Rainflow Counting Algorithm Research Articles

Impact of Chaos on MOSFET Thermal Stress and Lifetime

The reliability of power electronic switching components is of great concern for many researchers. For their usage in many mission profiles, it is crucial for them to perform for the duration of their intended lifetime; however, they can fail because of thermal stress. Thus, it is essential to analyze their thermal performance. Non-linear switching action, bifurcation and chaotic events may occur in DC-DC power converters. Consequently, they show different behaviors when their parameters change. However, this is an opportunity to study these bifurcation phenomena and the existence of chaos, e.g., in boost converters, on their performance as the effects of load variations (mission profiles) on the system’s behavior. These variations generate many non-linear phenomena such as periodic behavior, repeated period-doubling bifurcations and chaos in the MOSFET drain-source current. Thus, we propose, for the first time, an analysis of the influence of chaos on the junction temperature. First of all, this paper provides a step-by-step procedure to establish an electrothermal model of a C2M0080120D MOSFET with integrated power loss. Then, the junction temperature is estimated by computing the power losses and a thermal impedance model of the switch. Additionally, this model is used to investigate the bifurcation and chaotic behavior of the MOSFET junction temperature. The paper contributes by providing a mathematical model to calculate several coefficients based on experimental data and thermal oscillations. Estimation of the number of cycles to failure is given by the Coffin–Manson equation, while temperature cycles are counted using the rainflow counting algorithm. Further, the accumulated damage results are calculated using the Miner’s model. Finally, a comparison is made between the damage accumulated during different mission profiles: significant degradation of the MOSFET’s lifetime is pointed out for chaotic currents compared to periodic ones.

Design, structure analysis and shock control of aircraft landing gear system with MR damper

This study proposes a new magneto-rheological aircraft main landing gear (MRAMLG) system and comprehensively treats from a mathematical modelling to drop testing for the evaluation of the landing efficiency. A mathematical model is formulated based on specifications and requirements of existing small aircraft Oleo type landing gear system. To ensure structural stability of the landing gear components such as main trust, column and trunnion, a transient structural analysis is carried out using the finite element method (FEM) and a fatigue life is analysed based on empirical formulas and the rainflow-counting (RC) algorithm. Subsequently, a novel controller is formulated to enhance the landing efficiency by integrating the time delay model and 3-stage hysteresis regulator. In the synthesis of the controller, a desired force model based on the energy law is added to accurately track the desired yield stress needed for the desired field-dependent force. In this work, the proposed control algorithm is named as the model-based force-tracking (MBFT) controller. To evaluate the landing efficiency or shock struct efficiency (SSE) of the proposed MRAMLG, an experimental apparatus for drop test is designed and manufactured by considering a dummy (sprung) mass of 640–720 kg at the maximum sink speed of 3 m s−1. The sink speed represents the rate of descent of the MRAMLG’s tire just before it touches the ground. It is demonstrated from simulation and experiment that the SSE with the MBFT controller is higher than 83% across various landing conditions with different sprung mass and sink speed, while the conventional controllers, proportional-integral and skyhook, compared to MBFT, do not show consistent performance depending on the sprung mass and sink speed.

Online battery aging calculation in plug-in hybrid electric vehicle considering driving condition

ABSTRACT Online calculation of battery capacity loss and its instantaneous remaining life for electric and hybrid electric vehicles is a challenging subject, particularly for designing and optimizing vehicle energy management in real-life driving conditions. This paper presents an online method for estimating plug-in hybrid electric vehicle battery degradation, considering the driving conditions. For this purpose, a national parallel plug-in hybrid electric vehicle is employed, where its components have been sized based on some experimental map characteristics using a genetic algorithm. Also, a real-world driving cycle is developed based on the data gathered in the actual traffic conditions in Tehran. The vehicle’s energy management system is designed using an adaptive equivalent consumption minimization strategy. In addition, an empirical battery life model combined with an online cycle counting method is used for battery aging calculation. To evaluate the effectiveness of the proposed approach, the capacity fade of the vehicle battery over various driving cycles has been calculated. The comparison of the results confirms the efficacy of the proposed algorithm compared to the Rainflow counting algorithm. Applying the Rainflow to all driving cycles yields consistent outcomes. However, when employing the suggested method, capacity losses of approximately 2.4%, 1.9%, 2.1%, and 1.4% are detected in Tehran, FTP-75, WLTP, and NEDC, respectively, following one hundred driving cycles. This means the capacity loss increases by 35%, 50%, and 71% for FTP-75, WLTP, and Tehran, respectively, compared with the NEDC driving cycle.

