Statistical Methodologies of Functional Data Analysis for Industrial Applications

This thesis stands as one of the first attempt to connect the statistical object oriented data analysis (OODA) methodologies with the industry field. Indeed, the aim of this thesis is to develop statistical methods to tackle industrial problems through the paradigm of the OODA. The new framework of Industry 4.0 requires factories that are equipped with sensor and advanced acquisition systems that acquire data with a high degree of complexity. OODA can be particularly suitable to deal with this increasing complexity as it considers each statistical unit as an atom or a data object assumed to be a point in a well-defined mathematical space. This idea allows one to deal with complex data structure by changing the resolution of the analysis. Indeed, from standard methods where the atom is represented by vector of numbers, the focus now is on methodologies where the objects of the analysis are whole complex objects. In particular, this thesis focuses on functional data analysis (FDA), a branch of OODA that considers as the atom of the analysis functions defined on compact domains. The cross-fertilization of FDA methods to industrial applications is developed into three parts in this dissertation. The first part presents methodologies developed to solve specific applicative problems. In particular, a first consistent portion of this part is focused on \textit{profile monitoring} methods applied to ship CO\textsubscript{2} emissions. A second portion deals with the problem of predicting the mechanical properties of an additively manufactured artifact given the particle size distribution of the powder used for its production. And, a third portion copes with the cluster analysis for the quality assessment of metal sheet spot welds in the automotive industry based on observations of dynamic resistance curve. Stimulated by these challenges, the second part of this dissertation turns towards a more methodological line that addresses the notion of \textit{interpretability} for functional data. In particular, two new interpretable estimators of the coefficient function of the function-on-function linear regression model are proposed, which are named S-LASSO and AdaSS, respectively. Moreover, a new method, referred to as SaS-Funclust, is presented for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of domain. In the last part, two ongoing researches on FDA methods for industrial application are presented. In particular, the first one regards the definition of a new robust nonparametric functional ANOVA method (Ro-FANOVA) to test differences among group functional means by being robust against the presence of outliers with an application to additive manufacturing. The second one sketches a new methodological framework for the real-time profile monitoring

Smooth Lasso Estimator for the Function-on-Function Linear Regression Model

A new estimator, named as S-LASSO, is proposed for the coefficient function of a functional linear regression model where values of the response function, at a given domain point, depends on the full trajectory of the covariate function. The S-LASSO estimator is shown to be able to increase the interpretability of the model, by better locating regions where the coefficient function is zero, and to smoothly estimate non-zero values of the coefficient function. The sparsity of the estimator is ensured by a functional LASSO penalty whereas the smoothness is provided by two roughness penalties. The resulting estimator is proved to be estimation and pointwise sign consistent. Via an extensive Monte Carlo simulation study, the estimation and predictive performance of the S-LASSO estimator are shown to be better than (or at worst comparable with) competing estimators already presented in the literature before. Practical advantages of the S-LASSO estimator are illustrated through the analysis of the well known \textit{Canadian weather} and \textit{Swedish mortality dat

Functional clustering methods for resistance spot welding process data in the automotive industry

Quality assessment of resistance spot welding (RSW) joints of metal sheets in the automotive industry is typically based on costly and lengthy off-line tests that are unfeasible on the full production, especially on large scale. However, the massive industrial digitalization triggered by the industry 4.0 framework makes available, for every produced joint, on-line RSW process parameters, such as, in particular, the so-called dynamic resistance curve (DRC), which is recognized as the full technological signature of the spot welds. Motivated by this context, the present paper means to show the potentiality and the practical applicability to clustering methods of the functional data approach that avoids the need for arbitrary and often controversial feature extraction to find out homogeneous groups of DRCs, which likely pertain to spot welds sharing common mechanical and metallurgical properties. We intend is to provide an essential hands-on overview of the most promising functional clustering methods, and to apply the latter to the DRCs collected from the RSW process at hand, even if they could go far beyond the specific application hereby investigated. The methods analyzed are demonstrated to possibly support practitioners along the identification of the mapping relationship between process parameters and the final quality of RSW joints as well as, more specifically, along the priority assignment for off-line testing of welded spots and the welding tool wear analysis. The analysis code, that has been developed through the software environment R, and the DRC data set are made openly available online at https://github.com/unina-sfere/funclustRSW

funcharts: Control charts for multivariate functional data in R

Modern statistical process monitoring (SPM) applications focus on profile monitoring, i.e., the monitoring of process quality characteristics that can be modeled as profiles, also known as functional data. Despite the large interest in the profile monitoring literature, there is still a lack of software to facilitate its practical application. This article introduces the funcharts R package that implements recent developments on the SPM of multivariate functional quality characteristics, possibly adjusted by the influence of additional variables, referred to as covariates. The package also implements the real-time version of all control charting procedures to monitor profiles partially observed up to an intermediate domain point. The package is illustrated both through its built-in data generator and a real-case study on the SPM of Ro-Pax ship CO2 emissions during navigation, which is based on the ShipNavigation data provided in the Supplementary Material

New applications of Diffusion Tensor Imaging techniques in the morphological evaluation of healthy and injured muscles

Purpose of this study was to evaluate a new approach with a DTI technique for the study of architecture of healthy and injured striated muscle tissue in cases of strain injury. DTI technique allows to highlight the magnitude and direction of the diffusion of water molecules in tissues and it becomes an indicator of the functional organization, allowing the identification of connections between the different structures showing any pathological changes. Currently this technique is routinely used in the study of CNS but recently it has also been proposed in the morphological evaluation of skeletal muscle. The application of this technique allows us to detect the presence of anomalies such as the alteration and displacement of the muscle bundles [1,2] and could play a crucial role not only in diagnosis but also in managing the rehabilitation of muscle injuries. The entire study was performed using a 3T Achieva Philips scanner; a SENSE 8 channels head coil, acquiring DTI sequence and T1 weighted 3D TFE. DTI was performed in 10 men with a strain injuries (grade I or II) in the lower limb muscles previously diagnosed by ultrasound examination. For each patient, we analyzed both healthy and injured limbs. The examination performed in the acute phase (within ten days from the injury) showed the presence of an area of oedema or haemorrhage of variable size. The perilesional area, if compared to healthy tissue, showed a marked alteration of the alignment of fibers. The examination carried out at a distance of 15-20 days showed a progressive reduction in the extent of haemorrhage that highlighted the structural alterations of the injured area, and noted a reduction in muscle fiber size of the affected muscle. The DTI provides detailed information on anatomical alterations in muscles strain and therefore may play a crucial role in diagnostic classification of the lesions. The evaluation of the scar may also be used to evaluate the healing has occurred not only from the clinical but also from anatomical perspective

Model Interpretability, Explainability and Trust for Manufacturing 4.0

Manufacturing is currently characterized by a widespread availability of multiple streams of big data (e.g., signals, images, video-images, 3-dimensional voxel and mesh-based reconstructions of volumes and surfaces). Manufacturing 4.0 refers to the paradigm shift involving appropriate use of all this rich data environment for decision making in prognostic, monitoring, optimization and control of the manufacturing processes. The paper discusses how the new advent of Artificial Intelligence for manufacturing data mining poses new challenges on model interpretability, explainability and trust. Starting from this general overview, the paper then focuses on examples of big data mining in Additive Manufacturing. A real case study focusing on spatter modeling for process optimization is discussed, where a solution based on robust functional analysis of variance is proposed