概率密度曲线及其参数估计的模糊与随机方法

首次提出了概率密度曲线及其参数估计的模糊与随机方法,并以一组疲劳寿命数据为例描述了参数估计的具体过程。对随机样本分别采用模糊与随机方法和数理统计方法进行了参数估计,结果表明：用模糊与随机方法比用数理统计方法得到参数估计值更接近理论值。     

随机结构响应量置信区间的一种求解方法

基于经典的可靠性分析方法和非正态变量向正态变量的等价变换,提出了随机结构响应量置信区间估计的一种迭代方法,该方法可用于复杂响应量函数或隐式响应量函数的置信区间分析。在采用有精确解的算例验证了所提方法的有效性后,将所提方法用于2个工程实例,对10杆结构中的位移函数和某型飞机翼身连接接头模型中的响应面函数进行了置信区间估计,所提方法的计算结果与数值模拟方法计算结果的对照表明:所提方法计算工作量小且计算精度高。     

考虑状态与基本变量随机模糊性的广义响应面可靠性分析

针对复杂结构、机构可靠性分析中的隐式极限状态方程,建立了可以同时考虑基本变量和失效一安全状态随机模糊双重不确定性因素的广义响应面可靠性分析方法。该方法采用模糊基本变量的等效随机化变换,在不改变基本变量模糊分布的情况下,建立了基于有限元分析的复杂结构、机构多个随机一模糊基本变量情况下的广义响应面法,利用广义响应面函数和模糊随机事件概率的计算公式,定义了复杂结构、机构广义失效概率的计算公式,并给出了多个模式情况下体系同时考虑状态和基本变量随机模糊性的广义失效概率计算公式。在弹性连杆机构强度刚度多模式广义可靠性分析的应用算例说明了所提方法的合理性。     

薄壁板结构随机声激励振动响应计算与分析

针对航空发动机压气机转子叶片结构声振动问题,建立了薄壁板有限元简化模型,基于耦合有限元/边界元法对薄壁板在行波加载下随机声激励振动响应进行了仿真计算,得到了在不同声压级下的应力响应结果.改变声载荷激励方向,分别对薄壁板施加单音噪声激励和宽频随机噪声激励,通过仿真计算得到了不同角度随机声激励下薄壁板振动响应频响曲线.对比分析发现,薄壁板模态振型与噪声加载方向是引起薄壁板共振的重要因素.     

具有随机不确定性的机翼颤振优化

针对不确定性参数在颤振优化分析中的影响,提出了一种含颤振约束的、具有随机不确定性的机翼气动弹性优化设计方法.在MSC.NASTRAN平台上建立了结构的动力学模型、采用ZAERO程序进行了非定常气动力计算与颤振分析,用响应面方法计算了隐式失效功能函数,以重量最小为设计目标,对包含颤振概率约束的复合材料机翼进行了优化设计....     

基于响应面法的机翼气动/结构一体化优化设计研究

基于响应面法进行了机翼气动/结构一体化优化设计研究,流动控制方程为三维欧拉方程,采用有限体积法进行数值求解,应力和结构变形采用有限元方法计算,静气动弹性分析采用强耦合迭代方式,响应面模型采用二次多项式来构造。以跨音速M6机翼为初始机翼,进行了多目标、多约束情形下的气动/结构综合优化设计,优化后所得到的新机翼具有更佳的气动/结构综合性能,升阻比增加了9.25%,而重量减轻了4.84%;响应面模型精度满足设计要求,拟合误差均不超过1%;这说明本文所发展气动/结构综合优化设计方法是成功且有效的,具有广泛的应用前景。     

叶片安装角对叶盘结构受迫响应特性的影响

利用简化的叶盘结构有限元模型和基于极值原理的改进Monte Carlo模拟技术,详细分析了叶片安装角失谐对叶盘结构受迫响应特性的影响.分别对6种不同安装角误差的叶盘结构的受迫响应进行了数值计算,得到了各自对应的响应放大因子概率密度曲线,通过曲线比较,分析了叶片安装角误差对叶盘结构受迫响应特性的影响规律.研究表明:安装角误差虽对叶盘结构的固有频率影响较小,但对叶片受迫响应影响是很大的,并且受迫响应幅值放大因子随安装角失谐程度增加而增加.      

加筋板在热声载荷作用下随机疲劳寿命估算

薄壁结构在热声载荷作用下的应力响应对其疲劳寿命估算有着很大的影响.给出了热声载荷作用下加筋板结构的大挠度运动方程,运用有限元方法进行数值模拟,分别计算了四边简支薄壁板与加筋板在相同有限带宽高斯白噪声载荷和变化温度下的应力响应,得到了应力时间历程、应力概率密度分布和应力功率谱密度,利用改进的雨流计数法,结合线性累计损伤理论,采用Smith-Watson-Topper（SWT）平均应力模型估算了两种结构在热声载荷作用下的疲劳寿命,并进行了比较分析.     

