Modal Parameter Estimation Research Articles

Dynamics-Based Stereo Visual Inspection Using Multidimensional Modal Analysis

This paper proposes the concept of multidirectional-modal-parameter-based visual inspection with high-frame-rate (HFR) stereo video analysis as a novel active sensing methodology for determining the dynamic properties of a vibrating object. HFR stereo video is used for observing the 3-D vibration distribution of an object under unknown excitations in the audio-frequency range, and the projections of the vibration displacement vectors along multiple directions can be verified using output-only modal analysis that can estimate their modal parameters such as resonant frequencies and mode shapes. Through implementing a fast output-only modal parameter estimation algorithm on a 10000-fps stereo vision platform, we developed a real-time multidirectional-modal-parameter-based visual inspection system; it can measure the 3-D vibration displacement vectors of 30 points on a beam-shaped object from 512 × 96 pixel stereo images at 10000 fps and can determine its resonant frequencies and mode shapes along 72 different directions around its beam axis as its input-invariant modal parameters. To demonstrate the performance of our system in modal-parameter-based visual inspection, the asymmetric dynamic properties, caused by cracks, of several steel beams vibrating at dozens of hertz and having artificial cracks were inspected in real time by determining the modal parameters along 72 directions around their beam axes.

Identification of modal parameters of non-stationary systems with the use of wavelet based adaptive filtering

The Operational Modal Analysis (OMA) is a common tool for identification of parameters of mechanical structures during operation. Modal analysis can be applied for linear, stationary and undamped systems or systems with small and proportional damping. To apply this technique to other systems, mainly to non-stationary systems, new procedures are required.The paper focuses on the application of time–frequency signal filtration to the recursive method of the modal parameters' identification based on operational measurements, dedicated for non-stationary systems. The presented technique uses an adaptive wavelet signal filtering method to separate signal components and reduce the model order. This approach considerably facilitates selection of the wavelet function parameters and significantly improves the quality of the separated modal components. Thanks to the reduction of model order, estimation of modal parameters can be performed using a relatively simple mathematical formula. This approach significantly reduces the demand for computing power which has a direct impact on system's costs and modal parameter's estimation time. This is particularly an important problem when the system parameters are changing rapidly and the information about this changes is required in real-time. The algorithm allows assessing the quality of the estimated parameters by simultaneous estimation of confidence bounds. The method has been tested on numerical models, experimental laboratory test rig and applied to real data.

Estimating the modal parameters from multiple measurement setups using a joint state space model

Computing the modal parameters of structural systems often requires processing data from multiple non-simultaneously recorded setups of sensors. These setups share some sensors in common, the so-called reference sensors, which are fixed for all measurements, while the other sensors change their position from one setup to the next. One possibility is to process the setups separately resulting in different modal parameter estimates for each setup. Then, the reference sensors are used to merge or glue the different parts of the mode shapes to obtain global mode shapes, while the natural frequencies and damping ratios are usually averaged. In this paper we present a new state space model that processes all setups at once. The result is that the global mode shapes are obtained automatically, and only a value for the natural frequency and damping ratio of each mode is estimated. We also investigate the estimation of this model using maximum likelihood and the Expectation Maximization algorithm, and apply this technique to simulated and measured data corresponding to different structures.

Parametric modal identification of time-varying structures and the validation approach of modal parameters

This paper investigates the problem of output-only modal parameter estimation of time-varying structures. A two-stage least square method for modal parameter estimation of time-varying structures is presented, consisting of a least square complex frequency-domain stage for the modal parameter estimation of all discrete time samples and a weighted least square stage for the estimation of continuous-time-represented modal parameters. This paper introduces a fuzzy-clustering-based approach for validating and sifting the modal parameters and develops four modal assurance criterion-based distance functions to improve the quality of clustering of operational mode shapes. Furthermore, the proposed method has been validated by a simulation example and a laboratory experiment.

Variability of Modal Parameter Estimations Using Two Different Output-Only System Identification Methods

Abstract Accurate damage identification in a structure depends on the accurate estimation of modal parameters; therefore, an important step in the vibration-based structural health monitoring process is the estimation of modal parameters. The purpose of this study was to investigate systematically the variability of identified modal parameters of a steel model bridge with low damping using simple statistical measures. In order to achieve this objective, first the modal parameters of an actual steel bridge were estimated using two different and widely used output-only system identification methods, the natural excitation technique with an eigensystem realization algorithm and enhanced frequency domain decomposition. Then a calibrated finite element model of the bridge was developed using the estimated modal parameters. Using the simulated data from the calibrated model, the variability of modal parameter estimations due to variability of the spatial sensor density, measurement/sensor noise, and response data length input factors was investigated. The input factors chosen are significant for the performance of the output-only system identification methods used and therefore are deemed important for accurate damage detection.

