Modal analysis by free vibration response only for discrete and continuous systems

This work aims to develop the algorithm for modal analysis by free vibration response only (MAFVRO), in particular for the general or non-proportional viscous damping system model. If the structural displacement or acceleration response due to free vibration can be measured, the system response matrices, including the displacement, velocity and acceleration, can be obtained through numerical differential or integration methods. These response matrices can then be applied to the developed MAFVRO method to determine the structural modal parameters. The numerical differential and integration methods are introduced and adopted to establish the modal parameter prediction program for the non-proportional damping model of MAFVRO. This work also shows the applications of MAFVRO to the multiple degree-of-freedom (mdof) systems and the cantilever beam, respectively. Both the discrete and continuous systems are demonstrated for the feasibility of the MAFVRO algorithm. The developed method uses the free vibration output response only and can obtain the structural modal parameters successfully.     

Partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback

A new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper. Firstly, a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged. Secondly, based on this condition, an algorithm for determining the required control gain matrices of acceleration and displacement feedback, which assign the desired eigenstructure, is developed. This algorithm is easy to implement, and works directly on the second-order system model. More importantly, the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices. Finally, some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm.     

A sensitivity-based structural damage identification method with unknown input excitation using transmissibility concept

Unknown input excitation and local damages universally coexist in a practical situation. Therefore, in this paper a structural damage identification method based on the transmissibility concept in state space domain is proposed without the need for input measurements. On the basis of the transformation matrix which is computed using the system Markov parameters in state space, the relationship between two different sets of acceleration response measurements can be formulated under the same input excitation. A sensitivity-based model updating approach is applied to identify the local damages by minimizing the difference between the measured response and the reconstructed response. The sensitivity of the dynamic acceleration response with respect to the elemental stiffness factors is derived analytically in the state space domain, which accelerates the process of damage identification. A numerical cantilever beam is employed to validate that the variation of structural parameters induced by the local damages can be accurately and effectively identified without the input excitation information by the proposed method even with measurement noise considered. A laboratory test is further carried out to verify the proposed structural damage identification method based on the response reconstruction technique.     

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T-S fuzzy system.A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique.Then,the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established.Based on the discrete-time T-S fuzzy system,it proves that the chaos in the discretetime T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem.Finally,the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.     

车载状态下光电经纬仪的减振防护研究

针对光电经纬仪等高准确度仪器设备在运输过程中，对车载情况下产生的冲击和振动提出的具体要求，采用一套基于金属钢丝绳减震器的减振系统及加固装置对其进行抗振动防护．分析了车载情况下该减振系统的数学模型，并以某型号经纬仪模型为例，将其放置于满载质量15吨的某型号越野汽车中，在砂石路况下以30km／h的车速进行跑车试验，测得其加速度振动响应小于0．5g，冲击响应小于2．8g．     

Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering

This study presents a novel time series analysis methodology to detect, locate, and estimate the extent of the structural changes (e.g. damage). In this methodology, ARX models (Auto-Regressive models with eXogenous input) are created for different sensor clusters by using the free response of the structure. The output of each sensor in a cluster is used as an input to the ARX model to predict the output of the reference channel of that sensor cluster. Two different approaches are used for extracting Damage Features (DFs) from these ARX models. For the first approach, the coefficients of the ARX models are directly used as the DFs. It is shown with a 4 dof numerical model that damage can be identified, located and quantified for simple models and noise free data. To consider the effects of the noise and model complexity, a second approach is presented based on using the ARX model fit ratios as the DFs. The second approach is first applied to the same 4 DOF numerical model and to the numerical data coming from an international benchmark study for noisy conditions. Then, the methodology is applied to the experimental data from a large scale laboratory model. It is shown that the second approach performs successfully for different damage cases to identify and locate the damage using numerical and experimental data. Furthermore, it is observed that the DF level is a good indicator for estimating the extent of the damage for these cases. The potential and advantages of the methodology are discussed along with the analysis results. The limitations of the methodology, recommendations, and future work are also addressed.     

INPUT FORCES ESTIMATION OF BEAM STRUCTURES BY AN INVERSE METHOD

An on-line recursive inverse method to estimate the input forces of beam structures is presented. The inverse method is based on the Kalman filter and a recursive least-squares algorithm. The filter models the system dynamics in a linear set of state equations. The state equations of the beam structures were constructed using the finite element method. The practicability and accuracy of the estimation method were examined with numerical simulations from which the input forces of a cantilever beam with a lumped mass on the free end were estimated from the output responses. In the numerical experiments, the cantilever beam was subjected to five types of input forces, i.e., sinusoidal, triangular impulse, rectangular impulse, a series of impulses and random. The simulation results show that the inverse method has an excellent performance to estimate the input forces of beam structural systems from the noisy measurements.     

