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Open AccessArticle

Availability Analysis of an Unreliable Single Unit System Operating in a Doubly Stochastic Shock Environment

by Hemanth Kumar Sankaralingam and Thilaka Balakrishnan

Mathematics 2026, 14(10), 1730; https://doi.org/10.3390/math14101730 - 18 May 2026

Viewed by 287

This paper considers an unreliable system together with a repairman operating in a doubly stochastic environment. The system operates in a stochastic environment which alternates between two levels, namely less load and heavy load. The intrinsic life-time of the system is exponentially distributed with varying means depending on whether the system is working in less load period or heavy load period. Environment dependent shocks arrive to the system according to a Poisson process with different rates depending on whether the environment is in less load or in heavy load period. At the occurrence of a shock, the operating system fails and it is immediately taken to the repair facility and the repair commences instantaneously. The repair time is exponentially distributed whose mean is dependent on the type of failure and the level of the environment. After each repair, the system begins to function in heavy load environment or less load environment according to the level of the environment at the time of completion of the repair. The repair facility is unaffected by shocks. Kolmogorov equations governing the behaviour of the system are derived and the probability distribution of the states is obtained. The availability function is also obtained and the model is highlighted with a numerical illustration. Full article

(This article belongs to the Section D: Statistics and Operational Research)

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20 pages, 2932 KB

Open AccessArticle

Misalignment Fault Prediction of Wind Turbines Based on Combined Forecasting Model

by Yancai Xiao and Zhe Hua

Algorithms 2020, 13(3), 56; https://doi.org/10.3390/a13030056 - 1 Mar 2020

Cited by 9 | Viewed by 5304

Abstract

Due to the harsh working environment of wind turbines, various types of faults are prone to occur during long-term operation. Misalignment faults between the gearbox and the generator are one of the latent common faults for doubly-fed wind turbines. Compared with other faults like gears and bearings, the prediction research of misalignment faults for wind turbines is relatively few. How to accurately predict its developing trend has always been a difficulty. In this paper, a combined forecasting model is proposed for misalignment fault prediction of wind turbines based on vibration and current signals. In the modelling, the improved Multivariate Grey Model (IMGM) is used to predict the deterministic trend and the Least Squares Support Vector Machine (LSSVM) optimized by quantum genetic algorithm (QGA) is adopted to predict the stochastic trend of the fault index separately, and another LSSVM optimized by QGA is used as a non-linear combiner. Multiple information of time-domain, frequency-domain and time-frequency domain of the wind turbine’s vibration or current signals are extracted as the input vectors of the combined forecasting model and the kurtosis index is regarded as the output. The simulation results show that the proposed combined model has higher prediction accuracy than the single forecasting models. Full article

(This article belongs to the Special Issue Algorithms for Fault Detection and Diagnosis)

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