Reliability evaluation of carrier‐based pulse width modulated three‐level F‐type neutral point clamped inverter with power loss analysis

AbstractAn improved carrier‐based pulse‐width‐modulation (CBPWM) technique for a three‐level (3L) F‐type neutral point‐clamped (FNPC) inverter is presented in this paper. By using the proposed modulation scheme, the DC‐link capacitor voltage at the neutral point is balanced. For manufacturers, reliability is one of the major concerns for all power electronics devices and parts. This paper proposes an extensive reliability analysis of the 3L‐FNPC inverter. Considering the mean time to failure (MTTF) of each device, the reliability of the 3L‐FNPC inverter is analyzed in this present work by using two different methods, which are the approximate method and the exact method. To compute the failure rate of the equipment, only the number of components is considered in the approximate method. Alternatively, exact methods are utilized to evaluate the reliability of a system by knowing the different stress levels and various operating environments of a specific system. Because of the strong correlation between device failure and temperature stress factors, power loss analysis is used in the exact method. The MATLAB Simulink environment is used to determine the power loss of the switching devices. A solar off‐grid photovoltaic (PV) system is considered for reliability testing. Experimental mission profile data are used to estimate the lifetime of the 3L‐FNPC inverter by applying the rainflow counting algorithm, the Coffin‐Manson model, and Miner's rule. The competitiveness, effectiveness, and reliability of the 3L‐FNPC inverter with the proposed modulation technique are validated using a hardware prototype.

Deep gated recurrent unit networks for time-domain long-term fatigue analysis of mooring lines considering wave directionality

Mooring lines are a crucial component of offshore mooring systems, and long-term fatigue damage assessment is a challenging task in mooring line design and structural health monitoring. Traditional methods require a large number of structural time-domain simulations. Because the sea state varies over time, the variations in wave parameters (e.g., wave heights, periods, and directions) must be considered in long-term fatigue damage assessment. Wave directions have usually been ignored in previous studies, while the wave direction sensitive analysis conducted in this study showed that the wave directions could not be neglected in the long-term fatigue damage assessment of mooring lines. Recent deep neural network (DNN) methods have shown great potential in mooring line/riser response prediction for offshore structures. However, the utilization of float responses as input data in these DNNs restricts their applicability during the structure design phase. To address this issue, a gated recurrent unit (GRU) network is proposed for mooring line tension modeling. The proposed GRU network surrogate models are capable of accurately predicting the mooring line tension using wave elevation components or float motion responses. The rain-flow counting algorithm, T-N approach, and Miner's rule were employed to estimate the structural fatigue damage. The results showed that the proposed method could replace the heavy cost numerical computation, assess the long-term fatigue damage with high accuracy and alleviate the data dependency of DNN methods.

A Reactive Power Injection Algorithm for Improving the Microgrid Operational Reliability

Stand-alone microgrids have become reliable and efficient solutions for remote areas and critical infrastructures. However, the converters within these microgrids experience long-term complex power fluctuations caused by random variations in micro sources and loads. These power fluctuations induce thermal cycling in semiconductor chips, leading to thermal fatigue failure and compromising the safety and reliability of both the converter and microgrid operation. To address this issue, this paper proposes a reactive power injection algorithm aimed at reducing the output power fluctuation of the converter. The algorithm implements reactive power injection at the converter control level, thereby restructuring the output power profile and resulting in reduced junction temperature fluctuations in IGBTs. This approach effectively mitigates thermal stress within the material layers of the module, extending the lifetime of power devices and improving the operational reliability of the microgrid. The algorithm implementation is based on the PQ control strategy, integrating the power triangle with the envelope detection technique. Furthermore, the lifetime prediction process utilizes the electro-thermal coupling model, the rainflow counting algorithm, and the Lesit model. Simulation results demonstrate that, for an active power fluctuation range of 10 kW to 80 kW and an equivalent RC time constant of 22.5 s, the algorithm achieves a significant reduction of 62.64% in the amplitude of output power fluctuation and extends the lifetime of power devices by 74.13%. The obtained data showcase the effectiveness of the algorithm in enhancing the lifetime of power devices and further improving the microgrid operational reliability under specific parameter conditions.

