基于交叉降阶取样的改进响应面方法

针对经典响应面法和加权响应面法存在的计算精度不高和稳定性不强的问题,提出一种新的样本点选择策略,即交叉降阶思想,并基于此发展出一种新的改进响应面方法。该方法以均值点加上0.5倍的标准差作为初始迭代点。在Bucher试验设计的基础之上,将n维坐标系降阶为n个一维坐标系。然后,依据样本点的重要性,筛选出n+1个靠近真实失效面的优秀样本点,并用这些样本点去拟合线性响应面函数。最后依据样本中心间的距离与上一次迭代得到的设计点的范数之商作为其收敛准则。通过5个数值算例与工程算例,验证了交叉降阶响应面法具有较高的精度、效率、稳定性和一定的工程适用性。     

考虑塑性变形发展程度系数的RC梁开裂弯矩改进计算公式

针对RC梁开裂荷载计算方法尚未统一的现状，首先，结合18根RC梁试验数据对比了已有的6种RC梁开裂弯矩计算公式，发现开裂弯矩理论计算值与试验值的偏差大小和混凝土强度有关；然后，通过提出塑性变形发展程度系数k，推导新的RC梁开裂弯矩计算公式，并进一步基于k值和塑性影响系数计算值γ_k进行改进；最后，选取12根RC试验梁验证改进公式的准确性，证明改进公式的计算值与试验值吻合更好且偏于安全。     

基于Wilson-θ和Newmark-β法的非线性动力学方程改进算法

Wilson-θ法和Newmark-β法是非线性动力学方程求解的常用方法。它们的一个基本步骤是,将方程改写为增量平衡的形式,在每一个积分步长内用状态参量修正平衡方程的系数矩阵,其本质是在单个步长内对系统的非线性环节进行了线性化处理。本文基于增量思想分别改进了Wilson-θ法和Newmark-β法,根据即时解给出下一步的猜测解,然后对猜测解进行迭代校正,最终得到收敛的近似解。算例表明,改进算法的精度更高,且收敛准则简单。更为重要的是,本文方法无须对非线性项进行线性化处理,因而计算效率更高,适应范围更广。     

改进的Park-Ang再生混凝土柱地震破坏模型的试验研究

通过对不同配比的6根再生混凝土(RAC)柱进行低周反复加载试验。由于现有普通混凝土结构地震破坏损伤模型均为基于普通混凝土结构所构建的,是否适用于RAC结构的地震损伤破坏计算仍不明确;为能够有效考虑RAC中再生骨料取代率及混杂纤维掺量等因素所造成的普通混凝土结构地震破坏损伤模型中循环荷载系数β的不确定性及其对损伤指数计算结果的影响,同时提高计算模型的预见性与可靠性,本文提出了一种适用于RAC结构的改进的双参数损伤模型。通过模型的计算结果与实际结构各震害破损度D_c的对比,确定了适用于RAC结构的双参数损伤模型中循环荷载系数β的值。     

基于转捩/尺度适应模型与FW-H声学方程的气动噪声数值模拟研究

采用计算流体力学(CFD)同"声类比"相结合的方法进行噪声模拟,利用CFD数值模拟 MD30P30N多段翼型失速攻角附近流场以及其气动特性来校核近场精度,进一步通过结合可穿透数据面的FW-H声学方程进行气动噪声分析。为了准确捕捉近场流场信息,为噪声预测提供可靠的声源精度,本文基于k-ω剪应力输运(SST)湍流模型,建立了尺度适应分离流(SAS)模型,并采用γ-Re_θt转捩模型耦合k-ω SST湍流模型建立了边界层转捩数值模拟技术;充分利用尺度适应模型在边界层表现为雷诺平均(RANS)方法这一特点,将γ-Re_θt转捩模型与SAS模型结合,建立针对包含转捩、分离现象复杂流场的数值模拟技术。文中以RANS为控制方程,分别采用全湍流k-ω SST模型、γ-Re_θtSAS转捩/分离流模型对多段翼进行近场数值模拟计算,结合可穿透数据面的FW-H声学方程进行气动噪声预测,在分析其对流场及气动噪声影响的基础上,得出了几点结论。     

