Flutter analysis of an airfoil with bounded random parameters in incompressible flow via Gegenbauer polynomial approximation

The effects of parameter uncertainty on the flutter characteristics of a two-dimensional airfoil in an incompressible flow were investigated through Gegenbauer polynomial approximation. The uncertain parameters, such as the linear and cubic pitch stiffness coefficients are modeled as bounded random variables with λ-PDFs (probability density functions). With the aid of Gegenbauer polynomial approximation, the two-dimensional stochastic airfoil system is transformed at first into its equivalent deterministic one. Then the Hopf-bifurcation point is determined through the equivalent deterministic system, and the onset of the flutter, together with the flutter frequency against the probability density distribution parameter and the intensity of the random variable is explored. In addition, the ranges of the peak pitch and plunge responses against the flight speed and the PDFs of the peak pitch response are obtained. Numerical results show how the probability density distribution parameters and the intensities of random parameters affect the flutter onset speed, flutter angular frequency, the upper and lower boundaries of peak responses, and the PDFs of peak responses.     

概率盒全局灵敏度和活跃子空间跨层降维

航空航天仿真系统中的不确定性通常是多源的、混合的,并且系统参数的维数众多。针对高维混合不确定性量化问题,提出一种结合概率盒全局灵敏度和活跃子空间的跨层降维方法。在随机和认知不确定的概率盒表征基础上,使用不确定性缩减法分析参数的全局灵敏度继而进行参数筛选;基于输出梯度协方差矩阵的特征分解,使用活跃子空间法对参数进行降维;构造出一种概率盒表征下的参数筛选和跨层降维方法。最后以NASA多学科不确定性量化挑战问题为例,通过概率盒全局灵敏度分析进行第1层次的参数筛选,原有的21维输入参数减为13维;随后采用活跃子空间进行第2层次的参数降维,维数进一步降至一维。研究结果表明,所提出的方法能够对混合不确定性参数进行灵敏度排序,还能够有效降低模型输入参数的维度,为高维系统混合不确定性量化和进一步的优化工作奠定了基础。     

Hybrid uncertainty-based design optimization and its application to hybrid rocket motors for manned lunar landing

Design reliability and robustness are getting increasingly important for the general design of aerospace systems with many inherently uncertain design parameters. This paper presents a hybrid uncertainty-based design optimization (UDO) method developed from probability theory and interval theory. Most of the uncertain design parameters which have sufficient information or experimental data are classified as random variables using probability theory, while the others are defined as interval variables with interval theory. Then a hybrid uncertainty analysis method based on Monte Carlo simulation and Taylor series interval analysis is developed to obtain the uncer-tainty propagation from the design parameters to system responses. Three design optimization strategies, including deterministic design optimization (DDO), probabilistic UDO and hybrid UDO, are applied to the conceptual design of a hybrid rocket motor (HRM) used as the ascent propulsion system in Apollo lunar module. By comparison, the hybrid UDO is a feasible method and can be effectively applied to the general design of aerospace systems.     

Novel moderate transformation of fuzzy membership function into basic belief assignment

In information fusion, the uncertain information from different sources might be modeled with different theoretical frameworks. When one needs to fuse the uncertain information represented by different uncertainty theories, constructing the transformation between different frameworks is crucial. Various transformations of a Fuzzy Membership Function (FMF) into a Basic Belief Assignment (BBA) have been proposed, where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements. However, these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty. To avoid extreme attitudinal bias, a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred. In this paper, two moderate transformations of an FMF into a trade-off BBA are proposed. One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism, where the weighting factor can be user-specified or determined with some prior information. The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.     

