An iterative rational fraction polynomial technique for modal identification

Meccanica ◽  
1995 ◽  
Vol 30 (1) ◽  
pp. 63-75 ◽  
Author(s):  
Antonio Carcaterra ◽  
Walter D'Ambrogio
Keyword(s):  
Modal Identification ◽  
Rational Fraction ◽  
Rational Fraction Polynomial

scholarly journals Crack detection based on optimal control

2012 ◽  
Vol 18 (11) ◽  
pp. 1737-1749 ◽  
Author(s):  
B Chomette ◽  
J-J Sinou
Keyword(s):  
Optimal Control ◽  
Crack Detection ◽  
Polynomial Algorithm ◽  
Rational Fraction ◽  
Control Performance ◽  
Structure Modification ◽  
Closed Loop Systems ◽  
Controlled Systems ◽  
Rational Fraction Polynomial ◽  
Cracked Structure

Techniques for optimal control to increase system security attract a great deal of interest from industry. The presence of transversal cracks can considerably modify the dynamics of a system. In the case of closed-loop systems, i.e. controlled systems, these faults can cause the destabilization and variation of control performance. Consequently, such variations can be used to detect transversal cracks. Therefore, the present study proposes an investigation into the possibility of detecting structure modification based on estimated control performance by using the Rational Fraction Polynomial algorithm. This method is applied numerically to a multi-cracked controlled truss. Both the optimal control of the cracked structure and the possibility of detecting the presence of cracks by monitoring the evolution of control performance are studied. The efficiency of the proposed method is demonstrated through numerical simulations corresponding to different crack orientations and locations.

scholarly journals Modal control based on direct modal parameters estimation

2017 ◽  
Vol 24 (12) ◽  
pp. 2389-2399 ◽  
Author(s):  
Baptiste Chomette ◽  
Adrien Mamou-Mani
Keyword(s):  
Frequency Domain ◽  
Controller Design ◽  
State Space Model ◽  
Parameters Estimation ◽  
Modal Parameters ◽  
Rational Fraction ◽  
Modal Control ◽  
Identification Algorithm ◽  
Human Intervention ◽  
Rational Fraction Polynomial

Modal active control is based on a state model that requires the identification of modal parameters. This identification can typically be done through a rational fraction polynomial algorithm applied in the frequency domain. This method generates numerical problems when estimating high-order models, particularly when moving from the basis of orthogonal polynomials for the modal basis. This algorithm must therefore be applied independently on multiple frequency ranges with a low order for each range. In this case, the controller design cannot be automated and requires a lot of human intervention, especially to build the state space model. To address this issue, this paper presents the application of the direct modal parameters estimation (DMPE) algorithm for active modal control design. The identification algorithm is presented in a simplified version with only positive frequencies. Unlike other classical identification methods in the frequency domain, the DMPE algorithm provides a solution with a great numerical stability and allows estimating models with a higher order. Using this method, the design of the controller can be largely automated and requires a minimum of human intervention. After a theoretical presentation, the proposed method is experimentally validated by controlling the vibration modes of a suspended plate.

A tutorial on a multi-mode identification procedure based on the complex-curve fitting method

2022 ◽  
pp. 107754632110576
Author(s):  
Victor T Noppeney ◽  
Thiago Boaventura ◽  
Klaus Medeiros ◽  
Paulo Varoto
Keyword(s):  
Modal Analysis ◽  
Curve Fitting ◽  
Parameter Extraction ◽  
Modal Identification ◽  
Rational Fraction ◽  
Polynomial Method ◽  
Complex Curve ◽  
Mode Identification ◽  
Depth Analysis ◽  
Multi Mode

Modal identification is a key step in modal analysis. It enables the researcher to extract modal parameters, such as natural frequency, amplitude, and damping from a given structure. There are a considerable number of techniques in the state of the art aiming to address this problem, where multi-mode approaches arise as an appealing choice due to their ability to deal with mode coupling. This tutorial paper focuses on the complex-curve fitting technique, originally conceived for an application distinct from modal analysis. It aims at guiding other researchers by providing a tutorial-like and in-depth analysis of this important method, associated with a nonlinear weighting procedure for improved precision. Additionally, this paper fills a gap on the original technique, which is limited to the ratio of two polynomials, by proposing an automatic parameter extraction technique. The original and improved methods are applied on both simulated and experimental data, highlighting the effectiveness of the proposed changes. The proposed procedure is also compared with the rational fraction polynomial method.

Study on Global-Piecewise Fitting for Modal Parameter Identification

2014 ◽  
Vol 651-653 ◽  
pp. 2386-2389
Author(s):  
Feng Li Wang
Keyword(s):  
Curve Fitting ◽  
Polynomial Algorithm ◽  
Rational Fraction ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Response Data ◽  
Fitting Method ◽  
Simulation Results ◽  
Rational Fraction Polynomial ◽  
Fitting Model

Based on the global orthogonal polynomial algorithm, a global-piecewise fitting method for eliminating affections of modes outside of fitting bands is proposed. Both lower and higher modes outside of the fitting band are analyzed and processed. The frequency response data are revised by means of modes in two frequency bands close to the fitting band, and a curve fitting model is derived. Simulation results indicate that the proposed method possesses higher precision than the general rational fraction polynomial algorithm.

scholarly journals Cracks Detection Using Active Modal Damping and Piezoelectric Components

2013 ◽  
Vol 20 (4) ◽  
pp. 619-631 ◽  
Author(s):  
B. Chomette ◽  
A. Fernandes ◽  
J.-J. Sinou
Keyword(s):  
Crack Depth ◽  
Element Model ◽  
Piezoelectric Transducers ◽  
Detection Methods ◽  
Rational Fraction ◽  
Monitoring Strategies ◽  
Modal Damping ◽  
Small Parameters ◽  
Small Cracks ◽  
Rational Fraction Polynomial

The dynamics of a system and its safety can be considerably affected by the presence of cracks. Health monitoring strategies attract so a great deal of interest from industry. Cracks detection methods based on modal parameters variation are particularly efficient in the case of large cracks but are difficult to implement in the case of small cracks due to measurement difficulties in the case of small parameters variation. Therefore the present study proposes a new method to detect small cracks based on active modal damping and piezoelectric components. This method uses the active damping variation identificated with the Rational Fraction Polynomial algorithm as an indicator of cracks detection. The efficiency of the proposed method is demonstrated through numerical simulations corresponding to different crack depth and locations in the case of a finite element model of a clamped-clamped beam including four piezoelectric transducers.

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