Fatigue Damage Estimation Research Articles

Probabilistic model for fatigue damage estimation of wind turbines with hidden markov model and neural network

The growing demand for sustainable and affordable energy sources has led to rapid development in wind energy systems. Ensuring the long-term performance and reliability of wind turbines requires accurate estimation of fatigue damage under diverse environmental conditions. By incorporating probabilistic methods, this paper presents a comprehensive framework for long-term fatigue damage evaluation for wind turbines with high accuracy and efficiency. The proposed framework adopts the multivariate kernel density estimation to construct the high-dimensional joint probability distribution of environmental variables. A hidden Markov model serves as the driver to build the connection between historical records and future events. The short-term fatigue damage is estimated by the deep neural network based on future environmental parameters. The long-term fatigue damage is then achieved by accumulating the short-term fatigue damage evaluations with sufficient event instances. To demonstrate the applicability and effectiveness of the proposed framework, a case study is conducted with a wind turbine in the North Sea region. The fatigue damage analysis results highlight the necessity of regular inspections and maintenance for wind turbines to ensure their long-term service life and optimal performance. The framework is capable of considering a wide range of environmental factors and accounting for the inherent uncertainties and stochastic nature, providing a robust and comprehensive approach for estimating fatigue damage of wind turbines as well as other structures under long-term environmental conditions.

Optimal design of experiments for computing the fatigue life of an offshore wind turbine based on stepwise uncertainty reduction

The design of an offshore wind turbine to resist fatigue damage during its whole service life requires to estimate an expectation over the pluri-annual joint statistics of wind and wave variables. Using a full factorial-based integration for the estimation of the cumulative fatigue damage represents a tremendous computational cost with aero-servo-hydro-elastic solvers which is generally not affordable by industrial designers. To overcome this limitation, strong approximations with lumping of environmental discretized joint probability (scatter diagram) are generally employed. We present in this paper a new method, called MAKSUR, involving the iterative enrichment of a design of experiments tailored to provide a good approximation of the long term mean damage. This method relies on a Kriging response surface with a learning criterion defined as the variance of the mean damage integral. It is compared to another previous similar approach called AK-DA, also dedicated to damage prediction, but is shown to converge more efficiently and with less numerical parameters to define by the user. The potential of the method for offshore wind turbine is demonstrated by a realistic 6D floating wind turbine case study with six wind and wave input variables.

Optimizing dimension selection for rain flow counting in fatigue assessment of large-scale lattice wind turbine support structures: A comprehensive study and design guidance

The selection of dimension (d) for the rain flow counting matrix significantly influences the reliable prediction of fatigue life in wind turbine support structures. However, there are limited public reports on the impact of dimensions on the fatigue assessment of wind turbine structures. This study explores the influence of dimensions on the fatigue assessment process and outcomes, focusing on a large-scale ultra-high lattice wind turbine support structure from an engineering project. Through integrated load simulation, fatigue load time series for different design load cases (DLCs) are obtained for the overall structure. The rain flow counting method is utilized to derive the overall rain flow counting matrix (Markov_n) with varying dimensions. Subsequently, employing a multi-scale fatigue assessment method, the damage matrix (Markov_D), cumulative fatigue damage (D), and fatigue life are computed. A detailed exploration examines the impact of rain flow counting matrix dimensions on Markov_n, Markov_D, D, fatigue life, and calculation time (t). Furthermore, guidance is provided for selecting the optimal dimension for engineering design. The findings indicate that selecting dimensions that are too small results in the loss and merging of smaller mean and amplitude load values, thereby failing to accurately represent the load history. Moreover, a small dimension yields an excessively cautious estimation of cumulative fatigue damage (D) and underestimates the fatigue life, consequently inflating construction expenses.

An approach for fatigue damage estimation under broadband non-Gaussian random loadings based on the Johnson transformation model

Estimating fatigue damage of marine structures using spectral methods under broadband random loadings is a complex and challenging task. In the presence of non-Gaussian loading, the spectral method typically employs the Hermite polynomial model (HPM) to address the non-Gaussianity. However, the applicability of HPM is limited in certain non-Gaussian cases due to the requirement of monotonicity. This paper adopts the Johnson transformation model (JTM) instead of HPM and integrates it with the non-Gaussian TB method (Ding and Chen, 2015) to overcome the constraints in broadband non-Gaussian fatigue estimation. To verify the performance of the new approach, this paper analyses the transformation accuracy of the two models. Additionally, taking the time-domain fatigue damage obtained by the rainflow counting method and the linear damage accumulation rule as a benchmark, this paper compares the fatigue damage estimates obtained from the spectral methods. The comparative assessment encompasses various spectra, S-N curves, and non-Gaussian characteristics. The results indicate the performance of JTM within the non-Gaussian TB method is comparable to HPM in most cases and even surpasses it in hardening non-Gaussian cases. Given the broader applicability of JTM across ranges of skewness and kurtosis, it emerges a superior option for the non-Gaussian TB method in estimating broadband non-Gaussian fatigue damage. Furthermore, the limitations of the proposed approach are discussed.

