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Satish Nagarajaiah - One of the best experts on this subject based on the ideXlab platform.
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output only Modal Identification by compressed sensing non uniform low rate random sampling
Mechanical Systems and Signal Processing, 2015Co-Authors: Yongchao Yang, Satish NagarajaiahAbstract:Abstract Modal Identification or testing of structures consists of two phases, namely, data acquisition and data analysis. Some structures, such as aircrafts, high-speed machines, and plate-like civil structures, have active modes in the high-frequency range when subjected to high-speed or broadband excitation in their operational conditions. In the data acquisition stage, the Shannon–Nyquist sampling theorem indicates that capturing the high-frequency modes (signals) requires uniform high-rate sampling, resulting in sensing too many samples, which potentially impose burdens on the data transfer (especially in wireless platform) and data analysis stage. This paper explores a new-emerging, alternative, signal sampling and analysis technique, compressed sensing, and investigates the feasibility of a new method for output-only Modal Identification of structures in a non-uniform low-rate random sensing framework based on a combination of compressed sensing (CS) and blind source separation (BSS). Specifically, in the data acquisition stage, CS sensors sample few non-uniform low-rate random measurements of the structural responses signals, which turn out to be sufficient to capture the underlying mode information. Then in the data analysis stage, the proposed method uses the BSS technique, complexity pursuit (CP) recently explored by the authors, to directly decouple the non-uniform low-rate random samples of the structural responses, simultaneously yielding the mode shape matrix as well as the non-uniform low-rate random samples of the Modal responses. Finally, CS with l 1 -minimization recovers the uniform high-rate Modal response from the CP-decoupled non-uniform low-rate random samples of the Modal response, thereby enabling estimation of the frequency and damping ratio. Because CS sensors are currently in laboratory prototypes and not yet commercially available, their functionality—randomly sensing few non-uniform samples—is simulated in this study, which is performed on the examples of a numerical structural model, an experimental bench-scale structural model, and a real-world seismic-excited base-isolated hospital buildings. Results show that the proposed method in the CS framework can identify the modes using non-uniform low-rate random sensing, which is far below what is required by the Nyquist sampling theorem.
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time frequency blind source separation using independent component analysis for output only Modal Identification of highly damped structures
Journal of Structural Engineering-asce, 2013Co-Authors: Yongchao Yang, Satish NagarajaiahAbstract:AbstractOutput-only algorithms are needed for Modal Identification when only structural responses are available. The recent years have witnessed the fast development of blind source separation (BSS) as a promising signal processing technique, pursuing to recover the sources using only the measured mixtures. As the most popular tool solving the BSS problem, independent component analysis (ICA) is able to directly extract the time-domain Modal responses, which are viewed as virtual sources, from the observed system responses; however, it has been shown that ICA loses accuracy in the presence of higher-level damping. In this study, the Modal Identification issue, which is incorporated into the BSS formulation, is transformed into a time-frequency framework. The sparse time-frequency representations of the monotone Modal responses are proposed as the targeted independent sources hidden in those of the system responses which have been short-time Fourier-transformed (STFT); they can then be efficiently extracte...
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output only Modal Identification with limited sensors using sparse component analysis
Journal of Sound and Vibration, 2013Co-Authors: Yongchao Yang, Satish NagarajaiahAbstract:Abstract Blind source separation (BSS) based methods have been shown to be efficient and powerful to perform output-only Modal Identification. Existing BSS Modal Identification methods, however, require the number of sensors at least equal to that of sources (active modes). This paper proposes a new Modal Identification algorithm based on a novel BSS technique termed sparse component analysis (SCA) to handle even the underdetermined problem where sensors may be highly limited compared to the number of active modes. The developed SCA method reveals the essence of Modal expansion that the monotone Modal responses with disjoint sparsest representations in frequency domain naturally cluster in the directions of the mode matrix's columns (modeshapes), which are readily extracted from the measured system responses using a simple clustering algorithm. Then, in determined case where sensor number equals that of modes, the estimated square mode matrix directly decouples the system responses to obtain the Modal responses, whereby computing their frequencies and damping ratios; whereas with limited sensors, the Modal responses are efficiently recovered via the l 1 -minimization sparse recovery technique from the incomplete knowledge of the partial mode matrix and the system responses of inadequate sensors. Numerical simulations and experimental example show that whether in determined or underdetermined situations, the SCA method performs accurate and robust Identification of a wide range of structures including those with closely-spaced and highly-damped modes. The SCA method is simple and efficient to conduct reliable output-only Modal Identification even with limited sensors.
