Evolution systems of measures for stochastic flows

A new concept of an evolution system of measures for stochastic flows is considered. It corresponds to the notion of an invariant measure for random dynamical systems (or cocycles). The existence of evolution systems of measures for asymptotically compact stochastic flows is obtained. For a white noise stochastic flow, there exists a one to one correspondence between evolution systems of measures for a stochastic flow and evolution systems of measures for the associated Markov transition semigroup. As an application, an alternative approach for evolution systems of measures of 2D stochastic Navier–Stokes equations with a time-periodic forcing term is presented.     

Hybrid Subset Simulation method for reliability estimation of dynamical systems subject to stochastic excitation

A hybrid Subset Simulation approach is proposed for reliability estimation for general dynamical systems subject to stochastic excitation. This new stochastic simulation approach combines the advantages of the two previously proposed Subset Simulation methods, Subset Simulation with Markov Chain Monte Carlo (MCMC) algorithm and Subset Simulation with splitting. The new method employs the MCMC algorithm before reaching an intermediate failure level and splitting after reaching the level to exploit the causality of dynamical systems. The statistical properties of the failure probability estimators are derived. Two examples are presented to demonstrate the effectiveness of the new approach and to compare with the previous two Subset Simulation methods. The results show that the new method is robust to the choice of proposal distribution for the MCMC algorithm and to the intermediate failure events selected for Subset Simulation.     

Some aspects of chaotic and stochastic dynamics for structural systems

In this paper, the bifurcation behaviour of an externally excited four-dimensional nonlinear system is examined. Throughout this paper, a two-degree-of-freedom shallow arch structure under either a periodic or a stochastic excitation will be considered. For the case when the excitation is periodic, the local and global behaviour is examined in the presence of principalsubharmonic resonance and1:2 internal resonance. The method of averaging is used to obtain the first order approximation of the response of the system under resonant conditions. A standard Melnikov type perturbation method is used to show analytically that the system may exhibit chaotic dynamics in the sense of Smale horseshoe for the 1:2 internal resonance case in the absence of dissipation. In the case of stochastic excitation, the stability of the stationary solution is examined by determining themaximal Lyapunov exponent andmoment Lyapunov exponent in terms of system parameters. An asymptotic method is used to obtain explicit expressions for various exponents in the presence of weak dissipation and noise intensity. These quantities provide almost-sure stability boundaries in parameter space. When the system parameters lie outside these boundaries, it is essential to understand the nonlinear behaviour. The method of stochastic averaging is applied to obtain a set of approximate Itô equations which are then examined to describe the local bifurcation behaviour.     

Simulations and experiments of stochastic characteristics for collective short fatigue cracks in steels

ABSTRACT Stochastic characteristics prevail in the process of short fatigue crack progression. This paper presents a method taking into account the balance of crack number density to describe the stochastic behaviour of short crack collective evolution. The results from the simulation illustrate the stochastic development of short cracks. The experiments on two types of steels show the random distribution for collective short cracks with the number of cracks and the maximum crack length as a function of different locations on specimen surface. The experiments also give the variation of total number of short cracks with fatigue cycles. The test results are consistent with numerical simulations.     

Logical reconfiguration of reconfigurable manufacturing systems with stream of variations modelling: a stochastic two-stage programming and shortest path model

Designing flexible manufacturing systems in general, and flexible material handling system in particular, is a complex problem, typically approached through several stages. Here the focus is on the conceptual design stage during which valid approximation-based methods are needed. The segmented flow topology (SFT) AGV systems were developed to facilitate control of complex automated material handling systems. This paper introduces a decomposition method, directly derived from timed Petri nets (TPN) theories, to calculate the expected utilization of AGVs (as servers of SFT systems) and to derive simple operational decision rules leading to maximum system productivity at steady state, for a given deterministic routeing of discrete material through the manufacturing system.     

A financial model of flexible manufacturing systems planning under uncertainty: identification,valuation and applications of real options

Flexible manufacturing systems (FMS) have been considered to be essential for manufacturers to succeed in the uncertain market place. Flexibility typically comes at a price and is only valuable as a hedge against environmental uncertainty. It is important to determine an appropriate level of flexibility in the production system while considering the tradeoffs between its costs and benefits. This paper proposes to apply a real option theoretic approach to the modeling and analysis of various types of uncertainty involved in an FMS's operational environment. In comparison with financial options, real options in the context of an FMS, namely, production options, are identified and accordingly a pricing model for production options is proposed based on the option theory. Based on the valuation of production options, a general framework of flexibility planning is formulated. The real option approach surmounts traditional discounted cash flow analysis based valuation methods that tend to ignore the upside potentials to an investment from management flexibility. The proposed model is tested in a refrigerator company that deals with high product variety and uncertain demand.     

Models for automated storage and retrieval systems: a literature review

Automated Storage and Retrieval Systems (AS/RS) are warehousing systems that use mechanised devices to accomplish the repetitive tasks of storing and retrieving parts in racks. Since these systems represent a significant investment and considerable operating costs, their use must be as efficient as possible. AS/RS performance is the result of the interaction of many complex and stochastic subsystems. This reality creates a need for robust and efficient evaluation models. This article complements previous surveys on AS/RS by focusing on the particular research question addressed by each work and the associated assumptions used for the various models designed for evaluating AS/RS. Dynamic models based on simulation dominate the most recent literature; however, static approaches based on travel-time modelling have strongly contributed to the study of AS/RS. This review includes dynamic – simulation-based – models, but considers also steady-state (travel-time-based) models. We believe that this review may be of great help to researchers and industrial users in their search for the best modelling approach for a specific problem.     

