﻿ 船型优化敏感度分析方法研究综述
 舰船科学技术  2019, Vol. 41 Issue (3): 1-7 PDF

A overview of research on ship hull optimization sensitivity analysis methods
XU Qing, CHEN Jia-bao, TIAN Bin-bin
China Ship Development and Design Center, Wuhan 430064, China
Abstract: In the optimization of hull form based on CFD, when parameterization is used to express the hull accurately, a large number of hull parameters bring the computation cost and time cost. Sensitivity analysis can analyze the sensitivity of various parameters to ship performance, reduce the dimension of design space, save cost, and has guiding significance for the subsequent ship optimization. But so far, the application of sensitivity analysis in ship type optimization is relatively less, and the related research is still inadequate. Based on the existing achievements on carding, this paper summarizes sensitivity analysis method and the status quo of research on sensitivity analysis in ship and ship optimization field at home and abroad, put forward the problems, and points out the direction of development, in order to provide reference for the further development of sensitivity analysis in the field of ship optimization.
Key words: ship hull optimization     sensitivity analysis     ship hull parameters     overview
0 引　言

1 敏感度分析方法

1.1 局部敏感度分析方法

1.1.1 有限差分法

 $\frac{{\partial y}}{{\partial {x_i}}} \approx \frac{{y({X^i}) - y(X)}}{{\Delta {x_i}}},\;i = 1,\;...,\;m{\text{，}}\\ \;\; i = 1,\;...,\;m{\text{。}}$ (1)

 $\frac{{\partial y}}{{\partial {x_i}}} \approx \frac{{y({X^{i + }}) - y({X^{i - }})}}{{2\Delta {x_i}}},\;i = 1\;,\;...,\;\;m{\text{。}}$ (2)

1.1.2 直接微分法

 $\frac{{{\rm d}y}}{{{\rm d}t}} = f(X,y){\text{，}}$ (3)

 $\frac{{\rm d}}{{{\rm d}t}}\frac{{\partial y}}{{\partial {x_i}}} = { J}\frac{{\partial y}}{{\partial {x_i}}} + \frac{{\partial f}}{{\partial {x_i}}}{\text{，}}$ (4)

 $\dot S = { J}S + F\text{。}$ (5)

1.1.3 格林函数法

 $\frac{{\rm d}}{{{\rm d}t}}X(t,{t_0}) = J(t){{X}}(t,{t_0})\text{，}$ (6)

 ${ X}(t,{t_0}) = \left\{ {\frac{{\partial {c_j}(t)}}{{\partial c_i^0({t_0})}}} \right\},\;\;\;X(t,{t_0}) = 1,\;\;\;t \geqslant {t_0}{\text{，}}$

 $S({t_1},{t_2}) = \int_{{t_1}}^{{t_2}} {X({t_2},s)} F(s){\rm d}s{\text{。}}$ (7)

1.2 全局敏感度分析方法

1.2.1 筛选法

 $\begin{split} &{d_i}(X) = \\ &\frac{{y({x_1},...,{x_{i - 1}},{x_i} + \Delta ,{x_{i + 1}},...,{x_k}) - y(X)}}{\Delta }\text{。} \end{split}$ (8)

 ${\mu _i} = \frac{1}{r}\sum\limits_{j = 1}^r {{d_i}(j)} {\text{，}}$ (9)
 ${\sigma _i} = \sqrt {\frac{1}{{r - 1}}\sum\limits_{j = 1}^r {{{[{d_i}(j) - \frac{1}{r}\sum\limits_{j = 1}^r {{d_i}(j)} ]}}} }^2 {\text{。}}$ (10)

 $\mu _i^* = \frac{1}{r}\sum\limits_{j = 1}^i {\left| {{d_i}(j)} \right|} {\text{。}}$ (11)

μ用来评估每个参数对输出的总体影响，σ用来估计高阶效应，如非线性和输入之间的交互作用。如果 $\mu _i^*$ 与0相差很多，则表明参数i对输出具有较大的整体影响。σi的值大意味着参数i对输出具有非线性效应，或者参数i和其他参数之间存在交互作用。

