Reliability-Based Optimization

Simulation-based design (SBD) optimization assists the designer in the design process of complex engineering systems. In this context, real-world problems are affected by different sources of uncertainties (operational, environmental, geometrical or numerical) and require reliability-based robust design optimization (RBRDO) formulations to identify the optimal solution. RBRDO is usually computationally very costly (especially if high-fidelity simulations are used) and may be achieved by means of metamodels, with efficient optimization algorithms. Herein, a RBRDO for ship design is solved, for real ocean environment including stochastic sea state and speed. The problem is taken from [1] and is formulated as an unconstrained multi-objective optimization problem aimed at (a) the reduction of the expected value of the resistance in wave at sea state 5, varying the speed and (b) the increase of the ship operability, with respect to a set of motion-related constraints. The design space used is a four-dimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull . A metamodel based on stochastic radial basis function [3] is used, trained by URANS simulations. The ship considered is a 100m Delft catamaran, sailing in head waves in the North Pacific ocean.

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal fourdimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivative-free multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multi-objective extensions of the deterministic particle swarm optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness.