Some properties of finite-time stable stochastic nonlinear systems

In this paper we study some properties of finite-time stable stochastic nonlinear systems. We begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems. We then derive some regular properties of its stochastic settling time for a finite-time stable stochastic nonlinear system. We show continuity, positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions. Finally, a Lyapunov function is constructed by making use of the expectation of the stochastic settling time, and the infinitesimal generator of the stochastic system defined on the Lyapunov function is also given, and hence resulting in a converse Lyapunov theorem of finite-time stochastic stability.

Benchmark generation algorithm for stochastic mixed model assembly shop simulation and optimization

The Operations Research (OR) community have defined many deterministic manufacturing control problems mainly focused on scheduling. Well-defined benchmark problems provide a mechanism for communication of the effectiveness of different optimization algorithms. Manufacturing problems within industry are stochastic and complex. Common features of these problems include: variable demand, machine part specific breakdown patterns, part machine specific process durations, continuous production, Finished Goods Inventory (FGI) buffers, bottleneck machines and limited production capacity. Discrete Event Simulation (DES) is a commonly used tool for studying manufacturing systems of realistic complexity. There are few reports of detail-rich benchmark problems for use within the simulation optimization community that are as complex as those faced by production managers. This work details an algorithm that can be used to create single and multistage production control problems. The reported software implementation of the algorithm generates text files in eXtensible Markup Language (XML) format that are easily edited and understood as well as being cross-platform compatible. The distribution and acceptance of benchmark problems generated with the algorithm would enable researchers working on simulation and optimization of manufacturing problems to effectively communicate results to benefit the field in general.

A reduced-order linear functional observer for linear stochastic systems

This paper presents necessary and sufficient conditions for the existence of a reduced-order linear functional state observer for linear stochastic systems. The order of the observer is the same as the dimension of the vectors to be estimated. A simple design algorithm is given together with a numerical example to illustrate the simplicity of the design procedure.

Possibilities to include in numerical simulation stochastic and discontinuous phenomena occurring in material

Simulation of materials processing has to face new difficulties regarding proper description of various discontinuous and stochastic phenomena occurring in materials. Commonly used rheological models based on differential equations treat material as continuum and are unable to describe properly several important phenomena. That is the reason for ongoing search for alternative models, which can account for non-continuous structure of the materials and for the fact, that various phenomena in the materials occur in different scales from nano to mezo. Accounting for the stochastic character of some phenomena is an additional challenge. One of the solutions may be the coupled Cellular Automata (CA) – Finite Element (FE) multi scale model. A detailed discussion about the advantages given by the developed multi scale CAFE model for strain localization phenomena in contrast to capabilities provided by the conventional FE approaches is a subject of this work. Results obtained from the CAFE model are supported by the experimental observations showing influence of many discontinuities existing in the real material on macroscopic response. An immense capabilities of the CAFE approach in comparison to limitations of the FE method for modeling of real material behavior is are shown this work as well.

Deterministic versus stochastic quantitative microbial Risk Assessment models for wastewater irrigation of food crops

Reuse of wastewater to irrigate food crops is being practiced in many parts of the world and is becoming more commonplace as the competition for, and stresses on, freshwater resources intensify. But there are risks associated with wastewater irrigation, including the possibility of transmission of pathogens causing infectious disease, to both workers in the field and to consumers buying and eating produce irrigated with wastewater. To manage these risks appropriately we need objective and quantitative estimates of them. This is typically achieved through one of two modelling approaches: deterministic or stochastic. Each parameter in a deterministic model is represented by a single value, whereas in stochastic models probability functions are used. Stochastic models are theoretically superior because they account for variability and uncertainty, but they are computationally demanding and not readily accessible to water resource and public health managers. We constructed models to estimate risk of enteric virus infection arising from the consumption of wastewater-irrigated horticultural crops (broccoli, cucumber and lettuce), and compared the resultant levels of risk between the deterministic and stochastic approaches. Several scenarios were tested for each crop, accounting for different concentrations of enteric viruses and different lengths of environmental exposure (i.e. the time between the last irrigation event and harvest, when the viruses are liable to decay or inactivation). In most situations modelled the two approaches yielded similar estimates of risk (within 1 order-of-magnitude). The two methods diverged most markedly, up to around 2 orders-of-magnitude, when there was large uncertainty associated with the estimate of virus concentration and the exposure period was short (1 day). Therefore, in some circumstances deterministic modelling may offer water resource managers a pragmatic alternative to stochastic modelling, but its usefulness as a surrogate will depend upon the level of uncertainty in the model parameters.

Accuracy and precision assesment of stochastic simulation tools for springback variation

The sheet forming industry is plagued by inherent variations in its many input variables, making quality control and improvements a major hurdle. This is particularly poignant for Advanced High Strength Steels (AHSS), which exhibit a large degree of property variability. Current FE-based simulation packages are successful at predicting the manufacturability of a particular sheet metal components, however, due to their numerical deterministic nature are inherently unable to predict the performance of a real-life production process. Though they are now beginning to incorporate the stochastic nature of production in their codes. This work investigates the accuracy and precision of a current stochastic simulation package, AutoForm Sigma v4.1, by developing an experimental data set where all main sources of variation are captured through precise measurements and standard tensile tests. Using a Dual Phase 600Mpa grade steel a series of semi-cylindrical channels are formed at two Blank Holder Pressure levels where the response metric is the variation in springback determined by the flange angle. The process is replicated in AutoForm Sigma and an assessment of accuracy and precision of the predictions are performed. Results indicate a very good correspondence to the experimental trials, with mean springback response predicted to within 1 ° of the flange angle and the interquartile spread of results to within 0.22°.

