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.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Environmental indifference? A critique of environmentally deterministic theories of peatland archaeological site construction in Ireland

Climate change, whether gradual or sudden, has frequently been invoked as a causal factor to explain many aspects of cultural change during the prehistoric and early historic periods. Critiquing such theories has often proven difficult, not least because of the imprecise dating of many aspects of the palaeoclimate or archaeological records and the difficulties of merging the two strands of research. Here we consider one example of the archaeological record – peatland site construction in Ireland – which has previously been interpreted in terms of social response to climate change and examine whether close scrutiny of the archaeological and palaeoenvironmental records uphold the climatically deterministic hypotheses. We evaluate evidence for phasing in the temporal distribution of trackways and related sites in Irish peatlands, of which more than 3,500 examples have been recorded, through the examination of ~350 dendrochronological and 14C dates from these structures. The role of climate change in influencing when such sites were constructed is assessed by comparing visually and statistically the frequency of sites over the last 4,500 years with well-dated, multi-proxy climate reconstructions from Irish peatlands. We demonstrate that national patterns of “peatland activity” exist that indicate that the construction of sites in bogs was neither a constant nor random phenomenon. Phases of activity (i.e. periods in which the number of structures increased), as well as the ‘lulls’ that separate them, show no consistent correlation with periods of wetter or drier conditions on the bogs, suggesting that the impetus for the start or cessation of such activity was not climatically-determined. We propose that trigger(s) for peatland site construction in Ireland must instead also be sought within the wider, contemporary social background. Perhaps not surprisingly, a comparison with archaeological and palynological evidence shows that peatland activity tends to occur at times of more expansive settlement and land-use, suggesting that the bogs were used when the landscape was being more widely occupied. Interestingly, the lulls in peatland site construction coincide with transitional points between nominal archaeological phases, typically defined on the basis of their material culture, implying that there may indeed have been a cultural discontinuity at these times. © 2012 Elsevier Ltd. All rights reserved.

Relative role of deterministic and stochastic determinants of soil animal community: a spatially explicit analysis of oribatid mites

1. Ecologists are debating the relative role of deterministic and stochastic determinants of community structure. Although the high diversity and strong spatial structure of soil animal assemblages could provide ecologists with an ideal ecological scenario, surprisingly little information is available on these assemblages.
2. We studied species-rich soil oribatid mite assemblages from a Mediterranean beech forest and a grassland. We applied multivariate regression approaches and analysed spatial autocorrelation at multiple spatial scales using Moran's eigenvectors. Results were used to partition community variance in terms of the amount of variation uniquely accounted for by environmental correlates (e.g. organic matter) and geographical position. Estimated neutral diversity and immigration parameters were also applied to a soil animal group for the first time to simulate patterns of community dissimilarity expected under neutrality, thereby testing neutral predictions.
3. After accounting for spatial autocorrelation, the correlation between community structure and key environmental parameters disappeared: about 40% of community variation consisted of spatial patterns independent of measured environmental variables such as organic matter. Environmentally independent spatial patterns encompassed the entire range of scales accounted for by the sampling design (from tens of cm to 100 m). This spatial variation could be due to either unmeasured but spatially structured variables or stochastic drift mediated by dispersal. Observed levels of community dissimilarity were significantly different from those predicted by neutral models.
4. Oribatid mite assemblages are dominated by processes involving both deterministic and stochastic components and operating at multiple scales. Spatial patterns independent of the measured environmental variables are a prominent feature of the targeted assemblages, but patterns of community dissimilarity do not match neutral predictions. This suggests that either niche-mediated competition or environmental filtering or both are contributing to the core structure of the community. This study indicates new lines of investigation for understanding the mechanisms that determine the signature of the deterministic component of animal community assembly.

Stochastic and deterministic processes interact in the assembly of desert microbial communities on a global scale

Extreme arid regions in the worlds' major deserts are typified by quartz pavement terrain. Cryptic hypolithic communities colonize the ventral surface of quartz rocks and this habitat is characterized by a relative lack of environmental and trophic complexity. Combined with readily identifiable major environmental stressors this provides a tractable model system for determining the relative role of stochastic and deterministic drivers in community assembly. Through analyzing an original, worldwide data set of 16S rRNA-gene defined bacterial communities from the most extreme deserts on the Earth, we show that functional assemblages within the communities were subject to different assembly influences. Null models applied to the photosynthetic assemblage revealed that stochastic processes exerted most effect on the assemblage, although the level of community dissimilarity varied between continents in a manner not always consistent with neutral models. The heterotrophic assemblages displayed signatures of niche processes across four continents, whereas in other cases they conformed to neutral predictions. Importantly, for continents where neutrality was either rejected or accepted, assembly drivers differed between the two functional groups. This study demonstrates that multi-trophic microbial systems may not be fully described by a single set of niche or neutral assembly rules and that stochasticity is likely a major determinant of such systems, with significant variation in the influence of these determinants on a global scale.

Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.