Rainflow Counting Method Research Articles

Response spectrum method for fatigue damage assessment of aero-hydraulic pipeline systems

This paper proposes a response spectrum method to assess the fatigue damage of aero-hydraulic pipeline systems subjected to random airframe motion. A real-valued analytical formula for calculating the random stress response of a clamp-pipeline model transporting fluid is derived using the complex modal superposition method and random vibration theory. Based on our previous work on the response spectrum method for fatigue damage assessment, the authors establish a set of complex modal combination formulas for the expected damage rate, introducing new velocity-velocity and displacement-velocity combination coefficients. These formulas characterise the expected damage rate as a linear combination of the damage responses that are not reliant on the spatial distribution of the pipeline model. The fatigue damage assessment of different pipeline models is computationally efficient as only the natural frequencies and the mode shapes need to be calculated. The correctness of the complex modal combination equation is verified by the rain-flow counting method, and the effect of the fluid velocity on the expected damage rate is discussed.

A comparison of two wave energy converters’ power performance and mooring fatigue characteristics – One WEC vs many WECs in a wave park with interaction effects

The production of renewable energy is key to satisfying the increasing demand for energy without further increasing pollution. Harnessing ocean energy from waves has attracted attention due to its high energy density. This study compares two generations of floating heaving point absorber WEC, WaveEL 3.0 and WaveEL 4.0, regarding their power performance and mooring line fatigue characteristics, which are essential in, e.g., LCoE calculations. The main differences between the two WECs are the principal dimensions and minor differences in their geometries. The DNV software SESAM was used for simulations and analyses of these WECs in terms of buoy heave motion resonances for maximising energy harvesting, motion characteristics, mooring line forces, fatigue of mooring lines, and hydrodynamic power production. The first part of the study presents results from simulations of unit WEC in the frequency domain and in the time domain for regular wave and irregular sea state conditions. A verification of the two WECs’ motion responses and axial mooring line forces is made against measurement data from a full-scale installation. In the second part of the study, the influence of interaction effects is investigated when the WECs are installed in wave parks. The wave park simulations used a fully-coupled non-linear method in SESAM that calculates the motions of the WECs and the mooring line forces simultaneously in the time domain. The amount of fatigue damage accumulated in the mooring lines was calculated using a relative tension-based fatigue analysis method and the rainflow counting method. Several factors that influence the power performance of the wave park and the accumulated fatigue damage of the mooring lines, for example, the WEC distance of the wave park, the sea state conditions, and the direction of incoming waves, are simulated and discussed. The study's main conclusion is that WaveEL 4.0, which has a longer tube than WaveEL 3.0, absorbs more hydrodynamic energy due to larger heave motions and more efficient power production. At the same time, the accumulated fatigue damage in the moorings is lower compared to WaveEL 3.0 if the distance between the WECs in the wave park is not too short. Its motions in the horizontal plane are larger, which may require a larger distance between the WEC units in a wave park to avoid losing efficiency due to hydrodynamic interaction effects.

Flexible gear modeling and stress spectrum compilation of an artillery steering machine

To solve the load data lack problems when researching the fatigue life prediction of artillery steering machines, the flexible body model of an artillery steering gear was established using the recurdyn/fflex, based on the finite element flexible body theory. The complete artillery adjustment process of the steering gear was simulated and calculated, and the dynamic stress change of the gear under variable load conditions was obtained. Eight-level stress spectrum was compiled based on the rain flow counting method, which provides the load data basis for the subsequent reliability design and fatigue life research.

A spectral method for accurate evaluation of fatigue damage induced by wide-band non-Gaussian random processes

Evaluating the fatigue damage of marine structures subjected to random environmental loadings is of great practical significance at the design stage. In many situations, the structural responses of marine structures exhibit wide-band non-Gaussian properties. This study presents the fatigue damage assessment of wide-band softening non-Gaussian random processes by a spectral method proposed by Benasciutti and Tovo (2005b). Following this spectral method, the rainflow fatigue damage is approximated by a linear combination of its upper and lower bounds. A refined formulation of the weighting factor is proposed, which depends on the bandwidth parameters, slope parameter of the S‒N curve, and skewness and kurtosis of non-Gaussian processes. By introducing a suitable transformation function, the simulated non-Gaussian process is generated from its underlying Gaussian process. Through case studies, the effectiveness and accuracy of the present method for wide-band non-Gaussian processes are verified by comparisons with the results from the time-domain rainflow counting method and the other existing spectral methods.

