Empirical Lifetime Research Articles

Consumption dynamics and welfare under non-Gaussian earnings risk

Recent empirical studies document that the distribution of earnings changes displays substantial deviations from lognormality: in particular, earnings changes are negatively skewed with extremely high kurtosis (long and thick tails), and these non-Gaussian features vary substantially both over the life cycle and with the earnings level of individuals. Furthermore, earnings changes display nonlinear (asymmetric) mean reversion. In this paper, we embed a very rich “benchmark earnings process” that captures these non-Gaussian and nonlinear features into a lifecycle consumption-saving model and study its implications for consumption dynamics, consumption insurance, and welfare. We show four main results. First, the benchmark process essentially matches the empirical lifetime earnings inequality—a first-order proxy for consumption inequality—whereas the canonical Gaussian (persistent-plus-transitory) process understates it by a factor of five to ten. Second, the welfare cost of idiosyncratic risk implied by the benchmark process is between two-to-four times higher than the canonical Gaussian one. Third, the standard method in the literature for measuring the pass-through of income shocks to consumption—can significantly overstate the degree of consumption smoothing possible under non-Gaussian shocks. Fourth, the marginal propensity to consume out of transitory income (e.g., from a stimulus check) is higher under non-Gaussian earnings risk.

A breakthrough in creep lifetime prediction: Leveraging machine learning and service data

Improvement of data-driven techniques, specifically machine learning (ML), in material science turned it into a powerful tool for predicting materials behavior. Accordingly, this study provides a ML prediction of empirical creep lifetimes of 9Cr-1Mo ex-service heater tubes that have been used in industry for up to 47 years. Data from over 90,000 h of stress rupture tests shows that the service parameters influence creep lifetime similar to mechanical properties. Employing six different ML algorithms, viz., K Nearest Neighbors (KNN), Support Vector Regressor (SVR), Random Forest (RF), Gradient Boosting (GB), Gaussian Process (GP), and Multi-Layer Perceptron (MLP) demonstrated that the GP and MLP methods performed significantly better in predicting the creep lifetimes rather than other algorithms. Finally, a validation set involving 12 samples was conducted, and the GP algorithm showed better agreement with experimental values than other ML and Larson-Miller Parameter approaches, illustrating the capability of this model to predict creep lifetimes.

Physics of failure based lifetime modelling for sintered silver die attach in power electronics: Accelerated stress testing by isothermal bending and thermal shock in comparison

The employment of sintered silver (SAG) as die attach material is one of the most promising solutions to utilize the advantages of wide bandgap semiconductors in modern power electronic packaging. Its electrical, thermal and mechanical – i.e. reliability correlated – properties are far superior to those of time honored eutectic solders. To master the challenges of a high-quality production on an industrial level in accordance with the ever increasing application-driven reliability requirements, SAG die attach technology has to be developed, tested and lifetime-modelled in the context of a design for reliability approach, in order to be understood and thus savely put into application in the field. This requires the use of modern physics-of-failure paradigms, as today’s mostly used empirical lifetime models are meeting their limits with power electronics becoming more diverse in all relevant determinants such as materials, packaging technologies, geometric dimensions and reliability requirements. Introduced will be an isothermal bending test (ITBT) as highly accelerated, simple but very insightful test mimicking the power cycling load regime. This test will be combined with a physics of failure based approach, which will be presented including material characterization, modelling, simulation and definition of a failure parameter. This test method has the potential to produce reliability results much faster than non-mechanical tests, while the physical failure parameter still allows transferability of the resulting model. We show for the first time a physics-of-failure based lifetime model for SAG using isothermal bending in comparison with thermal shock test. For this we used the total inelastic strain (including plastic, primary and secondary creep) as local failure parameter for die attach degradation by fatigue crack growth.

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.

A Strategic Pathway from Cell to Pack-Level Battery Lifetime Model Development

The automotive energy storage market is currently dominated by the existing Li-ion technologies that are likely to continue in the future. Thus, the on-road electric (and hybrid) vehicles running on the Li-ion battery systems require critical diagnosis considering crucial battery aging. This work aims to provide a guideline for pack-level lifetime model development that could facilitate battery maintenance, ensuring a safe and reliable operational lifespan. The first of the twofold approach is a cell-level empirical lifetime model that is developed from a lab-level aging dataset of commercial LTO cells. The model is validated with an exhaustive sub-urban realistic driving cycle yielding a root-mean-square error of 0.45. The model is then extended to a 144S1P modular architecture for pack-level simulation. The second step provides the pack electro-thermal simulation results that are upscaled from a cell-level and validated 1D electrical model coupled with a 3D thermal model. The combined simulation framework is online applicable and considers the relevant aspects into account in predicting the battery system’s lifetime that results in over 350,000 km of suburban driving. This robust tool is a collaborative research outcome from two Horizon2020 EU projects—GHOST and Vision xEV, showcasing outstanding cell-level battery modeling accuracies.

