Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements m in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes' theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito-Taylor's discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplifiedmby considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations. (C) 2010 Elsevier Ltd. All rights reserved.

An Accurate Model For Interference From Spatially Distributed Shadowed Users in CDMA Uplinks

A detailed characterization of interference power statistics in CDMA systems is of considerable practical and theoretical interest. Such a characterization for uplink inter-cell interference has been difficult because of transmit power control, randomness in the number of interfering mobile stations, and randomness in their locations. We develop a new method to model the uplink inter-cell interference power as a lognormal distribution, and show that it is an order of magnitude more accurate than the conventional Gaussian approximation even when the average number of mobile stations per cell is relatively large and even outperforms the moment-matched lognormal approximation considered in the literature. The proposed method determines the lognormal parameters by matching its moment generating function with a new approximation of the moment generating function for the inter-cell interference. The method is tractable and exploits the elegant spatial Poisson process theory. Using several numerical examples, the accuracy of the proposed method in modeling the probability distribution of inter-cell interference is verified for both small and large values of interference.

Different phenomenological theories and their abilities to describe the interdiffusion process in a binary system during multiphase growth

There are essentially two different phenomenological models available to describe the interdiffusion process in binary systems in the olid state. The first of these, which is used more frequently, is based on the theory of flux partitioning. The second model, developed much more recently, uses the theory of dissociation and reaction. Although the theory of flux partitioning has been widely used, we found that this theory does not account for the mobility of both species and therefore is not suitable for use in most interdiffusion systems. We have first modified this theory to take into account the mobility of both species and then further extended it to develop relations or the integrated diffusion coefficient and the ratio of diffusivities of the species. The versatility of these two different models is examined in the Co-Si system with respect to different end-member compositions. From our analysis, we found that the applicability of the theory of flux partitioning is rather limited but the theory of dissociation and reaction can be used in any binary system.

Switching Process in Ferroelectric Triglycine Selenate

Triglycine selenate (TGSe) is isomorphous with Triglycine sulphate and is ferroelectric below 22°C. It is interesting to study the switching process in TGSe in the ferro-state with a view to comparing the results with TSG. The switching process was studied by applying electrical square pulses to produce fields up to 5 kV/cm on the sample, and measuring the parameters characterizing the transient current flowing in the sample, according to the Merz method. The temperature range in which the process was studied was 15°C to -20°C. The results were analysed by applying the Pulvari-Kuebler theory and the parameters α the activation field and µ the mobility of the domains were evaluated. It is found that µ varies with temperature in TGSe in a manner similar to TGS. µ is lesser for TGSe than for TGS for the same shift of temperature from Tc. The switching behaviour of γ-irradiated TGSe is qualitatively similar to that of unirradiated crystal eventhougth the process gets slowed down as a result of irradiation.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

The perturbational treatment of the process of hydrogen abstraction by ketones

The change in energy during hydrogen abstraction by ketones is estimated for different electronic states as a function of the intermolecular orbital overlap employing perturbation theory. The results suggest that ketones preferentially undergo the in-plane reaction and abstract a hydrogen atom in their triplet nπ* state. For ketones where the triplet ππ* state lies below the triplet nπ* state, hydrogen abstraction can take place in the ππ* state owing to the crossing of the zero order reaction surfaces of the nπ* and ππ* states.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

An elementary introduction to solar dynamo theory

The cyclically varying magnetic field of the Sun is believed to be produced by the hydromagnetic dynamo process. We first summarize the relevant observational data pertaining to sunspots and solar cycle. Then we review the basic principles of MHD needed to develop the dynamo theory. This is followed by a discussion how bipolar sunspots form due to magnetic buoyancy of flux tubes formed at the base of the solar convection zone. Following this, we come to the heart of dynamo theory. After summarizing the basic ideas of a turbulent dynamo and the basic principles of its mean field formulation, we present the famous dynamo wave solution, which was supposed to provide a model for the solar cycle. Finally we point out how a flux transport dynamo can circumvent some of the difficulties associated with the older dynamo models.

Process variability-aware statistical hybrid modeling of dynamic power dissipation in 65 nm CMOS designs

A generalized technique is proposed for modeling the effects of process variations on dynamic power by directly relating the variations in process parameters to variations in dynamic power of a digital circuit. The dynamic power of a 2-input NAND gate is characterized by mixed-mode simulations, to be used as a library element for 65mn gate length technology. The proposed methodology is demonstrated with a multiplier circuit built using the NAND gate library, by characterizing its dynamic power through Monte Carlo analysis. The statistical technique of Response. Surface Methodology (RSM) using Design of Experiments (DOE) and Least Squares Method (LSM), are employed to generate a "hybrid model" for gate power to account for simultaneous variations in multiple process parameters. We demonstrate that our hybrid model based statistical design approach results in considerable savings in the power budget of low power CMOS designs with an error of less than 1%, with significant reductions in uncertainty by atleast 6X on a normalized basis, against worst case design.

