Genetic Algorithm Based Design Optimization of a Passive Anti-Roll Tank in a Sea Going Vessel
Introduction
The roll motion of a ship is of significant practical importance. It not only dictates the stability and safety aspects of the vessel, but also governs the comfort levels and its safe operational limits. Large roll motions can induce significant transverse accelerations which could result in structural damage, shifting of cargo and discomfort to the passenger and crew. There is therefore great commercial interest to reduce the roll motions of a sea-going vessel.
There are several means to control the amount of roll. These include both active and passive devices. Roll mitigation devices include Gyro stabilizers, fins, rudder and tanks. One of the most cost effective method used is the U-tube passive Anti-Roll Tank (ART), which works on the principle of creating a fluid flow induced counter moment due to the dynamic oscillating flow of liquid from one vertical limb to the other through the cross-connecting duct every time the ship rolls. The geometric dimensions of the vertical limb and the cross-connecting duct together decide the fluid oscillation frequency. An important design aspect involves tuning the tank to ensure the fluid oscillation frequency is close to the roll natural frequency of the ship to obtain the maximum stabilization by roll reduction. Unlike fin stabilizers, which are only effective at forward speed conditions, the ART is effective both in stationary and forward speed conditions. The effectiveness of the ART depends on many geometric parameters of the design.
Several researchers have attempted to mathematically model the ART over the years. Goodrich (1969) developed one of the earliest models of an ART. A modified version has been developed by Moaleji and Greig (2007). In this model, the ART effect on the roll motion is only via a single linear term proportional to the difference in fluid depths in the two reservoirs. Lloyd (1989) presented a simplified 4-DOF coupling the liquid motions to the sway, roll and yaw motions of the vessel. Recently, Holden et al. (2011) developed a nonlinear Lagrangian approach for modeling the U-tube ART for large roll amplitudes. The body motions were restricted only to roll. This work was expanded to include all degrees of freedom in Holden and Fossen (2012). To accurately predict the damping inside the passive ART, Taskar et al. (2014) proposed a CFD-based methodology to find the ART damping coefficient. Diebold et al. (2018) presented an application of ART for a barge shaped ship and the subsequent roll mitigation brought by these ARTs. A coupled potential flow – viscous solver approach was used to model the ART – ship motion problem.
Genetic Algorithm (GA) belongs to a class of artificial intelligence (AI) based techniques known as Evolutionary Algorithm (EA). EA takes a heuristic approach to solving problems by applying fundamental concepts in cell biology such as selection, reproduction and mutation. Other EA based techniques include Evolutionary Strategies (ESs) and Evolutionary Programming (EP). In GA, the individuals are typically coded as integers. The selection is done by selecting parents proportional to their fitness. The genetic operators work on the individuals representing the parametric variables which are in turn usually represented at the bit-level. In evolutionary strategies, the individuals are coded as vectors or real numbers. The evolutionary programming highlights the development of behavioral models and not genetic models. EP is derived from the simulation of adaptive behavior in evolution. At present, GA and ES are amongst the most widely used optimization methods (Alajmi and Wright, 2014). GA based optimization schemes enjoy some key advantages over conventional methods such as hill-climbing. The main advantages include insensitivity to the initial guess solution(s) for multimodal optimization problems, avoidance of computation of derivatives and ease of coding and implementation (Charbonneau, 2002). In addition, many engineering problems contain nonlinear constraints, which can be handled in a straightforward manner (Chehouri et al., 2016).
Several examples of GA based optimization techniques can be found in recent literature. Zhang et al. (2012) employed a nonlinear programming for the optimization of anti-roll tank. Viviani et al. (2017) used a multidisciplinary optimization procedure for the self-generation of re-entry vehicle shapes. An application of GA for vessel optimization is presented in Luo and Lan (2017), where a single objective genetic algorithm method was developed to minimize the resistance of a ship. Guha and Falzarano (2015) applied a multi-objective genetic algorithm optimization scheme to optimize a hull form of an ocean going vessel in terms of it is seakeeping performance. Bagheri et al. (2014) employed single objective genetic algorithm method for ship hull form improvement for better sea-keeping performance in head seas.
Recently, Subramanian et al. (2018) developed a new body-exact scheme to predict ship roll responses in large amplitude waves. This methodology has been extended in the present investigation to include an ART module to implicitly solve a 7-DOF dynamical system. The equations of motion governing the tank dynamics have been derived from first principles using Lagrangian mechanics similar to the approach used by Holden et al. (2011). The dynamical system can be modeled to include all the nonlinear terms in all seven degrees of freedom. However, with optimization being the key focus for the present study, a linearized ART model has been derived and used. A nonlinear body-exact strip theory method is used to solve the external wave-body problem, which has the key advantage of allowing for faster computational time and simplified body geometry definition when compared with fully three-dimensional methods. The coupled ship motion — ART simulator is linked to a GA based optimization routine to determine the optimum ART size. The present methodology has been applied to the case of a coastal research vessel requiring roll reduction using a passive U-tube ART. Experiments have been conducted on a 1:17 scaled model of the test vessel fitted with an ART in order to validate the computational model.
