Abstract
In this chapter, physics-based prognostics approaches are discussed. The fundamental assumption is that there exists a physical model that describes the evolution of damage or degradation.
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Notes
- 1.
The number 0.01 in line 19 is a default value for the initial LM parameter \( \lambda \). As \( \lambda \) is smaller, the Gauss–Newton update is more dominant in the LM method, while the gradient descent update is for the opposite case. Also, as the parameters are close to the optimal results, the update method is changed from the gradient descent to the Gauss–Newton update. Thereby, the LM parameter \( \lambda \) changes during the update process. See Gavin (2016) for more detailed explanation about the LM method, and see the Help in MATLAB for other options in the optimization process.
- 2.
Model parameters are considered as time independent variables. However, the model parameters undergo updating process, and the subscripts are just to denote the time step during the process.
- 3.
In PF, zero standard deviation is not need to be corrected as 1e-5 because it is related with random sampling rather than a PDF calculation.
- 4.
Smaller time interval means more iterations, which requires more computational time and prone to yield numerical error. To prevent this error, the initial distribution of model parameters should be set properly.
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Kim, NH., An, D., Choi, JH. (2017). Physics-Based Prognostics. In: Prognostics and Health Management of Engineering Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-44742-1_4
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DOI: https://doi.org/10.1007/978-3-319-44742-1_4
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