Review of Structural Modal Tracking in Operational Modal Analysis: Methods and Applications

One of the most critical components of wind turbines is the blades. As blades are constantly exposed to weather and high loads, they can wear and become damaged. Performing in-situ continuous monitoring can help detect sudden damages and prevent further degradation, which is imperative to avoid economic losses and fatal accidents. However, monitoring a rotating rotor blade presents some challenges. One challenge is the consideration of lightning protection. Hence, a non-conductor measurement system must be used. Another challenge is system identification and modal tracking considering environmental and operational conditions (EOCs). Furthermore, vibration-based monitoring results from actual and operational rotor blades are scarce in the existing literature. This study centres on operational modal analysis (OMA) using covariance- driven stochastic subspace identification (SSI-COV) of an offshore wind turbine blade in operation employing eight months of data from fibre optic accelerometers (FOA) and fibre Bragg grating (FBG) strain gauges. The identification focuses on the first two bending modes in flapwise and edgewise directions and the first torsional mode. The study aims to determine which fibre optic sensor delivers better results. Furthermore, it addresses the effect of EOCs on the modal parameters, where system identification and modal tracking are discussed. It was found that tracked modes showed similar trends with respect to time, and a high connection was observed between wind speed, rotor speed, and pitch angle with frequency and damping. Additionally, acceleration and strain measurements deliver the same frequency and damping values. FBG better identified the first flapwise mode. On the other hand, FOA was superior in almost all other modes. This study points towards employing FOA for vibration-based monitoring of wind turbine blades using modal parameters.

Modal analysis has developed into a major technology for the study of structural dynamics in the past several decades. Through it, complex structural dynamics phenomena can be represented in terms of structural invariants, i.e., the modal parameters: natural frequencies, damping ratios and mode shapes. Operational Modal Analysis (OMA) deals with the estimation of modal parameters on vibration data measured for operational conditions, when the excitation on the structure is not measured. In this work, OMA is performed on a wind turbine blade undergoing wind tunnel testing. These tests included different wind speeds, pitch angles and also different health conditions of the blade, where masses of different magnitude were fixed to the blade on different locations to emulate damage conditions. In order to monitor the modal parameters across multiple days of varied tests in the wind tunnel, the Polymax modal parameter estimator was implemented, coupled with an Automated Modal Analysis methodology. This methodology included an automatic modal parameter selection technique, using a Machine Learning (ML) clustering algorithm, coupled with a modal tracking procedure which applied statistical thresholds on the modal parameters’ values. The tracking procedure searches for modes similar to the ones calculated for healthy conditions. The results show how the modal parameters of the wind turbine blade vary with the different measured conditions in the wind tunnel. Moreover, a damage detection methodology is implemented to differentiate between the healthy and damaged conditions on the blade, by leveraging an anomaly detection algorithm using the Multivariate Gaussian Distribution (MGD). This algorithm takes as input the modal parameters calculated by the previous Automated Modal Analysis methodology and detects statistical deviations among them which could indicate the presence of damage. All steps of this work contribute to developing an automatic framework able to detect damages on a wind turbine blade, and therefore perform Structural Health Monitoring (SHM) for different operational conditions.

Modal tracking plays a vital role in structural health monitoring since changes in modal parameters help us understand a structure’s dynamic characteristics and may reflect the potential deterioration of structural performance. Although numerous modal parameter estimation (MPE) methods exist, it is not guaranteed that an MPE process will exclude all spurious modes and not lose any physical modes every time over a long-term monitoring period. Relatively large damping of a structure, poor data quality, and significant changes in structural modal parameters may make the estimated modal parameters spurious, missing, or misclassified. It makes long-term modal tracking semiautomated or manual, which constrains timely downstream applications such as anomaly detection, condition assessment, and decision making. This research aims to propose a long-term continuous automatic modal tracking algorithm based on Bayesian inference even when the modal parameters, damping, and data quality change significantly. Bayesian inference is used to determine the physical modes from the results of existing MPE methods. Both the modes identified from the most recent response set and the modal probability model from multiple previous response sets are considered in the Bayesian model to better determine the physical modes from the results of MPE. Moreover, the proposed algorithm requires only three extra hyperparameters compared to general modal tracking algorithms, and they can be quickly determined by a grid search method. The performance of the proposed algorithm is verified by a numerical example and a real-world civil structure Z24 Bridge benchmark.

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.