The paper is organized in the following manner. The details of the nonlinear coupled ship motion — ART computational model are first presented in Section 2. The results of the validation studies using experiments are presented in Section 3. The GA scheme is introduced in Section 4. The details of the optimization procedure are given in Sections 5 Interfacing of the genetic algorithm routine with the seakeeping program, 6 Procedure for optimizing the ART. Finally, results are discussed in Section 8.
Section snippets
Nonlinear strip theory formulation
The fluid flow problem consists of two sub-problems. The external flow consists of the flow over the ship hull involving the response of the ship to incident waves. The internal flow problem consists of the fluid flow of the liquid in the ART. Since the key focus of the present work is the application of the optimization scheme, the description of the fluid flow problem will be kept concise and presented in detail in a future publication.
Validation of the computational model
Before proceeding with the optimization, scaled down models were fabricated and experiments were conducted to validate the computational model. Three sets of experiments were conducted, all of which will be described below.
Genetic algorithm for optimization of the ART
Genetic Algorithm (GA) is part of the branch of evolutionary computing and has been found to enjoy a high probability of finding the global optimum solution (McCall, 2005). The technique is based on the principles of genetics and natural selection from Darwin’s Theory of Evolution namely, the concept of “Survival of the Fittest”. Thus, GA can be used as a tool for solving both constrained and unconstrained optimization problems. It assumes that the solution of a problem is an individual and can
Interfacing of the genetic algorithm routine with the seakeeping program
The interface between the optimization routine and the coupled ART–ship motions solver rBEST-ART facilitates the GA routine to exchange input/output information. This is done by calling rBEST-ART as an external program. Fig. 11 shows the structure of the data-exchange between GA program and the computational solver. At each stage of generation, the GA performs genetic operations such as selection, cross-over, and mutation, and then passes the design variables to the computational model. At this
Procedure for optimizing the ART
The following section describes the optimization algorithm. Every design parameter of the ART is represented by a string of digits. Each digit represents a “gene”, biologically speaking. The number of digits is determined based on the precision level desired. Since three design parameters are used in the problem (, and ), these representations are combined to form a digit genotype or “chromosome”, an individual representing each design of the ART. The basic algorithm can be
Parametric study of ART
For the purpose of validating the GA based optimized results, an independent systematic parametric study was conducted by choosing the variants and evaluating the roll reduction. In this manner the best performing ART was determined. The parameters of the most successful ART was compared with those evolved from the GA scheme.
Results and discussion
The computational scheme was run with a population size of , corresponding to the candidate ART forms at each stage of generation, to arrive at the optimized tank. The main dimensions of the base design and optimized ART are given in Table 8. The comparison of the roll response of the optimized ART from GA with the base design (ART-1) is shown in Fig. 15. For comparison, the performance of ART-5 based on the parametric study is also plotted on the same graph.
The convergence of the ART
Summary and conclusions
A Genetic Algorithm (GA) based optimization scheme has been developed and applied to optimize the performance of a passive U-tube type Anti roll tank fitted in the case of a sea-going coastal research vessel.
A recently developed nonlinear time-domain strip theory model — rBEST was used to solve the external wave-body problem. The strip-theory formulation allows for computational efficiency and simplified body geometry definition. In order to analyze the fluid flow in the ART, a 7-DOF
CRediT authorship contribution statement
Rahul Subramanian: Conceptualization, Methodology, Formal analysis, Software, Writing - original draft, Writing - review & editing, Supervision. Jyothish P.V.: Visualization, Validation, Investigation. Anantha Subramanian V.: Supervision, Investigation, Project administration, Writing - review & editing, Resources.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like to sincerely acknowledge the support from the project on the assessment of the coastal research vessel by the National Institute of Ocean Technology (NIOT), India . The present investigation was carried out as an extension of the original scope of the work, focusing on the performance prediction and optimization of the anti-roll tank.
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2022, Aquacultural EngineeringCitation Excerpt :The GA is one of the most typical and popular evolutionary algorithms. Theoretical evidence of its effectiveness at solving different optimization problems has been reported (Motlagh, 2021; Zhou et al., 2020; Subramanian et al., 2020; Sharp et al., 2018). Moreover, it was reported that by performing certain operations on the operators, namely mutation, crossover, and selection, the GA can produce high-quality optimal solutions (Briggs et al., 2015; Giassi et al., 2018).