Probabilistic modeling of a nonlinear dynamical system used for producing voice

This paper is devoted to the construction of a stochastic nonlinear dynamical system for signal generation such as the production of voiced sounds. The dynamical system is highly nonlinear, and the output signal generated is very sensitive to a few parameters of the system. In the context of the production of voiced sounds the measurements have a significant variability. We then propose a statistical treatment of the experiments and we developed a probability model of the sensitive parameters in order that the stochastic dynamical system has the capability to predict the experiments in the probability distribution sense. The computational nonlinear dynamical system is presented, the Maximum Entropy Principle is used to construct the probability model and an experimental validation is shown.     

Probabilistic modeling of fatigue crack growth in Ti–6Al–4V

This paper proposes an approximate approach to efficient estimation of some variabilities caused by the material microstructural inhomogeneities. The approach is based on the results of a combined experimental and analytical study of the probabilistic nature of fatigue crack growth in Ti–6Al–4V. A simplified experimental fracture mechanics framework is presented for the determination of statistical fatigue crack growth parameters from two fatigue tests. The experimental studies suggest that the variabilities in long fatigue crack growth rate data and the Paris coefficient are well described by the log-normal distributions. The variabilities in the Paris exponent are also shown to be well characterized by a normal distribution. The measured statistical distributions are incorporated into a probabilistic fracture mechanics framework for the estimation of material reliability. The implications of the results are discussed for the probabilistic analysis of fatigue crack growth.     

Probabilistic modeling of threshold stress intensity factor for fatigue endurance reliability prediction

This study develops a probabilistic model for the threshold stress intensity factor range, which is a critical parameter in infinite fatigue life design under material flaws. The model is based on the proposed concept of probability of propagation in the probabilistic framework, allowing for deriving the probability density function of the threshold intensity factor range. The uncertainty in fatigue crack growth can naturally be incorporated into the resulting distribution. By further introducing the derived distribution into the Kitagawa–Takahashi diagram, the fatigue endurance reliability model can be established in a rational manner. With the first-order asymptotic approximation, the analytical form of fatigue endurance reliability index is obtained. The usefulness of the overall method is demonstrated using realistic engineering application examples.     

A hybrid S-N formulation for fatigue life modeling of composite materials and structures

A semi-empirical S-N formulation for the modeling of the constant amplitude fatigue behavior of composite materials and structures is introduced in this paper. The new S-N formulation is based on the commonly used exponential and power law fatigue models. It is a hybrid formulation combining the two existing models in order to improve their modeling accuracy in the low and high cycle fatigue regions. This formulation was applied to a number of fatigue databases for different composite materials and structural elements in order to simulate their fatigue behavior. The modeling accuracy of the hybrid model was compared to the accuracy of commonly used S-N models for composite materials. As proved, the hybrid model performs better in the majority of the examined cases and is able to overcome the disadvantages of previously developed models without introducing any complexity in the fitting procedure.     

Probabilistic 3-D turbulence modeling for gust buffeting of structures

Literature on turbulence modeling is rich in empirical, semi-empirical and theoretical spectral equations whose parameters assume deterministic values. Starting from a critical review of the state of the art, this paper proposes a unified model of atmospheric turbulence especially suited to determine the 3-D gust-excited response of structures. Unlike classical models, all parameters are assigned through first and second order statistical moments derived from a wide set of selected experimental measurements. A general discussion is also provided about model errors and other sources of randomness. Due to these properties the model proposed is suitable for carrying out reliability analyses which take into account the propagation of the uncertainties.     

Optical properties of oxide glasses containing transition metals: Case of titanium- and chromium-containing glasses

One of the major driving forces for the development of new glasses is the demand for high optical non-linearity with reduced cost and a higher damage resistance. Oxide glasses with large non-linear refractive index and non-linear absorption coefficient are promising materials for fiber telecommunication and for non-linear optical devices such as ultrafast optical switches, power limiters, real time holography, self-focusing, white-light continuum generation and photonic applications. To get insight into the optical absorption in amorphous materials, studies are still needed for revealing the nature of photoelectronic excitations in these materials by comparison with that in crystals which have been understood firmly based on band theory. Although the IR absorption loss in oxide glasses is larger than of fluorides, low light scattering loss is expected in these oxide glasses because they have lower glass transition temperature. In addition, small concentration of dopant such as alkaline metal and alkaline earth metal elements gives rise to the structural relaxation of the frozen-in density fluctuations even below glass transition temperature T_g, adding to the reduction of T_g as well. A review of the fundamentals and recent research advances in optical properties of oxide glasses containing chromium or titanium is presented.     

