Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Fault isolation schemes for a class of continuous-time stochastic dynamical systems

In this paper a new method for fault isolation in a class of continuous-time stochastic dynamical systems is proposed. The method is framed in the context of model-based analytical redundancy, consisting in the generation of a residual signal by means of a diagnostic observer, for its posterior analysis. Once a fault has been detected, and assuming some basic a priori knowledge about the set of possible failures in the plant, the isolation task is then formulated as a type of on-line statistical classification problem. The proposed isolation scheme employs in parallel different hypotheses tests on a statistic of the residual signal, one test for each possible fault. This isolation method is characterized by deriving for the unidimensional case, a sufficient isolability condition as well as an upperbound of the probability of missed isolation. Simulation examples illustrate the applicability of the proposed scheme.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Development of rapid and highly resolving combinatorial genotyping schemes for Campylobacter jejuni and Campylobacter coli

Campylobacter jejuni followed by Campylobacter coli contribute substantially to the economic and public health burden attributed to food-borne infections in Australia. Genotypic characterisation of isolates has provided new insights into the epidemiology and pathogenesis of C. jejuni and C. coli. However, currently available methods are not conducive to large scale epidemiological investigations that are necessary to elucidate the global epidemiology of these common food-borne pathogens. This research aims to develop high resolution C. jejuni and C. coli genotyping schemes that are convenient for high throughput applications. Real-time PCR and High Resolution Melt (HRM) analysis are fundamental to the genotyping schemes developed in this study and enable rapid, cost effective, interrogation of a range of different polymorphic sites within the Campylobacter genome. While the sources and routes of transmission of campylobacters are unclear, handling and consumption of poultry meat is frequently associated with human campylobacteriosis in Australia. Therefore, chicken derived C. jejuni and C. coli isolates were used to develop and verify the methods described in this study. The first aim of this study describes the application of MLST-SNP (Multi Locus Sequence Typing Single Nucleotide Polymorphisms) + binary typing to 87 chicken C. jejuni isolates using real-time PCR analysis. These typing schemes were developed previously by our research group using isolates from campylobacteriosis patients. This present study showed that SNP + binary typing alone or in combination are effective at detecting epidemiological linkage between chicken derived Campylobacter isolates and enable data comparisons with other MLST based investigations. SNP + binary types obtained from chicken isolates in this study were compared with a previously SNP + binary and MLST typed set of human isolates. Common genotypes between the two collections of isolates were identified and ST-524 represented a clone that could be worth monitoring in the chicken meat industry. In contrast, ST-48, mainly associated with bovine hosts, was abundant in the human isolates. This genotype was, however, absent in the chicken isolates, indicating the role of non-poultry sources in causing human Campylobacter infections. This demonstrates the potential application of SNP + binary typing for epidemiological investigations and source tracing. While MLST SNPs and binary genes comprise the more stable backbone of the Campylobacter genome and are indicative of long term epidemiological linkage of the isolates, the development of a High Resolution Melt (HRM) based curve analysis method to interrogate the hypervariable Campylobacter flagellin encoding gene (flaA) is described in Aim 2 of this study. The flaA gene product appears to be an important pathogenicity determinant of campylobacters and is therefore a popular target for genotyping, especially for short term epidemiological studies such as outbreak investigations. HRM curve analysis based flaA interrogation is a single-step closed-tube method that provides portable data that can be easily shared and accessed. Critical to the development of flaA HRM was the use of flaA specific primers that did not amplify the flaB gene. HRM curve analysis flaA interrogation was successful at discriminating the 47 sequence variants identified within the 87 C. jejuni and 15 C. coli isolates and correlated to the epidemiological background of the isolates. In the combinatorial format, the resolving power of flaA was additive to that of SNP + binary typing and CRISPR (Clustered regularly spaced short Palindromic repeats) HRM and fits the PHRANA (Progressive hierarchical resolving assays using nucleic acids) approach for genotyping. The use of statistical methods to analyse the HRM data enhanced sophistication of the method. Therefore, flaA HRM is a rapid and cost effective alternative to gel- or sequence-based flaA typing schemes. Aim 3 of this study describes the development of a novel bioinformatics driven method to interrogate Campylobacter MLST gene fragments using HRM, and is called ‘SNP Nucleated Minim MLST’ or ‘Minim typing’. The method involves HRM interrogation of MLST fragments that encompass highly informative “Nucleating SNPS” to ensure high resolution. Selection of fragments potentially suited to HRM analysis was conducted in silico using i) “Minimum SNPs” and ii) the new ’HRMtype’ software packages. Species specific sets of six “Nucleating SNPs” and six HRM fragments were identified for both C. jejuni and C. coli to ensure high typeability and resolution relevant to the MLST database. ‘Minim typing’ was tested empirically by typing 15 C. jejuni and five C. coli isolates. The association of clonal complexes (CC) to each isolate by ‘Minim typing’ and SNP + binary typing were used to compare the two MLST interrogation schemes. The CCs linked with each C. jejuni isolate were consistent for both methods. Thus, ‘Minim typing’ is an efficient and cost effective method to interrogate MLST genes. However, it is not expected to be independent, or meet the resolution of, sequence based MLST gene interrogation. ‘Minim typing’ in combination with flaA HRM is envisaged to comprise a highly resolving combinatorial typing scheme developed around the HRM platform and is amenable to automation and multiplexing. The genotyping techniques described in this thesis involve the combinatorial interrogation of differentially evolving genetic markers on the unified real-time PCR and HRM platform. They provide high resolution and are simple, cost effective and ideally suited to rapid and high throughput genotyping for these common food-borne pathogens.

