Multidisciplinary Robust Optimization for Ship Design (Contributo in atti di convegno)

Type
Label
  • Multidisciplinary Robust Optimization for Ship Design (Contributo in atti di convegno) (literal)
Anno
  • 2010-01-01T00:00:00+01:00 (literal)
Alternative label
  • Matteo Diez (1) Daniele Peri (1) Giovanni Fasano (2) Emilio F. Campana (1) (2010)
    Multidisciplinary Robust Optimization for Ship Design
    in 28th Symposium on Naval Hydrodynamics, Pasadena, California, 12-17 September 2010
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Matteo Diez (1) Daniele Peri (1) Giovanni Fasano (2) Emilio F. Campana (1) (literal)
Note
  • Google Scholar (literal)
  • PuM (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • INSEAN - The Italian Ship Model Basin, Italy, Università Ca'Foscari - Dipartimento di Matematica Applicata, Italy (literal)
Titolo
  • Multidisciplinary Robust Optimization for Ship Design (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#isbn
  • 9780979809538 (literal)
Abstract
  • Design optimization formulations and techniques are intended for supporting the designer in the decision making process, relying on a rigorous mathematical framework, able to give the \"best\" solution to the design problem at hand. Over the years, optimization has been playing an increasingly important role in engineering. Advanced modeling and algorithms in optimization constitute now an essential part in the design and in the operations of complex aerospace (Hicks and Henne, 1978; Sobieszczanski-Sobieski and Haftka, 1997; Alexandrov and Lewis, 2002;Willcox andWakayama, 2003; Morino et. al., 2006; Iemma and Diez, 2006) and automotive (Baumal et. al., 1998; Kodiyalam and Sobieszczanski- Sobieski, 2001) applications, when, for example, it is by all means important to reduce costs and shorten time of development. In the design of large and complex systems, the use of efficient optimization tools leads to better product quality and improved functionality (Mohammadi et. al., 2001). The success of design optimization has attracted the naval community, so that the recent years have seen progress in optimization for ships too (Ray et. al., 1995; Peri and Campana, 2003; Parsons and Scott, 2004; Pinto et al., 2004; Peri and Campana, 2005; Campana et al., 2007, 2009; Papanikolaou, 2009). Generally speaking, the task of designing a ship (as well as an aerial or ground vehicle) possibly requires that the engineering team considers a host of multidisciplinary design goals and requirements. Multidisciplinary Design Optimization (MDO) classically refers to the quest for the best solution with respect to optimality criteria and constraints, whose definition involves a number of disciplines mutually coupled. Therefore, MDO encompasses the interaction of different discipline-systems, formally joined together and inter-connected in a multidisciplinary framework, which leads to a multidisciplinary equilibrium. In this context, design engineers increasingly rely on computer simulations to develop new designs and to assess their models. However, even if most simulation codes are deterministic, in practice systems' design should be permeated with uncertainty. On this guideline, the most straightforward example in the naval hydrodynamics context is offered by any existing ship, that must perform under a variety of operating conditions (e.g. different, stochastic environmental conditions). The general question is now: \"how can the results of computer simulations be properly exploited in the framework of design optimization, when the overall context is affected by uncertainty ?\" Moreover \"how can deterministic analysis be integrated in an ad hoc formulation that includes uncertainty ? How can it be used to get designs that are relatively insensible to stochastic variations of the external inputs and of the variables?\". The latter questions stress one of the major issues arising in the optimization of a (ship) design: the perspective from which the optimization task has to be formulated and per- formed. Indeed, one may argue that a \"tight\" deterministic optimization leads to specialized solutions that are often inadequate to face the \"real-life\" world, which is instead characterized by a high level of uncertainty. In other words, specialized optimization procedures which include only deterministic parameters are often unable to model the overall problem and, consequently, are unable to provide adequate solutions to it. In this respect Marczyk (2000) states that, in a deterministic engineering context, optimization is the synonymous of specializa- tion and, consequently, the opposite of robustness. The perspective we try to give in the present work has the aim of broadening the standard-optimization-problem framing, leading to a formulation in which optimality is redefined in terms of robustness, rather than specializa- tion. To the aim of clarifying the latter perspective, it may be useful to summarize the following statements: - Design optimization is always about answering a question, i.e. assisting the designer in the decision making process. - As a consequence and necessarily, before going through the optimization procedure, special attention has to be paid to the formulation of the problem. In the context of design optimization, incomplete or coarse models very often yield inadequate answers. - In this work we try to re-formulate the optimization perspective by looking at the design problem from a broader standpoint. Moreover, we bring the uncertainty related to