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In Operational Modal Analysis applications, it is assumed that the structure is excited by white noise. However, in some cases, the operational vibration data are acquired while rotating equipment is active in the background or while it is even the main source of excitation. The structural responses will then consists of a broadband response from w...
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... Operational Modal Analysis applications, it is assumed that the structure is excited by white noise. However, in some cases, the operational vibration data are acquired while rotating equipment is active in the background or while it is even the main source of excitation. The structural responses will then consists of a broadband response from which the structural modes can be determined and additional harmonic response at discrete frequencies, which are disturbing the parameter identification process. Sometimes, the harmonic response is dominating and the Operational Modal Analysis methods only find poles at these harmonic frequencies. Therefore, it is desired to try to remove the disturbing harmonics from the data before applying Operational Modal Analysis. In this paper, a method that serves this purpose will be discussed. If the fundamental frequency of the disturbing harmonics is not known, it will be estimated by applying a “tacho-less rpm extraction” procedure. Using the (possibly fluctuating) rpm, the data can be converted to the angle domain and, then time (or better: angle) synchronous averaging is applied to remove the harmonics. This procedure will be illustrated using simulated data as well as real industrial operational data from an in-flight helicopter test and from a running large diesel engine. Operational Modal Analysis (OMA) is used to derive an experimental dynamics model from vibration measurements on a structure in operational conditions (as opposed to dedicated laboratory testing). Cases exist where it is rather difficult to apply an artificial force and where one has to rely upon available ambient excitation sources. It is practically impossible to measure this ambient excitation and the outputs are the only information that can be passed to the system identification algorithms. In this case one speaks of Operational Modal Analysis. During the last 15 years or so, Operational Modal Analysis developed and reached a mature state with advanced parameter estimation algorithms, commercial software implementations, and very relevant industrial applications. The number of applications is constantly increasing, and recently a considerable interest was raised in the application of OMA in the presence of rotating machinery. Two cases can be distinguished: • The engine is running through its operational rotation speed (rpm) range. In this case the different engine orders (harmonics) are sweeping through a broad frequency band and can be considered as unknown, but useful excitation and there is no need to apply any kind of filtering. In some cases, one has to be careful in the interpretation of certain modes as some of them are so-called “end-of order” effects. More details on this approach can be found in [1]. An example can be found in Figure 1. The engine is running at fixed (or slowly varying) rotation speed. In this case, the best excitation is at the fixed harmonic frequencies. However, these represent only a few spectral lines and do not contain sufficient information to base OMA curve-fitting on. So the modal parameter estimation also relies on the broadband excitation that is supposed to be present next to the harmonics. Unfortunately, the harmonics hamper considerably the identification process since the modal estimators will preferably find harmonics instead of structural modes. Therefore they should be removed from the data. An example can be found in Figure 2. The paper discusses the second case by presenting a method to remove the disturbing harmonics from the data before applying Operational Modal Analysis (Section 2). In Section 3, a simulated example is discussed and in Section 4, some industrial examples are given. Different methods exist in trying to separate discrete harmonic components from broadband random response. In [2] some of these are discussed, including synchroneous averaging [3], adaptive noise cancellation (ANC) [4] and the so-called Discrete-random separator (DRS) [5], which can be used in case of stationary signals (non-varying rpm) and is more efficient and robust than ANC. The difference compared with synchronous averaging is that the discrete frequency components are not required to have harmonic relationships. In [6], a method is discussed to remove order domain content in rotating equipment signals by double resampling. Double resampling refers to the fact that the time signal is first resampled in angle domain, after which the order content can be removed and then a second resampling takes place to convert the signal back to time domain. In [7], such an adaptive resampling procedure is discussed. Figure 3 shows the resampling principle. Figure 4 compares the same signal represented in frequency domain and order domain. In the angle or order domain, it will be possible to remove the disturbing chirping harmonics. Based on the ideas found in the above-cited literature, and after carrying out numerous evaluations [8], the following 4-step method (called “harmonic filter”) was found to be practical and reliable for removing harmonic disturbances in Operational Modal Analysis: 1. Measure (preferred) or estimate the fundamental harmonic / rpm of the rotational phenomenon. 2. Resample the data in angle domain (after upsampling) 3. Apply sliding window (angle) synchroneous averaging for separating discrete (harmonic) and random (broadband response) components (see also Figure 5). 