Abstract
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.
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Notes
- 1.
All MATLAB codes in this book can be found in the companion website http://www2.mae.ufl.edu/nkim/PHM/. The naming convention is functionname.m. For example, the MATLAB code for least squares method is LS.m.
- 2.
In this text, many data are generated from the assumed true parameters. This is useful to check if the identified parameters are accurate or not, compared to the true parameters.
- 3.
More specifically, the following condition is required: \( {\mathbf{y}}^{\text{T}} {\bar{\mathbf{y}}} = {\mathbf{z}}^{\text{T}} {\bar{\mathbf{y}}} \), where \( {\bar{\mathbf{y}}} \) is the constant vector all of whose elements are the mean data and \( {\mathbf{z}} \) is a vector of model predictions at \( x_{k} \).
- 4.
More detailed information on the variance of the parameters are found in Montgomery et al. (1982).
- 5.
A sample mean of \( n_{y} \) data from the population \( A \) is not the same if another \( n_{y} \) data are collected, which means the sample mean is also a random variable and denoted by \( \bar{A} \). In this case, the mean and standard deviation of \( \bar{A} \) is \( \mu \) and \( \sigma /\sqrt {n_{y} } \), respectively. See a book by Haldar and Mahadevan (2000).
- 6.
The confidence/prediction intervals are meaningful under the assumption that the model form is correct. If most degradation data are obtained only at early stage, the intervals will be narrow, but the error of degradation prediction at future cycles can be large when the prediction performed based on a different model form from true behavior. Usually, however, more data reflect more degradation behavior, which means the degradation prediction taking account of uncertainty becomes more reliable as more data are employed.
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Kim, NH., An, D., Choi, JH. (2017). Tutorials for Prognostics. In: Prognostics and Health Management of Engineering Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-44742-1_2
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