Probabilistic fatigue life assessment of steel rail-bridge in dual response surface framework

A new probabilistic fatigue life assessment (PFLA) procedure is proposed considering dynamic effects of train loading, possible enhancement of axle load, and uncertainty there-in. In conventional PFLA, Monte Carlo simulation (MCS) is used to simulate stochastic load. Thereafter, rainflow counting method is used to obtain mean stress ranges. However, it is well-established now that only mean stress range may not depict the detailed stochastic nature of train axle load time-histories. Moreover, such MCS-based PFLA is computationally demanding for real-life complex structures, and routine implementation of it is quite troublesome due to dearth of skilled engineers in advanced fatigue analysis and interface software. To circumvent this, the proposed PFLA procedure resorts to dual response surface method (DRSM), which yields explicit equations for mean as well as standard deviation of stress range. Using these equations, the proposed approach directly relates fatigue life with the input factors (train speed, axle load, etc.) through an excel spreadsheet without requiring MCS. The effectiveness of the proposed procedure is elucidated through an existing steel railway bridge in India. The accuracy of the approach is also validated with four other steel bridges practically failed in fatigue. The results show that the proposed PFLA is in excellent agreement with the most accurate direct MCS-based PFLA, and the practical data obtained from failed steel bridges; whereas, the conventional moving load analysis-based deterministic fatigue life assessment approach yields significantly deviated results. Also, the proposed DRSM-based PFLA approach is observed to be computationally more efficient than the conventional direct MCS-based PFLA.

Fatigue life prediction of aircraft gun cabin structure under impact

The aircraft gun firing will cause serious impact on airframe structure. According to the gun firing principle, the muzzle blast wave is simulated by chemical explosion. ALE method is used to deal with the fluid-structure interaction between high-pressure flowing air and the surface of the cabin. Then the expression model of the impact load is established. The numerical calculation is completed to analyse the dynamic response of the cabin structure under the impact load. The parameters of load and cabin model are modified by using the experiment results. Comparing the calculated dynamic response with the experiment results, the error is within acceptable range. Multiaxial stress equivalence and rain-flow counting method are used to process the simulation impact response data to estimate the impact fatigue life. In conclusion, the paper provides a feasible method for analysing dynamic response and fatigue life of gun cabin structure.

Extreme structural response prediction and fatigue damage evaluation for large-scale monopile offshore wind turbines subject to typhoon conditions

Offshore wind is becoming the way forward for green energy harnessing worldwide. However, frequent typhoons are a major constraint for the development of offshore wind power for some regions in Asia and North America. Typhoons may pose a huge challenge to offshore wind farm development in southern China. In this paper, a fully-coupled analysis was carried out for a 10 MW large-scale monopile offshore wind turbine (OWT) using SIMO-Riflex-Aerodyn (SRA) code. The response characteristics of the OWTs in different typhoon regions are investigated based on the measured typhoon conditions in China. The effect of aerodynamic damping on the response and the load effect is analyzed in detail. Two different distribution methods are used to statistically extrapolate the response value and get the short-term extreme response. Cumulative linear fatigue damage is evaluated by the rain-flow counting method to explore the possible failure modes of large wind turbines during typhoons. The results show that aerodynamic loads play an important role in large monopile OWTs during high wind speeds in parked conditions. The extreme response and fatigue analyses from this study indicate that fatigue is a dominant failure mode for the large OWT tower during typhoons, while buckling is unlikely.

Structural fatigue reliability analysis based on active learning Kriging model

The paper introduces the active learning Kriging (ALK) model into the structural fatigue reliability analysis. Firstly, the structural variable stress is obtained by experimental tests or finite element simulation (FES). On this basis, the cyclic stress corresponding to the fatigue life is analyzed based on the rain-flow counting method and the structural fatigue life is correspondingly computed using the Miner-Palmgren damage rule. Secondly, the uncertainties to affect the structural variable stress are considered and thus the prediction of structural fatigue lives can be obtained. Further, the structural fatigue reliability model is established, and its reliability is obtained by computing the probability that the predicted fatigue lives are greater than the allowable life. Finally, to balance the accuracy and efficiency for computing the structural fatigue reliability, a small number of boundary sample points for experiment or FES are produced and the corresponding fatigue lives are computed. Sequentially, the Kriging model is adopted to approximate the structural fatigue reliability model and it is adaptively updated by the active learning strategy. Several examples are also given to demonstrate the effectiveness of the proposed ALK-based structural fatigue reliability method.

