A robust functional-data-analysis method for data recovery in multichannel sensor systems

Multichannel sensor systems are widely used in condition monitoring for effective failure prevention of critical equipment or processes. However, loss of sensor readings due to malfunctions of sensors and/or communication has long been a hurdle to reliable operations of such integrated systems. Moreover, asynchronous data sampling and/or limited data transmission are usually seen in multiple sensor channels. To reliably perform fault diagnosis and prognosis in such operating environments, a data recovery method based on functional principal component analysis (FPCA) can be utilized. However, traditional FPCA methods are not robust to outliers and their capabilities are limited in recovering signals with strongly skewed distributions (i.e., lack of symmetry). This paper provides a robust data-recovery method based on functional data analysis to enhance the reliability of multichannel sensor systems. The method not only considers the possibly skewed distribution of each channel of signal trajectories, but is also capable of recovering missing data for both individual and correlated sensor channels with asynchronous data that may be sparse as well. In particular, grand median functions, rather than classical grand mean functions, are utilized for robust smoothing of sensor signals. Furthermore, the relationship between the functional scores of two correlated signals is modeled using multivariate functional regression to enhance the overall data-recovery capability. An experimental flow-control loop that mimics the operation of coolant-flow loop in a multimodular integral pressurized water reactor is used to demonstrate the effectiveness and adaptability of the proposed data-recovery method. The computational results illustrate that the proposed method is robust to outliers and more capable than the existing FPCA-based method in terms of the accuracy in recovering strongly skewed signals. In addition, turbofan engine data are also analyzed to verify the capability of the proposed method in recovering non-skewed signals.

Asymptotics of nonparametric L-1 regression models with dependent data

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

Reference curves based on non-parametric quantile regression

Reference curves which take time into account, such as those for age, are often required in medicine, but simple systematic and efficient statistical methods for constructing them are lacking. Classical methods are based on parametric fitting (polynomial curves). Semi-parametric methods are also widely used especially in Europe. Here, we propose a new methodology for the estimation of reference intervals for data sets, based on non-parametric estimation of conditional quantiles. The derived methods should be applicable to all clinical (or more generally biological) variables that are measured on a continuous quantitative scale. As an example, we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy French women. The results are compared to those obtained with Royston's polynomial parametric method and the semi-parametric LMS approach.