Equivalent Fatigue Loads Research Articles

Study on the delamination damage prediction of wind turbine blade spar cap based on morphology feature recognition

In order to study the degradation of local mechanical properties caused by delamination defects of wind turbine blades, a progressive damage prediction method of blade spar cap based on quantitative identification of delamination morphology features by infrared thermal image was proposed in this paper. Firstly, based on the thermal conduction theory of laminate plates, infrared thermal imaging technology was used to realize quantitatively identify delamination morphology features. Then, based on the cohesive zone model (CZM) and the classical laminate theory (CLT), a numerical analysis model of unidirectional laminate with delamination defects was established, and the accuracy of the numerical model was verified by comparison with the experimental results of axial tensile and compressive displacement loads. Finally, a 2 MW-45.3 blade spar cap with maximum chord cross-section was used as a prediction model, and the effect of different delamination sizes and depths on the failure mode, failure strength and damage evolution of the blade spar cap was successfully predicted by using the equivalent fatigue load. The research shows that the delamination depth has a more profound influence on the damage of spar cap compared with the delamination size. With the increase of delamination depth, the delamination failure modes undergo the evolution process of non-buckling, local buckling, delamination expansion and strength failure. Shallow delamination causes local buckling and strength failure of blade spar cap. When the delamination depth reaches half of the spar cap thickness, the delamination extends to intralaminar and interlaminar, the local failure changes to global failure.

Proposal and application of onshore lattice wind turbine support structure and integrated multi-scale fatigue assessment method

To accommodate the development of wind turbines in areas with weak wind speeds, an upright ultra-high lattice support structure is proposed for the large wind turbine, which is prefabricated and assembled mainly from thin-walled circular hollow steel (CHS) tube elements. As a practical example, a 180 m wind turbine support structure is presented. To evaluate the fatigue performance of the new structure type with modular assembly, a new integrated multi-scale fatigue assessment method is proposed to address the shortcomings of the equivalent fatigue load method commonly used in engineering design. For any fatigue load condition, the integrated multi-scale fatigue assessment method enables accurate and efficient calculation of the relationship curve between fatigue load and hot spot stress, and identification of the locations in the structure where fatigue accumulation damage is the greatest. Furthermore, fatigue damage accumulation and fatigue life can also be predicted accurately and efficiently by the proposed method. The results show that for the maximum fatigue cumulative damage of the proposed new structural systems, as the effect of average stress is not considered and the assumption of superposition of principal stresses, the traditional equivalent fatigue load method is too conservative compared to the proposed integrated multi-scale fatigue assessment method, detrimental to cost decreasing and benefit increasing of the wind turbine structures.

Fluid-structure interaction analysis of wind turbine aerodynamic loads and aeroelastic responses considering blade and tower flexibility

With the increasing size of wind turbines, the aeroelastic phenomenon plays an essential role in the safety of wind turbines. A fluid-structure interaction (FSI) analysis for wind turbine by integrating the LES turbulent model and a structural dynamic model is carried out to investigate the aerodynamic loads and aeroelastic responses considering different inflow conditions, and blade and tower flexibility. For the first time, the time series and statistical features of aerodynamic loads, the exceedance probability, the equivalent fatigue loads, and the time series and statistical features of aeroelastic responses of wind turbine are calculated by the two-way FSI model. Furthermore, effects of inflow wind conditions and the blade and tower flexibility are investigated. It is noted that the turbulent winds result in increased fluctuations of aerodynamic loads and the equivalent fatigue load. The flap-wise motions of blades are more critical to load magnitude than the edgewise motions, and the inclusion of tower motion mitigates this aerodynamic load due to the coupling effects. Finally, it is also observed that the tower motion has a noticeable impact on the flap-wise displacement at the blade tip, and the flap-wise motions of blades significantly affect the fore-aft displacement at the tower top.

Bending moment characteristic analysis of utility-scale onshore wind turbine blades based on monitoring data

Bending moment is an important parameter in structural design of the wind turbine blades. The purpose of the present study is to accurately determine the actual bending moments on the blades of wind turbine in service and study the characteristics. It can be helpful to provide supports for the design load of wind turbine blades. For this purpose, a blade load monitoring system was developed and installed on a 2 MW onshore wind turbine to measure bending moments at the blade root. A simulation model which is consistent with the monitoring wind turbine was used to verify the availability of the system. Based on the monitored bending moments and operational conditions of the wind turbine, the characteristics and fatigue load of blade root bending moments were analyzed. Meanwhile, the relationship between bending moments of blade root and operational parameters was discussed. A thrust estimation method based on monitored bending moments of blade root was presented which will help to assess the loads on the tower and foundation of the wind turbine. At last, a calculation method of equivalent fatigue load based on wind speed-rotor speed joint distribution was established which will contribute to the fatigue design of blades.

