The design and assessment of structural dynamics behaviour often rely on the ‘modal properties’ (primarily modal frequencies, damping ratios and mode shapes) of a structure. Modal properties are frequently identified in vibration related applications as their information can benefit design theory validation and in-situ property updating and monitoring. Given the prospect of flexibility and high implementation economy, operational modal analysis (OMA) aims to identify the modal properties using only ambient vibration response whose amplitude can be small. When instrument noise becomes a non-negligible part of measured data, the identified result can have significant uncertainty, calling for proper uncertainty quantification. Amidst the complex composition of ambient vibration data of civil structures, conventional noise assumption may not always apply. Motivated by issues about uncertainty modelling and computation, this thesis contributes to the theory and computational algorithm of OMA from a Bayesian perspective in the frequency domain. Focusing on the resonance band of vibration modes, a Bayesian probabilistic approach provides a fundamental mathematical framework for OMA. The ‘posterior’ (i.e., given data) most probable value (MPV) of modal properties maximising the likelihood of data informs about the best estimate. The uncertainty associated with the estimate is quantified by the posterior covariance matrix, which can be calculated as the inverse of the Hessian of negative log-likelihood function (NLLF) at the MPV. Existing formulations assume independent and identically distributed (i.i.d.) prediction errors among different channels, which account for both instrument noise and modelling error. While the assumption significantly simplifies theory and computation, and may not matter when the signal-to-noise (s/n) ratio is high, it is prone to be violated in OMA. For example, large disparity among noise intensities may exist, and significant correlation can occur because of the presence of unmodelled dynamics, which may affect identification results. To understand and manage the consequence of these potential violations, a comprehensive investigation on the effect of prediction error models with different statistical assumptions is presented in this work. Beyond the i.i.d. assumption, two generalised prediction error models have been considered to account for the disparity and correlation that may arise in applications. Such investigation was previously hindered by computational issues because the general prediction error models feature more parameters carrying somewhat different mathematical roles from the existing ones, making the computation of posterior MPV and covariance matrix more challenging in the first place. As a contribution to computation and enabling scientific investigation, new efficient algorithms applicable to general prediction error models are developed in this work for their computation. As a contribution to theory, a mathematical analogy for general noise is established with i.i.d. model for OMA problems. Not only does this provide a simple approximate way for handling general noise with existing tools based on i.i.d. assumption, it also allows the understanding and experience accumulated with i.i.d. model to be generalised. As a spin-off of this opportunity, asymptotic formulae for identification uncertainty are developed for general prediction error models in this work, which yield a generalised definition for s/n ratio that provides a fundamental quantification of data quality in OMA. The theory and algorithms are developed and tested against synthetic, laboratory and field data. As a further contribution to computation, motivated by existing overheads and hurdles in computer code development, this work proposes an alternative semi-analytical means for calculating the Hessian of NLLF in OMA. The proposed method explores a mathematical identity in the theory of expectation-maximisation (EM) algorithm to allow the Hessian matrix to be calculated via Monte Carlo simulation, which offers an alternative means for counter-checking/benchmarking during computer code development. Theoretical implications of the identity are also explored, and numerical examples are presented to illustrate implementation aspects.
Counter-checking uncertainty calculations in Bayesian operational modal analysis with EM techniques
Counter-checking uncertainty calculations in Bayesian operational modal analysis with EM techniques
21Asymptotic identification uncertainty of well-separated modes in operational modal analysis with multiple setups
Asymptotic identification uncertainty of well-separated modes in operational modal analysis with multiple setups
32SSI-LSTM network for adaptive operational modal analysis of building structures
SSI-LSTM network for adaptive operational modal analysis of building structures
2Signal Processing for Operational Modal Analysis of a Jacket-Type Offshore Platform: Sea Test Study
Operational modal analysis (OMA) has been widely used for large structures. However, measured signals are inevitably contaminated with noise and may not be clean enough for identifying the modal parameters with proper accuracy. The traditional methods to estimate modal parameters in noisy situation are usually absorbing the “noise modes” first, and then using the stability diagrams to distinguish the true modes from the “noise modes.” However, it is still difficult to sort out true modes because the “noise modes” will also tend to be stable as the model order increases. This study develops a noise reduction procedure for polyreference complex exponential (PRCE) modal analysis based on ambient vibration responses. In the procedure, natural excitation technique (NExT) is first applied to get free decay responses from measured (noisy) ambient vibration data, and then the noise reduction method based on solving the partially described inverse singular value problem (PDISVP) is implemented to reconstruct a filtered data matrix from the measured data matrix. In our case, the measured data matrix is block Hankel structured, which is constructed based on the free decay responses. The filtered data matrix should maintain the block Hankel structure and be lowered in rank. When the filtered data matrix is obtained, the PRCE method is applied to estimate the modal parameters. The proposed NExT-PDISVP-PRCE scheme is applied to field test of a jacket type offshore platform. Results indicate that the proposed method can improve the accuracy of OMA.