4. Restore the signal in time domain Note that after the procedure, a time signal is obtained with the same length and sampling frequency as the original signal. Therefore it is possible to apply also time-domain OMA methods. It is also worth noting that in [9] an alternative approach was developed consisting in the reformulation of some classical modal parameter estimation algorithms to account for the presence of undamped harmonics, i.e. the modal equations were complemented by harmonics with fixed and known frequencies, but amplitudes and phases which are estimated together with the modal parameters. A 6 Degree-of-Freedom (DOF) system was excited by white noise. A disturbing harmonic was added to the excitation. In order to make it challenging, the frequency did not remain constant, but was constructed as an FM-modulated 12 Hz component of which the frequency could vary with about ± 4 %. Moreover, the carrier frequency (12 Hz) of the disturbance coincides with a mode of the system. Figure 6 shows the simulation results. When the disturbing component is not removed from the data, the modes could be identified, but in addition, much more modes around 12 Hz showed up in the stabilization diagram. Also the mode shape estimation is seriously compromised by the disturbing high-amplitude peaks in the spectra. When removing the disturbance using the 4- step approach outlined in Section 2, the PolyMAX modal parameter estimation results correspond very well to the true values. In this section, the procedure outlined in Section 2 will be applied to real industrial operational data from an in-flight helicopter test and from a running large diesel engine (Figure 7). Key to the method is the knowledge of the fundamental frequency of the disturbing harmonics. It is always a good idea to measure it during the operational test using a tacho probe. However, when it is not available, the “tacho-less rpm extraction” procedure developed in [10] can be applied to a response signal which is “close” to the harmonic excitation source. Also the Hilbert transform is useful to verify the stationarity and phase of these signals: Figure 8 shows the envelope of two helicopter roof acceleration signals which were band-pass filtered around the blade-pass frequency. It is clear that in this 30s recording, the harmonic amplitude is not constant (non-stationary signal). Figure 9 shows the phase of the Hilbert transform from which the instantaneous pulsation can be obtained by derivation (Figure 10). In this way, also an estimate of the rpm can be obtained. The 2 signals seem to agree well, except for some spikes in the signal, which indicate a bad estimate of the instantaneous pulsation in the signal due to low amplitudes (spikes in Figure 10 correspond to low envelope values in Figure 8. Using the measured or estimated (possibly fluctuating) rpm, the data can be converted to the angle domain and, then time (or better: angle) synchronous averaging is applied to remove the harmonics. Such a filtered spectrum is shown in Figure 11. A typical in- flight helicopter mode shape is shown in Figure 7. mode was found (Figure 12 – Top). After filtering the harmonics from the time series, OMA could be successfully applied (Figure 12 – Bottom). Moreover, it was found that the OMA modal parameters were in good agreement with the modal parameters identified using impact test and classical modal analysis (the engine was not running during impact testing). This paper introduced the “harmonic filter”, a method which is able to filter disturbing harmonics from broadband time data. The envisaged application is Operational Modal Analysis, where it was observed that the applicability to certain industrial problems was hampered by the presence of these harmonics. It was shown that the harmonic filter successfully filters the measured time signals so that the, originally hidden, structural modes can be identified using e.g. Operational PolyMAX. This work was carried out in the frame of the EUREKA project E! 3341 FLITE2. The financial support of the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) is gratefully ...
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Citations
... The presence of harmonics in the vibration measurements can lead to th e failure of typical OMA techniques in numerous ways. If the harmonic response is dominant , it can mask and suppress the true modal content of the structure [9], or it can be wrongfully identified as a lightly damped structural resonance [10]. When structural and periodic modes are close, further errors in parameter estimation can arise as the identification methods usually result in poor convergence of the parameters [11]. ...
The safety of dams is of extreme importance, considering the high economic value and cost of failure. To assess the performance of these structures over their lifetime, vibration monitoring can be a useful tool. However, in hydroelectric generating power plants, rotating machinery can introduce harmonics into the measurements and make current methods of modal parameter estimation invalid, necessitating harmonic removal. While recent research has focused on harmonic removal in rotating mechanical machinery like wind turbines and large generators, there is a gap in understanding of monitoring gravity dams in environments with significant harmonic contamination. Most ambient vibration tests of dams have been conducted on arch and buttress-type structures, which have experienced relatively low harmonic contamination. To address this gap, a study was performed on the Mactaquac Generating Station, the largest hydroelectric power plant in the Maritime provinces, using full-scale monitoring data as part of the Mactaquac Life Achievement Project (MLAP). The study found that under low operation demand, it was possible to successfully estimate the benchmark modal parameters of the structure. However, during high operational demand, the measured signals were dominated by harmonic content, which caused several errors in the modal estimation results compared to periods of low demand. However , by reducing the harmonics in the signal, the first four mode shapes of the dam structure were successfully identified. This demonstrates that harmonics can significantly impact the accuracy of mode estimation, but their effects can be mitigated through harmonic reduction techniques.