热结构在随机压力载荷作用下跳变响应计算与分析

先进的航空航天器结构暴露在严酷的工作载荷环境中,包括复杂的机械力载荷、压力载荷、声载荷和热载荷,这些载荷会导致结构以非线性方式响应。研究了随机压力载荷作用下高温薄壁结构动态响应计算方法,并构建了计算模型。首先讨论了温度对结构刚度的影响,分析表明屈曲前结构刚度随温度升高而降低,屈曲后结构刚度随温度升高而升高。在此基础上着重讨论了随机压力载荷作用下高温薄板跳变响应,对热载荷作用下的结构屈曲,以及在随机压力载荷作用下呈现出的复杂非线性动态响应特征进行了分析。     

高精度火箭橇试验轨道随机不平顺分析

对实测高精度火箭橇试验轨道随机不平顺功率谱密度(PSD)进行B样条插值,得到拟合用PSD平均曲线.对此曲线采用最小X方回归与粒子群优化算法,得到了指数函数形式的PSD函数参数值.基于PSD进行频率采样,利用Monte Carlo法模拟得到随机相位,然后利用Blackman-Turkey法模拟得到试验轨道空间域内的不平顺大小.分析与模拟结果表明:高精度火箭橇轨道随机不平顺具有低频、低幅值和低功率特性.随机不平顺对数PSD值随频率的增加而趋于稳定值.     

考虑桥塔风效应的斜拉桥时域抖振分析

大跨度桥梁频域及时域抖振分析中通常仅考虑主梁的脉动风效应.本文根据大跨度斜拉桥结构形式及振动型态的特点,结合自然风的相关特性,对大跨度斜拉桥三维脉动风场进行简化,从而基于谱解法同时模拟了主梁及桥塔的脉动风速场.基于模拟的随机风场对结构风荷载进行时域化,进而建立系统运动控制方程.由于自激力的存在,结构的运动控制方程为非线性方程,本文提出了一种迭代方法来考虑由自激力引起的运动方程的非线性.为考察桥塔脉动风速场的影响,分别进行了考虑桥塔风场和不考虑桥塔风场两种情况下桥梁抖振响应的分析,两种方法的分析结果表明,考虑桥塔风场将显著增大桥塔横桥向抖振响应.     

Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink

This paper draws attention to the issue of the vibration absorption of nonlinear mechanical system coupled to nonlinear energy sink(NES) under the impact of the narrow band stochastic excitation. Firstly, based on the complex-averaging method and frequency detuning methodology,response regimes of oscillators have been researched under the linear impact of coupling a nonlinear attachment with less relativistic mass and an external sinusoidal forcing, of which results turn out that the quasi-periodicity response regime of system which occurs when the external excitation amplitude exceeds the critical values will be the precondition of the targeted energy transfer.Secondly, basing on the path integration method, vibration suppression of NES has been researched when it is affected by a main oscillator with a narrow band stochastic force in the form of trigonometric functions, of which results show that response regimes are affected by the amplitude of stochastic excitation and the disturbance strength. Finally, all these conclusions have been approved by the numerical verification and coincided with the theoretical analysis; meanwhile, after the comparing analysis with the optimal linear absorber, it turns out that the NES which is affected by the narrow band stochastic force could also suppress the vibration of system with a better effect.     

冲击风作用下大跨屋盖多模态随机风致响应研究

雷暴冲击风是一种近地面短时产生的瞬态强风,它与传统的边界层风场特征具有明显的差别,冲击风将会引起屋盖的强烈振动,甚至发生破坏.本文根据混合随机模型,详细研究了冲击风风场的数值模拟方法.应用Wood竖直风剖面方程与Holmes经验模型模拟平均风场,使用稳态高斯随机过程模拟脉动风场,模拟的风场与实际的雷暴冲击风较为一致.结合多阶模态加速度法和等效风荷载原理,详细推导了大跨屋盖随机风致响应的计算方法.结合边界层风洞试验,比较冲击风产生的表面风压特性,计算得到屋盖冲击风致动力响应时程,并研究了冲击风作用下大跨屋盖荷载风效应系数和位移风效应系数的分布特点.研究结果可作为评估大跨屋盖冲击风致响应的一种参考.     

