Numerical simulation of righting process for damaged-capsized hull
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摘要: 考虑了破舱倾覆船体浮性和稳性, 研究了船体在扳正过程中空间位置和受力状态; 采用欧拉旋转变换方法建立了船体空间力学平衡方程, 根据船舶静力学原理, 得到了破舱倾覆船体稳性和扳正力数学模型; 根据伯努利定理计算了破舱进水量及其对船体重心和浮心位置的影响; 利用GHS软件模拟了破舱倾覆船体的扳正过程, 求解了其最大扳正力和进水量, 计算了船体纵向6个位置的剪力、弯矩和扭矩。计算结果表明: 在最初扳正时, 破舱进水导致倾覆船体扳正力矩降低了130.312 MN·m, 说明破舱进水降低了倾覆船体的稳性, 可以减小最初扳正力, 降低了扳正难度; 在扳正后期时, 破舱进水产生的倾斜力矩最大值为163.594 MN·m, 说明破舱进水降低了船体的稳性, 提高了扳正难度, 仍需要施加较大的扳正力平衡船体; 船体纵向强度分布会随着扳正力和破舱进水量的变化而改变, 多点扳正船体的最大扳正力小于单点最大扳正力的40%, 最大扭矩小于单点扭矩的50%;方案1~4的最大进水量分别为6 269.76、6 781.01、5 830.76、6 653.33t, 因此, 合理布置扳正点的位置, 单点扳正(方案1~3) 的进水量小于多点扳正(方案4)。Abstract: The buoyancy and stability of damaged-capsized hull were considered, and the spatial position and mechanical of hull state were studied during righting process.The spatial mechanical equilibrium equation of hull was established by Euler rotation transformation method.The stability and righting mathematical model of hull were derived by using the hydrostatical theory of ship.The flooding quantity was calculated according to Bernoulli theorem and its impact on the positions of barycenter and buoyant centre were obtained.The righting process of damagedcapsized hull was simulated by using General HydroStatics (GHS) software, the maximum righting force and flooding quantity were solved, and the shear force, bending moment, torque of six longitudinal positions along the hull were calculated.Computation result shows that the righting moment of damaged-capsized hull decreases by 130.312 MN·m in the early righting process because water floods damaged cabins.So, the flooding water decreases the stability ofdamaged-capsized hull and the righting force, which results in the decrease of righting difficulty.In the later righting process, the maximum tilting moment of damaged-capsized hull is163.594 MN·m because water floods damaged cabins.Thus, flooding water decreases the stability of hull, increases the righting difficulty, and the larger righting force is needed to balance the hull.The longitudinal strength distribution of hull changes in response to the righting force and flooding quantity.The maximum force and torque of multi-point righting are less than40% and 50% of the corresponding values of single-point righting, respectively.The maximum flooding quantities in Schemes 1-4 are 6 269.76, 6 781.01, 5 830.76 and 6 653.33 t, respectively, which shows that the flooding quantities of single-point righting (Schemes 1-3) are less than the flooding quantity of multi-point righting (Scheme 4) through reaonably arranging the positions of righting points.
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Key words:
- ship engineering /
- wreck salvage /
- capsized hull /
- righting scheme /
- righting force /
- GHS
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0. 引言
