Damage detection in a benchmark structure using AR-ARX models and statistical pattern recognition

Structural health monitoring (SHM) is related to the ability of monitoring the state and deciding the level of damage or deterioration within aerospace, civil and mechanical systems. In this sense, this paper deals with the application of a two-step auto-regressive and auto-regressive with exogenous inputs (AR-ARX) model for linear prediction of damage diagnosis in structural systems. This damage detection algorithm is based on the. monitoring of residual error as damage-sensitive indexes, obtained through vibration response measurements. In complex structures there are. many positions under observation and a large amount of data to be handed, making difficult the visualization of the signals. This paper also investigates data compression by using principal component analysis. In order to establish a threshold value, a fuzzy c-means clustering is taken to quantify the damage-sensitive index in an unsupervised learning mode. Tests are made in a benchmark problem, as proposed by IASC-ASCE with different damage patterns. The diagnosis that was obtained showed high correlation with the actual integrity state of the structure. Copyright © 2007 by ABCM.

Statistical quark models for the nucleon structure functions

We consider some existing relativistic models for the nucleon structure functions, relying on statistical approaches instead of perturbative ones. These models are based on the Fermi-Dirac distribution for the confined quarks, where a density of energy levels is obtained from an effective confining potential. In this context, it is presented some results obtained with a recent statistical quark model for the sea-quark asymmetry in the nucleon. It is shown, within this model, that experimental available observables, such as the ratio and difference between proton and neutron structure functions, are quite well reproduced with just three parameters: two chemical potentials used to reproduce the valence up and down quark numbers in the nucleon, and a temperature that is being used to reproduce the Gottfried sum rule violation. © 2010 American Institute of Physics.

Advances on statistical/thermodynamical models for unpolarized structure functions

During the eights and nineties many statistical/thermodynamical models were proposed to describe the nucleons' structure functions and distribution of the quarks in the hadrons. Most of these models describe the compound quarks and gluons inside the nucleon as a Fermi / Bose gas respectively, confined in a MIT bag[1] with continuous energy levels. Another models considers discrete spectrum. Some interesting features of the nucleons are obtained by these models, like the sea asymmetries d̄/ū and d̄-ū. © 2013 American Institute of Physics.

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions.

Statistical models for experimental model membranes.

Biological membranes are constituted from lipid bilayers and proteins. Investigation of protein-membrane interaction, essential for biological function of cells, must rest upon solid knowledge of lipid bilayer behavior. Thus, extensive studies of an experimental model for membranes, lipid bilayers in water solution, have been undertaken in the last decades. These systems present structural, thermal and electrical properties which depend on temperature, ionic strength or concentration. In this talk, we shall discuss statistical models for lipid bilayers, as well as the relation between their properties and results for properties of lipid dispersions investigated by the laboratories supervised by Teresa Lamy (IF-USP) and Amando Ito (FFCL-USP).

Statistical Mechanics of Monomer-Dimer Models on Complete and Erdös-Rényi Graphs

Nella tesi sono trattate due famiglie di modelli meccanico statistici su vari grafi: i modelli di spin ferromagnetici (o di Ising) e i modelli di monomero-dimero. Il primo capitolo è dedicato principalmente allo studio del lavoro di Dembo e Montanari, in cui viene risolto il modello di Ising su grafi aleatori. Nel secondo capitolo vengono studiati i modelli di monomero-dimero, a partire dal lavoro di Heilemann e Lieb,con l'intento di dare contributi nuovi alla teoria. I principali temi trattati sono disuguaglianze di correlazione, soluzioni esatte su alcuni grafi ad albero e sul grafo completo, la concentrazione dell'energia libera intorno al proprio valor medio sul grafo aleatorio diluito di Erdös-Rényi.

Statistical analysis of the error associated with the simplification of the stratigraphy in geotechnical models

The uncertainties in the determination of the stratigraphic profile of natural soils is one of the main problems in geotechnics, in particular for landslide characterization and modeling. The study deals with a new approach in geotechnical modeling which relays on a stochastic generation of different soil layers distributions, following a boolean logic – the method has been thus called BoSG (Boolean Stochastic Generation). In this way, it is possible to randomize the presence of a specific material interdigitated in a uniform matrix. In the building of a geotechnical model it is generally common to discard some stratigraphic data in order to simplify the model itself, assuming that the significance of the results of the modeling procedure would not be affected. With the proposed technique it is possible to quantify the error associated with this simplification. Moreover, it could be used to determine the most significant zones where eventual further investigations and surveys would be more effective to build the geotechnical model of the slope. The commercial software FLAC was used for the 2D and 3D geotechnical model. The distribution of the materials was randomized through a specifically coded MatLab program that automatically generates text files, each of them representing a specific soil configuration. Besides, a routine was designed to automate the computation of FLAC with the different data files in order to maximize the sample number. The methodology is applied with reference to a simplified slope in 2D, a simplified slope in 3D and an actual landslide, namely the Mortisa mudslide (Cortina d’Ampezzo, BL, Italy). However, it could be extended to numerous different cases, especially for hydrogeological analysis and landslide stability assessment, in different geological and geomorphological contexts.

Statistical mechanics of polymer models: rigorous results and applications

Monomer-dimer models are amongst the models in statistical mechanics which found application in many areas of science, ranging from biology to social sciences. This model describes a many-body system in which monoatomic and diatomic particles subject to hard-core interactions get deposited on a graph. In our work we provide an extension of this model to higher-order particles. The aim of our work is threefold: first we study the thermodynamic properties of the newly introduced model. We solve analytically some regular cases and find that, differently from the original, our extension admits phase transitions. Then we tackle the inverse problem, both from an analytical and numerical perspective. Finally we propose an application to aggregation phenomena in virtual messaging services.

Statistical evaluation of alternative models of human evolution

An appropriate model of recent human evolution is not only important to understand our own history, but it is necessary to disentangle the effects of demography and selection on genome diversity. Although most genetic data support the view that our species originated recently in Africa, it is still unclear if it completely replaced former members of the Homo genus, or if some interbreeding occurred during its range expansion. Several scenarios of modern human evolution have been proposed on the basis of molecular and paleontological data, but their likelihood has never been statistically assessed. Using DNA data from 50 nuclear loci sequenced in African, Asian and Native American samples, we show here by extensive simulations that a simple African replacement model with exponential growth has a higher probability (78%) as compared with alternative multiregional evolution or assimilation scenarios. A Bayesian analysis of the data under this best supported model points to an origin of our species approximately 141 thousand years ago (Kya), an exit out-of-Africa approximately 51 Kya, and a recent colonization of the Americas approximately 10.5 Kya. We also find that the African replacement model explains not only the shallow ancestry of mtDNA or Y-chromosomes but also the occurrence of deep lineages at some autosomal loci, which has been formerly interpreted as a sign of interbreeding with Homo erectus.