Sensitivity Analysis Based on Polynomial Chaos Expansions and Its Application in Ship Uncertainty‐Based Design Optimization

Abstract

In order to truly reflect the ship performance under the influence of uncertainties, uncertainty-based design optimization (UDO) for ships that fully considers various uncertainties in the early stage of design has gradually received more and more attention. Meanwhile, it also brings high dimensionality problems, which may result in inefficient and impractical optimization. Sensitivity analysis (SA) is a feasible way to alleviate this problem, which can qualitatively or quantitatively evaluate the influence of the model input uncertainty on the model output, so that uninfluential uncertain variables can be determined for the descending dimension to achieve dimension reduction. In this paper, polynomial chaos expansions (PCE) with less computational cost are chosen to directly obtain Sobol' global sensitivity indices by its polynomial coefficients; that is, once the polynomial of the output variable is established, the analysis of the sensitivity index is only the postprocessing of polynomial coefficients. Besides, in order to further reduce the computational cost, for solving the polynomial coefficients of PCE, according to the properties of orthogonal polynomials, an improved probabilistic collocation method (IPCM) based on the linear independence principle is proposed to reduce sample points. Finally, the proposed method is applied to UDO of a bulk carrier preliminary design to ensure the robustness and reliability of the ship.

Shape Optimization under Stochastic Conditions by Design-space Augmented Dimensionality Reduction

“…This limitation can be assessed by variance-based methods like Sobol sensitivity analysis [29]. The preliminary design of a bulk carrier to enhance its robustness and reliability by focusing only on the most influential random variables, thereby reducing the complexity of the optimization problem, was performed in [30], where polynomial chaos expansion was employed in combination with sensitive analysis to calculate Sobol's indices, by deriving them directly from the coefficients of the polynomial representing the output variable. The approximate local solution of Sobol's indices was applied to the reliability-based robust design optimization of composite structures in [31].…”

Application of Basis Functions for Hull Form Surface Modification

“…With the rapid development of computer technology and computational fluid dynamics (CFD), simulation-based hull line optimization has become a central research topic. Cheng et al [1], Abt et al [2], Peri et al [3,4], Campana et al [5], Li [6], Zhao et al [7], Yang et al [8,9], Tahara et al [10], Feng Baiwei [11,12] Chang Haichao [13,14], Wei [15,16], and Zheng [17] integrated computer-aided design (CAD) with CFD based on numerical simulation techniques and optimization algorithms, established CFD-based hull line optimization platforms, successfully completed optimized designs of hull lines through simulation, and obtained optimized hull forms with excellent hydrodynamic performance.…”

An Effective Approach for Uncertain Aerodynamic Analysis of Airfoils via the Polynomial Chaos Expansion

“…Since a large number of aerodynamic analyses are embedded in the brutal-force Monte Carlo simulation, this generally results in computationally demanding cost. e PCE approach was combined with the Gaussian quadrature scheme and the dimensional reduction method [38]. However, the standard Gaussian method might result in the problem of the curse of dimensionality [39], which motives the nonintrusive and the statistical regression method to determine expansion coefficients in this paper.…”