Rainflow Counting Method Research Articles

Fatigue Damage and Reliability Assessment of Wind Turbine Structure During Service Utilizing Real-Time Monitoring Data

Under the action of wind load, a wind turbine tower will produce alternating stress, which leads to fatigue failure. According to the mean wind speed at the wind turbine impeller collected from the SCADA system, the mean wind speed of the simulation point is calculated by using the wind speed exponential model formula. Davenport spectra are used to simulate the pulsating wind speed time series. The wind spectrum is obtained using the harmonic superposition method. Subsequently, the wind speed time series and wind load time series at the simulation point are calculated. Structural modeling of a 5 MW wind turbine tower is performed in ABAQUS 2021. The modal shape and natural frequency are obtained by modal analysis to verify the rationality of the model. Subsequently, wind loads are applied to the model, and structural stress time history is obtained by transient modal dynamics analysis. The stress time history of the maximum stress area of the tower structure is extracted, and the rain flow counting method is applied to it to obtain the stress spectrum. The Weibull distribution of the stress spectrum is fitted, the mean and variance of the total damage in one day are calculated, and the fatigue reliability analysis of the maximum stress area of the tower structure is carried out. And the nonlinear fatigue cumulative damage analysis of the region is carried out. This work has implications for fatigue reliability studies for approximate operating conditions.

Multi-Stage Rolling Grid Expansion Planning for Distribution Networks Considering Conditional Value at Risk

Existing single-stage planning and multi-stage non-rolling planning methods for distribution networks have problems such as low equipment utilization efficiency and poor investment benefits. In order to solve the above problems, this paper firstly proposes a multi-stage rolling planning method for distribution networks based on analyzing the limitations of the existing planning methods, which divides the planning cycle of the distribution network into multiple planning stages, and makes rolling amendments to the planning scheme of each stage according to the latest information during the planning cycle. Then, a multi-stage rolling planning model of distribution network taking into account conditional value at risk is established with the objective of minimizing the total investment and operation cost of the distribution network. On the one hand, the users’ electricity bill is taken into account in the objective function, and the necessity of this part of the benefits is demonstrated. On the other hand, the conditional value at risk is used to quantify the uncertainty of the operation cost in the process of the expansion planning of the distribution network, which reduces the operation cost risk of the distribution network. Next, this paper uses the rainflow counting method to characterize the capacity decay characteristics of energy storage in the distribution network, and proposes an iterative solution framework that considers energy storage capacity decay to solve the proposed model. Finally, the proposed method is applied to an 18-node distribution network planning case. This confirms that the multi-stage rolling planning method could improve the investment benefits and reduce the investment cost by approximately 27.27%. Besides, it will increase the total cost by approximately 2750 USD in the case if the users’ electricity bill is not taken into account. And the maximum capacity of energy storage may decay to 87.6% of the initial capacity or even lower during operation, which may cause the line current to exceed the limit if it is not taken into account.

Tendon fatigue analysis of tension leg platform using a new time-domain quasi-dynamic method

Due to the non-Gaussian characteristics of the tendon tension response of tension leg platform (TLP), the common statistical model is not adequate to estimate the fatigue damage accurately in the frequency domain, thus the time domain analysis is required. A new quasi-dynamic method is proposed to calculate the tendon tension response considering various factors. An equivalent analytical tendon model is employed and the post-treatment has been carried out for the reconstruction of the high-frequency stress response based on the vertical motion QTFs of each tendon by HydroSTAR. Forty sets of environmental cases are extracted from a scatter diagram. The rainflow counting method is applied to deal with the stress time series and the fatigue damage can be obtained combined with the relevant S-N curve. The number of cycles of tension for each tendon is discussed, considering the contribution of the first-order wave load, the second-order diff-frequency wave load, and the second-order sum-frequency wave load. The comparison of annual fatigue damage based on the quasi-dynamic method and coupled method by Orcaflex is carried out. The study proves that the quasi-dynamic method is an efficient way to estimate the fatigue life of each tendon in the time domain considering numerous cases of discrete sea states.