... The oldest reported methods belong to the techniques denoted broadly as Time Synchronous Averaging (TSA), which are intuitively sound and easy to implement, at least in their most basic form. TSA was proposed for wind turbines in Peeters et al. [12] and has been more recently used in Manzato et al. [10]. The idea is to average consecutive cycles of the signal to eliminate its stochastic part and retain the deterministic (periodic) one; this is to say, TSA is an implementation of a so called comb filter, as shown in Braun [13]. ...
... Finally, the modified DFT is transformed back in the angular domain and the resulting signal is resampled in the time domain. To improve the accuracy, the process relies on large oversampling factors (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). ...
... The figures have the same internal inlet structure, as explained next. (12) corresponding to 1P, 3P, 6P and 9P. The analysis frame duration used was 10 s (CS1), 11 s (CS2) and 14 s (CS3) according to the criterion from Section 2.3. ...
We present a novel approach to harmonic disturbance removal in single-channel wind turbine acceleration data by means of time-variant signal modeling. Harmonics are conceived as a set of quasi-stationary sinusoids whose instantaneous amplitude and phase vary slowly and continuously in a short-time analysis frame. These non-stationarities in the harmonics are modeled by low-degree time polynomials whose coefficients capture the instantaneous dynamics of the corresponding waveforms. The model is linear-in-parameters and is straightforwardly estimated by the linear least-squares algorithm. Estimates from contiguous analysis frames are further combined in the overlap-add fashion in order to yield overall harmonic disturbance waveform and its removal from the data. The algorithm performance analysis, in terms of input parameter sensitivity and comparison against three state-of-the-art methods, has been carried out with synthetic signals. Further model validation has been accomplished through real-world signals and stabilization diagrams, which are a standard tool for determining modal parameters in many time-domain modal identification algorithms. The results show that the proposed method exhibits a robust performance particularly when only the average rotational speed is known, as is often the case for stand-alone sensors which typically carry out data pre-processing for structural health monitoring. Moreover, for real-world analysis scenarios, we show that the proposed method delivers consistent vibration mode parameter estimates, which can straightforwardly be used for structural health monitoring.
... It was applied to near healthy gears, and used mainly to extract the time varying mesh stiffness (TVMS), and separate it from the geometric transmission error (GTE). In [42], the signals were pre-processed by the time synchronous averaging (TSA) method [43] to remove the deterministic components, which may cause disturbances in the OMA process. The transfer functions were identified from the extracted random part of the signals by the cepstrum-based OMA, and were then removed from the original TE measurements to reconstruct the forcing functions. ...
... Secondly, the random excitation of the system needs to be frequentially smooth and flat (on a log scale). For gear signals, it is reasonable to assume that the system has broadband excitation after removing the deterministic components by the time synchronous averaging (TSA) method [43] or the cepstral editing technique [17]. Detailed justifications of these two assumptions were provided in [42]. ...
Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.
... To some extent, the drawbacks of harmonic filtering can be alleviated by using time synchronous averaging (TSA) (Peeters et al., 2007), where harmonics can be removed by isolating them from the measurement data. In this method, given the known rotor speed, the response data are resampled into the "angle" domain using constant angular speed increments. ...
To increase the contribution of offshore wind energy to the global energy mix in an economically sustainable manner, it is required to reduce the costs associated with the production and operation of offshore wind turbines (OWTs). One of the largest uncertainties and sources of conservatism in design and lifetime prediction for OWTs is the determination of the global damping level of the OWT. Estimation of OWT damping based on field measurement data has hence been subject to considerable research attention and is based on the use of (preferably operational) vibration data obtained from sensors mounted on the structure. As such, it is an output-only problem and can be addressed using state-of-the-art operational modal analysis (OMA) techniques, reviewed in this paper. The evolution of classical time- and frequency-domain OMA techniques has been reviewed; however, the literature shows that the OWT vibration data are often contaminated by rotor speed harmonics of significantly high energy located close to structural modes, which impede classical damping identification. Recent advances in OMA algorithms for known or unknown harmonic frequencies can be used to improve identification in such cases. Further, the transmissibility family of OMA algorithms is purported to be insensitive to harmonics. Based on this review, a classification of OMA algorithms is made according to a set of novel suitability criteria, such that the OMA technique appropriate to the specific OWT vibration measurement setup may be selected. Finally, based on this literature review, it has been identified that the most attractive future path for OWT damping estimation lies in the combination of uncertain non-stationary harmonic frequency measurements with statistical harmonic isolation to enhance classical OMA techniques, orthogonal removal of harmonics from measured vibration signals, and in the robustification of transmissibility-based techniques.
