Optimal plan for Wiener constant-stress accelerated degradation model

This paper explores inferential procedures for the Wiener constant-stress accelerated degradation model under degradation mechanism invariance. The exact confidence intervals are obtained for the parameters of the proposed accelerated degradation model. The generalized confidence intervals are also proposed for the reliability function and pth quantile of the lifetime at the normal operating stress level. In addition, the prediction intervals are developed for the degradation characteristic, lifetime and remaining useful life of the product at the normal operating stress level. The performance of the proposed generalized confidence intervals and the prediction intervals is assessed by the Monte Carlo simulation. Furthermore, a new optimum criterion is proposed based on minimizing the mean of the upper prediction limit for the degradation characteristic at the design stress level. The exact optimum plan is also derived for the Wiener accelerated degradation model according to the proposed optimal criterion. The proposed interval procedures and optimum plan are the free of the equal testing interval assumption. Finally, two examples are provided to illustrate the proposed interval procedures and exact optimum plan. Specifically, based on the degradation data of LEDs, some interval estimates of quantities related to reliability indicators are obtained. For the degradation data of carbon-film resistors, the optimal allocation of test units is derived in terms of the proposed optimal criterion.     

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES＊

This article deals with a nonlocal heat system subject to null Dirichlet boundary conditions,where the coupling nonlocal sources consist of mixed type asymmetric nonlinearities.We at first give the cri...     

Bayesian accelerated life test plans for series systems with Weibull component lifetimes

This article presents optimal Bayesian accelerated life test plans for series systems under Type-I censoring scheme. First, the component lifetimes are assumed to follow independent Weibull distributions. The scale parameters of Weibull lifetime distributions are related to the external stress variable through a general stress translation function. For a fixed number of design points, optimal Bayesian ALT plans are first obtained by solving constrained optimization problems under two different Bayesian design criteria. The global optimality of the resulting fixed-point optimal designs is then verified via the General Equivalence Theorem. This article also provides the optimized compromise ALT plans which are extremely useful in real-life applications. A detailed sensitivity analysis is then performed to find out the effect of various planning inputs on the resulting optimal Bayesian ALT plans. A simulation study is then conducted to visualize the resulting sampling variations from the optimal Bayesian ALT plans. Finally, this article considers a series system with dependent component lifetimes. Optimal ALT plans are obtained assuming a Gamma frailty model.     

Model Identification for Flow Simulations in Geothermal Reservoirs: Towards Optimally Drilling Boreholes

In geothermal reservoir engineering, one is interested in determining the location of boreholes such that measurements taken therein, say temperature, will allow the estimation of unknown parameters such as porosity and permeability. We formulate such a particular borehole location problem and find its solution by techniques from optimal experimental design. More precisely, we minimize the D-optimality criterion to find an optimal location of a single borehole to estimate hydraulic permeability from temperature measurements in two boreholes. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability criterion for synchronization of linearly coupled unified chaotic systems

This paper investigates the synchronization of two linearly coupled unified chaotic systems. A new stability criterion for asymptotic synchronization is attained using the Lyapunov stability theory and linear matrix inequality (LMI) approach. A numerical example is given to illuminate the design procedure and advantage of the result derived.     

Observability of continuous Petri nets with infinite server semantics

Timed continuous Petri net (contPN) systems with infinite server semantics are nonlinear systems, particularly a subclass of piecewise linear (PWL) systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and by measuring the marking of some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable modes is introduced which helps us in giving a necessary and sufficient criterion for the observability in infinitesimal time. Structural observability, i.e., observability for all possible values of firing rates of transitions, is studied and it is proved that in some cases it can be reduced to a linear problem, even if the system is nonlinear. Using results from linear structured systems, the concept of weak structural or generic observability is considered.     

Limit circle invariance for two differential systems on time scales

In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter λ. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value λ₀, then this property is preserved for all complex values λ. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non‐hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.     

