Accelerated Degradation Wiener Model for Lithiumion Battery Considering Individual Difference

For the accelerated degradation test (ADT) of lithium-ion battery, the degradation path models are usually applied with the fixed parameters. To optimize the degradation path models, so many battery cells are required for the ADT models based on the degradation path. However, for some lithium-ion batteries with long cycle life and high reliability, the samples are limited due to experimental cost constraints. Meanwhile, owing to the differences in raw materials and manufacturing processes, it is easy to observe variations among the degradation path of lithium-ion battery cells. Fortunately, Wiener process model considering the individual difference can express the variations and be modeled with limited samples for lithium-ion battery. Motivated by this issue, an improved method with random effects Wiener process (REWP) is proposed in this article. First, to verify the degradation process following the Wiener process, the Shapiro-Wilk test is carried out on the basis of a significance level of 0.05. Second, we analyze the varieties of every lithium-ion battery cell. To select a suitable Wiener process model, we apply the coefficient of variation as a measure of random parameters selection for Wiener process. Meanwhile, the maximum likelihood estimation (MLE) is used to optimize parameters of the proposed model. Next, the three different REWP models and general Wiener process model are compared. Finally, to demonstrate the proposed method, the lithium-ion battery cells used for a spacecraft in low Earth orbit (LEO) are conducted for ADTs. The results suggest that the REWP model has a better performance for assessing reliability of lithium-ion battery with long cycle life.

Remaining Useful Life Prediction of Lithium-ion Batteries Based on Wiener Process Under Time-Varying Temperature Condition

According to the present works, it is more efficient by carrying out accelerated degradation test (ADT) with step-down stress than constant and step-up stress. However, maximum likelihood estimation (MLE) is currently the main analysis method for step-down stress accelerated degradation test (SDSADT), which is difficult to be applied into small sample size occasion. To solve this problem, the paper proposes a Bayesian analysis method for SDSADT based on Wiener process. Firstly, degradation path of product performance is described by Wiener process, and then data analysis of SDSADT is carried out by a segmented Bayesian method which can update the evaluation values of model parameters under different accelerated stresses. Lastly, recursive algorithm for parameters estimation is established for reliability assessment of SDSADT. Simulation studies show that the method is more accuracy by comparing with MLE in case of small sample size.

Lithium-cobalt oxide has become a new generation of highly promising anode materials for lithium-ion batteries due to its low price, environmental friendliness, high platform voltage, and high theoretical capacity. In this paper, the working characteristics and related parameters of lithium-ion batteries are sorted out, and the influence factors of the decline mechanism of lithium-ion batteries are investigated from the perspective of chemical composition. Regarding the cycle life of lithium-ion battery cathode materials, this paper establishes a cycle life prediction model for lithium-ion batteries based on the LSTM model. It optimizes the hyperparameters of the model using the PSO algorithm. In addition, this paper also prepared lithium cobalt oxide cathode materials and carried out a validation analysis of the factors affecting their electrochemical performance. It is found that the cycle life prediction of lithium-ion battery based on LSTM has an RMSE of 3.27%, and the capacity of lithium cobalt oxide soft pack full battery decays from 249.81mAh to 137.04mAh at 26°C. The cycle life of its lithium cobalt oxide lithium-ion battery is around 250 cycles, and the average decay is 0.445mAh during one charge/discharge. Different charge/discharge cycles and diversity will have a significant effect on the cycle life of lithium-ion battery cathode materials, and it is necessary to pay attention to the parameter changes in the preparation of lithium cobalt oxide cathode materials in order to increase the cycle life of lithium-ion batteries.

In this paper, a novel approach is proposed to determine target reliability index based on modeling performance degradation of concrete structures as a stochastic process. First, the Wiener process with drift is used to simulate the degradation process of relative dynamic elastic modulus of concrete, and the drift coefficient and diffusion coefficient of Wiener process are estimated according to the experimental data of degradation of relative dynamic elastic modulus. Then, based on the relations between concrete compressive strength, dynamic elastic modulus, and relative dynamic elastic modulus, the relationship between compressive strength and the amount of degradation of relative dynamic elastic modulus are deduced, and then, the statistical parameters of concrete compressive strength under different service time can be calculated. Finally, based on the established limit state equation of flexural capacity of the weak section and the statistical parameters of compressive strength at different times, the reliability index of a structure under different service life is calculated. On the other hand, according to the drift Wiener process model of relative dynamic elastic modulus degradation of concrete, the time‐varying failure probability of structural durability degradation is calculated based on the first‐passage failure probability formula of drift Wiener process. Taking a concrete plant structure as an example, the time‐varying reliability index calculated based on the limit state equation and the time‐varying failure probability obtained based on the first‐passage failure probability analysis of drift Wiener process are compared, and then the recommended values of target reliability index of structural bearing capacity are comprehensively determined.

