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Article

Estimating Shear Strength of Marine Soft Clay Sediment: Experimental Research and Hybrid Ensemble Artificial Intelligence Modeling

by
Shuyu Hu
1,†,
Zhikang Li
1,†,
Haoyu Wang
1,
Zhibo Xue
2,3,*,
Peng Tan
4,
Kun Tan
5,
Yao Wu
6 and
Xianhui Feng
7
1
School of Merchant Marine and School of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 200135, China
2
China Water transport Research Institute, Ministry of Transport, Beijing 100088, China
3
School of Architecture and Engineering, Tianjin University, Tianjin 300072, China
4
School of Physical Education and Health Management, Chongqing Second Normal University, Chongqing 400065, China
5
School of Engineering, Qufu Normal University, Qufu 273165, China
6
Pearl River Hydraulic Research Institute, Pearl River Water Resources Commission, Guangzhou 510611, China
7
School of Civil and Resources Engineering, University of Science and Technology Beijing, Beijing 100083, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Water 2024, 16(12), 1664; https://doi.org/10.3390/w16121664
Submission received: 24 May 2024 / Revised: 4 June 2024 / Accepted: 7 June 2024 / Published: 11 June 2024
(This article belongs to the Special Issue Coast Sediment Dynamics: Historical Development, Current Situation and Perspectives)
Browse Figures
Versions Notes

Abstract

:
In the design of offshore engineering foundations, a critical consideration involves determining the peak shear strength of marine soft clay sediment. To enhance the accuracy of estimating this value, a database containing 729 direct shear tests on marine soft clay sediment was established. Employing a machine learning approach, the Particle Swarm Optimization algorithm (PSO) was integrated with the Adaptive Boosting Algorithm (ADA) and Back Propagation Artificial Neural Network (BPANN). This novel methodology represents the initial effort to employ such a model for predicting the peak shear strength of the soil. To validate the proposed approach, four conventional machine learning algorithms were also developed as references, including PSO-optimized BPANN, Support Vector Machine (SVM), BPANN, and ADA-BPANN. The study results show that the PSO-BPANN model, which has undergone optimization via Particle Swarm Optimization (PSO), has prediction accuracy and efficiency in determining the peak shear performance of marine soft clay sediments that surpass that offered by traditional machine learning models. Additionally, a sensitivity analysis conducted with this innovative model highlights the notable impact of factors such as normal stress, initial soil density, the number of drying–wetting cycles, and average soil particle size on the peak shear strength of this type of sediment, while the impact of initial soil moisture content and temperature is comparatively minor. Finally, an analytical formula derived from the novel algorithm allows for precise estimation of the peak shear strength of marine soft clay sediment, catering to individuals lacking a background in machine learning.

