scholarly journals Smooth orthogonal decomposition for modal analysis of randomly excited systems

2008 ◽  
Vol 316 (1-5) ◽  
pp. 137-146 ◽  
Author(s):  
U. Farooq ◽  
B.F. Feeny
Keyword(s):  
Modal Analysis ◽  
Orthogonal Decomposition ◽  
Smooth Orthogonal Decomposition

Modal Analysis With Smooth Karhunen-Loe`ve Decomposition

2009 ◽  
Author(s):  
S. Bellizzi ◽  
Rubens Sampaio
Keyword(s):  
Random Field ◽  
Modal Analysis ◽  
Covariance Matrix ◽  
Random Fields ◽  
Time Derivative ◽  
Normal Modes ◽  
Orthogonal Decomposition ◽  
White Noise Excitation ◽  
Smooth Orthogonal Decomposition ◽  
Vibrating Systems

In this paper, the Smooth Orthogonal Decomposition is formulated in term of a Smooth Karhunen-Loe`ve Decomposition (SKLD) to analyze random fields. The SKLD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random field and the covariance matrix of the associated time derivative random field. The main properties of the SKLD are described and compared to the classical Karhunen-Loe`ve decomposition. The SKLD is then applied to the responses of randomly excited vibrating systems with a view to performing modal analysis. The associated SKLD characteristics are interpreted in case of linear vibrating systems subjected to white noise excitation in terms of normal modes. Discrete and continuous mechanical systems are considered in this study.

Extended Smooth Orthogonal Decomposition for Modal Analysis

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Zhi-Xiang Hu ◽  
Xiao Huang ◽  
Yixian Wang ◽  
Feiyu Wang
Keyword(s):  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Problems ◽  
Search Algorithm ◽  
Damping Ratio ◽  
Orthogonal Decomposition ◽  
Vibration System ◽  
Output Only ◽  
Damped Systems ◽  
Smooth Orthogonal Decomposition

The smooth orthogonal decomposition (SOD) is an output-only modal analysis method, which has simple structure and gives good results for undamped or lightly damped vibration systems. In the present study, the SOD method is extended to incorporate various measurements that contain the displacement, the velocity, the acceleration, and even the jerk (derivation of the acceleration). Several generalized eigenvalue problems (EVPs) are put forward considering different measurement combinations, and it is proved that all these EVPs can reduce to the eigenvalue problems of the undamped vibration system. These different methods are called extended smooth orthogonal decomposition (ESOD) methods in this paper. For the damped vibration system, the frequencies obtained by different ESOD methods are different from each other. Thus, a cost function is defined and a search algorithm is proposed to find the optimal frequency and damping ratio that can explain these differences. Although the search algorithm is derived for the single-degree-of-freedom (SDOF) vibration systems, it is effective for the multi-degrees-of-freedom (MDOF) vibration system after assuming that the smooth orthogonal coordinates (SOCs) computed by the ESOD methods are approximate to the modal coordinate responses. In order to verify the ESOD methods and the search algorithm, simulations are carried out and the results indicate that all ESOD methods reach correct results for undamped vibration systems and the search algorithm can give accurate frequency and damping ratio for damped systems. In addition, the effects of measurement noises are considered and the results show that the proposed method has anti-noise property to some extent.

Nonlinear Smooth Orthogonal Decomposition of Kinematic Features of Sawing Reconstructs Muscle Fatigue Evolution as Indicated by Electromyography

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
David B. Segala ◽  
Deanna H. Gates ◽  
Jonathan B. Dingwell ◽  
David Chelidze
Keyword(s):  
Muscle Fatigue ◽  
Fixed Number ◽  
Orthogonal Decomposition ◽  
Muscle Injuries ◽  
Individual Muscle ◽  
Dimensional Reconstruction ◽  
Order Of Magnitude ◽  
Muscle Groups ◽  
The Right ◽  
Smooth Orthogonal Decomposition

Tracking or predicting physiological fatigue is important for developing more robust training protocols and better energy supplements and/or reducing muscle injuries. Current methodologies are usually impractical and/or invasive and may not be realizable outside of laboratory settings. It was recently demonstrated that smooth orthogonal decomposition (SOD) of phase space warping (PSW) features of motion kinematics can identify fatigue in individual muscle groups. We hypothesize that a nonlinear extension of SOD will identify more optimal fatigue coordinates and provide a lower-dimensional reconstruction of local fatigue dynamics than the linear SOD. Both linear and nonlinear SODs were applied to PSW features estimated from measured kinematics to reconstruct muscle fatigue dynamics in subjects performing a sawing motion. Ten healthy young right-handed subjects pushed a weighted handle back and forth until voluntary exhaustion. Three sets of joint kinematic angles were measured from the right upper extremity in addition to surface electromyography (EMG) recordings. The SOD coordinates of kinematic PSW features were compared against independently measured fatigue markers (i.e., mean and median EMG spectrum frequencies of individual muscle groups). This comparison was based on a least-squares linear fit of a fixed number of the dominant SOD coordinates to the appropriate local fatigue markers. Between subject variability showed that at most four to five nonlinear SOD coordinates were needed to reconstruct fatigue in local muscle groups, while on average 15 coordinates were needed for the linear SOD. Thus, the nonlinear coordinates provided a one-order-of-magnitude improvement over the linear ones.

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