Wind turbine foundation ring fatigue reliability analysis under wind-load using SCADA system

Under the action of wind load, the foundation ring of the fan will generate stress concentration and alternating stress, leading to fatigue failure. Based on the average wind speed obtained from the supervisory control and data acquisition (SCADA) system, the orthogonal expansion method of random pulsating wind field and the number theory point selection method are used to calculate and simulate the corresponding pulsating wind speed time series, and then calculate the wind speed time series and wind load time series. Based on the ABAQUS finite element software, a model of a 5 MW wind turbine is established. The modal analysis is used to obtain the modal vibration pattern and the intrinsic frequency to verify the reasonableness of the structural modeling. Subsequently, the wind load time series is applied to the wind turbine model to obtain the stress time series using instantaneous modal dynamic analysis (Modal dynamics). The stress time series at the location of maximum stress concentration in the foundation ring is extracted, and the stress time series with the same stress amplitude is obtained through conversion, which has Wiener characteristics. After obtaining the stress amplitude using the rainflow counting method, the fatigue reliability is calculated based on the structural fatigue reliability analysis method considering the threshold crossing duration of the random process. This research holds reference significance for the calculation of fatigue reliability under approximate working conditions.

Prediction of fatigue life of a bolted joint in railway steel arch bridge using multiaxial fatigue criteria

Fatigue represents a critical condition for infrastructure subjected to repeated cyclic loads, such as steel railway bridges. The literature offers several methods to estimate fatigue life, consisting of three main phases: cycle counting, fatigue damage criterion, and damage accumulation criterion. Applying S–N curves might not be conservative in the case of railway bridges subjected to traffic because the stress-time history is complex and cannot be reduced to a sinusoidal history. Additionally, the presence of a multiaxial stress state must be considered. Therefore, this work compares eight multiaxial fatigue damage criteria for evaluating fatigue life in a scenario between high and low-cycle fatigue. Specifically, the authors considered four low-cycle fatigue criteria, namely Smith–Watson–Topper (SWT), Kandil, Brown and Miller (KBM), Glinka, Fatemi and Socie (FS), and four high-cycle fatigue criteria, Crossland, Basquin and the methods recommended by Eurocode 3 and British Standard. The rainflow counting method in ASTM E1049-85 (2011) and Miner’s rule for damage accumulation were used. The Polcevera railway steel bridge was selected as a case study. A 3D numerical model was developed for this purpose using Midas Civil software, taking into account the material non-linearity of the bridge’s elements. Once the area with the highest stress concentration was identified, a detailed analysis was conducted to estimate the stress and strain time histories induced by train traffic. A sensitivity analysis was conducted after critically comparing the eight methods for predicting fatigue life to assess the impact of traffic parameters, train velocity, axle load, and convoy length on fatigue life. It has been found that the criteria considering axial stress tend to overestimate the number of fatigue cycles to failure compared to the criteria, including the effect of shear stress components.

Fatigue life assessment of thermite welded rails based on laboratory tests and field measurement data

This in-depth study assesses the fatigue life of thermite-welded 60E1 rails by combining fatigue experimental tests with field measurement data. Material characterization, conducted using X-ray Diffraction (XRD), X-ray Fluorescence (XRF), and Scanning Electron Microscopy (SEM), aimed to understand the fatigue behavior of these materials. The research was particularly focused on high-speed rail lines in South Korea, targeting areas with influence of track condition to collect strain data. By combining dynamic modulus calculations from high-speed tensile tests with the rain flow counting method for determining wheel loads, and employing the Linear Cumulative Damage method for estimating rail fatigue life, this study provides novel insights into the maintenance and durability of thermite welded rails. The integration of detailed laboratory experiments with field stress data offers a significant contribution to the predictive maintenance and lifecycle management of high-speed railway infrastructure.

A CFD-DEM-FEM coupling method for the ice-induced fatigue damage assessment of ships in brash ice channels

Polar transport ships frequently traverse in the brash ice channel opened by icebreakers. Although the substantial ice resistance caused by direct collisions with the level ice is avoided, the hull still encounters collisions with the brash ice, leading to periodic damage and exacerbating the fatigue issues of the hull structure. To address the fatigue challenges faced by ships sailing in the brash ice channels, this paper proposes an ice-induced fatigue damage assessment method based on the CFD-DEM-FEM. Referring to the brash ice model test conducted at the Hamburg Ship Model Basin (HSVA), a discrete element ice model and a numerical brash ice tank are established using the CFD-DEM coupling method. The simulated ship-ice interaction is compared with HSVA’s experimental results to validate the reliability of the numerical brash ice tank and ice load. The ice load time history resulting from the ship-brash ice collision is applied to the hull, and the hot spot stress time history under each fatigue sub-condition is calculated using the FEM. The improved rain-flow counting method is employed to determine the stress level of the hot spot stress time history, and the S-N curve method based on the linear cumulative damage criterion is used to calculate the total fatigue damage of hot spots. Finally, the results of the proposed method are compared with those of the LR method. This study can serve as a valuable reference for the ice-induced fatigue assessment of ships navigating in brash ice channels.

