The basic mathematic models, such as the statistic model, the time-serial model, the spatial dynamic model etc., and some typical analysis methods based on 3DCM are proposed and discussed. A few typical spatial decision making methods integrating the spatial analysis and the basic mathematical models are also introduced, e.g. visual impact assessment, dispersion of noise immissions, base station plan for wireless communication. In addition, a new idea of expectation of further applications and add-in-value service of 3DCM is promoted. As an example, the sunshine analysis is studied and some helpful conclusions are drawn. 相似文献
In risk analysis, a complete characterization of the concentration distribution is necessary to determine the probability
of exceeding a threshold value. The most popular method for predicting concentration distribution is Monte Carlo simulation,
which samples the cumulative distribution function with a large number of repeated operations. In this paper, we first review
three most commonly used Monte Carlo (MC) techniques: the standard Monte Carlo, Latin Hypercube sampling, and Quasi Monte
Carlo. The performance of these three MC approaches is investigated. We then apply stochastic collocation method (SCM) to
risk assessment. Unlike the MC simulations, the SCM does not require a large number of simulations of flow and solute equations.
In particular, the sparse grid collocation method and probabilistic collocation method are employed to represent the concentration
in terms of polynomials and unknown coefficients. The sparse grid collocation method takes advantage of Lagrange interpolation
polynomials while the probabilistic collocation method relies on polynomials chaos expansions. In both methods, the stochastic
equations are reduced to a system of decoupled equations, which can be solved with existing solvers and whose results are
used to obtain the expansion coefficients. Then the cumulative distribution function is obtained by sampling the approximate
polynomials. Our synthetic examples show that among the MC methods, the Quasi Monte Carlo gives the smallest variance for
the predicted threshold probability due to its superior convergence property and that the stochastic collocation method is
an accurate and efficient alternative to MC simulations. 相似文献