Abstract: This work assesses the performance of an analytical
model framework to generate daily flow duration curves, FDCs,
based on climatic characteristics of the catchments and on their
streamflow recession coefficients. According to the analytical model
framework, precipitation is considered to be a stochastic process,
modeled as a marked Poisson process, and recession is considered
to be deterministic, with parameters that can be computed based
on different models. The analytical model framework was tested
for three case studies with different hydrological regimes located in
Switzerland: pluvial, snow-dominated and glacier. For that purpose,
five time intervals were analyzed (the four meteorological seasons
and the civil year) and two developments of the model were tested:
one considering a linear recession model and the other adopting
a nonlinear recession model. Those developments were combined
with recession coefficients obtained from two different approaches:
forward and inverse estimation. The performance of the analytical
framework when considering forward parameter estimation is poor in
comparison with the inverse estimation for both, linear and nonlinear
models. For the pluvial catchment, the inverse estimation shows
exceptional good results, especially for the nonlinear model, clearing
suggesting that the model has the ability to describe FDCs. For
the snow-dominated and glacier catchments the seasonal results are
better than the annual ones suggesting that the model can describe
streamflows in those conditions and that future efforts should focus
on improving and combining seasonal curves instead of considering
single annual ones.
Abstract: Floods have huge environmental and economic impact. Therefore, flood prediction is given a lot of attention due to its importance. This study analysed the annual maximum streamflow (discharge) (AMS or AMD) of Karkheh River in Karkheh River Basin for flood predicting using ARIMA model. For this purpose, we use the Box-Jenkins approach, which contains four-stage method model identification, parameter estimation, diagnostic checking and forecasting (predicting). The main tool used in ARIMA modelling was the SAS and SPSS software. Model identification was done by visual inspection on the ACF and PACF. SAS software computed the model parameters using the ML, CLS and ULS methods. The diagnostic checking tests, AIC criterion, RACF graph and RPACF graphs, were used for selected model verification. In this study, the best ARIMA models for Annual Maximum Discharge (AMD) time series was (4,1,1) with their AIC value of 88.87. The RACF and RPACF showed residuals’ independence. To forecast AMD for 10 future years, this model showed the ability of the model to predict floods of the river under study in the Karkheh River Basin. Model accuracy was checked by comparing the predicted and observation series by using coefficient of determination (R2).
Abstract: Traditionally in sensor networks and recently in the
Internet of Things, numerous heterogeneous sensors are deployed
in distributed manner to monitor a phenomenon that often can be
model by an underlying stochastic process. The big time-series
data collected by the sensors must be analyzed to detect change
in the stochastic process as quickly as possible with tolerable
false alarm rate. However, sensors may have different accuracy
and sensitivity range, and they decay along time. As a result,
the big time-series data collected by the sensors will contain
uncertainties and sometimes they are conflicting. In this study, we
present a framework to take advantage of Evidence Theory (a.k.a.
Dempster-Shafer and Dezert-Smarandache Theories) capabilities of
representing and managing uncertainty and conflict to fast change
detection and effectively deal with complementary hypotheses.
Specifically, Kullback-Leibler divergence is used as the similarity
metric to calculate the distances between the estimated current
distribution with the pre- and post-change distributions. Then mass
functions are calculated and related combination rules are applied to
combine the mass values among all sensors. Furthermore, we applied
the method to estimate the minimum number of sensors needed to
combine, so computational efficiency could be improved. Cumulative
sum test is then applied on the ratio of pignistic probability to detect
and declare the change for decision making purpose. Simulation
results using both synthetic data and real data from experimental
setup demonstrate the effectiveness of the presented schemes.
Abstract: The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.
Abstract: One of the major difficulties introduced with wind
power penetration is the inherent uncertainty in production originating
from uncertain wind conditions. This uncertainty impacts many
different aspects of power system operation, especially the balancing
power requirements. For this reason, in power system development
planing, it is necessary to evaluate the potential uncertainty in future
wind power generation. For this purpose, simulation models are
required, reproducing the performance of wind power forecasts.
This paper presents a wind power forecast error simulation models
which are based on the stochastic process simulation. Proposed
models capture the most important statistical parameters recognized
in wind power forecast error time series. Furthermore, two distinct
models are presented based on data availability. First model uses
wind speed measurements on potential or existing wind power plant
locations, while the seconds model uses statistical distribution of wind
speeds.