Optimization of typical structural components of composite materials based on fatigue life

Abstract Optimizing the fatigue life of reinforced composite panels in hypersonic aircraft is crucial for enhancing performance and reliability. Employing the rainflow counting method and a linear cumulative damage model, we process stress-time history data under random loading. The optimization model, with structural fatigue life as the objective function and parameters as constraints, is tackled using genetic algorithms. This efficient approach, exemplified with needle-punched C/SiC composite reinforced panels, significantly improves fatigue life, offering substantial benefits to hypersonic aircraft.

Operation strategy and optimization configuration of hybrid energy storage system for enhancing cycle life

Hybrid energy storage system (HESS) can take advantage of complementarity between different types of storage devices, while complementary strategies applied to configuration or operation have a significant impact on the battery cycle life. Therefore, in order to enhance the battery cycle life, this paper proposes an operation strategy and configuration technique for HESS and verifies it by a scenario of HESS tracking scheduling plan. Firstly, a linear rainflow counting method, which can be embedded in the optimization process, is proposed to quantitatively evaluate the cycle life of energy storage based on the half cycle identification model. Secondly, an operation strategy with the integration of the constraint of state-of-charge (SOC) recovery capability considering the dynamic degradation of energy storage cycle life during operation is proposed to ensure a certain charging and discharging margin for storages, thereby enhancing the cycle life of HESS. Thirdly, an optimization configuration model considering the operation strategy of HESS is established based on the minimum annualized investment cost. And the linearization techniques are used to transform the original problem into a mixed-integer linear programming problem, and the mathematical programming technique is adopted to solve the problem. Finally, the effectiveness of the proposed method is validated through case studies. The results of the case studies show that the use of the HESS operation strategy proposed in this paper can manage the VRB's SOC more efficiently, and the control effect of VRB's SOC is improved by 71.5 %. Meanwhile, by controlling the VRB's SOC, the cycle life of the energy storage in the HESS can be effectively improved, which reduces the annualized cost of the HESS by 53 %.

Nonlinear fatigue damage constrained topology optimization

In engineering applications, plenty of components are subjected to variable-amplitude cyclic loading, resulting in fatigue damage, which is one of the main forms of structural damage. While the linear damage rule has long served as a fundamental approach, its limitations necessitate advancements for more accurate fatigue life predictions. Hence, this paper introduces a pioneering method termed nonlinear fatigue damage constrained topology optimization (NFDCTO). This method integrates several key components: the rainflow counting method to evaluate the non-proportional cyclic load levels, Basquin's equation to describe the S-N curve, and Morrow's plastic work interaction rule to calculate the nonlinear cumulative damage of the structure. Consequently, we establish a mathematical model for the NFDCTO method based on these components. The incorporation of penalized damage aggregation with the P-Normal function is used to address significant constraints and singularity challenges. Furthermore, by employing the adjoint method, we derive sensitivity equations for both the objective function and fatigue constraint function concerning the design variables. Subsequently, the superiority of the NFDCTO method over traditional linear fatigue damage method were verified applying 2D l-shaped beam and simply supported structures as examples. Concurrently, bridge structures were employed to investigate the effect of the sensitivity index of the material to the history of variable amplitude stresses on the optimization results. In addition, the influence of the fatigue penalty factor on the topology optimization results was assessed using a 2D cantilever beam. Finaly, we verify the effectiveness and feasibility of the NFDCTO method in addressing fatigue optimization challenges for 3D structures utilizing two 3D examples.

