Sampling from Complex Probability Distributions: A Monte Carlo Primer for Engineers

Models which are constructed to represent the uncertainty arising in engineered systems can often be quite complex to ensure they provide a reasonably faithful reflection of the real-world system. As a result, even computation of simple expectations, event probabilities, variances, or integration over utilities for a decision problem can be analytically intractable. Indeed, such models are often sufficiently high dimensional that even traditional numerical methods perform poorly. However, access to random samples drawn from the probability model under study typically simplifies such problems substantially. The methodologies to generate and use such samples fall under the stable of techniques usually referred to as ‘Monte Carlo methods’. This chapter provides a motivation, simple primer introduction to the basics, and sign-posts to further reading and literature on Monte Carlo methods, in a manner that should be accessible to those with an engineering mathematics background. There is deliberately informal mathematical presentation which avoids measure-theoretic formalism. The accompanying lecture can be viewed at https://www.louisaslett.com/Courses/UTOPIAE/.

High performance of excitation system for synchronous generator based on modeling analysis

Mathematical description of electromechanical systems operation is powerful parameter to get high performance with practical implement of the systems. This paper describes a mathematical presentation for the behavior excitation system of synchronous generator based on the optimal values of the parameters. The study of the mathematical modeling for dynamics of excitation system required the knowledge for the effect of each parameter to get the typical values provided by the manufacturer implementing. The simulation of the final model which obtained was conducted on Matlab version 2019b. The final results of simulation for the mathematical model are satisfactory, and it proves the ability of independence this model as practical implement.

Analysis and demonstration: Wallis and Newton on mathematical presentation

Emulating the Greek geometers, Newton used synthetic demonstration to present the ground-breaking arguments of the Principia . This paper argues that we can better understand Newton's reasons for using geometry by considering John Wallis's interpretation of synthetic demonstration. Wallis condemned demonstration for failing to explain the mathematical truths it presented. He opposed to it a presentation that combined symbolic analysis with a documented account of discovery. In preferring symbols, Wallis was motivated both by the nascent tradition of symbolic analysis and by contemporary interest in artificial languages. Newton maintained Wallis's characterization of Greek demonstration as adapted to common understanding rather than as strictly elucidating, but he inverted the values Wallis associated with synthesis and analysis. In Newton's new account, synthetic demonstration was preferable precisely because it could address inexpert readers without exposing them to the complications of symbols-based analysis. Newton advanced his arguments on behalf of geometry through portraits of ancient mathematicians: Archimedes and Pythagoras.

Flux intensification during microfiltration of distillery stillage using a kenics static mixer

The present work studies the effect of operating parameters (pH, feed flow rate, and transmembrane pressure) on microfiltration of distillery stillage. Experiments were conducted in the presence of a Kenics static mixer as a turbulence promoter, and its influence on the flux improvement and specific energy consumption was examined. Response surface methodology was used to investigate the effect of selected factors on microfiltration performances. The results showed that response surface methodology is an appropriate model for mathematical presentation of the process. It was found that the use of a static mixer is justified at the feed flow rates higher than 100 L/h. In contrast, the use of a static mixer at low values of feed flow rate and transmembrane pressure has no justification from an economic point of view.

Virtual Assembly Operation Modeling Based on Colored Petri Net

In this paper, a Colored Petri Net modeling method for early stage design of virtual assembly operation is presented. The characteristics of virtual assembly system, Petri Net and Colored Petri Net are analyzed. Some previous work in Petri Net application in assembly and virtual assembly system is discussed. The theoretical aspects of Colored Petri Net are introduced mathematically. Based on the mathematical presentation and the process of fasteners assembly operation, a Colored Petri Net model is constructed for the simulation of assembly operation in virtual environment. With CPN Tools software package, the simulation for evaluating the feasibility of modeling is implemented. It is demonstrated that the modeling approach can support the early stage design of virtual assembly system.