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Joseph Lardies - One of the best experts on this subject based on the ideXlab platform.
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Modal Parameter identification by an iterative approach and by the state space model
Mechanical Systems and Signal Processing, 2017Co-Authors: Joseph LardiesAbstract:The problem of estimating a spectral representation of exponentially decaying signals from a set of sampled data is of considerable interest in several applications such as in vibration analysis of mechanical systems. In this paper we present a nonparametric and a parametric method for Modal Parameter identification of vibrating systems when only output data is available. The nonparametric method uses an iterative adaptive algorithm based in the formation of a two dimensional grid mesh, both in frequency and damping domains. We formulate the identification problem as an optimization problem where the signal energy is obtained from each frequency grid point and damping grid point. The Modal Parameters are then obtained by minimizing the signal energy from all grid points other than the grid point which contains the Modal Parameters of the system. The parametric approach uses the state space model and properties of the controllability matrix to obtain the state transition matrix which contains all Modal information. We discuss and illustrate the benefits of the proposed algorithms using a numerical and two experimental tests and we conclude that the nonparametric approach is very time consuming when a large number of samples is considered and does not outperform the parametric approach.
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Modal Parameter identification of a CMUT membrane using response data only
Mechanics & Industry, 2017Co-Authors: Joseph Lardies, Gilles Bourbon, Patrice Moal, Najib Kacem, Vincent WalterAbstract:Capacitive micromachined ultrasonic transducers (CMUTs) are microelectromechanical systems used for the generation of ultrasounds. The fundamental element of the transducer is a clamped thin metallized membrane that vibrates under voltage variations. To control such oscillations and to optimize its dynamic response it is necessary to know the Modal Parameters of the membrane such as resonance frequency, damping and stiffness coefficients. The purpose of this work is to identify these Parameters using only the time data obtained from the membrane center displacement. Dynamic measurements are conducted in time domain and we use two methods to identify the Modal Parameters: a subspace method based on an innovation model of the state-space representation and the continuous wavelet transform method based on the use of the ridge of the wavelet transform of the displacement. Experimental results are presented showing the effectiveness of these two procedures in Modal Parameter identification.
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Modal Parameter identification from output data only : equivalent approaches
Shock and Vibration, 2015Co-Authors: Joseph LardiesAbstract:The problem of Modal Parameter identification from output data only is presented. To identify the Modal Parameters different algorithms are presented: the block Hankel matrix and its shifted version and the block observability and block controllability matrices and their shifted version. These algorithms are derived from properties of the subspace approach. It is shown in the paper that these algorithms give the same results even in the noisy data case. Numerical and experimental results are presented showing the effectiveness of the procedure. In particular a microsystem constituted of a perforated microplate is analysed.
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Modal Parameter identification of stay cables from output-only measurements
Mechanical Systems and Signal Processing, 2011Co-Authors: Joseph Lardies, T NgiAbstract:Stay cables are one of the most critical structural components in modern cable-stayed bridges and the cable tension plays an important role in the construction, control and monitoring of cable-stayed bridges. We propose a time domain and a time–frequency domain approaches for Modal Parameter identification of stay cables using output-only measurements. The time domain approach uses the subspace algorithm which is improved with a new Modal coherence indicator. The time–frequency approach uses the wavelet transform of signals which is improved with a new analyzing wavelet. The wavelet transform is applied to the free response of ambient vibration which is obtained using the random decrement technique. Two experiments of stay cables are presented. The first experiment concerns a stay cable in laboratory where the external load is applied through an impact hammer and the vibratory signals are acquired through four accelerometers. The second experiment concerns the Jinma cable-stayed bridge that connects Guangzhou and Zhaoqing in China. It is a single tower, double row cable-stayed bridge supported by 112 stay cables. Ambient vibration of each stay cable is carried out using accelerometers. From output-only measurements, the Modal Parameters of stay cables are extracted. Once the eigenfrequencies and the damping coefficients are obtained, the cable forces and the Scruton number are derived. In a continuous monitoring and Modal analysis process, the tension forces and Scruton numbers could be used to assess the health of stay cables in cable-stayed bridges.