Bottlenecks detection of track allocation schemes at rail stations by Petri nets

Robustness of the track allocation problem is rarely addressed in literatures and the obtained track allocation schemes (TAS) embody some bottlenecks. Therefore, an approach to detect bottlenecks is needed to support local optimization. First a TAS is transformed to an executable model by Petri nets. Then disturbances analysis is performed using the model and the indicators of the total trains' departure delays are collected to detect bottlenecks when each train suffers a disturbance. Finally, the results of the tests based on a rail hub linking six lines and a TAS about thirty minutes show that the minimum buffer time is 21 seconds and there are two bottlenecks where the buffer times are 57 and 44 seconds respectively, and it indicates that the bottlenecks do not certainly locate at the area where there is minimum buffer time. The proposed approach can further support selection of multi schemes and robustness optimization.

Test and evaluation system for multi-protocol sampled value protection schemes

Proposed transmission smart grids will use a digital platform for the automation of substations operating at voltage levels of 110 kV and above. The IEC 61850 series of standards, released in parts over the last ten years, provide a specification for substation communications networks and systems. These standards, along with IEEE Std 1588-2008 Precision Time Protocol version 2 (PTPv2) for precision timing, are recommended by the both IEC Smart Grid Strategy Group and the NIST Framework and Roadmap for Smart Grid Interoperability Standards for substation automation. IEC 61850-8-1 and IEC 61850-9-2 provide an inter-operable solution to support multi-vendor digital process bus solutions, allowing for the removal of potentially lethal voltages and damaging currents from substation control rooms, a reduction in the amount of cabling required in substations, and facilitates the adoption of non-conventional instrument transformers (NCITs). IEC 61850, PTPv2 and Ethernet are three complementary protocol families that together define the future of sampled value digital process connections for smart substation automation. This paper describes a specific test and evaluation system that uses real time simulation, protection relays, PTPv2 time clocks and artificial network impairment that is being used to investigate technical impediments to the adoption of SV process bus systems by transmission utilities. Knowing the limits of a digital process bus, especially when sampled values and NCITs are included, will enable utilities to make informed decisions regarding the adoption of this technology.

A transport protocol for real-time applications in wireless networked control systems