1. Introduction

Marine soft clay sediment is a commonly employed foundation material in various offshore engineering projects, including embankments and breakwaters [1,2,3,4]. Consequently, the mechanical properties of marine soft clay sediment, particularly its peak shear strength, play a pivotal role in ensuring the stability of ocean engineering structures [5,6,7]. The decline in the peak shear strength of marine soft clay sediment can lead to instability and potential damage to foundations or even the entire offshore engineering application [8,9,10]. This underscores the significance of accurately assessing the peak shear strength of marine soft clay sediment for the operational safety of engineering infrastructures [11,12,13,14].
Throughout the operational phase, the marine soft clay sediment foundation is unavoidably subjected to diverse environmental factors within the ocean, which can exert a substantial influence on its peak shear strength [15,16,17]. For instance, in offshore regions, the climate is changeful, such as alternating periods of rainfall and shine. These changes can induce drying–wetting cycles in the marine soft clay sediment, causing frequent expansion and shrinkage, which can reduce the clay peak shear strength [18,19,20]. Furthermore, the thermal reactions resulting from the climatic changes can cause temperature variations, which can either strengthen or weaken the mechanical properties of the soil [21,22,23]. Additionally, inherent properties of the marine soft clay sediment, such as soil density, moisture content, and other factors, can also have an impact on its peak shear strength [10,24,25,26]. Considering the prediction of the peak shear strength of marine soft clay sediment, the impact of both external and internal influencing factors cannot be overlooked [27,28,29].
To precisely evaluate the peak shear strength of marine soft clay sediment, researchers have designed specialized testing equipment capable of simulating the unique service conditions within these environments [30,31,32,33]. Notably, Chao and Fowmes [33] introduced a custom apparatus capable of quantifying the peak shear strength of soil or the soil-geosynthetics interface under varying temperature conditions during drying–wetting cycles. By utilizing these custom test devices, the peak shear resistance of marine soft clay sediment in practical offshore engineering environments can be assessed. However, there are several limitations associated with laboratory test approaches. Firstly, developing bespoke apparatuses can be costly and requires specialized mechanical and design knowledge, which may not be readily available to every environmental or construction engineering researcher. Secondly, operating the custom apparatuses typically requires the continuous involvement of a skilled practitioner, which can be labor intensive. Thirdly, the process of simulating the real offshore engineering environment, including reaching temperature equilibrium or conducting drying–wetting cycles, can be time consuming [34,35,36]. Developing precise predictive models that accurately estimate the peak shear strength of marine soft clay sediments under real-world conditions have the potential to significantly address the aforementioned challenges.
As previously mentioned, the peak shear strength of marine soft clay sediments is influenced by a diverse array of variables exhibiting intricate interaction mechanisms [37,38,39]. The intricate nature of this problem poses significant challenges in establishing direct empirical equations through conventional statistical methods, thereby making it challenging to accurately replicate the nonlinear relationship between these influences [40,41]. This relationship is crucial for precise estimation of peak shear strength [42,43,44]. This underscores the pressing need for reliable approaches capable of providing accurate and efficient estimation of the peak shear strength of marine soft clay sediment [45,46].
The scientific community has shown significant interest in machine learning techniques, leading to their widespread application in marine engineering. This widespread adoption is primarily attributed to the techniques’ remarkable capacity to precisely capture the intricate and non-linear relationships among various factors [47]. Notably, Cavalcante et al. [42] utilized machine learning approaches to estimate rock tensile strength, demonstrating the powerful predictive capacity of machine learning techniques in such applications. Likewise, in the domain of predicting soil peak shear strength, efforts have been made to leverage machine learning models for precise estimations. Khodkari et al. [47,48,49,50,51] utilized Genetic Algorithm (GA) optimized Artificial Neural Networks (ANNs) to evaluate soil shear strength based on the inherent characteristics of the soil. Meanwhile, Chao et al. [51] applied a hybrid Support Vector Machine (SVM) model to assess soil shear strength, and Xu et al. [52] developed a Particle Swarm Optimization (PSO) optimized Support Vector Machine (SVM) model for the same purpose. Despite these advancements, existing research on machine learning models for soil peak shear strength exhibits certain deficiencies that necessitate further refinement [53,54]. Firstly, soil shear strength modeling often ignores the effects of environmental factors such as dry and wet cycles and temperature, thus limiting its ability to assess the peak shear strength of marine soft clay sediments under real-world conditions of use [55,56]. Secondly, prior studies predominantly relied on basic and overly simplified machine learning algorithms, ignoring the potential for greater advanced algorithms, including technology sets such as the ADA combined with BPANN, for precise estimation of peak shear strength in soil [57,58,59].
The predictive performance of machine learning algorithms is significantly influenced by a subset of parameters referred to as hyperparameters [60,61,62]. Prior to modeling, the hyperparameters of the machine learning model must be optimized by employing appropriate optimization algorithms. This step is crucial as it can significantly improve the predictive performance of the models [63,64,65]. Extensive research in the literature supports this claim, with various academic researchers acknowledging the notable advancements achieved through the employment of optimization algorithms [66,67,68]. In general, the machine learning models without combining optimization algorithms are inefficient, with slow convergence speed, overtraining, or are prone to converging to local optima, and often pose a convergence problem. More importantly, there is subjectivity in the artificially determining of initial model parameters, which causes low predictive accuracy. Hence, the optimized algorithms, such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) have been applied by some researchers to optimize the initial parameters of machine learning models for evaluating the properties of geotechnical materials, and an increase in both predictive accuracy and convergence speed of the constructed machine learning models after combining optimization algorithms has been demonstrated. For instance, Chao et al. [33] applied PSO and Genetic Algorithm (GA) to optimize the performance of BPANN and Support Vector Machine (SVM) algorithms when assessing the peak shear strength for the soil-geosynthetics interface. Nevertheless, there is a lack of reports on how optimization algorithms can be used to improve the predictive performance of machine learning algorithms when estimating the peak shear strength of marine soft clay sediments.
In this study, we introduced an innovative PSO-tuned ADABPANN algorithm to predict the peak shear strength of marine soft clay sediment using a database derived from 729 laboratory tests. This marks the first application of the PSO-tuned ADABPANN algorithm in forecasting soil peak shear strength. Simultaneously, five distinct traditional machine learning models, including PSO-tuned BPANN and SVM models, BPANN, and ADABPANN algorithms, were established to assess the applicability of the newly proposed model. Utilizing the PSO-optimized ADABPANN model, susceptibility analysis was conducted, leading to the formulation of an analytical formula for precise predictions of the peak shear strength of marine soft clay sediment, catering to practitioners lacking machine learning expertise. The proposed PSO-tuned ADABPANN model demonstrates accurate and efficient estimation of the peak shear strength for marine soft clay sediment, serving as a pivotal element in advancing the design and operational safety of foundations.

