Analysis of nystagmus response to pseudorandom velocity input

This report describes a method to analyse the vestibular system when subjected to a pseudorandom angular velocity input. A sum of sinusoids (pseudorandom) input lends itself to analysis by linear frequency methods. Resultant horizontal ocular movements were digitized, filtered and transformed into the frequency domain. Programs were developed and evaluated to obtain the auto spectra of input stimulus and resultant ocular response, cross spectra, the estimated vestibular-ocular system transfer function gain and phase, and coherence function between stimulus and response functions.     

多自由度粘弹性非线性随机系统的瞬态响应

研究了高斯白噪声激励下多自由度粘弹性非线性系统的瞬态响应.首先,通过将粘弹性项对系统的作用近似地简化为对原系统阻尼部分以及刚度部分的修正,得到近似的不具粘弹性项的等效非线性随机系统.然后,应用基于广义谐和函数的随机平均法,导出关于幅值瞬态概率密度的平均Fokker-Planck-Kolmogorov方程.该方程的解可通过多重级数式表示,基函数为幅值相关正交函数,系数为时间函数.应用Galerkin方法,关于时间的系数可由一阶线性微分方程组解得,从而得出幅值响应的瞬态概率密度、状态空间概率密度及幅值统计矩的半解析表达式.最后,以耦合的二自由度Duffing-van der Pol振子系统为例,通过与原系统数值模拟结果的比较分析验证了所提出的半解析方法的有效性,并讨论了粘弹性对系统响应的影响.     

A probability method for prediction on High Cycle Fatigue of blades caused by aerodynamic loads

A probability method for prediction on High Cycle Fatigue (HCF) of blades caused by aerodynamic loads (PHBA) is erected and two approaches are adopted: improving the numerical method to obtain the dynamical responses of blades caused by aerodynamic loads and introducing probability theory into predicting HCF. The basic governing equations of fluid domain, solid domain and fluid–solid interface are given for flow-blade interaction system. Furthermore a numerical method named bidirectional sequential method is illuminated, and the corresponding physical process of vibration from unsteady state to steady state is described. The dynamical response can be obtained by this time domain method conveniently by the use of commercial softwares. Then PHBA is put forward based on vibration stress according to the probabilistic accumulative damage model. Finally an engineering sample is discussed to illuminate PHBA flow clearly. PHBA is performed on two types of second-stage stators to evaluate the operation security, thus the probabilistic accumulative damages altering with operation time are calculated, and the operational reliabilities are also obtained. The results can describe the possibility of HCF intuitively and quantitatively, which shows PHBA is very helpful in the HCF prediction and failure analysis.     

Impulse response function identification of linear mechanical systems based on Kautz basis expansion with multiple poles

The impulse response function (IRF) identification of linear mechanical systems is important in many engineering applications. This paper proposes a novel IRF identification method of linear systems based on Kautz basis expansion with multiple poles. In order to reduce the parameters to be identified, the IRF is expanded in terms of orthogonal Kautz functions with multiple poles, and the poles in Kautz functions should be optimised. This allows the identification of IRF for linear mechanical systems operated under more than one mode, such as systems under the white noise excitation or the swept frequency excitation with a wide range of frequency, and can improve the identification accuracy. Furthermore, based on the backpropagation through-time technique and the expectation maximisation algorithm, a pole optimisation algorithm is presented in this paper. The simulation studies verify the effectiveness of the proposed IRF identification method.     

螺旋槽型干气密封系统轴向工作模态研究

干气密封系统的轴向动态特性会影响密封气膜的密封特性,从而影响机械密封的稳定性和可靠性,采用高灵敏加速度传感器和数据采集装置,设计螺旋槽型干气密封装置轴向振动测试试验,采用半互功率谱密度函数实现对干气密封装置的工作状态模态分析,分别利用平均相位偏差、模态相位线性度、模态复杂性和模态指示函数4个数学指标对模态参数辨识结果进行验证,结果表明:半互功率谱密度函数的模态分析验证结果较好,适用于干气密封组合型装置的环境激励工作状态模态分析。     

随机路面激励下整车NVH有限元分析

针对应用刚体动力学方法不能得到驾驶员可以直接感知的振动加速度的缺陷,提出应用整车柔性体模型进行汽车随机路面平顺性分析的方法.对一种典型路面不平度数据进行处理并将得到的功率谱密度(Power Spectral Density,PSD)作为激励,建立整车有限元模型,通过试验模态验证该模型后进行传递函数分析;根据所得的激励和传递函数的结果计算得出汽车方向盘处的速度响应.该速度响应与随机路面平顺性试验一致性较好。     

