Modal identification of a machine tool structure during machining operations

This paper investigates the use of conventional operational modal analysis (OMA) techniques for modal parameters identification of a rotating system supported by roller bearings. Although largely applied in civil engineering, in-depth studies on different types of systems are still limited in the literature. The novel of the paper is to address such issue by applying conventional OMA methods, such as enhanced frequency domain decomposition (EFDD) and stochastic subspace identification (SSI-data), to identify the modal parameters of a rotating machine, investigating the challenging particularities of these systems due to their inherent operating conditions, especially regarding the presence of harmonic forces, eventually closed-spaced modes, and non-proportional damping due to the bearings. The results presented in the experimental tests showed that, with the use of specific tools, in comparison with traditional experimental modal analysis (EMA), the used OMA methods have managed to successfully identify the modal parameters of a roller bearing supported rotor.

Operational Modal Analysis (OMA) is a methodology to obtain the modal properties of a structure using the dynamical responses of the system only. That methodology is very useful in aeroelastic in-fligh testing where there are difficulties in measuring directly the aerodynamic loads on aircraft. For risk reduction in the future flight operations of the EOLO at ITA, wind-tunnel tests were performed. EOLO is an Unmanned Aerial Vehicle (UAV) with high aspect ratio and structural flexibility, designed to study aeroelastic phenomena and to evaluate the interaction of flexible effects with the aircraft flight dynamics. In this work The Frequency Domain OMA techniques: Decomposition (FDD), Enhanced Frequency Domain Decomposition (EFDD), Spatial and Frequency Domain Decomposition (SFDD) are applied to the vibrational data from wing tunnel test campaign in different operation conditions, using acceleration and strain measurements. The results between the OMA techniques are compared with previous modal characterization from Ground Vibration Test (GVT) and numerical aeroelastic analysis. The different generations of the frequency domain decomposition methods proved their suitability for use in aircraft aeroelastic characterization using accelerations and strain measurements.

Contributions for enhanced tracking of (onshore) wind turbines modal parameters

In recent years, theoretical and experimental efforts have transformed the conventional tilting-pad journal bearing (TPJB) into a smart mechatronic machine element. The application of electromechanical elements into rotating systems makes feasible the generation of controllable forces over the rotor as a function of a suitable control signal. The servovalve input signal and the radial injection pressure are the two main parameters responsible for dynamically modifying the journal oil film pressure and generating active fluid film forces in controllable fluid film bearings. Such fluid film forces, resulting from a strong coupling between hydrodynamic, hydrostatic and controllable lubrication regimes, can be used either to control or to excite rotor lateral vibrations. If non-invasive forces are generated via lubricant fluid film, in situ parameter identification can be carried out, enabling evaluation of the mechanical condition of the rotating machine. Using the lubricant fluid film as a non-invasive calibrated shaker is troublesome, once several transfer functions among mechanical, hydraulic and electronic components become necessary. In this framework the main original contribution of this paper is to show experimentally that the knowledge about the several transfer functions can be bypassed by using output-only identification techniques. The manuscript links controllable (active) lubrication techniques with operational modal analysis, allowing for in-situ parameter identification in rotordynamics, i.e. estimation of damping ratio and natural frequencies. The experimental analysis is carried out on a rigid rotor-level system supported by one single pair of pads. The estimation of damping and natural frequencies is performed using classical experimental modal analysis (EMA) and operational modal analysis (OMA). Very good agreements between the two experimental approaches are found. Maximum values of the main input parameters, namely servovalve voltage and radial injection pressure, are experimentally found with the objective of defining ranges of non-invasive perturbation forces.

Safety assessment of structures for near-field blast-induced ground excitations using operational modal analysis

A recent development in operational modal analysis (OMA) is the possibility of using measured, artificial loads in addition to the unmeasured, ambient excitation, while the ratio between forced and ambient excitation can be low compared to classical experimental modal analysis (EMA). Most of these so-called OMAX algorithms lack the intuitiveness of their EMA and OMA counterparts, since they fit a system model that takes both the measured and the operational excitation into account directly to the measured signals. A more physically intuitive subspace algorithm for OMAX, that starts with an accurate decomposition of the measured joint response in a forced and an ambient part, was recently introduced. In this paper, the performance of this algorithm, which is called CSI-ic/ref, is assessed by means of a case study, where a two-span steel arch footbridge is tested in operational conditions, with and without using additional actuators. From a comparison of the modal parameters with results from a finite elementmodel, an OMA algorithm, and an alternative OMAX algorithm, it can be concluded that CSI-ic/ref yields accurate modal parameter estimates.KeywordsMode ShapeModal ParameterBridge DeckModal Assurance CriterionExperimental Modal AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

