Rainflow Counting Research Articles

On non‐parametric fatigue optimization

AbstractThe present work presents a novel approach for semi‐analytic adjoint sensitivity‐based design optimization for nonproportional fatigue damage. In order to apply fatigue damage in sensitivity‐based design optimizations, an essential part is to calculate correct sensitivities. However, this is not straight forward since fatigue damage calculation typically include rainflow counting and critical plane search algorithms. Therefore, no derivatives are directly available for the fatigue damage calculation, only functional values given by numerical computation. In existing literature the considered fatigue damage calculation is simplified until a closed‐form differentiability is satisfied. However, these simplifications are not applicable for industrial examples where accurate fatigue life estimates are required. In the present work numerical differentiation of the fatigue damage values with respect to the stress tensor is applied to calculate semi‐analytical adjoint sensitivities at material points for multiple load cases. The proposed method is verified and demonstrated using different damage parameter types including critical plane analysis. Additionally, different academic and industrial numerical examples are compared to stress and stiffness optimized designs. The fatigue damage optimized designs show improved fatigue damage results for both the specific damage parameter types and when comparing to stress and stiffness optimized designs. Furthermore, it is successfully applied for different design variables (sizing, non‐parametric shape and bead) as well as different optimization formulations using fatigue damage either as objective or constraint.

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.

Comparison of some selected time-domain fatigue failure criteria dedicated for multi input random non-proportional loading conditions in industrial components

This paper presents time-domain procedure to evaluate High-Cycle Fatigue (HCF) life of industrial components with complicated geometries and subjected to multi-input random loading conditions. To this end, the authors discuss some well-known equivalent stress criteria which can consider the orientation of critical plane changes with the time in non-proportional loading conditions to estimate the time history of equivalent stress. This task is successfully accomplished by knowing time histories of local stress tensor components in a critical area of the part that is prone to failure. Next, two different categories were used to predict fatigue life of component: 1- Linear Damage Accumulation (LDA) rule by employing Rain-flow cycle counting and 2- probabilistic approach by utilizing level crossing counting method. To apply these methodologies and awareness of their challenges, a case study was performed on the automotive steering knuckle. Finally, the predicted lives were compared to experimental results, and the accuracies of different fatigue life assessment techniques were reported. The obtained results show that combination of Rain-flow cycle counting with the Liu-Zenner criterion and especially, with the Energy-based instant fatigue damage tracing proposed by Shariyat lead to the highest accuracies. However, using the probabilistic approach, we will get the response in a much shorter time compared to another category. Therefore, the choice which method to use also depends on the parameters of the research situation, and the interaction of the two factors of prediction accuracy and prediction time in the industry.

Online Battery Protective Energy Management for Energy-Transportation Nexus

Grid-connected electric vehicles (GEVs) and energy-transportation nexus bring a bright prospect to improve the penetration of renewable energy and the economy of microgrids (MGs). However, it is challenging to determine optimal vehicle-to-grid (V2G) strategies due to the complex battery aging mechanism and volatile MG states. This article develops a novel online battery anti-aging energy management method for energy-transportation nexus by using a novel deep reinforcement learning (DRL) framework. Based on battery aging characteristic analysis and rain-flow cycle counting technology, the quantification of aging cost in V2G strategies is realized by modeling the impact of number of cycles, depth of discharge, and charge and discharge rate. The established life loss model is used to evaluate battery anti-aging effectiveness of agent actions. The coordination of GEVs charging is modeled as multiobjective learning by using a DRL algorithm. The training objective is to maximize renewable penetration while reducing MG power fluctuations and vehicle battery aging costs. The developed energy-transportation nexus energy management method is verified to be effective in optimal power balancing and battery anti-aging control on a MG in the U.K. This article provides an efficient and economical tool for MG power balancing by optimally coordinating GEVs charging and renewable energy, thus helping promote a low-cost decarbonization transition.

Experimental Fatigue Evaluation of Bogie Frames on Metro Trains

Metro vehicles have always been known for their high passenger density, frequent traffic flow and strong alternating loads due to their severe running environment. As the major support component, the bogie frame suffers from fatigue damages and receives a high intensity of interest. In this work, a theoretical model is presented between the measured strain and the structural stress via multiple load identification, wherein recognition matrices and stress evaluations of the bogie frame are defined according to the locations found in finite element analysis (FEA). The model is validated through random loading in FE simulation, and the load deviation is within 1.1 kN. A vehicle experiment was performed on the second bogie of the head car on a six-car metro train. The signed von Mises (SVM) stress was calculated at critical locations with the proposed method and compared with what was measured. The excessive part was no more than 14.97%, comparing the reconstructed with the measured amounts. Stress spectra were developed utilizing rain-flow counting and evaluated in terms of the damage accumulation rule with the optimal spectra groups determined from convergence analysis. The evaluation indicates that, when the running mileage increases to the full life cycle of 3,960,000 km, the maximum equivalent damage reaches 0.35 and 0.46 at the gear box base for measured and reconstructed amounts, respectively. Research outcomes suggest that the proposed method offers an alternative for fatigue assessment and maintenance strategies on metro vehicles, as well as other types of rail-transit vehicles.