A Networked Control System (NCS) is a feedback-driven control system wherein the control loops are closed through a real-time network. Control and feedback signals in an NCS are exchanged among the system’s components in the form of information packets via the network. Nowadays, wireless technologies such as IEEE802.11 are being introduced to modern NCSs as they offer better scalability, larger bandwidth and lower costs. However, this type of network is not designed for NCSs because it introduces a large amount of dropped data, and unpredictable and long transmission latencies due to the characteristics of wireless channels, which are not acceptable for real-time control systems. Real-time control is a class of time-critical application which requires lossless data transmission, small and deterministic delays and jitter. For a real-time control system, network-introduced problems may degrade the system’s performance significantly or even cause system instability. It is therefore important to develop solutions to satisfy real-time requirements in terms of delays, jitter and data losses, and guarantee high levels of performance for time-critical communications in Wireless Networked Control Systems (WNCSs). To improve or even guarantee real-time performance in wireless control systems, this thesis presents several network layout strategies and a new transport layer protocol. Firstly, real-time performances in regard to data transmission delays and reliability of IEEE 802.11b-based UDP/IP NCSs are evaluated through simulations. After analysis of the simulation results, some network layout strategies are presented to achieve relatively small and deterministic network-introduced latencies and reduce data loss rates. These are effective in providing better network performance without performance degradation of other services. After the investigation into the layout strategies, the thesis presents a new transport protocol which is more effcient than UDP and TCP for guaranteeing reliable and time-critical communications in WNCSs. From the networking perspective, introducing appropriate communication schemes, modifying existing network protocols and devising new protocols, have been the most effective and popular ways to improve or even guarantee real-time performance to a certain extent. Most previously proposed schemes and protocols were designed for real-time multimedia communication and they are not suitable for real-time control systems. Therefore, devising a new network protocol that is able to satisfy real-time requirements in WNCSs is the main objective of this research project. The Conditional Retransmission Enabled Transport Protocol (CRETP) is a new network protocol presented in this thesis. Retransmitting unacknowledged data packets is effective in compensating for data losses. However, every data packet in realtime control systems has a deadline and data is assumed invalid or even harmful when its deadline expires. CRETP performs data retransmission only in the case that data is still valid, which guarantees data timeliness and saves memory and network resources. A trade-off between delivery reliability, transmission latency and network resources can be achieved by the conditional retransmission mechanism. Evaluation of protocol performance was conducted through extensive simulations. Comparative studies between CRETP, UDP and TCP were also performed. These results showed that CRETP significantly: 1). improved reliability of communication, 2). guaranteed validity of received data, 3). reduced transmission latency to an acceptable value, and 4). made delays relatively deterministic and predictable. Furthermore, CRETP achieved the best overall performance in comparative studies which makes it the most suitable transport protocol among the three for real-time communications in a WNCS.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Computationally sound automated proofs of cryptographic schemes

Proving security of cryptographic schemes, which normally are short algorithms, has been known to be time-consuming and easy to get wrong. Using computers to analyse their security can help to solve the problem. This thesis focuses on methods of using computers to verify security of such schemes in cryptographic models. The contributions of this thesis to automated security proofs of cryptographic schemes can be divided into two groups: indirect and direct techniques. Regarding indirect ones, we propose a technique to verify the security of public-key-based key exchange protocols. Security of such protocols has been able to be proved automatically using an existing tool, but in a noncryptographic model. We show that under some conditions, security in that non-cryptographic model implies security in a common cryptographic one, the Bellare-Rogaway model [11]. The implication enables one to use that existing tool, which was designed to work with a different type of model, in order to achieve security proofs of public-key-based key exchange protocols in a cryptographic model. For direct techniques, we have two contributions. The first is a tool to verify Diffie-Hellmanbased key exchange protocols. In that work, we design a simple programming language for specifying Diffie-Hellman-based key exchange algorithms. The language has a semantics based on a cryptographic model, the Bellare-Rogaway model [11]. From the semantics, we build a Hoare-style logic which allows us to reason about the security of a key exchange algorithm, specified as a pair of initiator and responder programs. The other contribution to the direct technique line is on automated proofs for computational indistinguishability. Unlike the two other contributions, this one does not treat a fixed class of protocols. We construct a generic formalism which allows one to model the security problem of a variety of classes of cryptographic schemes as the indistinguishability between two pieces of information. We also design and implement an algorithm for solving indistinguishability problems. Compared to the two other works, this one covers significantly more types of schemes, but consequently, it can verify only weaker forms of security.

Collective dynamics and control of a 3-D small-world network with time delays

The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize the 3-D network system. And with properly chosen delay and gain in the delayed feedback path, the hybrid controlled model may have stable equilibrium, or periodic solutions resulting from the Hopf bifurcation, or complex stranger attractor from the period-doubling bifurcation. Moreover, the direction of Hopf bifurcation and stability of the bifurcation periodic solutions are analyzed. The results are further extended to any "d" dimensional network. It shows that to stabilize a "d" dimensional delayed small-world network, at least a "d – 1" order completed differential feedback is needed. This work provides a constructive suggestion for the high dimensional delayed systems.