Application of a data-driven approach for maximum fatigue damage prediction of an unbonded flexible riser

The fatigue damage prediction is a challenging issue in the design and maintenance phases of unbonded flexible pipes. This arises from the necessity of conducting numerous numerical analyses, encompassing both global performance and local structural assessments, to determine the long-term fatigue damage. To handle the computational-demanding problem for fatigue damage estimation, this work applies an efficient machine learning approach known as the AK-MDAmax approach for maximum fatigue damage estimation of unbonded flexible risers. Kriging surrogate models are employed to predict the short-term distribution of fatigue damage over the sea states. The maximum long-term fatigue damage of the flexible risers is then estimated using the AK-MDAmax approach. The verification process of the AK-MDAmax model unfolds incrementally, testing its feasibility and stability across four different scenarios with varying numbers of considered locations, ranging from 4 to 512. Comparative analyses against numerical results reveal that the AK-MDAmax approach efficiently and accurately estimates maximum long-term fatigue damage across different locations. Remarkably, a 25-fold increase in efficiency is achieved with an error margin of less than 1%. This study demonstrates the substantial potential of the proposed machine learning methodology, offering designers an efficient tool for optimizing flexible risers and mitigating computational costs and time constraints.

An efficient active learning Kriging approach for expected fatigue damage assessment applied to wind turbine structures

Estimating fatigue damage in wind turbine structures over their lifetime is a time-demanding task, necessitating simulations encompassing all the wind and wave conditions. Typically, this involves expending several thousand hours in simulation efforts. Given formidable computational demand, this study proposes an efficient active learning Kriging approach named ALK-EFDA for estimating expected fatigue damage in wind turbines. The ALK-EFDA framework leverages a Kriging surrogate model to predict fatigue damage levels across various wind-wave scenarios, and a learning function is designed to reduce Kriging prediction error in the high probability of occurrences of wind-wave cases. An active learning approach is proposed to estimate the expected fatigue damage efficiently. To validate the effectiveness of this approach, we applied it to a 15 MW Semi-submersible floating wind turbine model. The proposed approach estimates the expected short-term fatigue damage of the wind turbine tower and mooring lines. Our findings demonstrate that the ALK-EFDA method efficiently and accurately estimates fatigue damage in wind turbine structures. Compared to simulation methods, the proposed ALK-EFDA approach significantly reduces computational expenses by over 30 times. Furthermore, the absolute error, when compared to simulated results, remains at approximately 1%. This method will be a useful tool for offshore wind turbine designers.

Wind Turbine Blade Damage Evaluation under Multiple Operating Conditions and Based on 10-Min SCADA Data

The present paper aims to enable the assessment of the fatigue damage of wind turbine blades over a long duration (e.g., several months/years) in conjunction with different operating regimes and based on two information sources: the 10-min SCADA data and an interpolation using response surfaces identified using the FAST aeroelastic numerical tool. To assess blade damage, prior studies highlighted the need for a high-frequency (>1 Hz) sampling rate. Because of data availability and computation resource limitations, such methods limit the duration of the analysis period, making the direct use of such an approach based on a 1 Hz wind speed signal in current wind farms impractical. The present work investigates the possibility of overcoming these issues by estimating the equivalent damage using a 1 Hz wind speed for each 10-min sample stored in the SCADA data. In the literature, the influence of operating regimes is not considered in fatigue damage estimation, and for the first time, the present project takes a pioneering approach by considering these operating regimes.

Effects of sampling from a naval destroyer’s operational history on fatigue damage estimation

The service history of a naval destroyer, HMCS IROQUOIS, was analyzed to develop an operational profile for structural fatigue assessment. The data from 1972 through 2012 provides insights for developing data sample requirements and wave data collection approaches applicable to other aging vessels. The results show that capturing daily wave data at the recorded position sufficiently describes the encountered seaways. Artificially reducing the data set to represent incomplete hull monitoring or operational data indicates that 5–9 years of wave data were required to limit the damage rate coefficient of variation to within 15%. However, operational changes, such as those observed after this destroyer’s midlife refit, may increase data requirements. Similar requirements for convergence were observed in duration-at-sea data derived from annual days at sea or distance sailed. The findings, consistent across the class and another class of ships, show that results for this ship are not anomalous.

