Modelling, control and supervision for a class of hybrid systems

The aim of this thesis is to narrow the gap between two different control techniques: the continuous control and the discrete event control techniques DES. This gap can be reduced by the study of Hybrid systems, and by interpreting as Hybrid systems the majority of large-scale systems. In particular, when looking deeply into a process, it is often possible to identify interaction between discrete and continuous signals. Hybrid systems are systems that have both continuous, and discrete signals. Continuous signals are generally supposed continuous and differentiable in time, since discrete signals are neither continuous nor differentiable in time due to their abrupt changes in time. Continuous signals often represent the measure of natural physical magnitudes such as temperature, pressure etc. The discrete signals are normally artificial signals, operated by human artefacts as current, voltage, light etc. Typical processes modelled as Hybrid systems are production systems, chemical process, or continuos production when time and continuous measures interacts with the transport, and stock inventory system. Complex systems as manufacturing lines are hybrid in a global sense. They can be decomposed into several subsystems, and their links. Another motivation for the study of Hybrid systems is the tools developed by other research domains. These tools benefit from the use of temporal logic for the analysis of several properties of Hybrid systems model, and use it to design systems and controllers, which satisfies physical or imposed restrictions. This thesis is focused in particular types of systems with discrete and continuous signals in interaction. That can be modelled hard non-linealities, such as hysteresis, jumps in the state, limit cycles, etc. and their possible non-deterministic future behaviour expressed by an interpretable model description. The Hybrid systems treated in this work are systems with several discrete states, always less than thirty states (it can arrive to NP hard problem), and continuous dynamics evolving with expression: with Ki ¡ Rn constant vectors or matrices for X components vector. In several states the continuous evolution can be several of them Ki = 0. In this formulation, the mathematics can express Time invariant linear system. By the use of this expression for a local part, the combination of several local linear models is possible to represent non-linear systems. And with the interaction with discrete events of the system the model can compose non-linear Hybrid systems. Especially multistage processes with high continuous dynamics are well represented by the proposed methodology. Sate vectors with more than two components, as third order models or higher is well approximated by the proposed approximation. Flexible belt transmission, chemical reactions with initial start-up and mobile robots with important friction are several physical systems, which profits from the benefits of proposed methodology (accuracy). The motivation of this thesis is to obtain a solution that can control and drive the Hybrid systems from the origin or starting point to the goal. How to obtain this solution, and which is the best solution in terms of one cost function subject to the physical restrictions and control actions is analysed. Hybrid systems that have several possible states, different ways to drive the system to the goal and different continuous control signals are problems that motivate this research. The requirements of the system on which we work is: a model that can represent the behaviour of the non-linear systems, and that possibilities the prediction of possible future behaviour for the model, in order to apply an supervisor which decides the optimal and secure action to drive the system toward the goal. Specific problems can be determined by the use of this kind of hybrid models are: - The unity of order. - Control the system along a reachable path. - Control the system in a safe path. - Optimise the cost function. - Modularity of control The proposed model solves the specified problems in the switching models problem, the initial condition calculus and the unity of the order models. Continuous and discrete phenomena are represented in Linear hybrid models, defined with defined eighth-tuple parameters to model different types of hybrid phenomena. Applying a transformation over the state vector : for LTI system we obtain from a two-dimensional SS a single parameter, alpha, which still maintains the dynamical information. Combining this parameter with the system output, a complete description of the system is obtained in a form of a graph in polar representation. Using Tagaki-Sugeno type III is a fuzzy model which include linear time invariant LTI models for each local model, the fuzzyfication of different LTI local model gives as a result a non-linear time invariant model. In our case the output and the alpha measure govern the membership function. Hybrid systems control is a huge task, the processes need to be guided from the Starting point to the desired End point, passing a through of different specific states and points in the trajectory. The system can be structured in different levels of abstraction and the control in three layers for the Hybrid systems from planning the process to produce the actions, these are the planning, the process and control layer. In this case the algorithms will be applied to robotics ¡V a domain where improvements are well accepted ¡V it is expected to find a simple repetitive processes for which the extra effort in complexity can be compensated by some cost reductions. It may be also interesting to implement some control optimisation to processes such as fuel injection, DC-DC converters etc. In order to apply the RW theory of discrete event systems on a Hybrid system, we must abstract the continuous signals and to project the events generated for these signals, to obtain new sets of observable and controllable events. Ramadge & Wonham¡¦s theory along with the TCT software give a Controllable Sublanguage of the legal language generated for a Discrete Event System (DES). Continuous abstraction transforms predicates over continuous variables into controllable or uncontrollable events, and modifies the set of uncontrollable, controllable observable and unobservable events. Continuous signals produce into the system virtual events, when this crosses the bound limits. If this event is deterministic, they can be projected. It is necessary to determine the controllability of this event, in order to assign this to the corresponding set, , controllable, uncontrollable, observable and unobservable set of events. Find optimal trajectories in order to minimise some cost function is the goal of the modelling procedure. Mathematical model for the system allows the user to apply mathematical techniques over this expression. These possibilities are, to minimise a specific cost function, to obtain optimal controllers and to approximate a specific trajectory. The combination of the Dynamic Programming with Bellman Principle of optimality, give us the procedure to solve the minimum time trajectory for Hybrid systems. The problem is greater when there exists interaction between adjacent states. In Hybrid systems the problem is to determine the partial set points to be applied at the local models. Optimal controller can be implemented in each local model in order to assure the minimisation of the local costs. The solution of this problem needs to give us the trajectory to follow the system. Trajectory marked by a set of set points to force the system to passing over them. Several ways are possible to drive the system from the Starting point Xi to the End point Xf. Different ways are interesting in: dynamic sense, minimum states, approximation at set points, etc. These ways need to be safe and viable and RchW. And only one of them must to be applied, normally the best, which minimises the proposed cost function. A Reachable Way, this means the controllable way and safe, will be evaluated in order to obtain which one minimises the cost function. Contribution of this work is a complete framework to work with the majority Hybrid systems, the procedures to model, control and supervise are defined and explained and its use is demonstrated. Also explained is the procedure to model the systems to be analysed for automatic verification. Great improvements were obtained by using this methodology in comparison to using other piecewise linear approximations. It is demonstrated in particular cases this methodology can provide best approximation. The most important contribution of this work, is the Alpha approximation for non-linear systems with high dynamics While this kind of process is not typical, but in this case the Alpha approximation is the best linear approximation to use, and give a compact representation.

Modelling the global coastal ocean

Shelf and coastal seas are regions of exceptionally high biological productivity, high rates of biogeochemical cycling and immense socio-economic importance. They are, however, poorly represented by the present generation of Earth system models, both in terms of resolution and process representation. Hence, these models cannot be used to elucidate the role of the coastal ocean in global biogeochemical cycles and the effects global change (both direct anthropogenic and climatic) are having on them. Here, we present a system for simulating all the coastal regions around the world (the Global Coastal Ocean Modelling System) in a systematic and practical fashion. It is based on automatically generating multiple nested model domains, using the Proudman Oceanographic Laboratory Coastal Ocean Modelling System coupled to the European Regional Seas Ecosystem Model. Preliminary results from the system are presented. These demonstrate the viability of the concept, and we discuss the prospects for using the system to explore key areas of global change in shelf seas, such as their role in the carbon cycle and climate change effects on fisheries.

Modelling the hydraulics of the Carlisle 2005 flood event

The performance of a 2D numerical model of flood hydraulics is tested for a major event in Carlisle, UK, in 2005. This event is associated with a unique data set, with GPS surveyed wrack lines and flood extent surveyed 3 weeks after the flood. The Simple Finite Volume (SFV) model is used to solve the 2D Saint-Venant equations over an unstructured mesh of 30000 elements representing channel and floodplain, and allowing detailed hydraulics of flow around bridge piers and other influential features to be represented. The SFV model is also used to corroborate flows recorded for the event at two gauging stations. Calibration of Manning's n is performed with a two stage strategy, with channel values determined by calibration of the gauging station models, and floodplain values determined by optimising the fit between model results and observed water levels and flood extent for the 2005 event. RMS error for the calibrated model compared with surveyed water levels is ~±0.4m, the same order of magnitude as the estimated error in the survey data. The study demonstrates the ability of unstructured mesh hydraulic models to represent important hydraulic processes across a range of scales, with potential applications to flood risk management.

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km2), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R 2) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.

