Sensitivity analysis of initial value problems with mixed odes and algebraic equations

An efficient method is described for sensitivity analysis of nonlinear initial value problems, which may include algebraic equations as well as ordinary differential equations.The linearity of the sensitivity equations is utilized to solve them directly via the local Jacobian of the state equations. The method is implemented with the implicit integrator DASSL and is demonstrated on a stiff industrial reaction model.     

Optimal tool replacement with asymmetric quadratic loss

In this paper, an analysis of a tool replacement problem with asymmetric quadratic loss function is presented. The expected average cost per unit time is derived and it is shown that the optimal initial setting and the optimal replacement time can be found by solving two nonlinear equations. The paper generalizes and improves on previous work in the area.     

The E3 architecture: enabling future cellular networks with cognitive and self‐x capabilities

Future mobile networks are expected to be complex heterogeneous systems. On the one hand this will enable users to take advantage of a number of different access technologies. On the other hand it will seriously affect network management procedures since more extensive operations and decisions will have to be dealt with. To tackle these challenges a number of new dynamic mechanisms need to be designed. It is imperative that certain network management tasks have to be performed without human intervention to reduce the OPEX costs and achieve faster responses in different events. To achieve this goal, the introduction of self‐x functionalities, combined with cognitive mechanisms and the ability to reconfigure network entities and terminals, is required. Moreover, the introduction of a new pilot channel needs to be considered to assist the terminals in selecting the most suitable radio access technology according to their requirements. We present the functional architecture of an evolved network that was designed in the context of the EU‐funded IP project ‘E³: End‐to‐End Efficiency’. This architecture aims to enhance existing procedures usually performed in traditional operation and maintenance systems (e.g. spectrum management, network planning, configuration actions). We explain the rationale of our design and provide specific examples to illustrate the role of the different functional entities and their interfaces. A considerable part of this architecture has recently been approved as a feasibility study by the ETSI Committee Reconfigurable Radio System. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal Bayesian maintenance policy for a gearbox subject to two dependent failure modes

Most maintenance optimization models of gear systems have considered single failure mode. There have been very few papers dealing with multiple failure modes, considering mostly independent failure modes. In this paper, we present an optimal Bayesian control scheme for early fault detection of the gear system with dependent competing risks. The system failures include degradation failure and catastrophic failure. A three‐state continuous‐time–homogeneous hidden Markov model (HMM), namely the model with unobservable healthy and unhealthy states, and an observable failure state, describes the deterioration process of the gear system. The condition monitoring information as well as the age of the system are considered in the proposed optimal Bayesian maintenance policy. The objective is to maximize the long‐run expected average system availability per unit time. The maintenance optimization model is formulated and solved in a semi‐Markov decision process (SMDP) framework. The posterior probability that the system is in the warning state is used for the residual life estimation and Bayesian control chart development. The prediction results show that the mean residual lives obtained in this paper are much closer to the actual values than previously published results. A comparison with the Bayesian control chart based on the previously published HMM and the age‐based replacement policy is given to illustrate the superiority of the proposed approach. The results demonstrate that the Bayesian control scheme with two dependent failure modes can detect the gear fault earlier and improve the availability of the system.     

Maximum Likelihood Estimation for a Hidden Semi‐Markov Model with Multivariate Observations

In this paper, a parameter estimation procedure for a condition‐based maintenance model under partial observations is presented. The deterioration process of the partially observable system is modeled as a continuous‐time homogeneous semi‐Markov process. The system can be in a healthy or unhealthy operational state, or in a failure state, and the sojourn time in the operational state follows a phase‐type distribution. Only the failure state is observable, whereas operational states are unobservable. Vector observations that are stochastically related to the system state are collected at equidistant sampling times. The objective is to determine maximum likelihood estimates of the model parameters using the Expectation–Maximization (EM) algorithm. We derive explicit formulae for both the pseudo likelihood function and the parameter updates in each iteration of the EM algorithm. A numerical example is developed to illustrate the efficiency of the estimation procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Availability maximization under partial observations

In this paper, we propose a new model for availability maximization under partial observations for maintenance applications. Compared with the widely studied cost minimization models, few structural results are known about the form of the optimal control policy for availability maximization models. We consider a failing system with unobservable operational states. Only the failure state is observable. System deterioration is driven by an unobservable, continuous-time homogeneous Markov process. Multivariate condition monitoring data which is stochastically related to the unobservable state of the system is collected at equidistant sampling epochs and is used to update the posterior state distribution for decision making. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The objective is to determine the form of the optimal control policy that maximizes the long-run expected average availability per unit time. We formulate the problem as an optimal stopping problem with partial information. Under standard assumptions, we prove that a control limit policy is optimal. A computational algorithm is developed, illustrated by numerical results.     

Scheduling of the optimal tool replacement times in a flexible manufacturing system

In Flexible Manufacturing Systems (FMSs). a cutting tool is frequently used for different operations and on different part types to minimize tool change-overs and the number of tools required, and to increase part-routing flexibility. In such situations, the tools become shared resources and work in job-dependent, changeable and nonhomogeneous conditions. It is well known that the tool failure rate depends on both age and machining conditions and that tool reliability is a function of the duration, machining conditions, and the sequence of the operations in FMS. The objective of this paper is to obtain a schedule of the optimal preventive replacement times for the cutting tools over a finite time horizon in a flexible manufacturing system. We assume that the tool will be replaced either upon failure during an operation or preventively after the completion of each operation, incurring different replacement costs. A standard stochastic dynamic programming approach is taken to obtain the optimal tool replacement times. The optimal schedule is obtained by minimizing the total expected cost over a finite time horizon for a given sequence of operations. A computational algorithm is developed and a numerical example is given to demonstrate the procedure.