Abstract: Most papers model Joint Replenishment Problem
(JRP) as a (kT,S) where kT is a multiple value for a common review
period T,and S is a predefined order up to level. In general the (T,S)
policy is characterized by a long out of control period which requires
a large amount of safety stock compared to the (R,Q) policy. In this
paper a probabilistic model is built where an item, call it item(i),
with the shortest order time between interval (T)is modeled under
(R,Q) policy and its inventory is continuously reviewed, while the
rest of items (j) are periodically reviewed at a definite time
corresponding to item
Abstract: Since supply chains highly impact the financial
performance of companies, it is important to optimize and analyze
their Key Performance Indicators (KPI). The synergistic combination
of Particle Swarm Optimization (PSO) and Monte Carlo simulation is
applied to determine the optimal reorder point of warehouses in
supply chains. The goal of the optimization is the minimization of the
objective function calculated as the linear combination of holding and
order costs. The required values of service levels of the warehouses
represent non-linear constraints in the PSO. The results illustrate that
the developed stochastic simulator and optimization tool is flexible
enough to handle complex situations.
Abstract: The study of non-equilibrium systems has attracted
increasing interest in recent years, mainly due to the lack of
theoretical frameworks, unlike their equilibrium counterparts.
Studying the steady state and/or simple systems is thus one of the
main interests. Hence in this work we have focused our attention on
the driven lattice gas model (DLG model) consisting of interacting
particles subject to an external field E. The dynamics of the system
are given by hopping of particles to nearby empty sites with rates
biased for jumps in the direction of E. Having used small two
dimensional systems of DLG model, the stochastic properties at nonequilibrium
steady state were analytically studied. To understand the
non-equilibrium phenomena, we have applied the analytic approach
via master equation to calculate probability function and analyze
violation of detailed balance in term of the fluctuation-dissipation
theorem. Monte Carlo simulations have been performed to validate
the analytic results.
Abstract: This paper proposes the analysis and design of robust
fuzzy control to Stochastic Parametrics Uncertaint Linear systems.
This system type to be controlled is partitioned into several linear
sub-models, in terms of transfer function, forming a convex polytope,
similar to LPV (Linear Parameters Varying) system. Once defined the
linear sub-models of the plant, these are organized into fuzzy Takagi-
Sugeno (TS) structure. From the Parallel Distributed Compensation
(PDC) strategy, a mathematical formulation is defined in the frequency
domain, based on the gain and phase margins specifications,
to obtain robust PI sub-controllers in accordance to the Takagi-
Sugeno fuzzy model of the plant. The main results of the paper are
based on the robust stability conditions with the proposal of one
Axiom and two Theorems.
Abstract: Recordings from recent earthquakes have provided evidence that ground motions in the near field of a rupturing fault differ from ordinary ground motions, as they can contain a large energy, or “directivity" pulse. This pulse can cause considerable damage during an earthquake, especially to structures with natural periods close to those of the pulse. Failures of modern engineered structures observed within the near-fault region in recent earthquakes have revealed the vulnerability of existing RC buildings against pulse-type ground motions. This may be due to the fact that these modern structures had been designed primarily using the design spectra of available standards, which have been developed using stochastic processes with relatively long duration that characterizes more distant ground motions. Many recently designed and constructed buildings may therefore require strengthening in order to perform well when subjected to near-fault ground motions. Fiber Reinforced Polymers are considered to be a viable alternative, due to their relatively easy and quick installation, low life cycle costs and zero maintenance requirements. The objective of this paper is to investigate the adequacy of Artificial Neural Networks (ANN) to determine the three dimensional dynamic response of FRP strengthened RC buildings under the near-fault ground motions. For this purpose, one ANN model is proposed to estimate the base shear force, base bending moments and roof displacement of buildings in two directions. A training set of 168 and a validation set of 21 buildings are produced from FEA analysis results of the dynamic response of RC buildings under the near-fault earthquakes. It is demonstrated that the neural network based approach is highly successful in determining the response.
Abstract: Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.
Abstract: Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.
