scholarly journals A Parameter Estimation Method of Shock Model Constructed with Phase-Type Distribution on the Condition of Interval Data

2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Long Wang ◽  
Yue Li ◽  
Yanling Qian ◽  
Xu Luo
Keyword(s):  
Parameter Estimation ◽  
Likelihood Function ◽  
Estimation Method ◽  
Interval Data ◽  
Shock Model ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Ph Distribution ◽  
Parameter Estimation Method ◽  
Phase Type

The phase-type distribution (also known as PH distribution) has mathematical properties of denseness and closure in calculation and is, therefore, widely used in shock model constructions describing occurrence time of a shock or its damage. However, in the case of samples with only interval data, modeling with PH distribution will cause decoupling issues in parameter estimation. Aiming at this problem, an approximate parameter estimation method based on building PH distribution with dynamic order is proposed. Firstly, the shock model established by PH distribution and the likelihood function under samples with only interval data are briefly introduced. Then, the principle and steps of the method are introduced in detail, and the derivation processes of some related formulas are also given. Finally, the performance of the algorithm is illustrated by a case with three different types of distributions.

scholarly journals Parameter Estimation Method of Mixture Distribution for Construction Machinery

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Xinting Zhai ◽  
Jixin Wang ◽  
Jinshi Chen
Keyword(s):  
Parameter Estimation ◽  
Likelihood Function ◽  
Estimation Method ◽  
Mixture Distribution ◽  
Information Criterion ◽  
Working Environment ◽  
Practical Case ◽  
Chi Square ◽  
Construction Machinery ◽  
Parameter Estimation Method

Due to the harsh working environment of the construction machinery, a simple distribution cannot be used to approximate the shape of the rainflow matrix. In this paper, the Weibull-normal (W-n) mixture distribution is used. The lowest Akaike information criterion (AIC) value is employed to determine the components number of the mixture. A parameter estimation method based on the idea of optimization is proposed. The method estimates parameters of the mixture by maximizing the log likelihood function (LLF) using an intelligent optimization algorithm (IOA), genetic algorithm (GA). To verify the performance of the proposed method, one of the already existing methods is applied in the simulation study and the practical case study. The fitting effects of the fitted distributions are compared by calculating the AIC and chi-square (χ2) value. It can be concluded that the proposed method is feasible and effective for parameter estimation of the mixture distribution.

scholarly journals Reliability assessment of system under a generalized run shock model

2018 ◽  
Vol 55 (4) ◽  
pp. 1249-1260 ◽  
Author(s):  
Min Gong ◽  
Min Xie ◽  
Yaning Yang
Keyword(s):  
Arrival Time ◽  
Reliability Assessment ◽  
State System ◽  
Shock Model ◽  
External Shocks ◽  
Phase Type Distribution ◽  
Type Distribution ◽  
Markovian Property ◽  
Phase Type ◽  
Real Practice

Abstract In this paper we are concerned with modelling the reliability of a system subject to external shocks. In a run shock model, the system fails when a sequence of shocks above a threshold arrive in succession. Nevertheless, using a single threshold to measure the severity of a shock is too critical in real practice. To this end, we develop a generalized run shock model with two thresholds. We employ a phase-type distribution to model the damage size and the inter-arrival time of shocks, which is highly versatile and may be used to model many quantitative features of random phenomenon. Furthermore, we use the Markovian property to construct a multi-state system which degrades with the arrival of shocks. We also provide a numerical example to illustrate our results.

scholarly journals Modeling and Fault Diagnosis of Interturn Short Circuit for Five-Phase Permanent Magnet Synchronous Motor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-wei Yang ◽  
Man-feng Dou ◽  
Zhi-yong Dai
Keyword(s):  
Parameter Estimation ◽  
Fault Diagnosis ◽  
Permanent Magnet ◽  
Fault Tolerant ◽  
Short Circuit ◽  
Estimation Method ◽  
Trust Region ◽  
Fault Tolerant Control ◽  
Trust Region Algorithm ◽  
Parameter Estimation Method

Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.

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