResNet101 and the feature pyramid network (FPN) to extract the features of the image of the breakwater armor block [47]. The ResNet101 network contains 101 convolution layers, and features are extracted by convolution, forming a five-layer feature map of Stage 1, Stage 2, Stage 3, Stage 4, and Stage 5. The size and dimensions of feature maps in different stages are different. Stage 5 contains strong semantic information, but its feature map is the smallest, and its spatial information is greatly lost. The feature maps of the various stages are fused using the FPN network to fully utilize the features retrieved at each stage of the ResNet101 network, and the resulting feature maps are then input into regional candidate networks. FPN is a feature pyramid network, which adds a top-down feature fusion process after the bottom-up feature extraction process and connects the two processes horizontally, that is, the face-protecting block image. The model’s detection performance is improved by placing the spatial information at the bottom and the semantic information at the top.

3.3. Wave Prediction and Analysis of Breakwaters Based on Bidirectional Encoder Representations from Transformer and BiLSTM

Wave prediction refers to the forecasting or estimation of the characteristics of waves near or around a breakwater structure. This prediction typically involves analyzing factors such as wave height, period, direction, and energy dissipation, taking into account the presence and design of the breakwater. The accurate prediction of wave behavior near breakwaters is essential for various purposes, including coastal engineering, port safety, and environmental impact assessments. When forecasting and analyzing waves, because of their time series differences, this paper combines the feature pre-training selection and model integration capabilities of BERT [48] and the sequence modelling and time series feature extraction capabilities of Bi-Directional Long Short-Term Memory (BiLSTM) [49] to improve the accuracy and stability of wave forecasting. The specific breakwater wave prediction model based on BERT fusion with BiLSTM is shown in Figure 3.

In the wave prediction analysis of breakwater based on BERT fusion with BiLSTM, firstly, it is necessary to use BERT for feature pre-selection and select the features with the most predictive ability as the input for the BiLSTM model. Then, the pre-processed wave data are input into BiLSTM model for training and prediction. The primary aim of the fusion algorithm used in this model is to reduce the risk of overfitting and enhance the generalization ability of the model.

In this model, the loss function L during model training can be expressed as Equation (1):

$$L=\frac{1}{N_{train}}{\displaystyle \sum }_{t=2}^{N_{train}}{\left(T_t-T_{predict,t}\right)}^2$$

(1)

$N_{train}$ is the number of samples in the training set. $T_t$ refers to the real value of breakwater wave at time t. $T_{predict,t}$ refers to the predicted value of breakwater wave at time t.

3.4. Experimental Design and Evaluation

The purpose of this paper is to verify the recognition effect of the posture and postural variation of breakwater armor blocks based on Mask R-CNN and the prediction effect of the breakwater wave prediction model based on BERT fusion with BiLSTM. The data in this paper come from the CLASH dataset. This dataset is a tool developed by Delft University to estimate wave overtopping. It collects experimental data about wave overtopping in various countries, including various breakwater types, and each piece of data includes wave factor parameters, wave overtopping, breakwater structure parameters, and other parameters [50]. D refers to the average particle size of the upper and lower slope armor blocks, which mainly refers to the block size near the water surface, and can be obtained according to the particle size D_u of the upper slope block and the particle size D_d of the lower slope block, as shown in Equation (2):

$$D=\frac{D_d\times \left(h_{sub}-h_b\right)+D_u\times \left(h_b+h_{em}\right)}{h_{sub}+h_{em}}$$

(2)

$h_b$ refers to the water depth on the platform. $h_{sub}$ and $h_{em}$ are expressed as Equation (3):

$$\{\begin{array}{l}{h}_{sub}=\mathit{min}\left(1.5·H_{m0,t};h\right)\\ h_{em}=\mathit{min}\left(1.5·H_{m0,t};A_c\right)\end{array}$$

(3)

h refers to the water depth in front of the structure. $H_{m0,t}$ refers to the effective wave height in front of the dike, and $A_c$ refers to the elevation of the dike top.

