Sparse time-frequency data analysis : a multi-scale approach

In this work, we further extend the recently developed adaptive data analysis method, the Sparse Time-Frequency Representation (STFR) method. This method is based on the assumption that many physical signals inherently contain AM-FM representations. We propose a sparse optimization method to extract the AM-FM representations of such signals. We prove the convergence of the method for periodic signals under certain assumptions and provide practical algorithms specifically for the non-periodic STFR, which extends the method to tackle problems that former STFR methods could not handle, including stability to noise and non-periodic data analysis. This is a significant improvement since many adaptive and non-adaptive signal processing methods are not fully capable of handling non-periodic signals. Moreover, we propose a new STFR algorithm to study intrawave signals with strong frequency modulation and analyze the convergence of this new algorithm for periodic signals. Such signals have previously remained a bottleneck for all signal processing methods. Furthermore, we propose a modified version of STFR that facilitates the extraction of intrawaves that have overlaping frequency content. We show that the STFR methods can be applied to the realm of dynamical systems and cardiovascular signals. In particular, we present a simplified and modified version of the STFR algorithm that is potentially useful for the diagnosis of some cardiovascular diseases. We further explain some preliminary work on the nature of Intrinsic Mode Functions (IMFs) and how they can have different representations in different phase coordinates. This analysis shows that the uncertainty principle is fundamental to all oscillating signals.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deterioration—Part I : Modeling methodology and strategy

This paper aims to develop the methodology and strategy for concurrent finite element modeling of civil infrastructures at the different scale levels for the purposes of analyses of structural deteriorating. The modeling strategy and method were investigated to develop the concurrent multi-scale model of structural behavior (CMSM-of-SB) in which the global structural behavior and nonlinear damage features of local details in a large complicated structure could be concurrently analyzed in order to meet the needs of structural-state evaluation as well as structural deteriorating. In the proposed method, the “large-scale” modeling is adopted for the global structure with linear responses between stress and strain and the “small-scale” modeling is available for nonlinear damage analyses of the local welded details. A longitudinal truss in steel bridge decks was selected as a case to study how a CMSM-of-SB was developed. The reduced-scale specimen of the longitudinal truss was studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details, while the multi-scale models using constraint equations and substructuring were developed for numerical simulation. The comparison of dynamic and static response between the calculated results by different models indicated that the proposed multi-scale model was found to be the most efficient and accurate. The verification of the model with results from the tested truss under the specific loading showed that, responses at the material scale in the vicinity of local details as well as structural global behaviors could be obtained and fit well with the measured results. The proposed concurrent multi-scale modeling strategy and implementation procedures were applied to Runyang cable-stayed bridge (RYCB) and the CMSM-of-SB of the bridge deck system was accordingly constructed as a practical application.

Concurrent multi-scale modeling of civil infrastructures for analyses on structural deteriorating—Part II : Model updating and verification

This paper is a continuation of the paper titled “Concurrent multi-scale modeling of civil infrastructure for analyses on structural deteriorating—Part I: Modeling methodology and strategy” with the emphasis on model updating and verification for the developed concurrent multi-scale model. The sensitivity-based parameter updating method was applied and some important issues such as selection of reference data and model parameters, and model updating procedures on the multi-scale model were investigated based on the sensitivity analysis of the selected model parameters. The experimental modal data as well as static response in terms of component nominal stresses and hot-spot stresses at the concerned locations were used for dynamic response- and static response-oriented model updating, respectively. The updated multi-scale model was further verified to act as the baseline model which is assumed to be finite-element model closest to the real situation of the structure available for the subsequent arbitrary numerical simulation. The comparison of dynamic and static responses between the calculated results by the final model and measured data indicated the updating and verification methods applied in this paper are reliable and accurate for the multi-scale model of frame-like structure. The general procedures of multi-scale model updating and verification were finally proposed for nonlinear physical-based modeling of large civil infrastructure, and it was applied to the model verification of a long-span bridge as an actual engineering practice of the proposed procedures.

Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Multi-scale numerical simulations of thermal expansion properties of CNT-reinforced nanocomposites

In this work, the thermal expansion properties of carbon nanotube (CNT)-reinforced nanocomposites with CNT content ranging from 1 to 15 wt% were evaluated using a multi-scale numerical approach, in which the effects of two parameters, i.e., temperature and CNT content, were investigated extensively. For all CNT contents, the obtained results clearly revealed that within a wide low-temperature range (30°C ~ 62°C), thermal contraction is observed, while thermal expansion occurs in a high-temperature range (62°C ~ 120°C). It was found that at any specified CNT content, the thermal expansion properties vary with temperature - as temperature increases, the thermal expansion rate increases linearly. However, at a specified temperature, the absolute value of the thermal expansion rate decreases nonlinearly as the CNT content increases. Moreover, the results provided by the present multi-scale numerical model were in good agreement with those obtained from the corresponding theoretical analyses and experimental measurements in this work, which indicates that this multi-scale numerical approach provides a powerful tool to evaluate the thermal expansion properties of any type of CNT/polymer nanocomposites and therefore promotes the understanding on the thermal behaviors of CNT/polymer nanocomposites for their applications in temperature sensors, nanoelectronics devices, etc.

Fault symptoms of rolling element bearings under variable operating conditions - a multi domain analysis

Diagnostics of rolling element bearings have been traditionally developed for constant operating conditions, and sophisticated techniques, like Spectral Kurtosis or Envelope Analysis, have proven their effectiveness by means of experimental tests, mainly conducted in small-scale laboratory test-rigs. Algorithms have been developed for the digital signal processing of data collected at constant speed and bearing load, with a few exceptions, allowing only small fluctuations of these quantities. Owing to the spreading of condition based maintenance in many industrial fields, in the last years a need for more flexible algorithms emerged, asking for compatibility with highly variable operating conditions, such as acceleration/deceleration transients. This paper analyzes the problems related with significant speed and load variability, discussing in detail the effect that they have on bearing damage symptoms, and propose solutions to adapt existing algorithms to cope with this new challenge. In particular, the paper will i) discuss the implication of variable speed on the applicability of diagnostic techniques, ii) address quantitatively the effects of load on the characteristic frequencies of damaged bearings and iii) finally present a new approach for bearing diagnostics in variable conditions, based on envelope analysis. The research is based on experimental data obtained by using artificially damaged bearings installed on a full scale test-rig, equipped with actual train traction system and reproducing the operation on a real track, including all the environmental noise, owing to track irregularity and electrical disturbances of such a harsh application.

Multi-scale bio-inspired place recognition

This paper presents a novel place recognition algorithm inspired by the recent discovery of overlapping and multi-scale spatial maps in the rodent brain. We mimic this hierarchical framework by training arrays of Support Vector Machines to recognize places at multiple spatial scales. Place match hypotheses are then cross-validated across all spatial scales, a process which combines the spatial specificity of the finest spatial map with the consensus provided by broader mapping scales. Experiments on three real-world datasets including a large robotics benchmark demonstrate that mapping over multiple scales uniformly improves place recognition performance over a single scale approach without sacrificing localization accuracy. We present analysis that illustrates how matching over multiple scales leads to better place recognition performance and discuss several promising areas for future investigation.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Large-scale analysis of soccer matches using spatiotemporal tracking data

Although the collection of player and ball tracking data is fast becoming the norm in professional sports, large-scale mining of such spatiotemporal data has yet to surface. In this paper, given an entire season's worth of player and ball tracking data from a professional soccer league (approx 400,000,000 data points), we present a method which can conduct both individual player and team analysis. Due to the dynamic, continuous and multi-player nature of team sports like soccer, a major issue is aligning player positions over time. We present a "role-based" representation that dynamically updates each player's relative role at each frame and demonstrate how this captures the short-term context to enable both individual player and team analysis. We discover role directly from data by utilizing a minimum entropy data partitioning method and show how this can be used to accurately detect and visualize formations, as well as analyze individual player behavior.

A cyclostationary multi-domain analysis of fluid instability in Kaplan turbines

Hydraulic instabilities represent a critical problem for Francis and Kaplan turbines, reducing their useful life due to increase of fatigue on the components and cavitation phenomena. Whereas an exhaustive list of publications on computational fluid-dynamic models of hydraulic instability is available, the possibility of applying diagnostic techniques based on vibration measurements has not been investigated sufficiently, also because the appropriate sensors seldom equip hydro turbine units. The aim of this study is to fill this knowledge gap and to exploit fully, for this purpose, the potentiality of combining cyclostationary analysis tools, able to describe complex dynamics such as those of fluid-structure interactions, with order tracking procedures, allowing domain transformations and consequently the separation of synchronous and non-synchronous components. This paper will focus on experimental data obtained on a full-scale Kaplan turbine unit, operating in a real power plant, tackling the issues of adapting such diagnostic tools for the analysis of hydraulic instabilities and proposing techniques and methodologies for a highly automated condition monitoring system. © 2015 Elsevier Ltd.