Reconstruction of in vivo time-evolving neuroendocrine dose - response properties unveils admixed deterministic and stochastic elements

Homeostasis in the intact organism is achieved implicitly by repeated incremental feedback (inhibitory) and feedforward (stimulatory) adjustments enforced via intermittent signal exchange. In separated systems, neurohormone signals act deterministically on target cells via quantifiable effector-response functions. On the other hand, in vivo interglandular signaling dynamics have not been estimable to date. Indeed, experimentally isolating components of an interactive network definitionally disrupts time-sensitive linkages. We implement and validate analytical reconstruction of endogenous effector-response properties via a composite model comprising (i) a deterministic basic feedback and feedforward ensemble structure; (ii) judicious statistical allowance for possible stochastic variability in individual biologically interpretable dose–response properties; and (iii) the sole data requirement of serially observed concentrations of a paired signal (input) and response (output). Application of this analytical strategy to a prototypical neuroendocrine axis in the conscious uninjected horse, sheep, and human (i) illustrates probabilistic estimation of endogenous effector dose–response properties; and (ii) unmasks statistically vivid (2- to 5-fold) random fluctuations in inferred target-gland responsivity within any given pulse train. In conclusion, balanced mathematical formalism allows one to (i) reconstruct deterministic properties of interglandular signaling in the intact mammal and (ii) quantify apparent signal-response variability over short time scales in vivo. The present proof-of-principle experiments introduce a previously undescribed means to estimate time-evolving signal-response relationships without isotope infusion or pathway disruption.

A stochastic derivation of the ratio form of contest success functions

This note provides a distribution-based justification for the ratio form of contest success functions (CSFs), in which a player’s success depends positively on her effort relative to that of her opponents. I show that the inverse exponential distribution of the random shocks yields the ratio form. Extending this approach to asymmetric contests, I also derive an asymmetric ratio form of CSFs.

Modelling the linkages between the Australian and G7 stock markets : common stochastic trends and regime shifts

This paper examines whether the Australian equity market is integrated with the equity markets of the G7 economies by applying both the Johansen (Statistical analysis of conintegrating vectors, Journal of Economic Dynamics and Control, 12, 231-54, 1988) and Gregory and Hansen (Residual-based tests for cointegration in models with regime shifts, Journal of Econometrics, 70, 99-126, 1996) approaches to cointegration. Some evidence of a pairwise long-run relationship between the Australian stock market and the stock markets of Canada, Italy, Japan and the United Kingdom is found, but the Australian equity market is not pairwise cointegrated with the equity markets of France, Germany or the USA.

Experiments with stochastic processes : facade subdivision based on wind motion

Constraint based tools for architectural design exploration need to satisfy aesthetic and functional criteria as well as combine discrete and continuous modes of exploration. In this paper, we examine the possibilities for stochastic processes in design space exploration.

Specifically, we address the application of a stochastic wind motion model to the subdivision of an external building envelope into smaller discrete components. Instead of deterministic subdivision constraints, we introduce explicit uncertainty into the system of subdivision. To address these aims, we develop a model of stochastic wind motion; create a subdivision scheme that is governed by the wind model and explore a design space of a facade subdivision problem. A discrete version of the facade, composed of light strips and panels, based on the bamboo elements deformed by continuous wind motion, is developed. The results of the experiments are presented in the paper.

Stochastic atmospheric assistance and the use of emergency staging sites by migrants

Numerous animals move vast distances through media with stochastic dynamic properties. Avian migrants must cope with variable wind speeds and directions en route, which potentially jeopardize fine-tuned migration routes and itineraries. We show how unpredictable winds affect flight times and the use of an intermediate staging site by red knots (Calidris canutus canutus) migrating from west Africa to the central north Siberian breeding areas via the German Wadden Sea. A dynamic migration model incorporating wind conditions during flight shows that flight durations between Mauritania and the Wadden Sea vary between 2 and 8 days. The number of birds counted at the only known intermediate staging site on the French Atlantic coast was strongly positively correlated with simulated flight times. In addition, particularly light-weight birds occurred at this location. These independent results support the idea that stochastic wind conditions are the main driver of the use of this intermediate stopover site as an emergency staging area. Because of the ubiquity of stochastically varying media, we expect such emergency habitats to exist in many other migratory systems, both airborne and oceanic. Our model provides a tool to quantify the effect of winds and currents en route.

Comments on "finite-time stability theorem of stochastic nonlinear systems" [Automatica 46 (2010) 2105-2108]

In this comment, we will point out some errors existing in Chen and Jiao (2010) from definitions to the proof of the main result, where the authors discussed the finite-time stability of stochastic nonlinear systems and proved a Lyapunov theorem on the finitetime stability.