Rainflow Algorithm Research Articles

A new fast four-point rainflow cycle counting algorithm by employing a new loop iteration mode for fatigue life estimation

Purpose In order to improve the computation efficiency of the four-point rainflow algorithm, a new fast four-point rainflow cycle counting algorithm (FFRA) using a novel loop iteration mode is proposed.Design/methodology/approach In this new algorithm, the loop iteration mode is simplified by reducing the number of iterations, tests and deletions. The high efficiency of the new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.Findings The extensive simulation results show that the extracted cycles by the new FFRA are the same as those by the four-point rainflow cycle counting algorithm (FRA) and the three-point rainflow cycle counting algorithm (TRA). Especially, the simulation results indicate that the computation efficiency of the FFRA has improved an average of 12.4 times compared to the FRA and an average of 8.9 times compared to the TRA. Moreover, the equivalence of cycle extraction results between the FFRA and the FRA is proved mathematically by utilizing some fundamental properties of the rainflow algorithm. Theoretical proof of the efficiency improvement of the FFRA in comparison to the FRA is also given.Originality/value This merit makes the FFRA preferable in online monitoring systems of structures where fatigue life estimation needs to be accomplished online based on massive measured data. It is noticeable that the high efficiency of the FFRA attributed to the simple loop iteration, which provides beneficial guidance to improve the efficiency of existing algorithms.

Optimal energy management of battery with high wind energy penetration: A comprehensive linear battery degradation cost model

Lithium-ion batteries have drawn considerable attention due to their different applications in smart grids. Nevertheless, various factors, including the charging/discharging process, can cause battery capacity degradation and reduce its lifetime. Considering the high investment cost of the battery, employing an appropriate approach to integrate the battery degradation cost into the scheduling problem is vital to optimizing the battery performance. This paper proposes a novel degradation cost model for optimal battery scheduling. A linear model based on the semi-empirical approach is introduced to model the battery capacity degradation process. Moreover, a novel linear algorithm based on the rain-flow algorithm is presented to count complete and incomplete cycles. Then, a degradation cost model is presented based on the amount of battery capacity fade and engineering economics principles. The battery scheduling problem is formulated as a mixed-integer linear programming (MILP) model. In the next stage, a novel approach based on model predictive control (MPC) is utilized to decline the degradation cost and improve battery energy management. The simulation results show that integrating the battery degradation cost into the battery scheduling problem significantly influences the charge/discharge strategy and achieves more benefits for battery owners. In this regard, the proposed scheme can decrease the battery degradation cost and the amount of capacity fade by 31.62% and 37.23%, respectively. Also, considering the battery degradation process in the optimization problem leads to a more optimal and accurate outcome.

Modelling and Energy Management of an Off-Grid Distributed Energy System: A Typical Community Scenario in South Africa

Conventional power systems have been heavily dependent on fossil fuel to meet the increasing energy demand due to exponential population growth and diverse technological advancements. This paper presents an optimal energy model and power management of an off-grid distributed energy system (DES) capable of providing sustainable and economic power supply to electrical loads. The paper models and co-optimizes multi-energy generations as a central objective for reliable and economic power supply to electrical loads while simultaneously satisfying a set of system and operational parameters. In addition, mixed integer nonlinear programing (MINLP) optimization technique is exploited to maximize power system generation between interconnected energy sources and dynamic electrical load with highest reliability and minimum operational and emission costs. Due to frequent battery cycling operation in the DES, rainflow algorithm is applied to the optimization result to estimate the depth of discharge (DOD) and subsequently count the number of cycles. The validity and performance of the power management strategy is evaluated with an aggregate load demand scenario of sixty households as a benchmark in a MATLAB program. The simulation results indicate the capability and effectiveness of optimal DES model through an enhanced MINLP optimization program in terms of significant operational costs and emission reduction of the diesel generator (DG). Specifically, the deployment of DES minimizes the daily operational cost by 71.53%. The results further indicate a drastic reduction in CO2 emissions, with 22.76% reduction for the residential community load scenario in contrast to the exclusive DG system. This study provides a framework on the economic feasibility and effective planning of green energy systems (GESs) with efficient optimization techniques with capability for further development.

