Time-Varying Modal Analysis by SDOF Wavelets

2000 ◽  
Author(s):  
Arata Masuda ◽  
Akira Sone
Keyword(s):  
Matching Pursuit ◽  
Damping Ratio ◽  
Identification Problem ◽  
Mode Shapes ◽  
Time Varying ◽  
Identification Method ◽  
Time Varying Systems ◽  
Single Input ◽  
Expansion Coefficients ◽  
The Time Domain

Abstract The purpose of this paper is to provide a modal expression of a time-varying MDOF system and to develop an identification method for it. The single-input-multi-output relation of a time-varying N-DOF system is expressed as a superposition of N time-varying SDOF subsystems in the time domain, where the expansion coefficients represent the time-varying mode-shapes, and the natural frequency and the damping ratio of each subsystem represent the time-varying modal parameters of each mode. Then we define the SDOF wavelets, which correspond to the time-varying impulse responses of SDOF subsystems and show that the output of the entire system can be expressed by a superposition of SDOF wavelets. Then, the identification problem is reduced to an atomic decomposition problem of choosing the nearly best set of SDOF wavelets and determining the expansion coefficients. We develop a modified matching pursuit algorithm, called modal pursuit, to solve the problem. Basic examples are numerically examined to show that the proposed modal representation and the identification method are applicable to track the modal characteristics of time-varying systems.

scholarly journals Time-Domain Substructure Transient Vibration Transfer Path Analysis Based on Time-Varying Frequency Response Functions under Operational Excitations

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Rong He ◽  
Hong Zhou
Keyword(s):  
Path Analysis ◽  
Frequency Response ◽  
Time Domain ◽  
Time Varying ◽  
Response Functions ◽  
Transient Vibration ◽  
Transfer Path ◽  
Time Varying Systems ◽  
Transfer Path Analysis ◽  
The Time Domain

The time-domain substructure inverse matrix method has become a popular method to detect and diagnose problems regarding vehicle noise, vibration, and harshness, especially for those impulse excitations caused by roads. However, owning to its reliance on frequency response functions (FRFs), the approach is effective only for time-invariable linear or weak nonlinear systems. This limitation prevents this method from being applied to a typical vehicle suspension substructure, which shows different nonlinear characteristics under different wheel transient loads. In this study, operational excitation was considered as a key factor and applied to calculate dynamic time-varying FRFs to perform accurate time-domain transient vibration transfer path analysis (TPA). The core idea of this novel method is to divide whole coupled substructural relationships into two parts: one involved time-invariable components; normal FRFs could be obtained through tests directly. The other involved numerical computations of the time-domain operational loads matrix and FRFs matrix in static conditions. This method focused on determining dynamic FRFs affected by operational loads, especially the severe transient ones; these loads are difficult to be considered in other classical TPA approaches, such as operational path analysis with exogenous inputs (OPAX) and operational transfer path analysis (OTPA). Experimental results showed that this new approach could overcome the limitations of the traditional time-domain substructure TPA in terms of its strict requirements within time-invariable systems. This is because in the new method, time-varying FRFs were calculated and used, which could make the FRFs at the system level directly adapt to time-varying systems from time to time. In summary, the modified method extends TPA objects studied in time-invariable systems to time-varying systems and, thus, makes a methodology and application innovation compared to traditional the time-domain substructure TPA.

scholarly journals Damping Effects Induced by a Mass Moving along a Pendulum

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. Gandino ◽  
S. Marchesiello ◽  
A. Bellino ◽  
A. Fasana ◽  
L. Garibaldi
Keyword(s):  
Linear Time ◽  
Damping Ratio ◽  
System Response ◽  
Time Varying ◽  
Simple Method ◽  
Equivalent Damping ◽  
Stochastic Subspace Identification ◽  
Time Varying Systems ◽  
Instantaneous Frequencies ◽  
Short Time

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.

Inverse control of single-input/single-output nonlinear time-varying systems with noise disturbances by multi-dimensional Taylor network

2020 ◽  
Vol 42 (13) ◽  
pp. 2450-2464
Author(s):  
Hong-Sen Yan ◽  
Chao Zhang
Keyword(s):  
Real Time ◽  
Recursive Least Squares ◽  
Time Varying ◽  
Single Input Single Output ◽  
Inverse Control ◽  
The Real ◽  
Single Output ◽  
Time Varying Systems ◽  
Single Input ◽  
Noise Disturbances

In this paper, an inverse control scheme based on the novel dynamic network (multi-dimensional Taylor network (MTN)) is proposed for the real-time tracking control of nonlinear time-varying systems with noise disturbances. Utilized in this scheme are the three MTNs: the adaptive model identifier for system modeling, the adaptive inverse controller for inverse modeling, and the adaptive nonlinear filter for eliminating the noise disturbances, whose weights are modified by the variable forgetting factor recursive least squares (VFF-RLS), back propagation through model (BPTM), normalized least mean square (NLMS) algorithms, respectively. To avoid “compromise”, this scheme is designed into a structure wherein controlling the object dynamic response and eliminating the noise disturbances are implemented in two relatively independent processes. Furthermore, the weight-elimination algorithm is introduced for choice of effective regression items to avoid the dimension explosion, thus overcoming the shortcoming that the number of middle nodes needs to be determined before using the traditional neural network. After a certain number of training, the more streamlined MTNs are observed to contribute to satisfying the real-time requirements of software implementation and engineering application. To ensure that MTN inverse control is strict in theory, the general conditions for the existence of single-input/single-output (SISO) nonlinear inverse systems are identified. Simulation of the MTN inverse control is conducted to confirm the effectiveness of the proposed method.