Multi-scale interactions and predictability of the Indian summer monsoon

Following the seminal work of Charney and Shukla (198 1), the tropical climate is recognised to be more predictable than extra tropical climate as it is largely forced by 'external' slowly varying forcing and less sensitive to initial conditions. However, the Indian summer monsoon is an exception within the tropics where 'internal' low frequency (LF) oscillations seem to make significant contribution to its interannual variability (IAV) and makes it sensitive to initial conditions. Quantitative estimate of contribution of 'internal' dynamics to IAV of Indian monsoon is made using long experiments with an atmospheric general circulation model (AGCM) and through analysis of long daily observations. Both AGCM experiments and observations indicate that more than 50% of IAV of the monsoon is contributed by 'internal' dynamics making the predictable signal (external component) burried in unpredictable noise (internal component) of comparable amplitude. Better understanding of the nature of the 'internal' LF variability is crucial for any improvement in predicition of seasonal mean monsoon. Nature of 'internal' LF variability of the monsoon and mechanism responsible for it are investigated and shown that vigorous monsoon intraseasonal oscillations (ISO's) with time scale between 10-70 days are primarily responsible for generating the 'internal' IAV. The monsoon ISO's do this through scale interactions with synoptic disturbances (1-7 day time scale) on one hand and the annual cycle on the other. The spatial structure of the monsoon ISO's is similar to that of the seasonal mean. It is shown that frequency of occurance of strong (weak) phases of the ISO is different in different seasons giving rise to stronger (weaker) than normal monsoon. Change in the large scale circulation during strong (weak) phases of the ISO make it favourable (inhibiting) for cyclogenesis and gives rise to space time clustering of synoptic activity. This process leads to enhanced (reduced) rainfall in seasons of higher frequency of occurence strong (weak) phases of monsoon ISO.

A multi-level multi-scale approach to study essential genes in Mycobacterium tuberculosis

Background: The set of indispensable genes that are required by an organism to grow and sustain life are termed as essential genes. There is a strong interest in identification of the set of essential genes, particularly in pathogens, not only for a better understanding of the pathogen biology, but also for identifying drug targets and the minimal gene set for the organism. Essentiality is inherently a systems property and requires consideration of the system as a whole for their identification. The available experimental approaches capture some aspects but each method comes with its own limitations. Moreover, they do not explain the basis for essentiality in most cases. A powerful prediction method to recognize this gene pool including rationalization of the known essential genes in a given organism would be very useful. Here we describe a multi-level multi-scale approach to identify the essential gene pool in a deadly pathogen, Mycobacterium tuberculosis. Results: The multi-level workflow analyses the bacterial cell by studying (a) genome-wide gene expression profiles to identify the set of genes which show consistent and significant levels of expression in multiple samples of the same condition, (b) indispensability for growth by using gene expression integrated flux balance analysis of a genome-scale metabolic model, (c) importance for maintaining the integrity and flow in a protein-protein interaction network and (d) evolutionary conservation in a set of genomes of the same ecological niche. In the gene pool identified, the functional basis for essentiality has been addressed by studying residue level conservation and the sub-structure at the ligand binding pockets, from which essential amino acid residues in that pocket have also been identified. 283 genes were identified as essential genes with high-confidence. An agreement of about 73.5% is observed with that obtained from the experimental transposon mutagenesis technique. A large proportion of the identified genes belong to the class of intermediary metabolism and respiration. Conclusions: The multi-scale, multi-level approach described can be generally applied to other pathogens as well. The essential gene pool identified form a basis for designing experiments to probe their finer functional roles and also serve as a ready shortlist for identifying drug targets.

A multi-scale approach to shaping carbon nanotube structures for hollow microneedles

The concept of a carbon nanotube microneedle array is explored in this thesis from multiple perspectives including microneedle fabrication, physical aspects of transdermal delivery, and in vivo transdermal drug delivery experiments. Starting with standard techniques in carbon nanotube (CNT) fabrication, including catalyst patterning and chemical vapor deposition, vertically-aligned carbon nanotubes are utilized as a scaffold to define the shape of the hollow microneedle. Passive, scalable techniques based on capillary action and unique photolithographic methods are utilized to produce a CNT-polymer composite microneedle. Specific examples of CNT-polyimide and CNT-epoxy microneedles are investigated. Further analysis of the transport properties of polymer resins reveals general requirements for applying arbitrary polymers to the fabrication process.