Read more147Fast Bayesian ambient modal identification in the frequency domain, Part II: Posterior uncertainty
Fast Bayesian ambient modal identification in the frequency domain, Part II: Posterior uncertainty
22Modal properties of floating wind turbines: Analytical study and operational modal analysis of an utility-scale wind turbine
Structural health monitoring through Operational Modal Analysis based on output-only methods has already a long term successful history of applications in conventional civil engineering structures and, more recently, onshore and offshore bottom fixed wind turbines. Although the former application has been proven as a reliable and relevant source of information regarding the dynamic response of the structure and ultimately in the definition of operation strategies, its application to floating offshore structures is yet to be explored, a gap that is tackled in this work. Since the introduction of a floating device, typically associated with very low frequency motions, impacts the relevant modal properties for the tower design, a preliminary and simplified analytical approach is presented, where these effects are properly characterised. The derived expressions, that are ready for design purposes, are validated based on numerical simulations in OpenFAST. After that, experimental data from a full scale floating wind turbine is used as input for Operational Modal Analysis for the first time. Here, not only some key features that are intrinsically associated with these type of structures are unveiled, but also the applicability of output-only methods for dynamic identification is confirmed.
Read more3Multi-channel sub-Nyquist cross-spectral estimation for modal analysis of vibrating structures
Operational modal analysis (OMA) is a widely used construction verification and structural health monitoring technique aiming to obtain the modal properties of vibrating civil engineering structures subject to ambient dynamic loads by collecting and processing structural response acceleration signals. Motivated by the need for cost-efficient OMA using wireless sensor networks which acquire and transmit measurements at a lower than the Nyquist rate, a novel OMA approach is put forth to derive modal properties directly from sub-Nyquist sampled (compressed) acceleration measurements from arrays of sensors. This is achieved by adopting sub-Nyquist deterministic non-uniform multi-coset sampling devices and by extending a previously proposed in the literature power spectrum blind sampling method for single-channel spectral estimation of stochastic processes to treat the case of multiple channel cross-spectral estimation. The standard frequency domain decomposition is used to obtain the modal properties from the cross-spectral matrix derived directly from the sub-Nyquist measurements. The applicability and efficiency of the proposed approach is exemplified by retrieving mode shapes of a white-noise excited simply supported steel beam with good accuracy according to the widely used modal assurance criterion using 70% less than the Nyquist rate measurements.
Read more1A novel mode shape identification approach for structures having planes with rigid-like behavior
A novel mode shape identification approach for structures having planes with rigid-like behavior
208Bayesian operational modal analysis: Theory, computation, practice
Bayesian operational modal analysis: Theory, computation, practice
18Data Normalization and Anomaly Detection in a Steel Plate-Girder Bridge Using LSTM
Modal properties are recognized as indicators reflecting structural condition in structural health monitoring (SHM). However, changing environmental and operational variables (EOVs) cause variability in the identified modal parameters and subsequently obscure damage effects. To address the issue caused by EOV-related variability, this study investigated the variability of modal frequencies in long-term SHM of a steel plate-girder bridge. A Bayesian fast Fourier transform (FFT) method was used for operational modal analysis in a probabilistic viewpoint. Bayesian linear regression (BLR) and Gaussian process regression (GPR) models were utilized to capture the variability in the identified most probable values (MPVs) of modal frequencies as temperature-driven models, and the limitation of these models for data normalization with latent EOVs is discussed. To overcome the interference of latent EOVs indirectly, a long short-term memory (LSTM) network was established to trace the variability as an autocorrelated process, with a traditional seasonal autoregressive integrated moving average (SARIMA) model as a benchmark. Finally, an anomaly detection method based on residuals of one-step-ahead predictions by LSTM was proposed associating with the Mann-Whitney U-test.