Operational modal analysis of a rectangular plate using non-contact excitation and measurement

Operational modal analysis (OMA), or output-only modal analysis, has been extensively developed in the past decades and widely used especially when the input is unknown and difficult to measure. This paper presents a non-contact experimental technique for measuring modal parameters of a rectangular aluminum plate with free boundaries using only the output data, with the intention to apply the technique to turbine blades. OMA is used to analyze both the out-of-plane and in-plane vibrations of the plate in the frequency range of up to 15,000Hz, which can be an operation frequency range of a turbine blade, under white noise acoustic excitation in a direction of interest. It is shown that OMA can be performed when the types of measurement at the measurement and reference points are different, since the associated cross-correlation functions contain modal characteristics of the test structure. A single-point laser vibrometer and a free-field microphone are used to simultaneously measure the responses of the plate in a non-contact manner, with the microphone measurement serving as the reference. The pressure measured by the microphone near the reference point is shown to be proportional to the normal surface acceleration at the reference point, and the cross power spectral densities obtained by the current test method can be used for modal parameter estimation. A method for measuring the in-plane modes of the plate by shining the laser beam on the plate surface with an incident angle is developed. Experimental modal analysis (EMA) is also performed on the plate using an impact hammer and the laser vibrometer. The measured natural frequencies and mode shapes of the out-of-plane and in-plane modes of the plate using OMA and EMA are compared with those calculated using commercial finite element software. The maximum error between the measured and calculated natural frequencies of the plate is 1.53 percent for the first 18 elastic modes, including 16 out-of-plane and two in-plane modes. The modal assurance criterion values between the corresponding measured and calculated mode shapes of the plate are all above 93 percent.

Estimation of CNC machine–tool dynamic parameters based on random cutting excitation through operational modal analysis

Dynamic properties of the whole machine tool structure including tool, spindle, and machine tool frame contribute greatly to the reliability of the machine tool in service and machining quality. However, they will change during operation compared with the results from static frequency response function measurements of classic experimental modal analysis. Therefore, an accurate estimation of the dynamic modal parameters of the whole structure is of great value in real time monitoring, active maintenance, and precise prediction of a stability lobes diagram.Operational modal analysis (OMA) developed from civil engineering works quite efficiently in modal parameters estimation of structure in operation under an intrinsic assumption of white noise excitation. This paper proposes a new methodology for applying this technique in the case of computer numerically controlled (CNC) machine tools during machining operations. A novel random excitation technique based on cutting is presented to meet the white noise excitation requirement. This technique is realized by interrupted cutting of a narrow workpiece step while spindle rotating randomly. The spindle rotation speed is automatically controlled by G-code part program, which contains a series of random speed values produced by MATLAB software following uniform distribution. The resulting cutting produces random pulses and excites the structure in all three directions. The effect of cutting parameters on the excitation frequency and energy was analyzed and simulated. The proposed technique was experimentally validated with two different OMA methods: the Stochastic Subspace Identification (SSI) method and the poly-reference least square complex frequency domain (pLSCF or PolyMAX) method, both of which came up with similar results. It was shown that the proposed excitation technique combined successfully with OMA methods to extract dynamic modal parameters of the machine tool structure.

Structural health monitoring with a distributed mass damper system

Recent developments of a distributed mass damper (DMD) system integrate structural and environmental control systems to improve building safety and energy efficiency. Such a system can also enhance Structural health monitoring (SHM) by using its multiple active mass dampers to excite the structure and analyze the resulting responses. SHM reliability depends on accurate estimations of structural characteristics from structural response measurements. However, some structural characteristics, such as structural modes, may not be well represented or identifiable depending on how structures are excited, thereby compromising the effectiveness of SHM. Utilizing combinations of the DMD's multiple active dampers to target structural modes of interest, the authors showed that damage detection in structures was significantly improved. In this paper, algorithms are derived for modal parameter estimations using the DMD system to excite the structure. Stiffness estimations and damage detections are then computed from the estimated model parameters. Harmonic excitations are used with the DMD system to target specific structural modes/frequencies and to amplify structural responses. Different configurations of excitations are then compared on the basis of the accuracy of stiffness estimations. A 20-story model structure is simulated with four damage patterns to demonstrate accurate damage detection. Copyright © 2013 John Wiley & Sons, Ltd.