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.

Influence of loading sequence on wind induced fatigue assessment of bolts in TV-tower connection block

Bolted connections are widely employed in structures like transmission poles, wind turbines, and television (TV) towers. The behaviour of bolted connections is often complex and plays a significant role in the overall dynamic characteristics of the structure. The goal of this work is to conduct a fatigue lifecycle assessment of such a bolted connection block of a 193 m tall TV tower, for which 205 days of real measurement data have been obtained from the installed monitoring devices. Based on the recorded data, the best-fit stochastic wind distribution for 50 years, the decisive wind action, and the locations to carry out the fatigue analysis have been decided. A 3D beam model of the entire tower is developed to extract the nodal forces corresponding to the connection block location under various mean wind speeds, which is later coupled with a detailed complex finite element model of the connection block, with over three million degrees of freedom, for acquiring stress histories on some pre-selected bolts. The random stress histories are analysed using the rainflow counting algorithm (RCA) and the damage is estimated using Palmgren-Miner's damage accumulation law. A modification is proposed to integrate the loading sequence effect into the RCA, which otherwise is ignored, and the differences between the two RCAs are investigated in terms of the accumulated damage.

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.

Lidar-assisted model predictive control of wind turbine fatigue via online rainflow counting considering stress history

Abstract. The formulation of parametric online rainflow counting implements the standard fatigue estimation process and a stress history in the cost function of a model predictive controller. The formulation is tested in realistic simulation scenarios in which the states are estimated by a moving horizon estimator and the wind is predicted by a lidar simulator. The tuning procedure for the controller toolchain is carefully explained. In comparison to a conventional model predictive controller (MPC) in a turbulent wind setting, the novel formulation is especially superior with low lidar quality, benefits more from the availability of wind prediction, and exhibits a more robust performance with shorter prediction horizons. A simulation excerpt with the novel formulation provides deeper insight into the update of the stress history and the fatigue cost parameters. Finally, in a deterministic gust setting, both the conventional and the novel MPC – despite their completely different fatigue costs – exhibit similar pitch behavior and tower oscillations.

Assessment of an actuator disk‐based approach for the prediction of fatigue loads in a perspective of wind farm‐scale application

AbstractThis work aims at assessing the loads and the fatigue estimates computed using an advanced actuator disk (AD) method coupled to large eddy simulation, at a resolution appropriate for large wind farm calculations. In order to compute pertinent fatigue loads, blade trajectories are replicated through the disk, and the AD aerodynamic forces are interpolated onto these “virtual blades” at each time step. This approach, denoted AD‐B, is verified against a Vortex‐Particle Mesh (VPM) method coupled to immersed lifting lines at a fine resolution, through simulations of an isolated rotor in a turbulent wind. Two different methods are used to evaluate the fatigue damages: the widely used Rainflow counting (RFC) procedure and the spectral Dirlik's approach (DK), both combined with a Palgrem–Miner rule. In the present work, the DK counting method is considered to further investigate the potential of extrapolating some loading data in the high frequencies, uncaptured by the AD‐B model at a coarse resolution. The results show that the fatigue estimates computed using the RFC procedure are very similar for the VPM and the AD‐B methods, thus without any modeling of the unresolved scales for the disk. Indeed, the AD‐B model captures the loads of middle and large amplitudes that contribute the most to the rotor damage. The use of extrapolated loading data makes the AD‐B fatigue estimates closer to the VPM ones, but the DK counting method globally leads to results that are quite different from those obtained using the RFC procedure. Further investigations are thus required for the combination of extrapolated loading information and spectral counting methods.

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%.

Fatigue analysis of marine diesel engine crankshaft

As one of the critical components of the main engine, the crankshaft must not be damaged during the whole operating life. Hence, fatigue characteristic analysis and life assessment plays an important role in crankshaft development. This paper analyses the fatigue strength of a marine diesel engine crankshaft and the influence of different fillet structures on the safety factor. First of all, in order to get the stress results and the stress load history of crankshaft fillet, this paper uses the finite element method to analyze the whole model and sub-model. Then, the occurrence time and position of the maximum stress in the running process is located by using the programming script. And the load spectrum is obtained by using the rain flow counting method. Finally, through the calculation, the state of maximum stress and fatigue strength are obtained. The minimum safety factor of the crankshaft fillet is 2.209, which is larger than the specified value. Therefore, the diesel engine has high reliability during operation. In order to solve the problem of stress concentration and machining at the fillet, the crankshaft fillets with different structures are also analyzed in this paper. Through the comparative analysis of the proposed scheme, the most suitable crankshaft fillet structure is two-way sinking groove fillet. So the application of this type of fillet should be considered in the design stage of diesel engine crankshaft.