... The first, that the excitation is a broadband stochastic process, has been extensively studied, with techniques put forward for both strongly harmonic or cyclic loading and mitigating the impact of non-stochastic loading (e.g. [2], [3], [4], [5]). The second, that the systems behaviour is linear; for a given input force the response of the system is constant, has seen growing interest in recent years due to increased adoption of long-term monitoring of structures. ...
A challenge in identifying the dynamic properties of large structures through operational modal analysis (OMA), whereby the response of a structure is measured under ambient excitation, is the changes in added mass and temperature which may occur during data collection. The effect of these changes may mask any damage to the structure or lead the investigator to incorrectly conclude damage has occurred. Quantification of such effects requires the use of short-time OMA methods, where the structure’s response is assumed to be linear across short periods of time. Two experiments were carried out to identify methods through which such variations can be accurately identified and quantified. The first experiment consisted of a simple I-beam with spring supports to which a small mass was added at a variety of locations. This simulated changes in mass similar to that which may be induced by pedestrian or vehicle loading of civil structures. The changes in the dynamic properties were quantified through the short-time Fourier transform and a variant on the random decrement technique to test their ability to detect small changes in mass. An inversion of the mass change method is used to estimate both the quantity and location of the added mass. The second experiment investigated the efficacy of the same short-time OMA methods in the presence of temperature variation. A flat plate was heated in laboratory conditions using radiant panels. The changes in dynamic properties were measured during heating, steady temperature and cooling of the plate. The results were correlated to the changes in temperature using variations on established relationships between elastic modulus and temperature. The results presented within this paper provide an experimental basis for the viability of short-time OMA methods for quantifying temperature and added mass induced variation in dynamic parameters which may be used to guide future structural monitoring.
... The well-established methods, namely stochastic subspace identification (SSI), a parametric time-domain technique, and enhanced frequency domain decomposition (EFDD), a non-parametric frequency-domain technique, are known to have imprecise identification when dealing with random loads combined with a steady-state signal. In frequency analysis, the harmonics are known to hide or bias the estimation of physical mode [18], while in the SSI algorithm, the harmonics are usually identified as very lightly damped stable poles [19]. ...
The paper investigates the use of operational modal analysis (OMA) techniques applied directly into a rotating machinery with hydrodynamic journal bearings. OMA has proven to be a strong tool for analyzing the dynamics of large structures, especially to its capabilities in civil engineering; however, its application in rotordynamics is still very incipient. The objective here is to make a broader analysis of how this technique can be used in the universe of rotating machines and how the results become reliable. The application of this technique in rotating machines implies some care due to the inherent operating conditions of the system, especially regarding the presence of harmonic forces. The study emphasizes resonance problems with the early natural modes of the structure and its damping. The main novelty of the paper is to present a simple procedure, tapping throughout the rotor, which made possible the application of OMA to extract the modal parameters with satisfactory results in a system in which the classical EMA steeped sine technique was insufficient to provide a good analysis of the rotor. In this type of system, the hydrodynamic bearings and misalignments caused by the coupling of shaft and motor (something quite common in real systems) may cause difficulty in extracting modal parameters depending on the technique used. However, when applying traditional OMA methods, using both the frequency domain (enhanced frequency domain decomposition) and the time domain (stochastic subspace identification), it was possible to make a good identification of the modal parameters of the rotor, with promising results to encourage a broader modal identification of rotating machinery in operating conditions.
... An analysis of simulated vibration data by the pLSCF method showed that a harmonic frequency, coinciding with a structural mode, led to spurious stable poles around this frequency [11]. The authors also analyzed operational data of a large diesel engine. ...
... Although different studies report successful utilization of SSI [6,12] and pLSCF [4,10,11] methods for OMA of rotating machinery, it is believed that no direct performance comparison of these methods has been conducted yet. ...
... In a 6 DOF simulation [11], the method was able to remove the disturbing influence of harmonics on the subsequent modal estimation with the pLSCF method despite a harmonic coinciding with a structural mode. Results from a real operational inflight helicopter and a running diesel engine showed that TSA resulted in much cleaner stabilization diagrams and thus facilitated the estimation of structural modes. ...
Current demands for operational efficiency and safety of aircraft engines require a deep understanding of engine component behavior. Mechanical spinning tests can be utilized for this purpose by extracting modal properties of the tested hardware by Operational Modal Analysis. However, this process is challenging because the operational input force is unknown and is disturbed by influences such as harmonics in the excitation, which are characteristic for rotating hardware. To address this issue, this paper provides a qualitative review of existing methods for Operational Modal Analysis (OMA) applied to rotating machinery. A plate structure under random excitation with additional harmonic loading, which resembles the effect of rotation, is presented. The vibration response of the plate has been processed by six different OMA methods to estimate their applicability and output variance. The results of the conducted research and experimental analysis indicate that a hybrid approach based on machine learning and different vibration analysis methods can be beneficial. Specifically, data fusion and condition monitoring can be facilitated to acquire more consistent and accurate analysis results and ultimately contribute to optimized engine system designs.
... • Second approach to address the problem of white excitation in OMA involves removal of harmonic components from the signal in pre-processing stage [68] by using different methods. These methods include cepstrum editing [69,70], nonparametric estimate of the harmonic frequency, time-synchronous averaging, joint use of the "entropy" and Hilbert transform, random decrement technique [71][72][73][74][75]. Despite all these techniques, the problem of harmonics in OMA still remains [76]. ...
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.
... For example, time-synchronous-averaging (TSA) is a method extracting periodic waveforms from signals by averaging their blocks synchronized in the angular domain. For OMA, this averaged signal is subtracted from the raw measurements, which results in the removal of the periodic frequencies selected to synchronize the blocks [4]. Angle matching is often achieved with tachometer measurements, which is not practical in real-life applications and was attempted to be overcome in the context of TSA in [5]. ...
The modes of linear time invariant mechanical systems can be estimated from output-only vibration measurements under ambient excitation conditions with subspace-based system identification methods. In the presence of additional unmeasured periodic excitation, for example due to rotating machinery, the measurements can be described by a state-space model where the periodic input dynamics appear as a subsystem in addition to the structural system of interest. While subspace identification is still consistent in this case, the periodic input may render the modal parameter estimation difficult, and periodic modes often disturb the estimation of close structural modes. The aim of this work is to develop a subspace identification method for the estimation of the structural parameters while rejecting the influence of the periodic input. In the proposed approach, the periodic information is estimated from the data with a non-steady state Kalman filter, and then removed from the original output signal by an orthogonal projection. Consequently, the parameters of the periodic subsystem are rejected from the estimates, and it is shown that the modes of the structural system are consistently estimated. Furthermore, standard data analysis procedures, like the stabilization diagram, are easier to interpret. The proposed method is validated on Monte Carlo simulations and applied to both a laboratory example and a full-scale structure in operation.
... Stable milling operations consist of both periodic content and random background noise [14,15]. In addition, application of OMA in fields outside manufacturing, such as in vibrating civil structures [16], in-flight helicopters [17], and wind turbines [18], have shown that forces containing both types of signals can generate broadband excitation of the structures, which enables estimation of FRFs. Because 6-dof industrial robots are significantly more compliant than their CNC machine tool counterparts, the background random noise can excite the robot's natural modes of vibration to measureable levels suitable for OMA. ...
Impact hammer experiments are typically used for identifying the Frequency Response Function (FRF) of six-degree-of-freedom (6-dof) industrial robots for machining applications. However, the modal properties of 6-dof industrial robots change as a function of robot arm configuration. Hence, describing the robot’s modal parameters within its workspace requires off-line impact hammer experiments performed at discrete robot end effector positions, which are costly and time consuming. Instead, it is more efficient to calculate the robot FRF using Operational Modal Analysis (OMA), a method that utilizes data acquired during the actual machining process. This paper presents an OMA approach to identify the robot FRF from measured milling forces and robot tool tip vibrations. Analysis of the milling process data reveal that periodic forces produced in the milling process are accompanied by background white noise that induce broadband excitation across the robot structure’s frequency spectrum. Hence, the tool tip vibration signal contains the signature of the structure’s free response that enables the use of OMA to estimate the robot’s FRF. The FRF calculated using OMA is shown to be in good agreement with results obtained from impact hammer experiments.