Directional alongwind and crosswind effects on the performance of a 15-storey steel braced frame building in seismic environment

The effect of crosswind loads on buildings has been studied since the 1980s, but only a few researchers reported on the nonlinear response of tall buildings under ultimate crosswind loads. Performance-based wind design procedures provide a structurally efficient and economical alternative to prescriptive code based design, however their establishment necessitates further research in the following areas: i) development of a straightforward procedure for the derivation of reliable wind time-history loadings from wind tunnel data; ii) assessment of the dynamic behavior of tall buildings excited by wind in the full range of response: linear-nonlinear-near collapse; and iii) quantification of the effect of directionality on building performance in the full range of response. Herein, local aerodynamic data are used to produce reliable estimations of the directional alongwind and crosswind time-history loadings for a 15-storey steel braced frame hospital building, in Montreal, Canada. The case study is designed to withstand the code-based wind and earthquake loads, as independent load combination cases. Then, advanced finite element models are employed to assess the effect of directional alongwind and crosswind loads on the building performance under increasing levels of input wind motion. Ten excitation angles from 0° to 90° are considered. Incremental dynamic analysis is employed to assess the building performance under recurring winds, including the wind directionality effect. To monitor fatigue failure, the rainflow counting method is used to approximate the number and amplitude of loading cycles exhibited by ductile brace members of the lateral force resisting system.

Structural improvement of a dredge pump based on numerical analysis to prolong its service life

Abstract Dredge pumps are prone to irreparable damage during offshore constructions: the flow passage components are rapidly worn out, and pump shafts often break. It seriously affects the construction efficiency and progress. For the case of high concentration conveying of medium coarse sand, the flow in a dredge pump was numerically studied to analyze the flow force on the impeller and the trajectories of sand particles in the impeller. A discrete phase model was introduced to predict the wear on the impeller, and the life of the pump shaft was predicted using S-N curves and the Rain-flow counting method. A new blade profile and an endwall profile were proposed to use to reduce the wear on the impeller and the structure of the shaft head were optimized to reduce the stress concentration coefficient. The numerical results showed that these measures can significantly improve the service life of the pump.

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.

Non-proportionality quantification of noisy stress-time signals using a new rainflow-based noise removal method for fatigue assessment

Non-proportional stresses near welded joints are well known to cause increased fatigue damages as compared to proportional stresses. In this paper, a new method to remove noise from stress-time signals is developed and implemented in a principal component analysis-based approach for non-proportionality quantification. The noise removal method makes it possible to remove noise from stress-time signals causing low stress ranges, while still keeping the overall shape of the signal. When the signal shape is kept it is possible to accurately predict the levels of non-proportionality. The noise removal method is based on the standard rainflow counting method. By choosing a lower stress range limit, the stress ranges assumed to be caused by noise can be excluded and the original signal shape is kept by utilizing simple polynomial fitting. This makes the approach easy to implement and easy to control as it requires only two inputs. The noise removal method and non-proportionality quantification approach are then validated against simulated signals with noise and a simple experiment with proportional loading. The results show that the newly developed method for noise reduction accurately removes noise while keeping the signal shape.

A probability density function of stress amplitude applicable to power spectral density curves of structural random vibration response

The power spectral density curves of the random vibration response of a plate specimen with different spectral width coefficients were obtained by selecting different frequency ranges, and the probability distributions of the stress amplitudes were obtained by applying Monte Carlo method and rainflow counting method. Each probability distribution was divided into three segments by the corresponding zero-order spectral moment value, and each segment was fitted using either a Rayleigh function or an exponential function. Finally, a probability density function of stress amplitude was proposed by combining two Rayleigh functions and an exponential function. The proposed probability density function can be used to obtain the stress amplitude probability distribution for the power spectral density curves of structural random vibration response with any bandwidth, and the accuracy of the proposed function was verified based on the response data of a specimen of 7075-T651 aluminum alloy material under the action of six typical power spectral curves.

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.

Enhancing fatigue reliability prediction of offshore wind turbine jacket joints through individual uncertainties for each degree of freedom of stress concentration factor