Why SoHC and SoHR Alone Are Not Enough - A Study on Cyclic Aging of Automotive Lithium-Ion Cells

Lifetime validation is crucial to the development of lithium-ion cells, especially in the automotive context as high regulatory and warranty requirements have to be met. As the experimental lifetime validation can get tedious and costly, lifetime modelling is a way to cut down experimental effort and predict cell aging based on accelerated aging experiments with well selected aging conditions.Using these experiments with constant aging conditions, lifetime models are widely built in a path independent way, where the aging is expressed as a function of only the state of health in capacity (SoHC) and resistance (SoHR). The SoH hereby defines the relative capacity and resistance in comparison to their values at begin of life.Following a design of experiment approach, 62 large format NMC/graphite lithium-ion pouch-cells were tested at 28 different aging conditions, coming close to realistic cyclic aging conditions. This experiment was initially set up in order to build such an empirical lifetime prediction model, capable of predicting SoHC and SoHR in dependence of factors such as the state-of-charge window of the cyclation, the temperature and the charging power.Analyzing this accelerated aging experiment, we show that the definition of a state of health based on only capacity and inner resistance is falling short.This is deduced from differential voltage analysis (DVA) and post mortem analysis from cells with comparable SoH. With differential voltage analysis, changes in the electrochemically active parts of the lithium-ion cell that arise from aging and affect the open circuit potential can be visualized and assigned to certain parts of the cell without its destruction.Hereby a published fitting algorithm is used that can estimate losses of active material (LAM) and the loss of active, cyclable lithium (LL) from slow-discharge potential curves. Following the destructive post mortem analysis of a cell, we validate the results of this algorithm with 3-electrode-measurements.Together with further material analytics entirely different internal states become apparent when LAM on anode and cathode side as well as the loss of active lithium and its distribution in the electrodes are compared.Based on these findings we discuss the implication of the underlying variation in internal states at similar SoH of lithium-ion cells to the modelling of cyclic aging with a path-independent damage accumulation approach following Miner’s rule.

Distance Dependence of Förster Resonance Energy Transfer Rates in 2D Perovskite Quantum Wells via Control of Organic Spacer Length.

Two-dimensional (2D) semiconductors are attractive candidates for a variety of optoelectronic applications owing to the unique electronic properties that arise from quantum confinement along a single dimension. Incorporating nonradiative mechanisms that enable directed migration of bound charge carriers, such as Förster resonance energy transfer (FRET), could boost device efficiencies provided that FRET rates outpace undesired relaxation pathways. However, predictive models for FRET between distinct 2D states are lacking, particularly with respect to the distance d between a donor and acceptor. We approach FRET in systems with binary mixtures of donor and acceptor 2D perovskite quantum wells (PQWs), and we synthetically tune distances between donor and acceptor by varying alkylammonium spacer cation lengths. FRET rates are monitored using transient absorption spectroscopy and ultrafast photoluminescence, revealing rapid picosecond lifetimes that scale with spacer cation length. We theoretically model these binary mixtures of PQWs, describing the emitters as classical oscillating dipoles. We find agreement with our empirical lifetimes and then determine the effects of lateral extent and layer thickness, establishing fundamental principles for FRET in 2D materials.

Thermal Performance and Reliability Analysis of a Medium-Voltage Three-Phase Inverter Considering the Influence of High $dv/dt$ on Parasitic Filter Elements

In recent years, the use of silicon carbide (SiC) power semiconductor devices in medium-voltage (MV) applications has been made possible due to the development of high blocking voltage (10–15 kV)-based devices. While the use of these devices brings in a lot of advantages, the semiconductor devices are exposed to high peak stress (of up to 15 kV) and a very high $dv/dt$ (of up to 100 kV/ $\mu \text{s}$ ). The high $dv/dt$ across the devices leads to a high $dv/dt$ across other components connected to the system. This makes the effect of the parasitic capacitance across the components to be of paramount importance since an additional current flows through the components and, consequently, through the switching device. This additional current flows during each switching transition and leads to increased switching losses in the device. This article analyzes the effect of these additional losses on the lifetime of the device. The thermal performance of a three-phase inverter power block is provided, and a mission profile (solar irradiance and temperature)-based analysis is carried out to account for the additional junction temperature rise. The rainflow counting method is implemented to identify the mean and amplitude of each thermal cycle. An empirical device lifetime model is used to calculate the number of cycles to failure. Finally, the Palgrem Miner rule is used to quantify the total damage in the device. Comparisons have been carried out on basis of lifetime for both the cases (with and without the influence of parasitic capacitances). This analysis can be helpful in validating the importance of the design of filter inductors in these MV applications.