Digital twin approach with minimal sensors for Riser's fatigue-damage estimation

This study proposes riser fatigue monitoring based on digital twin models with a motion sensor attached to the platform and riser. The reference model was a spread-moored Floating Production Storage and Offloading (FPSO) with Steel Lazy-Wave Risers (SLWR). Coupled dynamics simulations under given environmental conditions were performed to generate synthetic sensor signals for digital twin models. Finite-element-based riser digital twin models were then constructed to run with the synthetic sensor inputs. A machine learning algorithm that estimates the 3D current profile along the water column was employed to improve the digital twin models by inputting the estimated current profile as additional loads. The digital twin models with or without the estimated current produce the time histories of behaviors and stresses along the riser, and the corresponding fatigue damage and life were estimated by the rainflow-counting method. The fatigue assessment results demonstrate its feasibility through small errors in fatigue damage.

A New Theory of Damage Estimation and Fatigue Life Prediction

There are a considerable number of fatigue damage estimation theories and fatigue life prediction of mechanical components. The most popular one is Palmgren-Minor (P-M) theory. This theory has been used in the standards for selecting the bearing –as a component subject to fatigue loading- and for expecting the bearings lives. In Wind Turbine Gearboxes (WTGs), the bearings were selected to be without maintenance for 20 to 25 years; however, in real service life, the bearing suffer from premature failure within a life span of quite less than the design life (1 to 5 years). A new applicable methodology and a procedure of calculation for damage estimation due to fatigue loading and predicting the life has been suggested and tested. Results of 20 rolling and sliding tests which conducted under severe contact loading are used to test this method. The suggested method depends on calculating the number of operating cycles under a specific contact loading level to an equivalent number of loading cycles under the average loading level. This method depends on the area under the S-N curve without any correction or loading factors and can be used to predict the WTG bearings failure to manage the maintenance because the current life prediction standards have very high percentages of error (> 400%). The reliability of this approach can be further verified by utilizing actual operational data from Supervisory Control and Data Acquisition (SCADA), used for overseeing wind turbine operations. Additional examinations are necessary to confirm the dependability of this novel method.

A Novel Method for Fatigue Damage Assessment in Bimodal Processes Considering High- and Low-Frequency Reduction Effects

Due to inherent nonlinearities within floating systems and the second-order wave forces affecting them, the dynamic responses of floating systems manifest as bimodal Gaussian processes. Consequently, the classical spectral fatigue assessment method grounded in the Rayleigh distribution cannot be applied. This paper introduces the double frequency coupled (DFC) method as a spectral fatigue assessment approach, providing an accurate estimation of fatigue damage originating from bimodal Gaussian processes. Within the DFC method, the bimodal Gaussian process is partitioned into two components: low-frequency (LF) and high-frequency (HF) processes. A Gaussian distribution is employed to describe the probability distribution function (PDF) of the amplitude reduction induced by the interaction between LF and HF processes. The PDF of small-cycle fatigue can be computed by convoluting the PDF of HF amplitudes and the reduction amplitude between LF and HF. Similarly, the PDF of large-cycle fatigue can be determined through convolution, which involves the PDF of LF amplitudes and small-cycle fatigue. The overall fatigue damage arising from the bimodal Gaussian process is obtained by directly summing the contributions of small-cycle and large-cycle fatigue. Numerical investigations of the DFC method’s effectiveness are presented through a series of parametric studies, demonstrating its robustness, efficiency, and accuracy within engineering expectations. Furthermore, the DFC method is found to be applicable to both single-slope and two-slope S-N curves.

Special mathematical transformation-based fatigue damage estimation under narrowband non-Gaussian random loadings

The frequency-domain method for estimating fatigue damage is important and efficient for engineering applications. However, when dealing with non-Gaussian loadings, the widely used method based on Hermite polynomials model (HPM) has some limitations. To overcome this problem, this paper proposes a new frequency-domain method based on a special mathematical transformation model which was proposed by Johnson (JTM) for narrowband non-Gaussian cases. Numerical simulations are used to validate the new method. Considering different types of spectra and different combinations of kurtosis and skewness, Gaussian and non-Gaussian stress time series are generated for fatigue analysis. The fatigue damage estimates from the time-domain method based on rainflow counting and the frequency-domain methods based on HPM and JTM are compared. The results demonstrate that frequency-domain fatigue damage estimation is effective, but has some errors, which are discussed in this paper. The main finding is that JTM performs as well as HPM when non-Gaussianity is not strong. Therefore, JTM can be used as an alternative to HPM for estimating fatigue damage in the frequency domain under narrowband non-Gaussian conditions.

