Functional data analysis techniques for the study of structural parameters in polymer composites

2016 ◽  
Vol 49 (2) ◽  
pp. 594-605 ◽  
Author(s):  
Thejas Gopal Krishne Urs ◽  
Karthik Bharath ◽  
Sangappa Yallappa ◽  
Somashekar Rudrappa
Keyword(s):  
Data Analysis ◽  
Polymer Composites ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Dopant Concentration ◽  
Structural Parameters ◽  
Principal Component ◽  
Global Features ◽  
Casting Technique ◽  
Microstructural Parameters

This article presents a novel method, based on functional data analysis, to analyse measurements of structural parameters of polymers and polymer composites. The method is demonstrated using newly developed biodegradable conducting polymer composites prepared via a solution casting technique. The measurements of the macro- and microstructural parameters that are used in the characterization of these films are obtained using X-ray diffraction, an impedance analyser and a UV–vis spectrometer. A functional representation of the measured values of the parameters at different dopant concentrations is adopted by viewing them as realizations of a continuous-time stochastic process observed with measurement error. This allows one to estimate the mean functional relationship between a parameter and the dopant concentration. A functional version of principal component analysis is performed, by which the major modes of variation are discovered and the correlations of parameter values at different concentrations are estimated. This provides insight into local and global features of the relationship between these parameters. Some comments are made on how the parameters vary as a function of dopant concentration.

scholarly journals Functional Data Analysis in Sport Science: Example of Swimmers’ Progression Curves Clustering

2018 ◽  
Vol 8 (10) ◽  
pp. 1766 ◽  
Author(s):  
Arthur Leroy ◽  
Andy MARC ◽  
Olivier DUPAS ◽  
Jean Lionel REY ◽  
Servane Gey
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Clustering Algorithms ◽  
Principal Component ◽  
Continuous Functions ◽  
Functional Principal Component Analysis ◽  
Data Set ◽  
Functional Clustering ◽  
Sport Science

Many data collected in sport science come from time dependent phenomenon. This article focuses on Functional Data Analysis (FDA), which study longitudinal data by modelling them as continuous functions. After a brief review of several FDA methods, some useful practical tools such as Functional Principal Component Analysis (FPCA) or functional clustering algorithms are presented and compared on simulated data. Finally, the problem of the detection of promising young swimmers is addressed through a curve clustering procedure on a real data set of performance progression curves. This study reveals that the fastest improvement of young swimmers generally appears before 16 years old. Moreover, several patterns of improvement are identified and the functional clustering procedure provides a useful detection tool.

The Oxford Handbook of Functional Data Analysis

2018 ◽  
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Principal Component ◽  
Regression Modeling ◽  
Functional Principal Component Analysis ◽  
Functional Regression ◽  
Vector Integration ◽  
Wide Range

This handbook presents the state-of-the-art of the statistics dealing with functional data analysis. With contributions from international experts in the field, it discusses a wide range of the most important statistical topics (classification, inference, factor-based analysis, regression modeling, resampling methods, time series, random processes) while also taking into account practical, methodological, and theoretical aspects of the problems. The book is organised into three sections. Part I deals with regression modeling and covers various statistical methods for functional data such as linear/nonparametric functional regression, varying coefficient models, and linear/nonparametric functional processes (i.e. functional time series). Part II considers related benchmark methods/tools for functional data analysis, including curve registration methods for preprocessing functional data, functional principal component analysis, and resampling/bootstrap methods. Finally, Part III examines some of the fundamental mathematical aspects of the infinite-dimensional setting, with a focus on the stochastic background and operatorial statistics: vector-valued function integration, spectral and random measures linked to stationary processes, operator geometry, vector integration and stochastic integration in Banach spaces, and operatorial statistics linked to quantum statistics.

scholarly journals A functional data analysis approach for the monitoring of ship CO2 emissions

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Christian Capezza ◽  
Fabio Centofanti ◽  
Antonio Lepore ◽  
Biagio Palumbo
Keyword(s):  
Data Analysis ◽  
Co2 Emissions ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Control Charts ◽  
Principal Component ◽  
Functional Principal Component Analysis ◽  
Unknown Parameters ◽  
Statistical Process ◽  
Data Set

Abstract Sensing networks provide nowadays massive amounts of data that in many applications provide information about curves, surfaces and vary over a continuum, usually time, and thus, can be suitably modelled as functional data. Their proper modelling by means of functional data analysis approaches naturally addresses new challenges also arising in the statistical process monitoring (SPM). Motivated by an industrial application, the objective of the present paper is to provide the reader with a very transparent set of steps for the SPM of functional data in real-world case studies: i) identifying a finite dimensional model for the functional data, based on functional principal component analysis; ii) estimating the unknown parameters; iii) designing control charts on the estimated parameters, in a nonparametric framework. The proposed SPM procedure is applied to a real-case study from the maritime field in monitoring CO2 emissions from real navigation data of a roll-on/roll-off passenger cruise ship, i.e., a ship designed to carry both passengers and wheeled vehicles that are driven on and off the ship on their own wheels. We show different scenarios highlighting clear and interpretable indications that can be extracted from the data set and support the detection of anomalous voyages.

scholarly journals Functional data analysis in forecasting Serbian fertility

Stanovnistvo ◽  
2011 ◽  
Vol 49 (2) ◽  
pp. 73-89 ◽  
Author(s):  
Vladimir Nikitovic
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Principal Component ◽  
Data Series ◽  
Fertility Rates ◽  
Demographic Rates ◽  
Functional Time Series ◽  
Functional Product ◽  
Sources Of Variation

A new approach, combining functional data analysis and principal components decomposition in order to forecasting demographic rates, introduced recently by Hyndman and his associates, is tested on official data series of Serbian age-specific fertility rates available for period 1950-2009. The original concept of the method with its extensions and improvements is applied to region-specific data for the country (Central Serbia and Vojvodina). One of the most important benefits of the method reflected in confirmation that is essentially to model and forecast more than one principal component in order to adequately address sources of variation in fertility. Similarly, modelling and forecasting fertility rates with regards to age and not total fertility rates shows how important it is for the recognized tendency of postponing childbearing in Serbia to be included in coefficients of functional time series. Besides, the method is based completely on evaluation of historical data, without subjective views of forecasters having to be taken into account. Coherent functional product ratio forecasts of two regions proved to be highly convergent on the long-term not allowing for outliers to contaminate the forecast.

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