ship design, manufacturing and operations, into the decision problem. - The formulation of the question (we try to answer to, using optimization) relies on optimal statistical decision theory and, specifically, on Bayes criteria, defining a rigorous mathematical framework in which the \"robust\" decision making process is embedded. In general, in any engineering system, the uncertainty is due to variations of design, operating or environmental conditions. The uncertainty is also related to the evaluation of the relevant functions, due to inaccuracy in modeling or computing. Using ideas from statistical decision theory, and specifically Bayes criteria (De Groot, 1970), the problem of robust decision making in design can be formulated as an optimization problem (Robust Design Optimization, RDO). In the framework of Bayes theory, we assume that the original \"deterministic\" design goal is the minimization of a general loss function (e.g., the performance). The expectation of this loss, with respect to the uncertainty involved in the process, is defined as the risk associated to the stochastic scenario assumed. In this context, the final goal is that of minimizing the risk, looking for the so-called Bayesian solution to the problem. In other words, once a probabilistic scenario is assumed, the optimization task reduces to the minimization of a related loss expectation. The difficulty with exploiting this framework is both theoretical and computational. The latter is due to the fact that the evaluation of the loss expectation involves the numerical integration of expensive simulation outputs, with respect to uncertain quantities. The former can also be easily understood: in a more standard MDO formulation (as well as in standard deterministic numerical optimization), all the relevant variables, parameters and functions are defined from a deterministic viewpoint and, apparently, the optimization process does not involve any kind of stochastic variation. The resulting optimal solutions are therefore likely specialized for the specific scenario assumed. Nevertheless, the performances of the final design may significantly drop in off-design conditions, when the deterministic assumptions used no longer hold. In this context, we look for a robust solution to the MDO problem, i.e., a solution able to represent a good performance on average, in the whole range of variations of the probabilistic scenario. The effects of properly considering the uncertainty, mainly consist in a loss in specialization of the system and a gain in robustness. The MDO problem, re-formulated to take into account uncertainty, becomes a Multidisciplinary Robust Design Optimization (MRDO) problem. The aim of the present work is to analyze the combined effects of considering several disciplines and uncertainty in ship design problems, developing a MRDO procedure that utilizes efficient methods for uncertainty analysis and encompasses the features of the MDO framework. Theory and applications of MDO subject to uncertainty may be found in, e.g., Agarwal et al. (2004); Du and Chen (2000a,b, 2002); Giassi et al. (2004); Mavris et al. (1999); Smith and Mahadevan (2005), and Sues et al. (1995). It may be noted that, in naval applications (Diez and Peri, 2009, 2010a,b), as well as in aeronautical problems (Padula et al., 2006), the usage and environmental conditions may be considered as \"intrinsic\" stochastic functions, whose expected values and standard deviations can neither be influenced by the designer nor by the manufacturer. Conversely, uncertainties related to design variables and functions' evaluation reflect the current state of and technology, and theoretically may be reduced by improving modeling, computing and manufacturing processes. Thus, in this work, the MRDO problem is formulated taking into account the stochastic variation of the operating conditions. The (joint) probability density function of the operating scenario are taken as a design requirement and the expectation of the relevant merit factors is assessed during the optimization task. For solving the minimization problem, a Particle Swarm Optimization (PSO) algorithm, in the form proposed by Campana et al. (2009), is used. The application studied in this work consists in the optimization of a keel fin of a sailing yacht. The keel fin provides the side force able to contrast the wind, allowing the yacht to travel along directions not aligned with the wind itself. The keel sustains an heavy ballast bulb, and the bending moment generated by this configuration, as well as by the hydrodynamic loads, generate an elastic displacement, which cannot be ignored in the computation of the hydrodynamic performances. As a consequence, a fully coupled hydroelastic problem is considered. The solution of the deterministic configuration has been illustrated in Campana et. al (2006). In this paper, a MRDO problem will be defined and solved, considering a probabilistic sailing scenario, in terms of cruise speed, heel and yaw angles. The paper is organized as follows. The next section presents the general context of optimization problems affected by uncertainty. Then, in Section 3, Bayes theory is exploited to formulate the present problem for RDO. The general framework of MDO is presented in Section 4, whereas the \"robust\" extension of MDO to MRDO is given in Section 5. Finally, the numerical results are pre- sented in Section 6 and the concluding remarks are given in Section 7. (literal)
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