On the limiting distribution of the failure time of fibrous materials

1983 ◽  
Vol 15 (2) ◽  
pp. 331-348 ◽  
Author(s):  
Wagner De Souza Borges
Keyword(s):  
Materials Science ◽  
Failure Time ◽  
Large Deviation ◽  
Limiting Distribution ◽  
Statistical Characteristics ◽  
Fibrous Materials ◽  
Large Deviation Theorem ◽  
Science Area ◽  
The Individual ◽  
Failure Time Distributions

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statistical distribution of the failure time of fibrous materials. For that, fibrous materials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the number n of filaments in each bundle fixed and increasing only the chain length k leads to a Weibull limiting distribution for the failure time, letting both increase in such a way that log k(n) = o(n), we show that the limit distribution is for . Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.

On the limiting distribution of the failure time of fibrous materials

1983 ◽  
Vol 15 (02) ◽  
pp. 331-348
Author(s):  
Wagner De Souza Borges
Keyword(s):  
Materials Science ◽  
Failure Time ◽  
Large Deviation ◽  
Limiting Distribution ◽  
Statistical Characteristics ◽  
Fibrous Materials ◽  
Large Deviation Theorem ◽  
Science Area ◽  
The Individual ◽  
Failure Time Distributions

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statisticaldistribution of the failure time of fibrous materials. For that, fibrousmaterials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the numbernof filaments in each bundle fixed and increasing only the chain lengthkleads to a Weibull limiting distribution for the failure time, letting both increase in such a way that logk(n)= o(n), we show that the limit distribution isfor. Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.

scholarly journals Unsupervised Offline Changepoint Detection Ensembles

2021 ◽  
Vol 11 (9) ◽  
pp. 4280
Author(s):  
Iurii Katser ◽  
Viacheslav Kozitsin ◽  
Victor Lobachev ◽  
Ivan Maksimov
Keyword(s):  
Numerical Experiment ◽  
Failure Time ◽  
Cost Functions ◽  
Technical Diagnostics ◽  
Classification Problems ◽  
Tennessee Eastman Process ◽  
Changepoint Detection ◽  
Aggregation Functions ◽  
The Individual ◽  
Ensemble Algorithms

Offline changepoint detection (CPD) algorithms are used for signal segmentation in an optimal way. Generally, these algorithms are based on the assumption that signal’s changed statistical properties are known, and the appropriate models (metrics, cost functions) for changepoint detection are used. Otherwise, the process of proper model selection can become laborious and time-consuming with uncertain results. Although an ensemble approach is well known for increasing the robustness of the individual algorithms and dealing with mentioned challenges, it is weakly formalized and much less highlighted for CPD problems than for outlier detection or classification problems. This paper proposes an unsupervised CPD ensemble (CPDE) procedure with the pseudocode of the particular proposed ensemble algorithms and the link to their Python realization. The approach’s novelty is in aggregating several cost functions before the changepoint search procedure running during the offline analysis. The numerical experiment showed that the proposed CPDE outperforms non-ensemble CPD procedures. Additionally, we focused on analyzing common CPD algorithms, scaling, and aggregation functions, comparing them during the numerical experiment. The results were obtained on the two anomaly benchmarks that contain industrial faults and failures—Tennessee Eastman Process (TEP) and Skoltech Anomaly Benchmark (SKAB). One of the possible applications of our research is the estimation of the failure time for fault identification and isolation problems of the technical diagnostics.

Recent developments in dislocation pattern dynamics: Current opinions and perspectives

2018 ◽  
Vol 03 (03n04) ◽  
pp. 1840002 ◽  
Author(s):  
Dandan Lyu ◽  
Shaofan Li
Keyword(s):  
Crystal Plasticity ◽  
Materials Science ◽  
Pattern Dynamics ◽  
Future Challenges ◽  
Recent Developments ◽  
Computational Aspects ◽  
Stochastic Events ◽  
The Individual ◽  
Micro Structures ◽  
Dislocation Patterns