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output only Modal Identification and structural damage detection using time frequency wavelet techniques
Earthquake Engineering and Engineering Vibration, 2009Co-Authors: Satish Nagarajaiah, Biswajit BasuAbstract:The primary objective of this paper is to develop output only Modal Identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their Modal components. Once the Modal components are obtained, each one is processed using Hilbert transform to obtain the Modal frequency and damping ratios. In addition, the ratio of Modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only Modal Identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only Modal Identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only Modal Identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for Modal Identification and their potential for real world applications where output only Identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based Modal Identification can be performed.
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output only Modal Identification and structural damage detection using time frequency wavelet techniques
Earthquake Engineering and Engineering Vibration, 2009Co-Authors: Satish Nagarajaiah, Biswajit BasuAbstract:The primary objective of this paper is to develop output only Modal Identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their Modal components. Once the Modal components are obtained, each one is processed using Hilbert transform to obtain the Modal frequency and damping ratios. In addition, the ratio of Modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only Modal Identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only Modal Identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only Modal Identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for Modal Identification and their potential for real world applications where output only Identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based Modal Identification can be performed.
Ayan Sadhu - One of the best experts on this subject based on the ideXlab platform.
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decentralized Modal Identification of structures using an adaptive empirical mode decomposition method
Journal of Sound and Vibration, 2019Co-Authors: M Lazhari, Ayan SadhuAbstract:Abstract With recent advancement of robotic technology, mobile wireless devices have made a paradigm shift in cost-effective and faster deployment of sensors towards health monitoring of large-scale infrastructure. A wide range of system Identification methods has been developed by the researchers to accurately identify unknown structural parameters from the measured vibration data. However, most of these techniques are suitable only when all key locations of the structure are instrumented. In case of decentralized mobile sensing network where a sensor is autonomously moved from one location to another, only a single sensor is available at a particular time. In this paper, a newer time-frequency analysis method, namely Empirical Mode Decomposition (EMD), is explored and improved to undertake system Identification using single channel measurement. Traditional EMD results in significant mode-mixing while analyzing closely-spaced modes and data with measurement noise. In this paper, Time-Varying Filtering based Empirical Mode Decomposition (TVF-EMD) is proposed to perform Modal Identification using decentralized sensing approach. The proposed method is fully adaptive and suitable for automation since it uses only one channel of data at a time. The proposed method is verified using a suite of numerical, experimental and full-scale studies using wireless sensors in a decentralized manner.
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a review of output only structural mode Identification literature employing blind source separation methods
Mechanical Systems and Signal Processing, 2017Co-Authors: Ayan Sadhu, Sriram Narasimhan, Jerome AntoniAbstract:Abstract Output-only Modal Identification has seen significant activity in recent years, especially in large-scale structures where controlled input force generation is often difficult to achieve. This has led to the development of new system Identification methods which do not require controlled input. They often work satisfactorily if they satisfy some general assumptions – not overly restrictive – regarding the stochasticity of the input. Hundreds of papers covering a wide range of applications appear every year related to the extraction of Modal properties from output measurement data in more than two dozen mechanical, aerospace and civil engineering journals. In little more than a decade, concepts of blind source separation (BSS) from the field of acoustic signal processing have been adopted by several researchers and shown that they can be attractive tools to undertake output-only Modal Identification. Originally intended to separate distinct audio sources from a mixture of recordings, mathematical equivalence to problems in linear structural dynamics have since been firmly established. This has enabled many of the developments in the field of BSS to be modified and applied to output-only Modal Identification problems. This paper reviews over hundred articles related to the application of BSS and their variants to output-only Modal Identification. The main contribution of the paper is to present a literature review of the papers which have appeared on the subject. While a brief treatment of the basic ideas are presented where relevant, a comprehensive and critical explanation of their contents is not attempted. Specific issues related to output-only Modal Identification and the relative advantages and limitations of BSS methods both from theoretical and application standpoints are discussed. Gap areas requiring additional work are also summarized and the paper concludes with possible future trends in this area.
