A Gamma Process Based Degradation Model with Fractional Gaussian Noise

##plugins.themes.bootstrap3.article.main##

##plugins.themes.bootstrap3.article.sidebar##

Published Nov 5, 2024
Xiangyu Wang Xiaopeng Xi Marcos E. Orchard

Abstract

In modern industrial and engineering systems, stochastic degradation models are widely used for reliability analysis and maintenance decision-making. However, due to imperfect sensors and environmental influences, it is difficult to directly observe the latent degradation states. Traditional degradation models typically assume that measurement errors have simple statistical properties, but this assumption often does not hold in practical applications. To address this issue, this paper constructs a degradation model based on the Gamma process (GP) and assumes that measurement noise can be characterized by the fractional Gaussian noise (FGN). Furthermore, this paper proposes a method combining Gibbs sampling with the stochastic expectation-maximization (SEM) algorithm to achieve efficient estimation of the model parameters and accurate inference of the latent degradation states. Simulation results indicate that the proposed model exhibits better generalizability compared to the GP model with Gaussian noise.

How to Cite

Wang, X., Xi, X., & Orchard, M. (2024). A Gamma Process Based Degradation Model with Fractional Gaussian Noise. Annual Conference of the PHM Society, 16(1). https://doi.org/10.36001/phmconf.2024.v16i1.4022
Abstract 68 | PDF Downloads 53 Presentation Downloads 16

##plugins.themes.bootstrap3.article.details##

Keywords

Gamma process, Fractional Gaussian noise, Gibbs sampling, Latent degradation states estimation

References
Coeurjolly, J. (2000). Simulation and identification of the fractional brownian motion: a bibliographical and comparative study. Journal of statistical software, 5, 1–53.

Gebraeel, N., Lei, Y., Li, N., Si, X., Zio, E., et al. (2023). Prognostics and remaining useful life prediction of machinery: advances, opportunities and challenges. Journal of Dynamics, Monitoring and Diagnostics, 1–12.

Hong, G., Song,W., Gao, Y., Zio, E., & Kudreyko, A. (2022). An iterative model of the generalized cauchy process for predicting the remaining useful life of lithium-ion batteries. Measurement, 187, 110269.

Le Son, K., Fouladirad, M., & Barros, A. (2016). Remaining useful lifetime estimation and noisy gamma deterioration process. Reliability Engineering & System Safety, 149, 76– 87.

Li, H., Zhang, Z., Li, T., & Si, X. (2024). A review on physics-informed data-driven remaining useful life prediction: Challenges and opportunities. Mechanical Systems and Signal Processing, 209, 111120.

Li, Z., Hu, Q., Yang, Q., & Yu, D. (2022). Statistical analysis and optimal inspection planning for lifetime delayed gamma degradation processes. Quality and Reliability Engineering International, 38(6), 2986–3001.

Ling, M. H., Tsui, K. L., & Balakrishnan, N. (2014). Accelerated degradation analysis for the quality of a system based on the gamma process. IEEE Transactions on Reliability, 64(1), 463–472.

Liu, Q., Zhang, Y., Si, X., & Fan, Z. (2023). Dlvr-nwp: A novel data-driven bearing degradation model for rul estimation. IEEE Transactions on Instrumentation and Measurement, 72, 1–9.

Mukhopadhyay, K., Liu, B., Bedford, T., & Finkelstein, M. (2023). Remaining lifetime of degrading systems continuously monitored by degrading sensors. Reliability Engineering & System Safety, 231, 109022.

Pang, Z., Si, X., Hu, C., Du, D., & Pei, H. (2021). A bayesian inference for remaining useful life estimation by fusing ac celerated degradation data and condition monitoring data. Reliability Engineering & System Safety, 208, 107341.

Si, X., Li, T., & Zhang, Q. (2019). A general stochastic degradation modeling approach for prognostics of degrading systems with surviving and uncertain measurements. IEEE Transactions on Reliability, 68(3), 1080–1100.

Sottinen, T. (2001). Fractional brownian motion, random walks and binary market models. Finance and Stochastics, 5(3), 343–355.

Wang, H., Liao, H., Ma, X., & Bao, R. (2021). Remaining useful life prediction and optimal maintenance time determination for a single unit using isotonic regression and gamma process model. Reliability Engineering & System Safety, 210, 107504.

Xi, X., Chen, M., Zhang, H., & Zhou, D. (2018). An improved non-markovian degradation model with long-term dependency and item-to-item uncertainty. Mechanical Systems and Signal Processing, 105, 467–480.

Xi, X., Zhou, D., Chen, M., Balakrishnan, N., & Zhang, H. (2020). Remaining useful life prediction for multivariable stochastic degradation systems with non-markovian diffusion processes. Quality and Reliability Engineering International, 36(4), 1402–1421.

Zhang, H., Chen, M., Xi, X., & Zhou, D. (2017). Remaining useful life prediction for degradation processes with long-range dependence. IEEE Transactions on Reliability, 66(4), 1368–1379
Section
Technical Research Papers

Most read articles by the same author(s)

1 2 > >>