Response of lightly overconsolidated clay under irregular cyclic loading and comparison with predictions from the strain accumulation procedure

Offshore wind turbine foundations are designed to withstand environmental loads from the wind and waves, both of which are cyclic in nature. The current design methods consider site-specific cyclic load histories and typically require these to be translated from a time–load history with irregular characteristics to an idealised history of parcels of cycles with uniform amplitude and constant average load. The Rainflow counting method is typically used for this translation. The idealised history is then applied in a design method, for example the strain accumulation method. These methods assume that the idealised load history will give approximately the same effect on the soil as the irregular time history. This paper investigates this assumption by a laboratory test programme where the soil response under realistic irregular loading is compared with the response under idealised loading. The laboratory programme consists of cyclic direct simple shear tests on lightly overconsolidated North Sea clay. For most problems, the test results suggest that the assumption is reasonable and represents a convenient simplification for practical design. However, for load histories with large average load, prediction of permanent strain based on idealised histories may underestimate the strain observed in tests with irregular time histories.

A Machine Learning Method for Modeling Wind Farm Fatigue Load

Wake steering control can significantly improve the overall power production of wind farms. However, it also increases fatigue damage on downstream wind turbines. Therefore, optimizing fatigue loads in wake steering control has become a hot research topic. Accurately predicting farm fatigue loads has always been challenging. The current interpolation method for farm-level fatigue loads estimation is also known as the look-up table (LUT) method. However, the LUT method is less accurate because it is challenging to map the highly nonlinear characteristics of fatigue load. This paper proposes a machine-learning algorithm based on the Gaussian process (GP) to predict the farm-level fatigue load under yaw misalignment. Firstly, a series of simulations with yaw misalignment were designed to obtain the original load data, which considered the wake interaction between turbines. Secondly, the rainflow counting and Palmgren miner rules were introduced to transfer the original load to damage equivalent load. Finally, the GP model trained by inputs and outputs predicts the fatigue load. GP has more accurate predictions because it is suitable for mapping the nonlinear between fatigue load and yaw misalignment. The case study shows that compared to LUT, the accuracy of GP improves by 17% (RMSE) and 0.6% (MAE) at the blade root edgewise moment and 51.87% (RMSE) and 1.78% (MAE) at the blade root flapwise moment.

Compilation of Load Spectrum of PHEV Transmission Assembly and Its Simulation Application

This paper presents a method for compiling the load spectrum of the transmission assembly of plug-in hybrid electric vehicles (PHEVs). Based on the analysis of the control strategy of the test vehicle, the power flow transmission route in the transmission assembly is different under different operation modes, so it is necessary to divide different load spectrum blocks according to the operation mode. Based on the big data survey of China’s national standard, it is determined that the typical working conditions are urban road working conditions, high-speed road working conditions, provincial road working conditions and poor road conditions. The mileage proportion of the various working conditions is 55:30:10:5, and the mileage of one cycle is 300 km. A total of three cycles are collected. After data processing and time-domain verification, based on the principle of maximum damage, the cycle with the largest pseudo damage is selected as the sample load data for load spectrum extrapolation. The rain flow counting method is used to count the sample load, and a two-dimensional kernel density estimation mathematical model with adaptive bandwidth is established to estimate the probability density function of the data. The extrapolated rain flow matrix is obtained through Monte Carlo simulation. The load spectrum of the two-dimensional rain flow matrix is transformed into a one-dimensional eight-stage program load spectrum by using a variable mean method, Goodman equation and equal damage principle theory. Finally, the fatigue life of the transmission assembly is simulated and calculated under the environment of Romax Designer simulation software. The two-dimensional kernel density estimation model with adaptive bandwidth is used to fit and extrapolate the load rain flow matrix of each hybrid mode of the PHEV, which solves the problem wherein the shape of the rain flow matrix of each hybrid mode of the hybrid electric vehicle is complex and difficult to fit. Finally, taking the after-sales maintenance data of this model from 2020 to the present as auxiliary proof, the failure components and the failure mileage life of the simulation test results are consistent with the results used by the actual users. This shows that the kernel density estimation model proposed in this paper can well fit the rain flow matrix of the PHEV load spectrum. The extrapolated load spectrum based on this model has high accuracy and authenticity. The method of compiling the load spectrum of the transmission assembly of a hybrid electric vehicle in this paper is effective.