Numerical modeling of response of monolithic and bilayer plates to impulsive loads

In this paper, we present and discuss the results of our numerical simulation of the dynamic response and failure modes of circular DH-36 steel plates and DH-36 steel–polyurea bilayers, subjected to impulsive loads in reverse ballistic experiments. In our previous article, we reported the procedure and results of these experiments [MR Amini, JB Isaacs, S Nemat-Nasser. Experimental investigation of response of monolithic and bilayer plates to impulsive loads. accepted]. For the numerical simulations, we have used physics-based and experimentally-supported temperature- and rate-sensitive constitutive models for steel and polyurea, including in the latter case the pressure effects. Comparing the simulation and the experimental results, we focus on identifying the potential underpinning mechanisms that control the deformation and failure modes of both monolithic steel and steel–polyurea bilayer plates.The numerical simulations reveal that the bilayer plate has a superior performance over the monolithic plate if the polyurea layer is cast on its back face (opposite to the blast-receiving side). The presence of the polyurea layer onto the front face (blast-receiving side) amplifies the initial shock loading and thereby enhances the destructive effect of the blast, promoting (rather than mitigating) the failure of the steel plate. In addition, the interface bonding strength between polyurea and steel is examined numerically and it is observed that the interface bonding strength has a significant effect on the performance of the steel–polyurea bilayer plates. The numerical simulations support the experimentally observed facts provided the entire experiment is simulated, employing realistic physics-based constitutive models for all constituents.     

Effects of Ti transition layer on stability of silver/titanium dioxide multilayered structure

Thermal stability is critically important for silver-based multilayered structures such as Ag/TiO₂. Al and NiCr are reported to be applied as interlayers between Ag and TiO₂ to improve the thermal stability but both decrease the transparency in visible region. In this work, a Ti interlayer can effectively improve the thermal stability of the Ag film but does not adversely affect the optical transmission through the multilayer from the near ultraviolet to near infrared spectral region. Atomic force microscopy indicates that the titanium interlayer improves the surface quality and agglomeration resistance of the Ag film. Depth profiles obtained by Auger electron spectroscopy show that the L₃M₂₃V line of titanium shifts to a higher binding energy after annealing, indicating that the titanium layer is oxidized during annealing at 573 K in air for 30 min. X-ray diffraction results indicate that the transition layer is oxidized to Ti₂O₃ during deposition and the Ag (111) orientation preferentially emerges after the thermal treatment. The Ag layer remains chemically stable but some diffusion is observed through the top dielectric layer after annealing. About 10% degradation in the visible light transmission and 20% in near IR reflection are observed from the samples without the interlayers after annealing. In comparison, less than 10% decrease in the near IR reflectivity is observed from the samples with the interlayers. The transition layer is found to stabilize the silver film by improving the wettability, agglomeration resistance, and diffusion resistance.     

Numerical modeling of the ductile-brittle transition

Numerical studies of the ductile-brittle transition are described that are based on incorporating physically based models of the competing fracture mechanisms into the material's constitutive relation. An elastic-viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Cleavage is modeled in terms of attaining a temperature and strain rate independent critical value of the maximum principal stress over a specified material region of the order of one or two grain sizes. Various analyses of ductile-brittle transitions carried out within this framework are discussed. The specimens considered include the Charpy V-notch test and cracked specimens under mode I or mode II loading conditions. The fracture mode transition emerges as a natural outcome of the initial-boundary value problem solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

A methodology for fast finite element modeling of electrostatically actuated MEMS

In this paper, a methodology is proposed for expediting the coupled electro‐mechanical finite element modeling of electrostatically actuated MEMS. The proposed methodology eliminates the need for repeated finite element meshing and subsequent electrostatic modeling of the device during mechanical deformation. We achieve this by using an approximation of the charge density on the movable electrode in the deformed geometry in terms of the charge density in the non‐deformed geometry and displacements of the movable electrode. The electrostatic problem has to be solved only once and thus this method speeds up the coupled electro‐mechanical simulation process. The proposed methodology is demonstrated through its application to the modeling of four MEMS devices with varying length‐to‐gap ratios, multiple dielectrics and complicated geometries. Its accuracy is assessed through comparisons of its results with results obtained using both analytical solutions and finite element solutions obtained using ANSYS. Copyright © 2008 John Wiley & Sons, Ltd.     

