装备维修规划的多目标优化模型和求解算法

为有效地刻画和求解军事装备系统的维修规划问题,建立了一个以维修费用和任务能力为目标的约束优化模型,提出了一种求解装备维修规划问题的多目标禁忌搜索算法。模型考虑了维修器材和工时两种费用指标,并在数质量评估的基础上通过二次回归方程来分层评估装备系统的任务能力指标。算法采用两阶段搜索策略,第一阶段从维修数量下限出发,以任务能力为演化目标进行搜索,直至找到一个可行解;第二阶段以任务能力/维修费用比为演化目标进行搜索,不断改善整个非支配解集。实验表明,算法能够求解型号≥500种,数量≥45000的大规模问题,模型和算法求解的质量也在实际应用中得到了验证。

Study on reactive extrusion processes of block copolymer

The anionic copolymerization process of styrene-buradiene (S/B) block copolymer in a closely intermeshing co-rotating twin screw extruder with butyl-lithium initiator was studied. According to the anionic copolymerization mechanism and the reactive extrusion characteristics, the mathematical models of monomer conversion, average molecular weight and fluid viscosity during the anionic copolymerization of S/B were constructed, and then the reactive extrusion process was simulated by means of the finite volume method and the uncoupled semi-implicit iterative algorithm. Finally, the influence of the feeding mixture composition on conversion was discussed. The simulated results were nearly in agreement with the experimental results.

螺旋桨驱动UUV推进系统研究

为了实现水下机器人(UUV,Unmanned Underwater Vehicle)的高精度控制,深入研究了螺旋桨驱动UUV推进系统各个环节运行机理,并建立了它们各自的数学模型,包括PWM模块、直流永磁电机、螺旋桨、舵的数学模型。多功能仿真试验和湖试试验的系统响应曲线基本吻合,一方面表明本文建立的推进系统模型的正确性,另一方面体现了在多功能仿真平台上调试的控制策略和控制器参数具有很大的可信度。

西峰油田特低渗透油藏渗流机理及开发对策研究

Micro-pore-throat, micro-fracture and low permeability are the most obvious characters of Xifeng ultra-low permeability reservoir, and threshold pressure gradient and medium deformation during the period of oilfield developing results non-linear seepage feature of the formation liquid flowing in the porous medium underground. It is impossible to solve some problems in the ultra-low permeability reservoir development by current Darcy filtration theory and development techniques. In the view of the characters of ultra-low permeability and powerful-diagenesis and fracture up-growth, the paper quantitatively characterizes of through-going scope for reservoir parameters together with some materials such as similarity field outcrop, rock core, drilling, well logging and production dynamic, which provides geological base for further development adjustment. Based on the displacement experiment of different kinds of seepage fluid and oil-water two phases, this paper proves the relationship between threshold pressure gradient and formation permeability in experiment and theory, which is power function and its index is about -1. The variation rule and the mechanism of oil-water two phases threshold pressure gradient are studied. At the same time, based on the experiment of medium deformation, the variation rule of formation physical property parameters and the deformation mechanism are researched, and the influential factors on the medium deformation are analyzed systematically. With elastic unsteady filtration theory, nonlinear mathematical models of the steady and unsteady flow of single phase as well as horizontal well flow and oil-water two phases flow are deduced with the influence of nonlinear factors including threshold pressure gradient and media deformation. The influences of nonlinear factors upon well deliverability and reservoir pressure distribution as well as the saturation variation pattern of oil-water front are analyzed. By means of the researches such as reasonable well pattern, reasonable well array ration, artificial fracture length optimization advisable water flood timing and feasibility of advanced water flooding, it is necessary to find out effective techniques in order to improve development result of this kind of reservoir. This research result develops and improves on low-velocity nonlinear seepage theory, and offers ways to study similar kind of reservoir; it is meaningful to the development of the ultra-low permeability oil and gas reservoir.

