Dynamic Stability Analysis of Linear Time-varying Systems via an Extended Modal Identification Approach

The problem of linear time-varying（LTV） system modal analysis is considered based on time-dependent state space representations, as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the ＂frozen-time＂ assumption are not able to determine the dynamic stability of LTV systems. Time-dependent state space representations of LTV systems are first introduced, and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation. The time-varying modes of LTV systems are extended in terms of uniqueness, and are further interpreted to determine the system＇s stability. An extended modal identification is proposed to estimate the time-varying modes, consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition. The proposed approach is numerically validated by three numerical cases, and is experimentally validated by a coupled moving-mass simply supported beam exper- imental case. The proposed approach is capable of accurately estimating the time-varying modes, and provides anew way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.

ELAPSED TIME OF PERIODIC MOTION WITH NEGATIVE DAMPING

An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows the result has a good approximation and is easy to calculate.

A Measure for Assessing Functions of Time-Varying Effects in Survival Analysis

A standard approach for analyses of survival data is the Cox proportional hazards model. It assumes that covariate effects are constant over time, i.e. that the hazards are proportional. With longer follow-up times, though, the effect of a variable often gets weaker and the proportional hazards (PH) assumption is violated. In the last years, several approaches have been proposed to detect and model such time-varying effects. However, comparison and evaluation of the various approaches is difficult. A suitable measure is needed that quantifies the difference between time-varying effects and enables judgement about which method is best, i.e. which estimate is closest to the true effect. In this paper we adapt a measure proposed for the area between smoothed curves of exposure to time-varying effects. This measure is based on the weighted area between curves of time-varying effects relative to the area under a reference function that represents the true effect. We introduce several weighting schemes and demonstrate the application and performance of this new measure in a real-life data set and a simulation study.

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

NUMERICAL ANALYSIS AND EXPERI-MENT OF UNSTEADY THERMAL FIELD OF ROTOR PLATE FOR EDDY CURRENT RETARDER

The physical model based on heat transfer theory and virtual boundary method for analyzing unsteady thermal field of rotor plate for eddy current retarder used in automobile is established and boundary conditions are also defined. The finite element governing equation is derived by Galerkin method. The time differential item is discrete based on Galerkin format that is stable at any condition. And a new style of varying time step method is used in iteration process. The thermal field on the rotor plate at the radial and axle directions is analyzed and varying temperature at appointed points on two side-surfaces is measured. The testing and analytical data are uniform approximately. Finite element method can be used for estimating thermal field of the rotor plate at initial design stage of eddy current retarder.

Adaptive Control of MIMO Mechanical Systems with Unknown Actuator Nonlinearities Based on the Nussbaum Gain Approach

This paper investigates MIMO mechanical systems with unknown actuator nonlinearities. A novel Nussbaum analysis tool for MIMO systems is established such that unknown time-varying control coefficients are tackled. In contrast to existing literatures on continuous-time systems, the newly-developed Nussbaum tool focuses on extending the traditional Nussbaum result from one dimensional case to the multiple one. Specifically, not only the multiple unknown input coefficients are extended to the time-varying, but also the limitation of the prior knowledge of coefficients' upper and lower bounds is removed. Furthermore, an adaptive robust controller associated with the proposed tool is presented. The asymptotic tracking of MIMO mechanical systems is guaranteed with the help of the Lyapunov Theorem. Finally, a simulation example is provided to examine the validity of the proposed scheme. © 2014 Chinese Association of Automation.

New algorithm applied to vibration equations of time-varying system

Vibration equations of time-varying system are transformed to the form which is suitable to precise integration algorithm.Precision analysis and computation efficiency of new algorithm are implemented.The following conclusions can be got.Choosing matrixes M,G and K is certainly flexible.We can place left side of nonlinear terms of vibration equations of time-varying system into right side of equations in precise integration algorithms.The key of transformation from vibration equations of time-varying system to first order differential equations is to form matrix H,which should be assured to be nonsingular.With suitable disposal,precision and computation efficiency of precise integration algorithms are greatly larger than those of general methods.

ICA Based Identification of Time-Varying Linear Causal Model

Recently, several approaches have been proposed to discover the causality of the time-independent or fixed causal model. However, in many realistic applications, especially in economics and neuroscience, causality among variables might be time-varying. A time-varying linear causal model with non-Gaussian noise is considered and the estimation of the causal model from observational data is focused. Firstly, an independent component analysis(ICA) based two stage method is proposed to estimate the time-varying causal coefficients. It shows that, under appropriate assumptions, the time varying coefficients in the proposed model can be estimated by the proposed approach, and results of experiment on artificial data show the effectiveness of the proposed approach. And then, the granger causality test is used to ascertain the causal direction among the variables. Finally, the new approach is applied to the real stock data to identify the causality among three stock indices and the result is consistent with common sense.

