scholarly journals A New Mathematical Model for Flank Wear Prediction Using Functional Data Analysis Methodology

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sonja Jozić ◽  
Branimir Lela ◽  
Dražen Bajić
Keyword(s):  
Mathematical Model ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Flank Wear ◽  
End Milling ◽  
Cutting Parameters ◽  
Machining Process ◽  
Wear Prediction ◽  
Analysis Methodology

This paper presents a new approach improving the reliability of flank wear prediction during the end milling process. In the present work, prediction of flank wear has been achieved by using cutting parameters and force signals as the sensitive carriers of information about the machining process. A series of experiments were conducted to establish the relationship between flank wear and cutting force components as well as the cutting parameters such as cutting speed, feed per tooth, and radial depth of cut. In order to be able to predict flank wear a new linear regression mathematical model has been developed by utilizing functional data analysis methodology. Regression coefficients of the model are in the form of time dependent functions that have been determined through the use of functional data analysis methodology. The mathematical model has been developed by means of applied cutting parameters and measured cutting forces components during the end milling of workpiece made of 42CrMo4 steel. The efficiency and flexibility of the developed model have been verified by comparing it with the separate experimental data set.

scholarly journals Basis Expansions for Functional Snippets

Biometrika ◽  
2020 ◽  
Author(s):  
Zhenhua Lin ◽  
Jane-Ling Wang ◽  
Qixian Zhong
Keyword(s):  
Data Analysis ◽  
Convergence Rate ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Covariance Function ◽  
Covariance Estimation ◽  
Simulation Studies ◽  
Finite Sample ◽  
Covariance Functions ◽  
The Mean

Summary Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed estimator enjoys a convergence rate that is adaptive to the smoothness of the underlying covariance function, and has superior finite-sample performance in simulation studies.

scholarly journals Novel Analytic Approaches to Investigate Minute-Level Actigraphy and Associations With Physical Function

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 194-195
Author(s):  
Kaiyuan Hua ◽  
Sheng Luo ◽  
Katherine Hall ◽  
Miriam Morey ◽  
Harvey Cohen
Keyword(s):  
Physical Activity ◽  
Data Analysis ◽  
Physical Function ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Gait Speed ◽  
Community Dwelling ◽  
Accelerometer Data ◽  
Single Leg Stance ◽  
Minute Walk

Abstract Background. Functional decline in conjunction with low levels of physical activity has implications for health risks in older adults. Previous studies have examined the associations between accelerometry-derived activity and physical function, but most of these studies reduced these data into average means of total daily physical activity (e.g., daily step counts). A new method of analysis “functional data analysis” provides more in-depth capability using minute-level accelerometer data. Methods. A secondary analysis of community-dwelling adults ages 30 to 90+ residing in southwest region of North Carolina from the Physical Performance across the Lifespan (PALS) study. PALS assessments were completed in-person at baseline and one-week of accelerometry. Final analysis includes 669 observations at baseline with minute-level accelerometer data from 7:00 to 23:00, after removing non-wear time. A novel scalar-on-function regression analysis was used to explore the associations between baseline physical activity features (minute-by-minute vector magnitude generated from accelerometer) and baseline physical function (gait speed, single leg stance, chair stands, and 6-minute walk test) with control for baseline age, sex, race and body mass index. Results. The functional regressions were significant for specific times of day indicating increased physical activity associated with increased physical function around 8:00, 9:30 and 15:30-17:00 for rapid gait speed; 9:00-10:30 and 15:00-16:30 for normal gait speed; 9:00-10:30 for single leg stance; 9:30-11:30 and 15:00-18:00 for chair stands; 9:00-11:30 and 15:00-18:30 for 6-minute walk. Conclusion. This method of functional data analysis provides news insights into the relationship between minute-by-minute daily activity and health.

A kNN procedure in semiparametric functional data analysis

2021 ◽  
pp. 109028
Author(s):  
Silvia Novo ◽  
Germán Aneiros ◽  
Philippe Vieu
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data

scholarly journals Wildfires Vegetation Recovery through Satellite Remote Sensing and Functional Data Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1305
Author(s):  
Feliu Serra-Burriel ◽  
Pedro Delicado ◽  
Fernando M. Cucchietti
Keyword(s):  
Remote Sensing ◽  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Vegetation Index ◽  
Vegetation Recovery ◽  
Functional Responses ◽  
Elapsed Time ◽  
Synthetic Controls ◽  
Available Information

In recent years, wildfires have caused havoc across the world, which are especially aggravated in certain regions due to climate change. Remote sensing has become a powerful tool for monitoring fires, as well as for measuring their effects on vegetation over the following years. We aim to explain the dynamics of wildfires’ effects on a vegetation index (previously estimated by causal inference through synthetic controls) from pre-wildfire available information (mainly proceeding from satellites). For this purpose, we use regression models from Functional Data Analysis, where wildfire effects are considered functional responses, depending on elapsed time after each wildfire, while pre-wildfire information acts as scalar covariates. Our main findings show that vegetation recovery after wildfires is a slow process, affected by many pre-wildfire conditions, among which the richness and diversity of vegetation is one of the best predictors for the recovery.

Modeling relationships for field strain data under thermal effects using functional data analysis

Measurement ◽  
2021 ◽  
Vol 177 ◽  
pp. 109279
Author(s):  
Huachen Jiang ◽  
Chunfeng Wan ◽  
Kang Yang ◽  
Youliang Ding ◽  
Songtao Xue
Keyword(s):  
Data Analysis ◽  
Functional Data Analysis ◽  
Functional Data ◽  
Thermal Effects ◽  
Field Strain ◽  
Strain Data
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