Analysing the effect of defects on stress concentration and fatigue life of L-PBF AlSi10Mg alloy using finite element modelling

Additive manufacturing (AM) is a developing manufacturing technology, which provides excellent attributes compared to other manufacturing techniques. However, one of the critical challenges is the presence of defects that hinder the mechanical properties of the parts, particularly the fatigue life. Experimental understanding of fatigue is a cumbersome process. Therefore, numerical prediction based on specified conditions (such as porosity and applied load) can be an alternative to experimental analysis at the design stage of AM parts. In this study, elastic–plastic finite element analysis (FEA) is performed to obtain the stress distribution around pores, and their resultant effect on fatigue life for L-PBF (laser powder bed fusion) produced AlSi10Mg alloy samples. The stress field is calculated for both single and multiple pore models, where stress concentration is evaluated as a function of the pore’s location and its size. It is found that both pore location and size affect the stress field; however, location effects dominate over pore size. For the same remote applied stress level, the stress concentration around the pore increases with an increase in pore size, and the local maximum stress occurs near the pores that are closest to the surface. The current study also evaluates the relative effect of porosity fraction, average pore size, and location. It is found that the magnitude and sensitivity of stress concentration are hierarchically controlled by porosity location, pore size, and porosity density. A multi-scale finite element (FE) model is proposed based on inherent porosity data measured using Computed Tomography (CT) to predict overall fatigue life. The fatigue cycles are calculated using the rainflow counting algorithm in FE Safe using the stress–strain data obtained from the proposed FEA model. Using the proposed model, it is possible to generate S–N curves for any loading condition for a given porosity condition (porosity density and average pore size). The S–N curve results obtained from the FE model are compared to the experimental observations. The predicted fatigue life shows approximately 5% error with experimental results at high stress loading conditions. However, the proposed model overpredicts the fatigue life at low stress loading by almost 30%.

Digital twin-based structural health monitoring by combining measurement and computational data: An aircraft wing example

Digital twin is a concept that utilizes digital technologies to mirror the real-time states of physical assets and extract the hidden yet valuable information of physical assets for optimization, decision-making or scheduling. By combining measurement and computational data, this paper presents a digital twin-based structural health monitoring framework of physical assets. The process for building the measurement-computation combined digital twin (MCC-DT) involves four steps. First, an artificial intelligence-driven load identification method combining measurement and computational data is employed to recognize the loads applied on physical assets. Two approaches were proposed to realize load identification, based on single fidelity surrogate models and deep learning techniques, respectively. Second, multi-fidelity surrogate (MFS) models are applied to improve the accuracy in the MCC-DT. Two routes for implementing the MFS models are introduced and the advantages and shortcomings of both are analyzed. Third, an online rainflow counting algorithm is developed to calculate the degradation of the physical assets. The main advantage of the algorithm is that it can provide a near real-time estimation for the damage accumulated of physical assets. Finally, the data generated from the first three steps can be fused into a three-dimensional scene using Web graphics library to provide an intuitive view of the MCC-DT. To describe the implementation details of the framework and verify its applicability and effectiveness, the MCC-DT was established using an aircraft model as an example.

Design Method of Full-scale Fatigue Test Load for Wind Turbine Blade

The blade is one of the key components of a wind turbine, and the alternating fatigue load is the main factor leading to the fatigue failure of wind turbine blades. The accuracy of load determines the accuracy of the wind turbine blade test. Based on the equivalent torque time history data from the wind load acting on the blade root, the load of the two-dimensional matrix is obtained by using data compression technology and a rain flow counting algorithm. According to the capture matrix of load data, the frequency of various design loading cases and the distribution of wind speed, the symmetrical load spectrum is calculated and compiled. The fatigue load of a wind turbine blade is calculated for a certain type of 2MW blade, which lays a foundation for the design and test of a wind turbine blade fatigue loading system.

COP: A Combinational Optimization Power Budgeting Method for Manycore Systems in Dark Silicon

Dark silicon is a phenomenon of under-utilization in today's manycore systems due to power and thermal limitations. In order to improve the performance of dark silicon systems, it is necessary to adopt dynamic power constraints for different core mapping decisions. However, existing power budgeting methods are generally over pessimistic, e.g. Thermal Safe Power (TSP), or over optimistic, e.g. Greedy based Dynamic Power (GDP). This paper proposes a practical power budgeting method, called Combinational Optimization Power (COP). Different from existing methods, which ignore some actual factors, such as communication overhead and lifetime reliability, COP formulates the power budgeting problem as a thermal-constrained combinational optimization power problem. For the steady-state case, COP achieves the target fusion of optimized temperature and communication energy consumption by applying task priority ranking and task-to-core mapping. For the transient case, COP uses the rainflow counting algorithm to construct the reliability framework based on the thermal cycling failure mechanism, and then establishes a linear time-invariant transient temperature model to obtain the core mapping selection and the corresponding dynamic power budget. Experimental results demonstrate that COP is capable of providing an optimized core mapping decision, which can maximize power budget while ensuring the system performance.

