Generating “idealised” impulse response functions to improve or repair single degree of freedom system measurements

A single degree of freedom (SDOF) system can be characterised using transient or continuous time signals and both should lead to the same frequency response function. As commonly defined, the equation of the displacement response of a SDOF system to impulse excitation alone is ambiguous leading to two possible interpretations: the impulse response (IR) and one corresponding to solely the free oscillation of the system (FR). These are analysed in detail for idealised and practical cases and it is found that the IR and FR yield two distinct acceleration spectra, and that only the phase distinguishes the normalised FR between displacement, velocity and acceleration alleviating the need to perform differentiation and integration to generate the response in other parameters. An unambiguous mathematical definition of the IR is suggested for the velocity response. Finally, it is shown that an idealised version of the IR can be artificially generated from the FR. This can be used to repair acceleration signals that have a truncated or distorted impulsive part, alleviate spectral windowing effects and generally allow cleaner response spectra. This is demonstrated experimentally.     

Improving the accuracy of the n-dB method for determining damping of non-lightly damped systems

Damping measurements using the spectral magnitude remain popular and are studied here for non-lightly damped systems using the variable bandwidth n-dB method, which is advantageous for non-lightly damped systems. The most commonly used estimator (based on normalised bandwidth) provides significant errors for non-lightly damped systems. An existing more accurate method (using the squares of the frequencies used in the former method) is exact for hysteretic damping, but still provides significant error for viscous damping. Improved estimators are developed in order to correct either exactly, or to insignificant errors, measurements taken with existing estimators. Neither further data nor the individual frequencies are required; the previously calculated damping values are corrected. The application of the improved estimators is dependent upon the existing estimator used and the damping type; however a strategy is suggested to reduce errors if the latter is unknown.     

一种基于遗传算法的混沌系统参数估计方法

通过构造一个适当的适应度函数,将混沌系统的参数估计问题转化为一个参数的寻优问题,然后利用遗传算法的全局优化搜索能力对其进行求解.以典型的Lorenz混沌系统为例进行了数值模拟.实际数值模拟表明,使用这种方法可以有效地对混沌系统的参数进行估计 关键词： 混沌系统 参数估计 遗传算法     

The effect of calibrated nonlocal constant on the modal parameters and stability of axially compressed CNTs

Nowadays investigating the vibration behavior of carbon nanotubes (CNTs) has drawn considerable attention due to the superior mechanical properties of the CNTs. One of the powerful theoretical methods to study the vibration behavior of CNTs is implementing the nonlocal theory. Most of studies on the vibration behavior of CNTs have assumed a fixed value for small scale parameter for all vibration modes, however, this value is mode-dependent. Therefore, in this paper, the small scale parameter is calibrated for a single-walled carbon nanotube (SWCNT) with respect to each vibration mode. For this propose, the governing equation of motion based on the nonlocal beam theory is extracted by applying the Hamilton's principle. Then, by using the power series method, an eigenvalue problem is defined to derive the calibrated value of small scale constant and nonlocal mode shapes of the CNT. By using the expansion theory, the equation of motion is discretized, and the effect of nonlocality on the modal parameters and stability of the CNT under compressive force is investigated. Finally, the possibility of estimating nonlocal parameter based on simulated frequency domain response of the system by using modal analysis methods is studied. The results show that the calibration of small scale constant is important and the critical axial force is highly sensitive to this value.     

Acoustic wireless communication based on parameter modulation and complex Lorenz chaotic systems with complex parameters and parametric attractors

As the competition for marine resources is increasingly fierce, the security of underwater acoustic communication has attracted a great deal of attention. The information and location of the communicating platform can be leaked during the traditional underwater acoustic communication technology. According to the unique advantages of chaos communication, we put forward a novel communication scheme using complex parameter modulation and the complex Lorenz system. Firstly, we design a feedback controller and parameter update laws in a complex-variable form with rigorous mathematical proofs (while many previous references on the real-variable form were only special cases in which the imaginary part was zero), which can be realized in practical engineering; then we design a new communication scheme employing parameter modulation. The main parameter spaces of the complex Lorenz system are discussed, then they are adopted in our communication scheme. We also find that there exist parametric attractors in the complex Lorenz system. We make numerical simulations in two channels for digital signals and the simulations verify our conclusions.     

Adaptive lag synchronization and parameter identification of fractional order chaotic systems

This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic Lü system is used to illustrate the validity of this theoretic method.     

基于强耦合Duffing振子的微弱脉冲信号检测与参数估计

耦合Duffing振子在检测强噪声中的微弱脉冲信号时具有可检测信噪比低等优点,但目前检测模型还存在系统性能与初始状态有关、只能工作在倍周期分岔状态等缺陷.为此本文构建了一种能克服上述缺点的新的微弱脉冲信号检测模型,通过对两个Duffing振子同时施加较大的恢复力和阻尼力耦合,可使振子间产生广义的"阱内失同步"现象,基于这种现象可实现微弱脉冲信号的检测与恢复.以信噪比改善和波形相似度为衡量指标,研究了周期策动力幅值与周期、耦合系数、计算步长、阻尼系数等参量对模型信号检测与波形恢复效果的影响.对方波、双指数脉冲和高斯导数脉冲进行检测和恢复的实验结果表明,本文所构建的模型能够在较低信噪比条件下有效地检测并恢复出高斯白噪声背景中的微弱脉冲信号,进而改善了现有的Duffing振子对非周期脉冲信号的检测能力并扩展了其应用领域.     