Read more26Contributions for enhanced tracking of (onshore) wind turbines modal parameters
Contributions for enhanced tracking of (onshore) wind turbines modal parameters
23Generalizing I-Vector Estimation for Rapid Speaker Recognition
An i-vector is a compact representation that captures both the speaker and session variabilities rendered in a spoken utterance. Over the past years, it has prevailed over other techniques and is now the de facto representation for text-independent speaker recognition. Standard i-vector extraction requires intense computation at run-time. Reducing the computation will allow effective use of i-vector in more applications. Such intense computation arises from the posterior covariance matrix, when estimating the i-vector. There have been studies on how to simplify the computation of posterior covariance matrix with modest success. In this paper, we propose a novel approach to i-vector extraction without the need to evaluate the full posterior covariance thereby speeding up the run-time extraction process. This is achieved by generalizing the i-vector estimation in two ways. First, we introduce the use of occupancy reweighting in conjunction with whitening over the Baum-Welch statistics as part of the preprocessing step. Second, we introduce the so-called subspace-orthogonalizing prior (SOP) to replace the standard Gaussian prior in i-vector formulation. Experiments conducted on the extended-core task of NIST SRE'10 show that the proposed rapid SOP approach achieves considerable speed-up over the standard i-vector with comparable equal error rates.
Read more20Modal identification of a machine tool structure during machining operations
The identification of modal parameters of a machine tool structure, in service, is important to ensure stability and productivity during machining operations. The characterization can be carried out through an Operational Modal Analysis (OMA). However, in the presence of strong harmonic excitation, the application of OMA is not straightforward. To overcome this difficulty, the Transmissibility Function-Based (TFB) method is proposed. The major advantage of this approach is its independence from the excitation nature and its ability to separate structural poles from spurious ones. The main novelty of this paper lies in the investigation of the TFB approach to identify the modal properties of a machine tool, during machining operations. Identified modal model through an Experimental Modal Analysis (EMA) of the considered machine tool, at rest, presents our reference modal base to validate results obtained through the TFB approach. For a comparison purpose, the modified Enhanced Frequency Domain Decomposition (EFDD) method is also investigated. Both methods enable the identification of the modal properties under operational conditions, with a clear advantage to the TFB approach due to its ability to eliminate all of the preponderant harmonic components from the measured data without the need of any additional selection criteria. The TFB method is thus a reliable technique for the identification of modal parameters of a machine tool in operational conditions.
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17Structural Identification of a 90 m High Minaret of a Landmark Structure under Ambient Vibrations
This paper presents the operational modal analysis of a 90-m-high RC minaret of an iconic mosque considered as a landmark of the city. The minaret was monitored for three days with 11 tri-axial MEMS accelerometers. The purpose of the study was to observe the behavior, develop a representative finite element (FE) model, and establish baseline data for health monitoring studies. The modal properties were extracted using three operational modal analysis techniques (OMA): Enhanced Frequency Domain Decomposition (EFDD), Stochastic Subspace Identification (SSI), and Natural Excitation Technique with Eigensystem Realization Algorithm (NExT-ERA). The first 10 identified modes were below 7 Hz. Eight modes out of the ten were bending-dominant, while the remaining two were torsion-dominant. A FE model was also developed in ETABS to ascertain and compare the response of the structure with the identified results. From the FE model, the modes corresponding to the first ten identified modes were considered for comparison with the identified frequencies from ambient monitoring. The maximum 7.71% error was observed between the experimental and numerical frequencies. The error was minimized by using the manual updating the material properties and adding the weight of nonstructural elements. The variation of identified modal frequencies with ambient temperature was observed to be linearly dependent to a reasonable degree. A general trend of decreasing identified frequencies was observed with the rise in temperature.
Read more18The use of operational modal analysis and mode tracking for insight into polar vessel operations
The use of operational modal analysis and mode tracking for insight into polar vessel operations
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