About the Approximation of Stochastic Petri Nets by Continuous Petri Nets: Several Regions

Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. Moreover, the convergence of stochastic estimators is slow. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes with timed continuous Petri nets. The contribution of this paper is to point out the limits of the fluidification in the context of the stochastic steady state approximation. Unfortunately, the asymptotic mean marking of stochastic and continuous Petri nets with same structure and same initial marking are mainly often different. This paper shows that this difficulty is related to the partition in regions of the reachability state space and the existence of critical region

On Minimum-time Control of Continuous Petri nets: Centralized and Decentralized Perspectives

Muchos sistemas artificiales, como los sistemas de manufactura, de logística, de telecomunicaciones o de tráfico, pueden ser vistos "de manera natural" como Sistemas Dinámicos de Eventos Discretos (DEDS). Desafortunadamente, cuando tienen grandes poblaciones, estos sistemas pueden sufrir del clásico problema de la explosión de estados. Con la intención de evitar este problema, se pueden aplicar técnicas de fluidificación, obteniendo una relajación fluida del modelo original discreto. Las redes de Petri continuas (CPNs) son una aproximación fluida de las redes de Petri discretas, un conocido formalismo para los DEDS. Una ventaja clave del empleo de las CPNs es que, a menudo, llevan a una substancial reducción del coste computacional. Esta tesis se centra en el control de Redes de Petri continuas temporizadas (TCPNs), donde las transiciones tienen una interpretación temporal asociada. Se asume que los sistemas siguen una semántica de servidores infinitos (velocidad variable) y que las acciones de control aplicables son la disminución de la velocidad del disparo de las transiciones. Se consideran dos interesantes problemas de control en esta tesis: 1) control del marcado objetivo, donde el objetivo es conducir el sistema (tan rápido como sea posible) desde un estado inicial a un estado final deseado, y es similar al problema de control set-point para cualquier sistema de estado continuo; 2) control del flujo óptimo, donde el objetivo es conducir el sistema a un flujo óptimo sin conocimiento a priori del estado final. En particular, estamos interesados en alcanzar el flujo máximo tan rápido como sea posible, lo cual suele ser deseable en la mayoría de sistemas prácticos. El problema de control del marcado objetivo se considera desde las perspectivas centralizada y descentralizada. Proponemos varios controladores centralizados en tiempo mínimo, y todos ellos están basados en una estrategia ON/OFF. Para algunas subclases, como las redes Choice-Free (CF), se garantiza la evolución en tiempo mínimo; mientras que para redes generales, los controladores propuestos son heurísticos. Respecto del problema de control descentralizado, proponemos en primer lugar un controlador descentralizado en tiempo mínimo para redes CF. Para redes generales, proponemos una aproximación distribuida del método Model Predictive Control (MPC); sin embargo en este método no se considera evolución en tiempo mínimo. El problema de control de flujo óptimo (en nuestro caso, flujo máximo) en tiempo mínimo se considera para redes CF. Proponemos un algoritmo heurístico en el que calculamos los "mejores" firing count vectors que llevan al sistema al flujo máximo, y aplicamos una estrategia de disparo ON/OFF. También demostramos que, debido a que las redes CF son persistentes, podemos reducir el tiempo que tarda en alcanzar el flujo máximo con algunos disparos adicionales. Los métodos de control propuestos se han implementado e integrado en una herramienta para Redes de Petri híbridas basada en Matlab, llamada SimHPN

Hybrid Petri net model of a traffic intersection in an urban network

Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the red-to-green switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to model-based optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way

A generic approach to behaviour-driven biochemical model construction

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Modelling of biochemical systems has received considerable attention over the last decade from bioengineering, biochemistry, computer science, and mathematics. This thesis investigates the applications of computational techniques to computational systems biology, for the construction of biochemical models in terms of topology and kinetic rates. Due to the complexity of biochemical systems, it is natural to construct models representing the biochemical systems incrementally in a piecewise manner. Syntax and semantics of two patterns are defined for the instantiation of components which are extendable, reusable and fundamental building blocks for models composition. We propose and implement a set of genetic operators and composition rules to tackle issues of piecewise composing models from scratch. Quantitative Petri nets are evolved by the genetic operators, and evolutionary process of modelling are guided by the composition rules. Metaheuristic algorithms are widely applied in BioModel Engineering to support intelligent and heuristic analysis of biochemical systems in terms of structure and kinetic rates. We illustrate parameters of biochemical models based on Biochemical Systems Theory, and then the topology and kinetic rates of the models are manipulated by employing evolution strategy and simulated annealing respectively. A new hybrid modelling framework is proposed and implemented for the models construction. Two heuristic algorithms are performed on two embedded layers in the hybrid framework: an outer layer for topology mutation and an inner layer for rates optimization. Moreover, variants of the hybrid piecewise modelling framework are investigated. Regarding flexibility of these variants, various combinations of evolutionary operators, evaluation criteria and design principles can be taken into account. We examine performance of five sets of the variants on specific aspects of modelling. The comparison of variants is not to explicitly show that one variant clearly outperforms the others, but it provides an indication of considering important features for various aspects of the modelling. Because of the very heavy computational demands, the process of modelling is paralleled by employing a grid environment, GridGain. Application of the GridGain and heuristic algorithms to analyze biological processes can support modelling of biochemical systems in a computational manner, which can also benefit mathematical modelling in computer science and bioengineering. We apply our proposed modelling framework to model biochemical systems in a hybrid piecewise manner. Modelling variants of the framework are comparatively studied on specific aims of modelling. Simulation results show that our modelling framework can compose synthetic models exhibiting similar species behaviour, generate models with alternative topologies and obtain general knowledge about key modelling features