One-stage extraction four-point algorithm for rainflow cycle counting in fatigue life estimation

PurposeIn order to improve the computation efficiency of the four-point rainflow algorithm, a one-stage extraction four-point rainflow algorithm is proposed based on a novel data preprocessing method.Design/methodology/approachIn this new algorithm, the procedure of cycle counting is simplified by introducing the data preprocessing method. The high efficiency of new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.FindingsAccording to the data preprocessing method, in the process of cycle extraction, all equivalent cycles can be extracted at just one stage instead of two stages in the four-point rainflow algorithm, where the cycle extraction has to be performed from the doubled residue. Besides, there are no residues in the new algorithm. The extensive numerical simulation results demonstrate that the accuracy of new algorithm is the same as that of the four-point rainflow algorithm. Moreover, a comparative study based on a long input data sequence shows that the computation efficiency of the new algorithm is 42% higher than that of the four-point rainflow algorithm.Originality/valueThis merit of new algorithm makes it preferable in some application scenarios where fatigue life estimation needs to be accomplished online based on massive measured data. And it may attribute to preprocessing of input data sequence before data processing, which provides beneficial guidance to improve the efficiency of existing algorithms.

Reinforcement Learning-Based Optimal Battery Control Under Cycle-Based Degradation Cost

Battery energy storage systems are providing increasing level of benefits to power grid operations by decreasing the resource uncertainty and supporting frequency regulation. Thus, it is crucial to obtain the optimal policy for utility-level battery to efficiently provide these grid-services while accounting for its degradation cost. To solve the optimal battery control (OBC) problem using the powerful reinforcement learning (RL) algorithms, this paper aims to develop a new representation of the cycle-based battery degradation model according to the rainflow algorithm. As the latter depends on the full trajectory, existing work has to rely on linearized approximation for converting it into instantaneous terms for the Markov Decision Process (MDP) based formulation. We propose a new MDP form by introducing additional state variables to keep track of past switching points for determining the cycle depth. The proposed degradation model allows to adopt the powerful deep Q-Network (DQN) based RL algorithm to efficiently search for the OBC policy. Numerical tests using real market data have demonstrated the performance improvements of the proposed cycle-based degradation model in enhancing the battery operations while mitigating its degradation, as compared to earlier work using the linearized approximation.

Prediction of Battery Lifetime using Hybrid Solar Power System

In recent years there has been a great concern to implement more renewable energy sources to supply energy around the world. Solar energy seems to be a good choice since it is accessible and does not cause pollution. The main problem with the solar system is that energy production only takes place when the sun is shining. Large storage systems need to be developed to provide a constant and reliable source of electricity when the sun is not shining at night or when a cloud goes overhead. The main objective of this study is to predict the lifetime of the battery in the solar hybrid system. This will involve investigating the stress factor that contributes to the battery. From the simulation done in Matlab Simulink, a graph of state of charge (SOC) versus time is gathered with the help of the Rainflow algorithm extracted from the fatigue cycle of the battery. Once the fatigue cycle is determined, the ageing rate will be calculated. The outcome of this study is battery lifetime can be predicted and the proper battery can be used to reduce for maintenance purposes.

Improving the Life Service of Fe-34Mn-10Al-0.76C Tidal Turbine Blades Using Variable PMF

This paper studied the effect of increasing pulsed magnetic field (PMF) voltage during treating a Fe-34Mn-10Al-0.76C steel alloy used in fabricating a blade to be installed in a tidal turbine on its fatigue lifetime. Fatigue strength for each sample treated using PMF voltages (0, 100 and 160 V) had been investigated experimentally to plot their S-N curves while fatigue lifetime of the tidal turbine had been predicted using mathematical model established by a MATLAB code. The cyclic loadings affect the studied turbine were rearranged using Rainflow algorithm. Results of the study showed that, the blade made of Fe-34Mn-10Al-0.76C steel alloy and treated using PMF 100 v had achieved the highest fatigue resistance. The aforementioned fact had investigated based on comparing among the three specimens under the same conditions. For each specimen, the effect of the tidal turbine operation period according to fatigue lifetime been examined as well and it was investigated that, increasing number of operation hours resulted in a drastic reduction in the turbine’s fatigue life of the turbine.