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

Operational modal analysis is a procedure that allows the extraction of modal parameters of a structure in its operating environment. It is based on the idealized premise that input to the structure is white noise. In some cases, when free decay responses are corrupted by unmeasured random disturbances, the response data can be processed into cross-correlation functions that approximate free decay responses. Modal parameters can be computed from these functions by time domain identification methods such as the Eigenvalue Realization Algorithm (ERA). The extracted modal parameters have the same characteristics as impulse response functions of the original system. Operational modal analysis is performed on Ares I-X in-flight data. Since the dynamic system is not stationary due to propellant mass loss, modal identification is only possible by analyzing the system as a series of linearized models over short periods of time via a sliding time-window of short time intervals. A time-domain zooming technique was also employed to enhance the modal parameter extraction. Results of this study demonstrate that free-decay time domain modal identification methods can be successfully employed for in-flight launch vehicle modal extraction.

Operational modal analysis (OMA) is a procedure that allows the modal parameters of a structure to be extracted from the measured response to an unknown excitation generated during operation. Nonlinearity is inevitably and frequently encountered in OMA. The problem: The traditional OMA method based on linear modal theory cannot be applied to a nonlinear oscillation system. The solution: This paper aims to propose a nonlinear OMA method for nonlinear oscillation systems. The new OMA method is based on the following: (1) a self-excitation phenomenon is caused by nonlinear components; (2) the nonlinear normal modes (NNMs) of the system appear under a single-frequency harmonic excitation; and (3) using forced response data, the symbolic regression method (SR) can be used to automatically search for the NNMs of the system, whose modal parameters are implicit in the expression structure expressing each NNM. The simulation result of a three-degree-of-freedom (3-DOF) nonlinear system verifies the correctness of the proposed OMA method. Then, a disc-rod rotor model is considered, and the proposed OMA method’s capability is further evaluated.

Rotating machines are key components in energy generation processes, and faults can lead to shutdowns or catastrophes encompassing economic and social losses. Structural Health Monitoring (SHM) of structures in operation is successfully performed via Operational Modal Analysis (OMA), which has advantages over traditional methods. In OMA, white noise inputs lead to the accurate extraction of modal parameters without taking the system out of operation. However, this excitation condition is not easy to attain for rotating machines used in power generation, and OMA can provide inaccurate information. This research investigates the applicability of machine learning as a pre-stage of OMA to differentiate adequate from inadequate excitations and prevent inaccurate extraction of modal parameters. Data from a rotor system was collected under different conditions and OMA was applied. In a training stage, measurements were characterized by statistical features and K-means was used to determine which features provided information about the excitation condition, that is, which excitation was adequate to extract the rotor’s modal parameters via OMA. In a testing stage, data were successfully classified as adequate or not adequate for OMA, achieving 100% accuracy and revealing the technique’s potential to support SHM of rotating machines. The technique is extendable to other monitoring systems based on OMA.

A new operational modal analysis (OMA) method is developed for estimation of modal parameters (MPs) of a rotating structure (RS) subject to random excitation using a nonuniform rotating beam model, an image processing method, and an improved demodulation method. The solution to the governing equation of a nonuniform rotating beam is derived, which can be considered as the response of the beam measured by a continuously scanning laser Doppler vibrometer (CSLDV) system. A recently developed tracking CSLDV system can track and scan the RS. The image processing method determines the angular position of the RS so that the tracking CSLDV system can sweep its laser spot along a time-varying path on it. The improved demodulation method obtains undamped mode shapes (UMSs) of the RS by multiplying its measured response by sinusoids whose frequencies are its damped natural frequencies (DNFs) that are obtained from the fast Fourier transform of the measured response. Experimental investigation of the OMA method using the tracking CSLDV system is conducted, and MPs of a rotating fan blade (RFB), including DNFs and UMSs, with different constant speeds and its instantaneous MPs with a non-constant speed are estimated. Estimated first DNFs and UMSs of the stationary fan blade and RFB are compared with those from the lifting method that was previously developed by the authors.

In order to identify time-varying transient modal parameters only from nonstationary vibration response measurement signals for slow linear time-varying (SLTV) structures which are weakly damped, a moving window differential evolution (DE) independent component analysis- (ICA-) based operational modal analysis (OMA) method is proposed in this paper. Firstly, in order to overcome the problems in traditional ICA-based OMA, such as easy to go into local optima and difficult-to-identify high-order modal parameters, we combine DE with ICA and propose a differential evolution independent component analysis- (DEICA-) based OMA method for linear time invariant (LTI) structures. Secondly, we combine the moving widow technique with DEICA and propose a moving window differential evolution independent component analysis- (MWDEICA-) based OMA method for SLTV structures. The MWDEICA-based OMA method has high global searching ability, robustness, and complexity of time and space. The modal identification results in a three-degree-of-freedom structure with slow time-varying mass show that this MWDEICA-based OMA method can identify transient time-varying modal parameters effectively only from nonstationary vibration response measurement signals and has better performances than moving window traditional ICA-based OMA.

