The aim of the paper is to point out that the Monte Carlo simulation is an easy and flexible approach when it comes to forecasting risk of an asset portfolio. The case study presented in the paper illustrates the problem of forecasting risk arising from a portfolio of receivables denominated in different foreign currencies. Such a problem seems to be close to the real issue for enterprises offering products or services on several foreign markets. The changes in exchange rates are usually not normally distributed and, moreover, they are always interdependent. As shown in the paper, the Monte Carlo simulation allows for forecasting market risk under such circumstances.
The paper is concerned with issues of the estimation of random variable distribution parameters by the Monte Carlo method. Such quantities can correspond to statistical parameters computed based on the data obtained in typical measurement situations. The subject of the research is the mean, the mean square and the variance of random variables with uniform, Gaussian, Student, Simpson, trapezoidal, exponential, gamma and arcsine distributions.
The purpose of this study is to identify relationships between the values of the fluidity obtained by computer simulation and by an experimental test in the horizontal three-channel mould designed in accordance with the Measurement Systems Analysis. Al-Si alloy was a model material. The factors affecting the fluidity varied in following ranges: Si content 5 wt.% – 12 wt.%, Fe content 0.15 wt.% – 0.3wt. %, the pouring temperature 605°C-830°C, and the pouring speed 100 g · s–1 – 400 g · s–1. The software NovaFlow&Solid was used for simulations. The statistically significant difference between the value of fluidity calculated by the equation and obtained by experiment was not found. This design simplifies the calculation of the capability of the measurement process of the fluidity with full replacement of experiments by calculation, using regression equation.
When an artificial neural network is used to determine the value of a physical quantity its result is usually presented without an uncertainty. This is due to the difficulty in determining the uncertainties related to the neural model. However, the result of a measurement can be considered valid only with its respective measurement uncertainty. Therefore, this article proposes a method of obtaining reliable results by measuring systems that use artificial neural networks. For this, it considers the Monte Carlo Method (MCM) for propagation of uncertainty distributions during the training and use of the artificial neural networks.
Improvements of modern manufacturing techniques implies more efficient production but also new challenges for coordinate metrologists. The crucial task here is a coordinate measurement accuracy assessment. It is important because according to technological requirements, measurements are useful only when they are stated with their accuracy. Currently used methods for the measurements accuracy estimation are difficult to implement and time consuming. It is therefore important to implement correct and validated methods that will also be easy to implement. The method presented in this paper is one of them. It is an on-line accuracy estimation method based on the virtual CMM idea. A model is built using a modern LaserTracer system and a common test sphere and its implementation lasts less than one day. Results obtained using the presented method are comparable to results of commonly used uncertainty estimation methods which proves its correct functioning. Its properties predispose it to be widely used both in laboratory and industrial conditions.
The paper presents a multi-scale mathematical model dedicated to a comprehensive simulation of resistance heating combined with the melting and controlled cooling of steel samples. Experiments in order to verify the formulated numerical model were performed using a Gleeble 3800 thermo-mechanical simulator. The model for the macro scale was based upon the solution of Fourier-Kirchhoff equation as regards predicting the distribution of temperature fields within the volume of the sample. The macro scale solution is complemented by a functional model generating voluminal heat sources, resulting from the electric current flowing through the sample. The model for the micro-scale, concerning the grain growth simulation, is based upon the probabilistic Monte Carlo algorithm, and on the minimization of the system energy. The model takes into account the forming mushy zone, where grains degrade at the melting stage – it is a unique feature of the micro-solution. The solution domains are coupled by the interpolation of node temperatures of the finite element mesh (the macro model) onto the Monte Carlo cells (micro model). The paper is complemented with examples of resistance heating results and macro- and micro-structural tests, along with test computations concerning the estimation of the range of zones with diverse dynamics of grain growth.