油藏动态模型和剩余油分布模式

This paper belong to national "973" technological project undertaken by Shengli Oilfield. Work area is composed of turbidite reservoir of S212 and delta reservoir of S283 of Sheng2 unit in Shengtuo Oilfield that has a 36 years water injection development history. Change of the macroscopic, microscopic and filterational parameters and its mechanism have been studied in the 4 water-cut stages i.e. the primary, moderate, high and supper-high stage by using multi-disciplinary theories and approaches, computer techniques and physical simulation comprehensively. Dynamic reservoir models to different water-cut stages have been established. The study of forming mechanism and distribution of residual oil revealed the main types and spatial distribution of residual oil in different water-cut stages and the distribution mode has also been built up. Macroscopic, microscopic and filterational parameters selecting principle, optimizing and selecting standard, matching standard and laws and related database of various dynamic parameters in different water-cut stages have been established, which laid good basis for revealing reservoir macroscopic, microscopic and filterational parameters' dynamic change and residual oil distribution. The study indicated that in general, the macroscopic, microscopic and filterational parameters will slowly increase and become better in both shallow turbidite and delta reservoirs with the increasing of water cut, but different reservoirs have their own characteristics and change laws. Parameters of I~2 unit, whose petrophysical properties are better, increase more quickly than 8~3, whose petrophysical properties are more unfavorable. The changes was relatively quickly in high water-cut stage, while relatively slowly from primary to moderate and from high to supper-high water-cut stage. This paper firstly put forward that reservoir macroscopic, microscopic and filterational parameters are controlled by dynamic geological function of reservoir fluid, which is considered the major reason of reservoir parameters' dynamic changes and residual oil formation and distribution during reservoir development. Physical simulation of filterational parameters verified that forming mechanism and distribution of residual oil in different water-cut stages are also controlled by dynamic geological function of reservoir fluid. The idea of fluid geological function during reservoir development developed the theory of development geology, and has important practical values. This paper firstly constructed dynamic geological and mathematical models and five modes of residual oil distribution in Shengtuo Oilfield, and achieved four-dimensional forecast of residual oil distribution in different watercut stages. Dynamic changes and mechanism of macroscopic, microscopic and fliterational parameters of reservoir and their change process have been revealed. Forecast of residual oil distribution has been achieved by computers. This paper established the related theories, approaches and techniques for residual oil study, characterization and in different water-cut stages, and realized dynamic forecast of residual oil. It gained remarkable economic benefit and social effect in guiding field development. These theories and techniques had important meaningfulness for residual oil prediction in the terrestrial faulted basins not only in Shengli Oilfield but also in the east of China. Furthermore, this study has developed the theory of development geology.

花岗岩风化土微观结构及其工程地质特性研究

Saprolite is the residual soil resulted from completely weathered or highly weathered granite and with corestones of parent rock. It is widely distributed in Hong Kong. Slope instability usually happens in this layer of residual soil and thus it is very important to study the engineering geological properties of Saprolite. Due to the relic granitic texture, the deformation and strength characteristics of Saprolite are very different from normal residual soils. In order to investigate the effects of the special microstructure on soil deformation and strength, a series of physical, chemical and mechanical tests were conducted on Saprolite at Kowloon, Hong Kong. The tests include chemical analysis, particle size analysis, mineral composition analysis, mercury injection, consolidation test, direct shear test, triaxial shear test, optical analysis, SEM & TEM analysis, and triaxial shear tests under real-time CT monitoring.Based on the testing results, intensity and degree of weathering were classified, factors affecting and controlling the deformation and strength of Saprolite were identified, and the interaction between those factors were analyzed.The major parameters describing soil microstructure were introduced mainly based on optical thin section analysis results. These parameters are of importance and physical meaning to describe particle shape, particle size distribution (PSD), and for numerical modeling of soil microstructure. A few parameters to depict particle geometry were proposed or improved. These parameters can be used to regenerate the particle shape and its distribution. Fractal dimension of particle shape was proposed to describe irregularity of particle shapes and capacity of space filling quantitatively. And the effect of fractal dimension of particle shape on soil strength was analyzed. At the same time, structural coefficient - a combined parameter which can quantify the overall microstructure of rock or soil was introduced to study Saprolite and the results are very positive. The study emphasized on the fractal characteristics of PSD and pore structure by applying fractal theory and method. With the results from thin section analysis and mercury injection, it was shown that at least two fractal dimensions Dfl(DB) and Df2 (Dw), exist for both PSD and pore structure. The reasons and physical meanings behind multi-fractal dimensions were analyzed. The fractal dimensions were used to calculate the formation depth and weathering rate of granite at Kowloon. As practical applications, correlations and mathematical models for fractal dimensions and engineering properties of soil were established. The correlation between fractal dimensions and mechanical properties of soil shows that the internal friction angle is mainly governed by Dfl 9 corresponding to coarse grain components, while the cohesion depends on Df2 , corresponding to fine grain components. The correlations between the fractal dimension, friction angle and cohesion are positive linear.Fractal models of PSD and pore size distribution were derived theoretically. Fragmentation mechanism of grains was also analyzed from the viewpoint of fractal. A simple function was derived to define the theoretical relationship between the water characteristic curve (WCC) and fractal dimension, based on a number of classical WCC models. This relationship provides a new analytical tool and research method for hydraulic properties in porous media and solute transportation. It also endues fractal dimensions with new physical meanings and facilitates applications of fractal dimensions in water retention characteristics, ground water movement, and environmental engineering.Based on the conclusions from the fractal characteristics of Saprolite, size effect on strength was expressed by fractal dimension. This function is in complete agreement with classical Weibull model and a simple function was derived to represent the relationship between them.In this thesis, the phenomenon of multi-fractal dimensions was theoretically analyzed and verified with WCC and saprolite PSD results, it was then concluded that multi-fractal can describe the characteristics of one object more accurately, compared to single fractal dimension. The multi-fractal of saprolite reflects its structural heterogeneity and changeable stress environment during the evolution history.