1.2.2 回归分析法

 ${y_i} = {a_0} + \sum\limits_j {{a_j}{x_{ij}} + {\varepsilon _i}} \;\;j = 1,2,...,k;\;\;i = 1,2,...,N{\text{。}}$

 $\frac{{y - \overline y }}{{\hat s}} = \sum\limits_j {\frac{{{a_j}{{\hat s}_j}}}{{\hat s}}} \frac{{{x_j} - \overline {{x_j}} }}{{{{\hat s}_j}}}{\text{。}}$ (12)

 $\begin{split} &\overline y = \sum\limits_i^N {\frac{{{y_i}}}{N}}{\text{，}} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\overline x _j} = \sum\limits_{i = 1}^N {\frac{{{x_{ij}}}}{N}}{\text{，}} \\ &\hat s = {\left[ {\sum\limits_{i = 1}^N {\frac{{{{({y_i} - \overline y )}^2}}}{{N - 1}}} } \right]^{1/2}}{\text{，}}\;\;\;\;\;\;\;\;\;\;{{\hat s}_j} = {\left[ {\sum\limits_{i = 1}^N {\frac{{{{({x_{ij}} - {{\overline x }_j})}^2}}}{{N - 1}}} } \right]^{1/2}}{\text{。}} \end{split}$

 $\begin{split} &\sum\limits_{i = 1}^N {{{({y_i} - \bar y)}^2}} = \sum\limits_{i = 1}^N {{{({{\hat y}_i} - \bar y)}^2}} + \sum\limits_{i = 1}^N {{{({{\hat y}_i} - {y_i})}^2}}{\text{，}} \\ &R_y^2 = \frac{{\sum\limits_{i = 1}^N {{{({{\hat y}_i} - \bar y)}^2}} }}{{\sum\limits_{i = 1}^N {{{({y_i} - \bar y)}^2}} }}{\text{。}} \end{split}$ (13)

1.2.3 基于方差的方法

 $V = \sum\limits_{i = 1}^k {{V_i}} + \sum\limits_{i = 1}^k {\sum\limits_{j > i}^k {{V_{ij}}} } + ... + {V_{1,2,...,k}}{\text{。}}$ (14)

 ${S_i} = \frac{{V[E(Y\left| {{x_i}} \right.)]}}{{V(Y)}}{\text{，}}$ (15)

 ${S_{{T_i}}} = \sum {{S_i}} + \sum\limits_{j \ne i} {{S_{ij}}} + ... + {S_{1...k}}{\text{。}}$ (16)

1阶和全阶敏感指数之间的差异可以看作是单个参数与其他参数之间相互作用的一个度量[12]。因为相互作用随着考虑的参数数量以及变化范围而增加，所以方差分解方法非常适合于具有许多参数的模型。有许多方法进行方差分解，如Sobol方法，傅里叶振幅敏感度测试（FAST）和扩展的FAST方法。

