Data-driven methods for operational modal parameters identification: A comparison and application (original) (raw)
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Applied Mechanics and Materials, 2011
Since the level of vibration always depends on the natural frequencies of the system, it is important to know the modal parameters of such system to control failure and provide prevention actions. However, for many mechanical engineering machines or structures, there is a demand and necessity to determine real-life modal parameters using actual operating condition. This type of testing condition cannot be done in lab environment because most of the mechanical structure is big in size and heavy. Thus, the purpose of this paper is to study the natural frequencies of a steel plate by using Operational Modal Analysis (OMA) and Ibrahim Time Domain (ITD). Comparison of results between both approaches will be shown.
Structural Identification from Operational Modal Analysis: The Case of Steel Structures
Buildings
In the case of old existing structures where the cultural value is very high, structural health analyses and investigations would be better performed without damages or service interruptions. Thus, modal analysis aimed at identifying eigenfrequencies and eigenmodes represents a very effective strategy to identify structural characteristics. In this paper, an innovative strategy to identify structural parameters exploiting the modal information obtained from operational modal analysis is proposed. The importance of the structural modeling in the problem formulation is highlighted. In the case of a simply supported beam, it was possible to assess the beam steel elastic modulus, while in the case of a cantilever beam, some constraint characteristics have been evaluated as well. In the steel frame case, the focus was on the constraint conditions of the structure determining the flexural stiffness of the springs representing the column base constraints. The method performances are promis...
Earthquake Engineering & Structural Dynamics, 2017
Output-only system identification is developed here towards assessing current modal dynamic properties of buildings under seismic excitation. Earthquake-induced structural response signals are adopted as input channels for two different Operational Modal Analysis (OMA) techniques, namely, a refined Frequency Domain Decomposition (rFDD) algorithm and an improved Data-Driven Stochastic Subspace Identification (SSI-DATA) procedure. Despite that short-duration, non-stationary, earthquake-induced structural response signals shall not fulfil traditional OMA assumptions, these implementations are specifically formulated to operate with seismic responses and simultaneous heavy damping (in terms of identification challenge), for a consistent estimation of natural frequencies, mode shapes, and modal damping ratios. A linear ten-storey frame structure under a set of ten selected earthquake base-excitation instances is numerically simulated, by comparing the results from the two identification methods. According to this study, best up-to-date, reinterpreted OMA techniques may effectively be used to characterize the current dynamic behaviour of buildings, thus allowing for potential Structural Health Monitoring approaches in the Earthquake Engineering range.
A review of operational modal analysis techniques for in-service modal identification
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2020
Vibrations are the root cause of many mechanical and civil structure failures. Dynamic characteristics of a structure must be extracted to better understand structural vibrational problems. Modal analysis is used to determine the dynamic characteristics of a system like natural frequencies, damping ratios and mode shapes. Some of the applications of modal analysis include damage detection, design of a structure/machine for dynamic loading conditions and structural health monitoring. The techniques used for modal analysis are experimental modal analysis (EMA), operational modal analysis (OMA) and a less known technique called impact synchronous modal analysis (ISMA), which is a new development. EMA is performed in simulated controlled environment, while OMA and ISMA are performed when the system is in operation. Although EMA is the oldest modal analysis technique, there is an increasing interest in operational modal analysis techniques in recent years. In this paper, operational modal analysis techniques OMA and ISMA are reviewed with their development over the years and their pros and cons discussed.
Neural network based modal identification of structural systems through output-only measurement
This paper proposes the application of neural networks for output-only modal identification of structural systems. Four frequency-dependent indicators, based on specific properties of the spectral tensor of vibration measurements, are defined and employed to build a likelihood function for the presence of structural resonances. Subsequently an artificial neural network (ANN), fed with the four indexes, was built and adopted to assess structural eigenvalues and eigenmodes. The proposed technique was tested on a three-storey steel-frame. After training the trained ANN was able to assess eigenvalues and eigenmodes, as demonstrated by comparison of the obtained results with those provided by literature methods.
A novel identification procedure from ambient vibration data
Meccanica, 2020
Ambient vibration modal identification, also known as Operational Modal Analysis, aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., no initial excitation or known artificial excitation. This procedure for testing and/or monitoring historic buildings, is particularly attractive for civil engineers concerned with the safety of complex historic structures. However, since the external force is not recorded, the identification methods have to be more sophisticated and based on stochastic mechanics. In this context, this contribution will introduce an innovative ambient identification method based on applying the Hilbert Transform, to obtain the analytical representation of the system response in terms of the correlation function. In particular, it is worth stressing that the analytical signal is a complex representation of a time domain signal: the real part is the time domain signal itself, ...