2. Machine Learning Algorithms

This paper employed three types of machine learning algorithms: BPANN, SVM, and Adaptive Boosting Algorithm-Back Propagation Artificial Neural Network (ADABPANN), alongside the optimization algorithm Particle Swarm Optimization (PSO). The basic explanation and fundamental specifications of these algorithms are outlined below.

2.1. BPANN

The BPANN model, as a general structure, consists of input, hidden, and output layers [69,70,71]. The number of neurons in the input and output layers is directly correlated with the number of input and output variables, respectively. In this study, this amounts to 6 and 1. The determination of the number of hidden layer neurons (9) was achieved through an exhaustive enumeration method, as illustrated in Figure 1. Furthermore, the BPANN model employs HTSTF as the activation function and the Levenberg–Marquardt Backpropagation Algorithm (LMBA) as the training algorithm for the network.

2.2. SVM

SVM has the capability to perform regression operations with limited sample data [72,73,74,75]. Furthermore, SVM can utilize kernel functions to project specimens from a low-dimensional space to a high-dimensional space, thus effectively transforming a nonlinear problem into a linear one [76].

2.3. ADA-BPANN

ADA-BPANN is a resilient ensemble machine learning algorithm that utilizes BPANN models with identical structures. This integration is based on the principles of bootstrap aggregating theory, which enhances its overall performance and robustness [75,77]. In this study, the specifications of the BPANN models align with the previously mentioned BPANN model. The ADA-BPANN algorithm offers advantages such as straightforward operation, cost-effective computation, superior predictive accuracy, and generalization capability [78,79].
The detailed configurations of the constructed models are illustrated in Table 1.

2.4. PSO

PSO is a heuristic optimization algorithm that simulates natural evolution principles to guide the optimization of a population [80]. Specifically, PSO is inspired by bird predation behavior, where particles within the population serve as potential solutions. Through the continuous adjustment of particle motion velocities, PSO strives to identify the optimal solution for the given problem [81,82].

3. Hyperparameters Optimization

In the study, PSO was employed to optimize the hyperparameters the machine learning algorithms proposed, utilizing RMSE (Root-Mean-Square Error) as the fitness metric. (Equation (1)). Given the commonality of PSO optimization processes and the availability of detailed introductions by many researchers, this study does not provide an in-depth explanation of the optimization procedures. The specific optimizing procedure is presented in Figure 2.
R M S E = ∑ i = 1 n ( y i − f i ) 2 n
where n denotes number of samples, denotes observed value, signifies the predicted value.
The parameters that control PSO are summarized in Table 2, while Table 3 presents the optimization hyperparameter and the corresponding ranges for optimization.

4. Methodology

4.1. Laboratory Tests

The physical experiments were conducted using a custom-designed temperature-controlled direct shear apparatus, which consists of several main components, including a temperature-controlled system, a drying–wetting cycles-controlled system, a normal pressure loading system, and a shear pressure loading system. The internal large interface shear system is placed inside the temperature chamber. The upper shear box has a square cross-sectional area of 300 mm by 300 mm and a thickness of 150 mm. The temperature-controlled system is capable of adjusting the temperature of the soil sample by utilizing a heating device located beneath the bottom shear box. The temperature can be adjusted within a range of 30 °C to 140 °C, with a high level of precision, maintaining control within 0.2 °C. Additionally, the drying–wetting cycles-controlled system can regulate the moisture status of the soil sample, allowing for controlled submersion in water or drying cycles. The normal pressure and shear pressure systems are capable of measuring the peak shear strength for soil in diverse normal pressure (0 kPa~400 kPa), with the maximum shear displacement being 100 mm.
The standard testing protocol is as follows: (1) Gently place the marine soft clay sediment sample into the upper and bottom shear boxes and compact it lightly. (2) Activate the temperature-controlled system to stabilize the soil sample temperature for the entire test duration. (3) Initiate the drying–wetting cycles-controlled system to subject the clay sample to cycles. Wetting cycles involve fully submerging the soil sample in water for 0.5 h, constituting one wetting cycle. During drying cycles, maintain the soil sample in a dry-state (soil samples were removed from water and dried using the ambient temperature chamber) for 0.5 h, constituting one drying cycle. One drying–wetting cycle comprises one wetting cycle and one drying cycle. (4) After a predetermined number of drying–wetting cycles, begin the undrained shearing procedure with a shear rate of 1 mm/minute and a maximum shearing displacement of 100 mm. (5) Derive the peak shear strength for marine soft clay sediment under specific temperatures during distinct drying–wetting cycles based on the test data. In the present study, the peak shear strength of marine soft clay sediment with varying mean soil particle sizes, initial density, and initial moisture content was measured under different temperatures, numbers of drying–wetting cycles, and normal pressure. The experimental condition involved unconsolidated undrained shearing. The properties of the marine soft clay sediment sample are listed in Table 4, and the test plan is detailed in Table 5. A total of 729 sets of tests were conducted.