1.2.4 代理模型法

1.2.5 基于熵的方法

2 敏感度分析在船型优化领域的研究现状及发展方向

2.1 国外研究现状

2.2 国内研究现状

2.3 敏感度分析在船型优化领域的发展方向

3 结　语

 [1] LU Y, CHANG X, HU A. A hydrodynamic optimization design methodology for a ship bulbous bow under multiple operating conditions[J]. Engineering Applications of Computational Fluid Mechanics, 2016, 10(1): 331-346. [2] HAN S, LEE Y S, CHOI Y B. Hydrodynamic hull form optimization using parametric models[J]. Journal of Marine Science & Technology, 2012, 17(1): 1-17. [3] 李睿. Sobol'灵敏度分析方法在结构动态特性分析中的应用研究[D]. 长沙: 湖南大学, 2003. [4] 吴琼莉. 参数全局敏感度分析及其在确定性复杂动态系统建模的应用[D]. 武汉: 武汉大学, 2013. [5] 陆正争. 软式飞艇参数敏感度分析与优化[D]. 哈尔滨: 哈尔滨工业大学, 2013. [6] MAX D. Morris faetoiral sampling pans for preliminary computational experiments[J]. Ameriean Statistieal Association and the American Soeiety for Quality Control, 1991, 33: 161-174. [7] CARIBONI J, GATELLI D, LISKA R, et al.. The role of sensitivity analysis in ecological modeling[J]. Ecol. Modell, 2007, 203(1-2): 167-182. DOI:10.1016/j.ecolmodel.2005.10.045 [8] SOBOL′, I. M.. Sensitivity analysis for nonlinear mathematical models. Math.Model[J]. Comput. Exp, 1993, 1(4): 407-414. [9] SALTELLI A, TARANTOLA S, CAMPOLONGO F, et al. Sensitivity analysis in practice-a guide to assessing scientific models. John Wiley & Sons Ltd, Chichester. 2004. [10] SALTELLI A, RATTO M, ANDRES T, et al. Global sensitivity analysis: the primer. john wiley & sons ltd, chichester. 2008. [11] MASSMANN C, HOLZMANN H.. Analysis of the behavior of a rainfall-runoff model using three global sensitivity analysis methods evaluated at different temporal scales[J]. J. Hydrol, 2012, 475: 97-110. DOI:10.1016/j.jhydrol.2012.09.026 [12] SONG X M, KONG F Z, ZHAN C S, et al.. Paramete identification and global sensitivity analysis of Xinanjiang model using meta-modeling approach[J]. Water Sci. Eng, 2013, 6(1): 1-17. DOI:10.5194/dwes-6-1-2013 [13] MOGHEIR Y, DE LIMA J L M P, et al.. Characterizing the spatial variability of groundwater quality using the entropy theory: Ⅰ. Synthetic data[J]. Hydrol.Process, 2004, 18: 2165-2179. DOI:10.1002/(ISSN)1099-1085 [14] MISHRA S, KNOWLTON R G. Testing for input-output dependence in performance assessment models. In: Proceedings of the Tenth International High-Level Radioactive Waste Management Conference, Las Vegas, Nevada. 2003. [15] [16] KIM DH, RHEE KP, KIM N. The effect of Hull appendages on maneuverability of naval ship by sensitivity analysis[J]. J Soc Naval Archit Korea, 2014, 51(2): 154-161. DOI:10.3744/SNAK.2014.51.2.154 [17] PADILLA A, BITTNER R, YUZ JI. Closed-loop identification and control of inland vessels. In: Ocampo-Martinez C, Negenborn R (eds) Transport of water versus transport over water. Springer International Publishing, New York, 2015: 345–368. [18] DOWNES J. Reliability-based sensitivity analysis of ships[J]. Eng Maritime Environ, 2004, 219: 11-23. [19] KIM S C, FUJIMOTO Y, SHINTAKU E. Sensitivity analysis on fatigue reliability and inspection of ship structural members[J]. Journal of the Society of Naval Architects of Japan, 2009, 1997(181): 367-375. [20] OBISESAN A, SRIRAMULA S, HARRIGAN J. Probabilistic considerations in the damage analysis of ship collisions. In: Kadry S(ed) Numerical methods for reliability and safety assessment.Springer International Publishing, New York, 2015: 197–214. [21] FONSECAN, SOARESC G. Sensitivity of the expected ships availability to different seakeeping criteria[C]//ASME 2002, International Conference on Offshore Mechanics and Arctic Engineering. 