Modal contribution and state space order selection in operational modal analysis

The estimation of modal parameters of a structure from ambient measurements has attracted the attention of many researchers in the last years. The procedure is now well established and the use of state space models, stochastic system identification methods and stabilization diagrams allows to identify the modes of the structure. In this paper the contribution of each identified mode to the measured vibration is discussed. This modal contribution is computed using the Kalman filter and it is an indicator of the importance of the modes. Also the variation of the modal contribution with the order of the model is studied. This analysis suggests selecting the order for the state space model as the order that includes the modes with higher contribution. The order obtained using this method is compared to those obtained using other well known methods, like Akaike criteria for time series or the singular values of the weighted projection matrix in the Stochastic Subspace Identification method. Finally, both simulated and measured vibration data are used to show the practicability of the derived technique. Finally, it is important to remark that the method can be used with any identification method working in the state space model.

Modal identification from nonstationary ambient response data using extended random decrement algorithm

The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm. If the ambient excitation can be modeled as a nonstationary white noise in the form of a product model, then the nonstationary cross randomdec signatures of structural response evaluated at any fixed time instant are shown theoretically to be proportional to the nonstationary cross-correlation functions, which is of the same form as the free-vibration decay or impulse response of the original system. The practical problem of insufficient data samples available for evaluating nonstationary randomdec signatures can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. However, the error involved in the approximate free-decay response would generally lead to a distortion in the modal identification. In the present paper, we also further propose that, if the ambient excitation can be modeled as a zero-mean nonstationary process, without any additional treatment of transforming the original nonstationary responses, the nonstationary cross randomdec signatures of structural response are shown in the same mathematical form as that of free vibration of a structure, from which modal parameters of the original system can thus be identified. Numerical simulations, including one example of using the practical excitation data, confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data only.

A comparative study on the identification of the dynamical model of multi-mass electrical drives using wavelet transforms

This paper deals with dynamical modelling and modal identification of a special class of electromechanical systems: the multi-mass electrical drives. The aim of the work is to investigate the usefulness and the performance of the continuous wavelet transform (CWT) for the estimation of modal parameters, such as damping ratios and natural frequencies of these electromechanical systems. For this investigation, two models of elastic drive systems are considered: the two-mass and the three-mass models. The modal analysis identification using CWT is compared to the Hilbert–Huang transform technique and evaluated in terms of accuracy and ability to estimate modal parameters with different inputs, aptitude to distinguish several modes especially in the case of closely spaced modes and resistance to noisy conditions. In view of the results of the study, the advantages and shortcomings of each technique are presented and discussed.

515 部分構造変更時の全系振動騒音予測技術の精度の検証 : 回転自由度整合のためのGuyan の静縮小とオーバーラップの誤差

515 部分構造変更時の全系振動騒音予測技術の精度の検証 : 回転自由度整合のためのGuyan の静縮小とオーバーラップの誤差

Modal parameter estimation using interacting Kalman filter

The focus of this paper is Bayesian modal parameter recursive estimation based on an interacting Kalman filter algorithm with decoupled distributions for frequency and damping. Interacting Kalman filter is a combination of two widely used Bayesian estimation methods: the particle filter and the Kalman filter. Some sensitivity analysis techniques are also proposed in order to deduce a recursive estimate of modal parameters from the estimates of the damping/stiffness coefficients.

Assessment of the continuous wavelet transform in the modal parameters estimation of 2MM and 3MM systems

AbstractIn this paper, our interest is in the identification of a special class of electromechanical systems: a motor‐drive system using the continuous wavelet transform method. This new modal analysis technique is evaluated in terms of its accuracy in the estimation of the modal parameters, its ability in distinguishing and separating several modes, its resistance to noisy conditions, and its usability with different excitations types. For this investigation, two models of elastic drive systems are considered: the two‐mass model and the three‐mass model. Simulation results of the study are presented, and the effectiveness of the developed identification method is discussed. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Analysis of bias of modal parameter estimators

S u m m a r y This paper presents an analysis based on a mathematical model of a bias in modal parameter estimators of a machine tool. The analytically determined amplitude-frequency characteristics were disturbed by random noise. The modal parameter estimation process was based on individual characteristics, followed by the determination of a bias in those parameters.

WAVELET-BASED ESTIMATION OF MODAL PARAMETERS OF A VEHICLE INVOLVED IN A FULL-SCALE IMPACT

In this paper, a wavelet-based approach is presented for estimation of vehicle modal parameters. The acceleration of a colliding vehicle is measured in its center of gravity — this crash pulse contains detailed information about vehicle behavior throughout a collision. Three types of signal analysis are elaborated here: time domain analysis (i.e. description of kinematics of a vehicle in time domain), the frequency analysis (identification of the parameters of the crash pulse in frequency domain), and the time-frequency analysis, which comprises those techniques that study a signal in both the time and frequency domains simultaneously, using Morlet wavelet properties. The frequency components of the recorded crash pulse are identified by determining the ridge of the wavelet coefficients matrix. Having knowledge of the natural frequency of the signal, the damping factor for a given mode shape of the signal is estimated. In this work the major frequencies of the crash pulse are determined and the damping factor for the major mode shape is identified. The comparative analysis between the current method's outcome, the response of a model established previously by using different approach and the behavior of a real car is performed and reliability of the actual methods and tools is evaluated.

