Diagnosis of Broken Rotor Bars during the Startup of Inverter-Fed Induction Motors Using the Dragon Transform and Functional ANOVA

A proper diagnosis of the state of an induction motor is of great interest to industry given the great importance of the extended use of this motor. Presently, the use of this motor driven by a frequency converter is very widespread. However, operation by means of an inverter introduces certain difficulties for a correct diagnosis, which results in a signal with higher harmonic content and noise level, which makes it difficult to perform a correct diagnosis. To solve these problems, this article proposes the use of a time-frequency technique known as Dragon Transform together with the functional ANOVA statistical technique to carry out a proper diagnosis of the state of the motor by working directly with the curves obtained from the application of the transform. A case study is presented showing the good results obtained by applying the methodology in which the state of the rotor bars of an inverter-fed motor is diagnosed considering three failure states and operating at different load levels.

Do Different Models Induce Changes in Mortality Indicators? That Is a Key Question for Extending the Lee-Carter Model

The parametric model introduced by Lee and Carter in 1992 for modeling mortality rates in the USA was a seminal development in forecasting life expectancies and has been widely used since then. Different extensions of this model, using different hypotheses about the data, constraints on the parameters, and appropriate methods have led to improvements in the model’s fit to historical data and the model’s forecasting of the future. This paper’s main objective is to evaluate if differences between models are reflected in different mortality indicators’ forecasts. To this end, nine sets of indicator predictions were generated by crossing three models and three block-bootstrap samples with each of size fifty. Later the predicted mortality indicators were compared using functional ANOVA. Models and block bootstrap procedures are applied to Spanish mortality data. Results show model, block-bootstrap, and interaction effects for all mortality indicators. Although it was not our main objective, it is essential to point out that the sample effect should not be present since they must be realizations of the same population, and therefore the procedure should lead to samples that do not influence the results. Regarding significant model effect, it follows that, although the addition of terms improves the adjustment of probabilities and translates into an effect on mortality indicators, the model’s predictions must be checked in terms of their probabilities and the mortality indicators of interest.

Functional Modeling of Plant Growth Dynamics

ABSTRACTRecent advances in automated plant phenotyping have enabled the collection time series measurements from the same plants of a wide range of traits over different developmental time scales. The availability of time series phenotypic datasets has increased interest in statistical approaches for comparing patterns of change between different plant genotypes and different treatment conditions. Two widely used methods of modeling growth over time are point-wise analysis of variance (ANOVA) and parametric sigmoidal curve fitting. Point-wise ANOVA yields discontinuous growth curves, which do not reflect the true dynamics of growth patterns in plants. In contrast, fitting a parametric model to a time series of observations does capture the trend of growth, however these models require assumptions regarding the true pattern of plant growth. Depending on the species, treatment regime, and subset of the plant lifecycle sampled this assumptions will not always hold true. Here we introduce a different approach – functional ANOVA – which yields continuous growth curves without requiring assumptions regarding patterns of plant growth. We compare and validate this approach using data from an experiment measuring growth of two maize (Zea mays ssp. mays) genotypes under two water availability treatments over a 21-day period. Functional ANOVA enables a nonparametric estimation of the dynamics of changes in plant traits over time without assumptions regarding curve shape. In addition to estimating smooth curves of trait values over time, functional ANOVA also estimates the the derivatives of these curves – e.g. growth rates – simultaneously. Using two different subsampling strategies, we demonstrate that this functional ANOVA method enables the comparison of growth curves between plants phenotyped on non-overlapping days with little reduction in estimation accuracy. This means functional ANOVA based approaches can allow larger numbers of samples and biological replicates to be scored in a single experiment given fixed amounts of phenotyping infrastructure and personnel.