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Modal Parameter identification based on ARMAV and state–space approaches
Archive of Applied Mechanics, 2010Co-Authors: Joseph LardiesAbstract:An accurate prediction for the response of civil and mechanical engineering structures subject to ambient excitation requires the information of dynamic properties of these structures including natural frequencies, damping ratios and mode shapes. Since the excitation force is not available as a measured signal, we need to develop techniques which are capable of accurately extracting the Modal Parameters from output-only data. This article presents the results of Modal Parameter identification using two time-domain methods as follows: the autoregressive moving average vector (ARMAV) method and the state–space method. These methods directly work with the recorded time signals and allow the analysis of structures where only the output is measured, while the input is unmeasured and unknown. The equivalence between ARMAV and state–space approaches for the problem of Modal Parameter identification of vibrating systems is shown in the article. Using only the singular value decomposition of a block Hankel matrix of sample covariances, it is shown that these two approaches give identical Modal Parameters in the case where the block Hankel matrix has full row rank. The time-domain Modal identification algorithms have a serious problem of model order determination: when extracting structural modes these algorithms always generate spurious modes. A Modal indicator to differentiate spurious and structural modes is presented. Numerical and experimental examples are given to show the effectiveness of the ARMAV or state–space approaches in Modal Parameter identification using response data only.
T Ngi - One of the best experts on this subject based on the ideXlab platform.
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Modal Parameter identification of stay cables from output-only measurements
Mechanical Systems and Signal Processing, 2011Co-Authors: Joseph Lardies, T NgiAbstract:Stay cables are one of the most critical structural components in modern cable-stayed bridges and the cable tension plays an important role in the construction, control and monitoring of cable-stayed bridges. We propose a time domain and a time–frequency domain approaches for Modal Parameter identification of stay cables using output-only measurements. The time domain approach uses the subspace algorithm which is improved with a new Modal coherence indicator. The time–frequency approach uses the wavelet transform of signals which is improved with a new analyzing wavelet. The wavelet transform is applied to the free response of ambient vibration which is obtained using the random decrement technique. Two experiments of stay cables are presented. The first experiment concerns a stay cable in laboratory where the external load is applied through an impact hammer and the vibratory signals are acquired through four accelerometers. The second experiment concerns the Jinma cable-stayed bridge that connects Guangzhou and Zhaoqing in China. It is a single tower, double row cable-stayed bridge supported by 112 stay cables. Ambient vibration of each stay cable is carried out using accelerometers. From output-only measurements, the Modal Parameters of stay cables are extracted. Once the eigenfrequencies and the damping coefficients are obtained, the cable forces and the Scruton number are derived. In a continuous monitoring and Modal analysis process, the tension forces and Scruton numbers could be used to assess the health of stay cables in cable-stayed bridges.
Si-da Zhou - One of the best experts on this subject based on the ideXlab platform.
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output only Modal Parameter estimator of linear time varying structural systems based on vector tar model and least squares support vector machine
Mechanical Systems and Signal Processing, 2018Co-Authors: Si-da Zhou, Li Liu, Jie KangAbstract:Abstract Identification of time-varying Modal Parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based Modal Parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland’s compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed Modal Parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.
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Operational Modal Identification of Time-Varying Structures via a Vector Multistage Recursive Approach in Hybrid Time and Frequency Domain
Shock and Vibration, 2015Co-Authors: Si-da Zhou, Wu Yang, Zhi-sai MaAbstract:Real-time estimation of Modal Parameters of time-varying structures can conduct an obvious contribution to some specific applications in structural dynamic area, such as health monitoring, damage detection, and vibration control; the recursive algorithm of Modal Parameter estimation supplies one of fundamentals for acquiring Modal Parameters in real-time. This paper presents a vector multistage recursive method of Modal Parameter estimation for time-varying structures in hybrid time and frequency domain, including stages of recursive estimation of time-dependent power spectra, frozen-time Modal Parameter estimation, recursive Modal validation, and continuous-time estimation of Modal Parameters. An experimental example validates the proposed method finally.
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Parametric Modal identification of time-varying structures and the validation approach of Modal Parameters
Mechanical Systems and Signal Processing, 2014Co-Authors: Si-da Zhou, Ward HeylenAbstract:Abstract This paper investigates the problem of output-only Modal Parameter estimation of time-varying structures. A two-stage least square method for Modal Parameter estimation of time-varying structures is presented, consisting of a least square complex frequency-domain stage for the Modal Parameter estimation of all discrete time samples and a weighted least square stage for the estimation of continuous-time-represented Modal Parameters. This paper introduces a fuzzy-clustering-based approach for validating and sifting the Modal Parameters and develops four Modal assurance criterion-based distance functions to improve the quality of clustering of operational mode shapes. Furthermore, the proposed method has been validated by a simulation example and a laboratory experiment.
