Fault-tree analysis for system design, development, modification,and verification

A methodology that uses fault-tree analysis (FTA) techniques to assess the weaknesses of a new chemical/process design at any time during system development is presented. FTA provides a cost-effective means of improving or verifying the reliability and efficiency of chemical/process design. It evaluates the consequences of conceivable failure to indicate where improvements are justified. FTA techniques were used to model the failure modes of an existing control-room heating, ventilation, and air-conditioning (HVAC) system of a large production facility. The fault-tree reduction revealed 129 single-, 434 double-, and 442 triple-failure combinations, any of which could cause system failure. Single failures and double failures consisting of an equipment malfunction and an operator failure error were targeted for design and/or procedural modifications. These modifications were then incorporated into the operating system design to enhance system availability. In an iterative fashion, FTA techniques were reapplied to the modified design and used to verify the adequacy of the proposed revisions prior to implementation. This resulted in a thorough review of system vulnerabilities and a clear understanding of how to correct them     

An inspection model with minimal and major maintenance for a systemwith deterioration and Poisson failures

A new condition-based maintenance model for a system, subject to deterioration-failures and to Poisson-failures, is presented. After an inspection, based on the degree of deterioration, a minimal maintenance or a major maintenance is performed, or no action is taken. Deterioration failures are restored by major repair; Poisson failures are restored by minimal repair. Major maintenance or major repair restores the system to “good as new” while minimal maintenance restores the system one stage. Generalized stochastic Petri Nets are used to represent and analyze the model, which represents a condition-based maintenance strategy. Based on maximization of the system throughput, an optimal inspection policy within this strategy and optimal inter-inspection time are obtained. The effects of inspection, maintenance and repair parameters are investigated. For a given inspection parameter, a 3-region diagram identifies the effectiveness of an inspection policy based on minimal maintenance, major maintenance, and major repair parameters     

High-speed digital signal processing and control

An attempt is made to organize and survey recent work, and to present it in a unified and accessible form. The need for a new approach suitable for high-speed processing is discussed in the context of several applications in control and communications, and a historical perspective of the use of difference operators in numerical analysis is presented. The general systems calculus, based on divided-different operators is introduced to unify the continuous-time and discrete-time systems theories. This calculus is then used as a framework to treat the three problems of system state estimation; system identification and time-series modeling; and control system design. Realization aspects of algorithms based on the difference operator representation, including such issues as coefficient rounding and implementation with standard hardware, are also discussed     

Imaging and PDA analysis of a GDI spray in the near-nozzle region

This paper describes a combined LDA, PDA and imaging analysis of the pressure swirl spray in the near-nozzle region of a GDI injector. This innovative approach in the use of multiple, complementary diagnostics facilitates the interpretation of a complex spray flow field.The LDA and PDA data were ensemble-averaged into time bins to produce comprehensive time-history and spatial profiles of liquid velocity, droplet velocity and size and the sample number. They indicated times at which the spray exhibited seven different characteristics. These were identified as: (a) pre-swirl spray, (b) spray cone develops, (c) spray cone relaxes, (d) maximum velocity in spray cone, (e) fully developed steady state, (f) spray cone collapses and (g) the spray detaches from the nozzle. The most effective method to present the spatial and temporal development of the spray was to superimpose the velocity vector and drop size field plots onto the spray images.This article is part of the special issue 11^th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisboa, Portugal, July 2002, January 2004, Vol. 36, Issue no. 1     

An infinitary polynomial Hales-Jewett theorem

A joint extension of H. Furstenberg’s central sets theorem, the Hales-Jewett coloring theorem and the polynomial van der Waerden theorem of V. Bergelson and A. Leibman is obtained by an elaboration on Furstenberg and Y. Katznelson’s approach to infinitary Ramsey theory via the enveloping semigroup.     

Orbits of parabolic subgroups on metabelian ideals

Let k be an algebraically closed field, t∈Z?1, and let B be the Borel subgroup of GLt(k) consisting of upper-triangular matrices. Let Q be a parabolic subgroup of GLt(k) that contains B and such that the Lie algebra qu of the unipotent radical of Q is metabelian, i.e. the derived subalgebra of qu is abelian. For a dimension vector with , we obtain a parabolic subgroup P(d) of GLn(k) from B by taking upper-triangular block matrices with (i,j) block of size di×dj. In a similar manner we obtain a parabolic subgroup Q(d) of GLn(k) from Q. We determine all instances when P(d) acts on qu(d) with a finite number of orbits for all dimension vectors d. Our methods use a translation of the problem into the representation theory of certain quasi-hereditary algebras. In the finite cases, we use Auslander-Reiten theory to explicitly determine the P(d)-orbits; this also allows us to determine the degenerations of P(d)-orbits.     

Parabolic conjugacy in general linear groups

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL _n (q). We show that the number of P(q)-conjugacy classes in GL _n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006)     

The structure of harmonizable isotropic random fields

The class of harmonizable processes and fields are a natural extension of the class of stationary processes and fields. Random fields admit an additional property called isotropy. The classical spectral and covariance representations for stationary isotropic random fields are extended to the harmonizable isotropic case. A classification of these fields is obtained based upon the smoothness properties of their covariances. In contrast to the stationary case, it is also shown that there exist non-trivial harmonizable isotropic fields which satisfy the Laplace operator in the L ²-sense