Ground vibration tests of a helicopter structure using OMA techniques

This paper is focused on an assessment of the state-of-the-art of operational modal analysis (OMA) methodologies in estimating modal parameters from output responses on helicopter structures. For this purpose, a ground vibration test was performed on a real helicopter airframe. In the following stages, several OMA techniques were applied to the measured data and compared with the results from typical input–output approach. The results presented are part of a more general research activity carried out in the Group of Aeronautical Research and Technology in Europe (GARTEUR) Action Group 19, helicopter technical activity, whose overall objective is the improvement of the structural dynamic finite element models using in-flight test data. The structure considered is a medium-size helicopter, a time-expired Lynx Mk7 (XZ649) airframe. In order to have a comprehensive analysis, the behaviour of both frequency- and time-domain-based OMA techniques are considered for the modal parameter estimates. An accuracy index and the reliability of the OMA methods with respect to the standard EMA procedures, together with the evaluation of the influence of the experimental setup on the estimate of the modal parameters, will be presented in the paper.

Modal parameter estimation by combining stochastic and deterministic frequency-domain approaches

The poly-reference Least squares Complex Frequency-domain (pLSCF) estimator—commercially known as the LMS PolyMAX estimator—is used intensively in modal analysis applications nowadays. pLSCF is non-iterative (deterministic) and relatively accurate modal parameter estimation algorithm. This algorithm has several advantages: it is polyreference, fast, numerically stable for large-bandwidth with high-model order analysis, and yields very clear stabilization diagrams even with highly noisy FRFs measurements. One drawback of the pLSCF-estimator is that it yields a poor damping estimates especially for highly damped and weakly excited modes when the FRFs are very noisy.In this contribution, an approach will be proposed to improve the accuracy of pLSCF estimator and in particular, the damping estimates in case of high noise level. The new proposed approach is a combined stochastic-deterministic frequency-domain algorithm. In this approach, a 2-step procedure is introduced to improve the damping estimates while maintaining the very clear stabilization diagrams. In the first step, a parametric Maximum Likelihood smoothing approach, which is the stochastic part, is used to remove the noise from the data and in the second step, the pLSCF estimator, which is the deterministic part, is applied to the smoothed data resulting in improved (damping) estimates.The presented algorithm is able to maintain the benefits of pLSCF and at the same time leads to an improvement of the damping estimates in highly damped and very noisy cases. In addition, the new procedure properly deals with uncertainty on the measurements where the data variance due to measurement noise is taken into account.The procedure is illustrated and tested by using simulated as well as experimental data. The presented procedure to process a highly damped noisy vibration data leads to very accurate estimates in comparison to the traditional pLSCF estimator.

Displacement modal identification method of elastic system under operational condition

Modal identification of engineering structure in operation deals with the estimation of modal parameters from vibration data obtained in working conditions rather than laboratory conditions. After one structure destruction during a flight test, it was strongly required to carry out full-scale model testing to acquire the low-frequency vibration acceleration data of the investigated rocket (its structural dynamic properties could be represented by a beam). These vibration data were used to assess the modal properties of the modified structure. In this paper, a new modal identification method based on vibration displacement is suggested. The displacements of the measured points on the rocket are obtained by the integration of the low-frequency vibration accelerations during free flight test. In the method, the data are filtered through wavelet transform. For comparison, several methods are used to extract the modal frequencies of the investigated beam. In terms of the results of standard deviation of identified frequencies, it is believed that the generalized displacement-based modal identification method is more practicable in modal identification for similar problems.

Global Piecewise Fitting Method for Modal Parameter Identification by Orthogonal Polynomials Based on Dynamic Systems

Global estimation of modal parameters for dynamic Systems using fraction orthogonal polynomials possesses higher precision than the general rational fraction orthogonal polynomials algorithm. The object of this paper is to introduce a new technique to derive the global piecewise fitting method for modal parameter identification of dynamic Systems. Based on the global fraction orthogonal polynomials algorithm, a global piecewise fitting method for eliminating affections of modes outside of fitting bands is proposed. Both lower and higher modes outside of the fitting band are analyzed and processed. The frequency response data are revised by means of modes in two frequency bands close to the fitting band, and a curve fitting model is derived. The proposed method is compared with that of the traditional estimation without regard to the affections of modes outside of the fitting band. For this comparative study, simulated data are used. Simulation research indicates that the processed approach is effective.