基于BP神经网络和Laplace渐进积分法的结构可靠性计算

传统基于代理模型的可靠性研究大多将抽样方法与代理模型相结合,并假定随机变量相互独立,且没有考虑到代理模型的不确定性对失效概率的影响。本文将反向传播(BP)神经网络和Laplace渐进积分法相结合,提出一种结合代理模型和高次阶矩的可靠性计算方法,称之为BP-Lap法。采用Latin超立方抽样技术,结合学习函数选取样本点,基于函数逼近原理,利用BP网络代理极限状态方程及其梯度向量和Hessian矩阵。利用训练好的BP网络通过Laplace渐进积分法求解失效概率,基于十折交叉验证思想,得到失效概率取值区间。通过四个算例,分别在随机变量相关和不相关的条件下,验证了BP-Lap法的有效性。研究表明：BP-Lap法可以衡量代理模型的不确定性对失效概率的影响,得到失效概率的上、下界;BP-Lap法同时适用于显示和隐式的极限状态方程,对相关随机变量的可靠性问题具有较高精度。     

压电压磁材料中正n边形孔边裂纹分析

基于电磁复合材料力学,运用Stroh型公式和复变函数方法,针对压电压磁材料中含正n边形孔边裂纹反平面问题进行了研究。利用Schwarz-Christoffel变换技术,结合Cauchy积分公式和留数定理,导出了磁电全非渗透型边界条件下任意正n边形裂纹尖端场强度因子和能量释放率的解析解。当缺失磁场时,所得解退化为已有结果,以此验证方法的有效性。通过数值算例,对比分析了n=3,n=4和n=5三种特殊情形对应的孔口边长、裂纹长度和受到的力、电和磁载荷对等效场强度因子和无量纲能量释放率的影响规律。研究结果发现,正n边形孔洞的尺寸和裂纹长度均会促进裂纹扩展,且前者的影响更显著一些;正n边形边的数量增加会阻止裂纹的扩展;在磁电全非渗透型边界条件下,机械载荷始终促进裂纹的扩展,电位移载荷可以促进或抑制裂纹的扩展,磁载荷对裂纹的扩展贡献较少。本研究结果适用于任意正n边形孔边裂纹求解问题,为压电压磁材料元器件的优化设计和断裂特性分析提供了新思路。     

基于突变特征的边坡双强度折减系数量化研究

边坡失稳是一个由渐变演化至突变破坏的过程，过程中土体的强度参数c和φ发挥作用的路径和衰减程度不同。目前，双强度折减策略DRM在边坡稳定性评估中已逐渐形成共识，但双强度参数间的真实折减关系或折减关系的求解方法难以准确定义。以坡体抵抗外部环境能力最大值原理为依据，引入非线性分析突变理论，以坡体的极限承载力为考察量，建立其与双强度折减比的突变模型函数来考察边坡整体稳定性，进而量化折减过程中c和φ的折减比。结合算例，通过与已有方法的计算结果进行对比，验证了方法的合理性，并探究了c和φ以及坡度与折减比间的演化规律及机理。研究的执行思路可为双强度折减技术的探讨提供有益参考。     

核级石墨PFC2D模型的宏细观参数分析

颗粒流软件PFC能够很好地处理非连续介质力学的问题,模拟核级石墨的损伤和断裂过程具有独特的优势。在采用PFC^2D模拟核级石墨时,为了增加模拟的便捷性,实现了PFC^2D细观参数的快速标定。本文首先设计了四因素四水平的正交试验,分析了核级石墨的宏观参数与PFC^2D的细观参数关系;然后基于建立的核级石墨宏细观参数的关系,采用PFC^2D模拟石墨IG11的三点弯曲试验,并从位移场变形、荷载-位移曲线和断裂参数三个方面验证其宏细观参数关系的正确性。结果表明,弹性模量E随平节理模量E_c的增加线性增加;抗拉强度σ_t随平节理抗拉强度σ_b的增加线性增加;泊松比ν随平节理刚度比k_n/k_s的增加先增大后减小;数值模拟的位移场变化和荷载-裂缝口张开位移P-CMOD曲线与试验结果较吻合,此外,断裂参数的最大误差不超过3.57%。     

基于主动学习Kriging模型与序列重要抽样的随机-区间混合可靠性分析

针对随机-区间混合可靠性分析中复杂功能函数的高非线性和多设计点问题,本文提出了一种结合主动学习Kriging模型与序列重要抽样方法的混合可靠性分析方法.在序列重要采样方法中采用高斯混合分布作为提议分布进行逐级采样,逐步逼近最优重要抽样函数的采样样本;结合序列重要抽样方法的特点,提出了主动学习Kriging模型的两步学习方案,保证算法精度的前提下显著提高了效率.通过数值算例将本文方法与已有的混合可靠性分析方法对比,验证本文方法的准确性和高效性.     

