تجزیه و تحلیل حساسیت در مهاجرت پرتوزا: دیفرانسیل مونت کارلو در مقابل تصادفی سازی دو برابر
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|25549||2000||12 صفحه PDF||سفارش دهید||4723 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Mathematics and Computers in Simulation, Volume 55, Issues 1–3, 15 February 2001, Pages 259–270
We address in this paper the efficient estimation of sensitivity coefficients by Monte Carlo simulations. In the context of geological performance for the risk assessment of radioactive waste repositories, a recent non-analog Monte Carlo simulation  based on an integral equation for the transport of radionuclides in porous media is examined in the view of sensitivity analysis. Two methods are compared: Differential Monte Carlo which requires special care when the integral kernel of the integral equation vanishes; and Double Randomization technique which is used to evaluate an effective sensitivity coefficient. Numerical results illustrate the methods for radionuclide migration and focus on the fraction reaching the upper surface of the medium.
The uncertainty about parameters values is a subject of main concern for migration modelling in the context of the risk assessment of radioactive waste repositories in deep geological formations. Sensitivity analysis is essential for the validation of geological performance results. Combined with parameter calibration by an inverse problem it also yields a way of reducing uncertainties. In the context of Monte Carlo calculations, the straightforward perturbation approach (also called “brute force” approach) which consists of making two independent runs and then calculating the difference of the two results is very time consuming. An extremely low statistical error must indeed be achieved in the two independent runs carried out for the unperturbed and perturbed problems. Therefore, we need to implement more sophisticated methods for an accurate estimation. We study here the implementation of two methods for the evaluation of sensitivity coefficients by using a non analog Monte Carlo simulation. The first method addressed is Differential Monte Carlo which is a perturbation method based on correlated tracking  and . It is a very appealing method because it allows to estimate the sensitivity coefficients simultaneously with the concentrations by computing, during the simulation, an additional score. The second method (called here the method of sampled parameters) is based on a systematic random sampling of the value of the parameters distributed according given probability densities. The random sampling of the parameters is coupled with random walks for the transport calculations. It is not based on correlated tracking and could then be expected to yield less accurate results. One of the objectives in this paper is to investigate the capabilities of the Double Randomization method  in this situation. Both methods are compared. Each one is based on the same stochastic process for the construction of the particle trackings, but differs in the way these particle trackings are utilized to evaluate the sensitivity coefficients. In the following, the sensitivity or importance coefficient S of a score J with respect to (w.r.t.) a parameter p is defined by equation(1) This normalized quantity is only defined if J is not zero. The score J is any quantity like the activity at a point, the cumulative activity on a surface over a given period of time, etc., to be determined in the risk analysis.
نتیجه گیری انگلیسی
The Differential Monte Carlo method yields the estimations of the derivative of the score and the sensitivity coefficient w.r.t. any parameter provided a theoretical work is allowed for the derivation of source term and integral kernels w.r.t. this parameter. The first numerical results obtained in this paper show that the accuracy on the sensitivity coefficient and the accuracy on the score are comparable. Moreover, the additional time required for the computation of the sensitivity coefficient remains limited. The method of sampled parameters combined with the Double Randomization technique is flexible and general. It does not require moreover any theoretical developments. By introducing a least-square optimization, the effective sensitivity coefficient takes into account non linear dependences of the score on the uncertain parameters. This is clearly an advantage of the method. Unlike the “brute force” approach, the method of sampled parameters yields usable results in a reasonable time. However, the numerical calculations of the estimator Ep lead to less accurate evaluations (in the tests, about 7.5 times less accurate) than with Differential Monte Carlo for similar simulation times. It seems then that the drawbacks of non-correlated tracking cannot be compensated entirely by the optimal use of the Double Randomization method. In our opinion, if a theoretical work is consented beforehand for Differential Monte Carlo, this method will be more efficient and thus preferred to the method of sampled parameters. These conclusions were drawn from numerical results concerning the fraction of radionuclide reaching the upper surface of the geological medium. In future works, the sensitivity analysis should be generalized to several scores of interest like the calculation of pointwise activities or the estimation of the radionuclide flux on specific surfaces. Finally, multiple parameters analysis should also be considered.