4.2. Database Creation and Data Processing

Using the above test data, a database containing 729 datasets was created for machine learning modeling. Within these datasets, 583 groups (80%) were randomly chosen for training datasets for constructing the machine learning algorithm. Meanwhile, 146 groups (20%) were randomly chosen as test datasets to evaluate the predictive ability of the proposed machine learning algorithm. Each data group consisted of six variables, namely initial soil density (D), initial soil moisture content (M), initial mean soil particle size (S), temperature (T), drying–wetting cycle number (C), and normal pressure (N), serving as input parameters. The output variable was determined as the peak shear strength of the marine soft clay sediment sample (H). Table 6 shows the statistics of the input and output variables in the database. Figure 3 shows the distribution of the input parameter data in the database, where the x-axis represents the count of data groups associated with the value of a particular input variable, and the y-axis represents the value of the input parameter. Also, the correlation between the input parameters was investigated, with the Pearson’s correlation matrix being illustrated in Figure 4. According to Figure 4, The correlation coefficients between the input parameters (initial density, initial moisture content, mean soil particle size, temperature, number of drying–wetting cycles, and normal pressure) are 0. This indicates that the input parameters are independent of each other and they do not have a correlation.
In this study, a machine learning model was constructed using Matlab. Before starting the machine learning modeling, the dimensions of the input and output variables were normalized to improve the predictive accuracy and effectiveness of the machine learning algorithm. The normalization formula is as follows (2).
x N o r m a l i s e d = 2 ( x − x min ) x max − x min − 1
where x N o r m a l i s e d and x represent normalized and initial data, respectively, x min and x max denote the minimum and maximum data, respectively.

4.3. Approaches for Evaluating Performance

The predictive accuracy of the constructed machine learning algorithm is evaluated by three parameters:
(i)
RMSE: The definition of RMSE is expressed in Equation (1), representing the standard error between the estimated and measured values. A lower RMSE value indicates higher accuracy in the model.
(ii)
Correlation coefficient (R2): The definition of R2 is expressed in Equation (3), which is the associated degree between the change of forecasted and observed value. R2 value is in the range of [−1, 1], with −1 and 1 representing the absolutely negative and positive correlations, respectively [82,83].
R ( f i , y i ) = cov ( f i , y i ) var f i var y i
where cov ( , ) means covariances, var means variances.
(iii)
Mean absolute percentage error (MAPE): MAPE is defined in Equation (4) as a dimensionless parameter. A smaller MAPE value indicates a more accurate model, with a value of 0 indicating a perfect prediction.
M A P E = 100 % n ∑ i = 1 n y i − f i y i

5. Predicting Performance

5.1. Results for Hyperparameter Optimization

The process of optimizing hyperparameters for ADABPANN, BPANN, and SVM models using PSO approach is depicted in Figure 5.
As depicted in Figure 5, for ADABPANN, BPANN, and SVM, the RMSE value gradually decreases with the increase in the iteration number during the PSO process. Comparing the optimized RMSE value to the value before optimization reveals a relatively significant decrease. Specifically, after optimization using PSO, the RMSE of ADABPANN, BPANN, and SVM decreases from 14.5 to 3.1, 16.9 to 5, and 14.7 to 6.9, respectively. This indicates the pronounced improvement effect of PSO on predictive accuracy.