Over the last 50 years, data from laboratory tests and post-earthquake reconnaissance have been used to gain knowledge about the dynamic and seismic behavior of geotechnical structures and to improve analysis and design procedures. The scarcity of reconnaissance data has pointed out the need for full-scale and near full-scale tests for research purposes in earthquake engineering. Structural health monitoring (SHM) systems have been applied to different kinds of structures, but although static control of displacements and pressures is quite common, dynamic monitoring is fairly limited in geotechnical engineering. In the present paper, an integrated structural and geotechnical monitoring program aimed at filling this knowledge gap is described with reference to a real flexible retaining wall. The objective of the research is to establish a combination of sensors, numerical analyses, and data processing procedures to turn the monitored retaining wall into a smart geotechnical structure. Attention is herein focused on two aspects related to the implementation of the monitoring system and the dynamic identification of the soil-structure system. Specifically, the paper describes an example of seismic monitoring system for full-scale flexible retaining walls based on sensors embedded in the reinforced concrete piles. Installation details are given together with a description of the monitoring system architecture in its current stage of implementation. Issues and requirements for the measurement chain are discussed, taking into account possible installation drawbacks (i.e., shocks) and the opportunity to monitor the response under operational conditions. Furthermore, a novel and successful application of operational modal analysis (OMA) to such a complex geotechnical system is reported. It allows for the identification of the fundamental modes of the soil-wall system in operation (but before the erection of a building on the excavated side). Implementation of the monitoring system prototype is still in progress, but some interesting results have already been outlined.

Operational modal analysis based dynamic parameters identification in milling of thin-walled workpiece

Operational modal analysis (OMA) enables the identification of modal characteristics under operational loads and conditions. Traditional frequency-domain methods cannot directly capture modal changes over time, while existing time-frequency representations are not sufficiently interpretable due to spurious modes and implicit parameter design. This paper develops a new OMA method in time-frequency representation based on frequency-domain decomposition (FDD). Short-time FDD and a convolution-based strategy are proposed to obtain singular values and local mode shape similarity, respectively, which are further fused into mode indicators by a fuzzy-based strategy mimicking the modal assurance criterion. The method provides not only a global view of the modal characteristics over time and frequency but also estimates of the modal parameters. It is applicable to strongly nonstationary responses under time-varying loads and conditions. All the parameters explicitly affect the time-frequency representation, and the interpretability is enhanced by including physical information from the user’s prior knowledge in selecting parameters and peak bands. The proposed method is validated based on a study of railway sleepers under train passage. The rigid-body motions and bending modes are identified at frequencies up to 6,500 Hz in laboratory tests and 4,500 Hz in field tests at speeds up to 200 km/h. The identified natural frequencies and mode shapes agree with experimental modal analysis (EMA). The proposed method outperforms EMA in terms of broad frequency range and low measurement cost and can be potentially applied to structural health monitoring under operational conditions.

Stability of lateral rotordynamic modes is an essential consideration during design and acceptance testing of rotating machinery. Experimental modal analysis (EMA) can be used for assessment but is in practice very difficult in actual operating conditions, principally due to the challenges of quantifying the excitation force. Operational modal analysis (OMA) does not require measurement of excitation forces and therefore presents significant logistical advantages over EMA. The background and theoretical concepts of OMA are presented and its use is demonstrated on a 500 kW centrifugal compressor. Measurements performed during commissioning at first raised suspicion that the stability was marginal. However OMA was used to confirm that the first forward mode of the compressor was actually stable and the measurements were reconciled with the predicted behavior. The results show that the assessment of stability margins of rotating machinery can be measured with OMA using only proximity probe data acquired during normal operation.

Beam mode characterization by applying operational modal analysis to neutron detectors data

Structural safety assessment of bowstring type RC arch bridges using ambient vibration testing and finite element model calibration

The accuracy of modal parameter estimates from estimation methods built in the framework of experimental modal analysis (EMA) can be assessed by several methods provided the information of input loadings and output responses. However, a deeper investigation is necessary for estimation methods built in the operational modal analysis (OMA) framework to establish confidence boundaries for the modal parameter estimates. This paper aims to estimate uncertainties of the modal parameter estimates by testing the sensitivity of the damped natural frequencies, damping ratios, and mode shapes to the choice of the estimation method and data acquisition settings used in this method. The uncertainty estimates of the modal parameter estimates are tested for changes in the boundary conditions. The tests provide insights into tendencies for the accuracy of the modal parameter estimates when the boundary conditions provide a different set of “true” modal parameter values. A simple cantilever beam experimental setup is used to obtain benchmark modal parameter estimates from EMA that are used to estimate the accuracy of the modal parameter estimates from OMA. The method’s robustness in estimating uncertainties and accuracies for modal parameter estimates is tested for several independent experiments. The boundary conditions for the cantilever beam are changed to test the influence of altering modal parameter estimates on the estimated uncertainties and accuracies. The boundary conditions are changed using materials with different elastic properties and the connection pressure between the clamping device and beam. A method presented in Paulsen et al. (Proceedings of the 9th International Operational Modal Analysis Conference, IOMAC, 2022) calculates a representative modal parameter estimate from a set of modal parameter estimates based on weightings obtained from the modal assurance criterion. The method’s ability to reduce uncertainties and increase accuracies of the representative estimate is demonstrated by repeating a test setup ten times. The results present simultaneously a reduction of uncertainties and an increase of accuracies for the representative modal parameter when the weighting method is used. An evaluation of dependencies between the estimated uncertainties and accuracies finds a proportional relation for the damped natural frequency when the uncertainties are described as a relative standard deviation. The analysis presents higher accuracy for the damped natural frequency and mode shape estimates compared to the damping factor, and the accuracy of the damping factor is dependent on the actual value of the damping factor. These phenomena for accuracy are well known and indicate that the uncertainties of modal parameter estimates can be assessed through a sensitivity test of estimation methods and data acquisition parameters.

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.