Methods of Hidden Periodicity Discovering for Gearbox Fault Detection

It is shown that the models of gear pair vibration, proposed in literature, are particular cases of the bi-periodically correlated random processes (BPCRPs), which describe its stochastic recurrence with two periods. The possibility of vibration and analysis within the framework of BPCRP approximation, in the form of periodically correlated random processes (PCRPs), is grounded and the implementation of vibration processing procedures using PCRP techniques, which are worked out by the authors, is given. Searching for hidden periodicities of the first and the second orders was considered as the main issue of this approach. The estimation of the non-stationary period (basic frequency) allowed us to carry out a detailed analysis of the deterministic part, the covariance structure of the stochastic part, and to form, using their parameters, the sensitive indicators for fault detection. The results of the processing of the wind turbine gearbox vibration signals are presented. The amplitude spectra of the deterministic oscillations and the time changes of the stochastic part power for different fault stages are analyzed. The most efficient indicators, which are formed using the amplitude spectra for practical applications, are proposed. The presented approach was compared with known in literature cyclostationary analysis and envelope techniques, and its advantages are shown.

CHARACTERIZATION OF THE TAIL BEHAVIOR OF A CLASS OF BEKK PROCESSES: A STOCHASTIC RECURRENCE EQUATION APPROACH

We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes $(X_t : t=1,2,\ldots )$ and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged $X_t$ ’s may load into the conditional covariance matrix of $X_t$ . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of $X_t$ may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

Modelling the risk of SARS-CoV-2 infection through PPE doffing in a hospital environment

Self-contamination during doffing of personal protective equipment (PPE) is a concern for healthcare workers (HCW) following SARS-CoV-2 positive patient care. Staff may subconsciously become contaminated through improper glove removal, so quantifying this risk is critical for safe working procedures. HCW surface contact sequences on a respiratory ward were modelled using a discrete-time Markov chin for: IV-drip care, blood pressure monitoring and doctors' rounds. Accretion of viral RNA on gloves during care was modelled using a stochastic recurrence relation. The HCW then doffed PPE and contaminated themselves in a fraction of cases based on increasing case load. The risk of infection from this exposure was quantified using a dose-response methodology. A parametric study was conducted to analyse the effect of: 1a) increasing patient numbers on the ward, 1b) the proportion of COVID-19 cases, 2) the length of a shift and 3) the probability of touching contaminated PPE. The driving factors for infection risk were surface contamination and number of surface contacts. HCWs on a 100% COVID-19 ward were less than 2-fold more at risk than on a 50% COVID ward (1.6% vs 1%), whilst on a 5% COVID-19 ward, the risk dropped to 0.1% per shift (sd=0.6%). IV-drip care resulted in higher risk than blood pressure monitoring (1.1% vs 1% p<0.0001), whilst doctors' rounds produced a 0.6% risk (sd=0.8%). Recommendations include supervised PPE doffing procedures such as the "doffing buddy" scheme, maximising hand hygiene compliance post-doffing and targeted surface cleaning for surfaces away from the patient vicinity.