Estimating the Probability Density Function of Remaining Useful Life for Wiener Degradation Process with Uncertain Parameters

Delamination is a failure mechanism which is intrinsic of laminated fibre-reinforced plastics and possibly one of the major concerns of laminated composite structures, since, under certain conditions, delaminations can grow up to an hazardous extent without visible traces. In order to keep pace with recent condition-based maintenance requirements, proper validated diagnostic and prognostic methods which should be capable of operating on-line and in real time are required. In this respect, particle filters provide a consistent Bayesian framework, where the posterior distribution of the system degradation status is recursively approximated based on a time-growing stream of observations measuring the system response. However, the real-time operation capability of such methods is hindered by their requirements in terms of analysis time, which is mainly due to the complexity of the models they rely upon. Within this work, a particle filter framework, able to deal with the inherent stochasticity of fatigue delamination growth – while simultaneously relieving the computational burden associated with the evaluation of the trajectory likelihoods – is provided, leveraging on surrogate modelling strategies. Simultaneous diagnosis and prognosis of a simulated carbon fibre-reinforced plastics double cantilever beam specimen subject to fatigue delamination growth are performed, based on the observation of the strain field pattern acquired at some specific locations. The posterior probability density function of the delamination extent during propagation is updated at each inspection time as well as the probability density function of the remaining useful life. Ultimately, the adoption of the augmented state formulation allows for the estimation and updating of the joint probability density function of the parameters driving the stochastic delamination propagation model. Results demonstrate the feasibility and potential of the proposed approach as a tool able to monitor the progressing delamination while simultaneously providing estimates about the remaining useful life of composite structures.

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

Applied Sciences ◽

10.3390/app11114773 ◽

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.

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Improved MCMC Method for Parameter Estimation Based on Marginal Probability Density Function

Volume 2: 31st Computers and Information in Engineering Conference, Parts A and B ◽

10.1115/detc2011-48784 ◽

2011 ◽

Author(s):

Dawn An ◽

Joo-Ho Choi

Keyword(s):

Monte Carlo ◽

Probability Density Function ◽

Probability Density ◽

Density Function ◽

Uncertain Parameters ◽

Marginal Probability ◽

Mcmc Method ◽

Proposal Distribution ◽

Engineering Problems ◽

Probability Density Function Pdf

In many engineering problems, sampling is often used to estimate and quantify the probability distribution of uncertain parameters during the course of Bayesian framework, which is to draw proper samples that follow the probabilistic feature of the parameters. Among numerous approaches, Markov Chain Monte Carlo (MCMC) has gained the most popularity due to its efficiency and wide applicability. The MCMC, however, does not work well in the case of increased parameters and/or high correlations due to the difficulty of finding proper proposal distribution. In this paper, a method employing marginal probability density function (PDF) as a proposal distribution is proposed to overcome these problems. Several engineering problems which are formulated by Bayesian approach are addressed to demonstrate the effectiveness of proposed method.

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