A marked Poisson process model of summer rainfall in southern Ontario

1985 ◽  
Vol 12 (4) ◽  
pp. 886-898 ◽  
Author(s):  
J. D. Bonser ◽  
T. E. Unny ◽  
K. Singhal
Keyword(s):  
Poisson Process ◽  
Process Model ◽  
Point Processes ◽  
Summer Rainfall ◽  
Model Parameters ◽  
Southern Ontario ◽  
Hourly Rainfall ◽  
Storm Duration ◽  
Rainfall Volume ◽  
Rainfall Occurrences

A mathematical description of summer rainfall occurrences in southern Ontario is developed in this paper. The theory of Poisson point processes with specific application to rainfall modelling is presented with a critical review of previous literature on Poisson rainfall models. A marked Poisson process model of summer storms is formulated, using the marks to represent the random duration and intensity of the events. Model parameters are estimated for four locations in southern Ontario using a total of 48 seasons of hourly rainfall data. The model is applied to calculate the seasonal return period of extreme storms and the probability distribution of total seasonal rainfall volume. These two examples demonstrate the accuracy and usefulness of the model. Key words: rainfall, storm duration, storm intensity, temporal storm pattern, probabilistic model, Poisson process, exponential distribution, gamma distribution, Weibull distribution.

Some models for rainfall based on stochastic point processes

1987 ◽  
Vol 410 (1839) ◽  
pp. 269-288 ◽  
Keyword(s):  
Poisson Process ◽  
Stochastic Models ◽  
Point Processes ◽  
Rainfall Intensity ◽  
Storm Events ◽  
Total Rainfall ◽  
Random Intensity ◽  
Hourly Rainfall ◽  
Complex Models ◽  
Stochastic Point Processes

Stochastic models are discussed for the variation of rainfall intensity at a fixed point in space. First, models are analysed in which storm events arise in a Poisson process, each such event being associated with a period of rainfall of random duration and constant but random intensity. Total rainfall intensity is formed by adding the contributions from all storm events. Then similar but more complex models are studied in which storms arise in a Poisson process, each storm giving rise to a cluster of rain cells and each cell being associated with a random period of rain. The main properties of these models are determined analytically. Analysis of some hourly rainfall data from Denver, Colorado shows the clustered models to be much the more satisfactory.

scholarly journals Characterization of Moisture Diffusion in Cured Concrete Slabs at Early Ages

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xiao Zhang ◽  
Hongduo Zhao
Keyword(s):  
Process Model ◽  
Model Simulation ◽  
Moisture Diffusion ◽  
Experimental Results ◽  
Concrete Slabs ◽  
Model Parameters ◽  
Early Age ◽  
Water Curing ◽  
Early Age Concrete

The objective of this paper is to investigate the characterization of moisture diffusion inside early-age concrete slabs subjected to curing. Time-dependent relative humidity (RH) distributions of three mixture proportions subjected to three different curing methods (i.e., air curing, water curing, and membrane-forming compounds curing) and sealed condition were measured for 28 days. A one-dimensional nonlinear moisture diffusion partial differential equation (PDE) based on Fick’s second law, which incorporates the effect of curing in the Dirichlet boundary condition using a concept of curing factor, is developed to simulate the diffusion process. Model parameters are calibrated by a genetic algorithm (GA). Experimental results show that the RH reducing rate inside concrete under air curing is greater than the rates under membrane-forming compound curing and water curing. It is shown that the effect of water-to-cement (w/c) ratio on self-desiccation is significant. Lower w/c ratio tends to result in larger RH reduction. RH reduction considering both effect of diffusion and self-desiccation in early-age concrete is not sensitive to w/c ratio, but to curing method. Comparison between model simulation and experimental results indicates that the improved model is able to reflect the effect of curing on moisture diffusion in early-age concrete slabs.

Convergence to equilibrium in a traffic model with restricted passing

1979 ◽  
Vol 16 (4) ◽  
pp. 881-889 ◽  
Author(s):  
Hans Dieter Unkelbach
Keyword(s):  
Poisson Process ◽  
Limit Theorems ◽  
Point Processes ◽  
Road Traffic ◽  
Poisson Processes ◽  
Traffic Model ◽  
Cluster Point ◽  
Convergence To Equilibrium ◽  
Constant Intensity

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

scholarly journals Determination of Combustion Process Model Parameters in Diesel Engine with Variable Compression Ratio

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Saša Milojević ◽  
Radivoje Pešić
Keyword(s):  
Diesel Engine ◽  
Compression Ratio ◽  
Process Model ◽  
Internal Combustion Engines ◽  
Combustion Process ◽  
Exhaust Emission ◽  
Model Parameters ◽  
Connecting Rod ◽  
Variable Compression Ratio ◽  
Variable Compression

