Modelling the probability assessment of system state prognosis using available condition monitoring information

^** Email: w.wang{at}salford.ac.uk This paper reports on a model to assess the current and futurestates of a monitored system based on measured condition monitoringinformation to date. The true state of the system is unobservable,but is assumed to be related to the measured condition monitoringinformation in a stochastic way. We further assume that thetransition of the system state follows a time-dependent Markovchain which has only three states, namely good, defective andfailed. This assumption effectively defines a two-stage failureprocess which is widely used in delay time modelling of maintainedsystems. Three modelling techniques are used to establish themodel. First, we use a hidden Markov model to describe the transitionsbetween system states. Second, the transition matrix is establishedbased on the well-known delay time concept. The last one isthe use of the filtering technique to construct the relationshipbetween measured condition information and the underlying truestate of the system. We also discuss the procedure for modelparameter estimation. A numerical example is presented to demonstratethe modelling ideas.     

The dialectics of analytical and synthetic approaches

The intention of this work is to show the differences and similarities between the analytical and synthetic approaches. The exposition is organized in the form of a dialectical discussion centered around the problem of pollution generated by the wastes of a petrochemical complex.     

A relationship between three analytical approaches to nonlinear problems

In this work, the relationship between three analytical techniques is demonstrated. The direct relationship between the variational approach (VA) and the Hamiltonian approach (HA) is illustrated for a first approximation, and subsequently the relationship between the variational approach and the harmonic balance method (HBM) is concluded. Moreover, the relationship between HA and VA is investigated for higher order solutions.     

Combining approaches for evaluating auditing populations: A simulation study

This research explores ways of combining four distinct bounds for the mean error in an auditing population. Two competing objectives for a bound are to be close to the true mean being estimated and to be reliable: not less than the true mean in more than 5% of estimations. The optimal combination should provide the best balance of these competing objectives. Estimating the mean error by a single approach is difficult because typically most accounts have no error and the distribution of the errors among those that do is discontinuous and highly skewed. This study reveals that the weights in the optimal combination are not constant but depend on the characteristic of the population being estimated. The optimally combined bound is only 7% smaller overall than the best of the constituents. However, while the best of the constituents fails in 50% of most challenging populations, the optimal combination never fails.     

Modeling and simulation of magnetorheological elastomers: A comparison of continuum and dipole approaches

In the present work, a comparison of the results of a microscale continuum and a dipolar mean-field approach with regard to their predictions for the magnetostrictive response of magnetorheological elastomers is presented. It turns out that – for random, isotropic microstructures – there is a very good agreement between both modeling strategies. This is in contrast to former comparisons of continuum and other dipole approaches, which have shown considerable deviations. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.     

Thermomigration in Sn-Pb solder bumps: Modelling and simulation

It is well known a homogeneous binary alloy subjected to a temperature gradient will become inhomogeneous. This decomposition phenomenon is called thermomigration or thermotransport or Soret effect, which is a cross-effect in irreversible processes between heat conduction and atomic diffusion. In the present contribution we focus on a diffuse interface model for separation processes affected by temperature gradients coupled with a heat diffusion equation in order to describe thermomigration effects caused by joule-heating. To be specific, we focus on phase separation in solder bumps consisting of tin and lead. Therefore we discuss the modelling of a Gibbs' configurational free energy density as well as the modelling of the chemical mobility, mobility of thermotransport and Dufour coefficient as sufficiently smooth functions in particle concentration and absolute temperature. The resulting set of partial differential equations involves spatial derivatives of fourth order. Consequently, the variational formulation of the problem mandates approximation functions which are at least C¹-continuous. In order to fulfill this requirement a B-Spline based finite element scheme is provided. One of the main advantages of B-Splines is the possibility to represent complex geometries exactly. However, it has been shown that especially curved B-Spline geometries can not be treated in a straight forward manner in finite element analysis. For this reason we demonstrate the implementation of boundary conditions to avoid the arising numerical perturbations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fixed point theorem involving a hybrid inwardness-contraction condition

A fixed point theorem is proved which involves a hybrid inwardness-contraction condition and simultaneously extends three earlier results of NADLER, CLARKE and REICH, respectively. The aim of this paper is to prove a fixed point theorem which will simultaneously extends three earlier results of NADLER [5], CLARKE [2], and REICH [7], respectively.     