Operational Modal Parameter Estimation from Short-Time Data Series
Conference Proceedings of the Society for Experimental Mechanics Series, 2015
Operational Modal Analysis (OMA) is a technique of extracting modal parameters of a system from output responses only. It is an emerging field in structural dynamics and has been applied to complex structures that are often difficult to analyze using traditional Experimental Modal Analysis (EMA) techniques. Since the input information is unavailable in OMA, the technique makes use of certain assumptions about the input excitation to the system and the data processing methods used by current OMA algorithms are based on these assumptions. However, in some real-world scenarios not only the forcing function to the system violates these assumptions but also the time data series of system response is short in length and buried under noise. In such cases, ensemble averaging techniques for filtering out noise are rendered ineffective and the current OMA algorithms which utilize power spectrum and correlation functions result in inconsistent modal parameters, especially modal damping. This research develops a time domain operational modal parameter estimation (MPE) method based on describing the total system response as a Nonlinear Auto Regressive process with eXogenous input (NARX) wherein the linear part of the model describes the response of the structure and the nonlinear terms fit the noise present in data series. The method is developed in line with the concept of Unified Matrix Polynomial Approach (UMPA) and utilizes a set of least squares solutions to compute modal parameters.
Methods for identifying models of complex structures using information from measured vibrations
University of Thessaly, 2009
This thesis concentrates on the development and validation of methods for identifying dynamic models of complex structures as well as predicting fatigue damage accumulation by exploiting measured vibration information. The identified models refer to mathematical modal models as well as linear finite element models of structures, while the applications cover mainly ground/air vehicles and civil structures. The thesis is divided into three interrelated parts. Part A: Least-squares optimization methods are introduced for identifying non-classically damped modal models of complex structures using (1) output response measurements obtained from measured excitations at multiple support, and (2) output-only ambient vibration measurements. In the first case, a common structure of the time and frequency formulations is revealed and exploited to develop an identification software common for both formulations. The measure of fit represents the difference between the measured response time histories (or their Fourier transform) and the response time histories (or their Fourier transforms) predicted by a modal model when subjected to multiple support measured excitations. In the second case, the measure of fit represents the difference between measured and modal model predicted cross power spectral density functions. Computationally efficient two-step and three-step algorithms are developed to solve the resulting highly non-convex nonlinear optimization problems and identify the modal characteristics such as number of contributing models, modal frequencies, modal damping ratios, modeshapes and modal participation factors or operational reference vectors. The two-step approach is a very fast and accurate non-iterative algorithm, involving solution of two linear systems and singular value decomposition operations for estimating the modal characteristics. The third step solves the original nonlinear optimization problem using the estimates from the two-step approach to notably accelerate convergence of gradient based optimization algorithms. It is demonstrated that the third step is required only for closely spaced and overlapping modes to improve the estimates of the modal characteristics. The proposed methodology automates the estimation of the modal characteristics without, or with minimal, user interference and thus is especially applicable to continuous, real-time, structural health monitoring purposes. Part B: The problem of finite element structural model updating and response prediction variability based on measured modal characteristics is revisited. The correspondence between the recently proposed multi-objective identification, the conventional single-objective weighted residuals identification and the Bayesian statistical identification is established. These methods result in multiple Pareto optimal finite element models. An optimally weighted modal residuals method is also proposed for selecting the most preferred Pareto optimal model. The variability of these optimal models depends on the model and measurement error and affects the variability in the response predictions. In particular, Bayesian statistical identification offers the advantage of quantifying the uncertainty in the Pareto optimal models and the response predictions. Theoretical and computational issues arising in multi-objective and single-objective identification are addressed, including issues related to estimation of global optima, convergence of the proposed algorithms, and identifiability. Hybrid methods are proposed to identify global optima and the normal boundary intersection method is adopted to efficiently estimate the Pareto front and the Pareto optimal models. Finally, computational efficient algorithms are developed for estimating the gradients and the Hessians of the single and multiple objectives based on Nelson’s method for finding the sensitivity of eigenproperties to model parameters. It is shown that the computation time for estimating the Pareto optimal models is independent of the number of model parameters involved. The simplified computation of the Hessians of the objectives is useful in the Bayesian asymptotic formulas quantifying the uncertainty in the Pareto optimal models. Particular emphasis is also given in generalizing the definition of objectives in model updating methods to face the severe problems of corresponding measured and model predicted modes encountered for closely spaced modes. Theoretical and computational issues are illustrated by applying the model updating methodologies to small-scale three-story laboratory steel building structure and small-scale vehicle structure using experimentally obtained modal data. Validation studies are performed to show the applicability of the methodologies, the advantages of the multi-objective identification, and the performance of the most preferred Pareto optimal model. The effect of model error uncertainty on model updating and model response prediction variability is assessed. Part C: A novel methodology is presented for estimating damage accumulation due to fatigue in the entire body of a metallic structure using output-only vibration measurements from a sensor network installed at a limited number of structural locations. Available frequency domain stochastic fatigue methods based on Palmgren-Miner damage rule, S-N fatigue curves on simple specimens subjected to constant amplitude loads, and Dirlik’s probability distribution of the stress range are used to predict the expected fatigue damage accumulation of the structure in terms of the power spectral density (PSD) of the stress processes. The PSD of stresses at unmeasured locations covering the entire body of the structure are estimated from the response time history measurements available at the limited measured locations using Kalman filter and a dynamic model of the structure. The accuracy of the Kalman filter predictions can be improved by integrating the model updating techniques developed in Part B. The effectiveness and accuracy of the proposed formulation is demonstrated using a multi-degree-of-freedom spring-mass chain model arising from structures that consist of members with uniaxial stress states.