Monitoring 3-D Temperature Distributions and Device Losses in Power Electronic Modules

This paper presents a methodology for real-time monitoring of 3-D temperature distributions and device losses within power electronic modules. It allows precise thermal management, empirical lifetime prognosis, and detection of critical degradation of the power module. By effective combination of thermal 3-D finite difference modeling, parametric loss models, and model truncation techniques, a compact thermal real-time model is derived. It enables the computation of device losses and temperatures at critical locations within a power module, e.g., at the devices, solder interfaces or the base plate, on a conventional digital signal processor. The real-time model as well as real-time junction temperature information are combined in a new Luenberger-style observer structure. Applying bandwidth partitioning, the observer estimates the temperatures throughout the power module every switching period and averaged over one excitation period with nearly zero lag, even if the junction temperature measurement exhibits delays and has noisy signals. Furthermore, it estimates errors in the loss prediction process that can be tracked over the lifetime of the power module to detect degradation of the devices or the power module. The observer and its features are experimentally evaluated under realistic operating conditions on a load emulator using a state-of-the-art automotive power module.

Lifetime prediction of natural gas polyethylene pipes with internal pressures

Abstract The purpose of this study was to propose a lifetime prediction model of aging natural gas polyethylene (PE) pipeline with various internal pressures by thermal-oxidative aging (TOA) test and oxidative induction time (OIT) test. By using a pressured natural gas PE80 pipe under the condition similar to actual urban natural gas working condition, an improved TOA experimental set-up was built, and had been used for accelerated TOA test of pressured PE pipes at different test temperatures. By using dynamic curve linearization method and based on Arrhenius fit of the data, an empirical lifetime prediction model of thermal oxidative aging law for PE pipes was developed to extrapolate lifetime of PE80 pipes with internal pressures. The results show that under the test internal pressure of 0.1 MPa, 0.2 MPa, 0.3 MPa, and 0.4 MPa, the lifetimes of aging PE gas pipes with internal pressure are 14%, 24.5%, 36.1%, and 41.6% shorter than those without internal pressure.

Future security of power supply in Germany-The role of stochastic power plant outages and intermittent generation

Many power plants in Germany and Europe are approaching the end of their technical lifetime. Moreover, the increasing wind and solar power generation reduces the operation times of thermal power plants, making future investments in new generation capacity uncertain under current market conditions. Consequently, the future development of security of power supply is unclear. In this paper, we assess the impact of stochastic fluctuations in power plant availability, renewable generation, and grid load on the future security of supply in Germany. We model variations in power plant availability by application of a combined Mean-reversion Jump-diffusion approach. On the basis of that and using Monte-Carlo methods, we simulate 300 different time series of availability. These profiles are fed into the fundamental power system model REMix, applied to evaluate the appearance of supply shortfalls in hourly resolution. We assess 6 scenarios for the year 2025, differing in renewable generation and demand profiles, as well as grid infrastructure. Geographical focus of the analysis is Germany, but the electricity exchange with its European neighbours is modelled as well. Our results show that the choice of the power plant availability profile can change the loss of load expectation and loss of load hours by up to 50%. However, the influence of load and renewable generation profiles is found to be significantly higher. Assuming that no new conventional power plants are built and existing plants are decommissioned at the end of their empirical lifetime, we identify supply gaps of up to 2.7 GW in Germany.

Predicting Membrane Lifetime with Cerium Oxide in Heavy Duty Fuel Cell Systems

Stringent reliability and durability requirements for fuel cells in heavy duty vehicles demand highly durable ionomer membranes. Fuel cell membranes degrade chemically and mechanically during operation, which can lead to membrane thinning, pinhole and crack formation and eventual failure due to hydrogen leaks. The chemical portion of degradation can be suppressed with the use of radical scavenging agents such as cerium oxide. In order to implement extended durability solutions in actual field operation, however, aptly designed accelerated durability tests and empirical models are needed to predict membrane lifetime under various operating conditions, while also considering additive stability over time. Here, an empirical membrane lifetime model recently developed for transit bus applications is modified and demonstrated to predict membrane lifetime with cerium oxide incorporated into the membrane electrode assembly as a chemical stabilizer. The lifetime prediction approach utilizes laboratory scale experimental data from an accelerated membrane durability test complemented by measured cerium washout rates. Provided that the cerium washout rates were relatively low, the predicted membrane lifetime of cerium supported membranes was found to significantly exceed the ultimate 25,000 h heavy duty durability target.