Quasi-static test loading protocols for modular steel construction joints

Owing to the different structural configuration of modular steel construction (MSC) joints compared with those in conventional structural frames, the existing loading protocols might not be applicable to MSC joints. Suitable loading protocols for MSC joints are therefore required for use in quasi-static cyclic tests, which is the focus of the present study. A representative three-dimensional MSC building was adopted in the numerical simulation programme. Dynamic analyses were carried out using the developed numerical model under a selection of seismic waves, from which the inter-storey displacements were obtained. The rainflow counting method was employed to process the obtained displacement–time histories, and the key parameters for the loading protocol, including the total number of cycles and maximum amplitude etc. were derived accordingly. A quasi-static cyclic loading protocol dedicated to MSC joints was subsequently established. The proposed loading protocol was compared with the existing loading protocols specified in ATC-24 and in FEMA-461 through numerical simulations. The examined loading protocols were applied to two typical MSC joints, and the numerical results indicated that the proposed protocol led to a small increment in the energy consumption, ductility and bearing capacity, in comparison with the two existing loading protocols. The results show that the existing and the proposed loading protocols are all deemed suitable for use in quasi-static cyclic testing of the MSC joints, and the proposed loading protocol with 37 cycles and 0.0158 rad loading peak value could provide a new and alternative loading program for the quasi-static test of MSC joint.

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.

Fatigue life and fatigue reliability assessment for long-span spatial structure based on long-term health monitoring data

Based on the structural health monitoring system of long-span cantilevered spatial structure in Taiyuan Botanical Garden, the welded details strain of the main truss welded tubular joints is monitored for a long time, and the massive monitoring data processing method and the structural fatigue performance evaluation method are studied. First, the key component of the structure is determined through using the measured data, to propose the empirical mode decomposition (EMD) method to compress the load time history, and the rain-flow counting method to extract the stress cycle to obtain the standard daily stress spectrum. Next, through the Palmgren-Miner linear cumulative damage criterion and the S-N curve, the fatigue damage analysis and fatigue life estimation method are established. Consequently, the Monte-Carlo method is used to analyze the fatigue reliability of the key component, on which basis, the influence of considering the load growth effect on the fatigue life and fatigue reliability index is analyzed. The study shows that the weld fatigue damage is mainly caused by the small number of medium amplitude strain cycles. When the load growth effect is considered, the fatigue damage development rate of the weld is significantly accelerated, resulting in a significant decrease in the fatigue life and fatigue reliability index of the weld.

Preliminary assessment of the mooring fatigue performance of a semi-submersible platform in time-domain utilizing fracture mechanics-based approach

• Fully coupled dynamic analysis of platform-mooring system is performed in time-domain. • A self-integrated program is developed for mooring fatigue analysis through fracture mechanics-based approach. • Mooring fatigue performance of a submerged platform is studied through the remaining fatigue life at different positions of diverse lines. • The influence of corrosion on fatigue performance is investigated through a finite element model with gradual degradation. This paper aims to propose a universal time-domain fatigue evaluation method for mooring fatigue analysis of marine structures utilizing a fracture mechanics-based approach. First, the tension history of the mooring lines is calculated in the time-domain through hydrodynamic analysis and converted into mooring tension cycles with corresponding ranges via the rain-flow counting method. Subsequently, mooring fatigue performance is characterized through a self-integrated program which can realize the automatic crack propagation, Stress Intensify Factor (SIF) calculation and fatigue life prediction. Finally, a comparative study is implemented to further investigate the fatigue performance at different evaluation positions of various mooring lines under various corrosion rates. Results illustrate that fatigue life is relatively longer for mooring lines on the wave-ward side and greater at both ends of each line for the applied semi-taut mooring system. Most residual mooring fatigue life is more than 129 years with an initial surface crack of a = 0.5 mm, and the crack growth rate accelerates dramatically when reaching about 2.1% of the chain diameter. Remaining fatigue life decreases significantly under increasing corrosion rates, which is typically reduced by 39.4%, 48%, 47.8% and 38.6% for mooring lines 2, 5, 8, and 11 at 0.2 mm/year corrosion rate.

