An Improved Perturbation Mechanism for Simulated Annealing Simulation

Simulated annealing (SA) is being increasingly used for the generation of stochastic models of spatial phenomena because of its flexibility to integrate data of diverse types and scales. The major shortcoming of SA is the extensive CPU requirements. We present a perturbation mechanism that significantly improves the CPU speed. Two conventional perturbation mechanisms are to (1) randomly select two locations and swap their attribute values, or (2) visit a randomly selected location and draw a new value from the global histogram. The proposed perturbation mechanism is a modification of option 2: each candidate value is drawn from a local conditional distribution built with a template of kriging weights rather than from the global distribution. This results in accepting more perturbations and in perturbations that improve the variogram reproduction for short scale lags. We document the new method, the increased convergence speed, and the improved variogram reproduction. Implementation details of the method such as the size of the local neighborhood are considered.     

Shallow landslides in deeply weathered slates of the Sierra de Collcerola (Catalonian Coastal Range, Spain)

Stability conditions in an area located NW of Barcelona (Spain) are discussed. Here, several mass movements were observed, mainly affecting weathered Paleozoic slates. Many of these failures involved slopes cut along recent infrastructures: debris flows, wedge and plane failures, generally surficial, occurred more frequently. After a detailed geological and geomorphologic survey, geomechanic characterization was carried out, according to RMR and SMR classifications. This rating gave a prediction of slope behaviour, in fairly good agreement with the real observed one.

Stability numerical analysis was carried out for the main cut slopes, based upon the Limit Equilibrium Method. First of all, the deterministic factor of safety was computed using the mean values of parameters. After that, a simulation technique based upon the Monte Carlo Method was applied in order to obtain factor of safety distributions. The probability of failure was estimated as P(F<1).

Finally, results from deterministic and probabilistic approaches were compared. The effectiveness of different possible remedial measures was highlighted by means of a sensitivity analysis, which showed that the more important parameters in the study area are the geometrical ones (height, slope and failure plane angles). The final technical solutions adopted are briefly outlined.     

铁路岩质边坡的RQD研究

以宝成铁路略阳站前后一段铁路工程边坡为例,采用蒙特卡洛原理和方法,计算模拟铁路边结构面概率参数,利用统计结果估算边坡岩体的岩石质量指标ＲＱＤ,提出方向ＲＱＤ的概念,初探方向ＲＱＤ值在铁路工程边坡中的应用及铁路开挖工程活动与自然地质环境间的相互影响。     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Efficient generation of conditional simulations by chebyshev matrix polynomial approximations to the symmetric square root of the covariance matrix

Consider the problem of generating a realization y₁ of a Gaussian random field on a dense grid of points ₁ conditioned on field observations y₂ collected on a sparse grid of points ₂. An approach to this is to generate first an unconditional realization y over the grid =_{1 2}, and then to produce y₁ by conditioning y on the data y₂. As standard methods for generating y, such as the turning bands, spectral or Cholesky approaches can have various limitations, it has been proposed by M. W. Davis to generate realizations from a matrix polynomial approximations to the square root of the covariance matrix. In this paper we describe how to generate a direct approximation to the conditional realization y₁, on ₁ using a variant of Davis' approach based on approximation by Chebyshev polynomials. The resulting algorithm is simple to implement, numerically stable, and bounds on the approximation error are readily available. Furthermore we show that the conditional realization y₁ can be generated directly with a lower order polynomial than the unconditional realization y, and that further reductions can be achieved by exploiting a nugget effect if one is present. A pseudocode version of the algorithm is provided that can be implemented using the fast Fourier transform if the field is stationary and the grid ₁ is rectangular. Finally, numerical illustrations are given of the algorithm's performance in generating various 2-D realizations of conditional processes on large sampling grids.     

A Monte Carlo Model Of The Nocturnal Surface Temperatures In Urban Canyons

A model for the urban canyon is formulated for meteorologicalconditions of weak winds at night time. Thermal radiation, conductivity and convection are simulated by means of the Monte Carlo method. These are the main physical processesof energy transfer that give rise to the characteristic temperaturedistribution in these systems. The model has been satisfactory tested under ideal conditions for which analytical solutions exist.The predictions of the model under morerealistic conditions accurately reproduce the observationalresults. A strong temperature gradient across streets, with the canyon corners up to 4 °C warmer than the canyon centre, is found for the deepest canyons. This theoretical predictionhas been successfully verified with measurementstaken in a number of streets of the city of Granada in Spain.     

Theoretical discussion and Monte-Carlo simulations for a Negative Binomial process paradox

The idea of an over-threshold sampling is to retain all the events of a time-series exceeding a given threshold. The probabilistic analysis implies estimating two statistical models, one describing the occurrence of the events (date of the events), the other describing their magnitude (value of the local maximum). These two models are then combined to obtain the distribution of the annual maxima. A well-known result of a Poisson process is that waiting time, defined as the duration between two successive events exceeding the threshold, is exponentially distributed. The assertion that the waiting time of a Negative Binomial process is also exponentially distributed seems to be in obvious contradiction with the Poisson process properties. A theoretical discussion and Monte-Carlo simulations are presented to solve this apparent paradox.     

Bootstrapping: A Fast Way to Simulate QTz Curves

The aim of this paper is to present a fast method based on bootstrapping, for simulating recoverable reserves for input to financial Monte Carlo simulations. In mining, the three parameters defining recoverable reserves are the cutoff grade, z, the ore tonnage above cutoff, T, and the metal quantity above cutoff, Q. After introducing the concept of 3-dimensional QTz curves, the statistical technique called bootstrapping is reviewed and applied to a set of South African gold grades. As selective mining is carried out on blocks not points, these curves have to be calculated for blocks. The QTz curves obtained by bootstrapping are compared to those obtained by conditionally simulating the same deposit. The procedure has been extended to incorporate geologists' ideas of the likely size of the ore volume. Lastly, the recoverable reserves obtained by bootstrapping are compared with those obtained by traditional risk analysis (base case ± 10% or 20%).