Sampling-theory approach to eigenwavefronts of imaging systems

We present a direct method based on the sampling theorem for computing eigenwavefronts associated with linear space-invariant imaging systems (including aberrated imaging systems). A potential application of the eigenwavefronts to inverse problems in imaging is discussed. A noise-dependent measure for the information-carrying capacity of an imaging system is also proposed.     

Development of maintainability index for mechanical systems

A procedure based on a digraph and matrix method is developed for evaluation of maintainability index of mechanical systems. Features which characterize or ease in maintenance of a system are identified and are called the maintainability attributes. Consideration of these attributes and their interrelations are rudiment in evaluating the index. This is modeled in terms of a Maintainability Attributes Digraph for the system. Nodes in the digraph represent these attributes and their interrelations are represented by the edges. The digraph is represented by one-to-one matrix for development of a maintainability expression, which is characteristic of the system. A Variable Maintainability Attributes Facilitation Permanent Matrix is defined to develop maintainability expression (VPF-m) which is also useful in comparing two systems. Maintainability Index of the system is obtained from the permanent of the matrix or from the maintainability expression by substituting numerical values of the attributes and their interrelations. A higher value of the index implies good maintainability of the system. The ideal value of maintainability index (I_mi) is also obtained from the matrix expression, which is useful in assessing relative maintainability, I_r, of the system alternative. The procedure is useful in design and development of maintainable systems. A step by step procedure for evaluation of maintainability index is also suggested and is illustrated by means of an example.     

The dynamics of surge in compression systems

In air-compression systems, instabilities occur during operation close to their peak pressure-rise capability. However, the peak efficiency of a compression system lies close to this region of instability. A surge is a violent mode of instability where there is total breakdown of flow in the system and pressure-rise capability is lost drastically. Generally, all compression systems operate with a margin defined as the ‘surge margin’, and, consequently, system operational efficiency is lower. It is of interest to study compression-system surge to understand its dynamics in order to operate compression systems close to the instability for achieving high efficiency safely without encountering surge. Unsteady pressure data from a compression system, captured during surge oscillations, reveal many aspects of flow physics and are analysed to understand the surge dynamics of the system. A set of controlled experiments was conducted with a simple desktop experimental test set-up and essential aspects of surge dynamics have been characterised.     

Slow dynamics simulation of power systems

This paper investigates the simulation of slow dynamics in two-time-scale power systems. A new approach is proposed to obtain the slow dynamics by projecting the trajectory of the post-fault system onto its slow manifold. This is achieved by a nonlinear projection of the full order system initial condition onto the slow manifold, such that the fast intraarea dynamics are not excited. A projection scheme is developed and applied to two-test power systems.     

Serviceability of earthquake-damaged water systems: Effects of electrical power availability and power backup systems on system vulnerability

Civil infrastructure systems, such as water, electrical power, natural gas, and transportation systems, are essential to the smooth functioning of modern society. Because of their inter-connected nature, once one infrastructure system is damaged by an earthquake or other natural hazard, other infrastructure systems may malfunction as well. A number of previous studies have assessed vulnerability of infrastructure systems to earthquakes, but seldom have failures due to infrastructure system interactions been considered. In its assessment of the earthquake-induced damage of a municipal water system, this paper includes the impact of damage to the supporting electrical power system using a fault tree analysis and a shortest-path algorithm. The effect of uncertainty of seismic intensity and component fragility on network integrity is evaluated. A case study involving a simple model of the electrical power system and water system in Shelby County, TN, which includes the city of Memphis, demonstrates the importance of taking infrastructure interactions into account when evaluating the seismic vulnerability and risk to a networked system, as well as the utility of back-up power systems in electric power facilities.     

Isochronous dynamical systems

This is a terse review of recent results on isochronous dynamical systems, namely systems of (first-order, generally nonlinear) ordinary differential equations (ODEs) featuring an open set of initial data (which might coincide with the entire set of all initial data), from which emerge solutions all of which are completely periodic (i.e. periodic in all their components) with a fixed period (independent of the initial data, provided they are within the isochrony region). A leitmotif of this presentation is that 'isochronous systems are not rare'. Indeed, it is shown how any (autonomous) dynamical system can be modified or extended so that the new (also autonomous) system thereby obtained is isochronous with an arbitrarily assigned period T, while its dynamics, over time intervals much shorter than the period T, mimics closely that of the original system, or even, over an arbitrarily large fraction of its period T, coincides exactly with that of the original system. It is pointed out that this fact raises the issue of developing criteria providing, for a dynamical system, some kind of measure associated with a finite time scale of the complexity of its behaviour (while the current, standard definitions of integrable versus chaotic dynamical systems are related to the behaviour of a system over infinite time).     