一种新的参数估计方法及其在混沌信号盲分离中的应用

为了有效地估计非线性映射中的参数,本文采用一种容积准则近似该映射的加权积分函数. 基于由状态空间模型建模的参数,提出了一种新的参数估计方法. 混沌信号的盲分离是一种具有挑战性的参数估计问题.将新的参数估计方法应用在该问题上, 实现混沌信号的有效重构.仿真结果表明该算法具有较快的收敛速度和较高的数值精度, 并能有效地分离原始混沌信号.     

General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rssler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.     

基于量子并行粒子群优化算法的分数阶混沌系统参数估计

分数阶混沌系统参数估计的本质是多维参数优化问题, 其对于实现分数阶混沌控制与同步至关重要. 提出一种基于量子并行特性的粒子群优化新算法, 用于解决分数阶混沌的系统参数估计问题. 利用量子计算的并行特性, 设计出了一种新的量子编码, 使每代运算的可计算次数呈指数增加. 在此基础上, 构建了由量子当前旋转角、个体最优旋转角和全局最优旋转角共同组成的粒子演化方程, 以约束粒子在量子空间中的运动行为, 使算法的搜索能力得到了较大提高. 以分数阶Lorenz混沌系统和分数阶Chen混沌系统的参数估计为例, 进行了未知参数估计的数值仿真, 结果显示本算法具有良好的有效性、鲁棒性和通用性.     

基于参数切换算法的混沌系统吸引子近似及其电路设计

基于参数切换算法和离散混沌系统, 设计一种新的混沌系统参数切换算法, 给出了两算法的原理. 采用混沌吸引子相图观测法, 研究了不同算法下统一混沌系统和Rössler混沌系统参数切换结果, 最后引入方波发生器, 设计了Rössler混沌系统参数切换电路. 结果表明, 采用参数切换算法可以近似出指定参数下的系统, 其吸引子与该参数下吸引子一致; 基于离散系统的参数切换结果更为复杂, 当离散序列分布均匀时, 只可近似得到指定参数下的系统; 相比传统切换混沌电路, 参数切换电路不用修改原有系统电路结构, 设计更为简单, 输出结果受方波频率影响, 通过加入合适频率的方波发生器, 数值仿真与电路仿真结果一致.     

基于稀疏分解的大功率半导体激光器1/f噪声参数估计的新方法

本文结合1/f噪声信号功率谱随频率成反比变化的关系, 以及稀疏分解可以根据信号灵活构造原子库的特点, 提出一种基于稀疏分解估计大功率半导体激光器1/f噪声的新方法, 构造了具备1/f噪声特点的过完备库. 在该过完备库中通过Matching Pursuit(MP)算法完成了白噪声与1/f噪声混叠信号的稀疏分解. 实验结果显示:该方法估计出淹没在白噪声环境中1/f噪声的γ 参数, 与频谱分析仪的测量结果有较好的一致性, 通过对比不同的过完备库证明了所构造的过完备库的优越性.     

基于MATLAB与LabVIEW的 Mie散射参数分析系统

针对激光散射法测量0.1 m~10 m微小球形颗粒过程中,Mie散射理论各参数的分析、计算、最优化选取比较复杂和繁琐,通过收敛速度、折射率和尺度参数测量范围、叠加次数的比较,采用球形粒子Mie散射参量的MATLAB改进算法, 结合MATLAB较强的计算能力和LabVIEW良好的图形化界面,进行LabVIEW和MATLAB混合编程。设计了Mie散射理论参数分析系统,系统实现散射系数的计算,并分别对散射系数与颗粒直径关系曲线、散射强度分布曲线、入射光波长与散射光强关系曲线、颗粒直径与散射光强关系曲线、入射光偏振角与散射光强关系曲线进行分析。通过实验结果和结论对比验证系统可行,且散射系数、消光系数和散射光强的计算结果可精确到小数点后17位,从而达到减少大量计算和编程工作的目的。     

Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent

We present a novel method for the parameter oriented analysis of mutual correlation between independent time series or between equivalent structures such as ordered data sets. The proposed method is based on the sliding window technique, defines a new type of correlation measure and can be applied to time series from all domains of science and technology, experimental or simulated. A specific parameter that can characterize the time series is computed for each window and a cross correlation analysis is carried out on the set of values obtained for the time series under investigation. We apply this method to the study of some currency daily exchange rates from the point of view of the Hurst exponent and the intermittency parameter. Interesting correlation relationships are revealed and a tentative crisis prediction is presented.