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Evaluation of damping estimates by automated Operational Modal Analysis for offshore wind turbine tower vibrations
Abstract
Reliable predictions of the lifetime of offshore wind turbine structures are influenced by the limited knowledge concerning the inherent level of damping during downtime. Error measures and an automated procedure for covariance driven Operational Modal Analysis (OMA) techniques has been proposed with a particular focus on damping estimation of wind turbine towers. In the design of offshore structures the estimates of damping are crucial for tuning of the numerical model. The errors of damping estimates are evaluated from simulated tower response of an aeroelastic model of an 8 MW offshore wind turbine. In order to obtain algorithmic independent answers, three identification techniques are compared: Eigensystem Realization Algorithm (ERA), covariance driven Stochastic Subspace Identification (COV-SSI) and the Enhanced Frequency Domain Decomposition (EFDD). Discrepancies between automated identification techniques are discussed and illustrated with respect to signal noise, measurement time, vibration amplitudes and stationarity of the ambient response. The best bias-variance error trade-off of damping estimates is obtained by the COV-SSI. The proposed automated procedure is validated by real vibration measurements of an offshore wind turbine in non-operating conditions from a 24-h monitoring period.
... It is reported that the O&M costs for OWT projects can potentially account for 30% of the total project costs [4], which represents a significant financial burden. Therefore, structural health monitoring for OWTs plays a critical role in observing structural state in real time and providing precise decision support for O&M cost reduction [5,6]. ...
... Subsequently, the automatic SSI-COV method was considered for OWT structural monitoring, and the results indicated that this method has high identification accuracy during idle or parked states [6]. Several studies also point out that OMA technology performs better when the OWT is in a parked state compared to operating states with blade rotation [5,26], mainly due to the limitations imposed by OMA's fundamental assumptions. Specifically, OMA technique assumes that the identified system is linear, time-invariant, and subject to stationary, white-noise-type excitation with no temporal or spatial correlation [29]. ...
... Relatively few studies have tackled these challenges directly. Some researchers have explored the effects of signal noise, measurement time, vibration amplitudes, and stationarity of the ambient response on the identification of damping, as opposed to the modal frequencies and mode shapes using SSI-COV method [5]. For non-white noise harmonic excitation, Dong et al. [33] introduced the harmonic modification SSI method to isolate the harmonic components. ...
Operational modal analysis (OMA) is essential for long-term health monitoring of offshore wind turbines (OWTs), helping identifying changes in structural dynamic characteristics. OMA has been applied under parked or idle states for OWTs, assuming a linear and time-invariant dynamic system subjected to white noise excitations. The impact of complex operating environmental conditions on structural modal identification therefore requires systematic investigation. This paper studies the applicability of OMA based on covariance-driven stochastic subspace identification (SSI-COV) under various non-white noise excitations, using a DTU 10 MW jacket OWT model as a basis for a case study. Then, a scaled (1:75) 10 MW jacket OWT model test is used for the verification. For pure wave conditions, it is found that accurate identification for the first and second FA/SS modes can be achieved with significant wave energy. Under pure wind excitations, the unsteady servo control behavior leads to significant identification errors. The combined wind and wave actions further complicate the picture, leading to more scattered identification errors. The SSI-COV based modal identification method is suggested to be reliably applied for wind speeds larger than the rated speed and with sufficient wave energy. In addition, this method is found to perform better with larger misalignment of wind and wave directions. This study provides valuable insights in relation to the engineering applications of in situ modal identification techniques under operating conditions in real OWT projects.
... The standard practice is to identify the modal properties of structures using Operational Modal Analysis (OMA) techniques, including natural frequencies, modal shapes, and modal damping ratios for the lower vibrational modes. Past studies ([1] [2] [3][4] [5]) have focused on obtaining the properties of classic modal models for operating or parked wind turbines. Here classic modal models imply that different modes in these models can be decoupled. ...
... Therefore, ̅ causes coupling between different modes and different vibration directions. It is possible to consider a particular number of modes by truncating the matrices and vectors in Eq. (5). Theoretically, considering more modes could result in more accurate dynamic responses. ...
... The finite element model of the 5 MW OWT is reduced to a 2-DOF model for a mean wind speed of 12 m/s, following Eqs. (4) and (5). For the 2-DOF model, there are a total of 8 parameters, namely the two modal masses, and two modal stiffnesses for the first bending modes in the FA and SS directions, and four modal damping coefficients in the modal damping matrix. ...
Uncertainties in dynamic parameters should be considered when modelling operating offshore wind turbines. Uncertainties arise from soil-structure interaction with changing stiffness (especially when supported on monopiles), and complex wind-rotor interaction causing uncertainty in time-varying aerodynamic damping. Information of the current parameters can be obtained by identification of modal model properties of the wind turbine system. A recently developed modal model is used as the identification target, where the aerodynamic damping is represented by an aerodynamic damping matrix accurately capturing the coupling between the fore-aft and side-side motions. Given the observed data in the form of power spectral densities of measured dynamic responses, a Bayesian inference frame based on the Metropolis-Hastings algorithm is proposed to obtain the posterior probability distributions of the parameters in the modal model. Two case studies, based on simulated data, demonstrated that the proposed Bayesian inference frame can obtain very close parameters of the modal model compared to the theoretical values.
... With the continuous advancements in offshore wind turbine structural health monitoring (SHM) technologies and finite element simulation techniques, it has become increasingly feasible to identify structural modal parameters using prototype observation data. Bajri et al. [170] developed an error measurement and covariance-driven automated operational modal identification system, which uses vibration response data collected during turbine shutdowns to validate its effectiveness in assessing structural safety. Similarly, Benedetti et al. [171] proposed using the strain difference between adjacent strain gauges as an indicator for tower safety evaluation, while Ziegler et al. [172] calculated damage-equivalent loads using strain gauges on the support structure, achieving a monthly prediction error of less than 4%. ...
... The failure modes of offshore wind turbine structures throughout their service life include structural failure, fatigue damage, and corrosion damage[165][166][167][168][169][170][171][172]. ...
In recent decades, Offshore Wind Turbines (OWTs) have become crucial to the clean energy transition, yet they face significant safety challenges due to harsh marine conditions. Key issues include blade damage, material corrosion, and structural degradation, necessitating advanced materials and real-time monitoring systems for enhanced reliability. Carbon fiber has emerged as a preferred material for turbine blades due to its strength-to-weight ratio, although its high cost remains a barrier. Structural Health Monitoring Systems (SHMS) play a vital role in detecting potential faults through real-time data on structural responses and environmental conditions. Effective monitoring approaches include vibration analysis and acoustic emission detection, which facilitate early identification of anomalies. Additionally, robust data transmission technologies are essential for SHMS effectiveness. This paper reviews material design strategies, data acquisition methods, and safety assessment techniques for OWTs, addressing current challenges and future directions in the field.
... The stochastic subspace identification method has been used to reveal the modal parameters of offshore wind turbines experiencing earthquakes [5]. Substructure damping [6], aerodynamic damping [7], and damping of wind turbine towers [8] have all discussed, and Eigensystem Realization Algorithm (ERA), SSI-COV, the Enhanced Frequency Domain Decomposition (EFDD) [8], and time-frequency analysis [7] have all been used. Estimating offshore wind turbine damping using state-of-the-art operational modal analysis (OMA) techniques was summarized in [9]. ...
... The stochastic subspace identification method has been used to reveal the modal parameters of offshore wind turbines experiencing earthquakes [5]. Substructure damping [6], aerodynamic damping [7], and damping of wind turbine towers [8] have all discussed, and Eigensystem Realization Algorithm (ERA), SSI-COV, the Enhanced Frequency Domain Decomposition (EFDD) [8], and time-frequency analysis [7] have all been used. Estimating offshore wind turbine damping using state-of-the-art operational modal analysis (OMA) techniques was summarized in [9]. ...
To deal with the uncertainties in modeling offshore wind turbines, we propose a parameter inversion method for the pile–soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in situ parameter. The proposed method is confirmed to converge after some number of iterations, depending on what the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying that the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed light on the influence of parameter uncertainties on offshore wind turbines.
... The stochastic subspace identification method also reveals the modal parameters of offshore wind turbines experiencing earthquakes [5]. Substructure damping [6], aerodynamic damping [7], and damping of wind turbine towers [8] were all discussed, and Eigensystem Realization Algorithm (ERA), SSI-COV, the Enhanced Frequency Domain Decomposition (EFDD) [8] or time-frequency analysis [7] were all used. Estimating offshore wind turbine damping using state-of-the-art operational modal analysis (OMA) techniques was summarized in [9]. ...
... The stochastic subspace identification method also reveals the modal parameters of offshore wind turbines experiencing earthquakes [5]. Substructure damping [6], aerodynamic damping [7], and damping of wind turbine towers [8] were all discussed, and Eigensystem Realization Algorithm (ERA), SSI-COV, the Enhanced Frequency Domain Decomposition (EFDD) [8] or time-frequency analysis [7] were all used. Estimating offshore wind turbine damping using state-of-the-art operational modal analysis (OMA) techniques was summarized in [9]. ...
To deal with the uncertainties in modeling offshore wind turbines, we proposed a parameter inversion method for the pile-soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in-situ parameter. The proposed method is confirmed to converge after some iterations, whatever the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed some light on the influence of uncertainties in offshore wind turbines, such as soil parameters in geological surveys.
... Other factors include the effect of the MPE method itself. Some studies have made a comparison of the performance of various MPE methods [1,15,16,17], concluding that while in overall most methods are able to detect the resonances, the lowest uncertainty is achieved with methods related to the Covariance-driven Stochastic Subspace Identification (SSI-COV) algorithm, which includes also the Multi-reference Ibrahim Time Domain (MITD) method [18]. Nonetheless, the optimal performance of each algorithm is bound to various decisions, for instance the data length, the number of correlation lags, the model order, selected sensors, among others [17,19,20,21]. ...
... Some studies have made a comparison of the performance of various MPE methods [1,15,16,17], concluding that while in overall most methods are able to detect the resonances, the lowest uncertainty is achieved with methods related to the Covariance-driven Stochastic Subspace Identification (SSI-COV) algorithm, which includes also the Multi-reference Ibrahim Time Domain (MITD) method [18]. Nonetheless, the optimal performance of each algorithm is bound to various decisions, for instance the data length, the number of correlation lags, the model order, selected sensors, among others [17,19,20,21]. ...
Structural damping is a critical quantity for condition assessment and fatigue lifetime prediction in wind energy. Its estimation from operational vibration data comes with a considerable amount of uncertainty, derived from environmental and operational variability and from the quality of the estimation process itself. In this paper, we aim to determine experimentally the damping values and their least possible uncertainty bounds for the first two modes of an idling offshore wind turbine. For this purpose, we use field measurements from a 3.6 MW offshore wind turbine located at the DanTysk wind farm. We select a subset of cases from the wind turbine on idling condition for a confined interval of environmental and operational conditions, in an attempt to minimize operational variability in the damping estimates. In addition, we make a study on the adjustment parameters of the automated operational modal analysis method, aiming at obtaining most consistent damping estimates.
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... The structural damping of the OWT is from steel material and foundation-soil interaction which usually depends on experience or tradition [22]. However, the theory-based method may not be convenient to apply, and the experience-based method may be not accurate [23]. An obvious example is that aerodynamic damping typically plays a prominent role [24], however, for most commercial wind turbines, the application of aerodynamic analysis is often restricted as wind turbine manufacturers may withhold blade information due to confidentiality concerns. ...
The identification of damping sources in the design of offshore wind turbine (OWT) structures has been approached in many different ways. Among all the methods, assessing damping sources based on monitoring data for OWT operations is more reliable compared to using experimental or empirical techniques. This study aims to perform an automated operational modal analysis of an instrumented OWT using detailed vibration monitoring to effectively assess different sources of damping. Firstly, continuous vibration acceleration of a monopile-supported utility-scale OWT is measured to obtain mode parameters by operational modal analysis. An automated modal identification method is designed to obtain mode parameters from a large of monitoring data. The natural frequency and damping ratio of both the first and second order bending modes of the OWT tower are observed. Besides, the characteristics of these mode parameters during the OWT operation are analysed. A data-driven damping assessment method is then introduced to access aerodynamic, hydrodynamic and structural damping. This assessment method is based on the identified damping from operational modal analysis, and it separates the different damping sources with regression techniques. The proposed assessment method provides a practical way to understand the damping sources of OWTs which is meaningful for the structural design. Furthermore, the method also holds potential applicability for damping assessment in various types of OWTs.
... First mode natural frequency: ω 1 = 3EI (0.2235m T + m RNA )L 3 E: elasticity modulus; I: moment of inertia; m T : tower mass; m RNA : RNA mass; L: tower height. [68,69] Buckling Analysis ...
Offshore wind energy leverages the high intensity and consistency of oceanic winds, playing a key role in the transition to renewable energy. As energy demands grow, larger turbines are required to optimize power generation and reduce the Levelized Cost of Energy (LCoE), which represents the average cost of electricity over a project's lifetime. However, upscaling turbines introduces engineering challenges, particularly in the design of supporting structures, especially towers. These towers must support increased loads while maintaining structural integrity, cost-efficiency, and transportability, making them essential to offshore wind projects' success. This paper presents a comprehensive review of the latest advancements, challenges, and future directions driven by Artificial Intelligence (AI) in the design optimization of Offshore Wind Turbine (OWT) structures, with a focus on towers. It provides an in-depth background on key areas such as design types, load types, analysis methods, design processes, monitoring systems, Digital Twin (DT), software, standards, reference turbines, economic factors, and optimization techniques. Additionally, it includes a state-of-the-art review of optimization studies related to tower design optimization, presenting a detailed examination of turbine, software, loads, optimization method, design variables and constraints, analysis, and findings, motivating future research to refine design approaches for effective turbine upscaling and improved efficiency. Lastly, the paper explores future directions where AI can revolutionize tower design optimization, enabling the development of efficient, scalable, and sustainable structures. By addressing the upscaling challenges and supporting the growth of renewable energy, this work contributes to shaping the future of offshore wind turbine towers and others supporting structures.
... ERA simplifies the modal identification process by automating tasks that traditionally require manual input, making it suitable for the real-time, continuous monitoring of structures in operational conditions. This automation facilitates the accurate identification of key modal parameters, which are essential for assessing the structural integrity and dynamic behavior of civil infrastructure, such as bridges, buildings, and offshore wind turbines [145]. ...
This paper presents a comprehensive review of automated modal identification techniques, focusing on various established and emerging methods, particularly Stochastic Subspace Identification (SSI). Automated modal identification plays a crucial role in structural health monitoring (SHM) by extracting key modal parameters such as natural frequencies, damping ratios, and mode shapes from vibration data. To address the limitations of traditional manual methods, several approaches have been developed to automate this process. Among these, SSI stands out as one of the most effective time-domain methods due to its robustness in handling noisy environments and closely spaced modes. This review examines SSI-based algorithms, covering essential components such as system identification, noise mode elimination, stabilization diagram interpretation, and clustering techniques for mode identification. Advanced SSI implementations that incorporate real-time recursive estimation, adaptive stabilization criteria, and automated mode selection are also discussed. Additionally, the review covers frequency-domain methods like Frequency Domain Decomposition (FDD) and Enhanced Frequency Domain Decomposition (EFDD), highlighting their application in spectral analysis and modal parameter extraction. Techniques based on machine learning (ML), deep learning (DL), and artificial intelligence (AI) are explored for their ability to automate feature extraction, classification, and decision making in large-scale SHM systems. This review concludes by highlighting the current challenges, such as computational demands and data management, and proposing future directions for research in automated modal analysis to support resilient, sustainable infrastructure.
... However, the accuracy and uncertainty of these identification methods are susceptible to the complex actual measurement environment. Bajric et al. 27 pointed out that the low signal-to-noise ratio and short measurement duration may result in low accuracy and large uncertainty of the damping identification. More importantly, these identification methods usually serve as a key role in the postconstruction structural health monitoring. ...
As wind farms are constantly being constructed, the risk of tower failure for wind turbines increases significantly under strong winds. Compared with the extensively concerned wind-induced behaviors during the operating state, those ones during the shutdown state attract little attention but may lead to serious problems of damages or even collapse. To clearly grasp the aero-structure interaction in the shutdown state, this paper develops an analytical model for estimating aerodynamic damping of wind turbines. In this method, an analytical expression of aerodynamic damping coupling matrix is derived via the combination of multibody dynamics and first-order Taylor expansion. This matrix is further quantified as the ratio of modal aerodynamic damping with the aid of state-space equation and complex eigenvalue analysis. This treatment can facilitate the straightforward application of efficient calculation methods, such as frequency domain analysis and uncoupled analysis. More importantly, the developed model is able to simultaneously consider multiple realistic factors, such as blade flexibility, tower top rotation, yaw error, wind shear, and pitch angle. This model may have the high calculation efficiency and accuracy, as well as strong applicability for estimating the aerodynamic damping. Numerical examples based on a typical 5 MW wind turbine are employed to validate the effectiveness of the developed model. Experimental analyses demonstrate that this model outperforms the existing formula and presents a high consistency with OpenFAST in the estimation of aerodynamic damping. Meanwhile, the influence of multiple realistic factors is quantitatively analyzed, which even makes the estimation error exceed 70%.
... The SSI method is usually used in the literature to obtain the modal parameters of operating wind turbines [45]. The SSI method is a technique based on the state-space model of random systems. ...
This study aims to comprehensively investigate the dynamic characteristics of the tower of a scaled wind turbine model through wind tunnel tests. A model was scaled from the NREL 5 MW prototype wind turbine with a geometric scale ratio of 1/75, based on the similarity rules in thrust coefficient and dynamic characteristics. A series of wind tunnel tests were carried out on the scaled wind turbine model under different operating conditions and parked conditions with different yaw angles, and the modal parameters of the scaled model were identified by the stochastic subspace identification method and rotor stop tests. It was found that the vibration response of the tower in the fore–aft direction achieved its maximum value when the yaw angle was 90° with feathered blades, while the tower vibration response in the side–side direction was relatively severe with the yaw angle ranging from 10° to 50°. These observations are found to be well aligned with the aerodynamic characteristics of the airfoil. Moreover, the experimental results indicate that the scaled wind turbine model can reflect the vibration responses of its full-scale counterpart in the fore–aft direction. The natural frequencies and mode shapes of the scaled model can be accurately identified by different methods, but the identified damping ratios are relatively scattered.
... The main limitation of FDD is the impossibility to estimate damping, which can be derived by referring the improved version of the algorithm, named enhanced FDD, EFDD [36]. Several research works employ the FDD approach for the most disparate uses, as for performing OMA on civil structures, such as offshore wind turbines [37], and footbridges [38], or on mechanical structures, such as a harvester thresher [39] and a centrifugal compressor [40]. ...
The paper presents a study on the dredging vibrational effects, for nourishment purpose, on the existing structures surrounding the worksite. Nourishment is a common operation when beach (or coasts, or ports) protection is required, allowing to reduce far-field impacts of coastal structures and improve navigability. Nourishment is then performed to reshape underwater land, and it is usually practiced by locating in the zones in which is required, soil coming from nearby areas. This latter is often obtained by a dredging process, in which the phases of excavation, transportation and soil placement are carried out. From the structural point of view, of interest is the excavation phase, which is usually performed in the water environment by a ship equipped with a dredge that mines the seabed, generating a new source of vibrations for the existing structures facing the working area. The aim of this paper is to assess the effects of vibrations induced by dredging operations, by taking as reference the recently performed nourishment in the port of Bari, Southern Italy. To this scope, an existing structure was selected and identified as sentry building, considering its extreme proximity to the worksite. Hence, a structural monitoring was performed, by investigating the behaviour of the structure before, during and after the dredging. Three main controls were carried out within the monitoring campaign: (a) check of the vibration levels and comparison with thresholds provided by the current Italian prescriptions for human comfort and structural damages; (b) operational modal analysis to assess the possible variations of the structural behaviour during dredging; (c) calibration of a numerical model to simulate the structural behaviour of the sentry building and to derive unknown geometrical and mechanical parameters. A full description of the reference building (characterized by a certain irregularity degree) and all the monitoring phases are reported throughout the manuscript. The results show that, over the monitoring period, the dredging vibration levels never exceeded the thresholds provided by code provisions, and subsequently, the sentry building did not report structural damages, as confirmed by the continuous control of dynamic parameters from experimental and numerical models. In addition, the contents of the paper show the paramount importance of the structural health monitoring, and the experience herein reported can inspire the management of buildings under particular actions like the ones herein investigated.
... In the process of enterprise O&M automation, load balancing becomes a necessary part to take into account the increasing number of services, users, and services. [9]Massive traffic is distributed to multiple servers in the background for processing to cope with high concurrency challenges. ...
The so-called automated operation and maintenance refers to a large number of repetitive tasks in daily IT operations (from simple daily checks, configuration changes and software installation to organizational scheduling of the entire change process) from manual execution in the past to standardized, streamlined and automated operations. This article delves into the realm of enterprise cloud resource optimization and management, leveraging automated operations (autoOps) as a fundamental strategy. As industries like banking witness exponential growth and innovation in IT systems, the complexity of managing resources escalates. Automated operations have emerged as a critical component, transitioning from manual interventions to encompass standardization, workflow optimization, and architectural enhancements. Through real-world deployments and theoretical frameworks, it elucidates effective strategies for optimizing and governing enterprise cloud resources, thereby enhancing efficiency, security, and resilience in IT operations.
... There are some published works that concentrate on a single turbine for a long period of time (weeks of months), and mainly under parking or cut-out conditions [6][7][8]. In others the measurement period is even shorter [9]. Analysis under operating conditions is even less frequent [10], since as already mentioned the presence of harmonics complicates the analysis. ...
... This method uses nonlinear normal modes (NNMs) to extract modal parameters to identify nonlinear vibration systems. In addition, OMA technology has been widely applied in online condition monitoring of a railway vehicle suspension system [27], on-orbit modal testing of spacecraft [28], damping estimation of offshore wind turbine towers [29], in-flight modal testing of airplanes, and other fields [30]. ...
The structural characteristics and application background of helicopters determine that the primary dynamic components work in environments with high cyclic amplitude and low-stress vibration fatigue load. As the most critical structural system of helicopters, structural health monitoring of the rotor blades is necessary to avoid fatigue damage under working conditions. Modal parameters, as functions of the physical properties of structural systems, change when there is damage or internal defects (the mass, stiffness, and damping of the structure will change). This article completes the identification of modal parameters of composite rotor blades under working conditions based on operational modal analysis (OMA). Specifically, using the AR/PR (autoregressive/polyreference) time-domain identification method, experiments are designed to identify the modal parameters (natural frequency, modal damping ratio, and mode shape) of composite rotor blades based on acceleration and strain signals. The results of the identification of modal parameters are verified through finite element simulation and modal measurement experiments. In addition, the application of OMA for the location of composite rotor blade damage is also studied.
... In the process of enterprise O&M automation, load balancing becomes a necessary part to take into account the increasing number of services, users, and services. [9]Massive traffic is distributed to multiple servers in the background for processing to cope with high concurrency challenges. ...
The so-called automated operation and maintenance refers to a large number of repetitive tasks in daily IT operations (from simple daily checks, configuration changes and software installation to organizational scheduling of the entire change process) from manual execution in the past to standardized, streamlined and automated operations. This article delves into the realm of enterprise cloud resource optimization and management, leveraging automated operations (autoOps) as a fundamental strategy. As industries like banking witness exponential growth and innovation in IT systems, the complexity of managing resources escalates. Automated operations have emerged as a critical component, transitioning from manual interventions to encompass standardization, workflow optimization, and architectural enhancements. Through real-world deployments and theoretical frameworks, it elucidates effective strategies for optimizing and governing enterprise cloud resources, thereby enhancing efficiency, security, and resilience in IT operations.
... There are some published works that concentrate on a single turbine for a long period of time (weeks of months), and mainly under parking or cut-out conditions [6][7][8]. In others the measurement period is even shorter [9]. Analysis under operating conditions is even less frequent [10], since as already mentioned the presence of harmonics complicates the analysis. ...
... The estimated modal parameters are valuable complementary data features to SCADA data and have been widely used for condition assessment of wind turbines. Bajric et al. performed automated modal analysis and focused on damping estimates of an 8 MW OWT [32]. Liu et al. proposed an improved modal strain energy method for damage localization of an OWT [33] and implemented an iterative high-energy noise elimination method to improve modal identification accuracy [34]. ...
... The second is time-variant uncertainty, described as a stochastic process consisting of a sequence of timedependent random variables. For example, in an offshore wind power system, the IGBT clamping force affected by the platform vibration should be considered a stochastic process [8]. In distribution network applications with flexible multi-state switches, the IGBT current load changes with the source/load states, which can be described as a stochastic process [9]. ...
Stress imbalance significantly affects the performance of a press-pack insulated gate bipolar transistor (IGBT). Time-variant loads and conditions lead to the stress fluctuations, exacerbating the impacts. The conventional reliability optimization faces efficiency barriers due to the nested time-variant reliability analysis and design optimization. In this paper, a time-variant reliability optimization approach for press-pack IGBTs is proposed to address the efficiency issue of the IGBT reliability optimization. The performance functions of the maximum and typical stresses are formulated as the optimization objective and constraint. A time-variant reliability optimization model is formulated considering the stress balance reliability degradation within the service cycle. A decoupling algorithm is proposed to transform the nested optimization into a sequential iteration of static reliability optimization and time-variant reliability analysis. The reliability analysis utilizes the performance function continuity in the time domain to reduce the evaluations for the most likelihood points, thereby enhancing efficiency. Numerical and experimental results on an actual IGBT demonstrate the accuracy of the stress balance performance analysis. The time-variant reliability optimization based on the performance functions improves the stress balance performance by 16.3% and meets the reliability requirements within the service cycle. Compared with the conventional double-loop approach, the difference between the solution of the proposed approach with the reference solution is 0.4%, and the efficiency is 334 times that of the double-loop approach. The performance advantages in accuracy and efficiency exhibit the application potential of this approach.
... Free decay response was also used for estimating side-side modal aerodynamic damping, by either 'rotor-stop' tests (Damgaard et al., 2013) or generator excitation (Hansen et al., 2006). A more advanced approach is to use Operational Modal Analysis (OMA) techniques (BogunovićJakobsen and Hjorth-Hansen, 1995;Bajrić et al., 2018) based on tower measurements from ambient excitation. OMA was employed to identify the modal damping ratios of parked WTs (Shirzadeh et al., 2013;Devriendt et al., 2014;Kramers et al., 2016), with the rotor being standstill or rotating very slowly. ...
... However, resilient control does not address the problem of controlling life consumption in wind turbine components to avoid early fatigue failures. Although new concepts like operational modal analysis (OMA), which relies on measurement data to analyze vibrating structures, are becoming the industry standard for condition monitoring and diagnosis especially for offshore wind turbines (Kim et al., 2019;Bajrić et al., 2018;Dong et al., 2018;Pegalajar-Jurado and Bredmose, 2019), these concepts have yet to be integrated for prognosis and lifetime control of wind turbines. ...
Variability in wind profiles in both space and time is responsible for fatigue loading in wind turbine components. Advanced control methods for mitigating structural loading in these components have been proposed in previous works. These also incorporate other objectives like speed and power regulation for above-rated wind speed operation. In recent years, lifetime control and extension strategies have been proposed to guarantee power supply and operational reliability of wind turbines. These control strategies typically rely on a fatigue load evaluation criteria to determine the consumed lifetime of these components, subsequently varying the control set point to guarantee a desired lifetime of the components. Most of these methods focus on controlling the lifetime of specific structural components of a wind turbine, typically the rotor blade or tower. Additionally, controllers are often designed to be valid about specific operating points and hence exhibit deteriorating performance in varying operating conditions. Therefore, they are not able to guarantee a desired lifetime in varying wind conditions. In this paper an adaptive lifetime control strategy is proposed for controlled aging of rotor blades to guarantee a desired lifetime while considering damage accumulation level in the tower. The method relies on an online structural health monitoring system to vary the lifetime controller gains based on a state-of-health (SoH) measure by considering the desired lifetime at every time step. For demonstration, a 1.5 MW National Renewable Energy Laboratory (NREL) reference wind turbine is used. The proposed adaptive lifetime controller regulates structural loading in the rotor blades to guarantee a predefined damage level at the desired lifetime without sacrificing the speed regulation performance of the wind turbine. Additionally, a significant reduction in the tower fatigue damage is observed.
... A challenging aspect associated with the estimation of the modal parameters, especially for AOMA, is the estimation of accurate damping ratios [5,12], yet their influence on structural behaviour is extensive [22]. The usage of damping as DSF are investigated in [9] for two types of infrastructures, namely reinforced concrete structures and composites. ...
The necessity of the green transition is today more extensive than ever before. Consequently, wind turbines along with wind farms are compelled to grow rapidly to encounter the obligation of a sustainable source of energy. Facing extensive expenses associated with maintenance, the exploration of a well-functional Structural Health Monitoring (SHM) system is crucial. Hence, by utilizing data from a laboratory-scale wind turbine blade in a controlled environment, numerous Damage Sensitive Features (DSFs) along with several techniques to mitigate the effect of Environmental and Operational Variability (EOV) are investigated. In this work, we consider DSFs originating from Vector Auto-Regressive (VAR) models, including natural frequencies and damping ratios as a physical quantity, and the parameters of the models as a non-physical quantity. The inevitable obscuring of the DSFs caused by EOV is mitigated by utilizing two distinct approaches. Bayesian non-linear regression models and the Principal Component Analysis (PCA) methodology, designated as an explicit and implicit approach respectively. In addition, a novel approach combining the implicit and explicit methodology is proposed. Through a comparative analysis, various considerations of interest were derived. The applicability of the various DSFs was measured in terms of correctly detected damages utilizing the multivariate squared Mahalanobis distance as a one-class classifier. The derivation was that the usage of the non-physical quantity did show prominent applicability. Generally, the combined implicit-explicit methodology showed superior efficiency. Despite the acknowledgement regarding complicating aspects entering an uncontrolled environment, the conviction of efficiency is preserved yet reduced to some extent.
... Several studies have analysed the effects of linear and nonlinear wind, waves, and currents loads over fixed structures, estimating the natural and damped period of the response (Aggarwal et al. 2017;Marino et al. 2017; Bajrić et al. 2018). Other studies highlighted that wind and wave loading mitigated vibrations of their offshore Monopile Wind Turbine (MWT) during earthquake excitations (Yang et al. 2020). ...
In order to demonstrate the relevance of considering Vortex-Induced Vibrations (VIV) in the structural design of marine structures, this study proposes an alternative experimental and analytical approach in wet conditions to measure the fluid–structure interaction in the near field and quantify the viscous damping with measured structural and 3D hydrodynamic accelerations. It was demonstrated that VIV caused and incremented 5.00% of the structural damping coefficient, and the extreme wind loading increased 74% of the offshore monopile’s structural damping, demonstrating the relevance of the high non-linear hydrodynamics effects during selecting parameters into the structural design in offshore applications.
... Besides that, Sun et al. (2017) introduced an automated operational modal analysis of a cable-stayed bridge by applying the proposed threshold for hierarchical clustering, two stages of k-means clustering were used to clear the stabilization diagram and identification of the final clusters and then density-based spatial clustering was applied to select the actual mode from each identified real cluster. In recent year, an automated procedure for covariance driven operational modal analysis (OMA) techniques was proposed to eliminate the need for a user interference for the selection of model order and size of the block-Hankel and block-Toeplitz matrices based on the reconstruction of the auto-correlation function from the cluster of complex poles (Bajrić et al., 2018). Then, the present study performed an autonomous modal parameter estimation with three-dimensional space optimization by using non-iterative correlation-based method and fuzzy c-means for the clustering and bootstrap sampling (Yaghoubi et al., 2018). ...
... OMA methods can be employed for different purposes such as model validation [6], calibration of Finite Elements Models (FEMs) [7], vibration control [8,9], Structural Health Monitoring (SHM) [10][11][12][13][14], damage detection [15], and structural identification [16][17][18]. Applications of OMA were conducted on bridges [19][20][21], historical buildings [17,22], dams [23], tall buildings [24,25], offshore platforms [26,27], and other kinds of structure [28][29][30]. ...
In this paper an innovative and simple Operational Modal Analysis (OMA) method for structural dynamic identification is proposed. It combines the recently introduced Time Domain–Analytical Signal Method (TD–ASM) with the Genetic Algorithm (GA). Specifically, TD–ASM is firstly employed to estimate a subspace of candidate modal parameters, and then the GA is used to identify the structural parameters minimizing the fitness value returned by an appropriately introduced objective function. Notably, this method can be used to estimate structural parameters even for high damping ratios, and it also allows one to identify the Power Spectral Density (PSD) of the structural excitation. The reliability of the proposed method is proved through several numerical applications on two different Multi Degree of Freedom (MDoF) systems, also considering comparisons with other OMA methods. The results obtained in terms of modal parameters identification, Frequency Response Functions (FRFs) matrix estimation, and structural response prediction show the reliability of the proposed procedure.
... Several studies analyzed the structural responses of fixed and floating structures because of the linear and non-linear wind, waves and currents loads, which estimated the natural and damped period of these structures [18][19][20][21][22][23][24][25][26][27]. Shirzadeh et al. [28] recommended experimental studies to analyze the structural behavior of offshore structures during wind and wave loads, including wind damping contribution. ...
Sea extreme events affect the integrity and operation of the offshore structures, then, it is important to analyze wind-waves-currents loads over the structural dynamics. Traditional offshore designing identifies structural parameters with certain limitations: physical modeling involves using shaking tables in dry conditions; numerical simulations have not sufficiently considered the effects of combined extreme waves-wind-current loads over the structure and the significance of the near and far hydrodynamic field over the structure. The non-linear interactions in the near hydrodynamic field generate viscous damping that modifies the dynamic structural parameters of the offshore structures. The traditional determination of structural parameters considers the hydrodynamic forces computed from wave records, omitting fluid-structure interactions that could generate unexpected damped periods and amplification peaks. This study applied physical modeling to determine floating structural parameters, considering combined loads and the effect of far and near hydrodynamic field in the fluid-structure interaction. The calculated transfer functions in the near hydrodynamic field revealed the highest amplification of the structural accelerations, and the transfer functions in the far field did not evidence structural resonance. Finally, this study recommends measuring the near hydrodynamic field and applying DOE-ANOVA for offshore designing to assess the viscous damping that may provoke dangerous structural amplifications.
This study explores tower vibrations in large-scale permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS). First, the aerodynamic characteristics of wind turbines, including wind shear (WS), tower shadow effect (TSE), and blade airfoil structure, are examined. Then, a mechanism model of tower vibration is established, and the impacts of WS and TSE on tower vibration are analyzed. Suppression schemes, including crossing resonance zone method and tower damping control, are evaluated, and a robust variable-pitch strategy based on sliding mode control is proposed to mitigate tower vibration. Comparative analysis suggests that the proposed strategy out-performs the crossing resonance zone method and the tower damping control in achieving more effective tower vibration suppression and reducing the influence of the 3p frequency component. The effectiveness of the model and algorithm is verified through simulation experiments.
Offshore wind turbines (OWTs) are subject to waves, currents, seabed shifts, and corrosion in harsh marine environment, posing significant challenges to structural integrity and durability. A prevalent issue of OWTs is the scour of foundations and cables, which can cause structural damage, interrupting the operation of OWTs and even leading to catastrophic failure. Timely detection and assessment of scour are crucial for maintaining the structural integrity and managing the operation of OWTs. This paper reviews the main methods utilized to assess scour for OWT. Three main types of scour assessment methods are reviewed, which are direct methods, vibration-based methods, and unmanned vehicle-based methods. For each type of methods, the reviewed contents mainly include the assessment principles, laboratory tests, and field applications, as well as data processing and interpretation. The limitations of existing methods and the new opportunities are discussed. This research promotes improvement of the monitoring and maintenance of OWTs.
This study investigates dynamic responses of wind turbines subjected to combined seismic and wind loads, with a particular focus on the influence of seismic input angles and the effect of aerodynamic damping. A wind tunnel‐shaking table (WTST) test platform was developed, capable of applying seismic and wind loads simultaneously. A 1:100 scale model wind turbine was tested using El‐Centro and Taft seismic records, sourced from the Pacific Earthquake Engineering Research (PEER) Strong Ground Motion Database, which were adjusted for amplitude and time to simulate realistic loading conditions. The experiments included a fixed wind input direction and seven different seismic input directions across six operational conditions (including the parked condition) to assess the influence of seismic direction on the dynamic responses of wind turbines in operation. The results show that as the seismic input angle increases from 0° to 180°, nacelle displacement initially decreases and then increases, with similar trends in nacelle acceleration and vibration. Increasing wind speed leads to a gradual reduction in nacelle displacement. While the standard deviation of acceleration initially decreases as the turbine transitions from stopped to operational, it becomes wind‐speed independent thereafter. The peak tower moment occurs in the side‐to‐side (S‐S) direction at a seismic input angle of 90°, and the acceleration amplification factor can soar to 4 at 0° and 180° seismic input angles, indicating up to a fourfold magnification of input acceleration at the nacelle. This study provides experimental evidence that seismic direction and aerodynamic damping are critical factors when evaluating the safety and reliability of operational wind turbines in earthquake‐prone areas.
Today, the green transition is being pursued more than ever, leading to a significant increase in the installation of wind turbines and wind farms. Maintaining and servicing the wind turbines is accompanied by extensive expenses. Therefore, predictive maintenance techniques are in increasing demand, including the implementation of a well-functioning Structural Health Monitoring (SHM) system. In this work, physical and non-physical vibration features along with various techniques to mitigate the effect of Environmental and Operational Variability (EOV) are investigated. Vibration features originating from Vector Auto-Regressive (VAR) models are considered. Physics-domain DSFs comprise the natural frequency, while the non-physical DSFs comprise the VAR model coefficients. A challenging and inevitable aspect in SHM is the effect of EOV that can alter the DSFs so as damage does. Two mitigation approaches are considered, the first based on Bayesian non-linear regression –explicit– and the second based on Principal Component Analysis (PCA) –implicit–. Additionally, a novel combined approach is proposed, featuring regression of Principal Components (PCs). As some of the PCs will be EOV-insensitive, the specific corrected PCs are automatically selected using the F-statistic of individual regressions. A comparative analysis is carried out in a controlled experiment, featuring the vibration response of a lab-scale wind turbine blade under various temperature and damage conditions. The methods are assessed in terms of correctly detected damages from a one-class classifier based on the squared Mahalanobis distance on the EOV-corrected features, and best performing method combinations are thereby identified.
This paper presents an automated harmonic removal technique as an efficient method for identifying and removing the influence of harmonics from the output signal. The method involves disregarding user-defined parameters during system initialization and reconstructing the output signal automatically so that it can be used for system identification. While stochastic subspace-based algorithms (SSI) are generally reliable for modal parameter estimation, applying them to structures with rotating machinery and harmonic excitations presents challenges. Because the SSI method necessitates designating parameters, such as the maximal within-cluster distance, at the outset of each dataset analysis, the issue remains unresolved. In addition to modal identification, the current research concentrates on image-based feature extraction for aggregating and classifying harmonic components and structural poles directly from a stabilization diagram. Utilizing online data sets to validate the algorithm’s efficacy. Using a comparative analysis, the proposed method is compared to existing techniques, namely orthogonal projection-based harmonic signal removal and smoothing techniques based on linear interpolation. The results indicate that the proposed algorithm estimates modal parameters precisely and consistently both before and after the removal of harmonic components from the response signal.
Modal parameters are critical for wind resistant design and vibrational serviceability assessments of long-span cable-supported bridges. In contrast to the successful research efforts into natural frequencies, there are still challenges in modeling the damping ratio due to the following aspects: (1) inherent errors in damping estimates, (2) lack of insight into the damping mechanisms, and (3) epistemic uncertainties on the effects of environmental and operational conditions (EOCs). This paper proposes a probabilistic regression model for damping using Deep Gaussian Processes (DGP) on damping estimates compiled from 2.5 years of structural health monitoring (SHM) data from a cable-stayed bridge. Input features representative of EOCs theorized to be related to damping ratios from past literature were used. Two data cleaning strategies based on statistics and knowledge-based criteria were used for enhancing the model performance. A comparative study with DGPs and different regression models were carried out to confirm the robustness of DGPs across different datasets. A knowledge-based feature engineering process examined the most significant predictor of the damping ratios. The proposed data-driven regression model can enable a probabilistic consideration of damping in structural design and vibrational serviceability assessments.
The variable-speed variable-pitch wind turbine is an important part of China's power and energy systems, and is also the main conversion form of wind energy utilization. Aiming at the problem that the traditional blade element-momentum theory cannot achieve the modeling and simulation of wind turbine plane wind unbalance caused by wind shear and tower shadow effect, the modeling and simulation numerical calculation method of aerodynamic load of wind turbine actuation disk with different blade wind unbalance pitch angles is proposed, This method can derive the analytical expressions for solving the key variables of load calculation, axial induction factor and tangential induction factor, and realize the aerodynamic load solution. At the same time, it is also verified that the characteristic vibration component of 3 times the low speed shaft rotation frequency (3P) is a typical dynamic load feature of tower shadow effect, and is also the most important aerodynamic load fluctuation feature of variable-speed variable-pitch wind turbine, However, under normal conditions, the wind shear effect has little effect on the wind turbine load fluctuation.
Operational modal analysis (OMA) methods are nowadays common in civil, mechanical and aerospace engineering to identify and monitor structural systems without any knowledge on the structural excitation provided that the latter is due to ambient vibrations. For this reason, OMA methods are embedded with stochastic concepts and then it is difficult for users that have no-knowledge in signal analysis and stochastic dynamics. In this paper an innovative method useful for structural health monitoring (SHM) is proposed. It is based on the signal filtering and on the Hilbert transform of the correlation function matrix. Specifically, the modal shapes are estimated from the correlation functions matrix of the filtered output process and then the frequencies and the damping ratios are estimated from the analytical signals of the mono-component correlation functions: a complex signals in which the real part represents the correlation function and the imaginary part is its Hilbert transform. This method is very simple to use since requires only few interactions with the users and thus it can be used also from users that are not experts in the aforementioned areas. In order to prove the reliability of the proposed method, numerical simulations and experimental tests are reported also considering comparisons with the most popular OMA methods.
In the long-term, the modal properties of Offshore Wind Turbines (OWT) exhibit significant variations due to constant changes in environmental and operational conditions. These variations have a substantial effect on the wind turbine loads and will lead, for instance, to large uncertainty in fatigue and useful life predictions. Due to the numerous sources of uncertainty, it is difficult to judge how independent environmental or operational parameters influence the modal properties of OWTs. In this work, we make a systematic analysis of the modal parameter estimates extracted from a long-term monitoring campaign in an OWT from the DanTysk wind farm while in its idling condition. We cluster the dataset of vibration responses of the idling OWT into bins of wind and wave characteristics, in order to isolate the effect of the different sources of uncertainty affecting the OWT modal properties. Once the trends in the data are confirmed, we use a simple linear regression model to extrapolate the damping estimates for zero wind speed and wave excitation, thus providing an estimate of the mean and standard errors of the OWT structural damping in the first fore-aft and side-to-side tower bending modes.
The information on long-term modal properties of civil structures under environmental and operational variations is generally required in structural health monitoring and vibration control. In operational modal analysis (OMA), damping estimates usually present larger fluctuations and uncertainties than natural frequency and mode shape estimates, which affects the precise determination of the long-term damping characteristics of civil structures. To this end, a combined OMA scheme is adopted in this paper based on the variational mode extraction technique and covariance-driven stochastic subspace identification algorithm to reduce errors in modal identification, especially for damping estimates. Through numerical simulation study of a three-story frame structure, the effectiveness and accuracy of the combined scheme for modal estimations are validated. Moreover, the combined approach is further utilized to evaluate the long-term modal properties of a 600 m high skyscraper under environmental and operational variations from the measured response records of 183 days. Based on the reliable modal estimates by the combined method, the effects of environmental factors (air temperature and relative humidity), wind conditions, and building response amplitudes on the long-term modal properties and their statistical characteristics are investigated in detail. This paper aims to provide an effective tool for analyzing the long-term modal properties of civil structures and further reveal the time evolution of the dynamical characteristics of supertall buildings under environmental and operation variations.
The correlation function-based methods have been widely in the operational modal analysis of engineering structures. However, the understanding of the advantages and disadvantages of these methods for modal estimation remains limited, which may result in inappropriate settings for key parameters adopted in these methods, thereby introducing errors in modal identification. Besides, the non-stationary features of the responses of high-rise buildings under severe wind conditions are a critical factor affecting the accuracy of modal estimates. To address these issues, the performances of several widely used correlation function-based methods are investigated via numerical simulation study of a frame structure. Then, two time-frequency domain methods with obvious advantages are selected and employed to analyze the dynamic responses of a 600 m high supertall building to determine the key parameters adopted in these techniques, and further evaluate the dynamic properties of the skyscraper during two super typhoons. Based on the reliable modal estimates, the time-varying features and amplitude dependency of modal properties as well as the natural frequency-dependent feature in damping ratios are presented and discussed. This paper aims to present effective tools for modal estimation through assessing the performances of the correlation function-based methods and determining the key settings in these methods as well as reveal the dynamic characteristics of high-rise buildings under severe typhoon conditions.
Accurate evaluation of aerodynamic damping and hydrodynamic damping is critical to response prediction and vibration control of spar-type floating offshore wind turbines. This paper presents a comprehensive analytical study of these two damping sources with respect to platform motions. Aerodynamic damping is evaluated by a newly derived aerodynamic damping matrix based on linearisation of aerodynamic resultant forces at tower top. Both radiation and viscous drag effects are considered for hydrodynamic damping. The former is analytically expressed in the form of a radiation damping matrix, while the latter is derived based on Morison's equation and strip theory. A simplified model is established based on the analytical damping expressions and successfully verified against FAST and Aqwa. Under various operational conditions, the damping ratios for different degrees of freedom of the platform are estimated using complex modal analysis. It is found that the modal damping ratios arising from different sources can be very different for different vibration modes of the platform, and the tower flexibility is proved to have negligible impact on the platform damping. For a typical operational state, surge, sway, pitch and yaw motions are highly damped, with the roll motion intermediately damped and the heave motion nearly undamped.
Various forms of energy dissipation by external damping are generated when the high-frequency vibrating pipe pile penetrates into the subsea strata. The lack of clarity in the damping mechanism limits the efficiency of marine vibratory pilesinking. In this study, a longitudinal vibration model of a pipe pile considering the coupling between the pile and the subsea strata is established. The attenuation coefficient for pile side viscous damping, the radial radiated power considering the Poisson effect of the pipe pile, and the work by the damping force at the pile bottom are derived. Adopting numerical simulations, the vibration characteristics of the pile and the energy dissipation mechanism of external damping in marine pilesinking are presented. The results show that the energy dissipated by external damping increases with the input frequency. The radial radiation loss is more than the damping energy on the pile side at the same frequency. Wall thickness affects the dissipation of viscous damping energy and radially radiated energy. Through the modulation of the input frequency and the optimization of the pipe pile structure, the energy dissipated by external damping can be reduced and the efficiency of pile sinking can be improved.
This paper is focused on a resonance phenomenon of a wind turbine system in 5. MW class, on the basis of dynamic signals acquired continuously from the tubular tower under normal operational conditions during two years. Firstly, technique specifications of the wind turbine system are introduced and a finite element model is developed to characterize the structural dynamic properties. The following part describes the continuous dynamic monitoring system integrated with an automated operational modal analysis procedure using the poly-reference Least Squares Complex Frequency domain (p-LSCF) method. Subsequently, variations and mutual relationships of environmental/operational factors such as vibration amplitude, temperature, wind speed, rotation speed of blades, pitch angle and nacelle direction are also presented. Finally, significant resonance is observed due to the fundamental frequency of the tower matching with the harmonic frequency induced by the rotation of three blades. As the rotation speed of rotor approaches to 8. rpm, the vibration amplitude of the tower increases significantly and the corresponding damping value decreases. With the further rising wind velocity, the rotation speed of blades stops increasing and the input energy just contribute to accumulate the vibration amplitude of tower. Such observation indicates the Sommerfeld effect that aggravates the resonance phenomenon. A vibration control device is necessary to minimize the excessive structural responses. A companion paper will further discuss the environmental/operational effects on dynamic properties of the wind turbine system under the operational conditions.
This study shows the first results of a long-term monitoring campaign on an offshore wind turbine in the Belgian North Sea. It focuses on the continuous monitoring of the resonant frequencies and damping values of the most dominant modes of the support structure. These parameters allow to better understand the dynamics of offshore wind turbines and are crucial in the fatigue assessment during the design phase. They can also help to minimise operation and maintenance (O&M) costs and to assess the lifetime of the offshore wind turbines structures during their operation. To do an accurate continuous monitoring of these parameters, a state-of-the-art operational modal analysis technique has been automated, so that no human-interaction is required and the system can track small changes in the dynamic behaviour of the offshore wind turbine. The study will analyse the resonant frequencies and damping values of the most dominant modes shapes while the wind turbine is in parked conditions.
It is our pleasure to present this Special Issue on "Data-Driven Approaches for Complex Industrial Systems" of the IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, which provides a forum for researchers and practitioners to report recent results on data-driven methods with applications to complex industrial systems, and to identify critical issues and challenges for future investigations in this field. Roughly, data-driven methods can be categorized into three sets, i.e., data-driven modeling, data-driven monitoring and fault diagnosis, and data-driven control and optimization (cf. Fig. 1). In this Special Issue, 13 papers are selected with novel contributions in data-driven modeling, data-driven monitoring and diagnosis, data-driven control and their industrial applications, respectively.
The focus of this work is on methods for modal identification of civil structures using output data only. An important family of time domain methods uses autoregressive time series models and exploits formulations developed in the field of system control. Another strategy consists of using methods well tested in the identification of structures on the basis of impulse response or free decay and extending them to the analysis of response signals generated by excitations of a more general nature. A third option refers to the Ho-Kalman minimal realization algorithm, which was extended by Akaike and Aoki to stochastic systems. These approaches, or their combinations, include a sizable proportion of the methods actually used in output-only identification of civil structures subjected to natural excitation, and most of them are based on stationarity assumptions. The question that prompted this study was as follows: what degrees of reliability and accuracy can such methods ensure when they are used, as is often the case in actual practice, in nonstationary conditions? An answer to this question was sought numerically by focusing on nonstationary conditions deemed typical of the actions naturally applied to civil structures. DOI: 10.1061/(ASCE)EM.1943-7889.0000503. (C) 2013 American Society of Civil Engineers.
Modal parameter estimation requires a lot of user interaction, especially when parametric system identification methods are used and the modes are selected in a stabilization diagram. In this paper, a fully automated, generally applicable three-stage clustering approach is developed for interpreting such a diagram. It does not require any user-specified parameter or threshold value, and it can be used in an experimental, operational, and combined vibration testing context and with any parametric system identification algorithm. The three stages of the algorithm correspond to the three stages in a manual analysis: setting stabilization thresholds for clearing out the diagram, detecting columns of stable modes, and selecting a representative mode from each column. An extensive validation study illustrates the accuracy and robustness of this automation strategy.
Operational modal analysis deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions. This paper extensively reviews operational modal analysis approaches and related system identification methods. First, the mathematical models employed in identification are related to the equations of motion, and their modal structure is revealed. Then, strategies that are common to the vast majority of identification algorithms are discussed before detailing some powerful algorithms. The extraction and validation of modal parameter estimates and their uncertainties from the identified system models is discussed as well. Finally, different modal analysis approaches and algorithms are compared in an extensive Monte Carlo simulation study.
An analytical comparison between three techniques for the identification of modal properties of structures when subjected to ambient vibrations is performed. The algorithms examined include the eigensystem realization algorithm with data correlations, the prediction error method through least squares, and the stochastic subspace identification (SSI) technique. Both analytical and experimental data from a four-storey building scaled at 1:3 are used to perform these evaluations. The level of noise added to the simulated data is varied to study the robustness of the techniques. All techniques are fully automated, allowing for assessments to be conducted through Monte Carlo simulations. The results indicate that the SSI technique provides the most accurate identification of natural frequencies and mode shapes even with high noise levels, all while requiring the least amount of experience for implementation.
A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.
The interest for robust automatic modal parameter extraction techniques has increased significantly over the last years, together with the rising demand for continuous health monitoring of critical infrastructure like bridges, buildings and wind turbine blades. In this study a novel, multi-stage clustering approach for Automated Operational Modal Analysis (AOMA) is introduced. In contrast to existing approaches, the procedure works without any user-provided thresholds, is applicable within large system order ranges, can be used with very small sensor numbers and does not place any limitations on the damping ratio or the complexity of the system under investigation. The approach works with any parametric system identification algorithm that uses the system order n as sole parameter. Here a data-driven Stochastic Subspace Identification (SSI) method is used. Measurements from a wind tunnel investigation with a composite cantilever equipped with Fiber Bragg Grating Sensors (FBGSs) and piezoelectric sensors are used to assess the performance of the algorithm with a highly damped structure and low signal to noise ratio conditions. The proposed method was able to identify all physical system modes in the investigated frequency range from over 1000 individual datasets using FBGSs under challenging signal to noise ratio conditions and under better signal conditions but from only two sensors.
An important step in the operational modal analysis of a structure is to infer on its dynamic behavior through its modal parameters. They can be estimated by various modal identification algorithms that fit a theoretical model to measured data. When output-only data is available, i.e. measured responses of the structure, frequencies, damping ratios and mode shapes can be identified assuming that ambient sources like wind or traffic excite the system sufficiently. When also input data is available, i.e. signals used to excite the structure, input/output identification algorithms are used. The use of input information usually provides better modal estimates in a desired frequency range. While the identification of the modal mass is not considered in this paper, we focus on the estimation of the frequencies, damping ratios and mode shapes, relevant for example for modal analysis during in-flight monitoring of aircrafts. When identifying the modal parameters from noisy measurement data, the information on their uncertainty is most relevant. In this paper, new variance computation schemes for modal parameters are developed for four subspace algorithms, including output-only and input/output methods, as well as data-driven and covariance-driven methods. For the input/output methods, the known inputs are considered as realizations of a stochastic process. Based on Monte Carlo validations, the quality of identification, accuracy of variance estimations and sensor noise robustness are discussed. Finally these algorithms are applied on real measured data obtained during vibrations tests of an aircraft.
This "Special Section on Real-Time Fault Diagnosis and Fault-Tolerant Control" of the IEEE Transactions on Industrial Electronics is motivated to provide a forum for academic and industrial communities to report recent theoretic/application results in real-time monitoring, diagnosis, and fault-tolerant design, and exchange the ideas about the emerging research direction in this field. Twenty-three papers were eventually selected through a strict peer-reviewed procedure, which represent the most recent progress on real-time fault diagnosis, fault-tolerant control design, and their applications. Twelve selected papers pay attention on fault diagnosis methods and applications, and the other eleven papers are concentrated on realtime fault-tolerant control and applications. We are going to overview the selected papers following fault diagnosis techniques and fault-tolerant control techniques, sequentially.
In this paper it is explained how the damping can be estimated using the Frequency Domain Decomposition technique for output-only modal identification, i.e. in the case where the modal parameters is to be estimated without knowing the forces exciting the system. Also it is explained how the natural frequencies can be accurately estimated without being limited by the frequency resolution of the discrete Fourier transform. It is explained how the spectral density matrix is decomposed into a set of single degree of freedom systems, and how the individual SDOF auto spectral density functions are transformed back to time domain to identify damping and frequency. The technique is illustrated on a simple simulation case with 2 closely spaced modes. On this example it is illustrated how the identification is influenced by very closely spacing, by non-orthogonal modes, and by correlated input. The technique is further illustrated on the output-only identification of the Great Belt Bridge. On this example it is shown how the damping is identified on a weakly exited mode and a closely spaced mode.
The support structure damping of a 3.6 MW pitch controlled variable speed offshore wind turbine on a monopile foundation is estimated both in standstill conditions and in normal operation. The net substructure damping is identified from the parameters of an exponential curve fitted to the relative maxima of an impulse response caused by a boat impact. The result is used in the verification of the non aerodynamic damping in normal operation for low wind speeds. The auto-correlation function technique for damping estimation of a structure under ambient excitation was validated against the identified damping from the decaying time series. The Enhanced Frequency Domain Decomposition (EFDD) method was applied to the wind turbine response under ambient excitation, for estimation of the damping in normal operation. The aero-servo-hydro-elastic tool HAWC2 is validated with offshore foundation load measurements. The model was tuned to the damping values obtained from the boat impact to match the measured loads. Wind turbulence intensity and wave characteristics used in the simulations are based on site measurements. A flexible soil model is included in the analysis. The importance of the correctly simulated damping in the model is stressed for accurate load prediction. Differences in the identified damping between the model and the wind turbine are detailed and explained. Discrepancies between simulated and measured loads are discussed.
The prevailing Operational Modal Analysis (OMA) techniques provide in most cases reasonably accurate estimates of structural frequencies and mode shapes. In contrast though, they are known to often produce poor structural damping estimates, which is mainly due to inherent random and/or bias errors. In this paper a comparison is made of the effectiveness of three existing OMA techniques in providing accurate damping estimates for varying loadings, levels of noise, number of added measurement channels and structural damping. The evaluated techniques are derived in the time domain and are namely the Ibrahim Time Domain (ITD), Eigenvalue Realization Algorithm (ERA) and the Polyreference Time Domain (PTD). The response of a two degree-of-freedom (2DOF) system is numerically established from specified modal parameters with well separated and closely spaced modes. Two types of response are considered, free response and random response from white noise loading. Finally, the results of the numerical study are presented, in which the error of the structural damping estimates obtained by each OMA technique is shown for a range of damping levels. From this, it is clear that there are notable differences in accuracy between the different techniques.
The second part of these companion papers mainly researches environmental/operational influences on structural dynamic properties under normal operational conditions during two years, in order to extract a statistical based damage-sensitive indicator for health monitoring of a wind turbine system. The correlation analyses between experimental identified frequencies, damping values as well as mode shapes and environmental/operational factors such as rotation speed of blades, wind speed, pitch angle, temperature and nacelle direction are presented. It is observed that the frequency estimates are influenced by the nacelle position, the activation of rotor, the rotation speed of blades and the wind speed as well as the temperature. Regarding to the damping estimates, they are mainly associated with variation of the aerodynamic damping due to the increasing wind speed. Besides, the resonance phenomenon is also observed in higher modes. The harmonic frequencies due to blades passing by tower are found and the corresponding damping value decreases. Moreover, the mode shapes in some modes are strongly affected by the position of the nacelle. Subsequently, two types of simulated damage including the reduction of stiffness in both the rotor blade and the tubular tower are successfully detected by applying the Principal Component Analysis (PCA) based methods to these temperature-sensitive frequency estimates. Comparison of change of the extracted health features indicates that they are more sensitive with the tower damage.
Offshore wind turbines are complex structures, and their dynamics can vary significantly because of changes in operating conditions, e.g., rotor-speed, pitch angle or changes in the ambient conditions, e.g., wind speed, wave height or wave period. Especially in parked conditions, with reduced aerodynamic damping forces, the response due to wave actions with wave frequencies close to the first structural resonance frequencies can be high. Therefore, this paper will present numerical simulations using the HAWC2 code to study an offshore wind turbine in parked conditions. The model has been created according to best practice and current standards based on the design of an existing Vestas V90 offshore wind turbine on a monopile foundation in the Belgian North Sea. The damping value of the model's first fore-aft mode has been tuned on the basis of measurements obtained from a long-term ambient monitoring campaign on the same wind turbine. Using the updated model of the offshore wind turbine, the paper will present some of the effects of the different design parameters and the different ambient conditions on the dynamics of an offshore wind turbine. The results from the simulations will be compared with the processed data obtained from the real measurements. The accuracy of the model will be discussed in terms of resonance frequencies, mode shapes, damping value and acceleration levels, and the limitations of the simulations in modeling of an offshore wind turbine will be addressed.
In this study, Operational Modal Analysis (OMA) is used to identify the damping value of the fundamental for-aft (FA) mode of an Offshore Wind Turbine (OWT) using both real life measurements and simulations. Estimations of the total damping of an offshore wind turbine (taking into account the effects of the aerodynamic, hydrodynamic and soil loads) give a quantitative view of the stability characteristics of the wind turbine. Two different test cases including an overspeed stop and ambient excitation have been considered. The experimental data has been obtained during a measurement campaign on an offshore wind turbine in the Belgian North Sea and the results are compared with the numerical simulations which have been carried out in HAWC2.
This paper aims at discussing the main challenges in testing and monitoring the in-operation vibration characteristics of wind turbines by presenting the results of the analyses performed using analytical models, aeroelastic simulations and infield vibration measurements. Within the scope of the research, the dynamic behavior of a 2.5 MW - 80 m diameter - wind turbine was monitored by using three different measurement systems namely, conventional strain gauges, photogrammetry and laser interferometry, while the turbine was both at parked condition and rotating. The modal parameters were extracted for several operation conditions and wind speeds. Similar modal analyses were also conducted on the response time histories which were generated by using an analytical mass-spring-damper model and an aeroelastic simulation tool. The main challenges in analyzing the dynamic properties of wind turbines, possible reasons of the uncertainty in the estimated modal parameters and the applicability limits of the utilized identification algorithms are discussed based on the results of these investigations.
According to the Danish wind turbine industry cross-wind vibrations due to wave loading misaligned with wind turbulence often have a significant influence on the fatigue lifespan of offshore wind turbine foundations. The phenomenon is characterised by increasing fatigue loads compared to the fore-aft fatigue and a small amount of system damping since almost no aerodynamic damping from the blades takes place. In addition, modern offshore wind turbines are flexible structures with resonance frequencies close to environmental loads and turbine blades passing the tower. Therefore, in order to avoid conservatism leading to additional costs during the load calculation and the design phase, the structural response must be analysed using reliable estimations of the dynamic properties of the wind turbines. Based on a thorough investigation of “rotor-stop” tests performed on offshore wind turbines supported by a monopile foundation for different wind parks in the period 2006–2011, the paper evaluates the first natural frequency and modal damping of the structures. In addition, fitting of theoretical energy spectra to measured response spectra of operating turbines is presented as an alternative method of determining the system damping. Analyses show distinctly time-dependent cross-wind dynamic properties. Based on numerical analysis, the variation is believed to be caused by sediment transportation at seabed level and varying performance of tower oscillation dampers.