Development of optical multipass matrix systems

Abstract

The basic principles of designing multipass matrix systems (MMSs) are considered. A promising version of the MMS providing complete stability of the exit image is discussed. The new matrix system is versatile and most suitable, due to its potentialities and optical properties, for use in laser spectroscopy. A multipass transferable gas analyser comprising this matrix system and non-cooled diode lasers enabled record (for instruments of this type) sensitivity values to be achieved. In particular, the threshold sensitivity to methane is 0.02 ppm and the long-time stability of the measurements is 0.1 ppm. Designs of small large-aperture four- and six-row matrix systems are depicted.     

Non-oscillatory damped multi-degree-of-freedom systems

Summary An analysis of the conditions under which a symmetric damped linear system does not oscillate is presented. A necessary and sufficient condition is formulated in terms of the definiteness of a Hankel's matrix whose elements depend on the coefficients of the characteristic polynomial of the system. From a practical point of view it is of interest to find conditions which are related in a simple way to the properties of the system matrices. Such previously developed criteria are indicated and compared, and a new sufficient condition for non-oscillation is derived. Results obtained for symmetric systems are then generalized to asymmetric and symmetrizable systems. Several examples are used to illustrate the validity and application of the presented criteria.     

Dynamics of adaptive optical systems

Dynamic (time) characteristics of adaptive systems are analyzed. A common adaptive system with a finite frequency band (or a finite response time) is described as a dynamic constant time-delay system, where time delay is to be much shorter than the time of coherence radius transfer through an optical beam by a mean wind speed. The questions of coherent beam formation are considered with use of the reference source. The analytical calculation of the Strehl parameter is made on basis of the generalized Huygens-Kirchhoff principle. An adaptive system is considered where the correcting phase is calculated with the use of both its derivatives and the signal, as well as adaptive systems using different time-predicting algorithms of the correcting signal for future time points. The use of a predicted phase front of the correcting wave allows much longer time delays. The stronger the phase distortions in the optical wave, the higher the time gain in comparison with common (with constant time delay) adaptive systems.     

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.     

Modeling an ensemble of systems coupled by the Lennard-Jones interaction

A system of oscillators forming a 2D lattice featuring the Lennard-Jones interaction, represented as a mathematically averaged ensemble of almost identical systems, is numerically modeled. The results show that an unstable configuration of oscillators can be retained over a greater time interval as compared to that for a single square lattice. A total energy of the system constructed as a mathematically averaged ensemble of almost identical systems is conserved up to the moment of losing stability and is not conserved after that, whereas the total energy of each system in the ensemble is conserved.     

On the selection of mass production systems

This paper is concerned with the comparison and selection of systems for the mass production, in particular the assembly, of complex discrete items. A possible procedure is proposed for system selection based upon (a) an examination of the feasibility of using certain basic system types in particular situations, (b) a comparison of feasible alternatives based upon certain quantifiable factors, and finally (c) a study of the non-quantifiable aspects of systems. Basic system types are listed, a detailed procedure is proposed for the quantitative analysis and some relevant non-quantifiable factors are identified.     

Reliability assessment of reliquefaction systems on LNG carriers

The paper gives an introduction to reliability assessment of reliquefaction systems for boil-off gas (BOG) on LNG carriers with focus on redundancy optimization and maintenance strategies. The reliability modeling is based on a time-dependent Markov approach. Four different system options are studied, with varying degree of redundancy. Failures in the reliquefaction system may require flaring of the BOG, and the associated cost is compared with the cost of introducing redundancy and the cost of onboard maintenance. A model for maintenance optimization is developed and exemplified on a main unit of the reliquefaction system. Reliability and maintenance cost data for reliquefaction systems on LNG ships are very scarce. The input data have been collected from the best available data sources and adjusted by expert judgement. A tailor-made computer program has been developed and may be supplied to interested readers.     