Transport and distribution of lindane and simazine in a riverine environment: measurements in bed sediments and modelling

Aquatic sediments often remove hydrophobic contaminants from fresh waters. The subsequent distribution and concentration of contaminants in bed sediments determines their effect on benthic organisms and the risk of re-entry into the water and/or leaching to groundwater. This study examines the transport of simazine and lindane in aquatic bed sediments with the aim of understanding the processes that determine their depth distribution. Experiments in flume channels (water flow of 10 cm s(-1)) determined the persistence of the compounds in the absence of sediment with (a) de-ionised water and (b) a solution that had been in contact with river sediment. In further experiments with river bed sediments in light and dark conditions, measurements were made of the concentration of the compounds in the overlying water and the development of bacterial/algal biofilms and bioturbation activity. At the end of the experiments, concentrations in sediments and associated pore waters were determined in sections of the sediment at 1 mm resolution down to 5 mm and then at 10 mm resolution to 50 mm depth and these distributions analysed using a sorption-diffusion-degradation model. The fine resolution in the depth profile permitted the detection of a maximum in the concentration of the compounds in the pore water near the surface, whereas concentrations in the sediment increased to a maximum at the surface itself. Experimental distribution coefficients determined from the pore water and sediment concentrations indicated a gradient with depth that was partly explained by an increase in organic matter content and specific surface area of the solids near the interface. The modelling showed that degradation of lindane within the sediment was necessary to explain the concentration profiles, with the optimum agreement between the measured and theoretical profiles obtained with differential degradation in the oxic and anoxic zones. The compounds penetrated to a depth of 40-50 rum over a period of 42 days. (C) 2004 Society of Chemical Industry.

A review of dissolved oxygen modelling techniques for lowland rivers

This review introduces the methods used to simulate the processes affecting dissolved oxygen (DO) in lowland rivers. The important processes are described and this provides a modelling framework to describe those processes in the context of a mass-balance model. The process equations that are introduced all require (reaction) rate parameters and a variety of common procedures for identifying those parameters are reviewed. This is important because there is a wide range of estimation techniques for many of the parameters. These different techniques elicit different estimates of the parameter value and so there is the potential for a significant uncertainty in the model's inputs and therefore in the output too. Finally, the data requirements for modelling DO in lowland rivers are summarised on the basis of modelling the processes described in this review using a mass-balance model. This is reviewed with regard to what data are available and from where they might be obtained. (C) 2003 Elsevier Science B.V. All rights reserved.

Modelling stream and soil water nitrate dynamics during experimentally increased nitrogen deposition in a coniferous forest catchment at Gardsjon, Sweden

Increased atmospheric deposition of inorganic nitrogen (N) may lead to increased leaching of nitrate (NO3-) to surface waters. The mechanisms responsible for, and controls on, this leaching are matters of debate. An experimental N addition has been conducted at Gardsjon, Sweden to determine the magnitude and identify the mechanisms of N leaching from forested catchments within the EU funded project NITREX. The ability of INCA-N, a simple process-based model of catchment N dynamics, to simulate catchment-scale inorganic N dynamics in soil and stream water during the course of the experimental addition is evaluated. Simulations were performed for 1990-2002. Experimental N addition began in 1991. INCA-N was able to successfully reproduce stream and soil water dynamics before and during the experiment. While INCA-N did not correctly simulate the lag between the start of N addition and NO 2 3 breakthrough, the model was able to simulate the state change resulting from increased N deposition. Sensitivity analysis showed that model behaviour was controlled primarily by parameters related to hydrology and vegetation dynamics and secondarily by in-soil processes.

The turnover of organic carbon in subsoils. Part 2. Modelling carbon turnover

A new model, RothPC-1, is described for the turnover of organic C in the top metre of soil. RothPC-1 is a version of RothC-26.3, an earlier model for the turnover of C in topsoils. In RothPC-1 two extra parameters are used to model turnover in the top metre of soil: one, p, which moves organic C down the profile by an advective process, and the other, s, which slows decomposition with depth. RothPC-1 is parameterized and tested using measurements (described in Part 1, this issue) of total organic C and radiocarbon on soil profiles from the Rothamsted long-term field experiments, collected over a period of more than 100 years. RothPC-1 gives fits to measurements of organic C and radiocarbon in the 0-23, 23-46, 46-69 and 69-92 cm layers of soil that are almost all within (or close to) measurement error in two areas of regenerating woodland (Geescroft and Broadbalk Wildernesses) and an area of cultivated land from the Broadbalk Continuous Wheat Experiment. The fits to old grassland (the Park Grass Experiment) are less close. Two other sites that provide the requisite pre- and post-bomb data are also fitted; a prairie Chernozem from Russia and an annual grassland from California. Roth-PC-1 gives a close fit to measurements of organic C and radiocarbon down the Chernozem profile, provided that allowance is made for soil age; with the annual grassland the fit is acceptable in the upper part of the profile, but not in the clay-rich Bt horizon below. Calculations suggest that treating the top metre of soil as a homogeneous unit will greatly overestimate the effects of global warming in accelerating the decomposition of soil C and hence on the enhanced release of CO2 from soil organic matter; more realistic estimates will be obtained from multi-layer models such as RothPC-1.