A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion-fatigue

A combined probabilistic physics-of-failure-based model for pitting and corrosion-fatigue degradation mechanisms is proposed to estimate the reliability of structures and to perform prognosis and health management. A mechanistic superposition model for corrosion-fatigue mechanism was used as a benchmark model to propose the simple model. The proposed model describes the degradation of the structures as a function of physical and critical environmental stresses, such as amplitude and frequency of mechanical loads (for example caused by the internal piping pressure) and the concentration of corrosive chemical agents. The parameters of the proposed model are represented by the probability density functions and estimated through a Bayesian approach based on the data taken from the experiments performed as part of this research. For demonstrating applications, the proposed model provides prognostic information about the reliability of aging of structures and is helpful in developing inspection and replacement strategies.     

Characterization and modeling of transition edge sensors for high resolution X-ray calorimeter arrays

Characterizing and understanding, in detail, the behavior of a Transition Edge Sensor (TES) is required for achieving an energy resolution of 2 eV at 6 keV desired for future X-ray observatory missions. This paper will report on a suite of measurements (e.g. impedance and I–V among others) and simulations that were developed to extract a comprehensive set of TES parameters such as heat capacity, thermal conductivity, and R(T,I), (T,I), and β_i(T,I) surfaces. These parameters allow for the study of the TES calorimeter behavior at and beyond the small signal regime.     

RC beams strengthened with NSM CFRP rods and modeling of peeling-off failure

The aim of the experimental programme developed in this work was to investigate the possibility of using Carbon Fibre-Reinforced Polymer (CFRP) rods to strengthen concrete structural members with the Near Surface Mounted reinforcement (NSM) technique. The global behaviour of reinforced cantilever concrete beams strengthened by the NSM technique and subjected to flexure is investigated. The specific problem of cantilever beams (strengthening outward pressure) was studied. The global behaviour of the cantilever concrete beams was compared with that of beams subjected to flexure with four points load test. A carbon–epoxy pultruded FRP (CFRP) rod of 6 mm in diameter was used. The study was carried out up to the failure load, and focused on the modifications in mechanical behaviour, cracking and failure mode of the beams. An analytical and Finite Element models to predict the peeling-off failure mode were compared.     

Probabilistic evaluation of initiation time of chloride-induced corrosion

The paper presents a model for chloride ingress into concrete. The model accounts for two mechanisms which control the chloride ingress—diffusion and convection. Using one-dimensional (1-D) formulation of the model, the influence of chloride binding and ambient humidity on chloride ingress into concrete has been investigated. Based on results of this investigation parameters for probabilistic analysis have been selected. Probabilistic evaluation of the time to corrosion initiation has then been carried out for a reinforced concrete (RC) wall (1-D problem) and a RC column (2-D problem) in a marine environment. Results of the analysis show that for the same thickness of the concrete cover the probability of corrosion initiation in the corner reinforcing bars of the RC column is much higher than in reinforcing bars in the middle part of the RC wall. The results demonstrate the importance of 2-D modelling for correct prediction of corrosion initiation in such RC elements as columns and beams.     

Probabilistic modeling of chloride-induced corrosion in concrete structures using first- and second-order reliability methods

Concrete structures are subjected to chloride-induced corrosion that can lead to shortened service life. Reliable predictions of life cycle performance of concrete structures are critical to the optimization of their life cycle design and maintenance to minimize their life cycle costs. This paper presents two simplified semi-analytical probabilistic models based on the first- and second-order reliability methods to model the uncertainty of the key parameters including surface chloride concentration, chloride threshold, cover depth and diffusion coefficient, which govern the chloride ingress into concrete and corrosion of reinforcing steel. A case study of a reinforced concrete highway bridge deck is used to illustrate the capability and efficiency of these simplified probabilistic models in modeling the uncertainty and predicting the time-dependent probability of corrosion. The models enable to quantify the impact of the different governing parameters on probability of corrosion and service life, which can be used to develop cost-effective management strategies.     

论分布式陀螺柔性体结构的动力学建模问题

针对含分布式控制力矩陀螺的柔性体结构动力学建模问题,研究了结构和陀螺之间相互耦合对结构固有振动的影响。通过基于有限元离散的建模思路,获得了含分布式控制力矩陀螺的结构动力学模型。对比模态叠加方法,提出原柔性体模态的概念。结果表明,分布控制力矩陀螺对结构固有振动产生了本质的影响。基于原柔性体结构前几阶模态的模态叠加法,由于没有计入结构和陀螺之间的耦合效应,所得到结构动力学降阶模型具有较大误差。