Dynamic Reliability Assessment of PEM Fuel Cell Systems

In this paper, a novel model for the dynamic reliability analysis of a polymer electrolyte membrane fuel cell system is developed to account for multi-state dynamics and ageing. The modelling approach involves the combination of physical and stochastic sub-models with shared variables. The physical model consists of deterministic calculations of the system state described by variables such as temperature, pressure, mass flow rates and voltage output. Additionally, estimated component degradation rates are also taken into account. The non-deterministic model is implemented with stochastic Petri nets which model the failures of the balance of plant components within the fuel cell system. Using this approach, the effects of the operating conditions on the reliability of the system were investigated. Monte Carlo simulations of the process highlighted a clear influence of both purging and load cycles on the longevity of the fuel cell system

Modelling polymer electrolyte membrane fuel cells for dynamic reliability assessment

Tackling climate change is arguably the biggest challenge humanity faces in the 21st century. Rising average global temperatures threaten to destabilize the fragile ecosystem of the Earth and bring unprecedented changes to human lives if nothing is done to prevent it. This phenomenon is caused by the anthropogenic greenhouse effect due to the increasing atmospheric concentrations of carbon dioxide (CO2). One way to avert the disaster is to drastically reduce the consumption of fossil fuels in all spheres of human activities, including transportation. To do this, research and development of electric vehicles (EVs) to make them more efficient, reliable and accessible is essential. [Continues.

On the Modeling of Signaling Networks with Petri Nets

The whole-cell behavior arises from the interplay among signaling, metabolic, and regulatory processes. Proper modeling of the overall function requires accurate interpretations of each component. The highly concurrent nature of the inner-cell interactions motivates the use of Petri nets as a framework for the whole-cell modeling. Petri nets have been successfully used in modeling of metabolic pathways, as it allows for a straightforward mapping from its stoichiometric matrix to the Petri net structure. The Boolean interpretation and modeling of transcription regulation networks also lends itself easily to Petri net modeling. However, Petri net modeling of signal transduction networks has been largely lacking, with the exception of simple ad hoc applications to specific signaling pathways. In this thesis, I investigate the applicability of Petri nets to modeling of signaling networks, by systematically analyzing initial token assignments, firing strategies, and robustness to errors and abstractions in the estimates of molecule concentrations and reaction rates

Low-dimensional representations of neural time-series data with applications to peripheral nerve decoding

Bioelectronic medicines, implanted devices that influence physiological states by peripheral neuromodulation, have promise as a new way of treating diverse conditions from rheumatism to diabetes. We here explore ways of creating nerve-based feedback for the implanted systems to act in a dynamically adapting closed loop. In a first empirical component, we carried out decoding studies on in vivo recordings of cat and rat bladder afferents. In a low-resolution data-set, we selected informative frequency bands of the neural activity using information theory to then relate to bladder pressure. In a second high-resolution dataset, we analysed the population code for bladder pressure, again using information theory, and proposed an informed decoding approach that promises enhanced robustness and automatic re-calibration by creating a low-dimensional population vector. Coming from a different direction of more general time-series analysis, we embedded a set of peripheral nerve recordings in a space of main firing characteristics by dimensionality reduction in a high-dimensional feature-space and automatically proposed single efficiently implementable estimators for each identified characteristic. For bioelectronic medicines, this feature-based pre-processing method enables an online signal characterisation of low-resolution data where spike sorting is impossible but simple power-measures discard informative structure. Analyses were based on surrogate data from a self-developed and flexibly adaptable computer model that we made publicly available. The wider utility of two feature-based analysis methods developed in this work was demonstrated on a variety of datasets from across science and industry. (1) Our feature-based generation of interpretable low-dimensional embeddings for unknown time-series datasets answers a need for simplifying and harvesting the growing body of sequential data that characterises modern science. (2) We propose an additional, supervised pipeline to tailor feature subsets to collections of classification problems. On a literature standard library of time-series classification tasks, we distilled 22 generically useful estimators and made them easily accessible.Open Acces