Near real-time tracking of dynamic properties for standalone structural health monitoring systems

In FE modeling of port crane structures, errors may be caused due to the simplification of complicated components, unclear physical properties, local approximation and inaccurate boundary conditions. So it is very important to update the FE model accuracy according to the experiment model and results. However there are two major problems when solving the model updating of port crane structure, the one is the difficulty of collecting the structure modal parameters with traditional modal experiment method because of the large scale of port crane structure, the other is mismatching problem while updating processing due to most of the model updating method currently constructing the objective function only by frequency. In this paper, an operational modal analysis is adopted to estimate the modal parameters of port crane structure based on the operational condition. A parametric model updating methodology of finite element (FE) model is proposed to solve port crane structure model updating: a series of design parameters of the FE model of port crane structure are selected as the main factors based on the sensitivity analysis, the objective function is built by considering the frequency correlation and the modal assurance criterion (MAC) together, and finally a zero-order/first-order combination algorithm is utilized to get the final accurate FE model of port crane structure. Research results showed that methodology proposed in this paper has satisfied updating accuracy for port crane structure, which verifies that the proposed method is suitable for model updating problem of this kind of structure.

Modal analysis techniques are widely used to characterize vibrations in structures, vehicles, machinery, etc. Modal parameters obtained through modal analysis are useful for structural health monitoring and condition monitoring. The common goal is to ensure the integrity of a mechanical system through monitoring of different operational conditions. Operational conditions described by spatial measurements can for instance be used to observe the vibration characteristics of the system and its parts. Therefore, the main originality of this work is to experimentally investigate if the presence of a turbulent gas flow in seal geometries can facilitate operational modal analysis for a coupled rotor–foundation system. A consistent and automatic way of obtaining the vibration characteristics is necessary to be included in the monitoring schemes. Therefore, this work also proposes a method to automatically obtain modal parameters for a bed plate of a rotor–foundation system when the rotor is affected by active magnetic bearings and gas seals. The automatic modal parameter algorithm is built on the stabilization diagram of modal parameters obtained from the stochastic subspace identification. Intermediate results from the automatic modal parameter algorithm show that some of the distance measures i.e., dωn,d, dζ, dMACX, dλ, dMACXωn,d, dMACXζ, and dMACXλ, for modal parameters in a stabilization diagram are better suited than others when distinguishing between possible physical modes and certainly spurious poles. The frequency band of interest for the system is found to influence the number of possible physical modes identified by the automatic algorithm. Measurements from 13 roving accelerometers are combined with the automatic modal parameter algorithm to obtain the vibration characteristics of the rotor and bed plate. For different operational conditions in the seal geometry, seven modes are consistently identified as physical modes by the automatic modal parameter algorithm. The algorithm uses (i) a combination of a white noise disturbance pattern intentionally introduced into the system through the active magnetic bearings and (ii) the operational disturbance coming from the seals, non-intentionally introduced by the turbulent gas flow. The seven physical modes are also identified when (iii) the rotor–foundation system is only disturbed from the turbulent gas flow in the seals. The seven physical modes identified by the algorithm under conditions (i), (ii), and (iii) compare well to the vibration characteristics found in experiments via experimental modal analysis and impact hammer testing as well as via a mathematical model of the rotor–foundation system.

<div class="htmlview paragraph">Operational Modal Analysis also known as Output Only Modal Analysis has in the recent years been used for extracting modal parameters of civil engineering structures and is now becoming popular for mechanical structures. The advantage of the method is that no artificial excitation needs to be applied to the structure or force signals to be measured. All the parameter estimation is based upon the response signals, thereby minimising the work of preparation for the test. This test case is a controlled lab set-up enabling different parameter estimation methods techniques to be used and compared to the Operational Modal Analysis. For Operational Modal Analysis two different estimation techniques are used: a non-parametric technique based on Frequency Domain Decomposition (FDD), and a parametric technique working on the raw data in time domain, a data driven Stochastic Subspace Identification (SSI) algorithm. These are compared to other methods such as traditional Modal Analysis. In the paper the method is illustrated by practical examples.</div>

SSI-LSTM network for adaptive operational modal analysis of building structures