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.

Internal Temperature of Skin when Surface Temperature Is Controlled with an Electromagnetic Beam

We study the thermal effect on skin exposed to an electromagnetic beam of time-dependent power. We consider two types of beam power time schedules. In the controlled temperature exposure, the skin surface temperature is increased quickly to a prescribed level using a high beam power;then the surface temperature is maintained at the prescribed level by adjusting the beam power adaptively. In the constant power exposure, the applied beam power is relatively low and stays unchanged over the time. We start both types of exposures at the same time and compare their internal temperatures of skin when they have the same surface temperature. In a non-dimensionalized formulation, we show that at the moment when both exposure types reach the same prescribed surface temperature level, the controlled temperature exposure has a higher internal temperature at all depths. This conclusion is mathematically rigorous and is independent of skin material properties.

Dynamics of a Dual Power-split Transmission Based on Loaded Tooth Contact Analysis

In order to implement the dynamic characteristic of a dual power-split transmission, a dynamic me- chanics model is built. Firstly, according to the method of theoretical analysis of the tooth contact analysis （TCA） and loaded tooth contact analysis （LTCA）, the actual meshing process of each gear pairs is simulated, and the time-varying mesh stiffness excitations are obtained, which can improve the numerical precision. Second- ly, by using the lumped mass method, the bending-torsional coupling three dimensional dynamic model of the dual power-split transmission is established, and the identical dimensionless equations are deduced by elimina- ting the effect of rigid displacement and the method of dimensional normalization. Finally, by the method of the fourth order Runge-Kutta algorithm with variable step lengths, the responses of this system in a frequency domain and time domain are obtained, and the dynamic load change characteristics of each gear pairs are analyzed. The results show that the establishment, solution and analysis of the system dynamics model could provide a basis for the dynamic design, and have an important significance for the dynamic efficiency analysis and dynamic perform- ance optimization design of the dual power-split transmission.

OFDM-UWB系统在时变信道中的性能分析

根据超宽带信道呈现频率选择性和时间选择性衰落之特征,分析正交频分复用超宽带(OFDM-UWB)系统的性能,并在基于散射体移动的时变多径信道模型上进行仿真。研究结果表明,当信号信噪比较小时散射体移动不会对系统性能产生太大的影响,同时缓慢移动的散射体对系统性能的影响也不大。因此,在大部分的室内环境下散射体移动对系统性能产生的影响可以忽略。

用EOF分析方法研究强震前中国大陆水平位移场时空分布特征

利用大气科学常用的经验正交函数(EOF)分解方法,对中国大陆连续观测的基准站的水平位移每周解时间序列进行分析。首先对时间序列中不连续的数据进行内插处理,并通过线性拟合从时间序列中去掉长期滑动速率的影响。结合震例研究强震前水平位移场在NS向和EW向的时间和空间的分布特征。

高速场景下基于OFDM的信道估计算法

针对正交频分复用系统在高速场景下,存在难以准确获取信道状态信息和载波间干扰增强的问题,提出一种基于基扩展模型的时变信道估计算法。采用基扩展模型拟合时变信道,将信道参数的估计转化为基函数系数的估计;利用正交频分复用系统各符号在传输过程中的相关性建立状态、测量方程,通过卡尔曼滤波技术追踪时变信道,同时结合组导频图样对载波间干扰进行抑制。仿真分析显示,在不同速度条件的时变环境下,所提算法在信噪比性能上有明显优势,能有效提升估计精度,保证移动端在高速运行下的通信质量。

Adaptive Robust Control for a Class of Uncertain MIMO Non-affine Nonlinear Systems

In this paper, the adaptive robust tracking control scheme is proposed for a class of multi-input and multi-output (MIMO) non-affine systems with uncertain structure and parameters, unknown control direction and unknown external disturbance based on backstepping technique. The MIMO non-affine system is first transformed into a time-varying system with strict feedback structure using the mean value theorem, and then the bounded time-varying parameters are estimated by adaptive algorithms with projection. To handle the possible 'controller singularity' problem caused by unknown control direction, a Nussbaum function is employed, and the dynamic surface control (DSC) method is applied to solve the problem of 'explosion of complexity' in backstepping control. It is proved that the proposed control scheme can guarantee that all signals of the closed-loop system are bounded through Lyapunov stability theorem and decoupled backstepping method. Simulation results are presented to illustrate the effectiveness of the proposed control scheme. © 2014 Chinese Association of Automation.

