The correlation between wind speed and failure rate (FR) of wind turbines is analyzed with time series approach. The time series of power index (PI) and FR of wind turbines are established based on historical data, which are pretreated by singularity processing, stationarity processing, and wavelet de-noising. The trend variations of the time series are analyzed from both time domain and frequency domain by extracting the indicator functions, including auto-correlation function, cross-correlation function, and spectral density function. A case study is given out to verify the validity of the model and the method, which is based on the wind speed and failure data from January 1995 to December of 2002 in Nordjylland, Denmark. Auto-correlation function and spectral density function show that time series of PI and FR have strong seasonal characteristics and quite similar periodicity, while the cross-correlation function shows they keep high consistency and strong correlation. The results indicate that by calculating and monitoring PI, the failure rule of wind turbines can be forecast, which provides theoretical basis for preventive maintenance of wind turbines.

Mechanical systems and their components usually have multiple failure modes and different performance states. Most existing system reliability modelling theories are developed on the basis of binary logic, which lack sufficient ability to describe the above phenomena. In this article, dynamic Bayesian network theory is employed to evaluate the multi-state reliability of a hydraulic lifting system. First, failure mode and effect analysis and structural analysis and design technique are comprehensively applied to analyse the functionalities and failure modes of the components. Afterwards, the time factor is integrated into the model by considering the state transition of the components. In this way, the multi-state reliability model of the system is established by dynamic Bayesian network. The reliability assessment and diagnostic analysis are performed by taking advantage of the dynamic Bayesian network's bi-directional reasoning ability, and the results are in good agreement with actual situation. It shows that the proposed approach is effective and convenient for multistate reliability modelling and analysis for mechanical systems.