Compound Compound Poisson Risk Model

2000 Mathematics Subject Classification: 60K10, 62P05.

A Markov chain location-allocation meta-model for hurricane relief

An emergency is a deviation from a planned course of events that endangers people, properties, or the environment. It can be described as an unexpected event that causes economic damage, destruction, and human suffering. When a disaster happens, Emergency Managers are expected to have a response plan to most likely disaster scenarios. Unlike earthquakes and terrorist attacks, a hurricane response plan can be activated ahead of time, since a hurricane is predicted at least five days before it makes landfall. This research looked into the logistics aspects of the problem, in an attempt to develop a hurricane relief distribution network model. We addressed the problem of how to efficiently and effectively deliver basic relief goods to victims of a hurricane disaster. Specifically, where to preposition State Staging Areas (SSA), which Points of Distributions (PODs) to activate, and the allocation of commodities to each POD. Previous research has addressed several of these issues, but not with the incorporation of the random behavior of the hurricane's intensity and path. This research presents a stochastic meta-model that deals with the location of SSAs and the allocation of commodities. The novelty of the model is that it treats the strength and path of the hurricane as stochastic processes, and models them as Discrete Markov Chains. The demand is also treated as stochastic parameter because it depends on the stochastic behavior of the hurricane. However, for the meta-model, the demand is an input that is determined using Hazards United States (HAZUS), a software developed by the Federal Emergency Management Agency (FEMA) that estimates losses due to hurricanes and floods. A solution heuristic has been developed based on simulated annealing. Since the meta-model is a multi-objective problem, the heuristic is a multi-objective simulated annealing (MOSA), in which the initial solution and the cooling rate were determined via a Design of Experiments. The experiment showed that the initial temperature (T0) is irrelevant, but temperature reduction (δ) must be very gradual. Assessment of the meta-model indicates that the Markov Chains performed as well or better than forecasts made by the National Hurricane Center (NHC). Tests of the MOSA showed that it provides solutions in an efficient manner. Thus, an illustrative example shows that the meta-model is practical.

Analysis of the moisture effect on the mechanical behaviour of an adhesively bonded joint under proportional multi-axial loads

The objective of the study is to identify the 3D behaviour of an adhesive in an assembly, and to take into account the effect of ageing in a marine environment. To that end, three different tests were employed. Gravimetric analyses were used to determine the water diffusion kinetics in the adhesive. Bulk tensile tests were performed to highlight the effects of humid ageing on the adhesive behaviour. Modified Arcan tests were performed for several ageing times to obtain the experimental database which was necessary to identify constitutive models. A Mahnken-Schlimmer type model was determined for the unaged state according to a procedure developed in a previous study. This identification used inverse techniques. It was based on the unaged modified Arcan results and on a coupling between an optimisation routine and finite-element analysis. Then, a global inverse identification procedure was developed. Its aim was to relate the unaged parameters to the moisture concentration and overcome the difficulties usually associated with ageing of bonded assemblies in a humid environment: a non-uniformity of the stress state and a gradient of mechanical properties in the adhesive. This procedure was similar to the one used in the first part but needed modified Arcan results for several ageing times. It also required an initial assumption for the evolution of the Mahnken-Schlimmer parameters with the moisture concentration.

Robust CDM and pole placement PID based thrust controllers for multirotor motor-rotor simplified model

Positioning and orientation precision of a multirotor aerial robot can be increased by using additional control loops for each of the driving units. As a result, one can eliminate lack of balance between true thrust forces. A control performance comparison of two proposed thrust controllers, namely robust controller designed with coefficient diagram method (CDM) and proportional, integral and derivative (PID) controller tuned with pole-placement law, is presented in the paper. The research has been conducted with respect to model/plant matching uncertainty and with the use of antiwindup compensators for a simple motor-rotor model approximated by first-order inertia plus delay. From the obtained simulation results one concludes that appropriate choice of AWC compensator improves tracking performance and increases robustness against parametric uncertainty.

Investigation of the hazards of substrate current injection: transient external latchup and substrate noise coupling

Substrate current injection is the origin of external latchup and substrate noise coupling. The trigger current for external latchup depends on the duration of the trigger event. A physics-based model is provided to model the effects of aggressor to victim spacing and orientation on transient triggering of external latchup. The latchup susceptibility of standard cell based designs is also investigated. Guard rings are used to reduce latchup susceptibility and to reduce the substrate noise coupled to sensitive analog circuits. In this work, the effectiveness of different guard ring topologies for the reduction of substrate noise coupling is also investigated.