Similarly, ${\gamma }_f$ refers to the comprehensive roughness of uphill and downhill, which can be obtained by the following equation:

$${\gamma }_f=\frac{{\gamma }_{fd}\times \left(h_{sub}-h_b\right)+{\gamma }_{fu}\times \left(h_b+h_{em}\right)}{h_{sub}+h_{em}}$$

(4)

${\gamma }_{fu}$ and ${\gamma }_{fd}$ refer to the roughness of the upper and lower slopes, respectively. In addition, $\mathit{cot}{\alpha }_{incl}$ refers to the average slope within the range of wave climbing height, as shown in Equation (5):

$$\mathit{cot} {\alpha }_{incl}=\frac{\mathit{cot} {\alpha }_d\times \left(h_{sub}-h_b\right)+B+\mathit{cot} {\alpha }_u\times \left(h_b+h_{em}\right)}{h_{sub}+h_{em}}$$

(5)

${\alpha }_u$ and ${\alpha }_d$ are the uphill and downhill slopes, respectively, and B is the platform width. Equation (5) applies to $\left|h_b\right|<1.5·H_{m0,t}$. If $\left|h_b\right|<1.5·H_{m0,t}$ is not satisfied, there is Equation (6):

$$\mathit{cot} {\alpha }_{incl}=\{\begin{array}{l}\mathit{cot} {\alpha }_u\left(h_b<0\right)\\ \mathit{cot} {\alpha }_d\left(h_b>0\right)\end{array}$$

(6)

The actual input data consist of 27 sets of irregular wave conditions simulations. Similar simulation tests have already concluded the stability of these 27 sets of armor blocks. Using the method proposed in this paper, the 27 sets of conditions were input again, and the results were compared and verified with the physical model tests. The original intention of this paper is to use deep learning algorithms to analyze and predict the stability of breakwater armor blocks based on their images. The test data are mentioned in

Table 2. Test data.

Condition	Waterline (z/Dn)	Wave Height (m)	Stability Coefficient	Number of Collisions	Maximum Impact Velocity (m/s)
W 1-1	−2	0.50	1.563	0.517	0.214
W 1-2	−2	0.55	1.719	0.556	0.231
W 1-3	−2	0.60	1.875	0.583	0.245
W 1-4	−2	0.65	2.031	0.635	0.253
W 1-5	−2	0.70	2.188	0.657	0.260
W 1-6	−2	0.75	2.344	0.678	0.271
W 1-7	−2	0.80	2.500	0.712	0.284
W 1-8	−2	0.85	2.656	0.734	0.288
W 1-9	−2	0.90	2.813	0.764	0.295
W 1-10	0	0.50	1.563	0.421	0.254
W 1-11	0	0.55	1.719	0.435	0.283
W 1-12	0	0.60	1.875	0.471	0.312
W 1-13	0	0.65	2.031	0.493	0.334
W 1-14	0	0.70	2.188	0.514	0.349
W 1-15	0	0.75	2.344	0.529	0.353
W 1-16	0	0.80	2.500	0.546	0.367
W 1-17	0	0.85	2.656	0.563	0.371
W 1-18	0	0.90	2.813	0.578	0.380
W 1-19	+2	0.50	1.563	0.254	0.183
W 1-20	+2	0.55	1.719	0.261	0.194
W 1-21	+2	0.60	1.875	0.293	0.205
W 1-22	+2	0.65	2.031	0.322	0.217
W 1-23	+2	0.70	2.188	0.343	0.224
W 1-24	+2	0.75	2.344	0.356	0.235
W 1-25	+2	0.80	2.500	0.370	0.256
W 1-26	+2	0.85	2.656	0.394	0.263
W 1-27	+2	0.90	2.813	0.413	0.270

.

