Stochastic Approximation Algorithms for Constrained Optimization via Simulation

We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.

Tunable Locally-Optimal Geographical Forwarding in Wireless Sensor Networks with Sleep-Wake Cycling Nodes

We consider a wireless sensor network whose main function is to detect certain infrequent alarm events, and to forward alarm packets to a base station, using geographical forwarding. The nodes know their locations, and they sleep-wake cycle, waking up periodically but not synchronously. In this situation, when a node has a packet to forward to the sink, there is a trade-off between how long this node waits for a suitable neighbor to wake up and the progress the packet makes towards the sink once it is forwarded to this neighbor. Hence, in choosing a relay node, we consider the problem of minimizing average delay subject to a constraint on the average progress. By constraint relaxation, we formulate this next hop relay selection problem as a Markov decision process (MDP). The exact optimal solution (BF (Best Forward)) can be found, but is computationally intensive. Next, we consider a mathematically simplified model for which the optimal policy (SF (Simplified Forward)) turns out to be a simple one-step-look-ahead rule. Simulations show that SF is very close in performance to BF, even for reasonably small node density. We then study the end-to-end performance of SF in comparison with two extremal policies: Max Forward (MF) and First Forward (FF), and an end-to-end delay minimising policy proposed by Kim et al. 1]. We find that, with appropriate choice of one hop average progress constraint, SF can be tuned to provide a favorable trade-off between end-to-end packet delay and the number of hops in the forwarding path.

Combined convection in power-law fluids along a nonisothermal vertical plate in a porous medium

The problem of combined convection from vertical surfaces in a porous medium saturated with a power-law type non-Newtonian fluid is investigated. The transformed conservation laws are solved numerically for the case of variable surface heat flux conditions. Results for the details of the velocity and temperature fields as well as the Nusselt number have been presented. The viscosity index ranged from 0.5 to 2.0.

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.

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.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

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.

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.

Effect of Constant and Cyclic Current Stressing on the Evolution of Intermetallic Compound Layers

In this paper the effects of constant and cyclic power loads on the evolution of interfacial reaction layers in lead-free solder interconnections are presented. Firstly, the differences in the growth behavior of intermetallic compound (IMC) layers at the cathode and anode sides of the interconnections are rationalized. This is done by considering the changes in the intrinsic fluxes of elements owing to electromigration as well as taking into account the fact that the growth of Cu3Sn and Cu6Sn5 are coupled via interfacial reactions. In this way, better understanding of the effect of electron flux on the growth of each individual layer in the Cu-Sn system can be achieved. Secondly, it is shown that there is a distinct difference between steady-state current stressing (constant current, constant temperature) and power cycling with alternating on- and off-cycle periods (accompanied by a change of temperature). The reasons behind the observed differences are subsequently discussed. Finally, special care is taken to ensure that the current densities are chosen in such a way that there is no risk for even partial melting of the solder interconnections.

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.

In-situ power monitoring scheme and its application in dynamic voltage and threshold scaling for digital CMOS integrated circuits

An in-situ power monitoring technique for Dynamic Voltage and Threshold scaling (DVTS) systems is proposed which measures total power consumed by load circuit using sleep transistor acting as power sensor. Design details of power monitor are examined using simulation framework in UMC 90nm CMOS process. Experimental results of test chip fabricated in AMS 0.35µm CMOS process are presented. The test chip has variable activity between 0.05 and 0.5 and has PMOS VTH control through nWell contact. Maximum resolution obtained from power monitor is 0.25mV. Overhead of power monitor in terms of its power consumption is 0.244 mW (2.2% of total power of load circuit). Lastly, power monitor is used to demonstrate closed loop DVTS system. DVTS algorithm shows 46.3% power savings using in-situ power monitor.

Fabrication and evaluation of 450 F electrochemical redox supercapacitors using inexpensive and high-performance, polyaniline coated, stainless-steel electrodes

Redox supercapacitors using polyaniline (PANI) coated. stainless-steel (SS) electrodes have been assembled and characterized. PANI has been deposited on SS substrate by a potentiodynamic method from an acidic electrolyte which contains aniline monomer. By employing stacks of electrodes, each with a geometrical area of 24 cm(2), in acidic perchlorate electrolyte, a capacitance value of about 450 F has been obtained over a long cycle-life. Characterization studies have been carried out by galvanostatic charge-discharge cycling of the capacitors singly, as well as in series and parallel configurations. Various electrical parameters have been evaluated. Use of the capacitors in parallel with a battery for pulse-power loads. and also working of a toy fan connected to the charged capacitors have been demonstrated. A specific capacitance value of about 1300 F g(-1) of PANI has been obtained at a discharge power of about 0.5 kW kg(-1). This value is several times higher than those reported in the literature for PANI and is, perhaps, the highest value known for a capacitor material. The inexpensive SS substrate and the high-capacitance PANI are favorable factors for commercial exploitation. (C) 2002 Elsevier Science B.V. All rights reserved.

Nonlinear Dynamics of Beams with Stochastic Parameter Variations

The aim of this paper is to investigate the steady state response of beams under the action of random support motions. The study is of relevance in the context of earthquake response of extended land based structures such as pipelines and long span bridges, and, secondary systems such as piping networks in nuclear power plant installations. The following complicating features are accounted for in the response analysis: (a) differential support motions: this is characterized in terms of cross power spectral density functions associated with distinct support motions, (b) nonlinear support conditions, and (c) stochastically inhomogeneous stiffness and mass variations of the beam structure; questions on non-Gaussian models for these variations are considered. The method of stochastic finite elements is combined with equivalent linearization technique and Monte Carlo simulations to obtain response moments.

Power Efficient Redundant Execution for Chip Multiprocessor

This paper describes the design of a power efficient microarchitecture for transient fault detection in chip multiprocessors (CMPs) We introduce a new per-core dynamic voltage and frequency scaling (DVFS) algorithm for our architecture that significantly reduces power dissipation for redundant execution with a minimal performance overhead. Using cycle accurate simulation combined with a simple first order power model, we estimate that our architecture reduces dynamic power dissipation in the redundant core by an mean value of 79% and a maximum of 85% with an associated mean performance overhead of only 1:2%