Quadrature Methods for Bayesian Optimal Design of Experiments With Nonnormal Prior Distributions

Many optimal experimental designs depend on one or more unknown model parameters. In such cases, it is common to use Bayesian optimal design procedures to seek designs that perform well over an entire prior distribution of the unknown model parameter(s). Generally, Bayesian optimal design procedures are viewed as computationally intensive. This is because they require numerical integration techniques to approximate the Bayesian optimality criterion at hand. The most common numerical integration technique involves pseudo Monte Carlo draws from the prior distribution(s). For a good approximation of the Bayesian optimality criterion, a large number of pseudo Monte Carlo draws is required. This results in long computation times. As an alternative to the pseudo Monte Carlo approach, we propose using computationally efficient Gaussian quadrature techniques. Since, for normal prior distributions, suitable quadrature techniques have already been used in the context of optimal experimental design, we focus on quadrature techniques for nonnormal prior distributions. Such prior distributions are appropriate for variance components, correlation coefficients, and any other parameters that are strictly positive or have upper and lower bounds. In this article, we demonstrate the added value of the quadrature techniques we advocate by means of the Bayesian D-optimality criterion in the context of split-plot experiments, but we want to stress that the techniques can be applied to other optimality criteria and other types of experimental designs as well. Supplementary materials for this article are available online.     

Finding the K best policies in a finite-horizon Markov decision process

Directed hypergraphs represent a general modelling and algorithmic tool, which have been successfully used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic and transportation networks. However, modelling Markov decision processes using directed hypergraphs has not yet been considered.In this paper we consider finite-horizon Markov decision processes (MDPs) with finite state and action space and present an algorithm for finding the K best deterministic Markov policies. That is, we are interested in ranking the first K deterministic Markov policies in non-decreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finite-horizon MDP. It is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time, with respect to the input data representing the MDP, using different additive optimality criteria.     

The effect of cyclone inlet dimensions on the flow pattern and performance

The effect of the cyclone inlet dimensions on the performance and flow field pattern has been investigated computationally using the Reynolds stress turbulence model (RSM) for five cyclone separators. The results show that, the maximum tangential velocity in the cyclone decreases with increasing the cyclone inlet dimensions. No acceleration occurs in the cyclone space (the maximum tangential velocity is nearly constant throughout the cyclone). Increasing the cyclone inlet dimensions decreases the pressure drop. The cyclone cut-off diameter increases with increasing cyclone inlet dimension (consequently, the cyclone overall efficiency decreases due to weakness of the vortex strength). The effect of changing the inlet width is more significant than the inlet height especially for the cut-off diameter. The optimum ratio of inlet width to inlet height b/a is from 0.5 to 0.7.     

On a bi-stability regime and the existence of odd subharmonics in a Comb-drive MEMS model with cubic stiffness

In this paper we study two different problems. First we present a novel result about the existence of a family of odd subharmonics with prescribed nodal properties for a general nonlinear oscillator with bounded domain and symmetries. Then we apply the general existence result to the Comb-drive finger MEMS model with a cubic nonlinear stiffness term, and prove analytically that the odd positive subharmonic of order two is linearly stable whenever the AC load of the input voltage is small enough. Moreover, we demonstrate a bi-stability regime for this model because the trivial solution $x\equiv 0$ is also linearly stable. The general existence result was obtained through a generalization of the Ortega’s variational principle (Ortega, 2016), and the stability assertions were obtained by following the perturbation approach in Cen et al. (2020) for the linear stability of a nontrivial periodic solution that emanates from the autonomous problem, and the well-known Zukovskii criterion.     

Elastic-plastic states of a rotating inhomogeneously heated strain hardening hollow shaft

Based on Tresca's yield criterion and the flow rule associated with it, the behaviour of a linearly strain-hardening elastic-plastic hollow shaft subject to a positive radial temperature gradient and monotonously increasing angular speed is studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mobile WiMAX MAC and PHY layer optimization for IPTV