A novel cycle counting perspective for energy management of grid integrated battery energy storage systems

Battery energy storage systems (BESS) are essential for flexible and reliable grid performance as the number of renewable energy sources in grids rises. The operational life of the batteries in BESS should be taken into account for maximum cost savings, despite the fact that they are beneficial for economical grid operation. In this context, this paper present a new battery cycle counting perspective for energy management of grid-connected BESS. For this purpose battery’s one full charge–discharge cycle characteristic is compared with the operating battery charge–discharge cycle every time step. This comparison was explained mathematically and graphically in detail. The results are compared with the rain flow counting method which is the most popular cycle counting algorithm. Consequently, this cycle counting approach successfully counts the battery charge/discharge cycles and it has shown that has an advantage for BESSs due to being specifically developed just for batteries.

Optimization control and economic evaluation of energy storage combined thermal power participating in frequency regulation based on multivariable fuzzy double-layer optimization

Energy storage auxiliary thermal power participating in frequency regulation of the power grid can effectively improve operating efficiency of thermal power units, but how to realize power distribution between energy storage system and thermal power units is the key to the frequency regulation operation of energy storage and thermal power combined system. Aiming at problems that full power compensation strategy is not conducive to the sustainability of energy storage output, a frequency regulation optimization control strategy of thermal powers and energy storage combined system based on multivariable fuzzy double-layer optimization is proposed in this paper. According to the output and compensation weights of the fuzzy controller, the state of charge for energy storage system can be adjusted adaptively to help thermal power units improve the dynamic frequency regulation performance of power grid. The equivalent cycle life of energy storage system is calculated by the rain-flow counting method, and the economy of system is evaluated by the net present value method in the whole life cycle of energy storage system. The effectiveness of the proposed control strategy is verified by the simulation analysis on the actual operation data which can provide a theoretical basis for frequency regulation of automatic generation control.

Four-Channel Vibrating Testbed Design for Full Vehicle Durability Simulation

The four-channel vibrating testbed for full vehicle durability simulation is indispensable for testing vehicle performance. This paper combines theoretical analysis with experimental verification, and the four-channel vibrating simulation testbed is designed. The hardware system consists of three parts: hydraulic mechanical components, sensors, and closed-loop control system, and the software system consists of platform configuration system, platform management system, and basic test system. Based on the design of the hardware system and software system, the emphasis is put on signal processing. Based on the least squares principle, the undetermined coefficients of trend items are determined, the trend items are transformed into the arithmetic mean of signal data, and the models that eliminate constant trend items are established to eliminate the trend items. In order to reflect the fatigue process of parts more truly, the anomaly points were identified and eliminated based on the two-parameter rain-flow counting method. By representing the transfer function in the frequency domain, the measured signal is changed quickly by Fourier, and the uniqueness of the transfer function is ensured by establishing an invariant system. Finally, test verification was performed on the designed testbed with the white powder noise taken as the driving signal. The test results agree well with field testing results. The design of the testbed can meet the requirements of engineering application, and its design method and signal processing method are reasonable, which has certain theoretical research significance and engineering application value.

Predicting the power module cumulative damage degree in new energy vehicle: Improved Manson model

The cumulative fatigue damage degree is a core parameter used to evaluate the service life of an IGBT module and accurately calculate the cumulative fatigue damage degree. This study is necessary to accurately evaluate the cumulative fatigue damage of insulated gate bipolar transistor (IGBT) power module in drivetrain system to improve the reliability of stable operation of electric vehicles. Especially, the improved Manson model calculates the cumulative fatigue damage of IGBT more accurately. The reliability of IGBT module is effectively evaluated to make the effective operation and maintenance strategy of drivetrain system in electric vehicles, and improving the reliability of electric vehicles. The limitations of the Manson model were considered, and an improved Manson model was proposed and the spectrum of temperature load was obtained by the rain-flow counting method of junction temperature-time curve. The cumulative fatigue damage of IGBT module was calculated using the improved Manson and Miner models. The results revealed that in situations 1 and 2, the total damage calculated by the improved Manson model was 230.25% and 8.39% higher than that of the Miner model. The working period was segmented. The results indicate that the damage degree calculated with non-segmentation was greater than that with segmentation. The total damage calculated by the improved Manson and Miner model was closer to the true value than that calculated by the Miner model.

