Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Uncertainty assessment approach for composite structures based on global sensitivity indices

The problem of uncertainty propagation in composite laminate structures is studied. An approach based on the optimal design of composite structures to achieve a target reliability level is proposed. Using the Uniform Design Method (UDM), a set of design points is generated over a design domain centred at mean values of random variables, aimed at studying the space variability. The most critical Tsai number, the structural reliability index and the sensitivities are obtained for each UDM design point, using the maximum load obtained from optimal design search. Using the UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on supervised evolutionary learning. Finally, using the developed ANN a Monte Carlo simulation procedure is implemented and the variability of the structural response based on global sensitivity analysis (GSA) is studied. The GSA is based on the first order Sobol indices and relative sensitivities. An appropriate GSA algorithm aiming to obtain Sobol indices is proposed. The most important sources of uncertainty are identified.

Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

Uncertainty analysis based on sensitivity applied to angle-ply composite structures

This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.

From local to global importance measures of uncertainty propagation in composite structures

The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Operational modal monitoring of ancient structures using wireless technology

Operational Modal Analysis is currently applied in structural dynamic monitoring studies using conventional wired based sensors and data acquisition platforms. This approach, however, becomes inadequate in cases where the tests are performed in ancient structures with esthetic concerns or in others, where the use of wires greatly impacts the monitoring system cost and creates difficulties in the maintenance and deployment of data acquisition platforms. In these cases, the use of sensor platforms based on wireless and MEMS would clearly benefit these applications. This work presents a first attempt to apply this wireless technology to the structural monitoring of historical masonry constructions in the context of operational modal analysis. Commercial WSN platforms were used to study one laboratory specimen and one of the structural elements of a XV century building in Portugal. Results showed that in comparison to the conventional wired sensors, wireless platforms have poor performance in respect to the acceleration time series recorded and the detection of modal shapes. However, for frequency detection issues, reliable results were obtained, especially when random excitation was used as noise source.

Effect of plug-filling, Testing velocity and temperature on the tensile strength of strap repairs on aluminium structures

In this work, an experimental study was performed on the influence of plug-filling, loading rate and temperature on the tensile strength of single-strap (SS) and double-strap (DS) repairs on aluminium structures. Whilst the main purpose of this work was to evaluate the feasibility of plug-filling for the strength improvement of these repairs, a parallel study was carried out to assess the sensitivity of the adhesive to external features that can affect the repairs performance, such as the rate of loading and environmental temperature. The experimental programme included repairs with different values of overlap length (L O = 10, 20 and 30 mm), and with and without plug-filling, whose results were interpreted in light of experimental evidence of the fracture modes and typical stress distributions for bonded repairs. The influence of the testing speed on the repairs strength was also addressed (considering 0.5, 5 and 25 mm/min). Accounting for the temperature effects, tests were carried out at room temperature (≈23°C), 50 and 80°C. This permitted a comparative evaluation of the adhesive tested below and above the glass transition temperature (T g), established by the manufacturer as 67°C. The combined influence of these two parameters on the repairs strength was also analysed. According to the results obtained from this work, design guidelines for repairing aluminium structures were

Strength prediction of adhesively-bonded scarf repairs in composite structures under bending

This work reports on the experimental and numerical study of the bending behaviour of two-dimensional adhesively-bonded scarf repairs of carbon-epoxy laminates, bonded with the ductile adhesive Araldite 2015®. Scarf angles varying from 2 to 45º were tested. The experimental work performed was used to validate a numerical Finite Element analysis using ABAQUS® and a methodology developed by the authors to predict the strength of bonded assemblies. This methodology consists on replacing the adhesive layer by cohesive elements, including mixed-mode criteria to deal with the mixed-mode behaviour usually observed in structures. Trapezoidal laws in pure modes I and II were used to account for the ductility of the adhesive used. The cohesive laws in pure modes I and II were determined with Double Cantilever Beam and End-Notched Flexure tests, respectively, using an inverse method. Since in the experiments interlaminar and transverse intralaminar failures of the carbon-epoxy components also occurred in some regions, cohesive laws to simulate these failure modes were also obtained experimentally with a similar procedure. A good correlation with the experiments was found on the elastic stiffness, maximum load and failure mode of the repairs, showing that this methodology simulates accurately the mechanical behaviour of bonded assemblies.

Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.

Numerical evaluation of three-dimensional scarf repairs in carbon-epoxy structures

The widespread employment of carbon-epoxy laminates in high responsibility and severely loaded applications introduces an issue regarding their handling after damage. Repair of these structures should be evaluated, instead of their disposal, for cost saving and ecological purposes. Under this perspective, the availability of efficient repair methods is essential to restore the strength of the structure. The development and validation of accurate predictive tools for the repairs behaviour are also extremely important, allowing the reduction of costs and time associated to extensive test programmes. Comparing with strap repairs, scarf repairs have the advantages of a higher efficiency and the absence of aerodynamic disturbance. This work reports on a numerical study of the tensile behaviour of three-dimensional scarf repairs in carbon-epoxy structures, using a ductile adhesive (Araldite® 2015). The finite elements analysis was performed in ABAQUS® and Cohesive Zone Modelling was used for the simulation of damage onset and growth in the adhesive layer. Trapezoidal cohesive laws in each pure mode were used to account for the ductility of the specific adhesive mentioned. A parametric study was performed on the repair width and scarf angle. The use of over-laminating plies covering the repaired region at the outer or both repair surfaces was also tested as an attempt to increase the repairs efficiency. The obtained results allowed the proposal of design principles for repairing composite structures.

Intrinsic fractal dynamics in the respiratory system by means of pressure-volume loops

This contribution presents novel concepts for analysis of pressure–volume curves, which offer information about the time domain dynamics of the respiratory system. The aim is to verify whether a mapping of the respiratory diseases can be obtained, allowing analysis of (dis)similarities between the dynamical pattern in the breathing in children. The groups investigated here are children, diagnosed as healthy, asthmatic, and cystic fibrosis. The pressure–volume curves have been measured by means of the noninvasive forced oscillation technique during breathing at rest. The geometrical fractal dimension is extracted from the pressure–volume curves and a power-law behavior is observed in the data. The power-law model coefficients are identified from the three sets and the results show that significant differences are present between the groups. This conclusion supports the idea that the respiratory system changes with disease in terms of airway geometry, tissue parameters, leading in turn to variations in the fractal dimension of the respiratory tree and its dynamics.

Tensile behaviour of single and double-strap repairs on aluminium structures

In this work, an experimental study was performed on the influence of plug filling, loading rate and temperature on the tensile strength of single-strap (SS) and double-strap (DS) repairs on aluminium structures. The experimental programme includes repairs with different values of overlap length (LO=10, 20 and 30 mm), and with and without plug filling. The influence of the testing speed on the repairs strength is also addressed (considering 0.5, 5 and 25 mm/min). Accounting for the temperature effects, tests were carried out at room temperature, 50ºC and 80ºC. This will permit a comparative evaluation of the adhesive tested below and above the Glass Transition Temperature (Tg), established by the manufacturer at 67ºC. The global tendencies of the test results concerning the plug filling and overlap length analyses are interpreted from the fracture modes and typical stress distributions for bonded repairs. According to the results obtained from this work, design guidelines for repairing aluminium structures were recommended.

A theoretical study on modelling the respiratory tract with ladder networks by means of intrinsic fractal geometry

Fractional order modeling of biological systems has received significant interest in the research community. Since the fractal geometry is characterized by a recurrent structure, the self-similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. To demonstrate the link between the recurrence of the respiratory tree and the appearance of a fractional-order model, we develop an anatomically consistent representation of the respiratory system. This model is capable of simulating the mechanical properties of the lungs and we compare the model output with in vivo measurements of the respiratory input impedance collected in 20 healthy subjects. This paper provides further proof of the underlying fractal geometry of the human lungs, and the consequent appearance of constant-phase behavior in the total respiratory impedance.