The bottom-up fabrication approach embodied by vertically-aligned carbon nanotubes allows for more direct construction of complex high-aspect ratio features than standard top-down fabrication approaches, making microneedles an ideal application for CNTs. However, current vertically-aligned CNT fabrication techniques only allow for the production of extruded geometries with a constant cross-sectional area, such as cylinders. To rectify this limitation, isotropic oxygen etching is introduced as a novel fabrication technique to create true 3D CNT geometry. Oxygen etching is utilized to create a conical geometry from a cylindrical CNT structure as well as create complex shape transformations in other CNT geometries.

CNT-polymer composite microneedles are anchored onto a common polymer base less than 50 µm thick, which allows for the microneedles to be incorporated into multiple drug delivery platforms, including modified hypodermic syringes and silicone skin patches. Cylindrical microneedles are fabricated with 100 µm outer diameter and height of 200-250 µm with a central cavity, or lumen, diameter of 30 µm to facilitate liquid drug flow. In vitro delivery experiments in swine skin demonstrate the ability of the microneedles to successfully penetrate the skin and deliver aqueous solutions.

An in vivo study was performed to assess the ability of the CNT-polymer microneedles to deliver drugs transdermally. CNT-polymer microneedles are attached to a hand actuated silicone skin patch that holds a liquid reservoir of drugs. Fentanyl, a potent analgesic, was administered to New Zealand White Rabbits through 3 routes of delivery: topical patch, CNT-polymer microneedles, and subcutaneous hypodermic injection. Results demonstrate that the CNT-polymer microneedles have a similar onset of action as the topical patch. CNT-polymer microneedles were also vetted as a painless delivery approach compared to hypodermic injection. Comparative analysis with contemporary microneedle designs demonstrates that the delivery achieved through CNT-polymer microneedles is akin to current hollow microneedle architectures. The inherent advantage of applying a bottom-up fabrication approach alongside similar delivery performance to contemporary microneedle designs demonstrates that the CNT-polymer composite microneedle is a viable architecture in the emerging field of painless transdermal delivery.

From molecules to organs : Microscopy and multi-scale nature of development

Morphogenesis is a phenomenon of intricate balance and dynamic interplay between processes occurring at a wide range of scales (spatial, temporal and energetic). During development, a variety of physical mechanisms are employed by tissues to simultaneously pattern, move, and differentiate based on information exchange between constituent cells, perhaps more than at any other time during an organism's life. To fully understand such events, a combined theoretical and experimental framework is required to assist in deciphering the correlations at both structural and functional levels at scales that include the intracellular and tissue levels as well as organs and organ systems. Microscopy, especially diffraction-limited light microscopy, has emerged as a central tool to capture the spatio-temporal context of life processes. Imaging has the unique advantage of watching biological events as they unfold over time at single-cell resolution in the intact animal. In this work I present a range of problems in morphogenesis, each unique in its requirements for novel quantitative imaging both in terms of the technique and analysis. Understanding the molecular basis for a developmental process involves investigating how genes and their products- mRNA and proteins-function in the context of a cell. Structural information holds the key to insights into mechanisms and imaging fixed specimens paves the first step towards deciphering gene function. The work presented in this thesis starts with the demonstration that the fluorescent signal from the challenging environment of whole-mount imaging, obtained by in situ hybridization chain reaction (HCR), scales linearly with the number of copies of target mRNA to provide quantitative sub-cellular mapping of mRNA expression within intact vertebrate embryos. The work then progresses to address aspects of imaging live embryonic development in a number of species. While processes such as avian cartilage growth require high spatial resolution and lower time resolution, dynamic events during zebrafish somitogenesis require higher time resolution to capture the protein localization as the somites mature. The requirements on imaging are even more stringent in case of the embryonic zebrafish heart that beats with a frequency of ~ 2-2.5 Hz, thereby requiring very fast imaging techniques based on two-photon light sheet microscope to capture its dynamics. In each of the hitherto-mentioned cases, ranging from the level of molecules to organs, an imaging framework is developed, both in terms of technique and analysis to allow quantitative assessment of the process in vivo. Overall the work presented in this thesis combines new quantitative tools with novel microscopy for the precise understanding of processes in embryonic development.