Time-domain fatigue assessment for blade root bolts of floating offshore wind turbine (FOWT)

A methodology for time-domain fatigue assessment for preloaded blade root bolts floating offshore wind turbine (FOWT) is proposed in the paper. The stress responses of the blade root bolts are calculated by finite element (FE) method in terms of the time history of environmental loading on the blade root joint where the wind, wave, and current are taken into account. Stress ranges on blade root bolts and the corresponding cycles are achieved by the rain-flow counting method. Fatigue life prediction for blade root bolts is then conducted with use of S–N curves and Palmgren-Miner's (PM) rule. During the fatigue assessment, the mean stress effects and the influence of different design and installation factors on fatigue strength of blade root bolts are considered. A fatigue assessment for blade root bolts of a NERL 5 MW Spar type FOWT is performed to demonstrate the capability of the proposed methodology. Fatigue lives of the blade root bolts with different design and installation factors are predicted and the impact of bolt preload, bolt size and thickness of connecting flange on the fatigue strength of blade root bolts is discussed.

Dynamics research on gear transmission system of oscillating float wave energy generator

Aiming at the problem of dynamic characteristics and dynamic reliability of gear transmission system in point wave acquisition system, combined with the characteristics of randomness and instability of waves, the dynamic model of gear transmission system is established based on the simulation of actual wave excitation, and the dynamic response of gear transmission system is solved. Using rain flow counting method, the time history of gear contact stress is statistically analyzed, and the contact stress spectrum and probability distribution function of each gear pair are obtained. Based on the random process function of the stress-strength interference model, the Monte Carlo method is used to calculate and analyze the change law of the reliability of the gear transmission system over time. The results show that the reliability of the gear transmission system gradually decreases with the increase of time within 20 years, and finally the reliability is 0.8. Speed increasing gear has the greatest impact on the reliability of the transmission system.

Experimental Safety Analysis for Transplanting Device of the 4-Bar Link Type Semi-Automatic Vegetable Transplanter

The goal of this research was to analyze the load and safety of the transplanting device of the 4-bar link type semi-automatic vegetable transplanter under different workload conditions. To measure the strain at the transplanting device, a load measurement system was developed using 15 strain gauges. Field tests were conducted at 4 levels of engine speeds (750, 1000, 1250, and 1500 rpm) and 10 levels of the planting distance (0.29–0.47 m). The static safety factor was defined as the ratio between the strength of the material and the maximum stress in the transplanting device. The calculated stress data were converted from the time domain to the frequency domain using the rain-flow counting methods and Goodman’s Equation. The sum of fatigue damage was acquired based on the Palmgren–Miner’s rule. It was observed that the stresses increased with increasing engine speed and planting distance. The results show the higher engine speed and the longer planting distance will decrease the static safety factor and fatigue life. The static safety factor value was more than 1.0 for all locations and all working conditions. The minimum fatigue life was 49,153.3 h at link A (S_14), under the working condition of engine speed 750 rpm and planting distance of 0.35 m.

Multi-objective planning and optimization of microgrid lithium iron phosphate battery energy storage system consider power supply status and CCER transactions

Lithium iron phosphate battery (LIPB) is the key equipment of battery energy storage system (BESS), which plays a major role in promoting the economic and stable operation of microgrid. Based on the advancement of LIPB technology and efficient consumption of renewable energy, two power supply planning strategies and the china certified emission reduction (CCER) model are proposed respectively. Based on it, the multi-objective planning optimization model with economic benefits, environmental benefits and power supply stability as the objective function is established for the first time, and the Newton Weighted Sum Frisch method (NWSFA) solution model is adopted. In the planning process, rain flow counting method is used to research the life of BESS, which improves the accuracy of energy storage annual cost calculation. A park in northern China is taken as a case study to demonstrate the application of this model. The simulation results show that the annual economic operating cost of BESS is decreased by 18.81%, the energy supply reliability is increased by 0.15%, and the optimal electricity price adjustment ratio of the system is 15%.