基于自适应蒙特卡洛法评定测量不确定度程序开发与应用

进行了基于自适应蒙特卡洛法评定测量不确定度的程序开发与应用。基于Python语言,设计开发自适应蒙特卡洛法评定测量不确定度程序,包含评定过程框架、自定义变量名称模块、过程参数关联计算模块以及蒙特卡洛法采样计算模块。程序界面简洁,操作简单,计算准确,适用于任意多个独立变量、任意多个过程参数及单一被测量的数学模型,为利用自适应蒙特卡洛法评定测量不确定度提供了方便。     

Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties

The ISO 98:1995 Guide to the expression of uncertainty in measurement (GUM) presents important application limitations. For its improvement, different supplements are being developed that will progressively enter into effect. The first of these supplements describes an alternative method for calculating uncertainties, the Monte Carlo method (MCM), which is not restricted to the conditions of the method described in the GUM: the linearity of the model and the application of the central limit theorem. MCM requires computer calculation systems for generating pseudo-random numbers and for evaluating the model a large number of times. There are software applications that have been specifically developed for calculating uncertainties, some of which include MCM; but they do not allow the user to control all factors in the process, particularly the result stabilization criteria. On the contrary, its implementation in a mathematical program for general purposes such as MATLAB, enables total control over the process, is simple and benefits from its calculation speed. This article details programming in MATLAB for the implementation of the adaptive MCM method.     

Comparison of different methods to estimate the uncertainty in composition measurement by chromatography

Natural gas is a mixture that contains hydrocarbons and other compounds, such as CO₂ and N₂. Natural gas composition is commonly measured by gas chromatography, and this measurement is important for the calculation of some thermodynamic properties that determine its commercial value. The estimation of uncertainty in chromatographic measurement is essential for an adequate presentation of the results and a necessary tool for supporting decision making. Various approaches have been proposed for the uncertainty estimation in chromatographic measurement. The present work is an evaluation of three approaches of uncertainty estimation, where two of them (guide to the expression of uncertainty in measurement method and prediction method) were compared with the Monte Carlo method, which has a wider scope of application. The aforementioned methods for uncertainty estimation were applied to gas chromatography assays of three different samples of natural gas. The results indicated that the prediction method and the guide to the expression of uncertainty in measurement method (in the simple version used) are not adequate to calculate the uncertainty in chromatography measurement, because uncertainty estimations obtained by those approaches are in general lower than those given by the Monte Carlo method.     

A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo

A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size.     

Algorithm and application of Monte Carlo simulation for multi-dispersive copolymerization system

A Monte Carlo algorithm has been established for multi-dispersive copolymerization system, based on the experimental data of copolymer molecular weight and dispersion via GPC measurement. The program simulates the insertion of every monomer unit and records the structure and microscopical sequence of every chain in various lengths. It has been applied successfully for the ring-opening copolymerization of 2,2-dimethyltrimethylene carbonate (DTC) with δ-caprolactone (δ-CL). The simulation coincides with the experimental results and provides microscopical data of triad fractions, lengths of homopolymer segments, etc., which are difficult to obtain by experiments. The algorithm presents also a uniform frame for copolymerization studies under other complicated mechanisms.     

石墨炉原子吸收光谱法测定土壤中铅量的测量不确定度评定

通过石墨炉原子吸收光谱法对土壤中的铅量进行了测定,对影响测量结果的不确定度分量进行了量化的计算.从而得出影响铅量测量不确定度的主要因素是测量样品消解液中的铅的质量浓度引起的不确定度.     

Uncertainty evaluation for the quantification of low masses of benzo[a]pyrene: Comparison between the Law of Propagation of Uncertainty and the Monte Carlo method

A proper evaluation of the uncertainty associated to the quantification of micropollutants in the environment, like Polycyclic Aromatic Hydrocarbons (PAHs), is crucial for the reliability of the measurement results. The present work describes a comparison between the uncertainty evaluation carried out according to the GUM uncertainty framework and the Monte Carlo (MC) method. This comparison was carried out starting from real data sets obtained from the quantification of benzo[a]pyrene (BaP), spiked on filters commonly used for airborne particulate matter sampling. BaP was chosen as target analyte as it is listed in the current European legislation as marker of the carcinogenic risk for the whole class of PAHs.     