Boltzmann, Lotka and Volterra and spatial structural evolution: an integrated methodology for some dynamical systems.

It is shown that Boltzmann's methods from statistical physics can be applied to a much wider range of systems, and in a variety of disciplines, than has been commonly recognized. A similar argument can be applied to the ecological models of Lotka and Volterra. Furthermore, it is shown that the two methodologies can be applied in combination to generate the Boltzmann, Lotka and Volterra (BLV) models. These techniques enable both spatial interaction and spatial structural evolution to be modelled, and it is argued that they potentially provide a much richer modelling methodology than that currently used in the analysis of 'scale-free' networks.     

An association model for mixtures containing any number of alkanes and any number of alcohols: Application to alcohol-alkane binary systems

A previously derived association model for mixtures of any number of alcohols and alkanes is applied here to alcohol-alkane binary systems. The model contains two adjustable parameters: a self-association constant for the alcohol and a parameter that reflects physical interactions. Correlations for the two parameters are presented which allow the model to be used as a two-, one-, or zero-parameter model, depending on the amount of experimental data available. All three forms of the model provide adequate results for these systems over a fairly wide temperature range.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Scheduling in production,supply chain and Industry 4.0 systems by optimal control: fundamentals,state-of-the-art and applications

This paper presents a survey on the applications of optimal control to scheduling in production, supply chain and Industry 4.0 systems with a focus on the deterministic maximum principle. The first objective is to derive major contributions, application areas, limitations, as well as research and application recommendations for the future research. The second objective is to explain control engineering models in terms of industrial engineering and production management. To achieve these objectives, optimal control models, qualitative methods of performance analysis and computational methods for optimal control are considered. We provide a brief historic overview and clarify major mathematical fundamentals whereby the control engineering terms are brought into correspondence with industrial engineering and management. The survey allows the grouping of models with only terminal constraints with application to master production scheduling, models with hybrid terminal–logical constraints with applications to short term job and flow shop scheduling, and hybrid structural–terminal–logical constraints with applications to customised assembly systems such as Industry 4.0. Computational algorithms in state, control and adjoint variable spaces are discussed.     

Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number.

Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R(0), provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R(0) for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R(0) were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R(0). The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate.     

Reliability performance of safety instrumented systems: A common approach for both low- and high-demand mode of operation

Safety instrumented systems (SISs) are usually divided into two modes of operation, low-demand and high-demand. Unfortunately, this classification is not easy to justify and the available formulas that are used to quantify the reliability performance in these two modes of operation are unable to capture combined effects of functional testing, spurious activations, and successful responses to demands. This article discusses some important modeling issues for SIS reliability performance quantification, and demonstrates their implementation in a Markov model. The accuracy of the Markov model for a simple case study of a pressure transmitter is verified through comparison with a scenario-based formula, and it is shown that the Markov approach gives a sufficiently accurate result for all demand rates, covering both low- and high-demand modes of operation.     

Human error risk management for engineering systems: a methodology for design, safety assessment, accident investigation and training

The objective of this paper is to tackle methodological issues associated with the inclusion of cognitive and dynamic considerations into Human Reliability methods. A methodology called Human Error Risk Management for Engineering Systems is presented that offers a ‘roadmap’ for selecting and consistently applying Human Factors approaches in different areas of application and contains also a ‘body’ of possible methods and techniques of its own. Two types of possible application are discussed to demonstrate practical applications of the methodology. Specific attention is dedicated to the issue of data collection and definition from specific field assessment.     

Robotics in order picking: evaluating warehouse layouts for pick,place, and transport vehicle routing systems

Motivated by recent technological advances in mobile robotics, this paper explores a novel approach for warehouse order picking. In particular, this work considers two types of commercially available mobile robots – one that can grasp items from a shelf (a picker) and another (a transporter) that can quickly deliver all items from the pick list to the packing station. A new vehicle routing problem is defined which seeks to minimise the time to deliver all items from a pick list to the packing station, a problem termed the pick, place, and transport vehicle routing problem. A mixed integer linear programming formulation is developed to answer three related research questions. First, what combination of picker and transport robots is required to obtain performance exceeding traditional human-based picking operations? Second, how should the composition of the robot fleet be altered to affect the greatest performance improvements? Finally, what are the impacts of warehouse layout designs when coordinated mobile robots are deployed? An extensive numerical analysis reveals that, (1) increasing the number of cross aisles decreases system performance; (2) centrally located packing stations improve system performance; and (3) the average distance from each pick location to the packing station and the average distance between pick locations are effective metrics for identifying specific fleet modifications that are likely to yield system improvements.     

Thermodynamic based comparison of sorption systems for cooling and heat pumping: Comparaison des performances thermodynamique des systèmes de pompes à chaleur à sorption dans des applications de refroidissement et de chauffage

A comparison of thermodynamic performances of sorption systems (liquid absorption, adsorption, ammonia salts and metal hydrides) is carried out for typical applications (deep-freezing, ice making, air-conditioning and heat pumping) with either air-cooled or water-cooled heat sink. The results are given in terms of cooling coefficient of performance (COP) (heating COP or coefficient of amplification (COA) for the heat pump), cooling (heating) power versus reactor volume or weight and thermodynamic efficiency. LiBr–water systems show the best results for air-conditioning except when small units are required (metal hydride systems lead to more compact units). Other systems, however, show better results for other applications (chemical reaction with ammonia salts for deep-freezing, adsorption for heat pumping).