Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Stochastic effects in a seasonally forced epidemic model

The interplay of seasonality, the system's nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Power Electronics Didactic Modules for Direct Current Machine Control

Several didactic modules for an electric machinery laboratory are presented. The modules are dedicated for DC machinery control and get their characteristic curves. The didactic modules have a front panel with power and signal connectors and can be configurable for any DC motor type. The three-phase bridge inverter proposed is one of the most popular topologies and is commercially available in power package modules. The control techniques and power drives were designed to satisfy static and dynamic performance of DC machines. Each power section is internally self-protected against misconnections and short-circuits. Isolated output signals of current and voltage measurements are also provided, adding versatility for use either in didactic or research applications. The implementation of such modules allowed experimental confirmation of the expected performance.

A regulatory framework for short-term stochastic maintenance outage scheduling in smart grids

The current regulatory framework for maintenance outage scheduling in distribution systems needs revision to face the challenges of future smart grids. In the smart grid context, generation units and the system operator perform new roles with different objectives, and an efficient coordination between them becomes necessary. In this paper, the distribution system operator (DSO) of a microgrid receives the proposals for shortterm (ST) planned outages from the generation and transmission side, and has to decide the final outage plans, which is mandatory for the members to follow. The framework is based on a coordination procedure between the DSO and other market players. This paper undertakes the challenge of optimization problem in a smart grid where the operator faces with uncertainty. The results show the effectiveness and applicability of the proposed regulatory framework in the modified IEEE 34- bus test system.

Adding value [valorization] to tannery fleshings: part II – effect of protein hydrolysates on leather dyeing

The tanning industry generates a high quantity of solid wastes. Therefore, there is a need to create valorization [added value] options for these wastes. The main objective of the present work was to study the effect of protein hydrolysates (HP) prepared from fleshings on leather dyeing. During previous studies it was found that the application of HP products, obtained from fleshings, in leather retannage intensified the colour of crust leather. In this work the CIELAB colour system was used to evaluate the effect of HP on retannage processes. The main conclusions of this study were: (i) HP can be used instead of a dicyanodiamide resin (Fortan DC) if the colour parameters of the standard procedure are to be maintained, and (ii) the replacement of an acrylic resin (Fortan A40) by glutaraldehyde-modified HP (GHP) results in a darker skin, and can therefore be interesting for the reduction of the quantity of dye used.

Stochastic short-term maintenance scheduling of GENCOs in an oligopolistic electricity market

In the proposed model, the independent system operator (ISO) provides the opportunity for maintenance outage rescheduling of generating units before each short-term (ST) time interval. Long-term (LT) scheduling for 1 or 2 years in advance is essential for the ISO and the generation companies (GENCOs) to decide their LT strategies; however, it is not possible to be exactly followed and requires slight adjustments. The Cournot-Nash equilibrium is used to characterize the decision-making procedure of an individual GENCO for ST intervals considering the effective coordination with LT plans. Random inputs, such as parameters of the demand function of loads, hourly demand during the following ST time interval and the expected generation pattern of the rivals, are included as scenarios in the stochastic mixed integer program defined to model the payoff-maximizing objective of a GENCO. Scenario reduction algorithms are used to deal with the computational burden. Two reliability test systems were chosen to illustrate the effectiveness of the proposed model for the ST decision-making process for future planned outages from the point of view of a GENCO.

A few what-ifs on using statistical analysis of stochastic simulation runs to extract timeliness properties

Modern real-time systems, with a more flexible and adaptive nature, demand approaches for timeliness evaluation based on probabilistic measures of meeting deadlines. In this context, simulation can emerge as an adequate solution to understand and analyze the timing behaviour of actual systems. However, care must be taken with the obtained outputs under the penalty of obtaining results with lack of credibility. Particularly important is to consider that we are more interested in values from the tail of a probability distribution (near worst-case probabilities), instead of deriving confidence on mean values. We approach this subject by considering the random nature of simulation output data. We will start by discussing well known approaches for estimating distributions out of simulation output, and the confidence which can be applied to its mean values. This is the basis for a discussion on the applicability of such approaches to derive confidence on the tail of distributions, where the worst-case is expected to be.

Adding local priority-based dispatching mechanisms to P-NET networks: a fixed priority approach

In this paper we address the real-time capabilities of P-NET, which is a multi-master fieldbus standard based on a virtual token passing scheme. We show how P-NET’s medium access control (MAC) protocol is able to guarantee a bounded access time to message requests. We then propose a model for implementing fixed prioritybased dispatching mechanisms at each master’s application level. In this way, we diminish the impact of the first-come-first-served (FCFS) policy that P-NET uses at the data link layer. The proposed model rises several issues well known within the real-time systems community: message release jitter; pre-run-time schedulability analysis in non pre-emptive contexts; non-independence of tasks at the application level. We identify these issues in the proposed model and show how results available for priority-based task dispatching can be adapted to encompass priority-based message dispatching in P-NET networks.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.

A framework for the response time analysis of fixed-priority tasks with stochastic inter-arrival times

Real-time scheduling usually considers worst-case values for the parameters of task (or message stream) sets, in order to provide safe schedulability tests for hard real-time systems. However, worst-case conditions introduce a level of pessimism that is often inadequate for a certain class of (soft) real-time systems. In this paper we provide an approach for computing the stochastic response time of tasks where tasks have inter-arrival times described by discrete probabilistic distribution functions, instead of minimum inter-arrival (MIT) values.

Spinning reserve and emission unit commitment through stochastic optimization

This paper proposes a stochastic mixed-integer linear approach to deal with a short-term unit commitment problem with uncertainty on a deregulated electricity market that includes day-ahead bidding and bilateral contracts. The proposed approach considers the typically operation constraints on the thermal units and a spinning reserve. The uncertainty is due to the electricity prices, which are modeled by a scenario set, allowing an acceptable computation. Moreover, emission allowances are considered in a manner to allow for the consideration of environmental constraints. A case study to illustrate the usefulness of the proposed approach is presented and an assessment of the cost for the spinning reserve is obtained by a comparison between the situation with and without spinning reserve.