基于返回散射探测的电离层MOF时变特性统计分析

电离层最高可观测频率(MOF)是电离层的一个重要的特征参数,它表征了电离层的实时状态信息。文中基于新乡市的返回散射探测系统,对2014—2016年采集的数据进行预处理分析,获得电离层F层模式对应的MOF在24 h内的月中值分布,讨论分析了MOF月中值参数的分布特征,并与适应于中国区域的亚大模型对应的结果进行对比。结果表明,在相同的群距离下,常规探测下的电离层MOF值在不同时刻下的分布趋势与理论结果一致,日出时刻MOF会逐渐增加,白天时刻MOF相对稳定,日落时刻MOF值逐渐降低,夜晚MOF值持续降低,凌晨时刻到达最低点,实测值与理论结果相差范围为0.8 MHz^5.4 MHz;电离层突发E层发生时,1000 km群距离对应的MOF值达到最大,主要是因为突发E层产生了遮蔽,通信距离受限所致。

Multi-agent consensus with time-varying delays and switching topologies

The consensus problems of multi-agents with time-varying delays and switching topologies are studied. First, assume that an agent receives state information from its neighbors with fixed communication delays and processes its own state information with time-varying self-delay respectively. The state time-delay feedback is introduced into the existing consensus protocol to begenerate an improved protocol. Then a sufficient condition is derived which can make the system with time-varying self-delays achieve the consensus. On this basis, a specific form of consensus equilibrium influenced by the initial states of agents, time-delays and state feedback intensity is figured out. In addition, the multi-agent consensus is considered with time-varying topologies. Finally, simulations are presented to il ustrate the validity of theoretical results.

考虑内、外圈复合故障的角接触球轴承振动特性研究

为描述考虑内、外圈复合故障角接触球轴承的振动特性,建立了角接触球轴承内、外圈复合故障时变位移激励模型;基于非线性Hertz接触理论,建立了角接触球轴承时变刚度模型;提出了考虑内、外圈复合故障的角接触球轴承动力学计算方法,研究了不同参数和工况条件下复合故障轴承的振动响应规律。研究结果表明:随着故障尺寸和轴承载荷的增大,复合故障轴承的振动特征频率不变,但其幅值增大;随着轴承转速的增大,复合故障轴承的振动特征频率及其幅值均增大;故障位置的变化将对复合故障轴承的振动特征产生很大影响,故障处越接近承载区,轴承的负载越大,振动特征越明显。

考虑材料时变性的服役中小跨径桥梁横向地震响应分析

构件材料性能会随服役时间的增加而退化,并导致桥梁结构抗震性能存在时变性。为探讨不同服役期下中小跨径桥梁抗震性能变化规律,以3跨预应力混凝土连续桥梁为例,通过分析材料力学性能指标时变性,量化不同服役期构件力学分析模型参数,并考虑桥墩、挡块及支座等构件力学性能退化,采用OpenSees软件建立桥梁有限元分析模型。基于非线性时程分析结果,揭示服役中小跨径桥梁横桥向地震响应时变性。研究结果表明,随着服役时间的增加,材料力学性能发生退化,使中小跨径桥梁各构件抗震能力下降;相同水平地震作用下,中小跨径桥梁主梁及挡块位移响应随服役时间的增加而降低,而桥墩损伤程度加剧,构件震害程度与不考虑构件力学性能时变性时相差较大,其中板式橡胶支座刚度及摩擦系数时变性是关键。因此,在服役中小跨径桥梁抗震分析中,有必要同时考虑桥墩、挡块及支座力学性能退化。

考虑氯离子侵蚀的深层隧道地震易损性分析

氯离子侵蚀对隧道的抗震性能产生不利影响,研究隧道在侵蚀环境下的地震易损性对全寿命周期的抗震评估至关重要.为了量化分析隧道长期在氯离子侵蚀作用下抗震性能的退化趋势,基于地震易损性理论,结合考虑氯离子侵蚀影响的混凝土和钢筋强度时变模型,分别选取峰值地面加速度和隧道直径变形率作为地震动强度指标和结构损伤指标,通过采用增量动力分析(incremental dynamic analysis,IDA)方法进行时程分析,深入探讨了深层隧道的地震易损性,得到了不同服役时间及不同损伤状态下的地震易损性曲线.结果表明:在相同的服役时间和地震动强度下,轻微损伤的发生概率最高,其次是中等和严重损伤;在相同的损伤状态和地震动强度下,随着服役时间的延长,氯离子侵蚀导致隧道抗震性能下降,损伤概率上升;在轻微损伤状态下,当峰值地面加速度为0.30g且服役达100 a时,损伤概率是服役初期的2.39倍.研究结果可为深层隧道的抗震设计提供科学依据.