Numerical and Experimental Investigation of Cumulative Fatigue Damage under Random Dynamic Cyclic Loads of Lattice Structures Manufactured by Laser Powder Bed Fusion

Lattice structures are lightweight engineering components suitable for a great variety of applications, including those in which the structural integrity under vibration fatigue is of paramount importance. In this work, we experimentally and numerically investigate the dynamic response of two distinct lattice configurations, in terms of fatigue damage and life. Specifically, Face-Centered-Cubic (FCC) and Diamond lattice-based structures are numerically studied and experimentally tested under resonant conditions and random vibrations, until their failure. To this end, Finite Element (FE) models are employed to match the dynamic behavior of the system in the neighborhood of the first natural frequency. The FE models are employed to estimate the structural integrity by way of frequency and tip acceleration drops, which allow for the identification of the failure time and a corresponding number of cycles to failure. Fatigue life under resonant conditions is well predicted by the application of conventional multiaxial high cycle fatigue criteria to the local state of stress. The same approach, combined with the Rainflow algorithm and Miner’s rule, provides good results in predicting fatigue damage under random vibrations.

Probabilistic characterization of the effect of transient stochastic loads on the fatigue-crack nucleation time

The rainflow counting algorithm for material fatigue is both simple to implement and extraordinarily successful for predicting material failure times. However, it neglects memory effects and time-ordering dependence, and therefore runs into difficulties dealing with highly intermittent or transient stochastic loads with heavy tailed distributions. Such loads appear frequently in a wide range of applications in ocean and mechanical engineering, such as wind turbines and offshore structures. In this work we employ the Serebrinsky–Ortiz cohesive envelope model for material fatigue to characterize the effects of load intermittency on the fatigue-crack nucleation time. We first formulate efficient numerical integration schemes, which allow for the direct characterization of the fatigue life in terms of any given load time-series. Subsequently, we consider the case of stochastic intermittent loads with given statistical characteristics. To overcome the need for expensive Monte-Carlo simulations, we formulate the fatigue life as an up-crossing problem of the coherent envelope. Assuming statistical independence for the large intermittent spikes and using probabilistic arguments we derive closed expressions for the up-crossing properties of the coherent envelope and obtain analytical approximations for the probability mass function of the failure time. The analytical expressions are derived directly in terms of the probability density function of the load, as well as the coherent envelope. We examine the accuracy of the analytical approximations and compare the predicted failure time with the standard rainflow algorithm for various loads. Finally, we use the analytical expressions to examine the robustness of the derived probability distribution for the failure time with respect to the coherent envelope geometrical properties.

A novel online 4-point rainflow counting algorithm for power electronics

The design of reliable products requires accurate load profiles as input for lifetime calculations. Different types of load profiles are required for different failure modes of a system. Lifetime models for IGBT power modules, as used in electric powertrains, are based on load cycles in the temperature time-history. These load cycles can be identified by rainflow counting algorithms with some adaptions to consider the power-on-time. At an early stage of development, load data are often estimated based on former experience with similar products. In order to acquire load data at large scale from field applications, it is required to implement the cycle counting algorithm in an electronic control unit (ECU) on the vehicle. This imposes constraints on the memory usage and computational complexity of the algorithm. Additionally, for an ECU implementation the algorithm has to be real-time capable and it has to work on a sample-per-sample basis. Herein, a novel and efficient online rainflow counting algorithm is presented, which accounts for power-on-time. The algorithm can also be applied to other load signals where rainflow counting is appropriate. Our algorithm is based on the well established 4-point rainflow algorithm which is considered superior to other algorithms.

Multi-body dynamic analysis of offshore wind turbine considering soil-structure interaction for fatigue design of monopile

Fatigue design of monopile foundation for an offshore wind turbine using multi-body dynamic analysis is the theme of this paper. For this purpose, a benchmark turbine is modelled in Kane's approach considering soil-structure interaction for a site at the North Sea. Each soil layer is modelled using the p-y curve, and the dynamic response of the combined system is simulated using aero-hydro-servo-elastic analysis. The fatigue life is estimated following IEC 61400-3 guidelines. The numerical analysis presented in this study shows stress-based fatigue analysis using rainflow algorithm in the light of soil-structure interaction for short-term damage accumulation. Besides short-term effects, the study also investigates serviceability criteria over the lifespan of the structure, i.e. long-term effects. Finally, design curves are developed for a given power rating. Overall, the study highlights the importance of soil-structure interaction and its impact on the fatigue life of offshore wind turbines.

