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Comparative Analysis of Stochastic and Uncertain Process Degradation Modeling Based on RQRL

Liu Kai, Zou Tianji, Xin Mincheng

Eksploatacja i Niezawodność

2024

Vol. 26, no. 3

art. no. 186823

Small sample sizes cause epistemic uncertainties in reliability estimation and even result in potential risks in maintenance strategies. To explore the difference between stochastic- and uncertain-process-based degradation modeling in reliability estimation for small samples, this study proposes a comparative analysis methodology based on the range of quantile reliable lifetime (RQRL). First, considering both unit-to-unit variability and epistemic uncertainty, we proposed the Wiener and Liu process degradation models. Second, based on the RQRL, a comparative analysis method of different degradation models for reliability estimation under various sample sizes and measurement times was proposed. Third, based on a case study, the sensitivities of the Wiener and Liu process degradation models for various sample sizes and measurement times were compared and analyzed based on the RQRL. The results demonstrated that using the uncertain process degradation model improved the uniformity and stability of reliability estimation under small-sample conditions.

Adaptive Predictive Controller Using Orthonormal Series Functions

Oliveira G. H. C., Amaral W. C., Favier G.

International Journal of Applied Mathematics and Computer Science

1999

Vol. 9, no 1

175-191

A constrained adaptive predictive control method that uses uncertain process modelling based on orthonormal series functions is considered. Such unstructured modelling is described as a weighted sum of orthonormal functions using approximate information about the time constant of the process. The orthonormal series functions model can thus be used to derive a j-step-ahead output prediction according to the constrained adaptive predictive control law. In relation to predictive controllers based on structured models, this approach presents the advantage of not requiring prior knowledge of the order or time delay, which decrease prediction errors and lead to a better closed loop performance when these parameters are not well known. Stability issues of the proposed control scheme are discussed and, finally, a simulation example is given to show the performance of the algorithm.