WiMAX (Worldwide Interoperability for Microwave Access) embodies the IEEE 802.16 family of standards that provision wireless broadband access. With the IEEE 802.16e?2005 mobility amendment, WiMAX promises to address the ever-increasing demand for mobile high speed wireless data in fourth-generation (4G) networks. WiMAX market studies continue to project increased subscriber growth rates and planned carrier trials worldwide. Coupled with these increasing growth rates and higher WiMAX throughput rates, bandwidth intensive video on demand (VoD), Internet Protocol TV (IPTV), and mobile TV services are emerging in the forefront of the mobile arena.In this paper, we explore and derive optimum system level WiMAX parameters by quantifying network performance using such video-rich services. The video traffic will sufficiently load and stress the network to exploit the potential bandwidth, delay, and mobility limitations. We use the OPNET Modeler to engineer simulation sequences and explore the impact of channel bandwidth, time division duplex (TDD) frame size, advanced antenna systems support, and retransmission schemes using four objective performance metrics while streaming a feature-length movie to a Mobile WiMAX subscriber. The objective of this paper is to provide greater insight into Mobile WiMAX system performance using emerging, load intensive and delay sensitive media streaming services.     

定数截尾恒定应力加速寿命试验的最优设计

本文讨论了在指数分布下K个应力情况满足条件（3．3）的恒加试验，并给出它的最优设计。     

Homothecy,bifurcations, continuity and monotonicity in timed continuous Petri nets under infinite server semantics

This work studies how equilibrium markings and throughputs change in Timed Continuous Petri Net (TCPN) systems as transition firing rates vary. In particular, it analyzes the bifurcations of the former, and the discontinuities and non-monotonicities of the latter; specifically, using structural objects of the net, such as P-semiflows, T-semiflows, and configurations, among others, the following properties can be obtained. For Join Free TCPN systems, a sufficient structural condition guaranteeing that the equilibrium markings do not bifurcate when firing rates vary, is derived. A dual result is obtained for Choice Free TCPN systems. For Mono-T-Semiflow TCPN systems, the equilibrium throughput is investigated; using a time-scale (a homothetic) property it is proven that a discontinuity of the equilibrium throughput implies its non-monotonicity, even if not evident at first glance. This is a connection of two timed behavioral properties of the equilibrium throughput. Moreover, a sufficient structural condition, parametrized by the equilibrium markings, ensures its continuity under firing rate variations. It is also proven that the monotonicity of the equilibrium throughput can be characterized by the previous structural condition. The convergence of the marking evolution of TCPN systems to its equilibrium markings is also discussed.     

The onset of mixed-mode intralaminar cracking in a cross-ply composite laminate

The intralaminar fracture toughness of a unidirectionally reinforced glass/epoxy composite is determined experimentally at several mode I and mode II loading ratios. The crack propagation criterion, expressed as a quadratic form in terms of single-mode stress intensity factors (alternatively, linear in terms of energy release rates), approximates the test results reasonably well. The mixed-mode cracking criterion obtained is used to predict the intralaminar crack on set in a cross-ply glass/epoxy composite under off-axis tensile loading. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 785–794, November–December, 2008.     

GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method

A Helmholtz equation in two dimensions discretized by a second order finite difference scheme is considered. Krylov methods such as Bi-CGSTAB and IDR(s) have been chosen as solvers. Since the convergence of the Krylov solvers deteriorates with increasing wave number, a shifted Laplace multigrid preconditioner is used to improve the convergence. The implementation of the preconditioned solver on CPU (Central Processing Unit) is compared to an implementation on GPU (Graphics Processing Units or graphics card) using CUDA (Compute Unified Device Architecture). The results show that preconditioned Bi-CGSTAB on GPU as well as preconditioned IDR(s) on GPU is about 30 times faster than on CPU for the same stopping criterion.     

A Criticality Criterion for Thermal Explosions in Well-stirred Systems with Reactant Consumption: Addendum

OUR attention has been drawn to the fact that the criticalitycondition ^* = 1 of Adler & Herbert (1985), for well-stirredreactive systems, has been derived previously (Gray, 1975).It arises from an examination of trajectories in the temperaturereactant phase plane when a tube stability argument is employed.Using the criterion ^* = 1, values of the critical Semenov numberhave also been obtained numerically (Gray & Jones, 1981). Our work on criticality for systems with reactant consumptioncame about by trying to reconcile the inflection criterion ofBoddington et al. (1983), for finite B, with the correspondingmaximum criterion in the limit B . Our contribution was to showthat the Semenov number versus maximum temperature ^* curvehas a bifurcation at ^* = 1 for all B. Both Gray's work and ourown are attempting to resolve the same problem; the approachesare, however, quite distinct and complement each other