A new gamma degradation process with random effect and state-dependent measurement error

2022 ◽  
pp. 1748006X2110672
Author(s):  
Nicola Esposito ◽  
Agostino Mele ◽  
Bruno Castanier ◽  
Massimiliano Giorgio
Keyword(s):  
Distribution Function ◽  
Measurement Error ◽  
Particle Filter ◽  
Cumulative Distribution Function ◽  
Random Effect ◽  
Degradation Process ◽  
Remaining Useful Life ◽  
Cumulative Distribution ◽  
Proposed Model ◽  
Useful Life

In this paper, a new gamma-based degradation process with random effect is proposed that allows to account for the presence of measurement error that depends in stochastic sense on the measured degradation level. This new model extends a perturbed gamma model recently suggested in the literature, by allowing for the presence of a unit to unit variability. As the original one, the extended model is not mathematically tractable. The main features of the proposed model are illustrated. Maximum likelihood estimation of its parameters from perturbed degradation measurements is addressed. The likelihood function is formulated. Hence, a new maximization procedure that combines a particle filter and an expectation-maximization algorithm is suggested that allows to overcome the numerical issues posed by its direct maximization. Moreover, a simple algorithm based on the same particle filter method is also described that allows to compute the cumulative distribution function of the remaining useful life and the conditional probability density function of the hidden degradation level, given the past noisy measurements. Finally, two numerical applications are developed where the model parameters are estimated from two sets of perturbed degradation measurements of carbon-film resistors and fuel cell membranes. In the first example the presence of random effect is statistically significant while in the second example it is not significant. In the applications, the presence of random effect is checked via appropriate statistical procedures. In both the examples, the influence of accounting for the presence of random effect on the estimates of the cumulative distribution function of the remaining useful life of the considered units is also discussed. Obtained results demonstrate the affordability of the proposed approach and the usefulness of the proposed model.

scholarly journals A Comparative Study on Computation of Cumulative Distribution Function in Predicting Time of Failure of Engineering Systems

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Gina Katherine Sierra Paez ◽  
Matthew Daigle ◽  
Kai Goebel
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Degradation Process ◽  
Cumulative Distribution ◽  
System State ◽  
Underlying Assumption ◽  
Hazard Zone ◽  
The Difference ◽  
Definition Of ◽  
Time Of Failure

Estimating accurate Time-of-Failure (ToF) of a system is key in making the decisions that impact operational safety and optimize cost. In this context, it is interesting to note that different approaches have been explored to tackle the problem of estimating ToF. The difference is in part characterized by different definitions of the hazard zones. The conventional definition for the cumulative distribution function (CDF) calculation is assumed to have well-defined hazard zones, that is, hazard zones defined as a function of the system state trajectory. An alternate method suggests the use of hazard zones defined as a function of the system state at time , instead of hazard zones defined as a function of system state up to and including time k (Acuña and Orchard 2018, 2017). This paper explores these differences and their impact on ToF estimation. Results for the conventional CDF definition indicated that, (i) the cumulative distribution function is always an increasing function of time, even when realizations of the degradation process are not monotonic, (ii) the sum of all probabilities is always 1 and does not need to be normalized, and (iii) all probabilities are positive and less than or equal to 1. Similar results are not observed for CDF calculation with hazard zones defined as a function only of the system state at time k. Results for ToF estimation using Acuña's definition differ, suggesting that there is an underlying assumption of independence in the hazard zone definition.  Therefore, we present an alternate definition of hazard zone which guarantees the properties of a well-defined CDF with a more straightforward ToF definition.

The Research on Degradation Failure Life and Degradation Data Structure

2013 ◽  
Vol 710 ◽  
pp. 294-297
Author(s):  
Yi Dong Wang ◽  
Yi Zhou He ◽  
Hai Bo Liu ◽  
Jun Wei Lei
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Reliability Assessment ◽  
Degradation Process ◽  
Cumulative Distribution ◽  
Degradation Data ◽  
Sudden Failure ◽  
Degradation Failure ◽  
Degradation Degree ◽  
Failure Life

In order to solve the reliability assessment in the case of competition failure induced by the coexistence between burst-type failure and degradation-type failure in the product, the method of degradation amount distribution was adopted to describe the degradation process of performance in product. Considering the relativity between sudden failure and degradation degree, the cumulative distribution function of sudden failure was calculated from the standpoint of degradation amount. Eliminating the affect of sudden failure according to a certain conditional probability in the degradation amount distribution function, which helps to realize reliability assessment based on competitive failure analysis.

An improved deep convolution neural network for predicting the remaining useful life of rolling bearings

2020 ◽  
pp. 1-9
Author(s):  
Yiming Guo ◽  
Hui Zhang ◽  
Zhijie Xia ◽  
Chang Dong ◽  
Zhisheng Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Degradation Process ◽  
Rolling Bearing ◽  
Remaining Useful Life ◽  
Convolution Neural Network ◽  
Dual Channel ◽  
Time Domain Data ◽  
Channel Input ◽  
Deep Convolution Neural Network ◽  
Useful Life

The rolling bearing is the crucial component in the rotating machinery. The degradation process monitoring and remaining useful life prediction of the bearing are necessary for the condition-based maintenance. The commonly used deep learning methods use the raw or processed time domain data as the input. However, the feature extracted by these approaches is insufficient and incomprehensive. To tackle this problem, this paper proposed an improved Deep Convolution Neural Network with the dual-channel input from the time and frequency domain in parallel. The proposed methodology consists of two stages: the incipient failure identification and the degradation process fitting. To verify the effectiveness of the method, the IEEE PHM 2012 dataset is adopted to compare the proposed method and other commonly used approaches. The results show that the improved Deep Convolution Neural Network can effectively describe the degradation process for the rolling bearing.

scholarly journals Predicting Remaining Useful Life of Rolling Bearings Based on Reliable Degradation Indicator and Temporal Convolution Network with the Quantile Regression

2021 ◽  
Vol 11 (11) ◽  
pp. 4773
Author(s):  
Qiaoping Tian ◽  
Honglei Wang
Keyword(s):  
Quantile Regression ◽  
Probability Density ◽  
Degradation Process ◽  
Remaining Useful Life ◽  
Health State ◽  
Rolling Bearings ◽  
Data Set ◽  
Time Frequency ◽  
Useful Life ◽  
Degradation Indicator

High precision and multi information prediction results of bearing remaining useful life (RUL) can effectively describe the uncertainty of bearing health state and operation state. Aiming at the problem of feature efficient extraction and RUL prediction during rolling bearings operation degradation process, through data reduction and key features mining analysis, a new feature vector based on time-frequency domain joint feature is found to describe the bearings degradation process more comprehensively. In order to keep the effective information without increasing the scale of neural network, a joint feature compression calculation method based on redefined degradation indicator (DI) was proposed to determine the input data set. By combining the temporal convolution network with the quantile regression (TCNQR) algorithm, the probability density forecasting at any time is achieved based on kernel density estimation (KDE) for the conditional distribution of predicted values. The experimental results show that the proposed method can obtain the point prediction results with smaller errors. Compared with the existing quantile regression of long short-term memory network(LSTMQR), the proposed method can construct more accurate prediction interval and probability density curve, which can effectively quantify the uncertainty of bearing running state.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

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