Fatigue Life Convergence of Offshore Wind Turbine Support Structure According to Wind Measurement Period

This paper investigated the fatigue life of offshore wind turbine (OWT) support structures. For this purpose, a 3 MW-capacity typical wind turbine is investigated using time-domain finite element simulations. In numerical simulations, different stochastic wind models corresponding to different accumulation periods are applied. Then, the stress-based fatigue life is estimated following the rain-flow counting algorithm and Palmgren-Miner linearly cumulative damage rule. The study also addresses the joint distribution of loads at the site of interest. Generally, the study emphasizes the significance of the long-term distribution of the applied environment loads and its influence on the fatigue life of OWT’s substructures. The results imply that the wind measurement period is directly linked to the fatigue life of offshore wind turbine support structures. Accordingly, its fatigue life is significantly reduced at the 25-year accumulative period of wind. Therefore, this study recommends that a sufficient number of accumulative periods of wind and other environmental loads should be considered appropriately.

Battery lifetime of electric vehicles by novel rainflow-counting algorithm with temperature and C-rate dynamics: Effects of fast charging, user habits, vehicle-to-grid and climate zones

The adoption of electric vehicles is expected to soon widespread to cope with energy transition needs; however, concerns on battery lifetime arise, especially related to charging behaviors, vehicle usage habits, vehicle-to-grid and weather conditions. In fact, lifetime battery modeling is a challenging dynamic to characterize, as it involves complex chemical processes related to charging, discharging and temperature dynamics over long time spans that are often difficult to dominate, given the large uncertainties. Having a fatigue-like behavior, the battery aging has sometimes been modeled using rainflow-counting algorithms, yet traditional modeling is not holistic and approximations are used, especially when considering temperature or current dynamics. Based on experimental data, this paper aims at developing a holistic battery degradation model based on rainflow-counting algorithm to properly account for all major determinants of capacity loss, namely cycling usage, calendar lifetime, dynamic temperature and battery current. The approach is coupled with a physical-electro-thermal modeling of the vehicle system, developed in Modelica language, to accurately simulate the intertwined thermal and electrical behavior of the system subject to different usage charging behaviors, including slow and fast charging, as well as vehicle-to-grid application. The proposed case study shows the expected lifetime of electric vehicles to be comparable with of traditional cars (10–20y) and that the proposed temperature-dependent battery modeling enables reducing estimation errors up to 27%. A sensitivity on different climate zones has been considered and results suggest that cool climates can increase life expectancy by 30% with respect to hot climates in typical Italian contexts.

Comparative Analysis of the Load Spectra Recorded During Photogrammetric Missions of Lightweight Uavs in Tailless and Conventional Configurations

Abstract The purpose of this article is to present the results of the investigation regarding the differences of the load spectra of two unmanned fixed-wing aircraft performing photogrammetry missions: X-8 (flying wing) and PW-ZOOM (conventional configuration). The focus was on the analysis of a number of load cycles for various load increments within the range of the operational loads. The load spectra were determined using the acceleration signal recorded in the autopilot logs as an input. This signal was transferred to the chain of local extreme values scaled in the form of discrete load levels, and then the transfer arrays were derived with use of the rainflow counting algorithm. On this basis, the incremental load spectra were determined for each flight. These load spectra were subjected to statistical analyses to determine the load spectra representative of the flight sessions in a few ways between non-conservative (i.e., focused on average load histories) and conservative (i.e., focused on the worst load histories observed during the flight session). Finally, the fatigue life was calculated by having the structural element of the assumed fatigue properties subjected to the load spectra of both airplanes. A large (exceeding one order of magnitude) difference in the number of load cycles for larger load increments in the analyzed load spectra was shown. This difference is related to the different dynamic characteristics of the two aircraft, in particular the gust response. As a result, there is a several-fold difference in fatigue life.

Strain Monitoring-Based Fatigue Assessment and Remaining Life Prediction of Stiff Hangers in Highway Arch Bridge

The fatigue problem of hangers is fatal for the safety of the whole bridge structure. The objective of this study is to present a strain monitoring-based method to assess the fatigue performance of stiff hangers in highway arch bridges and predict their remaining life. A vehicle–bridge interaction system was constructed to analyze the dynamic behavior in the area close to the key welding line where the hanger was connected to the deck slab. Then, the empirical mode decomposition (EMD) algorithm and rain-flow counting algorithm were used in signal preprocessing and statistical analysis of field monitoring data. Finally, the fatigue life was assessed according to the standards in the Chinese Code for the Design of Steel Structures, as well as the Eurocode 3 and AASHTO codes. Differences were found in the fatigue behavior of hangers, and the shortest hanger was shown to surfer more serious fatigue damage. The influence of vehicle volume growth and low-stress amplitude on the fatigue performance was also discussed.