Fatigue Analysis for Fe-34.5Mn-l0Al-0.76C Tidal Turbine Blades using Rainflow Algorithm

This study investigates the effect of the environmental conditions (seawater mean thrust force and flow velocity) on a tidal turbine for different thicknesses mathematically. This had been achieved through predicting the fatigue stresses applied on the turbine for different conditions using Rainflow algorithm. The blades of the tidal turbine should be characterized by a low roughness to reduce eddies formation downstream the seawater flow. Fe-34.5Mn-l0Al-0.76C alloy had been selected in this study. Obtained results showed that, increasing thickness of the blade resulted in increasing the turbine lifespan for each studied flow velocity and thrust forces. However, increasing the flow velocity is predicted to increase the thrust forces due to the wake region formed downstream the flow leading to increase the fatigue stress on the blade. Consequently, the blade thickness should be optimized based on the geographical location decided to be installed by a turbine. As the geographical location effects on the environmental conditions significantly, which should be considered during the design stage to prevent fatigue failure of the turbine. Optimizing the blade thickness would help in maximizing the energy conversion efficiency of the turbine as well, as a lightweight blade would be able of generating electricity higher than heavy ones.

On load assumptions for self-propelled forage harvesters

This article describes investigations into the subject of load assumptions on a self-propelled forage harvester. A measurement campaign during the maize harvest in hilly regions in Germany and the corresponding evaluations are presented. The investigations analyse both the usage profile of the machine and the load data for the chassis. The used sensors enable the acquisition of wheel forces and moments as well as the identification of different driving states. The wheel loads at the front axle are calculated to an auxiliary quantity (dimension of stress at the axle) for a summarised comparison of different load conditions. The stress signal is counted by a rainflow algorithm to implement a damage calculation. In addition to the known rainflow counting, information on the temporal reference of the hystereses within the load-time sequence is detected to assign damage values to defined driving states. The calculated damage values serve as relative comparison criteria for the different driving states.

An Improved Rainflow Algorithm Combined with Linear Criterion for the Accurate Li-ion Battery Residual Life Prediction

Li-ion battery health assessment has been widely used in electric vehicles, unmanned aerial vehicle and other fields. In this paper, a new linear prediction method is proposed. By weakening the sensitivity of the Rainflow algorithm to the peak data, it can be applied to the field of battery, and can accurately count the number of Li-ion battery cycles, and skip the cumbersome link of parameter identification. Then, a linear criterion is proposed based on the idea of proportion, which makes the life prediction of Li-ion battery linear. Under the verification of multiple sets of data, the prediction error of this method is kept within 2.53%. This method has the advantages of high operation efficiency and simple operation, which provides a new idea for battery life prediction in the field of electric vehicles and aerospace.

Effects of yaw misalignment on platform motions and fairlead tensions of the OO-Star Wind Floater Semi 10MW floating wind turbine

Floating offshore wind farms (FOWFs) are subject to wake effects similar to onshore and fixed-bottom offshore wind farms. Due to the smaller surface roughness, wake recovery is slower in offshore compared to onshore wind farms. Therefore, wake mitigation methods will become relevant for FOWFs as it is for onshore and fixed-bottom offshore wind farms. A common method is to apply yaw misalignment to steer the wake out of the rotor of the downwind turbine. However, it is necessary to investigate possible effects of yaw misalignment on a single turbine before farm-level investigations. This study focuses on the motion response of the platform and damage equivalent loads (DELs) of the mooring line tensions of the OO-Star Wind Floater Semi 10MW floating wind turbine. In order to satisfy environmental variability, the effect of yaw misalignment is investigated at different wind directions and wind/wave misalignments. DELs of three mooring line tensions at the fairleads were calculated using the rainflow algorithm and were reported as relative, normalized with respect to the aligned nacelle operation. Floater motions were analyzed to understand effects of misaligned operation. The results indicate that yawed inflow leads to a complex coupled response of floating offshore wind turbines (FOWTs). At slightly above rated wind speed, the yaw misalignment generally increases DELs due to the thrust increase. Conversely, yaw misalignment operation at below rated wind speeds leads to different responses on lines depending on environmental conditions. The steady state floater position has a large impact on DELs which may lead to a yet unknown response behavior of FOWFs. DEL trends in the presence of wind/wave misalignment are similar to those of aligned wind and wave.