Insight into permeability of protein through microcapsule membranes

The objective of this paper is to analyze the characteristics of protein permeability in alainate-polylysine-alginate (APA) and alginate-chitosan-alginate (ACA) microcapsules by mathematical models based on the balance of chemical potential. The comparison between calculated results and experimental data shows that the models can describe the process of protein diffusion from microcapsule and protein release into microcapsule successfully. The influences of membrane composition on the permeability of ACA microcapsule have been investigated and analyzed. The effect of resistance on the mass transfer is further analyzed theoretically with the aid of mathematical modeling. (c) 2005 Elsevier B.V. All rights reserved.

Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Analysing energy detector diversity receivers for spectrum sensing

The analysis of energy detector systems is a well studied topic in the literature: numerous models have been derived describing the behaviour of single and multiple antenna architectures operating in a variety of radio environments. However, in many cases of interest, these models are not in a closed form and so their evaluation requires the use of numerical methods. In general, these are computationally expensive, which can cause difficulties in certain scenarios, such as in the optimisation of device parameters on low cost hardware. The problem becomes acute in situations where the signal to noise ratio is small and reliable detection is to be ensured or where the number of samples of the received signal is large. Furthermore, due to the analytic complexity of the models, further insight into the behaviour of various system parameters of interest is not readily apparent. In this thesis, an approximation based approach is taken towards the analysis of such systems. By focusing on the situations where exact analyses become complicated, and making a small number of astute simplifications to the underlying mathematical models, it is possible to derive novel, accurate and compact descriptions of system behaviour. Approximations are derived for the analysis of energy detectors with single and multiple antennae operating on additive white Gaussian noise (AWGN) and independent and identically distributed Rayleigh, Nakagami-m and Rice channels; in the multiple antenna case, approximations are derived for systems with maximal ratio combiner (MRC), equal gain combiner (EGC) and square law combiner (SLC) diversity. In each case, error bounds are derived describing the maximum error resulting from the use of the approximations. In addition, it is demonstrated that the derived approximations require fewer computations of simple functions than any of the exact models available in the literature. Consequently, the regions of applicability of the approximations directly complement the regions of applicability of the available exact models. Further novel approximations for other system parameters of interest, such as sample complexity, minimum detectable signal to noise ratio and diversity gain, are also derived. In the course of the analysis, a novel theorem describing the convergence of the chi square, noncentral chi square and gamma distributions towards the normal distribution is derived. The theorem describes a tight upper bound on the error resulting from the application of the central limit theorem to random variables of the aforementioned distributions and gives a much better description of the resulting error than existing Berry-Esseen type bounds. A second novel theorem, providing an upper bound on the maximum error resulting from the use of the central limit theorem to approximate the noncentral chi square distribution where the noncentrality parameter is a multiple of the number of degrees of freedom, is also derived.

Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems

Spatially periodic vegetation patterns are well known in arid and semi-arid regions around the world. Mathematical models have been developed that attribute this phenomenon to a symmetry-breaking instability. Such models are based on the interplay between competitive and facilitative influences that the vegetation exerts on its own dynamics when it is constrained by arid conditions, but evidence for these predictions is still lacking. Moreover, not all models can account for the development of regularly spaced spots of bare ground in the absence of a soil prepattern. We applied Fourier analysis to high-resolution, remotely sensed data taken at either end of a 40-year interval in southern Niger. Statistical comparisons based on this textural characterization gave us broad-scale evidence that the decrease in rainfall over recent decades in the sub-Saharan Sahel has been accompanied by a detectable shift from homogeneous vegetation cover to spotted patterns marked by a spatial frequency of about 20 cycles km-1. Wood cutting and grazing by domestic animals have led to a much more marked transition in unprotected areas than in a protected reserve. Field measurements demonstrated that the dominant spatial frequency was endogenous rather than reflecting the spatial variation of any pre-existing heterogeneity in soil properties. All these results support the use of models that can account for periodic vegetation patterns without invoking substrate heterogeneity or anisotropy, and provide new elements for further developments, refinements and tests. This study underlines the potential of studying vegetation pattern properties for monitoring climatic and human impacts on the extensive fragile areas bordering hot deserts. Explicit consideration of vegetation self-patterning may also improve our understanding of vegetation and climate interactions in arid areas. © 2006 The Authors.