Monte Carlo simulation of polarizable systems: Early rejection scheme for improving the performance of adiabatic nuclear and electronic sampling Monte Carlo simulations

An early rejection scheme for trial moves in adiabatic nuclear and electronic sampling Monte Carlo simulation (ANES-MC) of polarizable intermolecular potential models is presented. The proposed algorithm is based on Swendsen–Wang filter functions for prediction of success or failure of trial moves in Monte Carlo simulations. The goal was to reduce the amount of calculations involved in ANES-MC electronic moves, by foreseeing the success of an attempt before making those moves. The new method was employed in Gibbs ensemble Monte Carlo (GEMC) simulations of the polarizable simple point charge-fluctuating charge (SPC-FQ) model of water. The overall improvement in GEMC depends on the number of swap attempts (transfer molecules between phases) in one Monte Carlo cycle. The proposed method allows this number to increase, enhancing the chemical potential equalization. For a system with 300 SPC-FQ water molecules, for example, the fractions of early rejected transfers were about 0.9998 and 0.9994 at 373 and 423 K, respectively. This means that the transfer moves consume only a very small part of the overall computing effort, making GEMC almost equivalent to a simulation in the canonical ensemble.     

A diagnostic tool for determining the quality of accuracy validation. Assessing the method for determination of nitrate in drinking water

Realistic internal validation of a method implies the performance validation experiments under intermediate precision conditions. The validation results can be organized in an X _Nr×Ns (replicates×runs) data matrix, analysis of which enables assessment of the accuracy of the method. By means of Monte Carlo simulation, uncertainty in the estimates of bias and precision can be assessed. A bivariate plot is presented for assessing whether the uncertainty intervals for the bias (E ± U(E)) and intermediate precision (RSDi ± U(RSDi) are included in prefixed limits (requirements for the method). As a case study, a method for determining the concentration of nitrate in drinking water at the official level set by 98/83/EC Directive is assessed by use of the proposed plot.     

Efficient protocol for quantum Monte Carlo calculations of hydrogen abstraction barriers: Application to methanol

Accurate calculation of hydrogen abstraction reaction barriers is a challenging problem, often requiring high level quantum chemistry methods that scale poorly with system size. Quantum Monte Carlo (QMC) methods provide an alternative approach that exhibit much better scaling, but these methods are still computationally expensive. We describe approaches that can significantly reduce the cost of QMC calculations of barrier heights, using the hydrogen abstraction of methanol by a hydrogen atom as an illustrative example. By analysing the combined influence of trial wavefunctions and pseudopotential quadrature settings on the barrier heights, variance, and time‐step errors, we devise a simple protocol that minimizes the cost of the QMC calculations while retaining accuracy comparable to large‐basis coupled cluster theory. We demonstrate that this protocol is transferable to other hydrogen abstraction reactions.     

Spatial Electron Relaxation: Comparison of Monte Carlo and Boltzmann Equation Results

In former investigations on the spatial relaxation of the electron component of weakly ionized plasmas a considerable spectrum of distinct spatial structures has been found in the velocity distribution function as well as in various macroscopic quantities of the electrons. These results have been mainly obtained by solving the spatially inhomogeneous electron Boltzmann equation considering the action of uniform electric fields and the impact of elastic and inelastic collisions of the electrons with the gas atoms. To verify these partly unexpected results on the complex structure formation, analogous Monte Carlo simulations were performed now for a helium plasma at various reduced electric field strengths. Detailed comparisons were made between the results of the two independent kinetic approaches with respect to the spatial evolution of the velocity distribution function as well as of associated macroscopic quantities. Good agreement was generally found, thus confirming the earlier results on the complex spatial relaxation structures.     

Molecular Modeling of Adsorption in Activated Carbon: Comparison of Monte Carlo Simulations with Experiment

We present Mont Carlo computer simulation results for a molecular model of fluids adsorbed in porous carbon materials. The model carbon used is based on the platelet model for carbon of Segarra and Glandt (1994). The model we use has a single basal plane per platelet and the structure is isotropic, disordered, with weak short-range correlations between the platelets. We have performed grand canonical Monte Carlo simulations of the adsorption isotherms for methane, ethane, and their mixtures in this model carbon. We find generally good agreement with experimental and the mixture results are quite accurately described by the ideal adsorbed solution theory. An exception to this is the behavior for the mixture at the highest pressures. In this case the experimental data show significant deviations from ideal adsorbed solution theory and the simulation results.     

The features of electron dose distributions in circular objects: Comparison of Monte Carlo calculation predictions with dosimetry

The features of electron dose field formation in the multi-layer circular objects are related with its surface irregularity such as convexity, concavity and roundness of inner and outer layers. The simulation of dose distributions in multi-layer tubes irradiated with a scanned electron beam (EB) was carried out by Monte Carlo (MC) method with utilization of the software ModeCEB. The effects of mutual influence on dose field formation in contacting multi-layers tubes irradiated with EB were MC simulated and measured with a film dosimetry. An experimental validation of the obtained simulation predictions for dose distributions in multi-layer tubes irradiated with 10 MeV electrons was performed on radiation facility with linear electron accelerator LAE 13/9, INCT, Warsaw. Comparison of MC simulation results with a film dosimetry is discussed in the report.     