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Time-Frequency Domain Modal Parameter Estimation of Time-Varying Structures Using a Two-Step Least Square Estimator
Topics in Modal Analysis I Volume 5, 2012Co-Authors: Si-da Zhou, Ward HeylenAbstract:Under natural stochastic excitations, responses of time-varying structures are always nonstationary stochastic signals, of which spectra change with time. This paper studies the time-dependent power spectrum density based on time-frequency analysis. Based on the time-dependent power spectrum density, a mathematical model of the time-frequency-domain two-step least square Modal Parameter estimator for time-varying structures is presented. In the first-step estimation, the Modal Parameters at each time instant are estimated using the least square complex frequency-domain method. Furthermore, the estimated Modal Parameters are sifted and sorted. Based on the sifted and sorted Modal Parameters, the time-varying resonance frequency, damping ratio and operational mode shapes are estimated in the second-step estimation. A numerical simulation example and a group of experiments validate this two-step least square Modal Parameter estimator for time-varying structures.
Patrick Guillaume - One of the best experts on this subject based on the ideXlab platform.
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Improving Modal Parameter Estimation by Complementary Output–Output Relations
Topics in Modal Analysis & Testing Volume 10, 2017Co-Authors: Oscar Olarte, Patrick GuillaumeAbstract:Frequency domain Modal Parameter estimation from input–output data requires direct measurement or estimation of the input and output signals. In different applications those measurements, especially the excitation signals, are difficult to obtain and/or the assumptions could be poor or inappropriate (high uncertainty or high levels of noise). In this situations, the output–output relations can be used as auxiliary or complementary equations. The current work presents a framework for the identification of Modal Parameters estimation using maximum likelihood estimation incorporating the output–output relations in addition to the input–output ones. Since the output–output relations are independent of the input signals and its related uncertainty they will improve the system estimation. The ML estimator presents properties of consistency and efficiency and converge to the noiseless solution, but it involve calculating the inverse of the covariance matrix. An extended practice is to consider or assume that the noise of the frequency responses is uncorrelated, in this sense the covariance matrix becomes diagonal and the computational time is reduced. However, the price to pay is that the efficiency of the estimator is altered (the estimator does not reach the Cramer-Rao lower bound). The current work shows that incorporating the output–output relations to the input–output set of equations generates results closer to the ML estimator with a reduced computational load.
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improving Modal Parameter estimation by complementary output output relations
2017Co-Authors: Oscar Olarte, Patrick GuillaumeAbstract:Frequency domain Modal Parameter estimation from input–output data requires direct measurement or estimation of the input and output signals. In different applications those measurements, especially the excitation signals, are difficult to obtain and/or the assumptions could be poor or inappropriate (high uncertainty or high levels of noise). In this situations, the output–output relations can be used as auxiliary or complementary equations. The current work presents a framework for the identification of Modal Parameters estimation using maximum likelihood estimation incorporating the output–output relations in addition to the input–output ones. Since the output–output relations are independent of the input signals and its related uncertainty they will improve the system estimation. The ML estimator presents properties of consistency and efficiency and converge to the noiseless solution, but it involve calculating the inverse of the covariance matrix. An extended practice is to consider or assume that the noise of the frequency responses is uncorrelated, in this sense the covariance matrix becomes diagonal and the computational time is reduced. However, the price to pay is that the efficiency of the estimator is altered (the estimator does not reach the Cramer-Rao lower bound). The current work shows that incorporating the output–output relations to the input–output set of equations generates results closer to the ML estimator with a reduced computational load.
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operational Modal Parameter estimation of mimo systems using transmissibility functions
Automatica, 2014Co-Authors: Wout Weijtjens, Gert De Sitter, Christof Devriendt, Patrick GuillaumeAbstract:Operational Modal Parameter estimation (OMA) techniques perform system identification without or with only limited knowledge of the operational inputs acting on the system. However, most of the current operational identification techniques impose multiple conditions on the spectral content of the unknown inputs. As a consequence, modeling errors occur if these assumptions are not met. Therefore, there is a general interest in operational identification techniques that can operate independent of the unknown input spectra. This paper introduces poly-reference Transmissibility based Operational Modal Analysis (pTOMA). pTOMA uses parametrically estimated transmissibility functions associated with different loading conditions to obtain the system eigenvalues and eigenvectors using output-only data. Unlike most OMA techniques no strong assumptions are necessary considering the input spectrum. The method is therefore able to correctly identify the system Parameters while the excitation may contain (varying) harmonics or strong coloration. A framework to use pTOMA is formulated, the algorithm is introduced and the claimed properties are illustrated by means of a numerical experiment.