Modelling the inorganic nitrogen behaviour in a small Mediterranean forested catchment, Fuirosos (Catalonia)

The aim of this work was to couple a nitrogen (N) sub-model to already existent hydrological lumped (LU4-N) and semi-distributed (LU4-R-N and SD4-R-N) conceptual models, to improve our understanding of the factors and processes controlling nitrogen cycling and losses in Mediterranean catchments. The N model adopted provides a simplified conceptualization of the soil nitrogen cycle considering mineralization, nitrification, immobilization, denitrification, plant uptake, and ammonium adsorption/desorption. It also includes nitrification and denitrification in the shallow perched aquifer. We included a soil moisture threshold for all the considered soil biological processes. The results suggested that all the nitrogen processes were highly influenced by the rain episodes and that soil microbial processes occurred in pulses stimulated by soil moisture increasing after rain. Our simulation highlighted the riparian zone as a possible source of nitrate, especially after the summer drought period, but it can also act as an important sink of nitrate due to denitrification, in particular during the wettest period of the year. The riparian zone was a key element to simulate the catchment nitrate behaviour. The lumped LU4-N model (which does not include the riparian zone) could not be validated, while both the semi-distributed LU4-R-N and SD4-R-N model (which include the riparian zone) gave satisfactory results for the calibration process and acceptable results for the temporal validation process.

Using remotely sensed data to support flood modelling

Recent severe flooding in the UK has highlighted the need for better information on flood risk, increasing the pressure on engineers to enhance the capabilities of computer models for flood prediction. This paper evaluates the benefits to be gained from the use of remotely sensed data to support flood modelling. The remotely sensed data available can be used either to produce high-resolution digital terrain models (DTMs) (light detection and ranging (Lidar) data), or to generate accurate inundation mapping of past flood events (airborne synthetic aperture radar (SAR) data and aerial photography). The paper reports on the modelling of real flood events that occurred at two UK sites on the rivers Severn and Ouse. At these sites a combination of remotely sensed data and recorded hydrographs was available. It is concluded first that light detection and ranging Lidar generated DTMs support the generation of considerably better models and enhance the visualisation of model results and second that flood outlines obtained from airborne SAR or aerial images help develop an appreciation of the hydraulic behaviour of important model components, and facilitate model validation. The need for further research is highlighted by a number of limitations, namely: the difficulties in obtaining an adequate representation of hydraulically important features such as embankment crests and walls; uncertainties in the validation data; and difficulties in extracting flood outlines from airborne SAR images in urban areas.

Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

PRISM and ENES: a European approach to Earth system modelling

Europe's widely distributed climate modelling expertise, now organized in the European Network for Earth System Modelling (ENES), is both a strength and a challenge. Recognizing this, the European Union's Program for Integrated Earth System Modelling (PRISM) infrastructure project aims at designing a flexible and friendly user environment to assemble, run and post-process Earth System models. PRISM was started in December 2001 with a duration of three years. This paper presents the major stages of PRISM, including: (1) the definition and promotion of scientific and technical standards to increase component modularity; (2) the development of an end-to-end software environment (graphical user interface, coupling and I/O system, diagnostics, visualization) to launch, monitor and analyse complex Earth system models built around state-of-art community component models (atmosphere, ocean, atmospheric chemistry, ocean bio-chemistry, sea-ice, land-surface); and (3) testing and quality standards to ensure high-performance computing performance on a variety of platforms. PRISM is emerging as a core strategic software infrastructure for building the European research area in Earth system sciences. Copyright (c) 2005 John Wiley & Sons, Ltd.