A numerical study, motivated by applications in structural engineering, is conducted to investigate the effects of using short data sets for the identification of system damping in correlation-driven stochastic realizations. Sets of single-degree-of-freedom systems are excited with white noise and the eigensystem realization algorithm, with the aid of the modal confidence factor, is employed for the identification scheme. The study reveals information regarding the effects of sample size and Hankel matrix dimension on the resulting estimates of system damping. Results illustrate that significant bias is associated with using short data sets in a correlation-driven framework; in particular errors are seen to increase for high frequency, high-damping systems. Some of this error can be attributed to the inclusion of problematic regions of the correlation function in addition to leakage from the correlation estimation.
A general theory of resolution bias errors inherent in the usual ensemble (segment) averaging estimation procedure for spectral density, frequency response and coherence functions has been developed. It is shown that the estimation procedure is mathematically equivalent to a situation where the true correlation functions would be modified in a specified manner: that is, they would be multiplied with the normalized autocorrelation function of the window function and transformed into the frequency domain to yield the spectral density estimates. The theory is worked out for an arbitrary ideal, linear, and time-invariant system which is driven by a stationary stochastic input and for an arbitrary window function. Specifically, the rectangular and Hanning windows are compared with each other and the theoretical results are verified experimentally to great accuracy by using electrical RC- and LRC-circuits and a true random noise generator (see later parts of this series of papers). Furthermore, as an application of the theory, approximate formulas for the bias errors of spectral estimators are derived and discussed, thus extending some older results given in the literature.
This paper aims the study of the accuracy provided by the identification of modal damping ratios based on ambient and free vibration tests. For that purpose, numerical simulations were developed to generate artificial experimental data concerning both types of tests. This simulated data allowed the illustration of the influence of factors like non-proportional damping or the proximity of natural frequencies on the quality of the estimates. The accuracy of two output-only identification algorithms (Enhanced Frequency Domain Decomposition and Covariance driven Stochastic Subspace Identification methods) and of two alternative procedures to process the free decays was also analyzed.
When performing vibration tests on civil engineering structures, it is often unpractical and expensive to use artificial excitation (shakers, drop weights). Ambient excitation on the contrary is freely available (traffic, wind), but it causes other challenges. The ambient input remains unknown and the system identification algorithms have to deal with output-only measurements. For instance, realisation algorithms can be used: originally formulated for impulse responses they were easily extended to output covariances. More recently, data-driven stochastic subspace algorithms which avoid the computation of the output covariances were developed. The key element of these algorithms is the projection of the row space of the future outputs into the row space of the past outputs. Also typical for ambient testing of large structures is that not all degrees of freedom can be measured at once but that they are divided into several set-ups with overlapping reference sensors. These reference sensors are needed to obtain global mode shapes. In this paper, a novel approach of stochastic subspace identification is presented that incorporates the idea of the reference sensors already in the identification step: the row space of future outputs is projected into the row space of past reference outputs. The algorithm is validated with real vibration data from a steel mast excited by wind load. The price paid for the important gain concerning computational efficiency in the new approach is that the prediction errors for the non-reference channels are higher. The estimates of the eigenfrequencies and damping ratios do not suffer from this fact.
This paper introduces the concept of the Complex Mode Indication Function (CMIF) and its application in spatial domain parameter estimation. The concept of CMIF is developed by performing singular value decomposition (SVD) of the Frequency Response Function (FRF) matrix at each spectral line. The CMIF is defined as the eigenvalues, which are the square of the singular values, solved from the normal matrix formed from the FRF matrix, [H(jω)]H[H(jω)], at each spectral line. The CMIF appears to be a simple and efficient method for identifying the modes of the complex system. The CMIF identifies modes by showing the physical magnitude of each mode and the damped natural frequency for each root. Since multiple reference data is applied in CMIF, repeated roots can be detected. The CMIF also gives global modal parameters, such as damped natural frequencies, mode shapes and modal participation vectors. Since CMIF works in the spatial domain, uneven frequency spacing data such as data from spatial sine testing can be used. A second-stage procedure for accurate damped natural frequency and damping estimation as well as mode shape scaling is also discussed in this paper.
The “Infante D. Henrique” bridge is a concrete arch bridge, with a span of 280 m that crosses the Douro River, linking the cities of Porto and Gaia located in the North of Portugal. This structure is being monitored by a recently installed dynamic monitoring system that comprises 12 acceleration channels. This paper describes the bridge structure, its dynamic parameters identified with a previously developed ambient vibration test, the installed monitoring equipment and the software that continuously processes the data received from the bridge through an Internet connection. Special emphasis is given to the algorithms that have been developed and implemented to perform the online automatic identification of the structure modal parameters from its measured responses during normal operation. The proposed methodology uses the covariance driven stochastic subspace identification method (SSI-COV), which is then complemented by a new algorithm developed for the automatic analysis of stabilization diagrams. This new tool, based on a hierarchical clustering algorithm, proved to be very efficient on the identification of the bridge first 12 modes. The results achieved during 2 months of observation, which involved the analysis of more than 2500 datasets, are presented in detail. It is demonstrated that with the combination of high-quality equipment and powerful identification algorithms, it is possible to estimate, in an automatic manner, accurate modal parameters for several modes. These can then be used as inputs for damage detection algorithms.
A part of the loading process for flexible structures exposed to wind may stem from the structural motion itself. For improved interpretation and prediction of structural response such influences have to be quantified through some type of system identification method. In the present article, ambient vibration data has been analyzed by a system identification method valid for a linear structure driven by a (linearly filtered) white noise loading process.
Thesis (M.S.)--University of Cincinnati, 1986. Bibliography: leaf [223] Includes abstract.
In the last few years various methods of identifying structural dynamics models from modal testing data have appeared. A comparison is presented of four of these algorithms: the Eigensystem Realization Algorithm (ERA), the modified version ERA/DC where DC indicated that it makes use of data correlation, the Q-Markov Cover algorithm, and an algorithm due to Moonen, DeMoor, Vandenberghe, and Vandewalle. The comparison is made using a five mode computer module of the 20 meter Mini-Mast truss structure at NASA Langley Research Center, and various noise levels are superimposed to produced simulated data. The results show that for the example considered ERA/DC generally gives the best results; that ERA/DC is always at least as good as ERA which is shown to be a special case of ERA/DC; that Q-Markov requires the use of significantly more data than ERA/DC to produce comparable results; and that is some situations Q-Markov cannot produce comparable results.
The theory and application of a method which utilizes the free response of a structure to determine its vibration parameters are described including a laboratory experiment in which the method was used to determine the parameters related to the first three modes of vibration of a cantilever beam. The technique is also applied to a more complex generalized payload model previously tested using sine sweep method and analyzed by NASTRAN. Ten modes of the payload model are identified.
Comparing sources of damping of cross-wind motion
- N J Tarp-Johansen
- L Andersen
- E D Christensen
- C Mørch
- S Frandsen
- B Kallesøe
N.J. Tarp-Johansen, L. Andersen, E.D. Christensen, C. Mørch, S. Frandsen,
B. Kallesøe, Comparing sources of damping of cross-wind motion, in: European Offshore Wind 2009: Conference & Exhibition, Stockholm, Sweden, 1416 September, 2009.
- J S Bendat
- A G Piersol
- Random Data
J.S. Bendat, A.G. Piersol, Random Data: Analysis and Measurement Procedures,
vol. 729, John Wiley Sons, 2011.
Estimation of damping in suspension bridges
- J M W Brownjohn
J.M.W. Brownjohn, Estimation of damping in suspension bridges, in: Proceedings of the Institution of Civil Engineers-structures and Buildings, vol.
104(4), 1994, pp. 401e416.
Estimation of Natural Frequency and Damping of Offshore WTGs on Monopiles from Measurements of Ambient Vibrations
- F Rüdinger
- Tarp-Johansen Nj
Rüdinger F and Tarp-Johansen NJ. Estimation of Natural Frequency and
Damping of Offshore WTGs on Monopiles from Measurements of Ambient
Vibrations. In preparation, 2016.
Automated frequency domain decomposition for operational modal analysis
- R Brincker
- P Andersen
- N J Jacobsen
R. Brincker, P. Andersen, N.J. Jacobsen, Automated frequency domain
decomposition for operational modal analysis, in: Proceedings of the 25th
International Modal Analysis Conference (IMAC), Orlando, USA, IMAC-XXIV,
2007.
FLEX4-Simulation of wind turbine dynamics, in: State of the Art of Aeroelastic Codes for Wind Turbine Calculations
- S Øye
S. Øye, FLEX4-Simulation of wind turbine dynamics, in: State of the Art of
Aeroelastic Codes for Wind Turbine Calculations, Kongens Lyngby, Denmark,
1996.
Control Design for a Pitch-regulated
- M H Hansen
- A D Hansen
- T J Larsen
- S Øye
- P Sørensen
- P Fuglsang
M.H. Hansen, A.D. Hansen, T.J. Larsen, S. Øye, P. Sørensen, P. Fuglsang, Control
Design for a Pitch-regulated, Variable Speed Wind Turbine, RisøNational
Laboratory, Roskilde, Denmark, 2005.