Uplift capacity prediction of suction caisson in clay using a hybrid intelligence method (GMDH-HS)
Introduction
Suction caissons are open bottom structures which can be used as anchor foundation for offshore structures such as highway bridges, harbors and wind turbines. These structures have a cylinder section tube, which is hollow or filling with sand. Suction caissons firstly mentioned by Senpere and Auverange (1982) as mooring anchor, because they reflected the multiple advantages than other alternatives. Suction caisson advantages are: 1) simple design 2) simple installation 3) fast installation 4) high resistance against vertical loading [1]. Uplift capacity in suction caissons in sand and clay is an important issue for their stabilities. If this parameter doesn’t estimate correctly, suction caisson may be collapsed [2]. The total uplift capacity of caisson depends upon passive suction under caisson-sealed cap, self- weight of caisson, frictional resistance along the soil-caisson interface, submerged weight of soil plug inside the caisson and uplift soil [3]. Different method including upper bound analysis [4], finite element method (FEM) [5], [6], [7], [8], [9], laboratory models [10], [11], [12], [13], [14], [15], [16], [17], [18], centrifuge model [19] and prototype model tests [20], [21] have been used to calculate axial and lateral load capacity of suction caisson for static and cyclic load under different soil conditions. The upper bound method and FEM along with the laboratory and centrifuge tests are the most popular methods in predicting the uplift capacity of suction [3]. Due to the complex behavior of suction caisson during the loading process, obtaining an accurate prediction is particularly difficult when the target system is governed by dynamic process under uncertainty conditions. To deal with this problem, relatively recent works apply artificial intelligent (AI) method to the problem of suction caisson uplift capacity prediction in order to generate more accurate and reliable models. Using convectional technique is not appropriate because of the poor understanding of the relationship among variable and the complex interactions between the processes. Hence there is a need for improvement in prediction techniques AI method and especially data driven model (DDM) offers flexible and non-parametric algorithms capable of modeling the relationship among inputs and output data set.
Some researchers used AI methods such as artificial neural network (ANN) [2], tree-based genetic programming(TGP) [22], linear genetic programming (LGP) [22], gene expression programming (GEP) [22], neuro-genetic [23], multi expression programming (MEP) [24], multivariate adaptive regression spline (MARS) [3], support vector machine and ANN (SVM- ANN) [25] and intelligent fuzzy radial basis function neural network inference method (IFRIM) [1] to predict the uplift capacity of suction caissons. The results of these studies indicated that AI techniques significantly outperformed FEM, and radial basis function neural network (RBFNN) in uplift capacity prediction.
Group method of data handling (GMDH) is one of DDMs that belong to self-organizing modeling approach. It was introduced by Ivankhenko in 1968. GMDH is similar to ANN but neither the number of neurons nor the number of layers in the network, nor the actual behavior of each created neuron is predefined [26]. This method is self-organizing, thus number of neurons, layers and the behavior of each neuron are adjusted during the process of training. Therefore complex system modeling in GMDH is more common than other artificial methods. In this method in training period, weights are calculated by least square estimation (LSE) method. Recently, some researches have been used GMDH for solving engineering some problems [27], [28], [29], [30]. Although several researchers applied ANN and GMDH in geotechnical issue [31], [32], [33], [34] but based on our knowledge it has not been used in suction caisson uplift capacity prediction.
Another AI method that has been used for optimization of engineering problems is harmony search (HS) algorithm. This method inspired by the improvisation process of musicians proposed by Geem(2011). In this algorithm, each musician (decision variable) plays (generates) a note (a value) for finding a best harmony (global optimum) all together. HS algorithm can be used for handling both continuous and discrete variables. This method has many successful applications in many aspect of optimization related problems such as optimal reservoir operation [35], design of water supply system [36], truss structure problems [37] and so on. HS presented a number of advantages over their optimization techniques. These advantages include less computational effort to find a solution derivative information is not needed, fast convergence rate, capability of significantly converge to the optimal solution.
In this research, based on combination of GMDH and HS algorithm, a new hybrid intelligent method called GMDH-HS is developed and used for suction caisson uplift capacity prediction. The code of new developed method is written in the MATLAB software. The developed method is validated using Mackey-Glass time series data and compared to two kinds of GMDH method, GMDH1 and GMDH 2. The results of developed model were evaluated using five statistical indices including coefficient of efficiency (CE), root mean square error (RMSE), mean square relative error (MSRE), mean absolute percentage error (MAPE) and relative bias (RB). Next, the GMDH-HS is used for the suction caisson uplift capacity prediction. Results of this method are evaluated with statistical indices. Also the results of GMDH-HS in uplift capacity prediction were compared to GMDH1, GMDH2 and the results of another works previously works [1], [2], [3], [22], [23], [24], [25], [38]. Finally, for better comparison between previously works and develop methods, a ranking system was applied.