Robust non-fragile dynamic vibration absorbers with uncertain factors

In this paper, the design problem for non-fragile dynamic vibration absorbers (DVAs) is investigated. Due to the imprecision of the manufacturing process or the variation during the operation, uncertainty in the parameters of the DVA is unavoidable. The uncertainty may degrade the performance of the designed DVA or even deteriorate the system. Hence, it is practically demanding to propose a design method for a non-fragile DVA, i.e., when the parameters of the DVA vary in an admissible range, an expected vibration suppression level should be guaranteed. The uncertainty of the DVA is feasibly assumed to be norm-bounded. Then, the design problem for the DVA is converted into a static output feedback (SOF) control problem. Sufficient condition for the existence of the non-fragile DVA with a prescribed H_∞ level is derived by using a bilinear matrix inequality (BMI). An iterative linear matrix inequality (ILMI) method is employed to solve the BMI condition. Finally, a design example is given to show the effectiveness of the proposed approach.     

陈氏混沌系统的采样数据反馈控制

提出了基于采样数据反馈控制技术对陈氏混沌系统进行控制的理论.以给定的采样速率对陈氏混沌系统的输出进行采样.利用采样数据去构造离散时间控制算法,以达到将陈氏混沌系统控制到原点的目的.给出了被控制系统渐近稳定的理论证明,并给出了数值试验的结果. 关键词：     

On the Relationship Between Continuous- and Discrete-Time Quantum Walk

Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete- time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations.     

Optimum vibration absorber (tuned mass damper) design for linear damped systems subjected to random loads

Optimum design of dynamic vibration absorbers (DVAs) installed on linear damped systems that are subjected to random loads is studied and closed-form design formulas are provided. Three cases are considered in the optimization process: Minimizing the variance of the displacement, velocity and acceleration of the main mass. Exact optimum design parameters for the velocity case, which to the best knowledge of the author do not exist in the literature, are derived for the first time. Exact solutions are found to be directly applicable for practical use with no simplification needed. For displacement and acceleration cases, a solution for the optimum absorber frequency ratio is obtained as a function of optimum absorber damping ratio. Numerical simulations indicate that optimum absorber damping ratio is not significantly related to the structural damping, especially when the displacement variance is minimized. Therefore, optimum damping ratio derived for undamped systems is proposed for damped systems for the displacement case. When acceleration variance is minimized, however, the optimum damping ratio derived for undamped systems is found not as accurate for damped systems. Therefore, a more accurate approximate expression is derived. Numerical comparisons with published approximate expressions at the same level of complexity indicated that proposed design formula yield more accurate estimates. Another important finding of the paper is that for specific applications where all of the response parameters are desired to be minimized simultaneously, DVAs designed per velocity criteria provide the best overall performance with the least complexity in the design equations.     

Dynamic behavior of time-delayed acceleration feedback controller for active vibration control of flexible structures

This paper addresses the design problem of the controller with time-delayed acceleration feedback. On the basis of the reduction method and output state-derivative feedback, a time-delayed acceleration feedback controller is proposed. Stability boundaries of the closed-loop system are determined by using Hurwitz stability criteria. Due to the introduction of time delay into the controller with acceleration feedback, the proposed controller has the feature of not only changing the mass property but also altering the damping property of the controlled system in the sense of equivalent structural modification. With this feature, the closed-loop system has a greater logarithmic decrement than the uncontrolled one, and in turn, the control behavior can be improved. In this connection, the time delay in the acceleration feedback control is a positive factor when satisfying some given conditions and it could be actively utilized. On the ground of the analysis, the developed controller is implemented on a cantilever beam for different controller gain–delay combinations, and the control performance is evaluated with the comparison to that of pure acceleration feedback controller. Simulation and experimental results verify the ability of the controller to attenuate the vibration resulting from the dominant mode.     

输入受限的混沌系统同步控制

在混沌系统的同步控制中, 由于混沌系统对初始状态的敏感性, 一旦两个混沌系统的状态初值偏差大, 其状态同步往往需要高幅值的控制律来达到, 这给同步控制实现带来了困难, 并且在同步控制中, 两个混沌系统的初始值通常是未知的. 本文考虑控制输入受限情况下的混沌同步控制问题, 基于符号函数的近似表示式, 将受限的控制输入建模为连续可微的光滑函数, 在每一个采样点将同步控制误差系统近似为局部最优线性模型并设计连续型线性二次型调节器(LQR)最优控制律. 为降低混沌同步控制律的幅值和维持同步系统采样时刻之间的动态, 设计了等价的离散最优控制律, 并通过调整LQR性能加权矩阵值, 确保同步控制信号不会超出其受限的上界. 最后对统一混沌模型下的三种不同混沌系统同步控制进行了仿真研究. 仿真结果验证了方法的有效性. 关键词： 统一混沌模型 符号函数 输入受限 同步控制     