考虑气动不确定性的气动弹性系统模型确认

研究了机翼气动弹性系统的不确定性建模及其模型确认问题。结构的不确定性考虑为参数形式,气动力的不确定性分为未建模动力学和参数不确定性两种形式进行讨论。建立不确定气动弹性系统的线性分式变换（LFT）模型,给出了频域的模型有效性检验方法,对有效模型集进行参数化并将不确定性幅值最小的模型集求解归结为优化问题。在建模中计入了实际存在的、未知但能量有界的外扰和噪声的影响,降低了结果的保守性。最后,根据模型确认的结果,使用结构奇异值μ 分析方法进行不确定系统的鲁棒颤振分析。仿真计算结果表明了模型确认方法的有效性。     

A novel method for importance measure analysis in the presence of epistemic and aleatory uncertainties

For structural systems with both epistemic and aleatory uncertainties, research on quantifying the contribution of the epistemic and aleatory uncertainties to the failure probability of the systems is conducted. Based on the method of separating epistemic and aleatory uncertainties in a variable, the core idea of the research is firstly to establish a novel deterministic transition model for auxiliary variables, distribution parameters, random variables, failure probability, then to propose the improved importance sampling(IS) to solve the transition model. Furthermore,the distribution parameters and auxiliary variables are sampled simultaneously and independently;therefore, the inefficient sampling procedure with an ‘‘inner-loop' for epistemic uncertainty and an‘‘outer-loop' for aleatory uncertainty in traditional methods is avoided. Since the proposed method combines the fast convergence of the proper estimates and searches failure samples in the interesting regions with high efficiency, the proposed method is more efficient than traditional methods for the variance-based failure probability sensitivity measures in the presence of epistemic and aleatory uncertainties. Two numerical examples and one engineering example are introduced for demonstrating the efficiency and precision of the proposed method for structural systems with both epistemic and aleatory uncertainties.     

Measuring reliability under epistemic uncertainty:Review on non-probabilistic reliability metrics

In this paper, a systematic review of non-probabilistic reliability metrics is conducted to assist the selection of appropriate reliability metrics to model the influence of epistemic uncertainty. Five frequently used non-probabilistic reliability metrics are critically reviewed, i.e., evidence-theory-based reliability metrics, interval-analysis-based reliability metrics, fuzzy-interval-analysis-based reliability metrics, possibility-theory-based reliability metrics (posbist reliability) and uncertainty-theory-based reliability metrics (belief reliability). It is pointed out that a qualified reli-ability metric that is able to consider the effect of epistemic uncertainty needs to (1) compensate the conservatism in the estimations of the component-level reliability metrics caused by epistemic uncertainty, and (2) satisfy the duality axiom, otherwise it might lead to paradoxical and confusing results in engineering applications. The five commonly used non-probabilistic reliability metrics are compared in terms of these two properties, and the comparison can serve as a basis for the selection of the appropriate reliability metrics.     

Probabilistic inference of fatigue damage propagation with limited and partial information

A general method of probabilistic fatigue damage prognostics using limited and partial information is developed.Limited and partial information refers to measurable data that are not enough or cannot directly be used to statistically identify model parameter using traditional regression analysis.In the proposed method, the prior probability distribution of model parameters is derived based on the principle of maximum entropy(Max Ent) using the limited and partial information as constraints.The posterior distribution is formulated using the principle of maximum relative entropy(MRE) to perform probability updating when new information is available and reduces uncertainty in prognosis results.It is shown that the posterior distribution is equivalent to a Bayesian posterior when the new information used for updating is point measurements.A numerical quadrature interpolating method is used to calculate the asymptotic approximation for the prior distribution.Once the prior is obtained, subsequent measurement data are used to perform updating using Markov chain Monte Carlo(MCMC) simulations.Fatigue crack prognosis problems with experimental data are presented for demonstration and validation.     

Fuzzy norm method for evaluating random vibration of airborne platform from limited PSD data

For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.     