Swept Blade Dynamic Investigations for a 100 kW Small Wind Turbine

Most small–medium-sized turbine studies have focused on presenting new design methods and corresponding performance improvements rather than detailed dynamic investigations. This paper presents comprehensive dynamic investigations of a straight and a swept-back blade for a 100 kW turbine by performing modal analysis, dynamic load analysis, and flutter analysis. The considered load cases include steady wind and operational conditions under normal and extreme turbulence. Modal results show that although both blades have similar natural frequencies, their mode shapes are quite different due to the couplings in flapwise-torsion directions introduced by the back-swept geometry. This coupling alters the aeroelastic response of the blade, which results in different loads in the operational conditions. The load analysis results show that the blade damage equivalent fatigue loads for the swept blade are much lower (up to 29% for the flapwise bending moment and 31% for the edgewise bending moment) than the straight blade. For the ultimate loads, blade root edgewise load for the swept blade is almost 50% lower than the straight blade while the flapwise ultimate load is similar for both blades. Moreover, both blades have no aeroelastic instability near the operational conditions, and the flutter limit for the swept-back blade is lower than the straight blade.

RESIDUAL PERFORMANCE ANALYSIS OF BRIDGE STRUCTURE CONSIDERING HEAVY LOAD EFFECT

The structural performance of bridges eventually decreases, and risk in bridge operations increase, as well as the equivalent effect of vehicle loads, particularly heavy traffic. To further clarify the relationship between the residual performance of the bridge under heavy traffic and the fatigue damage, a batch of prestressed concrete fatigue test beams was designed. The equivalent fatigue load, considering the heavy load effect, was determined through investigation and statistics of actual traffic load data. The fatigue failure morphology and crack development of the test beam under the equivalent fatigue load were analyzed based on the fatigue damage principle. The constant amplitude fatigue test method was used to analyze the development law of concrete residual strain, non-prestressed tendon residual strain, and prestressed tendon residual strain. Based on the damage model theory, the damage equation between the damage variable D and the cumulative residual plastic strain ?p considering the effects of heavy traffic was found. In addition, through the test data, the fatigue damage evolution curve based on the development of residual strain was obtained. Research results show that the fatigue test failure is a bending failure of the non-prestressed tendon fatigue fracture. The fatigue life of the beam reduced drastically when the heavy load effect is considered. From the perspective of residual performance, the residual strain of concrete is a good indicator for calculating the fatigue damage index of beams. The research results provide an early warning of fatigue failure and performance evaluation.

Stiffness Degradation Law of Prestressed Concrete Beams under Equivalent Fatigue Loads

Stiffness Degradation Law of Prestressed Concrete Beams under Equivalent Fatigue Loads

Optimal TMD design for floating offshore wind turbines considering model uncertainties and physical constraints

The wind resources can be efficiently tapped using floating offshore wind turbines (FOWTs). However, the increased loading due to coupled action of wind and waves can affect the efficiency of the wind turbines. Structural control utilizing tuned mass damper (TMD) is an effective solution for response control of FOWT. An efficient framework for optimal design of TMD is presented in this paper. The main features of the proposed framework are: (1) The design of TMD is cast in the form of feedback control problem. The parameters of the TMD like stiffness and damping acts like a static-controller, whose gains are evaluated such that the performance specifications (described by a certain norm of the FOWT and/or TMD responses) are minimized, (2) the performance specifications are reduced to a convex program using linear matrix inequalities (LMIs), (3) the optimization problem is solved using an iterative LMI procedure, (4) the design procedure incorporates model uncertainties and, (5) the physical constraints (like TMD relative displacement) can also be incorporated by formulating design problem as multi-objective optimization. The optimal TMD design is illustrated for a case where TMD is installed in nacelle. Finally, the nonlinear dynamic response of the FOWT with the optimized TMD is evaluated using aero-hydro-servo-elastic analysis. Five different load cases with varying wind and wave loading are considered for simulations. The performance assessment is carried out in terms of structural response, damage equivalent fatigue loads and fluctuations in power generation. The designed TMDs are found to be effective for all the load cases. The proposed methodology is found to be effective for optimal tuning of the TMDs for response control of FOWT.