A hybrid neuro-fuzzy analytical approach to mode choice of global logistics management

This paper presents a hybrid neuro-fuzzy methodology to identify appropriate global logistics (GL) operational modes used for global supply chain management. The proposed methodological framework includes three main developmental phases: (1) establishment of a GL strategic hierarchy, (2) formulation of GL-mode identification rules, and (3) development of a GL-mode choice model. By integrating advanced multi-criteria decision-making (MCDM) techniques including fuzzy analytical hierarchy process (Fuzzy-AHP), Fuzzy-MCDM, and the technique for order preference by similarity to an ideal solution (TOPSIS), six types of global logistics and operational modes coupled with corresponding fuzzy-based multi-criteria decision-making rules are specified in the second phase. Using the specified fuzzy decision-making rules as the input database, an adaptive neuro-fuzzy inference system (ANFIS) is then developed in the third phase to identify proper GL modes for the implementation of global supply chain management. A numerical study with a questionnaire survey database aimed at the information technology (IT) industries of Taiwan is conducted to illustrate the applicability of the proposed method.     

A necessary and sufficient condition for differentiability of integrals of random measures in Rn over n-dimensional intervals

Translated from Matematicheskie Zametki, Vol. 49, No. 4, pp. 63–68, April, 1991.     

A state space condition monitoring model for furnace erosion prediction and replacement

The paper develops a replacement action decision aid for a key furnace component subject to condition monitoring. A state space model is used to predict the erosion condition of the inductors in an induction furnace in which a measure of the conductance ratio (CR) is used to indirectly assess the relative condition of the inductors, and to guide replacement decisions. This study seeks to improve on this decision process by establishing the relationship between CR and the erosion condition of the inductors. To establish such a relationship, a state space model has been established and the system parameters estimated from CR data. A replacement cost model to balance at any time costly replacements with possible catastrophic failure is also proposed based upon the predicted probability of inductor erosion conditional upon all available information. The well known Kalman filter is employed to derive the predicted and updated probability of inductor erosion level conditional upon CR data to date. This is the first time the condition monitoring decision process has been modelled for real plant based upon filtering theory. The model fits the data well, gives a sensible answer to the actual problem, and is transferable to other condition monitoring contexts. Possible extensions are discussed in the paper.     

A flexible approach to the simulation of hybrid multibody systems

The present works deals with the incorporation of both flexible beam and shell structures into the realm of flexible multibody dynamics. Geometrically exact beam formulations based on classical Simo-Reissner kinematics are suitable for modelling beam-type flexible components in the context of finite-deformation multibody dynamics. So geometrically exact shell formulations are based on Reissner-Mindlin kinematics. In [2], a flexible framework for dealing with flexible structural elements in a multibody context is described. A specific isoparametric finite element discretization of a shell formulation leads to semi-discrete equations of motions assuming the form of differential-algebraic equations (DAEs). A compatible isoparametric formulation of beams has already been developed in [1]. The uniform DAE framework makes possible the incorporation of alternative finite element formulations. In addition to that, various time-stepping schemes such as energy-momentum methods or variational integrators can be applied. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On confidence intervals from simulation of finite Markov chains

Consider a finite state irreducible Markov reward chain. It is shown that there exist simulation estimates and confidence intervals for the expected first passage times and rewards as well as the expected average reward, with 100% coverage probability. The length of the confidence intervals converges to zero with probability one as the sample size increases; it also satisfies a large deviations property.     

SimHPN: A MATLAB toolbox for simulation, analysis and design with hybrid Petri nets

This paper presents a MATLAB embedded package for hybrid Petri nets called SimHPN. It offers a collection of tools devoted to simulation, analysis and synthesis of dynamical systems modeled by hybrid Petri nets. The package supports several server semantics for the firing of both, discrete and continuous, types of transitions. Besides providing different simulation options, SimHPN offers the possibility of computing steady state throughput bounds for continuous nets. For such a class of nets, optimal control and observability algorithms are also implemented. The package is fully integrated in MATLAB which allows the creation of powerful algebraic, statistical and graphical instruments that exploit the routines available in MATLAB.     