Compression ratio has very important influence on fuel economy, emission, and other performances of internal combustion engines. Application of variable compression ratio in diesel engines has a number of benefits, such as limiting maximal in cylinder pressure and extended field of the optimal operating regime to the prime requirements: consumption, power, emission, noise, and multifuel capability. The manuscript presents also the patented mechanism for automatic change engine compression ratio with two-piece connecting rod. Beside experimental research, modeling of combustion process of diesel engine with direct injection has been performed. The basic problem, selection of the parameters in double Vibe function used for modeling the diesel engine combustion process, also performed for different compression ratio values. The optimal compression ratio value was defined regarding minimal fuel consumption and exhaust emission. For this purpose the test bench in the Laboratory for Engines of the Faculty of Engineering, University of Kragujevac, is brought into operation.

scholarly journals Bayesian modeling and prediction of accrual in multi-regional clinical trials

2014 ◽  
Vol 26 (2) ◽  
pp. 752-765 ◽  
Author(s):  
Yi Deng ◽  
Xiaoxi Zhang ◽  
Qi Long
Keyword(s):  
Clinical Trials ◽  
Poisson Process ◽  
Process Model ◽  
Nonhomogeneous Poisson Process ◽  
Modeling And Prediction ◽  
Accuracy And Precision ◽  
Start Up ◽  
Accrual Rate ◽  
Model Region ◽  
Over Time

In multi-regional trials, the underlying overall and region-specific accrual rates often do not hold constant over time and different regions could have different start-up times, which combined with initial jump in accrual within each region often leads to a discontinuous overall accrual rate, and these issues associated with multi-regional trials have not been adequately investigated. In this paper, we clarify the implication of the multi-regional nature on modeling and prediction of accrual in clinical trials and investigate a Bayesian approach for accrual modeling and prediction, which models region-specific accrual using a nonhomogeneous Poisson process and allows the underlying Poisson rate in each region to vary over time. The proposed approach can accommodate staggered start-up times and different initial accrual rates across regions/centers. Our numerical studies show that the proposed method improves accuracy and precision of accrual prediction compared to existing methods including the nonhomogeneous Poisson process model that does not model region-specific accrual.

Model Calibration for the High-Purity Oxygen Activated Sludge Process – Algorithm Development and Evaluation

1993 ◽  
Vol 28 (11-12) ◽  
pp. 163-171 ◽  
Author(s):  
Weibo (Weber) Yuan ◽  
David Okrent ◽  
Michael K. Stenstrom
Keyword(s):  
Activated Sludge ◽  
High Purity ◽  
Model Calibration ◽  
Process Model ◽  
Model Parameters ◽  
Complex Method ◽  
Activated Sludge Process ◽  
Activated Sludge Model ◽  
Kinetic Coefficients ◽  
Calibration Algorithm

A model calibration algorithm is developed for the high-purity oxygen activated sludge process (HPO-ASP). The algorithm is evaluated under different conditions to determine the effect of the following factors on the performance of the algorithm: data quality, number of observations, and number of parameters to be estimated. The process model used in this investigation is the first HPO-ASP model based upon the IAWQ (formerly IAWPRC) Activated Sludge Model No. 1. The objective function is formulated as a relative least-squares function and the non-linear, constrained minimization problem is solved by the Complex method. The stoichiometric and kinetic coefficients of the IAWQ activated sludge model are the parameters focused on in this investigation. Observations used are generated numerically but are made close to the observations from a full-scale high-purity oxygen treatment plant. The calibration algorithm is capable of correctly estimating model parameters even if the observations are severely noise-corrupted. The accuracy of estimation deteriorates gradually with the increase of observation errors. The accuracy of calibration improves when the number of observations (n) increases, but the improvement becomes insignificant when n>96. It is also found that there exists an optimal number of parameters that can be rigorously estimated from a given set of information/data. A sensitivity analysis is conducted to determine what parameters to estimate and to evaluate the potential benefits resulted from collecting additional measurements.

Densities for stationary random sets and point processes

1984 ◽  
Vol 16 (02) ◽  
pp. 324-346 ◽  
Author(s):  
Wolfgang Weil ◽  
John A. Wieacker
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Convex Set ◽  
Compact Convex ◽  
Random Sets ◽  
Intensity Measure ◽  
Additive Functionals ◽  
Compact Convex Set ◽  
Classical Integral

For certain stationary random setsX, densitiesDφ(X) of additive functionalsφare defined and formulas forare derived whenKis a compact convex set in. In particular, for the quermassintegrals and motioninvariantX, these formulas are in analogy with classical integral geometric formulas. The case whereXis the union set of a Poisson processYof convex particles is considered separately. Here, formulas involving the intensity measure ofYare obtained.

Densities for stationary random sets and point processes

1984 ◽  
Vol 16 (2) ◽  
pp. 324-346 ◽  
Author(s):  
Wolfgang Weil ◽  
John A. Wieacker
Keyword(s):  
Poisson Process ◽  
Point Processes ◽  
Convex Set ◽  
Compact Convex ◽  
Random Sets ◽  
Intensity Measure ◽  
Additive Functionals ◽  
Compact Convex Set ◽  
Classical Integral

For certain stationary random sets X, densities Dφ (X) of additive functionals φ are defined and formulas for are derived when K is a compact convex set in . In particular, for the quermassintegrals and motioninvariant X, these formulas are in analogy with classical integral geometric formulas. The case where X is the union set of a Poisson process Y of convex particles is considered separately. Here, formulas involving the intensity measure of Y are obtained.

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