5.2. Predicting Performance

The predictive performance of the machine learning models developed for evaluating the drilling and measuring datasets is illustrated in Figure 6, Figure 7 and Figure 8.
When evaluated with the training datasets, as depicted in Figure 6, Figure 7 and Figure 8, the PSO-tuned ADABPANN model exhibits superior predictive performance compared to the other four algorithms. It is noteworthy that the model has the highest predictive accuracy with the lowest RMSE value of 2.7, the smallest MAPE value of 5.41%, and the highest R2 value of 0.99. The PSO-tuned SVM model follows closely in performance. In contrast, the predictive capabilities of the PSO-tuned BPANN model, SVM model, and BPANN model appear relatively inferior.
As depicted in Figure 7, Figure 8 and Figure 9, the PSO-tuned ADABPANN model consistently outperforms the other four machine learning models in terms of prediction performance when assessed with the test dataset. Notably, the PSO-tuned ADABPANN model shows the best prediction accuracy with the lowest RMSE value of 3.11, the smallest MAPE value of 6.33%, and the highest R2 value of 0.99. Among the rest of the machine learning models, the PSO-tuned SVM model performs relatively well. In summary, the PSO-tuned ADABPANN model demonstrates superior performance in evaluating both training and testing datasets compared to the PSO-tuned SVM model and BPANN model. Specifically, the PSO-tuned ADABPANN model excels in forecasting the peak shear strength for marine soft clay sediment with higher precision and efficiency. Notably, within the same machine learning algorithm, the models combined using the PSO algorithm outperform individual machine learning models, exhibiting higher predictive accuracy.

5.3. Sensitivity Analysis

In this comprehensive section, the meticulously crafted PSO-tuned ADABPANN model is utilized to conduct a rigorous sensitivity analysis. The purpose of this analysis is to scrutinize the relative importance of various input parameters in predicting the peak shear strength of marine soft clay sediments. By doing so, we aim to gain a deeper understanding of how these parameters influence the overall prediction accuracy and to identify any potential areas of improvement for future model iterations. The ADABPANN algorithm, composed of multiple BPANN models will be discussed. The relative importance of the input variables is assessed using the Garson’s algorithm as defined in Equation (5). Determining the relative importance of input variables in the BPANN algorithm using the Gasson algorithm serves as a surrogate measure for assessing the significance of these parameters in the ADABPANN model. As shown in Figure 10, this surrogate metric allows us to gain insight into the impact of various input factors on the overall predictive performance of the ADABPANN model. By analyzing these findings, we can identify potential areas for optimization and refinement, further enhancing the accuracy and reliability of the model [84,85].
R ik = ∑ j = 1 L ( W i j W j k / ∑ r = 1 N W r j ) ∑ i = 1 N ∑ j = 1 L ( W i j W j k / ∑ r = 1 N W r j )
where R ik signifies the relative significance for input variables, and W i j , W j k represents the connectivity weight for the hidden-input and hidden-output layers (N, M represents the input and output variable numbers, respectively).
As illustrated in Figure 10, normal stress is identified as having the highest impact on the peak shear resistance of marine soft clay sediment, with a relative significance of 27.17%. It is closely followed by initial soil density, the drying–wetting cycle number, and mean soil particle size, accounting for 20.33%, 19.24%, and 17.36%, respectively. Conversely, the influence of initial soil moisture content and temperature on peak shear strength is relatively small, contributing 9.6% and 6.3%, respectively. For a detailed understanding of the mechanism, please refer to the “Discussion” section.

6. Establishment of an Analytical Formula

The above analysis suggests that the constructed PSO-tuned ADABPANN model can offer accurate estimations of the peak shear strength for marine soft clay sediment. However, due to the intricacies of machine learning modeling, applying these models might pose a challenge for individuals without a background in machine learning. To address this limitation, this section proposes an analytical formula for forecasting the peak shear strength of marine soft clay sediment by utilizing the built PSO-tuned ADABPANN model. As previously mentioned, the ADABPANN model consists of a set of BPANN models, and the output values of the BPANN models can be calculated from the connection weights and biases of the nodes in the model using Equation (6). Therefore, the estimation of the PSO-ADABPANN model can be obtained from Equation (6) by using the average connection weights and biases calculated for the BPANN models that make up the ADABPANN algorithm, as detailed in Table 7 [86,87,88,89,90].
Y n = f s i g { b 0 + ∑ k = 1 h [ w k × f s i g ( b h k + ∑ i = 1 m w i k X i ) ] }
Utilizing Equation (6), the analytical formula for estimating the peak shear strength for marine soft clay sediment is derived and presented in Equation (7).
τ = 0.5 ( Y n + 1 ) ( Y max − Y min ) + Y min
where Y max and Y min denote the highest and lowest data for the peak shear strength in the database, respectively, Y max = 9   kPa and Y min = 41   kPa .
Among Equation (8):
Y n = e C 1 − e − C 1 e C 1 + e − C 1
Among Equation (9):
C 1 = 0.95 + ∑ i = 1 9 g i × e A i − e − A i e A i + e − A i
where g i denotes the connection weights between the i-th hidden layer junction and the output layer junction of the constructed PSO-ADABPANN algorithm, as detailed in Table 7.
In Equation (10):
A i = h i + ∑ j = 1 9 p j × N j
where h i denotes the biases for the j-th hidden layer node; p j denotes the connected weight between the j-th input layer junction and the i-th hidden layer junction; N j denotes the i-th uni-formalized input variable.