Modelling and simulation of bicable ropeways under cross-wind influence

Improvements of safety standards of ropeways are crucial in order to ensure a high level of operational reliability and safety. In this context, the question of cross-wind stability of ropeways is of particular concern. The real cross-inclination of the gondola and its correlation to wind speed and direction on an operating ropeway are of great interest for ropeway manufacturers and responsible authorities as well as for ropeway operators. As presented in this paper, a mathematical model for simulation was developed in order to gain a better understanding of the cross-wind behaviour of bicable ropeways. This model was established for a numerical dynamic simulation of the movement of gondolas with stiff connections, ‘hanger-cabins’, due to arbitrary cross-wind loads acting at a section of the studied span of the ropeway. All equations were solved using the program MATLAB® and the toolbox SIMULINK®. In addition, the results of a simulation of a real ropeway are presented.     

Modelling and simulation of steam turbine processes: individual models for individual tasks

Within power plants, several physical, chemical and mechanical processes are conducted to transfer the energy, stored in fossil fuel, into electrical energy. This energy conversion is divided into several stages. Hitherto, the largest conventional power plants employ steam turbines as prime movers to drive a generator. Hence, a steam turbine is one module to convert heat energy into mechanical energy. And thus it is one link in the chain of energy conversions with the aim of generating electrical energy. Today, steam turbine industry faces numerous challenges concerning efficiency, commissioning time, start-up times, operation, availability, safety, cost-effectiveness, etc. Many of these tasks can be supported by simulating the transient operational behaviour of the turbine in advance. For example, the commissioning time can be shortened if the turbine controllers are initialized with well-tuned pre-set parameters; cost-effectiveness can be increased by setting aside unnecessary devices and exactly determining material specifications; safety may be increased by predicting the impacts of failures and thus taking the necessary precautions. Different tasks require different details regarding the employed turbine simulation model. Thus, the turbine controller may be well tuned with less complex simulation models of turbine, generator and electrical grid, whereas detailed studies of failures, mainly the transient behaviour which may lead to serious damages, may require detailed modelling of the turbine-internal thermodynamic processes. Here, a brief overview of models which simulate the transient thermodynamic behaviour of a steam turbine is presented. Three different approaches will be introduced and compared with respect to different operating situations. Also, special attention is directed towards the time dependence of critical states, mainly turbine speed and pressure development in certain areas. The first model is based on a simple, linear approach and is suitable of giving a quick overview. The second one incorporates more details and is useful if the operating point is close to the design point. Finally, the last model incorporates mass and energy balances as well as the major non-linearities. Hence it depicts the turbine behaviour over a large range of operating points.     

On analytical and numerical approaches to division and label structured population models

Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.     

A computational study of hybrid approaches of metaheuristic algorithms for the cell formation problem

In this paper we solve the 0–1 cell formation problem where the number of cells is fixed a priori and where the objective is to maximize the overall efficiency of a production system by grouping together machines providing service to similar parts into a subsystem (denoted cell). Three different methods are introduced and compared numerically. The first local search method is an implementation of simulated annealing (SA) where the definition of the neighbourhood is specific to the application and requires using a diversification and intensification strategies. The second local search method is an adaptive simulated annealing method where the neighbourhood is selected randomly at each iteration. The procedure is adaptive in the sense that the probability of selecting a neighbourhood is updated during the process. The third method is a hybrid method (HM) of a population-based method and a local search method. To improve the solution obtained with HM, we apply a SA method afterward. The best variants are very efficient to solve the 35 benchmark problems commonly used in the literature.     

Modelling a Viennese ballroom: agent-based simulation to investigate complex behaviour

ABSTRACT

Dancing Viennese Waltz in one of the great historic ballrooms is an important and indispensable part of Austrian culture. This dance, while being tradition, is quite difficult to perform, especially if the dance-floor is crowded. There, it is additionally challenging to avoid collisions with other dancers, as they pace through the ballroom at a high velocity. Dependent on the dancer’s skill level, spinning speed can be adjusted to succeed. This paper presents an agent-based waltz model which makes it possible to investigate the influence of heterogeneously skilled dancers on the movement smoothness of the dancing crowd. Herein, each agent represents one dancing couple in reality and it moves on the dance-floor by a rotatory motion with periodically switching rotation axes. Interaction between agents occurs via inelastic collisions. By performing a couple of case studies, we analyse and quantify the widespread rumour that the presence of only a few unskilled dancers disturbs the flow of the dancing crowd.