INTELLIGENT MONITORING OF A LARGE CATAMARAN FERRY

Wave load cycles, wet-deck slamming events, accelerations and motion comfort are important considerations for high-speed catamarans operating in moderate to large waves. Although developing a hull monitoring system according to classification guidelines for such vessels is broadly acceptable, the data processing requirements for outputs such as rainflow counting, filtering, probability distribution, fatigue damage estimation and warning due to slamming can be as sophisticated to implement as the system components themselves. Advanced analytics such as machine learning and deep learning data pipelines will also create more complexities for such systems, if included. This paper provides an overview of data analytics methods and cloud computing resources for remotely monitoring motions and structural responses of a 111 m high-speed catamaran. To satisfy the data processing requirements, MATLAB Reference Architectures on Amazon Web Services (AWS) were used. Such combination enabled fast parallel computing and advanced feature engineering in a time-efficient manner. A MATLAB Production Server on AWS has been set up for near real-time analytics and execution of functions developed according to the class guidelines. A case study using Long Short‑Term Memory (LSTM) networks for ship speed and Motion Sickness Incidence (MSI) is provided and discussed. Such data architecture provides a flexible and scalable solution, leading to deeper insights through big data processing and machine learning, which supports hull monitoring functions as a service.

Modelling of rolling contact fatigue under various interface conditions

This study presents the results of modelling the rolling contact of the elastic sphere and the elastic half-space in the presence of a thin intermediate viscoelastic layer which properties are described by an elastic nonlinear Winkler body in the normal direction and a viscoelastic Maxwell body in the tangential direction. The analytical–numerical approach for the estimation of contact fatigue damage, accumulated in the elastic half-space under rolling friction conditions, is developed. The proposed model can be used, in particular, to study the effect of mechanical properties of the friction modifiers (elastic moduli and relaxation times) and its thickness as well as the relative slippage on the formation of the surface and under surface contact fatigue cracks in rails. The results of the analysis can also be applied for the estimation of efficiency of solid lubricants in rolling contacts under given operating conditions.

Estimation of the Ice-Induced Fatigue Damage to a Semi-Submersible Platform under Level Ice Conditions

This study presents a fatigue analysis procedure for inclined structures operated in level ice fields. Three methods for calculating the local ice load causing fatigue damage, namely the direct method, simplified method, and semi-analytical method, were introduced and compared. The direct method uses finite element analysis to simulate the continuous breaking of ice, while the simplified method and the semi-analytical method estimate the probability distribution of local ice loads based on theoretical equations and empirical data. The fatigue damage ratio at the target location was calculated by applying the ice load calculated by each method to a deformable finite element model of the structure. The results obtained from each method indicate that they provide a reasonable estimation of the local ice load causing fatigue damage in level ice fields. The direct method offers high accuracy but requires significant computational time, while the simplified method and semi-analytical method offer a faster analysis time and are more suitable for long-term time domain analysis. The semi-analytical method requires empirical data to supplement theoretical formulas due to the complex natural phenomena involving various environmental conditions that must be modeled. The findings of this study provide valuable insights into the prediction of fatigue damage in ice-going ships due to long-term ice impacts. The methods proposed in this study can aid in the design of Arctic ships exposed to various conditions and provide a more cost-effective and time-efficient approach to evaluating fatigue damage compared to field measurement. Future research in this field could investigate the application of these methods to other types of structures and further refine the methodology to improve accuracy and reduce computational costs.

Fatigue life analysis of monopile-supported offshore wind turbines based on hyperplastic ratcheting model

Fatigue life is an important factor to be considered in foundation design of offshore wind turbines (OWTs), and accurate prediction of fatigue damage is dependent on an appropriate foundation model. Currently, the rigid foundation is widely used to model the monopile foundation in most aero-hydro-servo-elastic simulation tools, and soil stiffness and damping are not considered. This will lead to an inaccurate estimation of fatigue damage of monopile-supported OWTs. Given this limitation, hyperplastic ratcheting model is incorporated into FAST v7, the variations of stiffness, damping and accumulated displacement for monopile-supported OWTs subjected to cyclic loadings are well considered. The validity of the implementation is demonstrated by presentation of non-linear soil resistance-displacement curves, and a series of hysteresis loops can be observed. Based on this integrated tool, extensive simulations and analyses for monopile-supported OWTs under different environmental states are performed. Furthermore, the effect of pile-soil interaction on fatigue life of monopile is quantified. The aim of this paper is to provide an accurate model to estimate fatigue life of monopile-supported OWTs.