Multifidelity multiobjective optimization for wake-steering strategies

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. A large eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. Multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost only 30 % that of the single-fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

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.

Circuit-Based Rainflow Counting Algorithm in Application of Power Device Lifetime Estimation

The software-assisted reliability assessment of power electronic converters is increasingly important due to its multi-domain nature and extensive parametric calculations. The rainflow counting algorithm is gaining popularity for its low relative error in device lifetime estimation. Nevertheless, the offline operation of the algorithm prevents most simulation software packages considering other parameters for the device under study, such as aging and the current state of health in the estimation, as it requires a complete loading profile to run recursive comparison. This also brings difficulties in realization in circuit simulators such as SPICE. To tackle the issue, an in-the-loop circuit-based rainflow counting algorithm is proposed in this paper, and applied to estimate the consumed lifetime of the MOSFET in a boost converter for illustration. Instantaneous electrical and thermal performances, and the accumulated stress of the device can be monitored. Not only does this assist in evaluating the state of health of a device, but also allows the possibility of integrating the aging into the lifetime evaluation. The method follows the four-point rainflow counting algorithms, which continuously compares three adjacent temperature fluctuations ΔTj to select full cycles for two rounds, and the remaining cycles are counted as half cycles. To validate the performance, a comparative analysis in terms of counting accuracy and simulation speed was performed alongside the proposed method, MATLAB® and also with a well-accepted half-cycle counting method. Reported results show that the proposed method has an improved counting accuracy compared to the half-cycle counting from 24% to 3.5% on average under different load stresses and length conditions. The accuracy can be effectively improved by a further 1.3–2% by adding an extra comparison round.

Enhancing reliability of photovoltaic power electronic converters under dynamic irradiance conditions

This paper presents a novel temperature-controlled maximum power point tracking (MPPT) algorithm for lifetime improvement of a photovoltaic (PV) converter under dynamic irradiance conditions. The proposed algorithm controls and limits the junction temperature change rate of switching devices, reducing the thermal stress and drastically reducing the damage received, hence improving the reliability and lifetime of power converters in PV systems. To evaluate the damage reduction, a lifetime estimation technique is applied which is composed of a Foster thermal model, a rainflow counting algorithm and an empirical lifetime model. Moreover, in this paper the energy and life consumption are calculated with the application of lookup tables to reduce computation time. The effectiveness of the proposed algorithm is verified using extensive simulations and by comparing energy generated and life consumption under irradiance profiles for different cloud conditions. The temperature-controlled algorithm is applied in parallel with a normal MPPT algorithm to a 10 kW photovoltaic system and results are compared using irradiance data from the province of Quebec, Canada to validate its efficacy. The obtained results show that for very variable cloud conditions, the modified algorithm managed to reduce the life consumption by 4.68 % at no extra cost, with just 0.08 % of energy generation reduction, proving its effectiveness.

Evaluating and Analyzing the Degradation of a Battery Energy Storage System Based on Frequency Regulation Strategies

The capacity aging of lithium-ion energy storage systems is inevitable under long-term use. It has been found in the literature that the aging performance is closely related to battery usage and the current aging state. It follows that different frequency regulation services, C-rates, and maintaining levels of SOC during operation will produce different battery aging rates. In the simulations, the researchers used real frequency data to generate SOC curves based on the Taiwan frequency regulation services under different C-rates and different battery SOC target levels. Then, the aging formula of lithium iron batteries (LiFePO4 battery, LFP battery) and the proposed improved rainflow counting algorithm were used. The capacity aging situation and economy under different usage scenarios were analyzed. The simulation results showed that using a high C-rate and a low SOC level had a higher net profit, and the income of dReg was more than that of sReg. The SOC of BESS has an important impact on the life cycle. Keeping the SOC at a lower level will help prolong the life cycle and increase the net income. In dReg0.5, maintaining the SOC at 30% would yield 8.5% more lifetimes than 50%, 20.6% more lifetimes than 70%.

An improved rainflow counting method for multiaxial stress states using the minimum circumscribed circle method to identify shear stress ranges

Most of the rainflow counting methods are developed for uniaxial stress states. In this paper, a new method for rainflow counting of multiaxial stress states has been proposed. The proposed method is a two-step procedure based on a modified three-point ASTM uniaxial rainflow counting algorithm where normal stress ranges are identified along with start and end indexes of each range. For each identified cycle, shear stress ranges are evaluated based on cycle start and end points using the minimum circumscribed circle method. The proposed algorithm is compared to two commonly applied multiaxial cycle counting methods on simulated and experimental data.