The development of crystal plasticity theory based on dislocation patterns dynamics has been an outstanding problem in materials science and condensed matter of physics. Dislocation is the origin of crystal plasticity, and it is both the individual dislocation behavior as well as the aggregated dislocations behaviors that govern the plastic flow. The interactions among dislocations are complex statistical and stochastic events, in which the spontaneous emergence of organized dislocation patterns formations is the most critical and intriguing events. Dislocation patterns consist of quasi-periodic dislocation-rich and dislocation poor regions, e.g. cells, veins, labyrinths, ladders structures, etc. during cyclic loadings. Dislocation patterns have prominent and decisive effects on work hardening and plastic strain localization, and thus these dislocation micro-structures are responsible to material properties at macroscale. This paper reviews the recent developments of experimental observation, physical modeling, and computer modeling on dislocation microstructure. In particular, we focus on examining the mechanism towards plastic deformation. The progress and limitations of different experiments and modeling approaches are discussed and compared. Finally, we share our perspectives on current issues and future challenges in both experimental, analytical modeling, and computational aspects of dislocation pattern dynamics.

scholarly journals Microstructural Dynamic Study of Grain Growth

1985 ◽  
Vol 63 ◽  
Author(s):  
M. P. Anderson ◽  
G. S. Grest ◽  
D. J. Srolovitz
Keyword(s):  
Monte Carlo ◽  
Grain Growth ◽  
Materials Science ◽  
Primary Recrystallization ◽  
Lattice Points ◽  
Microstructural Development ◽  
Continuous Systems ◽  
Monte Carlo Techniques ◽  
Topological Features ◽  
The Individual

The complete prediction of microstructural development in polycrystalline solids as a function of time and temperature is a major objective in materials science, but has not yet been possible primarily due to the complexity of the grain interactions. The evolution of the polycrystalline structure depends upon the precise specification of the coordinates of the grain boundary network, the crystallographic orientations of the grains, and the postulated microscopic mechanisms by which elements of the boundaries are assumed to move. Therefore, a general analytical solution to this multivariate problem has not yet been developed. Recently, we have been able to successfully incorporate these aspects of the grain interactions, and have developed a computer model which predicts the main features of the microstructure from first principles [1,2]., The polycrystal is mapped onto a discrete lattice by dividing the material into small area (2d) or volume (3d) elements, and placing the centers of these elements on lattice points. Interactions and dynamics are then defined for the individual elements which are analagous to those postulated in continuous systems. This discrete model preserves the topological features of real materials, and can be studied by computer simulation using Monte Carlo techniques. In this paper we report the application of the Monte Carlo method to the metallurgical phenomenon of grain growth with isothermal annealing. Extension of the model to treat primary recrystallization is presented elsewhere [3,4].

The effect of intermittent exposure to risk on failure time distributions

1974 ◽  
Vol 11 (2) ◽  
pp. 310-319 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
At Risk ◽  
Failure Time ◽  
Intermittent Exposure ◽  
Failure Time Distributions

The relation is investigated between the distributions of the total time until failure and the time of exposure to risk until failure, for individuals who are at risk only intermittently during their lifetimes. A specific example is considered in the case of computer failures.

scholarly journals Statistical characteristics of sources of vehicle kinematic excitation

2020 ◽  
Vol 313 ◽  
pp. 00011
Author(s):  
Jozef Melcer ◽  
Eva Merčiaková ◽  
Mária Kúdelčíková
Keyword(s):  
Probability Theory ◽  
Spectral Density ◽  
Surface Quality ◽  
Correlation Functions ◽  
Random Variable ◽  
Point Of View ◽  
Statistical Characteristics ◽  
Kinematic Excitation ◽  
Power Spectral ◽  
The Individual

The longitudinal and transverse road profiles represent the functions of a random variable from a mathematical point of view. It is appropriate to use methods of probability theory and mathematical statistics for their description. The unevenness of the runway surface is the main source of the vehicle's kinematic excitation. This paper describes the statistical properties of the mapped road profiles. It shows a way of categorizing road surface quality based on the power spectral density of unevenness. The interrelationships between the individual points of the profile and the profiles with one another are evaluated by correlation functions.

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