Degradation of many products in practical applications is often subject to unit-to-unit heterogeneity. Such heterogeneity can be attributed to the heterogeneous quality of the raw materials and the fluctuation of the manufacturing process, as well as the heterogeneous usage conditions and environments. The heterogeneity leads to the scattering of the degradation rates and diffusion intensities in the population. To model this phenomenon, this study proposes a general random-effects Wiener process model that accounts for the unit-to-unit heterogeneity in the degradation drift and the volatility simultaneously. In particular, the drift of the Wiener process is characterized by a normal distribution and the diffusion parameter is characterized by an independent inverse Gaussian distribution. The proposed model is flexible for characterization of heterogeneous degradation, and permits an analytically tractable model inference. An EM algorithm incorporating the variational Bayesian method is developed to estimate the model parameters, and a parametric bootstrap approach is proposed to construct confidence intervals. The performance of the proposed model and the estimation algorithm is validated by Monte Carlo simulations. The degradation data of an infrared LED device and the wear data of the magnetic head of a hard disk drive are studied based on the proposed model. With comprehensive comparative studies, the good performance of the proposed model in fitting the real degradation data is validated.

Relationships between yields and individual variation in the various characters in plant community were studied in upland-cultured paddy rice. In this experiment two varieties and three densities were adopted to cause individual variation in the various characters of upland-cultured paddy rice.The results are as follows:1. The coefficient of variation of the characters such as culm number, panicle number and dry weight was greater than that of plant height, culm length and ear length (Table 3).2. The individual variation of the characters such as culm number, panicle number and dry weight could be compared with coefficient of variation, because the actual data were in conformity with the regression line between the standard deviation of the above-mentioned characters and the mean value of those. On the other hand, with the characters such as plant height, culm length and ear length it could not be compared with coefficient of variation, because the above-mentioned phenomenon was not ob served.3. The individual variation of each character of “Myojoo”, panicle number type variety, was greater than that of “Fujiminori”, panicle weight type variety.4. The individual variation of each character of upland-cultured paddy rice under high plant density was greater than under low plant density. Because there was severe competition among individuals under the high plant density (Table 5).5. The individual variation of each character decreased with progress of growth stage under the low plant density, but increased under the high plant density (Fig.5).

The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time).

The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.

Life prediction is a complicated problem to be solved for the neutron tube which is widely used and plays an important role in many industries. In this paper, research on life prediction using regression analysis and Wiener process was carried out in order to evaluate the service life of the neutron tube quickly. Failure modes of the prefabricated target sealed deuterium-tritium neutron tube were firstly studied. Life tests of the neutron tube were conducted during laboratory at room temperature for about 55 hours. Regression analysis was performed on the experimental data obtained by the life tests of the neutron tube. The service life of the neutron tube was predicted using the regression function and the uncertainty analysis was performed. In order to take the stochasticity of the performance degradation and the yield measurement of the neutron tube into consideration, the Wiener process in which the Kalman filter and the maximum likelihood estimation methods were applied for the parameter solving process was adopted to assess the service life of the neutron tube. A program of the Wiener process was developed and the residual life distribution of the neutron tube was obtained. The predicted life which consisted of the expectation of the residual life and the time of life tests was consistent with that using the regression function. Finally, the scope of applications of the methods and the results in this paper were discussed. The general process in this paper may be used to estimate the service life of the neutron tube in the early stage of development.

Electric vehicles (EVs), in their pure and hybrid variants, have become the main alternative to ensure the decarbonization of the current vehicle fleet. Due to its excellent performance, EV technology is closely linked to lithium-ion battery (LIB) technology. A LIB is a complex dynamic system with extraordinary nonlinear behavior defined by electrical, thermal and electrochemical dynamics. To ensure the proper management of a LIB in such demanding applications as EVs, it is crucial to have an accurate mathematical model that can adequately predict its dynamic behavior. Furthermore, this model must be able to iteratively adapt its parameters to accommodate system disturbances during its operation as well as performance loss in terms of efficiency and nominal capacity during its life cycle. To this end, a methodology that employs the extended Kalman filter to iteratively improve a fuzzy model applied to a real LIB is presented in this paper. This algorithm allows to improve the classical Takagi–Sugeno fuzzy model (TSFM) with each new set of data obtained, adapting the model to the variations of the battery characteristics throughout its operating cycle. Data for modeling and subsequent validation were collected during experimental tests on a real LIB under EVs driving cycle conditions according to the “worldwide harmonised light vehicle test procedure” (WLTP) standard. The TSFM results allow the creation of an accurate nonlinear dynamic model of the LIB, even under fluctuating operating conditions, demonstrating its suitability for modeling and design of model-based control systems for LIBs used in EVs applications.