A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification

This paper proposes a novel model named as “imprecise stochastic process model” to handle the dynamic uncertainty with insufficient sample information in real-world problems. In the imprecise stochastic process model, the imprecise probabilistic model rather than a precise probability distribution function is employed to characterize the uncertainty at each time point for a time-variant parameter, which provides an effective tool for problems with limited experimental samples. The linear correlation between variables at different time points for imprecise stochastic processes is described by defining the auto-correlation coefficient function and the cross-correlation coefficient function. For the convenience of analysis, this paper gives the definition of the P-box-based imprecise stochastic process and categorizes it into two classes: parameterized and non-parameterized P-box-based imprecise stochastic processes. Besides, a time-variant reliability analysis approach is developed based on the P-box-based imprecise stochastic process model, through which the interval of dynamic reliability for a structure under uncertain dynamic excitations or time-variant factors can be obtained. Finally, the effectiveness of the proposed method is verified by investigating three numerical examples.     

Multi-function radar emitter identification based on stochastic syntax-directed translation schema

To cope with the problem of emitter identification caused by the radar words＇ uncertainty of measured multi-function radar emitters, this paper proposes a new identification method based on stochastic syntax-directed translation schema（SSDTS）. This method, which is deduced from the syntactic modeling of multi-function radars, considers the probabilities of radar phrases appearance in different radar modes as well as the probabilities of radar word errors occurrence in different radar phrases. It concludes that the proposed method can not only correct the defective radar words by using the stochastic translation schema, but also identify the real radar phrases and working modes of measured emitters concurrently. Furthermore, a number of simulations are presented to demonstrate the identification capability and adaptability of the SSDTS algorithm.The results show that even under the condition of the defective radar words distorted by noise,the proposed algorithm can infer the phrases, work modes and types of measured emitters correctly.     

进口总压随机脉动的数值模拟方法

为了能用数值计算方式模拟动态总压畸变对航空发动机稳定性的影响,首先要模拟出进口总压的随机脉动过程.根据进口总压随机脉动的正态分布特点及相关性特征,获得了带有指数自相关函数的动态总压畸变的随机过程,同时分析了积分时间常数、时间步长以及时间长度等参数对所生成的总压随机脉动过程的影响.结果表明,为了获得较好的模拟效果,时间步长应取得较小,时间长度应取得足够的长,而积分时间常数对模拟的可靠性则影响不大.      

Robust detection of small stochastic signals

We consider the problem of detecting a stochastic signal in white not-necessarily-Gaussian noise, using vector valued observations. The locally optimal detector is presented and its performance evaluated. The least-favorable signal spectrum and noise density (over specified classes) are found, and it is shown that the detector using these least-favorable assumptions is minimax robust. The class of spectra is that of any stochastic signal of specified power whose spectrum can be bounded from above and from below by two given positive functions. The class of densities is the ε-contamination model. We present examples of the performance achievable with the robust detector in one of these the spectral uncertainty class corresponds to the unknown Doppler shift of a radar return signal. It is demonstrated that the standard matched-filter's performance degradation with increasing Doppler shift can be avoided almost entirely through use of the robust processor     

正交多项式在不确定转子动态响应计算中的应用及对比分析

为研究航空发动机转子系统中的区间不确定性对系统动态响应的影响,提出利用正交多项式求解不确定转子响应的非嵌入式区间分析法,克服了传统概率方法需要参数先验概率分布的苛刻要求。用有限元法建立了悬臂转子的确定性运动方程,阐述了Chebyshev和Legendre两种正交多项式建立响应代理模型的原理和计算步骤。通过与Monte Carlo抽样对比,验证方法的可行性和精度。对照Monte Carlo方法500样本的计算结果,两种多项式区间法计算结果都具有较高精度,误差均小于1%,而计算时间则分别为Monte Carlo法的2.5%和5.4%,Chebyshev多项式方法具有更高的计算效率。分析了不同不确定参数在不同不确定水平下,系统的响应范围。研究表明,正交多项式区间分析法可高精度高效率地计算转子系统区间响应范围,不确定性对该转子系统动力特性影响很大,多源不确定性传播可引起转子系统大幅振动。      

Detailed magnetic structure and stochastic threshold

Non-linear evolution of reconnection is too slow to explain-by itself-fast phenomena such as internal disruptions in tokamaks or flares in the solar atmosphere. It has been proposed that the change in topology could lead to field line stochastization, and hence to highly increased transport. An important objection to this idea is that the increase of transport coefficients should smoothly follow the amplitude of the perturbation, while the observations show a catastrophic transition. We have shown 1) that the shape of the structures (and not only their size or amplitude) evolve during non-linear evolution 2) that the stochastic threshold can be strongly influenced by the detailed shape. Therefore, sharp transitions can appear during the evolution, due to the combination of these two effects. We will first consider an idealized situation, namely the two-waves problem in slab geometry, for which we will study the effect of the separatrix shape on the stochastic threshold. In the second part, we will present an application to the internal disruption in tokamaks, with anm=1 perturbation in a toroidal magnetic configuration. In the last part, we will discuss possible applications of the studies on shape effects to the behaviour of trapped particles in structures of the solar atmosphere.