7. Validation of the Predicting Performance with the Physical Tests

In order to assess the feasibility of the suggested analytical formulation and machine learning model, we compared the peak shear strengths of marine soft clay sediments predicted using the analytical formulation with the peak shear strengths acquired from physical tests. The overall process is outlined as follows: (1) Conduct large direct shear experiments on marine soft clay sediment with varying properties under different test conditions using the bespoke apparatus. The basic parameters of the marine soft clay sediment sample and the test plan are listed in Table 8 and Table 9, respectively, totaling 32 sets of tests. (2) Estimate the peak shear strength of marine soft clay sediment based on the soil sample properties and test conditions using Equation (7). (3) Compare the peak shear strength obtained from the analytical equation and machine learning model, with the results illustrated in Figure 11 [91,92,93,94,95].
As shown in Figure 11, the peak shear strengths of marine soft clay sediments predicted using the analytical equations are very close to the peak shear strengths obtained from laboratory tests [96,97,98]. Specifically, the RMSE, MAPE, and R2 values are 4.92, 4.36%, and 0.99, respectively. These results indicate that the prediction accuracy of the constructed analytical equations and machine learning model is satisfactory.

8. Discussion

The sensitivity analysis indicates a substantial impact of the drying–wetting cycle number on the peak shear strength of marine soft clay sediment used as foundations, with a notable relative significance of 19.24%. This influence is attributed to the expansion and shrinkage properties of marine soft clay sediment during the absorption and expulsion of water, respectively. The frequent alternation of soil expansion and shrinkage during drying–wetting cycles leads to volume variations, inducing the generation of cracks within the marine soft clay sediment. This damage to the structure consequently decreases the peak shear strength. Moreover, a larger drying–wetting cycle number is observed to cause more significant damage to the soil structure, resulting in a larger decreasing magnitude in the peak shear strength compared to a smaller number of cycles. Therefore, the drying–wetting cycle number exhibits a relatively high importance in determining the peak shear strength of marine soft clay sediment. It is essential to note that in this study, the relative significance of the initial soil moisture content for the peak shear strength is relatively small, at 9.6%. This is attributed to the requirement that marine soft clay sediment samples undergo drying–wetting cycles before conducting large direct shear tests. Consequently, the moisture content of the soil samples tends to converge to a similar level after the drying–wetting cycles, diminishing the impact of initial moisture content on the peak shear strength. Furthermore, the low relative significance of temperature, at 6.3%, can be explained by the moderate temperature range (20–60 °C) adopted in this research. This temperature range is not extreme enough to induce freezing or melting of the soil, which would significantly alter the soil structure and result in a large variation in peak shear strength.
Two critical aspects of this research warrant further improvement. (1) In actual offshore engineering sites, the environment of marine soft clay sediment is intricate, and the environmental factors affecting marine soft clay sediment extend beyond just drying–wetting cycles and temperature. Therefore, future research should strive to determine the peak shear resistance of marine soft clay sediment under the influence of various environmental loadings, including leachate erosion, to augment the current database. These enhancements will establish a robust foundation for the advancement of machine learning models, enabling more precise assessments of the peak shear strength of marine soft clay sediments in real-world offshore engineering applications. (2) In practical offshore engineering, the stress environment experienced by marine soft clay sediment is complex, involving factors such as triaxial shear stress, among others. Therefore, conducting tests to measure the peak shear strength of marine soft clay sediment under various stress conditions, including triaxial shearing and axial shearing, would be valuable. Based on these test results, existing databases can be extended to create more accurate machine learning models capable of predicting the peak shear performance of marine soft clay sediments in real stress environments.