Where and when should a robot look during interaction with humans? Intuitively, human-human interaction serves as the blueprint. In such interactions, gaze plays a central role, both in visually guiding action and in signaling communication. Yet, most social robotics research still relies on the oversimplified eye-mind assumption, equating gaze with visual attention, and often implements gaze behaviors without accounting for perceptual limits or individual variability. We identify three core challenges at the intersection of psychology, visual perception, and robotics: (1) disentangling the dual functions of gaze, (2) understanding the visual perceptual mechanisms underlying gaze perception, and (3) adapting to individual, cultural, and clinical variability in gaze behavior. By examining these challenges in both robot interpretation and production of gaze, we argue that social robotics benefits from insights into human gaze and provides a powerful testbed for theory development, enabling controlled, interactive experiments that deepen our understanding of social attention. We conclude by conceptualizing social gaze as a soft-constraints inference and production process under uncertainty, linking visual perceptual mechanisms and social meaning.

To describe the reliability of blood bicarbonate pharmacokinetics in response to sodium bicarbonate (SB) supplementation across multiple occasions and assess, using putative thresholds, whether individual variation indicated a need for individualized ingestion timings. Thirteen men (age 27 ± 5 yr; body mass [BM], 77.4 ± 10.5 kg; height, 1.75 ± 0.06 m) ingested 0.3 g·kg BM SB in gelatine capsules on three occasions. One hour after a standardized meal, venous blood was obtained before and every 10 min after ingestion for 3 h, then every 20 min for a further hour. Time to peak (Tmax), absolute peak (Cmax), absolute peak change ([INCREMENT]Cmax), and area under the curve were analyzed using mixed models, intraclass correlation coefficient, coefficient of variation and typical error. Individual variation in pharmacokinetic responses was assessed using Bayesian simulation with multilevel models with random intercepts. No significant differences between sessions were shown for blood bicarbonate regarding Cmax, [INCREMENT]Cmax or area under the curve (P > 0.05), although Tmax occurred earlier in SB2 (127 ± 36 min) than in SB1 (169 ± 54 min, P = 0.0088) and SB3 (159 ± 42 min, P = 0.05). Intraclass correlation coefficient, coefficient of variation, and typical error showed moderate to poor reliability. Bayesian modeling estimated that >80% of individuals from the population experience elevated blood bicarbonate levels above +5 mmol·L between 75 and 240 min after ingestion, and between 90 and 225 min above +6 mmol·L. Assessing SB supplementation using discrete values showed only moderate reliability at the group level, and poor reliability at the individual level, whereas Tmax was not reproducible. However, when analyzed as modeled curves, a 0.3-g·kg BM dose was shown to create a long-lasting window of ergogenic potential, challenging the notion that SB ingestion individualized to time-to-peak is a necessary strategy, at least when SB is ingested in capsules.

Behavioral and physiological ecologists have long been interested in explaining the causes and consequences of trait variation, with a focus on individual differences in mean values. However, the majority of phenotypic variation typically occurs within individuals, rather than among individuals (as indicated by average repeatability being less than 0.5). Recent studies have further shown that individuals can also differ in the magnitude of variation that is unexplained by individual variation or environmental factors (i.e., residual variation). The significance of residual variation, or why individuals differ, is largely unexplained, but is important from evolutionary, methodological, and statistical perspectives. Here, we broadly reviewed literature on individual variation in behavior and physiology, and located 39 datasets with sufficient repeated measures to evaluate individual differences in residual variance. We then analyzed these datasets using methods that permit direct comparisons of parameters across studies. This revealed substantial and widespread individual differences in residual variance. The magnitude of individual variation appeared larger in behavioral traits than in physiological traits, and heterogeneity was greater in more controlled situations. We discuss potential ecological and evolutionary implications of individual differences in residual variance and suggest productive future research directions.

Maximum Likelihood Estimation of Asymmetric Jump-Diffusion Processes: Application to Security Prices