Least Squares Support Vector Mechanics to Predict the Stability Number of Rubble-Mound Breakwaters

Gedik, Nuray

doi:10.3390/w10101452

Cited by 15 publications

(9 citation statements)

References 40 publications

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“…Using an approach that did not assume the functional form of the equation in advance and relied strictly on the data alone, would be preferable for dealing with both of the above issues. To overcome the limitations of empirical equations, the present study presents a data-driven method, known as an artificial neural network (ANN) method, which has been successfully employed in other fields to cope with complicated parameters in experimental data processing and to develop highly accurate predictive models [28][29][30][31][32][33]. In contrast to empirical equations, in which mathematical dependence was fixed in advance, the ANN method provides an approach in which both the explanatory and explained variables in the data ultimately define their internal relationship without any prior assumptions about the equation's functional form or physical constraints.…”

Section: Introductionmentioning

confidence: 99%

Using a Data Driven Approach to Predict Waves Generated by Gravity Driven Mass Flows

Meng

Ancey

2020

Water

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When colossal gravity-driven mass flows enter a body of water, they may generate waves which can have destructive consequences on coastal areas. A number of empirical equations in the form of power functions of several dimensionless groups have been developed to predict wave characteristics. However, in some complex cases (for instance, when the mass striking the water is made up of varied slide materials), fitting an empirical equation with a fixed form to the experimental data may be problematic. In contrast to previous empirical equations that specified the mathematical operators in advance, we developed a purely data-driven approach which relies on datasets and does not need any assumptions about functional form or physical constraints. Experiments were carried out using Carbopol Ultrez 10 (a viscoplastic polymeric gel) and polymer–water balls. We selected an artificial neural network model as an example of a data-driven approach to predicting wave characteristics. We first validated the model by comparing it with best-fit empirical equations. Then, we applied the proposed model to two scenarios which run into difficulty when modeled using those empirical equations: (i) predicting wave features from subaerial landslide parameters at their initial stage (with the mass beginning to move down the slope) rather than from the parameters at impact; and (ii) predicting waves generated by different slide materials, specifically, viscoplastic slides, granular slides, and viscoplastic–granular mixtures. The method proposed here can easily be updated when new parameters or constraints are introduced into the model.

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Section: Introductionmentioning

confidence: 99%

Using a Data Driven Approach to Predict Waves Generated by Gravity Driven Mass Flows

Meng

Ancey

2020

Water

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“…Recently, machine learning (ML) algorithms used in hydrology and hydraulics include Artificial Neural Networks (ANN) and variations [26,27], Random Forest [28], and Support Vector Machine [29]. ML has been previously successfully implemented in pipe flow systems.…”

Section: Introductionmentioning

confidence: 99%

Efficient Double-Tee Junction Mixing Assessment by Machine Learning

Grbčić

Kranjčević

Družeta

et al. 2020

Water

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A new approach in modeling of mixing phenomena in double-Tee pipe junctions based on machine learning is presented in this paper. Machine learning represents a paradigm shift that can be efficiently used to calculate needed mixing parameters. Usually, these parameters are obtained either by experiment or by computational fluid dynamics (CFD) numerical modeling. A machine learning approach is used together with a CFD model. The CFD model was calibrated with experimental data from a previous study and it served as a generator of input data for the machine learning metamodels—Artificial Neural Network (ANN) and Support Vector Regression (SVR). Metamodel input variables are defined as inlet pipe flow ratio, outlet pipe flow ratio, and the distance between the pipe junctions, with the output parameter being the branch pipe outlet to main inlet pipe mixing ratio. A comparison of ANN and SVR models showed that ANN outperforms SVR in accuracy for a given problem. Consequently, ANN proved to be a viable way to model mixing phenomena in double-Tee junctions also because its mixing prediction time is extremely efficient (compared to CFD time). Because of its high computational efficiency, the machine learning metamodel can be directly incorporated into pipe network numerical models in future studies.

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“…The modeling process starts with building a stationary set of runoff data based on mode functions which are used as input points in the prediction by the SVM technique when chaotic characteristics are present. Furthermore, reference [15] uses the technique of LS-SVMs as a less costly computational alternative that provides superior accuracy compared to other machine learning techniques in the civil engineering problem of predicting the stability of breakwaters. The LS-SVM framework was applied to tool fault diagnosis for ensuring manufacturing quality [16].…”

Section: Introductionmentioning

confidence: 99%

“…12: CSVM results for problem #4.This appendix shows how the method of Lagrange multiplies is used to solve nonlinear ODEs using the LS-SVM and CSVM methods. Equation(15) shows the Lagrangian for the LS-SVM method. The values where L are zero give candidates for the minimum.…”

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confidence: 99%

Analytically Embedding Differential Equation Constraints into Least Squares Support Vector Machines Using the Theory of Functional Connections

Leake

Johnston

Smith

et al. 2019

MAKE

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Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural bending, and systems dynamics. While there are many other techniques for finding approximate solutions to these equations, this paper looks to compare the application of the Theory of Functional Connections (TFC) with one based on least-squares support vector machines (LS-SVM). The TFC method uses a constrained expression, an expression that always satisfies the DE constraints, which transforms the process of solving a DE into solving an unconstrained optimization problem that is ultimately solved via least-squares (LS). In addition to individual analysis, the two methods are merged into a new methodology, called constrained SVMs (CSVM), by incorporating the LS-SVM method into the TFC framework to solve unconstrained problems. Numerical tests are conducted on four sample problems: One first order linear ordinary differential equation (ODE), one first order nonlinear ODE, one second order linear ODE, and one two-dimensional linear partial differential equation (PDE). Using the LS-SVM method as a benchmark, a speed comparison is made for all the problems by timing the training period, and an accuracy comparison is made using the maximum error and mean squared error on the training and test sets. In general, TFC is shown to be slightly faster (by an order of magnitude or less) and more accurate (by multiple orders of magnitude) than the LS-SVM and CSVM approaches. IntroductionDifferential equations (DE) and their solutions are important topics in science and engineering. The solutions drive the design of predictive systems models and optimization tools. Currently, these equations are solved by a variety of existing approaches with the most popular based on the Runge-Kutta family [1]. Other methods include those which leverage low-order Taylor expansions, namely Gauss-Jackson [2] and Chebyshev-Picard iteration [3,4,5], which have proven to be highly effective. More recently developed techniques are based on spectral collocation methods [6]. This approach discretizes the domain about collocation points, and the solution of the DE is expressed by a sum of "basis" functions with unknown coefficients that are approximated in order to satisfy the DE as closely as possible. Yet, in order to incorporate boundary conditions, one or more equations must be added to enforce the constraints.The Theory of Functional Connections (TFC) is a new technique that analytically derives a constrained expression which satisfies the problem's constraints exactly while maintaining a function that can be freely chosen [7]. This theory, initially called "Theory of Connections", has been renamed for two reasons. First, the "Theory of Connections" already identifies a specific theory in differential geometry, and second, what this theory is actually doing is "functional interpolation", as it provides all functions satisfying a set of constraints in terms of a function ...

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Least Squares Support Vector Mechanics to Predict the Stability Number of Rubble-Mound Breakwaters

Cited by 15 publications

References 40 publications

Using a Data Driven Approach to Predict Waves Generated by Gravity Driven Mass Flows

Using a Data Driven Approach to Predict Waves Generated by Gravity Driven Mass Flows

Efficient Double-Tee Junction Mixing Assessment by Machine Learning

Analytically Embedding Differential Equation Constraints into Least Squares Support Vector Machines Using the Theory of Functional Connections

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