Power spectrum model of visual masking: simulations and empirical data

In the study of the spatial characteristics of the visual channels, the power spectrum model of visual masking is one of the most widely used. When the task is to detect a signal masked by visual noise, this classical model assumes that the signal and the noise are previously processed by a bank of linear channels and that the power of the signal at threshold is proportional to the power of the noise passing through the visual channel that mediates detection. The model also assumes that this visual channel will have the highest ratio of signal power to noise power at its output. According to this, there are masking conditions where the highest signal-to-noise ratio (SNR) occurs in a channel centered in a spatial frequency different from the spatial frequency of the signal (off-frequency looking). Under these conditions the channel mediating detection could vary with the type of noise used in the masking experiment and this could affect the estimation of the shape and the bandwidth of the visual channels. It is generally believed that notched noise, white noise and double bandpass noise prevent off-frequency looking, and high-pass, low-pass and bandpass noises can promote it independently of the channel's shape. In this study, by means of a procedure that finds the channel that maximizes the SNR at its output, we performed numerical simulations using the power spectrum model to study the characteristics of masking caused by six types of one-dimensional noise (white, high-pass, low-pass, bandpass, notched, and double bandpass) for two types of channel's shape (symmetric and asymmetric). Our simulations confirm that (1) high-pass, low-pass, and bandpass noises do not prevent the off-frequency looking, (2) white noise satisfactorily prevents the off-frequency looking independently of the shape and bandwidth of the visual channel, and interestingly we proved for the first time that (3) notched and double bandpass noises prevent off-frequency looking only when the noise cutoffs around the spatial frequency of the signal match the shape of the visual channel (symmetric or asymmetric) involved in the detection. In order to test the explanatory power of the model with empirical data, we performed six visual masking experiments. We show that this model, with only two free parameters, fits the empirical masking data with high precision. Finally, we provide equations of the power spectrum model for six masking noises used in the simulations and in the experiments.

Numeric model to estimate pesticide deposition and losses from aerial spraying.

Pesticides applications have been described by many researches as a very inefficient process. In some cases, there are reports that only 0.02% of the applied products are used for the effective control of the problem. The main factor that influences pesticides applications is the droplet size formed on spraying nozzles. Many parameters affects the dynamic of the droplets, like wind, temperature, relative humidity, and others. Small droplets are biologically more active, but they are affected by evaporation and drift. On the other hand, the great droplets do not promote a good distribution of the product on the target. In this sense, associated with the risk of non target areas contamination and with the high costs involved in applications, the knowledge of the droplet size is of fundamental importance in the application technology. When sophisticated technology for droplets analysis is unavailable, is common the use of artificial targets like water-sensitive paper to sample droplets. On field sampling, water-sensitive papers are placed on the trials where product will be applied. When droplets impinging on it, the yellow surface of this paper will be stained dark blue, making easy their recognition. Collected droplets on this papers have different kinds of sizes. In this sense, the determination of the droplet size distribution gives a mass distribution of the material and so, the efficience of the application of the product. The stains produced by droplets shows a spread factor proportional to their respectives initial sizes. One of methodologies to analyse the droplets is a counting and measure of the droplets made in microscope. The Porton N-G12 graticule, that shows equaly spaces class intervals on geometric progression of square 2, are coulpled to the lens of the microscope. The droplet size parameters frequently used are the Volumetric Median Diameter (VMD) and the Numeric Median Diameter. On VMD value, a representative droplets sample is divided in two equal parts of volume, in such away one part contains droplets of sizes smaller than VMD and the other part contains droplets of sizes greater that VMD. The same process is done to obtaining the NMD, which divide the sample in two equal parts in relation to the droplets size. The ratio between VMD and NMD allows the droplets uniformity evaluation. After that, the graphics of accumulated probability of the volume and size droplets are plotted on log scale paper (accumulated probability versus median diameter of each size class). The graphics provides the NMD on the x-axes point corresponding to the value of 50% founded on the y-axes. All this process is very slow and subjected to operator error. So, in order to decrease the difficulty envolved with droplets measuring it was developed a numeric model, implemented on easy and accessfull computational language, which allows approximate VMD and NMD values, with good precision. The inputs to this model are the frequences of the droplets sizes colected on the water-sensitive paper, observed on the Porton N-G12 graticule fitted on microscope. With these data, the accumulated distribution of the droplet medium volumes and sizes are evaluated. The graphics obtained by plotting this distributions allow to obtain the VMD and NMD using linear interpolation, seen that on the middle of the distributions the shape of the curves are linear. These values are essential to evaluate the uniformity of droplets and to estimate the volume deposited on the observed paper by the density (droplets/cm2). This methodology to estimate the droplets volume was developed by 11.0.94.224 Project of the CNPMA/EMBRAPA. Observed data of herbicides aerial spraying samples, realized by Project on Pelotas/RS county, were used to compare values obtained manual graphic method and with those obtained by model has shown, with great precision, the values of VMD and NMD on each sampled collector, allowing to estimate a quantities of deposited product and, by consequence, the quantities losses by drifty. The graphics of variability of VMD and NMD showed that the quantity of droplets that reachs the collectors had a short dispersion, while the deposited volume shows a great interval of variation, probably because the strong action of air turbulence on the droplets distribution, enfasizing the necessity of a deeper study to verify this influences on drift.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.