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Identification of correlated damage parameters under noise and bias using Bayesian inference

This article presents statistical model parameter identification using Bayesian inference when parameters are correlated and observed data have noise and bias. The method is explained using the Paris model that describes crack growth in a plate under mode I loading. It is assumed that the observed data are obtained through structural health monitoring systems, which may have random noise and deterministic bias. It was found that a strong correlation exists (a) between two parameters of the Paris model, and (b) between initially measured crack size and bias. As the level of noise increases, the Bayesian inference was not able to identify the correlated parameters. However, the remaining useful life was predicted accurately because the identification errors in correlated parameters were compensated by each other. It was also found that the Bayesian identification process converges slowly when the level of noise is high.

Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method

An efficient method for a structural reliability analysis is proposed under the Bayesian framework, which can deal with the epistemic uncertainty arising from a limited amount of data. Until recently, conventional reliability analyses dealt mostly with the aleatory uncertainty, which is related to the inherent physical randomness and its statistical properties are completely known. In reality, however, epistemic uncertainties are prevalent, which makes the existing methods less useful. In the Bayesian approach, the probability itself is treated as a random variable of a beta distribution conditional on the provided data, which is determined by conducting a double loop of reliability analyses. The Kriging dimension reduction method is employed to promote efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy using a small number of analyses. Mathematical examples are used to demonstrate the proposed method. An engineering design problem is also addressed, which is to find an optimum design of a pigtail spring in a vehicle suspension, taking material uncertainty due to limited test data into account.

Bayesian Parameter Estimation for Prognosis of Crack Growth under Variable Amplitude Loading

In this study, crack-growth model parameters subjected to variable amplitude loading are estimated in the form of a probability distribution using the method of Bayesian parameter estimation. Huangs model is employed to describe the retardation and acceleration of the crack growth during the loadings. The Markov Chain Monte Carlo (MCMC) method is used to obtain samples of the parameters following the probability distribution. As the conventional MCMC method often fails to converge to the equilibrium distribution because of the increased complexity of the model under variable amplitude loading, an improved MCMC method is introduced to overcome this shortcoming, in which a marginal (PDF) is employed as a proposal density function. The model parameters are estimated on the basis of the data from several test specimens subjected to constant amplitude loading. The prediction is then made under variable amplitude loading for the same specimen, and validated by the ground-truth data using the estimated parameters.

Remaining Useful Life Prediction of Li-Ion Battery Based on Charge Voltage Characteristics

Batteries, which are being used as energy sources in various applications, tend to degrade, and their capacity declines with repeated charging and discharging cycles. A battery is considered to fail when it reaches 80% of its initial capacity. To predict this, prognosis techniques are attracting attention in recent years in the battery community. In this study, a method is proposed for estimating the battery health and predicting its remaining useful life (RUL) based on the slope of the charge voltage curve. During this process, a Bayesian framework is employed to manage various uncertainties, and a Particle Filter (PF) algorithm is applied to estimate the degradation of the model parameters and to predict the RUL in the form of a probability distribution. Two sets of test data-one from the NASA Ames Research Center and another from our own experiment-for an Li-ion battery are used for illustrating this technique. As a result of the study, it is concluded that the slope can be a good indicator of the battery health and PF is a useful tool for the reliable prediction of RUL.

Remaining useful life prediction of rolling element bearings using degradation feature based on amplitude decrease at specific frequencies

This research presents a new method of degradation feature extraction to predict remaining useful life, the remaining time to the maintenance, of rolling element bearings. Since bearing fault is the foremost cause of failure in rotating machinery, there are many studies for evaluating bearings’ health status to prevent a catastrophic failure. Most of these studies are based on health monitoring data, such as vibration signals that are indirectly related to bearing fault, from which degradation feature can be extracted. It is, however, challenging to extract a degradation feature that can be applied to all rolling elements. This study focuses on the amplitude decrease at specific frequencies, from which a robust degradation feature is extracted by employing the information entropy. Some important attributes are found from the degradation feature, which is used to predict the remaining useful life of bearings. This method is demonstrated using the real test data provided by FEMTO-ST Institute. The results show that bearings can be used up to 87% of their whole life and 59%–74% of life in average.

Applications of Prognostics

This chapter introduces several prognostics applications based on the real test data or data that are generated by simulating practical cases. Three major challenges are addressed for prognostics methods to be practical throughout this chapter.

Data-Driven Prognostics

The physics-based prognostics approaches in Chap. 4 is a powerful tool for predicting the future behavior of damage degradation with a relatively small number of observed data.

Tutorials for Prognostics

The performance of many engineering systems is gradually degraded, and eventually, the systems will fail under repeated usage conditions. Consider that a through-the-thickness center crack exists in an infinite plate under mode I fatigue loading condition.

Bayesian Statistics for Prognostics

One of key ideas in prognostics is how to utilize the information obtained from health monitoring systems in order to predict the behavior of damage; i.e., degradation.

Study on Attributes of Prognostics Methods

In this chapter, the attributes of various prognostics algorithms introduced in Chaps. 4 and 5 are discussed in details. Specifically, the following five algorithms will be considered in this chapter: three physics-based methods including nonlinear least squares (NLS), Bayesian method (BM) and particle filter (PF), and two data-driven methods including Gaussian process (GP) regression and neural network (NN).