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ambient Modal Identification using multi rank parallel factor decomposition
Structural Control & Health Monitoring, 2015Co-Authors: Ayan Sadhu, Arndt Goldack, S NarasimhanAbstract:Summary In this paper, the problem of underdetermined Modal Identification where the number of modes to be identified is larger than the available sensor measurements is addressed using parallel factor decomposition and blind source separation. Underdetermined situations not only arise when the number of sensors are limited but also when narrowband excitations are present in the measurements, for example, in pedestrian-induced vibration of footbridges. The basic premise of the proposed algorithm is based on multiple-rank parallel factor decomposition of covariance tensors constituted from vibration response measurements. Unlike conventional parallel factor decomposition using a single rank order, the proposed method utilizes multiple rank order decompositions. A stability chart constructed from identified sources through such multiple rank orders allows for the robust estimation of active modes. The statistical characteristics of the resulting modes are evaluated in order to delineate the sources corresponding to external disturbances versus inherent modes of the system. The proposed framework enables an automated selection of rank order, detection of external harmonics and an estimation of Modal parameters that are relatively insensitive to the sensor configuration. The performance of the algorithm is illustrated using both numerical studies and an experimental study using pedestrian-induced vibration measurements of a stress-ribbon bridge located at the Technical University—Berlin, Germany. Copyright © 2014 John Wiley & Sons, Ltd.
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decentralized Modal Identification of a pony truss pedestrian bridge using wireless sensors
Journal of Bridge Engineering, 2014Co-Authors: Ayan Sadhu, Sriram Narasimhan, Arndt GoldackAbstract:Most of the vibration-based ambient Modal Identification methods in the literature are structured to process vibration data collected from a dense array of sensors centrally to yield Modal information. For large systems, for example bridges, one of the main disadvantages of such a centralized architecture is the cost of dense instrumentation, predominantly consisting of the sensors themselves, the data acquisition system, and the associated cabling. Recent advances in wireless smart sensors have addressed the issue of sensor cost to some extent; however, most of the algorithms—with the exception of very few—still retain an essentially centralized architecture. To harness the full potential of decentralized implementation, the authors have developed a new class of algorithms exploiting the concepts of sparsity (using wavelet transforms) within the framework of blind source separation. The problem of Identification is cast within the framework of underdetermined blind source separation invoking transformations of measurements to the wavelet domain resulting in a sparse representation. Although the details of these decentralized algorithms have been discussed in other articles, in this paper, for the first time, these algorithms are studied experimentally on a full-scale structure using wireless sensors. In a truly decentralized implementation, only two sensors are roved along the length of a pedestrian bridge, and the performance of the proposed algorithms is studied in detail. A pedestrian bridge located in Montreal, Quebec, Canada, is chosen primarily to highlight the methodology used to address Modal Identification under low-sensor density and for pedestrian loading. Issues arising from several modes being excited on this bridge and the presence of narrowband pedestrian excitations are addressed. The accuracy of Modal Identification that is achieved using the proposed decentralized algorithms is compared with the results obtained from their centralized counterparts.
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decentralized Modal Identification of structures using parallel factor decomposition and sparse blind source separation
Mechanical Systems and Signal Processing, 2013Co-Authors: Ayan Sadhu, Budhaditya Hazra, Sriram NarasimhanAbstract:Abstract In this paper, a novel decentralized Modal Identification method is proposed utilizing the concepts of sparse blind source separation (BSS) and parallel factor decomposition. Unlike popular ambient Modal Identification methods which require large arrays of simultaneous vibration measurements, the decentralized algorithm presented here operates on partial measurements, utilizing a sub-set of sensors at-a-time. Mathematically, this leads to an underdetermined source separation problem, which is addressed using sparsifying wavelet transforms. The proposed method builds on a previously presented concept by the authors, which utilizes the stationary wavelet packet transform (SWPT) to generate an over-complete dictionary of sparse bases. However, the redundant SWPT can be computationally intensive depending on the bandwidth of the signals and the sampling frequency of the vibration measurements. This issue of computational burden is alleviated through a new method proposed here, which is based on a multi-linear algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the Modal responses. The underdetermined source identifiability of PARAFAC enables source separation in wavelet packet coefficients with considerable mode mixing, thereby relaxing the conditions to generate over-complete bases, thus reducing the computational burden. The proposed method is validated using a series of numerical simulations followed by an implementation on recorded ambient vibration measurements obtained from the UCLA factor building.