Experimental Modal Analysis using Ambient and Earthquake Vibrations: Theory, Software, Applications
University of Thessaly, 2012
This thesis addresses the problem of identifying the modal properties of structures using vibration measurements. Modal identification methodologies are proposed based on vibration measurements induced by artificial, ambient or earthquake loads applied on the structure. A modal model of the structure is identified using a weighted least-squares approach and measured time histories at selected locations of a structure. For artificially induced and ambient vibration measurements, the identification is performed in the frequency domain using respectively frequency response functions and cross power spectral densities. For earthquake induced vibrations, the identification is performed in both time and frequency domains. The modal identification methods presented in this work treat generalized non-classically damped modal models. The identification of the modal parameter (modal frequencies, modal damping ratios, modeshape components and modal participation factors) is accomplished by introducing a computationally very efficient three step approach as follows. In the first step, stabilization diagrams are constructed containing frequency and damping information. The modeshape components and participation factors are estimated in a second least-squares step, based on the user selection of the stabilized poles. The first two steps involve non-iterative procedures and result in solving linear algebraic systems of equations. Finally, in order to improve the estimation of the modal characteristics, especially for the challenging case of closely spaced and overlapping modes, a third step is introduced to solve a fully nonlinear optimization problem using available iterative gradient-based optimization algorithms. In this thesis, theoretical developments as well as software implementation issues are presented. The methodologies and software developed are applied for the identification of the modal characteristics of a small laboratory structure for the case of artificial induced vibration measurements, as well as the identification of the modal characteristics of three bridges, the under construction R/C bridge of Egnatia Odos located at Metsovo (Greece), and two other representative R/C bridges of Egnatia Odos located at Polymylos and Kavala (Greece) for the cases of ambient and earthquake induced vibration measurements. Results provide qualitative and quantitative information on the dynamic behaviour of the systems and their components under different types of excitations. All modal identification methodologies presented in this work are implemented in user-friendly software, termed Modal Identification Tool (MITooL). The software which includes graphical user interface allows the full exploration and analysis of signals that are measured on a structure when it is excited by artificial, ambient or earthquake loads. A user manual is also presented which gives details for the operations and prospects of the MITooL software. Step-by-step examples of modal identification are presented to demonstrate the applicability of the software.
Accurate Damping Estimation by Automated OMA Procedures
Conference Proceedings of the Society for Experimental Mechanics Series, 2013
Systems and techniques for fast damage detection based on vibration analysis are becoming very attractive in different engineering fields. Modal-based damage detection algorithms are well-known techniques for structural health assessment. However, the lack of automated modal identification and tracking procedures has been for long a relevant limit to their extensive use. The development of several automated output-only modal identification procedures in the last few years has led to a renewed interest in modal-based damage detection. However, robustness of automated modal identification algorithms, computational efforts and reliability of modal parameter estimates (in particular, damping) still represent open issues. In this paper, a novel algorithm for automated output-only modal parameter estimation is adopted to obtain reliable and very accurate modal parameter estimates. An extensive validation of the algorithm for continuous monitoring application is carried out based on simulated data. The obtained results point out that the algorithm provides fairly robust, accurate and precise estimates of the modal parameters, including damping ratios. This may potentially lead to a standardized, extensive characterization of modal damping ratios in structures, which is useful to gain knowledge about damping mechanisms in structures and to develop predictive models.