노후 함정 강재의 기계적 특성 평가

Ships operated at sea for a long time are subjected to various kinds of loads, which may cause various types of damage. Such damages will eventually reduce the strength of hull structures. Therefore, it is necessary to estimate and evaluate the residual strength and remaining fatigue life of aging ships in order to secure structural safety, establish a reasonable maintenance plan, and make a judgment of life extension. For this purpose, the corrosion damage and local denting damage should be measured, fatigue damage estimation should be performed, and material properties of aged steel should be identified. For this study, in order to investigate the mechanical properties of aged steel, steel plates were obtained from a naval ship that reached the end of her life span. The specimens were manufactured from the obtained steel plates, and static and dynamic tensile tests, fatigue tests, and metallographic tests were performed. The mechanical properties obtained from the aged steel plates were compared with those of new steel plates to quantify the aging effect on the mechanical properties of marine steel materials.

Experimental evaluation of strategies for wind turbine farm-wide fatigue damage estimation

A significant percentage of the existing wind turbines are reaching their theoretical design life. Therefore, important decisions about decommissioning or life extension will have to be made soon. Direct measurement of strains allows estimating the accumulated fatigue damage with good accuracy over the monitoring period, but these are still rare in this industry. As this paper demonstrates, this can be used for estimation of the damage prior to and after the measurement period. Furthermore, considering that similar wind turbines of the same wind farm have similar behaviour, the damage results can be extrapolated to the entire wind farm. In this work, the strain measurements on an onshore wind turbine over two years are used to evaluate the fatigue progression over time. The experimentally evaluated fatigue damage is analyzed against operational and environmental conditions and clustered into several load cases. Then, the damage values are stored in a database according to the corresponding environmental conditions. Based on this and on the variables that characterize operating conditions recorded since the wind farm installation, it is possible to probabilistically predict the fatigue consumption in the entire wind farm. Alternative approaches to estimate fatigue damage for non-monitored operating conditions are proposed and evaluated. The obtained results are an important step to demonstrated the feasibility of farm-wide fatigue assessment with limited additional instrumentation.

Effects of finite sampling on fatigue damage estimation of wind turbine components: A statistical study

The variability of the wind turbine loads complicates fatigue assessment in the design phase, as performing simulations covering the entire lifetime is computationally expensive. The current work provides important information for assessing the uncertainty in fatigue damage estimation due to finite data. We study the sample size effect on mean, variance, and skewness of damage in each wind bin, identify the important wind bins, and study the uncertainty propagation from each wind bin to the lifetime damage using 3600 aeroelastic simulations and bootstrapping. To achieve less than 1% error in the damage estimation across all load channels in the current case study, at least 100 turbulence seeds are needed. Damage in different wind bins follows a lognormal distribution when using the conventional approach of six seeds. The provided insights and information allow the designer to achieve a specific level of accuracy for a given computational cost using strategic bin sampling.

Development of a new spectral method for fatigue damage assessment in bimodal and trimodal Gaussian random processes

Fatigue damage assessment for marine structures subjected to random environmental loadings is an important issue at the design stage. The bimodal and trimodal Gaussian fatigue damage problems have attracted great attentions from scholars in recent decades. In this paper, several existing spectral methods for fatigue damage assessment are first reviewed, then a new spectral method, named as the improved bands method, is developed based on the spectral decomposition approach. In the present method, the power spectrum of either bimodal or trimodal Gaussian process is split into narrow frequency bands, and the total fatigue damage can then be predicted by means of summing up the damages of each individual band via a linear combination rule. A parameter μ is introduced in order to modify the zero order spectral moments, so that the effect of interaction of high-frequency process superimposed on the low-frequency process can be reflected. Through comprehensive case studies, comparisons with time-domain rain-flow counting method and the other spectral methods are conducted to validate the accuracy and robustness of the proposed method. It is demonstrated that the present method can provide accurate and reasonable fatigue damage estimations for wide ranges of bimodal and trimodal cases for marine structures.