2002: 595–603. [22] YIM S C S, RAMAN S, PALO P A. Nonlinear model for sub and superharmonic motions of a mdof moored structure, Part 2-Sensitivity analysis and comparison[J]. Journal of Offshore Mechanics & Arctic Engineering, 2005, 127(4): 291-299. [23] SPICER T C. Sensitivity analysis of transient and steady state characteristics of surface ship progressive flooding[J]. Thesis Collection, 1999. [24] KIM Y H, CHO D S. The sensitivity analysis of coupled axial and torsional undamped free vibration of ship propulsion shafting[J]. Journal of the Society of Naval Architects of Korea, 2001, 38(4). [25] VALORANI M, PERI D, CAMPANA E F. Sensitivity analysis methods to design optimal ship hulls[J]. Optimization & Engineering, 2003, 4(4): 337-364. [26] HEIMANN J. CFD - based optimization of the wave-making characteristics of ship hulls[J]. Prof. Dr.-Ing. Günther F. Clauss, 2005. [27] STÜCK A,, RUNG T. Adjoint-based hull design for wake optimisation[J]. Ship Technol Res, 2011, 58(1): 34-44. DOI:10.1179/str.2011.58.1.003 [28] 孙建刚, 邓德衡, 黄国樑. 水面船舶操纵性敏感性分析[J]. 中国航海, 2006(1): 49-52. DOI:10.3760/cma.j.issn.1009-6906.2006.01.017 [29] 徐锋, 邹早建, 尹建川, 等. 船舶操纵水动力导数的灵敏度分析[J]. 哈尔滨工程大学学报, 2013(6): 669-673. [30] 邹春平. 船舶结构振动响应灵敏度分析[J]. 中国舰船研究, 2006, 1(2): 26-31. ZOU C P. Sensitivity analysis of vibration response of ship structure[J]. Chinese Journal of Ship Research, 2006, 1(2): 26-31. DOI:10.3969/j.issn.1673-3185.2006.02.006 [31] 刘俊梅. 破损船体剩余极限强度的影响参数与敏感度分析[J]. 船舶工程, 2007, 29(3): 51-54. DOI:10.3969/j.issn.1000-6982.2007.03.028 [32] 周佳, 唐文勇, 张圣坤. 全垫升气垫船耐波性参数敏感度分析[J]. 上海交通大学学报, 2009(10): 1564-1567. DOI:10.3321/j.issn:1006-2467.2009.10.010 [33] 周耀华, 马宁, 顾解忡. 集装箱船横摇惯性矩计算方法对参数横摇敏感性预报影响研究[J]. 中国造船, 2013(3): 11-20. DOI:10.3969/j.issn.1000-4882.2013.03.002 [34] 张晓, 杨和振. 不规则波中船舶横摇参激振动敏感度分析[J]. 哈尔滨工程大学学报, 2015(12): 1539-1543. [35] 唐文勇, 周佳, 朱荣成. 基于人工神经网络方法的舰船参数灵敏度分析[J]. 舰船科学技术, 2006, 28(6): 111-114. TANG W Y, ZHOU J.ZHU R C.. Parametric sensitivity analysis of ships based on artificial neural network method[J]. Ship Science and Technology, 2006, 28(6): 111-114. [36] 喻曦. 基于人工神经网络的舰船灵敏度分析[J]. 舰船科学技术, 2015, 37(3): 147-150. YU X. Parametric sensitivity analysis of ships based on neural network[J]. Ship Science and Technology, 2015, 37(3): 147-150. DOI:10.3404/j.issn.1672-7649.2015.03.032 [37] 张恒, 詹成胜, 刘祖源, 等. 基于船舶阻力性能的船型主尺度参数敏感度分析[J]. 船舶工程, 2015(6): 11-14. [38] ZHANG H, LIU Z, ZHAN C, et al. A sensitivity analysis of a hull’s local characteristic parameters on ship resistance performance[J]. Journal of Marine Science & Technology, 2016, 21(4): 1-9. [39] LIU Q, FENG B, LIU Z, et al. The improvement of a variance-based sensitivity analysis method and its application to a ship hull optimization model[J]. Journal of Marine Science & Technology, 2017(10): 1-16. [40] 赵峰, 李胜忠, 杨磊, 等. 基于CFD的船型优化设计研究进展综述[J]. 船舶力学, 2010, 14(7): 812-821. ZHAO F, LI S Z, YANG L, et al. An overview on the design optimization of ship hull based on CFD techniques[J]. Journal of Ship Mechanics, 2010, 14(7): 812-821. DOI:10.3969/j.issn.1007-7294.2010.07.016