It is often necessary to estimate a probability density non-parametrically, that is, without making strong parametric assumptions such as normality. This R (R Core Team, 2019) package provides a non-parametric density estimator that can take advantage of some of the knowledge the user has about the probability density. Kernel density estimation (Silverman, 2018) is a popular method for non-parametric density estimation based on placing kernels on each data point. Hjort & Glad (1995) extended kernel density estimation with parametric starts. The parametric start is a parametric density that is multiplied with the kernel estimate. When the data-generating density is reasonably close to the parametric start density, kernel density estimation with that parametric start will outperform ordinary kernel density estimation.
Principal component analysis (PCA) is often used in anomaly detection and statistical process control tasks. For bivariate normal data, we prove that the minor projection (the least varying projection) of the PCA‐rotated data is the most sensitive to distributional changes, where sensitivity is defined as the Hellinger distance between the projections' marginal distributions before and after a change. In particular, this is almost always the case if only one parameter of the bivariate normal distribution changes, that is, the change is sparse. Simulations indicate that the minor projections are the most sensitive for a large range of changes and pre‐change settings in higher dimensions as well, including changes that are very sparse. This motivates using only a few of the minor projections for detecting sparse distributional changes in high‐dimensional data.
Motivated by a condition monitoring application arising from subsea engineering we derive a novel, scalable approach to detecting anomalous mean structure in a subset of correlated multivariate time series. Given the need to analyse such series efficiently we explore a computationally efficient approximation of the maximum likelihood solution to the resulting modelling framework, and develop a new dynamic programming algorithm for solving the resulting Binary Quadratic Programme when the precision matrix of the time series at any given time-point is banded. Through a comprehensive simulation study, we show that the resulting methods perform favourably compared to competing methods both in the anomaly and change detection settings, even when the sparsity structure of the precision matrix estimate is misspecified. We also demonstrate its ability to correctly detect faulty time-periods of a pump within the motivating application.
Motivated by a condition monitoring application arising from subsea engineering we derive a novel, scalable approach to detecting anomalous mean structure in a subset of correlated multivariate time series. Given the need to analyse such series efficiently we explore a computationally efficient approximation of the maximum likelihood solution to the resulting modelling framework, and develop a new dynamic programming algorithm for solving the resulting Binary Quadratic Programme when the precision matrix of the time series at any given time-point is banded. Through a comprehensive simulation study, we show that the resulting methods perform favourably compared to competing methods both in the anomaly and change detection settings, even when the sparsity structure of the precision matrix estimate is misspecified. We also demonstrate its ability to correctly detect faulty time-periods of a pump within the motivating application.
Thermal protection in marine electrical propulsion motors is commonly implemented by installing temperature sensors on the windings of the motor. An alarm is issued once the temperature reaches the alarm limit, while the motor shuts down once the trip limit is reached. Field experience shows that this protection scheme in some cases is insufficient, as the motor may already be damaged before reaching the trip limit. In this paper, we develop a machine learning algorithm to predict overheating, based on past data collected from a class of identical vessels. All methods were implemented to comply with real-time requirements of the on-board protective systems with minimal need for memory and computational power. Our two-stage overheating detection algorithm first predicts the temperature in a normal state using linear regression fitted to regular operation motor performance measurements, with exponentially smoothed predictors accounting for time dynamics. Then it identifies and monitors temperature deviations between the observed and predicted temperatures using an adaptive cumulative sum (CUSUM) procedure. Using data from a real fault case, the monitor alerts between 60 to 90 minutes before failure occurs, and it is able to detect the emerging fault at temperatures below the current alarm limits.
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