An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals

The reliability analysis approach based on combined probability and evidence theory is studied in this paper to address the reliability analysis problem involving both aleatory uncertainties and epistemic uncertainties with flexible intervals (the interval bounds are either fixed or variable as functions of other independent variables). In the standard mathematical formulation of reliability analysis under mixed uncertainties with combined probability and evidence theory, the key is to calculate the failure probability of the upper and lower limits of the system response function as the epistemic uncertainties vary in each focal element. Based on measure theory, in this paper it is proved that the aforementioned upper and lower limits of the system response function are measurable under certain circumstances (the system response function is continuous and the flexible interval bounds satisfy certain conditions), which accordingly can be treated as random variables. Thus the reliability analysis of the system response under mixed uncertainties can be directly treated as probability calculation problems and solved by existing well-developed and efficient probabilistic methods. In this paper the popular probabilistic reliability analysis method FORM (First Order Reliability Method) is taken as an example to illustrate how to extend it to solve the reliability analysis problem in the mixed uncertainty situation. The efficacy of the proposed method is demonstrated with two numerical examples and one practical satellite conceptual design problem.     

A bootstrap test for the comparison of nonlinear time series

The difference between the regression functions of two stationary conditional heteroskedastic autoregressive time series is tested. The functions can be equal, or shifted, under the null hypothesis. Local linear estimation of the regression function results in observable residuals. Bootstrap residuals lead to a marked empirical process as test statistic and a Kolmogorov-Smirnov version is applied. The simulation study for linear, exponential or trigonometric regression functions with homoskedastic or heteroskedastic errors finds the rejection probability under the null hypothesis to be near the level. Comparing series with different combinations of linear, exponential and trigonometric functions, the rejection probability under the alternative yields mixed results.     

含指数积分型阻尼和周期激励系统的稳态随机响应分析

运用基于短时高斯逼近的广义胞映射方法,研究了含指数积分型非粘性阻尼和周期激励系统在高斯白噪声作用下的稳态响应.首先介绍了方法的实施过程,并推导了系统的矩方程.然后给出了系统的稳态概率密度函数,分析了阻尼系数和松弛参数对稳态响应的影响,并通过直接Monte Carlo模拟的结果验证了广义胞映射方法的有效性.     

Integrating subset simulation with probabilistic re-analysis to estimate reliability of dynamic systems

It is often expensive to estimate the failure probability of highly reliable systems by Monte Carlo simulation. Subset Simulation breaks the original problem of estimating a small probability into the estimation of a sequence of large conditional probabilities, which is more efficient. The conditional probabilities are estimated by Markov Chain simulation. Uncertainty in the power spectral density of the excitation makes it necessary to re-evaluate the reliability for many power spectral densities that are consistent with the evidence about the system excitation. Subset Simulation is more efficient than Monte Carlo simulation, but still requires a new simulation for each admissible power spectral density. This paper presents an efficient method to re-evaluate the reliability of a dynamic system under stationary Gaussian stochastic excitation for different load spectra. We accomplish that by re-weighting the results of a single Subset Simulation. This method is applicable to both linear and nonlinear systems provided that all of the spectra contain the same amount of energy. The authors are currently working on an extension of the method to nonlinear systems, even when the sampling and true power spectral density functions contain different amounts of energy.     

用于统计测试概率分布生成的自动搜索方法

提出一种基于自动搜索的概率分布生成方法,设计对概率分布的表示形式与评估函数,同时结合模拟退火算法设计基于马尔可夫模型的自动搜索过程。实验结果表明,该方法能够有效地提高自动搜索的准确性,在一定时间内成功找到接近最优的概率分布,生成高效的测试数据,同时达到降低统计测试成本的目的。     

Robust PID‐PSD Controller Design: BMI Approach

A new robust proportional‐integral‐derivative (PID)–proportional‐sum‐derivative (PSD) controller design method based on linear (bilinear) matrix inequalities (LMI, BMI) is proposed for uncertain affine linear system. The design procedure guarantees the parameter dependent quadratic stability, and guaranteed cost control with a new quadratic cost function (LQRS) including the derivative term for the state vector as a tool to influence the overshoot and response rate. The second approach to the PSD controller design procedure is based on a Lyapunov function with a special term corresponding to the time‐delay part of the control algorithm. The results obtained are illustrated on three examples to show the robust PID, PSD control design procedure and the influence of the choice of matrix S in the extended cost function.     

Response CDF sensitivity and its solution based on sparse grid integration

The sensitivity of the cumulative distribution function (CDF) of the response with respect to the input parameters is studied in this work, to quantify how the model output is affected by input uncertainty. To solve the response CDF sensitivity more efficiently, a novel method based on the sparse grid integration (SGI) is proposed. The response CDF sensitivity is transformed into expressions involving probability moments, which can be efficiently estimated by the SGI technique. Once the response CDF sensitivity at one percentile level of the response is obtained, the sensitivity values at any other percentile level can be immediately obtained with no further call to the performance function. The proposed method finds a good balance between the computational burden and accuracy, and is applicable for engineering problems involving implicit performance functions. The characteristics and effectiveness of the proposed method are demonstrated by several engineering examples. Discussions on these examples have also validated the significance of the response CDF sensitivity for the purpose of variable screening and ranking.     

