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The development of advanced and efficient tools for uncertainty quantification and design optimization under uncertainty of ships operating in a real scenario are described. Under the assumption that objective functions and constraints are evaluated via high-fidelity, computationally expensive, unsteady Reynolds averaged Navier-Stokes equations solvers (URANS), the complexity of the task - compared to deterministic approaches - requires a significant mathematical reformulation of the optimization problem and of the solution methods. 58699
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To afford the cost of the stochastic optimization process, a number of advancements have been developed by the authors and their co-workers: (i) dynamic metamodels for the high-fidelity solvers and associated uncertainty quantification of stochastic simulation outputs; (ii) progress in evolutionary type derivative-free algorithms for global optimization; (iii) a new application of the Karhunen-Loève Expansion (KLE) method to - a priori - identify reduced dimensionality representations of large-scale design spaces, truncating basis functions (i.e. design variables) with small significance to the solution. An example of a ship hydrodynamic design optimization in real seas is finally presented. 1. INTRODUCTION In a few decades, maritime space will be intensively used not only for transport and trade, but also for offshore food production, renewable energy generation, and mineral exploitation. To face this development, design processes must be more automated, systematically including accurate simulations performed with tools of increasing accuracy and robustness. In the naval hydrodynamics context, the most up-to-date engineering reply to this trend is the development of deterministic Simulation-Based Design (SBD) frameworks, constantly developed by all the major shipyards, consisting of medium-to-large computational simulations, arranged in a heuristic way to evaluate performances and relative merit of alternative designs.58699
A further, advanced step has already be made, by embedding the SBD framework into a mathematical optimization problem, leading therefore to a fully automated SBD Optimization (SBDO) environment [1]. This can be obtained integrating (i) simulation tools (for structures, fluids, etc.), (ii) minimization algorithms, and (iii) geometry modification (and automatic re-meshing) algorithms, to obtain an automated process. This three fundamental elements have to be combined together in a robust and efficient way. The deterministic SBDO problem is simply defined: a desired ship operative profile has to be decided and the hull can be optimized for this limited set of missions, occasionally using some extra objective functions as constraints. This produces the best ship for the prescribed operative profile. SBDO limitations are of two types: (1) due to the stochastic inputs of the environment, a possible degradation of the ship’s performances in off-design conditions; (2) the attempt to formulate a multiobjective problem with inpidual objective functions for every operational condition of interest, easily leads to a stiff and almost intractable optimization problem [2]. Example of the use of SBDO are still limited in the ship design practice, whereas literature provides a reduced set of papers (see e.g. [1] and literature cited therein, [3,4]). What’s next? Future scenarios for the marine industrial activities [5] indicate that we will have to face not only the natural harshness of the environment, but also the relatively new effects of the climate changes (a constant rise of averaged sea states and wind speeds) as well as the volatile status of the global energy and fuel market prices. To have an impact on the final designs, these elements have to be considered since the early stage of the design cycle, driving the final product’s performances toward a safe and fully sustainable maritime vector: optimal designs should be permeated with uncertainty (hence becoming robust), because uncertainties permeate the real environment at any level. Deterministic SBDO can be then augmented in an ad hoc formulation that include uncertainties, leading to the development of a Stochastic-SBD Optimization framework (S-SBDO), with the goal of producing optimal designs relatively insensible to the stochastic variations of environment and operations, and safe with respect to degradation of the performances in off-design conditions. This can be realized by introducing user-defined probability density functions for some stochastic inputs, coming from real-life or full scale trials, to better characterize the effective environmental and operational conditions encountered by the ship. From the mathematical standpoint, the application of statistical decision theories to deterministic analysis requires the Uncertainty Quantification (UQ) of the simulation tools as a pre-requisite to Robust Design Optimization. The difficulty with exploiting this approach is mostly computational, since the solution always involves the integration of expensive simulation outputs with respect to uncertain quantities for the evaluation of mean, variance and distribution. If high-fidelity simulations are used, the evaluation of these integrals is very expensive, and for this reason, the application of statistical decision theory to high-fidelity robust design has been infrequently attempted and lies at the frontier of current computational science.