Bayesian Analysis of a Superimposed Renewal Process

Stochastic behavior of an aero-engine failure/repair process has been analyzed from a Bayesian perspective. Number of failures/repairs in the component-sockets of this multi-component system are assumed to follow independent renewal processes with Weibull inter-arrival times. Based on the field failure/repair data of a large number of such engines and independent Gamma priors on the scale parameters and log-concave priors on the shape parameters, an exact method of sampling from the resulting posterior distributions of the parameters has been proposed. These generated parameter values are next utilised in obtaining the posteriors of the expected number of system repairs, system failure rate, and the conditional intensity function, which are computed using a recursive formula.

Time-domain-finite-wave analysis of the engine exhaust system by means of the stationary-frame method of characteristics. Part I. Theory

Time-domain-finite-wave analysis of the engine exhaust system is usually done using the method of characteristics. This makes use of either the moving frame method, or the stationary frame method. The stationary frame method is more convenient than its counterpart inasmuch as it avoids the tedium of graphical computations. In this paper (part I), the stationary-frame computational scheme along with the boundary conditions has been implemented. The analysis of a uniform tube, cavity-pipe junction including the engine and the radiation ends, and also the simple area discontinuities has been presented. The analysis has been done accounting for wall friction and heat-transfer for a one-dimensional unsteady flow. In the process, a few inconsistencies in the formulations reported in the literature have been pointed out and corrected. In the accompanying paper (part II) results obtained from the simulation are shown to be in good agreement with the experimental observations.

Theory of electron transfer processes via chemisorbed intermediates: Part II. Current-potential characteristics

Current-potential characteristics are obtained numerically for a lone-adsorbate-mediated anodic charge transfer at the electrode-solution interface. An increase in the overpotential leads to the appearance of maxima in the anodic current-potential plots instead of the extended activationless region (i.e. a saturation current at large positive overpotentials) predicted by the direct heterogeneous outer-sphere anodic charge transfer process. A detailed analysis of the dependence of current-potential profiles and other kinetic parameters on various system parameters is also presented.

Theory of polymer breaking under tension

We consider the breaking of a polymer molecule which is fixed at one end and is acted upon by a force at the other. The polymer is assumed to be a linear chain joined together by bonds which satisfy the Morse potential. The applied force is found to modify the Morse potential so that the minimum becomes metastable. Breaking is just the decay of this metastable bond, by causing it to go over the barrier. Increasing the force causes the potential to become more and more distorted and eventually leads to the disappearance of the barrier. The limiting force at which the barrier disappears is D(e)a/2,D-e with a the parameters characterizing the Morse potential. The rate of breaking is first calculated using multidimensional quantum transition state theory. We use the harmonic approximation to account for vibrations of all the units. It includes tunneling contributions to the rate, but is valid only above a certain critical temperature. It is possible to get an analytical expression for the rate of breaking. We have calculated the rate of breaking for a model, which mimics polyethylene. First we calculate the rate of breaking of a single bond, without worrying about the other bonds. Inclusion of other bonds under the harmonic approximation is found to lower this rate by at the most one order of magnitude. Quantum effects are found to increase the rate of breaking and are significant only at temperatures less than 150 K. At 300 K, the calculations predict a bond in polyethylene to have a lifetime of only seconds at a force which is only half the limiting force. Calculations were also done using the Lennard-Jones potential. The results for Lennard-Jones and Morse potentials were rather different, due to the different long-range behaviors of the two potentials. A calculation including friction was carried out, at the classical level, by assuming that each atom of the chain is coupled to its own collection of harmonic oscillators. Comparison of the results with the simulations of Oliveira and Taylor [J. Chem. Phys. 101, 10 118 (1994)] showed the rate to be two to three orders of magnitude higher. As a possible explanation of discrepancy, we consider the translational motion of the ends of the broken chains. Using a continuum approximation for the chain, we find that in the absence of friction, the rate of the process can be limited by the rate at which the two broken ends separate from one another and the lowering of the rate is at the most a factor of 2, for the parameters used in the simulation (for polyethylene). In the presence of friction, we find that the rate can be lowered by one to two orders of magnitude, making our results to be in reasonable agreement with the simulations.

Two-dimensional approximations of 3-dimensional eigenvalue problems in plate-theory

The eigenvalues and eigenfunctions corresponding to the three-dimensional equations for the linear elastic equilibrium of a clamped plate of thickness 2ϵ, are shown to converge (in a specific sense) to the eigenvalues and eigenfunctions of the well-known two-dimensional biharmonic operator of plate theory, as ϵ approaches zero. In the process, it is found in particular that the displacements and stresses are indeed of the specific forms usually assumed a priori in the literature. It is also shown that the limit eigenvalues and eigenfunctions can be equivalently characterized as the leading terms in an asymptotic expansion of the three-dimensional solutions, in terms of powers of ϵ. The method presented here applies equally well to the stationary problem of linear plate theory, as shown elsewhere by P. Destuynder.

Relevance of local parallel theory to the linear stability of laminar separation bubbles

Laminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.