Model‐Driven and Risk‐Based Performance Analysis of Industrial Emergency Plans

This paper presents a methodology for the assessment of the performance of industrial hazardous materials emergency plans. This approach is based on a structuro‐functional model of the emergency plan, which highlights the plan's functions, resources, support services and interactions. A resource taxonomy is used to manage the complexity of the emergency response system. The model can be used both as a planning guide and for the analysis of the performance of the emergency response system, based on the risk assessment of the system. The failure probability is estimated through the plan's functions and resources fault trees. The failure severity of each function is determined by using the facility's hazard study. The failure criticality of each function is hence obtained.     

A novel evidence-based fuzzy reliability analysis method for structures

Epistemic uncertainties always exist in engineering structures due to the lack of knowledge or information, which can be mathematically described by either fuzzy-set theory or evidence theory (ET) In this work, the authors present a novel uncertainty model, namely evidence-based fuzzy model, in which the fuzzy sets and ET are combined to represent the epistemic uncertainty. A novel method for combining multiple membership functions and a corresponding reliability analysis method is also developed. In the combination method, the combined fuzzy-set representations are approximated by the enveloping lines of the multiple membership functions (smoothed by neglecting the valleys in the membership functions curves) and the Murphy’s average combination rule is applied to compute the basic probability assignment for focal elements. Then, the combined membership function is transformed to the equivalent probability density function by means of a normalizing factor. Finally, the Markov Chain Monte Carlo (MCMC) subset simulation method is used to solve reliability by introducing intermediate failure events. A numerical example and two engineering examples are provided to demonstrate the effectiveness of the proposed method.     

Monte Carlo solution of structural dynamics

The recent advent of high speed digital computers has made it not only possible but also highly practical to apply the Monte Carlo techniques to a large variety of engineering problems. In this paper a technique of digital simulation of multivariate and/or multidimensional Gaussian random processes (homogeneous or nonhomogeneous) which can represent physical processes germane to structural engineering is presented. The paper also describes a method of digital simulation of envelope functions. Such simulations are accomplished in terms of a sum of cosine functions with random phase angles and used as the basic tool in a general Monte Carlo method of solution of a wide class of problems in structural engineering. Most important problems for which the method is found extremely useful includes (a) numerical analysis of dynamic response of nonlinear structures to random excitations, (b) time domain analysis of linear structures under random excitations performed for the purpose of obtaining a kind of information, such as first excursion probability and time history of a sample function, that is not obtainable from the standard frequency domain analysis, (c) numerical solution of structural problems involving randomly nonhomogeneous material property such as wave propagation through random medium, and (d) dynamic analysis of extremely complex systems such as those involving structure-fluid interaction. Numerical examples of some of these problems are presented.     

Finite difference analysis of plate response to random loads

The application of the finite difference method to analyse the response of plates subjected to stationary random loading is presented. The discrete forced dynamical system generated by the finite difference approximations is analysed by a generalised harmonic analysis. The power spectral density (PSD) for displacement at each node is calculated directly for particular frequencies and subsequently these PSDs are integrated numerically over the frequency range to yield the mean square response. Both viscous and structural damping have been considered. For illustrative purposes the random excitation is taken to be clipped white noise with uniform spatial correlation. To validate the numerical procedure, further verification was obtained by comparing the numerical results with an analytic and with another numerical solution.     

可靠性工程原理在电子系统中的应用

可靠性是部件、元件产品或系统的完整性的最佳量度。可靠性是元件产品系统在规定的环境下，规定的时间内．规定的条件下无故障地完成其规定功能的概率。本文以数据采集电子系统为例．结合可靠性工程原理、方法，提供了电子系统可靠性评估预测和提高可靠性的设计方法。     

具有可控与不可控因素系统的可靠性维持方法

为了研究系统或元件可靠性维持方法,提出一种基于SFT的可靠性维持方法。在SFT框架下提出了可控与不可控因素的概念。目前SFT中的不可控因素指时间,其余为可控因素。给出了分析并制定系统或元件可靠性维持方法的步骤。分析表明在SFT内必须设定故障概率才能实施该方法。列举了一例进行分析,考虑的不可控因素为时间t,可控因素为温度c。分别将故障概率设置为10%、20%、30%、40%,50%,求出了元件更换周期,及其温度控制曲线和函数。与已有文献相比所得元件更换周期更为经济,方法更精确且可操作增强性。