scholarly journals A Copula Entropy Approach to Dependence Measurement for Multiple Degradation Processes

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 724 ◽  
Author(s):  
Fuqiang Sun ◽  
Wendi Zhang ◽  
Ning Wang ◽  
Wei Zhang
Keyword(s):  
Information Entropy ◽  
Complex Structure ◽  
Copula Function ◽  
Dependence Structure ◽  
Entropy Theory ◽  
Multiple Features ◽  
Reliability Modeling ◽  
Degradation Processes ◽  
Degradation Analysis ◽  
Complex Dependence

Degradation analysis has been widely used in reliability modeling problems of complex systems. A system with complex structure and various functions may have multiple degradation features, and any of them may be a cause of product failure. Typically, these features are not independent of each other, and the dependence of multiple degradation processes in a system cannot be ignored. Therefore, the premise of multivariate degradation modeling is to capture and measure the dependence among multiple features. To address this problem, this paper adopts copula entropy, which is a combination of the copula function and information entropy theory, to measure the dependence among different degradation processes. The copula function was employed to identify the complex dependence structure of performance features, and information entropy theory was used to quantify the degree of dependence. An engineering case was utilized to illustrate the effectiveness of the proposed method. The results show that this method is valid for the dependence measurement of multiple degradation processes.

Reliability modeling for a discrete time multi-state system with random and dependent transition probabilities

2019 ◽  
Vol 233 (5) ◽  
pp. 747-760 ◽  
Author(s):  
Linmin Hu ◽  
Rui Peng
Keyword(s):  
Discrete Time ◽  
Power Distribution ◽  
State Transition ◽  
Transition Probabilities ◽  
Survival Function ◽  
Copula Function ◽  
State System ◽  
Dependence Structure ◽  
Reliability Modeling ◽  
Dynamic Reliability

In a random environment, state transition probabilities of a multi-state system can change as the environment changes. Thus, a dynamic reliability model with random and dependent transition probabilities is developed for non-repairable discrete-time multi-state system in this article. The dependence among the random state transition probabilities of the system is modeled by a copula function. By probability argument and random process theory, we obtain explicit expressions of some reliability characteristics and joint survival function of random time spent by the system in all working states (partially and completely working states). A special case is considered when the state transition probabilities are dependent random variables with power distribution, and the dependence structure is modeled by Farlie–Gumbel–Morgenstern copula. Numerical examples are also presented to demonstrate the developed model and perform a comparison for the models with random and fixed transition probabilities.

Approach for cleaning uncertain data based on information entropy theory

2013 ◽  
Vol 33 (9) ◽  
pp. 2490-2492
Author(s):  
Yuanxiang QIN ◽  
Liang DUAN ◽  
Kun YUE
Keyword(s):  
Information Entropy ◽  
Uncertain Data ◽  
Entropy Theory

scholarly journals Research on Pattern Recognition Method of Blockage Signal in Pipeline Based on LMD Information Entropy and ELM

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Jingzong Yang ◽  
Xiaodong Wang ◽  
Zao Feng ◽  
Guoyong Huang
Keyword(s):  
Pattern Recognition ◽  
Impulse Response ◽  
Information Entropy ◽  
Operating Conditions ◽  
Support Vector ◽  
Entropy Theory ◽  
Pattern Recognition Method ◽  
Response Signal ◽  
Recognition Method ◽  
Learning Machine

Aiming at the nonstationary and nonlinear characteristics of acoustic impulse response signal in pipeline blockage and the difficulty in identifying the different degrees of blockage, this paper proposed a pattern recognition method based on local mean decomposition (LMD), information entropy theory, and extreme learning machine (ELM). Firstly, the impulse response signals of pipeline extracted in different operating conditions were decomposed with LMD method into a series of product functions (PFs). Secondly, based on the information entropy theory, the appropriate energy entropy, singular spectrum entropy, power spectrum entropy, and Hilbert spectrum entropy were extracted as the input feature vectors. Finally, ELM was introduced for classification of pipeline blockage. Through the analysis of acoustic impulse response signal collected under the condition of health and different degrees of blockages in pipeline, the results show that the proposed method can well characterize the state information. Also, it has a great advantage in terms of accuracy and it is time consuming when compared with the support vector machine (SVM) and BP (backpropagation) model.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

Attribute Recognition Model Based on Entropy Weight and Its Application to Evaluation of Groundwater Quality

2010 ◽  
Vol 29-32 ◽  
pp. 2698-2702
Author(s):  
Xian Qi Zhang ◽  
Wen Hong Feng ◽  
Nan Nan Li
Keyword(s):  
Water Quality ◽  
Groundwater Quality ◽  
Information Entropy ◽  
Simple Calculation ◽  
Weight Coefficient ◽  
Entropy Theory ◽  
Entropy Weight ◽  
Recognition Model ◽  
Model Based ◽  
Attribute Recognition

It is necessary to take into account synthetically attribute of every index because of independence and incompatibility resulted from single index evaluating outcomes. Through the information entropy theory and attribute recognition model being combined together, attribute recognition model based on entropy weight is constructed and applied to evaluating groundwater quality by a new method, weight coefficient by the law of entropy value is exercised so that it is more objective. The outcome from concrete application indicates that it is suitable to evaluate water quality with reasonable conclusion and simple calculation.

scholarly journals LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su ◽  
Chunping Li
Keyword(s):  
Random Effects ◽  
System Reliability ◽  
Light Emitting Diode ◽  
Copula Function ◽  
Performance Characteristics ◽  
Assessment Model ◽  
Gamma Process ◽  
Unknown Parameters ◽  
Reliability Modeling ◽  
Lighting Systems

Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e., illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that the system has two performance characteristics, and each performance characteristic is governed by a random effects Gamma process where the random effects can capture the unit to unit differences. The dependency of performance characteristics is described by a Frank copula function. Via the copula function, the reliability assessment model is proposed. Considering the model is so complicated and analytically intractable, the Markov chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about actual LED lamps data is given to demonstrate the usefulness and validity of the proposed model and method.

scholarly journals Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Nachatchapong Kaewsompong ◽  
Paravee Maneejuk ◽  
Woraphon Yamaka
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Method ◽  
Real Data ◽  
Copula Function ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Multivariate Normal ◽  
Empirical Comparison ◽  
Proposed Model ◽  
Conventional Models

We propose a high-dimensional copula to model the dependence structure of the seemingly unrelated quantile regression. As the conventional model faces with the strong assumption of the multivariate normal distribution and the linear dependence structure, thus, we apply the multivariate exchangeable copula function to relax this assumption. As there are many parameters to be estimated, we consider the Bayesian Markov chain Monte Carlo approach to estimate the parameter interests in the model. Four simulation studies are conducted to assess the performance of our proposed model and Bayesian estimation. Satisfactory results from simulation studies are obtained suggesting the good performance and reliability of the Bayesian method used in our proposed model. The real data analysis is also provided, and the empirical comparison indicates our proposed model outperforms the conventional models in all considered quantile levels.

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