公路工程项目经济评价是公路工程经济分析的核心内容, 目的在于确保决策的正确性和科学性, 避免或最大限度地减少公路工程项目投资的风险, 了解公路建设方案的经济效果, 最大限度地提高公路工程项目投资的综合经济效益[1-2]。公路工程项目投资决策正确与否在很大程度上取决于公路工程项目方案的评价结果。评价方法的研究始终是一个重点。目前, 确定条件下的经济评价方法已经相对成熟, 研究的重点集中在不确定条件下的经济评价。不确定条件主要指的是随机条件和模糊条件, 随机条件下的经济评价是在确定随机分布的情况下进行[3]。由于项目的一次性和独特性以及企业较少有自己的项目数据库, 不易获取方案现金流量的概率分布, 然而项目评估者却较善于进行模糊性的估计[4], 当方案的现金流量或参数为模糊变量时, 就很有必要探讨模糊条件下的方案评价方法, 目前对这一问题研究较少。评价方法主要涉及评价指标的计算实现问题, 基于此, 本文建立了模糊条件下公路工程项目经济评价指标体系, 利用模糊模拟技术实现指标值的计算。
1. 模糊变量及相关定义
设ξ是从可能性空间{ϕ, ψ(ϕ), P}到实数集R的一个函数, 则称ξ为一个模糊变量[5-6], 其中: ϕ为非空集; ψ(ϕ)为ϕ的幂集; P为可能性测度。常用的模糊变量有梯形模糊变量和三角形模糊变量。梯形模糊变量由4元组(r1, r2, r3, r4)完全决定, r1 < r2 < r3 < r4; 三角形模糊变量由3元组(r1, r2, r3)完全决定, r1 < r2 < r3。ξ的α水平集为
ξα={ξ(θ)θ∈Unknown node type: i,Ρ(θ)≥α}
ξ的隶属度函数为
μ(x)=Ρ[θ∈Unknown node type: iξ(θ)=x] x∈R
(1) 同一可能空间上的模糊运算。设
f∶Rn→R
是1个函数, ξ1、ξ2、…、ξn是可能性空间{ϕ, ψ(ϕ), P}上的模糊变量, 则
ξ=f(ξ1,ξ2,⋯,ξn)
是1个模糊变量, 定义为
ξ(θ)=f[ξ1(θ),ξ2(θ),⋯,ξn(θ)] θ∈Unknown node type: i
(2) 不同可能性空间上的模糊运算。
设f∶Rn→R是1个函数, 并且ξi是可能性空间{ϕi, ψ(ϕi), Pi}, i=1, 2, …, n上的模糊变量, 则
ξ=f(ξ1,ξ2,⋯,ξn)
是乘积可能性空间{ϕ, ψ(ϕ), P}上的模糊变量, 定义为
ξ(θ1, θ2, …, θn)=f[ξ1(θ1), ξ2(θ2), …, ξn(θn)] θi∈ϕ
模糊运算后隶属度可由Zadeh扩展原理获得
μ(x)=supx1,⋯,xi,⋯,xn{min1≤i≤nμi(xi)x=f(x1,⋯,xi,⋯,xn)}
模糊变量的比较常由模糊变量的可信性测度、关键值测度和期望值来完成[5-6]。
2. 模糊条件下的经济评价指标体系
模糊条件下公路工程项目各方案现金流量等基础数据不确定, 无法比较大小, 无法按确定条件下的指标体系进行经济评价。模糊条件下的项目经济评价就需要寻求模糊理论的支持, 模糊理论中的模糊期望值、可信性值和关键值理论可以解决这一问题, 原因在于模糊变量可通过其期望值、可信值和关键值比较大小, 因此, 模糊条件下的经济评价就转化为计算方案的评价指标的期望值、可信值和关键值。对应于这3个计算值, 在模糊条件下, 方案经济评价时可采用的形式就有3种: 一是求某一指标的模糊期望值; 二是考察指标值大于(或小于)某一指定值的可信性; 三是计算指标值达到某一可信性的最大指标值(关键值)。对应确定条件下的经济评价指标, 模糊条件条件下的经济评价指标体系就是模糊期望值(图 1)、可信值和关键值指标体系。按照计算模糊期望值、可信值和关键值时, 是否考虑资金时间价值, 可将指标体系又可分为静态和动态评价指标。
3. 模糊指标值计算方法
刘宝碇等提出了模糊模拟技术, 是对模糊系统模型进行抽样试验的一项技术[7-10]。f(ξ)的期望值E[f(ξ)]、可信性值C{f(ξ)≤r}(r为任意指定的实数, 如要求净现值大于等于0, 则r为0)和满足C{f(ξ)≥ˉf}≥a的最大ˉf‚在模拟次数充分多的情况下, 可通过模糊模拟求得。其中: a为任意指定可信值; 为相应指标值。模拟时, 分别从ϕ中均匀产生θk, 使得
式中: ε为充分小的正数。并记
该过程等价于分别从ξ1、ξ2、…、ξn的ε水平集中均匀地产生u1、u2、…、un, 因此, 有
式中: μi为ξi的隶属度函数。
3.1 可信性值的模糊模拟计算
步骤1:分别从ϕ中均匀产生θk, 使得P(θk)≥ε。
步骤2:置υk为P(θk)。
步骤3:通过估计公式返回L(r)
3.2 关键值的模糊模拟计算
步骤1:均匀产生θk, 使得P(θk)≥ε, 并记υk为P(θk)。
步骤2:找到满足L(r)≥a的最大值r。
步骤3:返回r。
3.3 期望值的模糊模拟计算
模糊变量的期望值为
其模糊模拟的过程如下。
步骤1:置变量e为0
步骤2:均匀产生θk, 使得P(θk)≥ε, 并记υk为P(θk)。
步骤3:置
步骤4:从[a, b]中均匀产生r。
步骤5:如果r≥0, 那么
如果r < 0, 那么
步骤6:重复步骤4、5共n次。
步骤7:最后得
4. 实例分析
某公路工程投资项目初始投资估计为三角模糊变量(130, 140, 150), 单位为万元; 投资后当年即可获得正常收益, 年净收益为梯形模糊变量(27, 28, 29, 30), 单位为万元; 寿命期为三角形模糊变量(14, 15, 16), 单位为年; 基准收益率为三角形模糊变量(10%, 11%, 12%)。投资、年净收益、寿命期和基准收益率均为模糊变量, 分别设为ξ1、ξ2、ξ3、ξ4, 则净现值为
也为模糊变量。采用前面介绍的模糊模拟技术, 通过5 000次的模糊模拟计算, 求得E[f(ξ)]为657 794.7元, C{f(ξ)≥0}为100%, 满足
的最大值为373 229.1元。工程项目的E[f(ξ)] > 0, 说明方案可行; 方案的可信性C{f(ξ)≥0}=100%, 说明方案一定可行; 方案有90%的把握能获利373 229.1元。
5. 结语
本文建立了模糊条件下的经济评价指标体系, 提出了评价指标值计算方法, 并利用指标值对模糊条件下的经济项目进行了评价。评价结果客观, 易于解释, 对历史数据要求不高。但是案例中的三角模糊数是在评估人员直接给出的情况下获得, 未来还需要进一步分析在有一定的历史数据时, 如何通过模糊统计分析来获取方案数据的模糊统计估计值。
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表 1 船体主尺度
Table 1. Principal dimensions of hull
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