The experiment entailed designing 27 sets of irregular wave conditions. We have selected irregular waves mainly because the wave impacts on real coasts are often random, and irregular waves precisely meet this characteristic. The placement of the armor blocks is set as follows: z/Dn = −2 indicates a position 2 times the nominal diameter of the blocks below the zero-water line; z/Dn = 0 indicates a position exactly at the zero-water line; z/Dn = +2 indicates a position 2 times the nominal diameter of the blocks above the zero-water line. The wave heights are set to 0.50 m, 0.55 m, 0.60 m, 0.65 m, 0.70 m, 0.75 m, 0.80 m, 0.85 m, and 0.90 m. The nominal diameter of the armor blocks is 0.32 m, as shown in Table 2.

Meanwhile, the data are denoised and normalized before the experiment to eliminate problems such as measurement error and large range gaps between different types of data and to improve the prediction accuracy of the model. This experiment uses the TensorFlow platform for simulation and uses various modules provided by Python, including Pandas, Numpy, Sklearn, Matplotlib, etc. Among them, Pandas and Numpy are scientific computing libraries for data processing. Sklearn is a common tool for building deep learning, which integrates many application program interfaces and is used to build the BERT model. Matplotlib is a chart drawing library that is used to draw graphs. The specific super parameter settings are as follows: the batch size is 100, and there are 100 iterations. The random gradient descent approach optimizes the loss function, and the starting learning rate is set to 0.001.

Table 3. Experimental environment configuration.

		Model
Software	Operating system	Windows 10
	Image processing library	OpenCV 4.2.0
	Python version	Python 3.7
	Deep learning framework	TensorFlow 2.3.0
Hardware	CPU	Intel core i5-7400 CPU @ 3.0 GHz (Santa Clara, CA, USA)
	Memory	512 GB SSD
	Internal storage	Kingston ddr4 2400 MHz 8 G (Santa Clara, CA, USA)
	GPU	Nvidia GeForce GTX 1080 Ti (Santa Clara, CA, USA)

displays the setup of the experimental setting in the simulation.

In order to evaluate the recognition effect of the model proposed in this paper on the posture and posture of the visor, it is compared with the accuracy of R-CNN [51], Faster R-CNN [52], and Fogarin et al. [31] under different IOU thresholds (0.5/0.6/0.7/0.8/0.9), and each algorithm is analyzed.

In addition, in order to evaluate the performance of the proposed breakwater wave prediction model, it is compared with the model algorithms proposed by BiLSTM, BERT, Nieves et al. [29], and Ali et al. [32] in terms of convergence, accuracy, and F1 value, respectively.

4. Results and Discussion

4.1. Performance Analysis

In this work, to evaluate the performance of the proposed model, various descriptors are employed to present results. The following are the definitions of some commonly used descriptors:

IOU (Intersection Over Union) threshold: This metric is used to evaluate the accuracy of an object detector on a particular dataset. It measures the overlap between the predicted bounding box and the ground truth bounding box. The minimum IOU value at which a predicted bounding box is considered a true positive.

$Accuracy$: It is the ratio of correctly predicted observations to total observations:

$$Accuracy=\frac{True Positives+True Negatives}{Total Number of Cases}$$

(7)

$F1$ score: It is a measure of a test accuracy that considers both the precision (P) and the recall (R) to compute the score.

$$F1=2\frac{Precision\times Recall}{Precision+Recall}$$

(8)

Figure 4 displays the results of comparing the accuracy of R-CNN, Faster R-CNN, and the approach of Fogarin et al. [31] with that of the model provided in this paper to assess the recognition effect of the model on posture and the posture of the visor.

In Figure 4, by comparing the accuracy of each algorithm under different thresholds, it can be found that with the increase in the IOU threshold, the accuracy rate first increases and then decreases, and the accuracy of each algorithm is the highest when the IOU threshold is 0.5. The accuracy of the Mask R-CNN algorithm used in this paper is obviously better than other algorithms, reaching 95.16%. And the accuracy of each algorithm is as follows: mask R-CNN > Fogarin et al. [31] > Faster R-CNN > R-CNN. Therefore, by comparing the accuracy under different IOU thresholds, this paper chooses 0.5 as the IOU threshold, and the accuracy reaches its maximum.