Framework for measuring complexity of aerospace systems

We propose a framework for measuring the complexity of aerospace systems and demonstrate its application. A measure that incorporates size, coupling, and modularity aspects of complexity is developed that emphasizes the importance of indirect coupling and feedback loops in the system. We demonstrate how hierarchical modular structure in the system reduces complexity and present an algorithm to decompose the system into modules. The measure is tested and found to be scalable for large-scale systems involving thousands of components and interactions (typical in modern aerospace systems). We investigate the sensitivity of the measure and demonstrate the ability of the framework to identify incorrectness in system representation. The merits of the framework are exemplified through a case study comparing three spacecraft. The framework provides the designer with three key capabilities that can positively influence the aerospace (or other) design process: the ability to identify complex subsystems, the ability to classify misrepresentations, and the ability to trade-off commercially of the shelf (COTS) and non-COTS components.     

Optimization of photovoltaic measurement systems

A comparative analysis of the most promising photovoltaic systems for the measurement of linear and angular quantities is presented. It is shown that by means of such a comparison it becomes possible to optimize a measurement system with respect to individual elements and converters as well as with respect to circuit designs so as to increase the performance and precision characteristics.     

Production reliability in flexible manufacturing systems

A typical flexible manufacturing system, Westland Helicopters' sheet metal detail manufacturing complex, has been analysed for reliability. The techniques of fault tree analysis and event tree analysis are presented and their applicability to this study investigated. Event tree analysis has been found to be a more effective method for analysing manufacturing systems. The failure states of the system have been identified from the construction of an event tree which considers random hardware faults that influence production. Failure rate data have been used to quantify the critical production failure states in terms of machine failures. Estimates are made of the system's MTTF and percentage availability using typical MTTR figures. The probability that a selected production route fails to complete the manufacture of a set of parts is also evaluated. A dependency of systems reliability on the production demand has been discovered, and a possible method for modelling and assessing the reliability of systems capable of producing several products is proposed.     

Risk-based analysis of manufacturing systems

A manufacturing system considered here consists of a machine that processes parts and an automatic conveyor that transports immediately a finished part to an assembly cell (i.e. a single workstation facility is examined). The system can hold a maximum number of processed parts on the conveyor, which determines its size. Modelling the system as a family of Birth–Death Processes with finite size in equilibrium, indexed by the system utilisation parameter, and depending on the concepts of system information and system entropy (i.e. mean information), we promote a risk-based analysis of manufacturing systems. The current number of processed parts on the conveyor determines the system particular states. The performance measures of a system are: risk (i.e. uncertainty) of the system (represented by system entropy), throughput of the system, utilisation of the machine, utilisation of the conveyor, and information range of the system. They are simultaneously investigated with respect to the system utilisation parameter, in order for an optimal trade-off among them to be established. This analysis is illustrated on the information linear, Erlang, Binomial and Pascal held manufacturing systems. Regarding the managerial insights, a use case of a system target output is considered, comparing the above system types. This approach can also be used for analysis of an assembly line consisting of multiple machines that have different operation times and buffers between them.     

Hamilton's principle for systems of changing mass

Summary An extended form of Hamilton's principle is developed for systems whose constituent particles change with time. By a suitable choice of system boundary it is demonstrated that in some cases stationary forms of the principle are possible. A simple example is considered.     

Nonstationary equivalent linearization of nonlinear continuous systems

This paper presents a technique for obtaining the nonstationary stochastic response of a nonlinear continuous system. The method of equivalent linearization is generalized to continuous systems subjected to nonstationary random excitation. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. A numerical implementation is also described. In this procedure, the linear replacement system is discretized by the finite element method. Application to systems satisfying the one-dimensional wave equation with a constitutive nonlinearity is discussed. Results are presented for nonlinear stress-strain laws of a strain-hardening type.     

Describing functions for nonlinear optical systems

The concept of describing functions is useful for analyzing and designing nonlinear systems. A proposal for using the idea of describing functions for studying the behavior of a nonlinear optical processing system is given. The describing function can be used in the same way that a coherent transfer function or optical transfer function is used to characterize linear, shift-invariant optical processors. Two coherent optical systems for measuring the magnitude of the describing function of nonlinear optical processors are suggested.