scholarly journals Instantaneous Frequency Identification Using Adaptive Linear Chirplet Transform and Matching Pursuit

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Chang Xu ◽  
Cong Wang ◽  
Jingbo Gao
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Vibration Signal ◽  
High Time Resolution ◽  
Nonlinear Frequency ◽  
Time Varying ◽  
Identification Method ◽  
Chirplet Transform ◽  
Comparison Results ◽  
Frequency Identification

An instantaneous frequency identification method of vibration signal based on linear chirplet transform and Wigner-Ville distribution is presented. This method has an obvious advantage in identifying closely spaced and time-varying frequencies. The matching pursuit algorithm is employed to select optimal chirplets, and a modified version of chirplet transform is presented to estimate nonlinear varying frequencies. Because of the high time resolution, the modified chirplet transform is superior to the original method. The proposed method is applied to time-varying systems with both linear and nonlinear varying stiffness and systems with closely spaced modes. A wavelet-based identification method is simulated to compare with the proposed method, with the comparison results showing that the chirplet-based method is effective and accurate in identifying both time-varying and closely spaced frequencies. A bat echolocation signal is used to verify the effectiveness of the modified chirplet transform. The result shows that it will significantly increase the accuracy of nonlinear frequency trajectory identification.

scholarly journals An Identification Method for the Unbalance Parameters of a Rotor-Bearing System

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Wengui Mao ◽  
Guiping Liu ◽  
Jianhua Li ◽  
Jie Liu
Keyword(s):  
Identification Problem ◽  
Convolution Integral ◽  
Test Rig ◽  
Identification Method ◽  
Rotor Bearing ◽  
Force Reconstruction ◽  
Deconvolution Problem ◽  
Unbalance Force ◽  
The Time Domain ◽  
Bearing System

This paper is to be submitting an identification method for the unbalance parameters of a rotor-bearing system. In the method, the unbalance parameters identification problem is formulated as the unbalance force reconstruction which belongs to solving deconvolution problem, in which the unbalance force is expressed in the time domain. The unbalance response is expressed by the convolution integral of Green’s function and the unbalance force. In order to avoid the unstable solution arising from the noisy responses and the deconvolution, a regularization method is adopted to stabilize the solution. Meanwhile, a searching of the sensitive measured point has also been carried out to confirm the robustness of the method. Numerical example and a test rig have been used to illustrate the proposed method.

scholarly journals A Single Differential Equation for First-Excursion Time in a Class of Linear Systems

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Matthew B. Greytak ◽  
Franz S. Hover
Keyword(s):  
Structural Dynamics ◽  
Closed Loop ◽  
Damping Ratio ◽  
Robotic Systems ◽  
Time Varying ◽  
Stochastic Environments ◽  
Closed Loop Systems ◽  
Time Varying Systems ◽  
Major Application ◽  
Excursion Time

First-excursion times have been developed extensively in the literature for oscillators; one major application is structural dynamics of buildings. Using the fact that most closed-loop systems operate with a moderate to high damping ratio, we have derived a new procedure for calculating first-excursion times for a class of linear continuous, time-varying systems. In several examples, we show that the algorithm is both accurate and time-efficient. These are important attributes for real-time path planning in stochastic environments, and hence the work should be useful for autonomous robotic systems involving marine and air vehicles.

scholarly journals Unidirectional amplification with acoustic non-Hermitian space−time varying metamaterial

2022 ◽  
Vol 5 (1) ◽  
Author(s):  
Xinhua Wen ◽  
Xinghong Zhu ◽  
Alvin Fan ◽  
Wing Yim Tam ◽  
Jie Zhu ◽  
...  
Keyword(s):  
Time Domain ◽  
Frequency Conversion ◽  
Space Time ◽  
Time Varying ◽  
Impulse Responses ◽  
Experimental Realization ◽  
Material Gain ◽  
Time Varying Systems ◽  
Hermitian Space ◽  
The Time Domain

AbstractSpace−time modulated metamaterials support extraordinary rich applications, such as parametric amplification, frequency conversion, and non-reciprocal transmission. The non-Hermitian space−time varying systems combining non-Hermiticity and space−time varying capability, have been proposed to realize wave control like unidirectional amplification, while its experimental realization still remains a challenge. Here, based on metamaterials with software-defined impulse responses, we experimentally demonstrate non-Hermitian space−time varying metamaterials in which the material gain and loss can be dynamically controlled and balanced in the time domain instead of spatial domain, allowing us to suppress scattering at the incident frequency and to increase the efficiency of frequency conversion at the same time. An additional modulation phase delay between different meta-atoms results in unidirectional amplification in frequency conversion. The realization of non-Hermitian space−time varying metamaterials will offer further opportunities in studying non-Hermitian topological physics in dynamic and nonreciprocal systems.

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