9. Conclusions

This study has established a comprehensive database comprising 729 large-scale direct shear tests, providing a robust foundation for developing a novel PSO-tuned ADABPANN model aimed at predicting the peak shear strength of marine soft clay sediment. The constructed model takes into account essential input parameters, including initial soil density, initial soil moisture content, mean soil particle size, number of drying–wetting cycles, temperature, and normal pressure. It is noteworthy that this marks the first application of the PSO-tuned ADABPANN model for estimating soil peak shear resistance. In order to authenticate and contrast the predictive performance of the proposed innovative algorithms, traditional machine learning models such as PSO-optimized BPANN and SVM were also developed. In addition, a sensitivity analysis based on the PSO-optimized ADABPANN algorithm was conducted to evaluate the relative importance of the input parameters on the peak shear strength of marine soft clay sediments. In addition, an analytical expression was devised to facilitate precise evaluation of peak shear strengths for organizations lacking expertise in machine learning techniques.
The current study confirms the efficacy of the proposed PSO-optimized ADABPANN algorithm in efficiently and accurately evaluating the peak shear performance of marine soft clay sediments, which outperforms conventional machine learning algorithms. Notably, this study observed superior optimization and efficiency when PSO was employed. Sensitivity analyses showed that normal stress, initial soil density, average soil grain size and number of wet and dry cycles had a significant effect on the peak shear strength of marine soft clay sediments, whereas the initial soil moisture content and temperature had relatively minor effects.
In conclusion, accurately estimating the peak shear strength of marine soft clay sediments poses significant challenges due to the presence of numerous influencing factors and intricate interaction mechanisms. Nevertheless, the introduction of the novel PSO-adjusted ADABPANN model successfully addresses these challenges, providing a reliable method for accurate and efficient prediction of peak shear strength. The model provides a solid foundation for future developments in foundation design, thereby improving the overall performance and effectiveness of offshore infrastructure.

Author Contributions

Conceptualization, Z.X. and X.F.; investigation, H.W. and Z.L.; resources, S.H. and Z.L.; data curation, Z.X. and Z.L.; writing—original draft, S.H. and Z.L.; writing—review and editing, Z.L., H.W., and Z.X.; visualization, P.T., K.T., and Y.W.; software, Z.L., S.H., and H.W.; supervision, X.F.; funding acquisition, Z.X. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