Abstract: Real options theory suggests that managerial flexibility embedded within irreversible investments can account for a significant value in project valuation. Although the argument has become the dominant focus of capital investment theory over decades, yet recent survey literature in capital budgeting indicates that corporate practitioners still do not explicitly apply real options in investment decisions. In this paper, we explore how real options decision criteria can be transformed into equivalent capital budgeting criteria under the consideration of uncertainty, assuming that underlying stochastic process follows a geometric Brownian motion (GBM), a mixed diffusion-jump (MX), or a mean-reverting process (MR). These equivalent valuation techniques can be readily decomposed into conventional investment rules and “option impacts", the latter of which describe the impacts on optimal investment rules with the option value considered. Based on numerical analysis and Monte Carlo simulation, three major findings are derived. First, it is shown that real options could be successfully integrated into the mindset of conventional capital budgeting. Second, the inclusion of option impacts tends to delay investment. It is indicated that the delay effect is the most significant under a GBM process and the least significant under a MR process. Third, it is optimal to adopt the new capital budgeting criteria in investment decision-making and adopting a suboptimal investment rule without considering real options could lead to a substantial loss in value.
Abstract: In a product development process, understanding the functional behavior of the system, the role of components in achieving functions and failure modes if components/subsystem fails its required function will help develop appropriate design validation and verification program for reliability assessment. The integration of these three issues will help design and reliability engineers in identifying weak spots in design and planning future actions and testing program. This case study demonstrate the advantage of unascertained theory described in the subjective cognition uncertainty, and then applies blind number (BN) theory in describing the uncertainty of the mechanical system failure process and the same time used the same theory in bringing out another mechanical reliability system model. The practical calculations shows the BN Model embodied the characters of simply, small account of calculation but betterforecasting capability, which had the value of macroscopic discussion to some extent.
Abstract: In this paper we discuss the effect of unbounded particle interaction operator on particle growth and we study how this can address the choice of appropriate time steps of the numerical simulation. We provide also rigorous mathematical proofs showing that large particles become dominating with increasing time while small particles contribute negligibly. Second, we discuss the efficiency of the algorithm by performing numerical simulations tests and by comparing the simulated solutions with some known analytic solutions to the Smoluchowski equation.
Abstract: For decades financial economists have been attempted to determine the optimal investment policy by recognizing the option value embedded in irreversible investment whose project value evolves as a geometric Brownian motion (GBM). This paper aims to examine the effects of the optimal investment trigger and of the misspecification of stochastic processes on investment in real options applications. Specifically, the former explores the consequence of adopting optimal investment rules on the distributions of corporate value under the correct assumption of stochastic process while the latter analyzes the influence on the distributions of corporate value as a result of the misspecification of stochastic processes, i.e., mistaking an alternative process as a GBM. It is found that adopting the correct optimal investment policy may increase corporate value by shifting the value distribution rightward, and the misspecification effect may decrease corporate value by shifting the value distribution leftward. The adoption of the optimal investment trigger has a major impact on investment to such an extent that the downside risk of investment is truncated at the project value of zero, thereby moving the value distributions rightward. The analytical framework is also extended to situations where collection lags are in place, and the result indicates that collection lags reduce the effects of investment trigger and misspecification on investment in an opposite way.
Abstract: To maximise furnace production it-s necessary to
optimise furnace control, with the objectives of achieving maximum
power input into the melting process, minimum network distortion
and power-off time, without compromise on quality and safety. This
can be achieved with on the one hand by an appropriate electrode
control and on the other hand by a minimum of AC transformer
switching.
Electrical arc is a stochastic process; witch is the principal cause
of power quality problems, including voltages dips, harmonic
distortion, unbalance loads and flicker. So it is difficult to make an
appropriate model for an Electrical Arc Furnace (EAF). The factors
that effect EAF operation are the melting or refining materials,
melting stage, electrode position (arc length), electrode arm control
and short circuit power of the feeder. So arc voltages, current and
power are defined as a nonlinear function of the arc length. In this
article we propose our own empirical function of the EAF and model,
for the mean stages of the melting process, thanks to the
measurements in the steel factory.
Abstract: In this paper, we investigate the strategic stochastic air traffic flow management problem which seeks to balance airspace capacity and demand under weather disruptions. The goal is to reduce the need for myopic tactical decisions that do not account for probabilistic knowledge about the NAS near-future states. We present and discuss a scenario-based modeling approach based on a time-space stochastic process to depict weather disruption occurrences in the NAS. A solution framework is also proposed along with a distributed implementation aimed at overcoming scalability problems. Issues related to this implementation are also discussed.