Self-consistent simulations of quantum cascade laser structures for frequency comb generation

Maxwell–Bloch equations are widely used to model the dynamics due to coherent light-matter interaction in quantum cascade laser (QCL) structures, which plays an essential role especially for the generation of frequency combs and mode-locked pulses. While the modest numerical complexity of the Maxwell–Bloch system allows for a full spatiotemporal treatment, its main disadvantage is the inclusion of dissipation by empirical dephasing rates and electron lifetimes. We present a self-consistent multi-domain approach which couples the Maxwell–Bloch equations to advanced carrier transport simulations based on a density matrix Monte Carlo technique, yielding the scattering and dephasing rates. In this way, the compact spatiotemporal modeling of the carrier-light dynamics by the Maxwell–Bloch system can be combined with the versatility and reliability of self-consistent carrier transport approaches. Simulation results are shown for a QCL-based terahertz frequency comb source, and good agreement with experiment is obtained.

Load profile based empirical model for the lifetime prediction of an automotive PEM fuel cell

The prediction of the lifetime of a PEM fuel cell under a specific electrical load profile is beneficial for automotive applications. An empirical lifetime prediction model coupled with an electrical load profile is presented based on an estimate of the degradation rate of the cell voltage. First, a cause and effect chain-based analysis of the PEM fuel cell's degradation process is presented. Second, a characteristic value is extracted and is treated as a numerical measurement of the effect of load profile on voltage degradation. The characteristic value is defined using both load current and load voltage. Third, an empirical model is proposed, modeling the voltage degradation rate as a linear function of the load profile's characteristic value. Finally, experimental data are used to fit the coefficients and validate the model.

Empirical membrane lifetime model for heavy duty fuel cell systems

Abstract Heavy duty fuel cells used in transportation system applications such as transit buses expose the fuel cell membranes to conditions that can lead to lifetime-limiting membrane failure via combined chemical and mechanical degradation. Highly durable membranes and reliable predictive models are therefore needed in order to achieve the ultimate heavy duty fuel cell lifetime target of 25,000 h. In the present work, an empirical membrane lifetime model was developed based on laboratory data from a suite of accelerated membrane durability tests. The model considers the effects of cell voltage, temperature, oxygen concentration, humidity cycling, humidity level, and platinum in the membrane using inverse power law and exponential relationships within the framework of a general log-linear Weibull life-stress statistical distribution. The obtained model is capable of extrapolating the membrane lifetime from accelerated test conditions to use level conditions during field operation. Based on typical conditions for the Whistler, British Columbia fuel cell transit bus fleet, the model predicts a stack lifetime of 17,500 h and a membrane leak initiation time of 9200 h. Validation performed with the aid of a field operated stack confirmed the initial goal of the model to predict membrane lifetime within 20% of the actual operating time.

Comparison of power electronics lifetime between vertical‐ and horizontal‐axis wind turbines

A comparison has been made of the power electronics lifetime for 5MW horizontal- and vertical-axis wind turbines, based on dynamic models supplied with generated wind speed time series. Both two- and three-bladed stall-regulated H-rotor vertical-axis turbines were modelled, with several different control parameters. Vertical-axis turbines are likely to lead to a shorter power electronics lifetime as the aerodynamic torque varies with rotor azimuth, leading to a cyclic generator torque, and increased thermal cycling in the power electronics. An electro-thermal model of a low-voltage converter was created, and used to calculate the switching device temperatures based on the generator torque and speed time series from the turbine model. An empirical lifetime model and rainflow-counting algorithm were used to calculate the lifetime, and this was repeated at different average wind speeds to determine the overall lifetime. The vertical-axis turbine was found to have a lower power electronics lifetime than the horizontal-axis, or require a larger number of parallel switching devices to achieve the same lifetime, although this was lessened by running the turbine with a more relaxed speed control, allowing the rotor inertia to partially absorb the aerodynamic torque ripple.

Equivalent Fatigue Zone in a Notched Elements Determined by Use of Non-Local Line Method with Weight Function

The work presents non-local line method by which the equivalent fatigue zones were designated. These zones are one-dimensional efficient lengths in which operating stress variables cause initiation of fatigue cracks. The algorithm of the presented method considers the issues of multi-axial stress state, critical plane and weighting function. Calculations of stresses in the test element were performed by using the FEM assuming cyclic material properties, which are described with the model for multi-linear hardening. The empirical lifetime of elements with a notch was assumed to define length of the crack amounting to 0.1 mm. As the result of calculations, the dependence of effective length on nominal stress and radius of the notch was determined.