Section snippets
Group method of data handling (GMDH)
In this section a brief definition of GMDH, problem solving by this method, formulating, and its structure and algorithm will be presented. GMDH is an inductive concept based on the perceptron theory, which has been developed for systems recognition, modeling, and prediction of sophisticated systems. GMDH is a combination of N-Adaline and compared to perceptron, its structure is more precise, since it has used data classification both usefully and uselessly, and needs less observational data.
Verification of GMDH-HS
The chaotic Mackey-Glass differential delay equation is recognized as a benchmark problem that has been used and reported by a number of researchers for comparing the learning and generalization ability of different models. The Mackey-Glass chaotic time series generated from the following equation:where a, b and are Mackey-Glass constants and is the time-series output at time t. Mackey-Glass time series prediction is complicated due in addition of time
Results
In this section, at the first results of GMDH1 and GMDH2 methods in suction caisson uplift capacity prediction are presented. Next, the results of uplift capacity in suction caisson using the GMDH-HS method are explained. The performance of each method for both training and testing period is evaluated using statistical indices and some figures. Then the results of developed method compared to another works that have been used AI method in suction caisson uplift capacity prediction. Finally a
Conclusion
In this study, a hybrid intelligent method based on combination of group method of data handling (GMDH)” and “harmony search (HS)” which is called GMDH-HS has been developed for uplift capacity prediction in clay. In GMDH-HS, neurons and layers were built based on GMDH and weights in each neuron were calibrated using HS optimization method. At the first, developed methods were validated using Mackey- Glass times series and its statistical indices were compared with GMDH1 and GMDH2. Five
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Prediction of uplift resistance of circular anchors in anisotropic clays using MLR, ANN, and MARS
2023, Applied Ocean ResearchApplication of artificial intelligence in geotechnical engineering: A state-of-the-art review
2022, Earth-Science ReviewsCitation Excerpt :Fig. 10 shows the number of papers published using different AI methods in shallow and deep foundation research. Intelligent prediction predominantly prevails in settlement and load capacity of pile foundations while few have emerged in bridge foundations (Akib et al., 2014; Yousefpour et al., 2014) and uplift capacity prediction of suction caisson (Shahr-Babak et al., 2016). ANN dominates the selection of AI methods overall.
Investigation into the influence of caisson installation process on its capacities in clay
2020, Applied Ocean ResearchCitation Excerpt :The short-term bearing capacity here means the caisson foundation undrained capacity prior to soil consolidation. Many studies focusing on the bearing capacity of caisson in clay have been conducted, including field tests (Houlsby et al., 2005; Le et al., 2018), model tests (Guo et al., 2018; Zhu et al., 2018), limit analysis (Aubeny and Murff, 2005; Tang et al., 2016), finite element analysis (Gourvenec and Barnett, 2011; Fu et al., 2018), finite element limit analysis (Ukritchon and Keawsawasvong, 2016) and artificial intelligence methods (Masoumi Shahr-Babak et al., 2016; Kim et al., 2017; Derakhshani, 2017 and 2018). However, in most of the available numerical studies, caissons were assumed ‘wished-in-place’, where the process of installation was neglected (Aubeny and Murff, 2005; Monajemi and Razak, 2009; Gourvenec and Barnett, 2011; Hung and Kim, 2012; Masoumi Shahr-Babak et al., 2016; Mehravar et al., 2016; Tang et al., 2016; Ukritchon and Keawsawasvong, 2016; Kim et al., 2017; Derakhshani, 2017 and 2018; Fu et al., 2018).
A T–S fuzzy model identification approach based on evolving MIT2-FCRM and WOS-ELM algorithm
2020, Engineering Applications of Artificial IntelligenceFinite element modeling of the tensile capacity of suction caissons in cohesionless soil
2019, Applied Ocean ResearchCitation Excerpt :The transient load effect, in which suction is generated for monotonic loads of a short duration, is also confirmed numerically by Thieken et al. [22] and Sørensen et al. [21]. Other investigations are presented by Masoumi Shahr-Babak et al. [11] that used GMDH-HS to analyse laboratory test results, whereas e.g. Cassidy et al. [5] use the laboratory data to fit a strain-hardening plasticity model that describes the caisson behavior. Wang and Cheng [26], Mehravar et al. [12], Ukritchon et al. [23] used numerical modeling to investigate the undrained pull-out capacity for suction caissons in clay.