This paper presents the fatigue reliability prediction for welded planar tubular joints of offshore fixed jacket support structures. A coupled model is employed to calculate the dynamic response of the jacket support structure under wind and wave loads. Stress concentration factors (SCFs) are evaluated using Efthymiou parametric equations, and the hot-spot stresses at eight locations on the chord and brace of the tubular joints are derived by summing the stress components from axial, in-plane, and out-of-plane actions. The stress distribution is determined using the rainflow counting method, fatigue damage from an S–N curve, and Miner’s rule. Uncertainties associated with the fatigue lifetime evaluation procedure are identified, quantified, and modeled. The focus is specifically given to modeling the uncertainty related to the SCFs, and a framework is proposed to evaluate the fatigue reliability of the joint by incorporating individual uncertainties for each degree of freedom of the SCFs (i.e., axial load crown, axial load saddle, in-plane bending moment, and out-of-plane bending moment). The results reveal that assuming the same uncertainty level (Coefficient of Variation of 0.2) as recommended by DNV-RP-C210 for each degree of freedom of the SCFs and including the uncertainty after obtaining the stress distribution from rainflow counting does not consistently yield conservative reliability index values, as it depends on the critical hot spot. It is essential to note that the simplified assumptions derived from the oil and gas sector may not directly translate to the offshore wind industry due to differences in loading conditions. A reduction of up to approximately 24% in the reliability index is observed for one critical hot spot, while an increase of up to 20% was observed for another. Overall, this paper provides valuable insights into the complex interplay of factors affecting the reliability of joints in offshore fixed jacket support structures, shedding light on the need for tailored approaches to address uncertainties in the specific context of the offshore wind industry.

Reliability evaluation of IGBT power module on electric vehicle using big data

There are challenges to the reliability evaluation for insulated gate bipolar transistors (IGBT) on electric vehicles, such as junction temperature measurement, computational and storage resources. In this paper, a junction temperature estimation approach based on neural network without additional cost is proposed and the lifetime calculation for IGBT using electric vehicle big data is performed. The direct current (DC) voltage, operation current, switching frequency, negative thermal coefficient thermistor (NTC) temperature and IGBT lifetime are inputs. And the junction temperature (T j) is output. With the rain flow counting method, the classified irregular temperatures are brought into the life model for the failure cycles. The fatigue accumulation method is then used to calculate the IGBT lifetime. To solve the limited computational and storage resources of electric vehicle controllers, the operation of IGBT lifetime calculation is running on a big data platform. The lifetime is then transmitted wirelessly to electric vehicles as input for neural network. Thus the junction temperature of IGBT under long-term operating conditions can be accurately estimated. A test platform of the motor controller combined with the vehicle big data server is built for the IGBT accelerated aging test. Subsequently, the IGBT lifetime predictions are derived from the junction temperature estimation by the neural network method and the thermal network method. The experiment shows that the lifetime prediction based on a neural network with big data demonstrates a higher accuracy than that of the thermal network, which improves the reliability evaluation of system.

Research on the Dynamic Stress Tracking Test Period of the Bogie Frame for Metro Vehicle

Dynamic stress is one of the key indicators reflecting the fatigue characteristics of metro bogie frames. Considering the test costs, operation safety, and other factors, it is impossible to record all the dynamic stress data for the whole service period in the tracking test. Therefore, the overall stress spectrum is statistically deduced based on limited dynamic stress data samples, which can not only provide a basis for the fatigue reliability research of the bogie frame, but also save costs. In this paper, the typical fatigue control points in different areas of the frame with large equivalent stress are selected for research. The daily measured stress spectrum samples are obtained through the rainflow counting method, and the statistical stress spectrum is then compiled. Weibull distribution fitting of the stress spectrum is carried out to obtain the scale and shape parameter samples for different fatigue control parts. After sampling of the obtained parameter samples and conducting variance homogeneity tests as well as t-tests, the minimum sample size representing the overall distribution of the interval is obtained. Therefore, the shortest tracking test period reflecting the overall stress distribution of typical fatigue control parts can be obtained.

A hybrid frequency‐time domain life prediction method based on the critical plane theory

AbstractThis study proposes a multiaxial rainflow counting method to realize simultaneous counting of four‐channel data. The power spectral density (PSD) expressions of stresses and strains in different planes are derived according to multiaxial theories to address the fatigue problems under random vibration loading. This study takes the plane with maximum variance of shear strain PSD as the critical plane and proposes a hybrid frequency‐time domain life prediction method for calculating the life under random vibration loading in combination with the proposed new multiaxial rainflow counting method. Both the feasibilities of the proposed multiaxial rainflow counting method and hybrid frequency‐time domain life prediction method are verified by using the multiaxial fatigue experimental results of 6061‐T6 and 7075‐T6 aluminum alloys under random loading. Meanwhile, the calculation results and efficiencies of the proposed life prediction method are summarized, and the prediction effects of the different multiaxial fatigue models are evaluated, and different rainflow counting methods are compared.