HPV clearance and the neglected role of stochasticity.

Clearance of anogenital and oropharyngeal HPV infections is attributed primarily to a successful adaptive immune response. To date, little attention has been paid to the potential role of stochastic cell dynamics in the time it takes to clear an HPV infection. In this study, we combine mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism. Our results suggest that chance-in form of the stochastic dynamics of basal stem cells-plays a critical role in the elimination of HPV-infected cell clones. In particular, we find that in immunocompetent adolescents with cervical HPV infections, the immune response may contribute less than 20% to virus clearance-the rest is taken care of by the stochastic proliferation dynamics in the basal layer. In HIV-negative individuals, the contribution of the immune response may be negligible.

A population model of folate-mediated one-carbon metabolism.

BACKGROUND: Previous mathematical models for hepatic and tissue one-carbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites that can be measured in the plasma are related to their respective intracellular concentrations. METHODS: The model consists of a set of ordinary differential equations, one for each metabolite in each compartment, and kinetic equations for metabolism and for transport between compartments. The model was validated by comparison to a variety of experimental data such as the methionine load test and variation in folate intake. We further extended this model by introducing random and systematic variation in enzyme activity. OUTCOMES AND CONCLUSIONS: A database of 10,000 virtual individuals was generated, each with a quantitatively different one-carbon metabolism. Our population has distributions of folate and homocysteine in the plasma and tissues that are similar to those found in the NHANES data. The model reproduces many other sets of clinical data. We show that tissue and plasma folate is highly correlated, but liver and plasma folate much less so. Oxidative stress increases the plasma S-adenosylmethionine/S-adenosylhomocysteine (SAM/SAH) ratio. We show that many relationships among variables are nonlinear and in many cases we provide explanations. Sampling of subpopulations produces dramatically different apparent associations among variables. The model can be used to simulate populations with polymorphisms in genes for folate metabolism and variations in dietary input.

Modelling of industrial multi-physics processes—a key role for computational mechanics.

In the analysis of industrial processes, there is an increasing emphasis on systems governed by interacting continuum phenomena. Mathematical models of such multi-physics processes can only be achieved for practical simulations through computational solution procedures—computational mechanics. Examples of such multi-physics systems in the context of metals processing are used to explore some of the key issues. Finite-volume methods on unstructured meshes are proposed as a means to achieve efficient rapid solutions to such systems. Issues associated with the software design, the exploitation of high performance computers, and the concept of the virtual computational-mechanics modelling laboratory are also addressed in this context.

AASK - Aircraft accident statistics and knowledge: A database of human experience in evacuation, derived from aviation accident reports

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in aviation safety. However such models have a heavy dependency on real evacuation data in order to (a) identify the key processes and factors associated with evacuation, (b) quantify variables and parameters associated with the identified factors/processes and finally (c) validate the models. The Fire Safety Engineering Group of the University of Greenwich is undertaking a large data extraction exercise from three major data sources in order to address these issues. This paper describes the extraction and application of data from one of these sources - aviation accident reports. To aid in the storage and analysis of the raw data, a computer database known as AASK (aircraft accident statistics and knowledge) is under development. AASK is being developed to store human observational and anecdotal data contained in accident reports and interview transcripts. AASK comprises four component sub-databases. These consist of the ACCIDENT (crash details), FLIGHT ATTENDANT (observations and actions of the flight attendants), FATALS (details concerning passenger fatalities) and PAX (observations and accounts from individual passengers) databases. AASK currently contains information from 25 survivable aviation accidents covering the period 4 April 1977 to 6 August 1995, involving some 2415 passengers, 2210 survivors, 205 fatalities and accounts from 669 people. In addition to aiding the development of aircraft evacuation models, AASK is also being used to challenge some of the myths which proliferate in the aviation safety industry such as, passenger exit selection during evacuation, nature and frequency of seat jumping, speed of passenger response and group dynamics. AASK can also be used to aid in the development of a more comprehensive approach to conducting post accident interviews, and will eventually be used to store the data directly.