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Modal Parameter estimation by combining stochastic and deterministic frequency domain approaches
Mechanical Systems and Signal Processing, 2013Co-Authors: Mahmoud Elkafafy, Patrick Guillaume, Bart PeetersAbstract:Abstract The poly-reference Least squares Complex Frequency-domain (pLSCF) estimator—commercially known as the LMS PolyMAX estimator—is used intensively in Modal analysis applications nowadays. pLSCF is non-iterative (deterministic) and relatively accurate Modal Parameter estimation algorithm. This algorithm has several advantages: it is polyreference, fast, numerically stable for large-bandwidth with high-model order analysis, and yields very clear stabilization diagrams even with highly noisy FRFs measurements. One drawback of the pLSCF-estimator is that it yields a poor damping estimates especially for highly damped and weakly excited modes when the FRFs are very noisy. In this contribution, an approach will be proposed to improve the accuracy of pLSCF estimator and in particular, the damping estimates in case of high noise level. The new proposed approach is a combined stochastic-deterministic frequency-domain algorithm. In this approach, a 2-step procedure is introduced to improve the damping estimates while maintaining the very clear stabilization diagrams. In the first step, a parametric Maximum Likelihood smoothing approach, which is the stochastic part, is used to remove the noise from the data and in the second step, the pLSCF estimator, which is the deterministic part, is applied to the smoothed data resulting in improved (damping) estimates. The presented algorithm is able to maintain the benefits of pLSCF and at the same time leads to an improvement of the damping estimates in highly damped and very noisy cases. In addition, the new procedure properly deals with uncertainty on the measurements where the data variance due to measurement noise is taken into account. The procedure is illustrated and tested by using simulated as well as experimental data. The presented procedure to process a highly damped noisy vibration data leads to very accurate estimates in comparison to the traditional pLSCF estimator.
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user assisting tools for a fast frequency domain Modal Parameter estimation method
Mechanical Systems and Signal Processing, 2004Co-Authors: P Verboven, S Vanlanduit, E Parloo, B Cauberghe, Patrick GuillaumeAbstract:Abstract Recently, the least-squares complex frequency-domain (LSCF) estimator has been developed for Modal analysis applications. This contribution elaborates in more detail the fast derivation of stabilisation charts and uncertainty bounds for the estimated poles. An alternative representation for the stabilisation chart as well as a robust cluster algorithm to identify clusters of poles using the chart information is presented. Based on the clusters, uncertainty bounds for the poles and an automation of the pole selection process are derived. The relation of these “variances” with the stochastic variances (or confidence bounds) introduced by the noise on the measurements is compared by means of Monte-Carlo simulations. The use of alternative representation for the stabilisation chart in combination with the robust cluster analysis as well as the availability of uncertainty bounds for the Modal Parameters, assist the user with the performance of an accurate Modal Parameter estimation.
Jie Kang - One of the best experts on this subject based on the ideXlab platform.
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output only Modal Parameter estimator of linear time varying structural systems based on vector tar model and least squares support vector machine
Mechanical Systems and Signal Processing, 2018Co-Authors: Si-da Zhou, Li Liu, Jie KangAbstract:Abstract Identification of time-varying Modal Parameters contributes to the structural health monitoring, fault detection, vibration control, etc. of the operational time-varying structural systems. However, it is a challenging task because there is not more information for the identification of the time-varying systems than that of the time-invariant systems. This paper presents a vector time-dependent autoregressive model and least squares support vector machine based Modal Parameter estimator for linear time-varying structural systems in case of output-only measurements. To reduce the computational cost, a Wendland’s compactly supported radial basis function is used to achieve the sparsity of the Gram matrix. A Gamma-test-based non-parametric approach of selecting the regularization factor is adapted for the proposed estimator to replace the time-consuming n-fold cross validation. A series of numerical examples have illustrated the advantages of the proposed Modal Parameter estimator on the suppression of the overestimate and the short data. A laboratory experiment has further validated the proposed estimator.