In this paper, all data, models, and code used during the study appear in the submitted article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Water 16 01664 g001
Figure 1. The typical structure of BPANN.
Figure 1. The typical structure of BPANN.
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Figure 2. The flow chart of PSO optimizing.
Figure 2. The flow chart of PSO optimizing.
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Figure 3. Data distributions for the database. (a) Initial soil density; (b) initial moisture content; (c) mean soil particle size; (d) number of drying–wetting cycles; (e) normal stress; (f) temperature.
Figure 3. Data distributions for the database. (a) Initial soil density; (b) initial moisture content; (c) mean soil particle size; (d) number of drying–wetting cycles; (e) normal stress; (f) temperature.
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Figure 4. Pearson correlation coefficients graph.
Figure 4. Pearson correlation coefficients graph.
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Figure 5. Optimization processes by PSO. (a) BPANN; (b) SVM; (c) ADABPANN.
Figure 5. Optimization processes by PSO. (a) BPANN; (b) SVM; (c) ADABPANN.
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Figure 6. The R value for the algorithms in training datasets. (a) BPANN; (b) SVM; (c) PSO−BPANN; (d) PSO−SVM; (e) PSO−ADABPANN.
Figure 6. The R value for the algorithms in training datasets. (a) BPANN; (b) SVM; (c) PSO−BPANN; (d) PSO−SVM; (e) PSO−ADABPANN.
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Figure 7. The RMSE values of the models.
Figure 7. The RMSE values of the models.
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Figure 8. The MAPE values of the models.
Figure 8. The MAPE values of the models.
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Figure 9. The R2 value for the algorithms in testing datasets. (a) BPANN; (b) SVM; (c) PSO-BPANN; (d) PSO-SVM; (e) PSO-ADABPANN.
Figure 9. The R2 value for the algorithms in testing datasets. (a) BPANN; (b) SVM; (c) PSO-BPANN; (d) PSO-SVM; (e) PSO-ADABPANN.
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Figure 10. Relative significance for the input variables.
Figure 10. Relative significance for the input variables.
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Figure 11. The validation results. (a) The MAPE and RMSE; (b) the R2 values; (c) the predicted and measured value.
Figure 11. The validation results. (a) The MAPE and RMSE; (b) the R2 values; (c) the predicted and measured value.
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Table 1. Configurations of the employed algorithms.
Table 1. Configurations of the employed algorithms.
AlgorithmInput Layer Node NumberHidden Layer Node NumberOutput Layer Node NumberBase Leaner Number
BPANN791X
ADABPANN79140
Table 2. The control variables for the optimization algorithm.
Table 2. The control variables for the optimization algorithm.
AlgorithmPSO
Individual number200
Number of subgroups
Number of the maximum iterations100
Cognitive constant/Social constant2.05
Inertia weight0.98
Var maximum1
Var minimum−1
Maximum velocity2
Minimum velocity0.01
Selection methodO
CrossoverO
MutationO
Mutation rateO
Selection pressureO
Table 3. The optimization hyperparameters.
Table 3. The optimization hyperparameters.
AlgorithmHyperparameterOptimisation Range
BPANNOriginal node weight−5–5
Original node threshold−10–10
SVMPenalty parameter c of SVM2−6–26
Penalty parameter g of kernel function4−6–46
ADA-BPANNBase leaner number 1–20
Original node weight for the base learner−5–5
Original node threshold for the base learner−10–10
Table 4. The basic parameters of soil sample.
Table 4. The basic parameters of soil sample.
Initial Density/g/cm3Initial Moisture Content/%Mean Soil Particle Size/mm
0.5, 2, 40, 24, 460.001, 0.02, 0.05
Table 5. The test plan.
Table 5. The test plan.
Temperature/°CNumber of Drying–Wetting CyclesNormal Pressure/kPa
20, 40, 600, 6, 1215, 30, 50
Table 6. The statistics.
Table 6. The statistics.
ParametersKindsMinimumMaximumAverageStandard Deviation
InputInitial soil density/g/cm3Numeric0.542.170.36
Initial soil moisture content/%04639.333.30
Mean soil particle size/mm0.0010.050.0240.03
Temperature/°C2060404.5
Number of drying–wetting cycles01261.24
Normal stress/kPa155031.664.29
OutputPeak shear strength/kPaNumeric941243.36
Table 7. Connected weights and biases for the constructed PSO-ADABPANN algorithm.
Table 7. Connected weights and biases for the constructed PSO-ADABPANN algorithm.
Hidden Layer Nodes Number WeightBias
Input ParameterOutput ParameterHidden
Layer		Output
Layer
DMSTCNH
10.240.920.451.260.920.630.920.140.95
2−0.930.411.332.331.361.221.220.11
3−1.290.06−2.723.26−2.392.340.36−1.29
41.24−0.36−2.141.294.363.261.900.79
51.36−0.993.090.450.601.92−0.060.17
60.72−1.223.632.92−0.250.240.304.36
70.792.340.633.021.452.46−0.271.33
82.272.630.29−0.720.42−0.10.94−0.90
9−3.363.062.67−2.904.600.46−4.19−0.07
Table 8. The fundamental parameters of the validation soil sample.
Table 8. The fundamental parameters of the validation soil sample.
Initial Density/g/cm3Initial Moisture Content/%Mean Soil Particle Size/mm
1.4, 3.615, 420.01, 0.30
Table 9. The validation test plan.
Table 9. The validation test plan.
Temperature/°CNumber of Drying–Wetting CyclesNormal Pressure/kPa
30, 454, 940
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MDPI and ACS Style

Hu, S.; Li, Z.; Wang, H.; Xue, Z.; Tan, P.; Tan, K.; Wu, Y.; Feng, X. Estimating Shear Strength of Marine Soft Clay Sediment: Experimental Research and Hybrid Ensemble Artificial Intelligence Modeling. Water 2024, 16, 1664. https://doi.org/10.3390/w16121664

AMA Style

Hu S, Li Z, Wang H, Xue Z, Tan P, Tan K, Wu Y, Feng X. Estimating Shear Strength of Marine Soft Clay Sediment: Experimental Research and Hybrid Ensemble Artificial Intelligence Modeling. Water. 2024; 16(12):1664. https://doi.org/10.3390/w16121664

Chicago/Turabian Style

Hu, Shuyu, Zhikang Li, Haoyu Wang, Zhibo Xue, Peng Tan, Kun Tan, Yao Wu, and Xianhui Feng. 2024. "Estimating Shear Strength of Marine Soft Clay Sediment: Experimental Research and Hybrid Ensemble Artificial Intelligence Modeling" Water 16, no. 12: 1664. https://doi.org/10.3390/w16121664

APA Style

Hu, S., Li, Z., Wang, H., Xue, Z., Tan, P., Tan, K., Wu, Y., & Feng, X. (2024). Estimating Shear Strength of Marine Soft Clay Sediment: Experimental Research and Hybrid Ensemble Artificial Intelligence Modeling. Water, 16(12), 1664. https://doi.org/10.3390/w16121664

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