Verification testing in computational fluid dynamics: an example using Reynolds‐averaged Navier–Stokes methods for two‐dimensional flow in the near wake of a circular cylinder

Verification testing was performed for various Reynolds‐averaged Navier–Stokes methods for uniform flow past a circular cylinder at Re= 5232. The standard and renormalized group (RNG) versions of the k–ε method were examined, along with the Boussinesq, Speziale and Launder constitutive relationships. Wind tunnel experiments for flow past a circular cylinder were also performed to obtain a comparative data set. Preliminary studies demonstrate poor convergence for the Speziale relationship. Verification testing with the standard and RNG k–ε models suggests that the simulations exhibit global monotonic convergence for the Boussinesq models. However, the global order of accuracy of the methods was much lower than the expected order of accuracy of 2. For this reason, pointwise convergence ratios and orders of accuracy were computed to show that not all sampling locations had converged (standard k–ε model: 19% failed to converge; RNG k–ε model: 14% failed to converge). When the non‐convergent points were removed from consideration, the average orders of accuracy are closer to the expected value (standard k–ε model: 1.41; RNG k–ε model: 1.27). Poor iterative and global grid convergence was found for the RNG k–ε/Launder model. The standard and RNG k–ε models with the Boussinesq relationship were compared with experimental data and yielded results significantly different from the experiments. Copyright © 2003 John Wiley & Sons, Ltd.     

POD-based surrogate modeling of transitional flows using an adaptive sampling in Gaussian process

A surrogate model, based on proper orthogonal decomposition (POD) with the adaptive sampling method, was proposed to predict the transitional flow past rough flat plates simulated by a four-equation k-ω-γ-A_r transition model. Gaussian process regression was used to map the input parameters to the POD expansion coefficients. The variance and gradient of Gaussian process were taken as the criteria for the adaptive sampling. The proposed methodology was applied to a one-dimensional heat conduction problem and two-dimensional transitional flow past rough flat plates. At the same time, the results were compared with those of Halton sequences. With the same sample size, the adaptive method achieved a higher accuracy on the test set, and the proposed adaptive criterion could serve as an indicator for the model discrepancies.     

Using the Sequential Self-calibration Method and Genetic Algorithm Method to Optimally Design Tracer Test to Estimate Conductivity Distribution

A gradient-based inverse method – the sequential self-calibrated method – is combined with a genetic algorithm method to search the optimal design scheme for a tracer test. The sequential self-calibrated method is developed for estimating conductivity distribution in a study domain conditioning on tracer test data. To improve the calculation efficiency, a fast streamline-based approach is used to compute the derivative of concentration with respect to the changes of hydraulic conductivity. Performance of the sequential self-calibrated method has been studied using a synthetic aquifer having a sandwich-like geologic structure where hypothetical tracer tests are conducted. The study results indicate that the locations and number of sampling wells will significantly affect accuracy in the estimates. To maximize estimating accuracy in the sequential self-calibrated method for a fixed number of sampling wells, a genetic algorithm method is applied to search the optimal locations for sampling wells. The results indicate that the optimal sampling well locations depend on the apparent geologic structure and the difference in conductivity values for the various regions. For the sandwich-like structure, when the difference between conductivity values in the two separate regions is large enough, the optimal locations for the sampling wells will be fixed, regardless of conductivity values. The study results also show that based on the optimal sampling-well scheme, estimating accuracy will increase as the number of sampling wells increases, even though the rate of increasing accuracy slows as the number of wells increases.     

Development of an Analytical <Emphasis Type="Italic">β</Emphasis>-Function PDF Integration Algorithm for Simulation of Non-premixed Turbulent Combustion

Among many presumed-shape pdf approaches for modeling non-premixed turbulent combustion, the presumed β-function pdf is widely used in the literature. However, numerical integration of the β-function pdf may encounter singularity difficulties at mixture fraction values of Z = 0 or 1. To date, this issue has been addressed by few publications. The present study proposes the Piecewise Integration Method (PIM), an efficient, robust and accurate algorithm to overcome these numerical difficulties with the added benefit of improving computational efficiency. Comparison of this method to the existing numerical integration methods shows that the PIM exhibits better accuracy and greatly increases computational efficiency. The PIM treatment of the β-function pdf integration is first applied to the Burke–Schumann solution in conjunction with the k − ε turbulence model to simulate a CH₄/H₂ bluff-body turbulent flame. The proposed new method is then applied to the same flow using a more complex combustion model, the laminar flamelet model. Numerical predictions obtained by using the proposed β-function pdf integration method are compared to experimental values of the velocity field, temperature and species mass fractions to illustrate the efficiency and accuracy of the present method.     