Thienphu Le - One of the best experts on this subject based on the ideXlab platform.
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blind source separation technique for operational Modal analysis in presence of harmonic excitation
2020Co-Authors: Vandong Do, Thienphu Le, Alexis BeakouAbstract:Operational Modal analysis (OMA) known as response-only Modal Identification, is extremely useful for large structures in civil engineering where the excitation is difficult or even impossible to measure. The unknown excitation is always assumed as white noise in OMA. In presence of harmonics, the white noise assumption is not verified that makes the Modal Identification process difficult, and eventually leading to biased results. In recent years, blind source separation (BSS) techniques have been shown to be robust and efficient for OMA. In this paper, a new BBS technique termed Sparse Component Analysis (SCA) without white noise assumption, is applied for operational Modal Identification in presence of harmonics. The performance of the proposed method is demonstrated using numerical examples of a two-degrees-of-freedom system and a cantilever beam.
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use of the morlet mother wavelet in the frequency scale domain decomposition technique for the Modal Identification of ambient vibration responses
Mechanical Systems and Signal Processing, 2017Co-Authors: Thienphu LeAbstract:Abstract The frequency-scale domain decomposition technique has recently been proposed for operational Modal analysis. The technique is based on the Cauchy mother wavelet. In this paper, the approach is extended to the Morlet mother wavelet, which is very popular in signal processing due to its superior time-frequency localization. Based on the regressive form and an appropriate norm of the Morlet mother wavelet, the continuous wavelet transform of the power spectral density of ambient responses enables modes in the frequency-scale domain to be highlighted. Analytical developments first demonstrate the link between Modal parameters and the local maxima of the continuous wavelet transform modulus. The link formula is then used as the foundation of the proposed Modal Identification method. Its practical procedure, combined with the singular value decomposition algorithm, is presented step by step. The proposition is finally verified using numerical examples and a laboratory test.
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Modal Identification of spindle tool unit in high speed machining
Mechanical Systems and Signal Processing, 2011Co-Authors: Vincent Gagnol, Thienphu LeAbstract:Abstract The accurate knowledge of high-speed motorised spindle dynamic behaviour during machining is important in order to ensure the reliability of machine tools in service and the quality of machined parts. More specifically, the prediction of stable cutting regions, which is a critical requirement for high-speed milling operations, requires the accurate estimation of tool/holder/spindle set dynamic Modal parameters. These estimations are generally obtained through Frequency Response Function (FRF) measurements of the non-rotating spindle. However, significant changes in Modal parameters are expected to occur during operation, due to high-speed spindle rotation. The spindle's Modal variations are highlighted through an integrated finite element model of the dynamic high-speed spindle-bearing system, taking into account rotor dynamics effects. The dependency of dynamic behaviour on speed range is then investigated and determined with accuracy. The objective of the proposed paper is to validate these numerical results through an experiment-based approach. Hence, an experimental setup is elaborated to measure rotating tool vibration during the machining operation in order to determine the spindle's Modal frequency variation with respect to spindle speed in an industrial environment. The Identification of natural frequencies of the spindle under rotating conditions is challenging, due to the low number of sensors and the presence of many harmonics in the measured signals. In order to overcome these issues and to extract the characteristics of the system, the spindle modes are determined through a 3-step procedure. First, spindle modes are highlighted using the Frequency Domain Decomposition (FDD) technique, with a new formulation at the considered rotating speed. These extracted modes are then analysed through the value of their respective damping ratios in order to separate the harmonics component from structural spindle natural frequencies. Finally, the stochastic properties of the modes are also investigated by considering the probability density of the retained modes. Results show a good correlation between numerical and experiment-based identified frequencies. The identified spindle-tool Modal properties during machining allow the numerical model to be considered as representative of the real dynamic properties of the system.
Siukui Au - One of the best experts on this subject based on the ideXlab platform.