Case-based analysis in user requirements modelling for knowledge construction

Context: Learning can be regarded as knowledge construction in which prior knowledge and experience serve as basis for the learners to expand their knowledge base. Such a process of knowledge construction has to take place continuously in order to enhance the learners’ competence in a competitive working environment. As the information consumers, the individual users demand personalised information provision which meets their own specific purposes, goals, and expectations. Objectives: The current methods in requirements engineering are capable of modelling the common user’s behaviour in the domain of knowledge construction. The users’ requirements can be represented as a case in the defined structure which can be reasoned to enable the requirements analysis. Such analysis needs to be enhanced so that personalised information provision can be tackled and modelled. However, there is a lack of suitable modelling methods to achieve this end. This paper presents a new ontological method for capturing individual user’s requirements and transforming the requirements onto personalised information provision specifications. Hence the right information can be provided to the right user for the right purpose. Method: An experiment was conducted based on the qualitative method. A medium size of group of users participated to validate the method and its techniques, i.e. articulates, maps, configures, and learning content. The results were used as the feedback for the improvement. Result: The research work has produced an ontology model with a set of techniques which support the functions for profiling user’s requirements, reasoning requirements patterns, generating workflow from norms, and formulating information provision specifications. Conclusion: The current requirements engineering approaches provide the methodical capability for developing solutions. Our research outcome, i.e. the ontology model with the techniques, can further enhance the RE approaches for modelling the individual user’s needs and discovering the user’s requirements.

Improving flood models using LiDAR: progress and problems

Airborne scanning laser altimetry (LiDAR) is an important new data source for river flood modelling. LiDAR can give dense and accurate DTMs of floodplains for use as model bathymetry. Spatial resolutions of 0.5m or less are possible, with a height accuracy of 0.15m. LiDAR gives a Digital Surface Model (DSM), so vegetation removal software (e.g. TERRASCAN) must be used to obtain a DTM. An example used to illustrate the current state of the art will be the LiDAR data provided by the EA, which has been processed by their in-house software to convert the raw data to a ground DTM and separate vegetation height map. Their method distinguishes trees from buildings on the basis of object size. EA data products include the DTM with or without buildings removed, a vegetation height map, a DTM with bridges removed, etc. Most vegetation removal software ignores short vegetation less than say 1m high. We have attempted to extend vegetation height measurement to short vegetation using local height texture. Typically most of a floodplain may be covered in such vegetation. The idea is to assign friction coefficients depending on local vegetation height, so that friction is spatially varying. This obviates the need to calibrate a global floodplain friction coefficient. It’s not clear at present if the method is useful, but it’s worth testing further. The LiDAR DTM is usually determined by looking for local minima in the raw data, then interpolating between these to form a space-filling height surface. This is a low pass filtering operation, in which objects of high spatial frequency such as buildings, river embankments and walls may be incorrectly classed as vegetation. The problem is particularly acute in urban areas. A solution may be to apply pattern recognition techniques to LiDAR height data fused with other data types such as LiDAR intensity or multispectral CASI data. We are attempting to use digital map data (Mastermap structured topography data) to help to distinguish buildings from trees, and roads from areas of short vegetation. The problems involved in doing this will be discussed. A related problem of how best to merge historic river cross-section data with a LiDAR DTM will also be considered. LiDAR data may also be used to help generate a finite element mesh. In rural area we have decomposed a floodplain mesh according to taller vegetation features such as hedges and trees, so that e.g. hedge elements can be assigned higher friction coefficients than those in adjacent fields. We are attempting to extend this approach to urban area, so that the mesh is decomposed in the vicinity of buildings, roads, etc as well as trees and hedges. A dominant points algorithm is used to identify points of high curvature on a building or road, which act as initial nodes in the meshing process. A difficulty is that the resulting mesh may contain a very large number of nodes. However, the mesh generated may be useful to allow a high resolution FE model to act as a benchmark for a more practical lower resolution model. A further problem discussed will be how best to exploit data redundancy due to the high resolution of the LiDAR compared to that of a typical flood model. Problems occur if features have dimensions smaller than the model cell size e.g. for a 5m-wide embankment within a raster grid model with 15m cell size, the maximum height of the embankment locally could be assigned to each cell covering the embankment. But how could a 5m-wide ditch be represented? Again, this redundancy has been exploited to improve wetting/drying algorithms using the sub-grid-scale LiDAR heights within finite elements at the waterline.