饱和两相介质动力固结问题时域求解的精细时程积分方法

针对u-p形式的饱和两相介质波动方程,采用精细时程积分方法计算固相位移u,采用向后差分算法求解流体压力p,建立了饱和两相介质动力固结问题时域求解的精细时程积分方法。针对标准算例,对该方法的计算精度进行了校核。开展了该方法相关算法特性的研究,对采用不同数值积分方法计算非齐次波动方程特解项计算精度的差异进行了对比研究,并对采用不同积分点数目的高斯积分法计算特解项条件下计算精度的差异进行了对比研究。研究结果表明,(1)该方法具有良好的计算精度。(2)计算非齐次波动方程特解项的数值积分方法中,梯形积分法的计算精度最差,高斯积分法、辛普生积分法和科茨积分法都具有较好的计算精度。(3)增加高斯积分点数目对于提高计算精度的作用并不显著。     

A New Algorithm for Estimating Three-Phase Relative Permeability from Unsteady-State Core Experiments

We present a new history matching method based on a Genetic Algorithm to estimate three-phase k _r (relative permeability) from unsteady-state coreflood experiments. In this method, relative permeabilities (k _r) are represented by quadratic B-Spline functions. Adjustable coefficients in k _r functions are changed in an iterative process to minimize an objective function. The objective function is defined as the difference between the measures and simulated values of the pressure drop across the core and fluids recovery during the experiment. One of the main features of this approach is that water and gas relative permeabilities (k _rw and k _rg) are assumed to be functions of two independent saturations as opposed to most of the existing empirical k _r models in which k _rw and k _rg are assumed to be only dependent of their own saturations. Another important aspect of this algorithm is that it considers inequality constrains to ensure that physically acceptable k _r curves are maintained throughout the iterative optimization process. A three-phase coreflood simulator has been developed based on this methodology that generates best k _r values by matching experimental data. The integrity of the developed software was first successfully verified by using two sets of experimental three-phase k _r data published in the literature. Then, the results of some three-phase coreflood experiments carried out in our laboratory were used to obtain three-phase k _r curves by this approach.     

基于主动学习Kriging模型的结构多失效模式可靠度计算

对于具有多失效模式的结构可靠度计算问题,利用多输出Kriging模型作为代理模型进行分析。该代理模型只需对所有功能函数进行一次建模,无需对每个功能函数建立各自的代理模型,且在建模过程中能够考虑各失效模式之间的相关性。本文方法设定的初始样本点不仅对随机变量均值附近区域给予足够重视,而且能够兼顾设计空间的边缘区域,进而确保初始代理模型在全局空间内具有较好精度,以减少后续利用学习函数更新代理模型的次数。数值算例表明,本文方法具有较好的计算精度和较高的计算效率,当失效模式较多时,计算效率大幅提升。     

结构可靠性优化的多输出高斯过程代理模型

对于具有多失效模式的结构,基于可靠性的结构优化计算成本是比较昂贵的。本文利用多输出高斯过程MOGP(Multiple Output Gaussian Process)代理模型以降低计算成本,首先利用Bucher方法生成初始样本,然后结合均匀训练样本和学习函数对MOGP代理模型进行构建。学习函数可在大范围内筛选出较为满意的训练样本,能够确保MOGP代理模型具有较好的全局精度,在整个优化过程中不再重新构建MOGP代理模型。利用协方差矩阵,MOGP代理模型能够考虑各失效模式的相关性,对多输入多输出系统具有良好的预测性能。数值算例表明,本文方法具有较好的计算结果,且计算效率较高,尤其是设计变量数目与失效模式数目较多时效率提升明显。     

Computational study on turbulent flows around modern tanker hull forms

To enhance the applicability of CFD techniques to the hull form design of modern commercial ships, an efficient and robust numerical method for turbulent flow calculation is developed. The preprocessor is composed of hull form presentation, surface mesh generation, and field grid generation. The finite‐volume method is utilised to solve the Reynolds‐averaged Navier–Stokes equations. Three k–? turbulence models, i.e., the standard k–? model (SKE), the RNG‐based k–? model (RNG), and the realisable k–? model (RKE), are evaluated to investigate the difference caused by the turbulence model. The developed numerical method is applied to two practical VLCC hull forms with the same forebody and the slightly different afterbodies in order to find out whether CFD can capture the difference of stern flow due to hull form variation. It is found that RKE successfully predict the strength and location of bilge vortex, while SKE and RNG fail. However, all three models can provide the right information on the nominal wake difference between two hull forms. Copyright © 2002 John Wiley & Sons, Ltd.