不确定性颤振风险定量分析

 针对小风险颤振定量分析,提出一种概率鲁棒颤振初步分析方法。该方法结合鲁棒颤振分析和概率颤振分析,针对不同层次风险和不确定性水平提供颤振边界特性全面信息,给决策制定提供更好参考。在鲁棒颤振分析中,采用振型迭代的方法,通过结构奇异值( μ )分析和特征值求解得到零风险的鲁棒颤振临界速度。在概率颤振分析中,采用标准蒙特卡罗模拟(MCS)方法得到较大风险时的颤振速度分布和概率临界速度。采用概率比较和二分法估计概率鲁棒颤振不确定度半径和概率鲁棒颤振临界速度,同时采用样本重新利用的随机方法估计颤振风险和不确定性定量关系。通过一个考虑集中质量不确定性的大展弦比双梁式机翼的颤振计算分析表明,确定型μ方法只能用于零风险颤振分析,标准的MCS方法只能用于较大风险颤振速度分布问题。概率鲁棒颤振分析结果表明增加1%颤振风险可以使不确定度半径增大62%或颤振速度边界增大5%,从而放宽了设计要求。     

蒸汽轮机叶片失速颤振的预测

本文移植了轴流压气机叶片失速颤振预测方法中一种半经验方法——变形激盘法,从自激振动的角度分析了蒸汽轮机末级工作叶片在某些工况下动应力突增的故障。本文中计算与实测值间的定性一致表明:末级工作叶片在低负荷状态的动应力突增是由于大负攻角失速颤振所引起的。本文对设计工况附近的动应力增加提出了一种解释,在设计工况叶片可能存在一种目前尚未分类过的“高负荷非失速颤振”。      

基于失效概率的涡轮后机匣全局灵敏度分析

涡轮后机匣是航空发动机安全的关键部件,但是其具有工况复杂、不确定性因素多的缺点。为了探究输入随机变量的不确定性对涡轮后机匣结构失效概率的影响,建立参数化有限元模型进行确定性分析。考虑材料性能、几何参数及外部载荷的不确定性,对涡轮后机匣两种典型失效模式：强度失效以及刚度失效建立极限状态函数;通过构造自适应Kriging 代理模型并结合重要抽样方法评估涡轮后机匣结构失效概率,利用基于失效概率的全局灵敏度方法对涡轮后机匣结构可靠度的不确定性来源进行分析,对各输入随机变量重要性进行排序,构建一种涡轮后机匣全局灵敏度分析框架。结果表明：涡轮后机匣在两种失效模式以及系统失效模式下,发动机推力以及线性膨胀系数对结构失效概率影响最为显著,应对其重点考虑;内外机匣长度以及材料弹性模量对涡轮后机匣结构失效概率影响较小,可对其适当忽略。     

一种基于亚临界响应的颤振稳定性边界预测新方法

基于地面模态试验事先获取的结构模态参数,通过弹性机翼在气流中的亚临界响应,解算出作用在机翼上的非定常模态气动力系数。以弹性机翼的模态位移作为系统输入,模态气动力系数作为系统输出,通过辨识方法获得弹性机翼振动的气动力模型。在时域内耦合结构运动方程和气动力模型,建立基于试验数据的气动弹性稳定性分析模型。通过分析系统稳定性随动压的变化规律,获得弹性机翼的颤振稳定性特性。与经典颤振边界外推方法的主要区别在于该方法实质上只需要一次亚临界响应试验即可预测颤振临界点,可极大降低颤振试验的风险和成本。该方法既可用于颤振风洞试验,也可用于颤振试飞。     

考虑不确定性的复合材料加筋壁板后屈曲分析模型验证方法

复合材料加筋壁板在结构轻量化设计中，由于材料组分、几何尺寸具有不确定性，导致了壁板结构在服役条件下承载特性的不确定性。针对上述问题，提出了一种考虑参数不确定性的复合材料加筋壁板后屈曲模型验证方法。首先基于正交试验设计方法进行了不确定性参数的显著性分析，然后采用Kriging模型构建了能够表征后屈曲特性的代理模型，利用蒙特卡洛随机模拟获得加筋壁板后屈曲载荷概率分布，最后通过壁板结构在典型承载条件下的力学实验数据验证了分析模型的准确性。该分析方法对于壁板件在实际工程中的应用具有一定指导意义。     