Model Predictive Active Power Control for Optimal Structural Load Equalization in Waked Wind Farms

In this article, we propose a model predictive active power control (APC) enhanced by the optimal coordination of the structural loadings of wind turbines (WTs) operating with fully developed wind farm (WF) flows that have extensive interactions with the atmospheric boundary layer. In general, the APC problem, that is, distributing a WF power reference among the operating WTs, does not have a unique solution; this fact can be exploited for structural load alleviation of the individual WTs. Therefore, we formulated a constrained optimization problem to simultaneously minimize the WF power reference tracking errors and the structural load deviations of the WTs from their mean value. The wind power plant is represented by a dynamic 3-D large-eddy simulation model, whereas the predictive controller employs a simplified, computationally inexpensive model to predict the dynamic power and load responses of the turbines that experience turbulent WF flows and wakes. An adjoint approach is an efficient tool used to iteratively compute the gradient of the formulated parameter-varying optimal control problem over a finite prediction horizon. We have discussed the applicability, key features, and computational complexity of the controller by using a WF example consisting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times 4$ </tex-math></inline-formula> turbines with different wake interactions for each row. The performance of the proposed adjoint-based model predictive control for APC was evaluated by measuring power reference tracking errors and the corresponding damage equivalent fatigue loads of the WT towers; we compared our proposed control design with recently published proportional–integral-based APC approaches.

Proposal of a novel GPU-accelerated lifetime optimization method for onshore wind turbine dampers under real wind distribution

In recent years, the criticality of fore-aft vibrations induced by winds on wind turbine towers has increased; these vibrations are generally evaluated using equivalent fatigue load (EFL). This is the first study to adopt wind speed histories from large eddy simulations as input for dynamic analysis of wind turbines, and to evaluate EFL against real wind distribution. Tuned mass damper (TMD) and rotational inertial double tuned mass damper (RIDTMD) were employed to control these vibrations. Parametric analysis of the damper parameters was conducted. An innovative global optimization tool was developed based on a radial basis function neural network and genetic algorithm. Moreover, for the first time, GPU acceleration technologies were adopted to enable the optimizations of dampers through massive cases. Numerical results show that damper optimizations under real wind distributions are essential, and that optimized dampers reduce 44% EFL. The performance of RIDTMD is better than TMD but has a narrower system control bandwidth. The optimized dampers are significantly affected by wind speed; however, they are least affected by wind direction. The developed GPU-based codes can run 2001 times faster than the CPU-based ones, and the optimization tool can further reduce 85% computational time, which is open to other researchers.

Optimization of wind turbine TMD under real wind distribution countering wake effects using GPU acceleration and machine learning technologies

Excessive fore-aft vibrations of wind turbine tower are the major reason for tower collapsing, which can be evaluated using the equivalent fatigue load (EFL). Wake effects are generated by the former wind turbines on the latter ones, and can greatly increase EFL and reduce lifetime of the latter ones, but they were seldom considered. Consequently, this study calculated EFL countering the wake effects under real wind distributions. The effects of wind turbine spacing on EFL indicate that the wake effects between wind turbines with spacing of approximately 2 times of rotor radius should be considered. Subsequently, tuned mass damper (TMD) was placed in the nacelle to passively control the fore-aft vibrations. An optimization tool for TMDs was developed based on the radial basis function neural network and genetic algorithm, which was compared with the theoretical equations and parametric analysis. GPU acceleration technology was utilized. Numerical results show that, under real wind distributions, the TMDs obtain at least 40.1% EFL reduction, which is 8.9% higher than the theoretically optimized one. Importantly, the GPU-based codes can run 2001 times faster than the CPU-based ones, and the optimization tool can reduce 44.9% computational time further. The codes are made available for other researchers.

Comparative study of short-term extreme responses and fatigue damages of a floating wind turbine using two different blade models

In this work, two different blade structural models are used to estimate the blade deformations and the global structural responses of a 10MW floating offshore wind turbine (FOWT). One model is based on the Euler-Bernoulli beam theory and it is solved by the linear normal mode superposition method. The other model is based on the geometry exact beam theory (GEBT) which can consider the full geometric nonlinearity and large deformation. The control equations of GEBT are discretized by Legendre spectral finite elements. The aero-hydro-servo-elastic fully coupled numerical simulations are conducted in the open-source analysis tool OpenFAST to explore the feasibility of the two different structural models for modeling large scale wind turbine blades. Both the steady-state and dynamic results show that power generation and thrust on rotor are similar for the different blade models. There is a small difference in the results of the blade pitch angle and flapwise and edgewise blade root bending moment at high wind speeds due to the lack of torsion degree of freedom in the mode-based method. The difference between the two models is mainly reflected in the prediction of blade tip deformations. The one-hour short-term extreme blade root bending moments and the damage equivalent fatigue loads at blade root are both compared based on the two models. For edgewise bending moment, the extreme value of GEBT model is found at cut-out wind speed, whereas the linear beam model predicts the extreme value around rated wind speed. For the flapwise bending moment, the extreme value is captured around the rated wind speed for both of the two models, but GEBT model presents a larger value. As for fatigue loads, the short-term 1 Hz damage equivalent loads calculated based on the linear beam model are smaller than GEBT model at almost all load cases for both edgewise and flapwise root bending moment, which implies that the linear beam model may underestimate the life time fatigue damage at blade root.