Model predictive control of wind turbine fatigue via online rainflow-counting on stress history and prediction

The standard fatigue estimation procedure is implemented in Model Predictive Control via externalization of the Rainflow algorithm from the optimization problem. Additionally, stress history is considered in a consistent manner by employing a so-called stress residue. The formulation is implemented in the state-of-the-art MPC framework acados and tested in closed-loop with the 5MW onshore turbine in OpenFAST. Simulation results indicate that the new formulation outperforms conventional PID- and MPC-controllers over the entire wind regime, and that the consideration of stress history is highly beneficial.

Fatigue Crack Growth Kinetics in a 2024-T3 Aluminum Alloy during Alternating Cyclic Loading

The fatigue crack growth kinetics in a 2024-T3 aluminum alloy during constant- and variable-amplitude loading a various stress ratios in the medium-amplitude segment of a fatigue crack growth rate curve is studied. Variable-amplitude loading is represented by quasi-random samples of standard random loading spectra, which were preliminarily schematized using a rainflow algorithm. Parameters are proposed to estimate the character of random loading. The influence of the character of random loading using various standard spectra on the fatigue crack growth rate is analyzed. The fatigue crack growth time is estimated with allowance for fatigue crack closure and the character of random loading using a proposed formula and a cycle-by-cycle calculation method.

Fatigue life estimation of components with use a non-linear energy model coupled a finite element method

The work presents a non-linear fatigue computation method together with finite element method, in which energy parameter has been used. The Proposed model has been used for simulation computations, based on experimental testing of Al-2024 aluminum alloy specimens subjected to two types of loads, i.e. variable blocs loading and random loading. Computations of energy parameter value have been donebased on the results of FEM elastic–plastic analysis of cyclic properties of a material. A computing Matlab-based algorithm of the fatigue life prediction methodology was developed. The proposed damage indicator is connected cycle by cycle to the Wöhler curve. Cycles were counted with the rain-flow algorithm, and damage was accumulated with this model and with the Palmgren–Miner rule. On the grounds of which fatigue life has been read off from only characteristics of specimens. An experimental verification shows a satisfactory agreement between the fatigue life calculation results by the proposed methodology and test results. Estimated and experimental lives are found to exhibit good agreement.

Energy Scheduling of Isolated Microgrid with Battery Degradation Cost using Hybrid Particle Swarm Optimization with Sine Cosine Acceleration Coefficients

The implementation of renewable generators together with a battery storage into an isolated Microgrid (MG) has become essential to minimise fuel utilization and contribute to maintain continuous supply of electricity. This paper studies the optimal set point of isolated MG units containing renewable generators, diesel generators and battery storage. The optimal energy dispatch of MG’s units is determined to supply the required load demand for a 48h horizon time. As the battery device has an important contribution in the MG, this paper proposes to implement battery degradation cost in the optimization model in addition to the fuel cost function. For this purpose, the Rainflow algorithm is used to count charging-discharging cycles and quantify the battery degradation. In addition, a Hybrid Particle Swarm Optimization with Sine Cosine Acceleration Coefficients (H-PSO-SCAC) algorithm is used to solve the defined objective function for an optimal energy management system of the isolated MG. A Weight Factor (WF) is proposed in the objective function. For the simulation tests, different values of WF are considered. The impact of WF is analysed on the algorithm behaviour, on the status of the State Of Charge (SOC) of the battery and its influence on the optimized MG cost function. The results demonstrate that the selection of an appropriate value of WF allows to the H-PSO-SCAC algorithm to achieve the best solution. In addition, with WF equals to 0.5, the charge/discharge cycles are reduced and the battery SOC is more stable.

Energy scheduling of community microgrid with battery cost using particle swarm optimisation

The integration of renewable energy sources together with an energy storage system into a distribution network has become essential not only to maintain continuous electricity supply but also to minimise electricity costs. The operational costs of this paradigm depend highly upon the optimal use of battery energy. This paper proposes day-ahead scheduling of the battery energy while considering its degradation costs due to charging-discharging cycles. The degradation costs with respect to the depth of charge are modelled and added to the objective function to determine the actual operational costs of the system. A framework to solve the function is developed in which particle swarm optimisation, the Rainflow algorithm and scenario techniques are integrated. Uncertainties of parameters, modelled by scenario generation and reduced by scenario reduction techniques, are discussed. Simulation results demonstrate that the proposed method can reduce the operational costs by around 40% compared to the baseline method. They also reveal that uncertainty in power generation and power demand has no influence on the energy schedule of the battery, but variation in electricity prices has an impact on the outcome. Several pragmatic tests verify the effectiveness of the proposed method.