Furthermore, the prediction effect of the breakwater wave prediction model algorithms proposed in this paper is compared with the model algorithm proposed by BiLSTM, BERT, Nieves et al., [29] and Ali et al. [32] in terms of convergence, accuracy, and F1 value, respectively, as shown in Figure 5, Figure 6 and Figure 7.

In Figure 5, through the analysis of the loss value of each algorithm, it can be found that the loss value of the model algorithm in this paper is the smallest, and it reaches a basically stable state when the iteration period is 16 and remains at about 0.01. However, the final loss functions of other algorithms all exceed 0.04. Therefore, the breakwater wave prediction model based on BERT fusion with BiLSTM as proposed in this paper has a better convergence effect and a lower loss value.

In Figure 6 and Figure 7, by further comparing the accuracy of each algorithm with the F1 value, it can be found that the prediction accuracy and F1 value of the model algorithm in this paper are 89.70% and 86.06%, respectively, by comparing it with BiLSTM, BERT, the approach of Nieves et al. [29] and the approach of Ali et al. [32]. Additionally, the prediction performance of each algorithm is in the order of the proposed algorithm > algorithm proposed by Ali et al. [32] > algorithm proposed by Nieves et al. [29]) > BiLSTM > BERT, and the accuracy is improved by at least 4.0% compared with other algorithms. Therefore, the breakwater wave prediction model based on BERT fusion with BiLSTM as constructed in this paper has better classification and prediction accuracy for breakwater waves.

4.2. Discussion

This paper discusses and analyzes the posture recognition model of the visor block based on Mask R-CNN and finds that under different thresholds, each algorithm achieves maximum accuracy by choosing 0.5 as the IOU threshold. Compared with other algorithms such as that proposed by Fogarin et al. [31], Faster R-CNN, and R-CNN, it is found that the Mask R-CNN algorithm used in this paper shows obvious advantages, and its accuracy reaches 95.16%. This is consistent with Hu et al. [53].

Further, this paper compares the proposed algorithm for the breakwater wave prediction model with those of BiLSTM, BERT, Nieves et al. [29] and Ali et al. [32]. Through the analysis of the loss value, it is found that the algorithm of this research model has a small loss value and reaches a basically stable state when the iteration period is 16. The loss function of other algorithms finally exceeds 0.04, which shows that the breakwater wave prediction model based on BERT fusion with BiLSTM as proposed in this paper has a better convergence effect. This is related to the discovery of Tao et al. [54]. Meanwhile, in the comparison accuracy and F1 value experiments, it was found that the prediction accuracy and F1 value of this research model algorithm reach 89.70% and 86.06%, respectively. Compared with other algorithms, this model has greatly improved the classification and prediction accuracy of breakwater waves and has a better application prospect for wave prediction in breakwater projects, thus having practical value for the stability optimization of breakwater lake blocks.

5. Conclusions

In this paper, aiming at the optimization of the stability of breakwater armor blocks, the influence factors of breakwater armor block stability were analyzed, and a posture recognition model of the armor block based on Mask R-CNN and a breakwater wave prediction model based on BERT fusion BiLSTM were constructed. Through experiments, it was discovered that the Mask R-CNN algorithm used in this paper has an accuracy of 95.16%, and the breakwater wave prediction model based on BERT fusion with BiLSTM has high prediction accuracy and a low loss value, demonstrating that this research model has clear advantages in the breakwater field. However, there are some restrictions in this paper. Firstly, the model’s performance is constrained by the quality and quantity of the data. However, by expanding the sample size and collecting more data, the model may be more generalizable. Secondly, this paper only focuses on the specific breakwater situation, and the application of other types of breakwaters and environmental conditions still needs further research and verification. Therefore, in the follow-up investigation, other data sources and numerous pieces of information can be integrated to further enhance the model’s capacity for prediction and generalization. Finally, in order to improve the stability of the breakwater armor block and ultimately have sustainability and disaster resistance, other factors affecting the stability of the breakwater armor block, such as the hydrodynamic effect and soil mechanical parameters, could be thoroughly studied and included in the model analysis.