Equivalent fatigue load approach for fatigue design of uncertain structures

Industrial structures undergo complex loading, often unsuitable for the design and validation phases of their development. Engineers seek simplified signals to replace them, yet equivalent in terms of fatigue. A general framework for the construction of equivalent fatigue loads is presented, intended to take into account some uncertainty on the structure of interest. The guiding idea is to describe this uncertainty through parameters of the structure model, and then to assure the equivalence of damage or failure behavior over the whole range of expected parameters. The approach is applied in the case of structures undergoing multiple channels of concentrated forces.

Equivalent constant-amplitude fatigue load method based on the energy equivalence principle

An equivalent constant-amplitude cyclic loading method for random vehicle load is proposed based on the concept of energy equivalence. The filtered compound Poisson process is adopted to describe random vehicle load, through which the vehicle load spectrum is gained. The total dissipated energy due to fatigue loads subjected to concrete structures is deduced by introducing a multi-scale model, in which the energy dissipation induced by the nano-cracks level is presented, and the energy transition from nano to macro scales is derived. By assuming that the total energy dissipation under random loading equals that under equivalent constant-amplitude loading, the equivalent load ratio and amplitude as well as the number of equivalent cycles for random vehicle load are obtained. To validate the effectiveness of the proposed method, a set of numerical simulations is presented. The fatigue damage accumulations for concrete structures under both the random load and the equivalent loads converted by the proposed method and the classic root mean square method are calculated. By comparing with the root mean square method, the accuracy and advantage of the proposed equivalent load model are verified.

An active power control approach for wake-induced load alleviation in a fully developed wind farm boundary layer

Abstract. This paper studies a closed-loop wind farm control framework for active power control (APC) with a simultaneous reduction of wake-induced structural loads within a fully developed wind farm flow interacting with the atmospheric boundary layer. The main focus is on a classical feedback control, which features a simple control architecture and a practical measurement system that are realizable for real-time control of large wind farms. We demonstrate that the wake-induced structural loading of the downstream turbines can be alleviated, while the wind farm power production follows a reference signal. A closed-loop APC is designed first to improve the power-tracking performance against wake-induced power losses of the downwind turbines. Then, the nonunique solution of APC for the wind farm is exploited for aggregated structural load alleviation. The axial induction factors of the individual wind turbines are considered control inputs to limit the power production of the wind farm or to switch to greedy control when the demand exceeds the power available in the wind. Furthermore, the APC solution domain is enlarged by an adjustment of the power set-points according to the locally available power at the waked wind turbines. Therefore, the controllability of the wind turbines is improved for rejecting the intensified load fluctuations inside the wake. A large-eddy simulation model is employed for resolving the turbulent flow, the wake structures, and its interaction with the atmospheric boundary layer. The applicability and key features of the controller are discussed with a wind farm example consisting of 3×4 turbines with different wake interactions for each row. The performance of the proposed APC is evaluated using the accuracy of the wind farm power tracking and the wake-induced damage equivalent fatigue loads of the towers of the individual wind turbines.

Decoupled simulations of offshore wind turbines with reduced rotor loads and aerodynamic damping

Abstract. Decoupled load simulations are a computationally efficient method to perform a dynamic analysis of an offshore wind turbine. Modelling the dynamic interactions between rotor and support structure, especially the damping caused by the rotating rotor, is of importance, since it influences the structural response significantly and has a major impact on estimating fatigue lifetime. Linear damping is usually used for this purpose, but experimentally and analytically derived formulas to calculate an aerodynamic damping ratio often show discrepancies to measurement and simulation data. In this study decoupled simulation methods with reduced and full rotor loads are compared to an integrated simulation. The accuracy of decoupled methods is evaluated and an optimization is performed to obtain aerodynamic damping ratios for different wind speeds that provide the best results with respect to variance and equivalent fatigue loads at distinct output locations. Results show that aerodynamic damping is not linear, but it is possible to match desired output using decoupled models. Moreover, damping ratios obtained from the empirical study suggest that aerodynamic damping increases for higher wind speeds.

