Optimal Energy Dissipation in Sliding Friction Simulations

Non-equilibrium molecular dynamics simulations, of crucial importance in sliding friction, are hampered by arbitrariness and uncertainties in the removal of the frictionally generated Joule heat. Building upon general pre-existing formulation, we implement a fully microscopic dissipation approach which, based on a parameter-free, non-Markovian, stochastic dynamics, absorbs Joule heat equivalently to a semi-infinite solid and harmonic substrate. As a test case, we investigate the stick-slip friction of a slider over a two-dimensional Lennard-Jones solid, comparing our virtually exact frictional results with approximate ones from commonly adopted dissipation schemes. Remarkably, the exact results can be closely reproduced by a standard Langevin dissipation scheme, once its parameters are determined according to a general and self-standing variational procedure

Analytical Results for a Single-Unit System Subject To Markovian Wear and Shocks

This thesis develops and analyzers a mathematical model for the reliability measures of a single-unit system subject to continuous wear due to its operating environment and randomly occurring shocks that inflict a random amount of damage to the unit. Assuming a Markovian operating environment and shock arrival mechanism, Laplace-Stieltjes transform expressions are obtained for the failure time distribution and all of its moments. Moreover, an analytical expression is derived for the long-run availability of the single-unit system when it is subject to an inspect-and-replace maintenance policy. The analytical results are illustrated, and their results compared with those of Monte Carlo-simulated failure data. The numerical results indicate that the reliability measures may be accurately computed via numerical inversion of the transform expressions in a straightforward manner when the input parameters are known a priori. In stark contrast to the simulation model which requires several hours to obtain the reliability measures, the analytical procedure computes the same measures in only a few seconds

The latent state hazard model, with application to wind turbine reliability

We present a new model for reliability analysis that is able to distinguish the latent internal vulnerability state of the equipment from the vulnerability caused by temporary external sources. Consider a wind farm where each turbine is running under the external effects of temperature, wind speed and direction, etc. The turbine might fail because of the external effects of a spike in temperature. If it does not fail during the temperature spike, it could still fail due to internal degradation, and the spike could cause (or be an indication of) this degradation. The ability to identify the underlying latent state can help better understand the effects of external sources and thus lead to more robust decision-making. We present an experimental study using SCADA sensor measurements from wind turbines in Italy.Comment: Published at http://dx.doi.org/10.1214/15-AOAS859 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Overview of Remaining Useful Life prediction techniques in Through-life Engineering Services

Through-life Engineering Services (TES) are essential in the manufacture and servicing of complex engineering products. TES improves support services by providing prognosis of run-to-failure and time-to-failure on-demand data for better decision making. The concept of Remaining Useful Life (RUL) is utilised to predict life-span of components (of a service system) with the purpose of minimising catastrophic failure events in both manufacturing and service sectors. The purpose of this paper is to identify failure mechanisms and emphasise the failure events prediction approaches that can effectively reduce uncertainties. It will demonstrate the classification of techniques used in RUL prediction for optimisation of products’ future use based on current products in-service with regards to predictability, availability and reliability. It presents a mapping of degradation mechanisms against techniques for knowledge acquisition with the objective of presenting to designers and manufacturers ways to improve the life-span of components

Optimal Periodic Inspection of a Stochastically Degrading System

This thesis develops and analyzes a procedure to determine the optimal inspection interval that maximizes the limiting average availability of a stochastically degrading component operating in a randomly evolving environment. The component is inspected periodically, and if the total observed cumulative degradation exceeds a fixed threshold value, the component is instantly replaced with a new, statistically identical component. Degradation is due to a combination of continuous wear caused by the component\u27s random operating environment, as well as damage due to randomly occurring shocks of random magnitude. In order to compute an optimal inspection interval and corresponding limiting average availability, a nonlinear program is formulated and solved using a direct search algorithm in conjunction with numerical Laplace transform inversion. Techniques are developed to significantly decrease the time required to compute the approximate optimal solutions. The mathematical programming formulation and solution techniques are illustrated through a series of increasingly complex example problems

A General Approach to the Stochastic Rotation Problem with Amenity Valuation

This paper presents a new approach to study the optimal rotation policy with amenity valuation under uncertainty. We first postulate the stochastic forest value and assume plausibly that monetary value of amenities is a continuous and non-negative function of forest value thus presenting the trade-off between timber revenues and amenity values. Second, instead of using a dynamic programming approach, we derive a recursive representation of the total forest value and solve the optimal rotation threshold by applying ordinary non-linear programming techniques. Third, we characterize under certain set of conditions how the properties of both the expected cumulative value and the expected marginal cumulative value, accrued from amenity services, depend on the precise nature of the monetary valuation of amenities and what is the impact of volatility on these concepts. Finally, we illustrate our results explicitly in models based on logistic growth by focusing on the role of amenity valuation and volatility of forest value in the determination of Wicksellian and Faustmannian thresholds. Our theoretical and numerical findings emphasize the crucial importance of the nature of amenity valuation for the impact of higher volatility of forest value on the rotation thresholds.amenity valuation, optimal Faustmannian and Wicksellian rotation policy, stochatic impulse control

Hybrid Stochastic Models for Remaining Lifetime Prognosis

The United States Air Force is developing its next generation aircraft and is seeking to reduce the risk of catastrophic failures, maintenance activities, and the logistics footprint while improving its sortie generation rate through a process called autonomic logistics. Vital to the successful implementation of this process is remaining lifetime prognosis of critical aircraft components. Complicating this problem is the absence of failure time information; however, sensors located on the aircraft are providing degradation measures. This research has provided a method to address at least a portion of this problem by uniting analytical lifetime distribution models with environment and/or degradation measures to obtain the remaining lifetime distribution

Age Replacement and Service Rate Control of Stochastically Degrading Queues

This thesis considers the problem of optimally selecting a periodic replacement time for a multiserver queueing system in which each server is subject to degradation as a function of the mean service rate and a stochastic and dynamic environment. Also considered is the problem of optimal service rate selection for such a system. In both cases, the performance metric is the long-run average cost rate. Analytical expressions are obtained, in terms of Laplace transforms, for the nonlinear objective functions, necessitating the use of numerical Laplace transform inversion to evaluate candidate solutions in conjunction with standard numerical algorithms. Due to the convexity of the objective function, the optimal replacement time is computed using a hybrid bisection-secant method which yields globally optimal solutions. The optimal service rates are obtained via gradient search methods but are only guaranteed to provide locally optimal solutions. The analytical results are implemented on three notional examples that demonstrate the benefits of dynamically adjusting service rates under the described maintenance policy

Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail