Abstract: This paper proposes, implements and evaluates an original discretization method for continuous random variables, in order to estimate the reliability of systems for which stress and strength are defined as complex functions, and whose reliability is not derivable through analytic techniques. This method is compared to other two discretizing approaches appeared in literature, also through a comparative study involving four engineering applications. The results show that the proposal is very efficient in terms of closeness of the estimates to the true (simulated) reliability. In the study we analyzed both a normal and a non-normal distribution for the random variables: this method is theoretically suitable for each parametric family.
Abstract: Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observations as a function of the explanatory factors has been a challenging problem. In this paper, we aim at estimating the effects of various factors on the number of breakdowns experienced by a passenger car based on a study performed in Mauritius over a year. We remark that the number of passenger car breakdowns is highly under-dispersed. These data are therefore modelled and analyzed using Com-Poisson regression model. We use quasi-likelihood estimation approach to estimate the parameters of the model. Under-dispersion parameter is estimated to be 2.14 justifying the appropriateness of Com-Poisson distribution in modelling under-dispersed count responses recorded in this study.
Abstract: Wind farms (WFs) with high level of penetration are
being established in power systems worldwide more rapidly than
other renewable resources. The Independent System Operator (ISO),
as a policy maker, should propose appropriate places for WF
installation in order to maximize the benefits for the investors. There
is also a possibility of congestion relief using the new installation of
WFs which should be taken into account by the ISO when proposing
the locations for WF installation. In this context, efficient wind farm
(WF) placement method is proposed in order to reduce burdens on
congested lines. Since the wind speed is a random variable and load
forecasts also contain uncertainties, probabilistic approaches are used
for this type of study. AC probabilistic optimal power flow (P-OPF)
is formulated and solved using Monte Carlo Simulations (MCS). In
order to reduce computation time, point estimate methods (PEM) are
introduced as efficient alternative for time-demanding MCS.
Subsequently, WF optimal placement is determined using generation
shift distribution factors (GSDF) considering a new parameter
entitled, wind availability factor (WAF). In order to obtain more
realistic results, N-1 contingency analysis is employed to find the
optimal size of WF, by means of line outage distribution factors
(LODF). The IEEE 30-bus test system is used to show and compare
the accuracy of proposed methodology.
Abstract: We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.
Abstract: Complex statistical analysis of stresses in concrete
slab of the real type of rigid pavement is performed. The
computational model of the pavement is designed as a spatial (3D) model, is based on a nonlinear variant of the finite element method
that respects the structural nonlinearity, enables to model different arrangement of joints, and the entire model can be loaded by the
thermal load. Interaction of adjacent slabs in joints and contact of the slab and the subsequent layer are modeled with help of special
contact elements. Four concrete slabs separated by transverse and
longitudinal joints and the additional subgrade layers and soil to the depth of about 3m are modeled. The thickness of individual layers,
physical and mechanical properties of materials, characteristics of
joints, and the temperature of the upper and lower surface of slabs are supposed to be random variables. The modern simulation technique
Updated Latin Hypercube Sampling with 20 simulations is used for statistical analysis. As results, the estimates of basic statistics of the
principal stresses s1 and s3 in 53 points on the upper and lower surface of the slabs are obtained.
Abstract: In this paper we introduce new data oriented modeling
of uniform random variable well-matched with computing systems. Due to this conformity with current computers structure, this modeling will be efficiently used in statistical inference.
Abstract: In This Article We establish moment inequality of
dependent random variables,furthermore some theorems of strong law
of large numbers and complete convergence for sequences of dependent
random variables. In particular, independent and identically
distributed Marcinkiewicz Law of large numbers are generalized to
the case of m0-dependent sequences.
Abstract: In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.
Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.
Abstract: A novel path planning approach is presented to solve
optimal path in stochastic, time-varying networks under priori traffic
information. Most existing studies make use of dynamic programming
to find optimal path. However, those methods are proved to
be unable to obtain global optimal value, moreover, how to design
efficient algorithms is also another challenge.
This paper employs a decision theoretic framework for defining
optimal path: for a given source S and destination D in urban transit
network, we seek an S - D path of lowest expected travel time
where its link travel times are discrete random variables. To solve
deficiency caused by the methods of dynamic programming, such as
curse of dimensionality and violation of optimal principle, an integer
programming model is built to realize assignment of discrete travel
time variables to arcs. Simultaneously, pruning techniques are also
applied to reduce computation complexity in the algorithm. The final
experiments show the feasibility of the novel approach.