Multiple-feedback control of power output and platform pitching motion for a floating offshore wind turbine-generator system

Abstract An approach for multiple-feedback control of generator power and nacelle fore-aft speed employing blade pitch and generator torque manipulations was developed for a spar-type floating offshore wind turbine-generator system. The development of this approach was carried out through numerical analysis using the aeroelastic simulation model (FAST), measured high wind speed data, and simulated irregular sea waves. The novelty of this multiple-feedback control approach is the increase of the generator torque in response to the platform pitching motion to the leeward side and the control of the generator power instead of the rotational speed. First, theoretical analysis of the open loop transfer function revealed that the multiple-feedback control approach improves the stability of the generator power control in the floating offshore wind turbine-generator system. Then, the optimal parameter settings of the multiple-feedback control were determined and the effectiveness of employing a first-order lag filter for the nacelle fore-aft speed was shown through a sensitivity analysis. A comparison of system performances demonstrated that the multiple-feedback control approach reduces the power output fluctuation, the platform pitching motion, and the damage equivalent fatigue load of the fore-aft bending moment at the tower-base part by 52%, 22%, and 16%, respectively, relative to the gain-scheduled feedback control of the rotational speed.

Elastic actuator line modelling for wake-induced fatigue analysis of horizontal axis wind turbine blade

Wake effect causes fatigue increase on the horizontal axis wind turbine (HAWT) blades. This wake-induced fatigue has significant impacts on the efficiency and lifespan of the whole wind farm. However, conventional aeroelastic codes are deficient in terms of turbulent wake modelling and wake interaction modelling. To accurately carry out the aeroelastic simulation in multi-wake operation, an “elastic actuator line” (EAL) model is proposed. Essentially, this model is the combination of the actuator line (AL) wake model and a finite difference structural model. The present research includes two parts. Firstly, the proposed EAL model is outlined. To better establish the two-way coupling between the structural model and the AL model, the transformation of a set of structural equations is presented. Secondly, numerical structural model is established. To verify the present model, the simulated results by EAL for a single NREL 5 MW turbine are compared with those obtained with the aeroelastic code FAST. And the comparison shows a good agreement for both high and low TSRs (Tip-Speed-Ratios). Another case study for the wake interaction involving two staggered HAWTs is also carried out, which shows that the downstream wind turbine truly experiences an obvious wake-induced fatigue increase based on our equivalent fatigue load analysis.

Uncertainty propagation through an aeroelastic wind turbine model using polynomial surrogates

Abstract Polynomial surrogates are used to characterize the energy production and lifetime equivalent fatigue loads for different components of the DTU 10 MW reference wind turbine under realistic atmospheric conditions. The variability caused by different turbulent inflow fields are captured by creating independent surrogates for the mean and standard deviation of each output with respect to the inflow realizations. A global sensitivity analysis shows that the turbulent inflow realization has a bigger impact on the total distribution of equivalent fatigue loads than the shear coefficient or yaw miss-alignment. The methodology presented extends the deterministic power and thrust coefficient curves to uncertainty models and adds new variables like damage equivalent fatigue loads in different components of the turbine. These surrogate models can then be implemented inside other work-flows such as: estimation of the uncertainty in annual energy production due to wind resource variability and/or robust wind power plant layout optimization. It can be concluded that it is possible to capture the global behavior of a modern wind turbine and its uncertainty under realistic inflow conditions using polynomial response surfaces. The surrogates are a way to obtain power and load estimation under site specific characteristics without sharing the proprietary aeroelastic design.

Prediction of wind‐turbine fatigue loads in forest regions based on turbulent LES inflow fields

AbstractLarge‐eddy simulations (LES) were used to predict the neutral atmospheric boundary layer over a sparse and a dense forest, as well as over grass‐covered flat terrain. The forest is explicitly represented in the simulations through momentum sink terms. Turbulence data extracted from the LES served then as inflow turbulence for the simulation of the dynamic structural response of a generic wind turbine. In this way, the impact of forest density, wind speed and wind‐turbine hub height on the wind‐turbine fatigue loads was studied. Results show for example significantly increased equivalent fatigue loads above the two forests. Moreover, a comparison between LES turbulence and synthetically generated turbulence in terms of load predictions was made and revealed that synthetic turbulence was able to excite the same spectral peaks as LES turbulence but lead to consistently lower equivalent fatigue loads. Copyright © 2016 John Wiley &amp; Sons, Ltd.