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fast bayesian approach for Modal Identification using free vibration data part ii posterior uncertainty and application
Mechanical Systems and Signal Processing, 2016Co-Authors: Yanchun Ni, Fengliang Zhang, Siukui AuAbstract:Abstract A Bayesian statistical framework has been developed for Modal Identification using free vibration data in the companion paper (Zhang et al., Mech. Syst. Sig. Process. (2015)). Efficient strategies have been developed for evaluating the most probable value (MPV) of the Modal parameters in both well-separated mode and general multiple mode cases. This paper investigates the posterior uncertainty of the Modal parameters in terms of their posterior covariance matrix, which is mathematically equal to the inverse of the Hessian of the negative log-likelihood function (NLLF) evaluated at the MPVs. Computational issues associated with the determination of the posterior covariance matrix are discussed. Analytical expressions are derived for the Hessian so that it can be evaluated accurately and efficiently without resorting to finite difference method. The proposed methods are verified with synthetic data and then applied to field vibration test data.
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fast bayesian ambient Modal Identification in the frequency domain part ii posterior uncertainty
Mechanical Systems and Signal Processing, 2012Co-Authors: Siukui AuAbstract:Abstract This paper investigates the determination of the posterior covariance matrix of Modal parameters within the framework of a Bayesian FFT approach for Modal Identification using ambient vibration data. The posterior covariance matrix is approximated by the inverse of the Hessian of the negative log-likelihood function (NLLF) with respect to the Modal parameters. To suppress the growth of computational effort with the number of measured dofs, a condensed form of the NLLF is derived that only involves matrix computation of dimension equal to the number of modes. Issues associated with the singularity of the Hessian due to mode shape scaling are discussed and a strategy is presented to properly evaluate its inverse. The theory described in Parts I and II of this work is applied to Modal Identification using synthetic and field data with a moderate to large number of measured dofs. It is demonstrated that using the proposed method Bayesian Modal Identification can be performed in a matter of seconds in typical cases, which is otherwise prohibitive based on the original formulation.
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fast bayesian ambient Modal Identification in the frequency domain part i posterior most probable value
Mechanical Systems and Signal Processing, 2012Co-Authors: Siukui AuAbstract:Abstract A Bayesian theory for Modal Identification using the fast Fourier transform (FFT) of ambient vibration data has been formulated previously. It provides a rigorous means for obtaining Modal properties as well as their uncertainties by operating in the frequency domain, which allows a natural partitioning of information according to frequencies. Since there is a one-to-one correspondence between the time-domain data and its FFT, the method can make full use of the relevant information contained in the data. In the context of Bayesian inference, the Identification results are in terms of a posterior distribution given the data, which can be characterized by the most probable value and covariance matrix. Determining these quantities, however, requires solving a numerical optimization problem whose dimension grows with the number of measured degrees of freedom; and whose objective function involves repeated inversion of ill-conditioned matrices. These have so far made the approach impractical for applications. For well-separated modes, an efficient algorithm has been developed recently. As a sequel to the development, this work considers the general case of multiple, possibly close modes. This paper focuses on the most probable values and develops an efficient iterative procedure for their determination. Asymptotic behavior of the Modal Identification problem is also investigated for high signal-to-noise ratios. The companion paper focuses on the posterior covariance matrix and applies the proposed method to simulated and field data.
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fast bayesian fft method for ambient Modal Identification with separated modes
Journal of Engineering Mechanics-asce, 2011Co-Authors: Siukui AuAbstract:Previously a Bayesian theory for Modal Identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining Modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable Modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the Modal Identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to Modal Identification of two field buildings. Using the proposed algorithm, Bayesian Modal Identification can now be performed in a few seconds even for a moderate to large number of measurement channels.
Sriram Narasimhan - One of the best experts on this subject based on the ideXlab platform.