Inverse vibration problem for un-damped 3-dimensional multi-story shear building models

Various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional (2-D) shear building structural models for a given set of vibratory frequencies. The suggested methods are based on the specific characteristics of the Jacobi matrices, i.e., symmetric, tri-diagonal and semi-positive definite matrices. However, in case of three dimensional (3-D) structural models, those methods are no longer applicable, since their stiffness matrices are not tri-diagonal. In this paper the inverse problem for a special class of vibratory structural systems, i.e., 3-D shear building models, is investigated. A practical algorithm is proposed for solving the inverse eigenvalue problem for un-damped, 3-D shear buildings. The problem is addressed in two steps. First, using the target frequencies, a so-called normalized eigenvector matrix, which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system, is determined. In this regard, similar to the solution of inverse problem for 2-D shear building structural models in which an auxiliary structure is constructed by adding constraints (or springs) to the original system, three auxiliary structures are proposed to solve the problem for 3-D cases. In the second step, the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix; in turn, this matrix is decomposed into the stiffness and mass matrices of the system. Finally, a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3-D structural model for a given set of target vibrational frequencies.     

Mathematical modeling of multicylinder compressor discharge system interactions

Gas oscillations are complicated in a multicylinder compressor discharge system because of the cylinder interactions. These are identified and modeled here as kinematic and geometric types of coupling. The kinematic coupling effect is incorporated with the input volume velocities, at the values, which are derived from the discharge mass flow rates. To account for the geometric interactions arising because of the interconnected cavities and passages, impedance matrices are formulated. The discharge system components are described by steady state acoustic impedances, in distributed parameters format. The overall discharge system mathematical model (in the frequency domain) is then coupled with the time domain compressor cylinder thermodynamic, and valve fluid and structural dynamic models. An iterative is used to account for the back pressure effect.The theory is applied to a two cylinder high speed refrigeration compressor. Unsteady flow pressures are predicted in the valve chamber (for capacity and energy consumption considerations), and at the manifold end (for muffling effectiveness consideration). Excellent agreements between theory and experiment are obtained. The technique as outlined in this paper should be applicable to any multicylinder/interstaged positive displacement type of fluid machine.     

基于深度神经网络的HL-2A等离子体水平位移研究

基于门控循环单元(GRU)的神经网络,构建预测模型的网络拓扑结构,训练和测试了HL-2A装置等离子体水平位移系统响应模型。测试结果显示了该模型对43%的样本数据的拟合度超过80%。把该网络模型作为被控对象,使用基于径向基函数(RBF)神经网络的模型参考自适应控制(MRAC)算法,设计了一个HL-2A等离子体水平位移的MRAC系统。仿真结果显示,该控制系统的输出响应能快速地跟踪各种输入参考信号,控制器能够较好地控制等离子体的水平位移并具有强的抗扰动能力。     

Study of the planar optical fiber Bragg grating hydrophone probe with acceleration compensation

Since the probe acceleration response of a planar optical FBG hydrophone is very obvious and has an adverse influence on normal underwater acoustic pressure detection,an acceleration desensitization method employing an acceleration compensation measure is presented here.Results indicate that by utilizing this method,the equivalent pressure output applied by one unit of acceleration(1m·s^-2) is reduced from a range of 2.52-3.26 Pa to 0.0758-0.217 Pa, while the structural sensitivity decreases from 28 fm/Pa to 20 fm/Pa,however,the resonance frequency increases slightly from 6.2 kHz to 6.5 kHz.The increased resonance frequency helps to improve the dynamic frequency characteristics,and while the structural sensitivity is reduced, it can be compensated for by improving the optical FBG dynamic wavelength interrogation sensitivity.The system sensitivity of the optical FBG hydrophone is mainly determined by its wavelength interrogation sensitivity and not the probe structure sensitivity.Therefore,the acceleration compensation method would have broad practical applications.     

压电陶瓷非线性对大功率换能器结构参数匹配影响的计算分析

在Guyomar非线性模型基础上,通过机电等效法将晶堆前向负载作为等效质量和阻尼加入振动方程的质量项和阻尼项,推导了换能器振速、辐射声压级和谐振频率偏移率等表达式,计算分析了压电陶瓷非线性参数和结构参数对换能器声辐射性能的影响,研究了压电陶瓷的非线性对换能器结构参数匹配的影响。结果表明,换能器节面靠前,前盖板厚度越小,前盖板大径越小,都可以减少压电陶瓷非线性引起的换能器频率偏移。当设计频率确定时,压电陶瓷处于非线性工作域的换能器的结构参数有所减小。换能器加入辐射端匹配后,可以改善压电晶堆前向负载匹配,降低换能器的谐振频率偏移率。换能器激励电流也会出现频率偏移现象。在提高换能器激励电压时,换能器的结构参数应适当减小。得到的结论可为换能器设计提供理论依据和帮助。