蒙特卡罗法估算真实溶液的无限稀释活度系数

在无限稀释活度系数实验测定、模型预测等方面的研究工作不断深入的同时，基干系统的微观分子结构信息通过计算机分子模拟方法来求取无限稀释活度系数的研究也更多地开展起来［‘，’］．但是鉴于摘类热力学性质，如自由能、化学位等的特殊性，开展的模拟工作总的说来是初步的·许多方法复杂，实现的难度较大，而研究的系统技多地针对于模型流体混合物（modelfluidrn－ixtures）．本文是蒙特卡罗法估算真实溶液的无限稀释活度系数的一个尝试，研究对象选取298．15K温度条件下甲醇的水溶液·1原理对于一个NTV系综，化学位定义为可以将UN－…     

Sampling potential energy surface of glycyl glycine peptide: Comparison of Metropolis Monte Carlo and stochastic dynamics

A comparative study was carried out to test the efficiency with which Metropolis Monte Carlo (MC) and stochastic dynamics (SD) sample the potential energy surface of the N-acetyl glycyl glycine methylamide peptide as defined by the united atom AMBER* force field. Boltzmann-weighted ensembles were generated with variations of all internal degrees of freedom (i.e., stretch, bend, and torsion) for a single N-acetyl glycyl glycine methylamide molecule at 300 K by 10⁸-step MC and 100-ns SD simulations. As expected, both methods gave the same final energetic results. However, convergence was found to be ∼10 times faster with MC than with SD as measured by comparisons of the populations of all symmetrically equivalent conformers. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1294–1299, 1998     

Kinetic lattice Monte Carlo model for oxygen vacancy diffusion in praseodymium doped ceria: Applications to materials design

Kinetic lattice Monte Carlo (KLMC) model is developed for investigating oxygen vacancy diffusion in praseodymium-doped ceria. The current approach uses a database of activation energies for oxygen vacancy migration, calculated using first-principles, for various migration pathways in praseodymium-doped ceria. Since the first-principles calculations revealed significant vacancy-vacancy repulsion, we investigate the importance of that effect by conducting simulations with and without a repulsive interaction. Initially, as dopant concentrations increase, vacancy concentration and thus conductivity increases. However, at higher concentrations, vacancies interfere and repel one another, and dopants trap vacancies, creating a “traffic jam” that decreases conductivity, which is consistent with the experimental findings. The modeled effective activation energy for vacancy migration slightly increased with increasing dopant concentration in qualitative agreement with the experiment. The current methodology comprising a blend of first-principle calculations and KLMC model provides a very powerful fundamental tool for predicting the optimal dopant concentration in ceria related materials.     

Efficient combination of Wang-Landau and transition matrix Monte Carlo methods for protein simulations

An efficient combination of the Wang-Landau and transition matrix Monte Carlo methods for protein and peptide simulations is described. At the initial stage of simulation the algorithm behaves like the Wang-Landau algorithm, allowing to sample the entire interval of energies, and at the later stages, it behaves like transition matrix Monte Carlo method and has significantly lower statistical errors. This combination allows to achieve fast convergence to the correct values of density of states. We propose that the violation of TTT identities may serve as a qualitative criterion to check the convergence of density of states. The simulation process can be parallelized by cutting the entire interval of simulation into subintervals. The violation of ergodicity in this case is discussed. We test the algorithm on a set of peptides of different lengths and observe good statistical convergent properties for the density of states. We believe that the method is of general nature and can be used for simulations of other systems with either discrete or continuous energy spectrum.     

Influence of buffer quality on pH measurement uncertainty: prediction and experimental evaluation

Dependence of the uncertainty of a pH measurement result on the quality of buffers (i.e. the uncertainty of their certified pH values) at different levels of instrumental uncertainty (pH-meter, etc.) was simulated using the Monte Carlo method and regression analysis. The contribution of the instrumental standard uncertainty (in the studied range from 0.1 to 1 mV) to the uncertainty of the pH measurement result is negligible, if the standard uncertainties of the pH buffers exceed 0.04 pH (e. g. for in-house buffers). It is shown how the choice of pH-meter and buffers should be correlated in order to meet the required uncertainty of a pH measurement result in a sample under analysis. The results of the simulation were compared with experimental data obtained from calibrations of a pH/ion-meter with a hydrogen working electrode (Radiometer PHM-240) and with a glass electrode (Metrohm 744). Buffers of different quality (National Institute for Standards and Technology standard reference materials, certified Radiometer buffers and Merck CertiPUR buffers) were used for the calibrations. The uncertainties of the experimental results are close to the predicted ones obtained by the simulation. Received: 16 June 2002 Accepted: 19 July 2002 Presented at the 14^th International Conference of the Israel Society for Quality, 18–21 November 2002, Jerusalem, Israel Correspondence to I. Kuselman