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a review of output only structural mode Identification literature employing blind source separation methods
Mechanical Systems and Signal Processing, 2017Co-Authors: Ayan Sadhu, Sriram Narasimhan, Jerome AntoniAbstract:Abstract Output-only Modal Identification has seen significant activity in recent years, especially in large-scale structures where controlled input force generation is often difficult to achieve. This has led to the development of new system Identification methods which do not require controlled input. They often work satisfactorily if they satisfy some general assumptions – not overly restrictive – regarding the stochasticity of the input. Hundreds of papers covering a wide range of applications appear every year related to the extraction of Modal properties from output measurement data in more than two dozen mechanical, aerospace and civil engineering journals. In little more than a decade, concepts of blind source separation (BSS) from the field of acoustic signal processing have been adopted by several researchers and shown that they can be attractive tools to undertake output-only Modal Identification. Originally intended to separate distinct audio sources from a mixture of recordings, mathematical equivalence to problems in linear structural dynamics have since been firmly established. This has enabled many of the developments in the field of BSS to be modified and applied to output-only Modal Identification problems. This paper reviews over hundred articles related to the application of BSS and their variants to output-only Modal Identification. The main contribution of the paper is to present a literature review of the papers which have appeared on the subject. While a brief treatment of the basic ideas are presented where relevant, a comprehensive and critical explanation of their contents is not attempted. Specific issues related to output-only Modal Identification and the relative advantages and limitations of BSS methods both from theoretical and application standpoints are discussed. Gap areas requiring additional work are also summarized and the paper concludes with possible future trends in this area.
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decentralized Modal Identification of a pony truss pedestrian bridge using wireless sensors
Journal of Bridge Engineering, 2014Co-Authors: Ayan Sadhu, Sriram Narasimhan, Arndt GoldackAbstract:Most of the vibration-based ambient Modal Identification methods in the literature are structured to process vibration data collected from a dense array of sensors centrally to yield Modal information. For large systems, for example bridges, one of the main disadvantages of such a centralized architecture is the cost of dense instrumentation, predominantly consisting of the sensors themselves, the data acquisition system, and the associated cabling. Recent advances in wireless smart sensors have addressed the issue of sensor cost to some extent; however, most of the algorithms—with the exception of very few—still retain an essentially centralized architecture. To harness the full potential of decentralized implementation, the authors have developed a new class of algorithms exploiting the concepts of sparsity (using wavelet transforms) within the framework of blind source separation. The problem of Identification is cast within the framework of underdetermined blind source separation invoking transformations of measurements to the wavelet domain resulting in a sparse representation. Although the details of these decentralized algorithms have been discussed in other articles, in this paper, for the first time, these algorithms are studied experimentally on a full-scale structure using wireless sensors. In a truly decentralized implementation, only two sensors are roved along the length of a pedestrian bridge, and the performance of the proposed algorithms is studied in detail. A pedestrian bridge located in Montreal, Quebec, Canada, is chosen primarily to highlight the methodology used to address Modal Identification under low-sensor density and for pedestrian loading. Issues arising from several modes being excited on this bridge and the presence of narrowband pedestrian excitations are addressed. The accuracy of Modal Identification that is achieved using the proposed decentralized algorithms is compared with the results obtained from their centralized counterparts.
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decentralized Modal Identification of structures using parallel factor decomposition and sparse blind source separation
Mechanical Systems and Signal Processing, 2013Co-Authors: Ayan Sadhu, Budhaditya Hazra, Sriram NarasimhanAbstract:Abstract In this paper, a novel decentralized Modal Identification method is proposed utilizing the concepts of sparse blind source separation (BSS) and parallel factor decomposition. Unlike popular ambient Modal Identification methods which require large arrays of simultaneous vibration measurements, the decentralized algorithm presented here operates on partial measurements, utilizing a sub-set of sensors at-a-time. Mathematically, this leads to an underdetermined source separation problem, which is addressed using sparsifying wavelet transforms. The proposed method builds on a previously presented concept by the authors, which utilizes the stationary wavelet packet transform (SWPT) to generate an over-complete dictionary of sparse bases. However, the redundant SWPT can be computationally intensive depending on the bandwidth of the signals and the sampling frequency of the vibration measurements. This issue of computational burden is alleviated through a new method proposed here, which is based on a multi-linear algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the Modal responses. The underdetermined source identifiability of PARAFAC enables source separation in wavelet packet coefficients with considerable mode mixing, thereby relaxing the conditions to generate over-complete bases, thus reducing the computational burden. The proposed method is validated using a series of numerical simulations followed by an implementation on recorded ambient vibration measurements obtained from the UCLA factor building.
