Critical earthquake input power spectral density function models for engineering structures

The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

Stochastic differential games: Occupation measure based approach

A new approach based on occupation measures is introduced for studying stochastic differential games. For two-person zero-sum games, the existence of values and optimal strategies for both players is established for various payoff criteria. ForN-person games, the existence of equilibria in Markov strategies is established for various cases.

Stochastic fluctuations of the solar dynamo

Attempts in the past to model the irregularities of the solar cycle (such as the Maunder minimum) were based on studies of the nonlinear feedback of magnetic fields on the dynamo source terms. Since the alpha-coefficient is obtained by averaging over the turbulence, it is expected to have stochastic fluctuations, and we show that these fluctuations can explain the irregularities of the solar cycle in a more satisfactory way. We solve the dynamo equations in a slab with a single mode, taking the alpha-coefficient to be constant in space but fluctuating stochastically in time with some given amplitude and given correlation time. The same level of percentile fluctuations (about 10 %) produces no effect on an alpha-omega dynamo, but makes an alpha-2 dynamo completely chaotic. The level of irregularities in an alpha-2-omega dynamo qualitatively agrees with the solar behavior, reinforcing the conclusion of Choudhuri (1990a) that the solar dynamo is of the alpha-2-omega-type. The irregularities are found to increase on increasing either the amplitude or the correlation time of the stochastic fluctuations. The alpha-quenching mechanism tends to make the system stable against the irregularities and hence it is inferred that the alpha-quenching should not be too strong so that the irregularities are not completely suppressed. We also present a simple-minded analysis to understand why the stochastic fluctuations in the alpha-omega, alpha-2-omega and alpha-2 regimes have such different outcomes.

Stochastic modelling of flexible manufacturing systems

Mathematical modelling plays a vital role in the design, planning and operation of flexible manufacturing systems (FMSs). In this paper, attention is focused on stochastic modelling of FMSs using Markov chains, queueing networks, and stochastic Petri nets. We bring out the role of these modelling tools in FMS performance evaluation through several illustrative examples and provide a critical comparative evaluation. We also include a discussion on the modelling of deadlocks which constitute an important source of performance degradation in fully automated FMSs.

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

A two timescale stochastic approximation scheme for simulation-based parametric optimization

A two timescale stochastic approximation scheme which uses coupled iterations is used for simulation-based parametric optimization as an alternative to traditional "infinitesimal perturbation analysis" schemes, It avoids the aggregation of data present in many other schemes. Its convergence is analyzed, and a queueing example is presented.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Stochastic Aeroelastic Analysis of Composite Helicopter Rotor

The effect of uncertainty in composite material properties on the aeroelastic response, vibratory loads, and stability of a hingeless helicopter rotor is investigated. The uncertainty impact on rotating natural frequencies of the blade is studied with Monte Carlo simulations and first-order reliability methods. The stochastic aeroelastic analyses in hover and forward flight are carried out with Monte Carlo simulations. The flap, lag, and torsion responses show considerable scatter from their baseline values, and the uncertainty impact varies with the azimuth angle. Furthermore, the blade response shows finite probability of resonance-type conditions caused by modal frequencies approaching multiples of the rotor speed. The 4/rev vibratory forces show large deviations from their baseline values. The lag mode damping shows considerable scatter due to uncertain material properties with an almost 40% probability of instability in hover.

Multiscale stochastic approximation for parametric optimization of hidden Markov models

A two-time scale stochastic approximation algorithm is proposed for simulation-based parametric optimization of hidden Markov models, as an alternative to the traditional approaches to ''infinitesimal perturbation analysis.'' Its convergence is analyzed, and a queueing example is presented.

Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

The actor-critic algorithm as multi-time-scale stochastic approximation

The actor-critic algorithm of Barto and others for simulation-based optimization of Markov decision processes is cast as a two time Scale stochastic approximation. Convergence analysis, approximation issues and an example are studied.

Stochastic dynamics modeling of the protein sequence length distribution in genomes: implications for microbial evolution

In this paper, we report an analysis of the protein sequence length distribution for 13 bacteria, four archaea and one eukaryote whose genomes have been completely sequenced, The frequency distribution of protein sequence length for all the 18 organisms are remarkably similar, independent of genome size and can be described in terms of a lognormal probability distribution function. A simple stochastic model based on multiplicative processes has been proposed to explain the sequence length distribution. The stochastic model supports the random-origin hypothesis of protein sequences in genomes. Distributions of large proteins deviate from the overall lognormal behavior. Their cumulative distribution follows a power-law analogous to Pareto's law used to describe the income distribution of the wealthy. The protein sequence length distribution in genomes of organisms has important implications for microbial evolution and applications. (C) 1999 Elsevier Science B.V. All rights reserved.