二维翼段颤振的μ控制

 采用超声电机作为作动器来实现含控制面的翼段颤振鲁棒抑制。针对作者设计的二维翼段颤振主动抑制系统，通过理论与实验相结合的方法，建立了考虑沉浮方向阻尼和作动器模型参数不确定性的控制系统模型，设计了μ控制器，并对控制器做了降阶处理。数值仿真和风洞试验表明，μ控制器可有效地抑制颤振的发生，将颤振临界速度提高23.4%。相对于H_∞控制器，μ控制器的控制效果和鲁棒性更好。     

轴流压气机进口小总压径向畸变对失速颤振的影响

对进口流场畸变失速颤振的影响进行了实验研究。实验结果表明:小的叶尖径向畸变能抑制颤振的发作。对此现象用三维变形激盘法进行了计算。计算结果与实验符合。      

Reliability and Sensitivity Analysis of Transonic Flutter Using Improved Line Sampling Technique

The improved line sampling (LS) technique, an effective numerical simulation method, is employed to analyze the probabilistic characteristics and reliability sensitivity of flutter with random structural parameter in transonic flow. The improved LS technique is a novel methodology for reliability and sensitivity analysis of high dimensionality and low probability problem with implicit limit state function, and it does not require any approximating surrogate of the implicit limit state equation. The improved LS is used to estimate the flutter reliability and the sensitivity of a two-dimensional wing, in which some structural properties, such as frequency, parameters of gravity center and mass ratio, are considered as random variables. Computational fluid dynamics (CFD) based unsteady aerodynamic reduced order model (ROM) method is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the safety margin of flutter is founded by using the critical velocity of flutter. The results show that the improved LS technique can effectively decrease the computational cost in the random uncertainty analysis of flutter. The reliability sensitivity, defined by the partial derivative of the failure probability with respect to the distribution parameter of random variable, can help to identify the important parameters and guide the structural optimization design.     

认知不确定性下可靠性灵敏度分析的新指标

传统的可靠性灵敏度指标只考虑了随机不确定性,当结构中还存在认知不确定性时,该指标难以反映出基本变量中认知不确定性对结构可靠性评估结果的影响程度.针对这一问题,引入概率包络来表达结构中的随机不确定性和认知不确定性,在此基础上建立了可靠性灵敏度分析的新指标——认知灵敏度系数,给出了其定义和代表的意义,并基于证据理论提出了认知灵敏度系数的计算方法.算例分析表明,认知灵敏度系数可以反映出基本变量中认知不确定性对结构可靠性评估结果的不确定性的影响程度,从而为有针对性地提高可靠性评估结果的准确性提供依据.另外,基于证据理论的认知灵敏度系数的计算方法适用于极限状态函数为单调、非单调的结构,以及变量服从正态、非正态的结构,具有普适性.     

机翼带外挂系统极限环颤振的区间分析

针对带有初偏间隙型非线性刚度的二元翼带外挂系统的极限环颤振,应用当量线化方法得出了颤振边界曲线,并根据颤振边界曲线用4阶Runge-Kutta法得到极限环相图,可明显看出极限环振动与普通周期振动的区别。然后引入了几个不确定量,通过区间分析方法给出了这些不确定量对机翼带外挂系统颤振边界曲线的影响,并用随机有限元法(FEM)验证区间分析方法的可靠性。进而可以得到一定来流速度下,具有不确定机翼外挂系统幅值的上下界,以及不确定参数对极限环相图的影响。知道机翼外挂幅值的上下界后,可以对外挂幅值进行适当控制。     

De-combination of belief function based on optimization

In the theory of belief functions, the evidence combination is a kind of decision-level information fusion. Given two or more Basic Belief Assignments(BBAs) originated from different information sources, the combination rule is used to combine them to expect a better decision result. When only a combined BBA is given and original BBAs are discarded, if one wants to analyze the difference between the information sources, evidence de-combination is needed to determine the original BBAs. Evidence d...