Analysis and determination of mechanical bearing load caused by unbalanced magnetic pull

Purpose – The purpose of this paper is to focus on the mechanical bearing load caused by the unbalanced magnetic pull (UMP), which is studied in detail. The applied approach is based on an analysis of static and dynamic eccentricities at different positions and different amplitudes. The influence of the operating points is calculated to show the effective bearing load for machines operating at different speeds. The decreasing lifetime of the applied bearings is examined and evaluated in detail. Design/methodology/approach – To evaluate the proposed methodology a permanent magnet synchronous machine (PMSM) with buried magnets is used. To consider effects of slotting and saturation, a finite element (FE) model is employed. The Monte Carlo method is used to determine the most likely amplitudes of the eccentricities. Calculating the UMP for all possible operating points using a control strategy for the machine and coupling this results with a drive cycle, determines the effective force acting on the bearing. Findings – It has been shown that the position of the eccentricity has a not significant influence on the behavior of the UMP and may therefore be neglected. The amplitude of the eccentricity vector influences the amplitude of the UMP including all harmonic force components. For technical relevant eccentricities, the influence is approximately linear for the average and the dominant harmonics of the UMP. In most cases, it is sufficient to displace the rotor at an arbitrary position and amplitude. It is sufficient to simulate one type of eccentricity (static or dynamic) with an arbitrary value of displacement (rotor or stator) to evaluate all possible airgap unbalances. Using stochastic simulations of the eccentricity amplitudes enables an a priori design and lifetime estimation of bearings. Originality/value – This paper gives a close insight on the effect of mechanical bearing load caused by rotor eccentricities. The effect of the position of the eccentricity vector, the operational range and a drive cycle are considered. A stochastic simulation and an empirical lifetime model of one bearing gives an example of using this methodological approach.

Statistical analysis of empirical lifetime mileage data for automotive LCA

Innovative fuel efficiency technologies as for example electrification and lightweight materials typically lead to a shift of emissions from the use phase to the production phase of a vehicle. Whether the efforts of applying sophisticated fuel saving technologies pay back in environmental terms over the products’ lifetime depends directly on the lifetime mileage assumed. Currently, different “educated guess” values of industry associations and car manufacturers ranging from 150,000 to 300,000 km are applied in automotive life cycle assessment (LCA). This study improves the database for LCA practitioners in the automotive industry by statistically determining empirical lifetime mileage values for different types of passenger cars. The analysis of different data sets of a sample of more than 800,000 vehicles in Germany is performed by using statistical techniques. Firstly, survival analysis is used to describe the typical lifetime of passenger cars by using the Weibull distribution. Secondly, regression analysis is used to describe the progression of mileage during the course of a car’s life. The analysis differentiates eight different segments from urban small cars (A000) over midsized cars (A00, A0, A, B, C, D) to ultra luxury cars (E) as well as Otto and diesel engines. The results show varying lifetimes and mileages of passenger cars depending on the engine type and vehicle segment. Many decisions on innovative automotive technologies are independent from the engine type. In this case, the recommendation of the authors is to differentiate between three different groups of segments (A00/A0, A/B, C) with mileages going from 170,000 over 200,000 to 230,000 km. There might even be cases where the usage of a segment-specific value is not recommended. In such cases, the average value of the obtained results of 200,000 km appears as feasible choice. Even though the primary data are from Germany only, it is assumed that the results obtained in this study can be used as a proxy estimate for the geographical area of Europe. The results of this paper can be used as default values for LCA practitioners performing automotive LCAs as they provide evidence-based values of passenger cars’ lifetimes and mileages in a disaggregated way. The previously often used assumption of 150,000 km based on educated guess represents an underestimated value and should be replaced by the data obtained in this study. Using the proposed lifetime mileage data improves the validity and representativeness of automotive LCAs in Europe.

ON-state Reliability of Cu Atom Switch Under Current–Temperature Stress

The dc current-stress tolerance of the ON-state Cu atom switch is evaluated at elevated temperature. It is revealed that the reset-direction current stress causes time-dependent failures, which originate from the $E$ -field-driven diffusion of Cu in the conducting bridge. A new empirical lifetime estimation model, including the Joule heating effect, gives an allowable maximum current per atom switch of $I_{{\textrm {max}}}= 115~\mu \text{A}$ , which is large enough to satisfy the requirements for signal routing under currents that are average (18 $\mu \text{A}$ ) and peak (63 $\mu \text{A}$ ) in the reconfigurable switch block operated at 500 MHz at 125 °C.