Identification of Dynamic Outliers

Several methods for performing the identification of outliers are described when dealing with functional data. The methods studied include prediction intervals for detection of dynamic functional outliers as well as related methods from the functional data literature. A comparison of methods is performed using metrics for dynamic outlier identification. Simulations and applications to environmental studies illustrate the applicability of the methods. Results obtained from simulation and application to real dataset suggest that Dynamic Function-on-Function Regression is a preferable method for detecting dynamic outliers. This method can detect outliers at a very high identification rate. Identification rate of dynamic outliers increases when a large number of curves and large size of outliers is observed

Machine Learning Techniques for Stellar Light Curve Classification

We apply machine learning techniques in an attempt to predict and classify stellar properties from noisy and sparse time series data. We preprocessed over 94 GB of Kepler light curves from MAST to classify according to ten distinct physical properties using both representation learning and feature engineering approaches. Studies using machine learning in the field have been primarily done on simulated data, making our study one of the first to use real light curve data for machine learning approaches. We tuned our data using previous work with simulated data as a template and achieved mixed results between the two approaches. Representation learning using a Long Short-Term Memory (LSTM) Recurrent Neural Network (RNN) produced no successful predictions, but our work with feature engineering was successful for both classification and regression. In particular, we were able to achieve values for stellar density, stellar radius, and effective temperature with low error (~ 2 - 4%) and good accuracy (~ 75%) for classifying the number of transits for a given star. The results show promise for improvement for both approaches upon using larger datasets with a larger minority class. This work has the potential to provide a foundation for future tools and techniques to aid in the analysis of astrophysical data.Comment: Accepted to The Astronomical Journa

Comparison of parametric, orthogonal, and spline functions to model individual lactation curves for milk yield in Canadian Holsteins

Test day records for milk yield of 57,390 first lactation Canadian Holsteins were analyzed with a linear model that included the fixed effects of herd-test date and days in milk (DIM) interval nested within age and calving season. Residuals from this model were analyzed as a new variable and fitted with a five parameter model, fourth-order Legendre polynomials, with linear, quadratic and cubic spline models with three knots. The fit of the models was rather poor, with about 30%-40% of the curves showing an adjusted R-square lower than 0.20 across all models. Results underline a great difficulty in modelling individual deviations around the mean curve for milk yield. However, the Ali and Schaeffer (5 parameter) model and the fourth-order Legendre polynomials were able to detect two basic shapes of individual deviations among the mean curve. Quadratic and, especially, cubic spline functions had better fitting performances but a poor predictive ability due to their great flexibility that results in an abrupt change of the estimated curve when data are missing. Parametric and orthogonal polynomials seem to be robust and affordable under this standpoint

A statistical treatment of the loss of stiffness during cyclic loading for short fiber reinforced injection molded composites

Injection molded short fiber reinforced composites (SFRC) have different local fiber orientation distribution (FOD) at every point. SN curves of short fiber reinforced composites are known to depend on the fiber orientation distribution. Such materials also suffer from continuous loss of stiffness during cyclic loading. It is not known whether the loss of stiffness is different for SFRC with different FOD. A statistical analysis of the loss of stiffness curves is presented in this paper. Tension-tension fatigue experiments are performed and loss of stiffness is collected for every data point in the SN curve. A systematic method for comparing the loss of stiffness is developed. It is concluded that the difference in loss of stiffness curves for coupons of SFRC with different FOD is not statistically significant. (C) 2016 Elsevier Ltd. All rights reserved

Quantifying Mechanical Properties of Automotive Steels with Deep Learning Based Computer Vision Algorithms

This paper demonstrates that the instrumented indentation test (IIT), together with a trained artificial neural network (ANN), has the capability to characterize the mechanical properties of the local parts of a welded steel structure such as a weld nugget or heat affected zone. Aside from force-indentation depth curves generated from the IIT, the profile of the indented surface deformed after the indentation test also has a strong correlation with the materials’ plastic behavior. The profile of the indented surface was used as the training dataset to design an ANN to determine the material parameters of the welded zones. The deformation of the indented surface in three dimensions shown in images were analyzed with the computer vision algorithms and the obtained data were employed to train the ANN for the characterization of the mechanical properties. Moreover, this method was applied to the images taken with a simple light microscope from the surface of a specimen. Therefore, it is possible to quantify the mechanical properties of the automotive steels with the four independent methods: (1) force-indentation depth curve; (2) profile of the indented surface; (3) analyzing of the 3D-measurement image; and (4) evaluation of the images taken by a simple light microscope. The results show that there is a very good agreement between the material parameters obtained from the trained ANN and the experimental uniaxial tensile test. The results present that the mechanical properties of an unknown steel can be determined by only analyzing the images taken from its surface after pushing a simple indenter into its surface

A Parametric Framework for the Comparison of Methods of Very Robust Regression

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.Comment: Published in at http://dx.doi.org/10.1214/13-STS437 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Mathematical description of lactation curves in dairy cattle

This review gives an overview of the mathematical modelling of lactation curves in dairy cattle. Over the last ninety years, the development of this field of study has followed the main requirements of the dairy cattle industry. Non-linear parametric functions have represented the preferred tools for modelling average curves of homogeneous groups of animals, with the main aim of predicting yields for management purposes. The increased availability of records per individual lactations and the genetic evaluation based on test day records has shifted the interest of modellers towards more flexible and general linear functions, as polynomials or splines. Thus the main interest of modelling is no longer the reconstruction of the general pattern of the phenomenon but the fitting of individual deviations from an average curve. Other specific approaches based on the modelling of the correlation structure of test day records within lactation, such as mixed linear models or principal component analysis, have been used to test the statistical significance of fixed effects in dairy experiments or to create new variables expressing main lactation curve traits. The adequacy of a model is not an absolute requisite, because it has to be assessed according to the specific purpose it is used for. Occurrence of extended lactations and of new productive and functional traits to be described and the increase of records coming from automatic milking systems likely will represent some of the future challenges for the mathematical modelling of the lactation curve in dairy cattle